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Mathematics : All Publications (in the database)

List most recent publications in the database.    :chronological  alphabetical  combined listing:
%% Abel, Michael   
@article{fds317698,
   Title = {HOMFLY-PT homology for general link diagrams and braidlike
             isotopy},
   Year = {2016},
   Month = {June},
   url = {http://arxiv.org/abs/1607.00314},
   Key = {fds317698}
}

@article{fds311722,
   Author = {M. Abel and M. Hogancamp},
   Title = {Stable homology of torus links via categorified Young
             symmetrizers II: one-column partitions},
   Year = {2016},
   Month = {February},
   url = {http://arxiv.org/abs/1510.05330},
   Key = {fds311722}
}

@article{fds300045,
   Author = {M. Abel and L. Rozansky},
   Title = {Virtual crossings and a filtration of the triply graded
             homology of a link diagram},
   Year = {2015},
   Month = {February},
   url = {http://arxiv.org/abs/1410.5892},
   Key = {fds300045}
}


%% Addington, Nicolas   
@article{fds226937,
   Author = {N. Addington and W. Donovan and C. Meachan},
   Title = {Mukai flops and P-twists},
   Year = {2015},
   Month = {July},
   url = {http://arxiv.org/abs/1507.02595},
   Key = {fds226937}
}

@article{fds226938,
   Author = {N. Addington and W. Donovan and C. Meachan},
   Title = {Moduli spaces of torsion sheaves on K3 surfaces and derived
             equivalences},
   Year = {2015},
   Month = {July},
   url = {http://arxiv.org/abs/1507.02597},
   Key = {fds226938}
}

@article{fds226939,
   Author = {N. Addington and W. Donovan and E. Segal},
   Title = {The Pfaffian-Grassmannian equivalence revisited},
   Journal = {Alg. Geom.},
   Volume = {2},
   Number = {3},
   Pages = {332-364},
   Year = {2015},
   url = {http://arxiv.org/abs/1401.3661},
   Key = {fds226939}
}

@article{fds225141,
   Author = {N. Addington},
   Title = {On two rationality conjectures for cubic
             fourfolds},
   Journal = {Math. Res. Lett.},
   Year = {2014},
   Month = {May},
   url = {http://arxiv.org/abs/1405.4902},
   Key = {fds225141}
}

@article{fds225601,
   Author = {N. Addington and M. Lehn},
   Title = {On the symplectic eightfold associated to a Pfaffian cubic
             fourfold},
   Journal = {J. Reine Angew. Math.},
   Year = {2014},
   Month = {April},
   url = {http://arxiv.org/abs/1404.5657},
   Key = {fds225601}
}

@article{fds224079,
   Author = {N. Addington and R. P. Thomas},
   Title = {Hodge theory and derived categories of cubic
             fourfolds},
   Journal = {Duke Math. J.},
   Volume = {163},
   Number = {10},
   Pages = {1885-1927},
   Year = {2014},
   url = {http://arxiv.org/abs/1211.3758},
   Key = {fds224079}
}

@article{fds225760,
   Author = {N. Addington and E. Segal and E. Sharpe},
   Title = {D-brane probes, branched double covers, and noncommutative
             resolutions},
   Journal = {Adv. Theor. Math. Phys.},
   Volume = {18},
   Number = {6},
   Pages = {1369-1436},
   Year = {2014},
   url = {http://arxiv.org/abs/1211.2446},
   Key = {fds225760}
}

@article{fds224497,
   Author = {N. Addington},
   Title = {The Brauer group is not a derived invariant},
   Booktitle = {Proceedings of "Brauer groups and obstruction problems:
             moduli spaces and arithmetic"},
   Year = {2013},
   Month = {June},
   url = {http://arxiv.org/abs/1306.6538},
   Key = {fds224497}
}

@article{fds219852,
   Author = {N. Addington and P. Aspinwall},
   Title = {Categories of massless D-branes and del Pezzo
             surfaces},
   Journal = {J. High Energy Phys.},
   Volume = {2013},
   Number = {7},
   Pages = {front matter + 39pp.},
   Year = {2013},
   url = {http://arxiv.org/abs/1305.5767},
   Key = {fds219852}
}

@article{fds223836,
   Author = {N. Addington},
   Title = {New derived symmetries of some hyperkaehler
             varieties},
   Year = {2011},
   Month = {December},
   url = {http://arxiv.org/abs/1112.0487},
   Key = {fds223836}
}

@article{fds212453,
   Author = {N. Addington},
   Title = {Spinor sheaves on singular quadrics},
   Journal = {Proc. Amer. Math. Soc.},
   Volume = {139},
   Number = {11},
   Pages = {3867-3879},
   Year = {2011},
   Month = {November},
   url = {http://www.ams.org/journals/proc/2011-139-11/S0002-9939-2011-10819-0/},
   Key = {fds212453}
}

@article{fds212452,
   Author = {N. Addington},
   Title = {The derived category of the complete intersection of four
             quadrics},
   Year = {2009},
   Month = {April},
   url = {http://arxiv.org/abs/0904.1764},
   Key = {fds212452}
}


%% Agarwal, Pankaj K.   
@article{fds328588,
   Author = {Agarwal, PK and Har-Peled, S and Suri, S and Yıldız, H and Zhang,
             W},
   Title = {Convex Hulls Under Uncertainty},
   Journal = {Algorithmica},
   Volume = {79},
   Number = {2},
   Pages = {340-367},
   Year = {2017},
   Month = {October},
   url = {http://dx.doi.org/10.1007/s00453-016-0195-y},
   Doi = {10.1007/s00453-016-0195-y},
   Key = {fds328588}
}

@article{fds329363,
   Author = {Agarwal, PK and Rubin, N and Sharir, M},
   Title = {Approximate nearest neighbor search amid higher-dimensional
             flats},
   Journal = {LIPIcs},
   Volume = {87},
   Year = {2017},
   Month = {September},
   ISBN = {9783959770491},
   url = {http://dx.doi.org/10.4230/LIPIcs.ESA.2017.4},
   Abstract = {© Pankaj K. Agarwal, Natan Rubin, and Micha Sharir. We
             consider the approximate nearest neighbor (ANN) problem
             where the input set consists of n k-flats in the Euclidean
             Rd, for any fixed parameters 0 ≤ k < d, and where, for
             each query point q, we want to return an input flat whose
             distance from q is at most (1 + ϵ) times the shortest such
             distance, where ϵ > 0 is another prespecified parameter. We
             present an algorithm that achieves this task with
             nk+1(log(n)/ ϵ)O(1) storage and preprocessing (where the
             constant of proportionality in the big-O notation depends on
             d), and can answer a query in O(polylog(n)) time (where the
             power of the logarithm depends on d and k). In particular,
             we need only nearquadratic storage to answer ANN queries
             amid a set of n lines in any fixed-dimensional Euclidean
             space. As a by-product, our approach also yields an
             algorithm, with similar performance bounds, for answering
             exact nearest neighbor queries amid k-flats with respect to
             any polyhedral distance function. Our results are more
             general, in that they also provide a tradeoff between
             storage and query time.},
   Doi = {10.4230/LIPIcs.ESA.2017.4},
   Key = {fds329363}
}

@article{fds328996,
   Author = {Agarwal, PK and Kumar, N and Sintos, S and Suri, S},
   Title = {Efficient algorithms for k-regret minimizing
             sets},
   Journal = {LIPIcs},
   Volume = {75},
   Year = {2017},
   Month = {August},
   ISBN = {9783959770361},
   url = {http://dx.doi.org/10.4230/LIPIcs.SEA.2017.7},
   Abstract = {© Pankaj K. Agarwal, Nirman Kumar, Stavros Sintos, and
             Subhash Suri. A regret minimizing set Q is a small size
             representation of a much larger database P so that user
             queries executed on Q return answers whose scores are not
             much worse than those on the full dataset. In particular, a
             k-regret minimizing set has the property that the regret
             ratio between the score of the top-1 item in Q and the score
             of the top-k item in P is minimized, where the score of an
             item is the inner product of the item's attributes with a
             user's weight (preference) vector. The problem is
             challenging because we want to find a single representative
             set Q whose regret ratio is small with respect to all
             possible user weight vectors. We show that k-regret
             minimization is NP-Complete for all dimensions d ≥ 3,
             settling an open problem from Chester et al. [VLDB 2014].
             Our main algorithmic contributions are two approximation
             algorithms, both with provable guarantees, one based on
             coresets and another based on hitting sets. We perform
             extensive experimental evaluation of our algorithms, using
             both real-world and synthetic data, and compare their
             performance against the solution proposed in [VLDB 14] . The
             results show that our algorithms are significantly faster
             and scalable to much larger sets than the greedy algorithm
             of Chester et al. for comparable quality
             answers.},
   Doi = {10.4230/LIPIcs.SEA.2017.7},
   Key = {fds328996}
}

@article{fds329182,
   Author = {Agarwal, PK and Fox, K and Panigrahi, D and Varadarajan, KR and Xiao,
             A},
   Title = {Faster algorithms for the geometric transportation
             problem},
   Journal = {LIPIcs},
   Volume = {77},
   Pages = {71-716},
   Year = {2017},
   Month = {June},
   ISBN = {9783959770385},
   url = {http://dx.doi.org/10.4230/LIPIcs.SoCG.2017.7},
   Abstract = {© Pankaj K. Agarwal, Kyle Fox, Debmalya Panigrahi, Kasturi
             R. Varadarajan, and Allen Xiao. Let R, B C R d for constant
             d, be two point sets with |R| + |B| = n, and let λ: R∪B
             → ℕ such that Σ r∈R λ(r) = Σ b∈B λ (b) be demand
             functions over R and B. Let d(·, ·) be a suitable distance
             function such as the L p distance. The transportation
             problem asks to find a map τ: R × B → ℕ such that Σ
             b∈B τ(r, b) = λ(r), Σ r∈R τ(r, b) = λ(b), and σ
             r∈Rb∈B τ(r, b)d(r, b) is minimized. We present three
             new results for the transportation problem when d(·, ·) is
             any L p metric: • For any constant ϵ > 0, an O(n 1+ϵ )
             expected time randomized algorithm that returns a
             transportation map with expected cost O(log 2 (1/ϵ)) times
             the optimal cost. • For any ϵ > 0, a (1 +
             ϵ)-approximation in O(n 3/2 ϵ -d polylog(U) polylog(n))
             time, where U = max p∈Rcup;B λ (p). •An exact strongly
             polynomial O(n 2 polylogn) time algorithm, for d =
             2.},
   Doi = {10.4230/LIPIcs.SoCG.2017.7},
   Key = {fds329182}
}

@article{fds330177,
   Author = {Wu, Y and Agarwal, PK and Li, C and Yang, J and Yu, C},
   Title = {Computational Fact Checking through Query
             Perturbations},
   Journal = {ACM Transactions on Database Systems},
   Volume = {42},
   Number = {1},
   Pages = {1-41},
   Year = {2017},
   Month = {January},
   url = {http://dx.doi.org/10.1145/2996453},
   Doi = {10.1145/2996453},
   Key = {fds330177}
}

@article{fds323822,
   Author = {Agarwal, PK and Pan, J and Victor, W},
   Title = {An efficient algorithm for placing electric vehicle charging
             stations},
   Journal = {LIPIcs},
   Volume = {64},
   Pages = {7.1-7.12},
   Year = {2016},
   Month = {December},
   ISBN = {9783959770262},
   url = {http://dx.doi.org/10.4230/LIPIcs.ISAAC.2016.7},
   Abstract = {© Pankaj K. Agarwal, Jiangwei Pan, and Will Victor.
             Motivated by the increasing popularity of electric vehicles
             (EV) and a lack of charging stations in the road network, we
             study the shortest path hitting set (SPHS) problem. Roughly
             speaking, given an input graph G, the goal is to compute a
             small-size subset H of vertices of G such that by placing
             charging stations at vertices in H, every shortest path in G
             becomes EV-feasible, i.e., an EV can travel between any two
             vertices of G through the shortest path with a full charge.
             In this paper, we propose a bi-criteria approximation
             algorithm with running time near-linear in the size of G
             that has a logarithmic approximation on |H| and may require
             the EV to slightly deviate from the shortest path. We also
             present a data structure for computing an EV-feasible path
             between two query vertices of G.},
   Doi = {10.4230/LIPIcs.ISAAC.2016.7},
   Key = {fds323822}
}

@article{fds323823,
   Author = {Ying, R and Pan, J and Fox, K and Agarwal, PK},
   Title = {A simple efficient approximation algorithm for dynamic time
             warping},
   Journal = {GIS: Proceedings of the ACM International Symposium on
             Advances in Geographic Information Systems},
   Year = {2016},
   Month = {October},
   ISBN = {9781450345897},
   url = {http://dx.doi.org/10.1145/2996913.2996954},
   Abstract = {© 2016 ACM. Dynamic time warping (DTW) is a widely used
             curve similarity measure. We present a simple and efficient
             (1 + ∈)- approximation algorithm for DTW between a pair of
             point sequences, say, P and Q, each of which is sampled from
             a curve. We prove that the running time of the algorithm is
             O( κ 2 /∈ n log σ) for a pair of κ-packed curves with a
             total of n points, assuming that the spreads of P and Q are
             bounded by σ. The spread of a point set is the ratio of the
             maximum to the minimum pairwise distance, and a curve is
             called κ-packed if the length of its intersection with any
             disk of radius r is at most κr. Although an algorithm with
             similar asymptotic time complexity was presented in [1], our
             algorithm is considerably simpler and more efficient in
             practice. We have implemented our algorithm. Our experiments
             on both synthetic and real-world data sets show that it is
             an order of magnitude faster than the standard exact DP
             algorithm on point sequences of length 5; 000 or more while
             keeping the approximation error within 5-10%. We demonstrate
             the eficacy of our algorithm by using it in two applications
             computing the k most similar trajectories to a query
             trajectory, and running the iterative closest point method
             for a pair of trajectories. We show that we can achieve 8-12
             times speedup using our algorithm as a subroutine in these
             applications, without compromising much in
             accuracy.},
   Doi = {10.1145/2996913.2996954},
   Key = {fds323823}
}

@article{fds323790,
   Author = {Nath, A and Fox, K and Agarwal, PK and Munagala, K},
   Title = {Massively parallel algorithms for computing TIN DEMs and
             contour trees for large terrains},
   Journal = {GIS: Proceedings of the ACM International Symposium on
             Advances in Geographic Information Systems},
   Year = {2016},
   Month = {October},
   ISBN = {9781450345897},
   url = {http://dx.doi.org/10.1145/2996913.2996952},
   Abstract = {© 2016 ACM. We propose parallel algorithms in the massively
             parallel communication (MPC) model (e.g. MapReduce) for
             processing large terrain elevation data (represented as a 3D
             point cloud) that are too big to fit on one machine. In
             particular, given a set S of 3D points that is distributed
             across multiple machines, we present a simple randomized
             algorithm to construct a TIN DEM of S by computing the
             Delaunay triangulation of the xy-projections of points in S,
             which is also stored across multiple machines. With high
             probability, the algorithm works in O(1) rounds and the
             total work performed is O(n log n). Next, we describe an
             efficient algorithm in the MPC model for computing the
             contour tree of the resulting DEM. Under some assumptions on
             the input, the algorithm works in O(1) rounds and the total
             work performed is O(n log n).},
   Doi = {10.1145/2996913.2996952},
   Key = {fds323790}
}

@article{fds318110,
   Author = {Agarwal, PK and Aronov, B and Har-Peled, S and Phillips, JM and Yi, K and Zhang, W},
   Title = {Nearest-Neighbor Searching Under Uncertainty
             II},
   Journal = {ACM Transactions on Algorithms},
   Volume = {13},
   Number = {1},
   Pages = {1-25},
   Year = {2016},
   Month = {October},
   url = {http://dx.doi.org/10.1145/2955098},
   Doi = {10.1145/2955098},
   Key = {fds318110}
}

@article{fds318111,
   Author = {Agarwal, PK and Kumar, N and Sintos, S and Suri, S},
   Title = {Range-max queries on uncertain data},
   Journal = {Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on
             Principles of Database Systems},
   Volume = {26-June-01-July-2016},
   Pages = {465-476},
   Year = {2016},
   Month = {June},
   ISBN = {9781450341912},
   url = {http://dx.doi.org/10.1145/2902251.2902281},
   Abstract = {© 2016 ACM. Let P be a set of n uncertain points in ℝ d ,
             where each point p i ∈ P is associated with a real value v
             i and a probability α i ∈ (0,1] of existence, i.e., each
             p i exists with an independent probability α i . We present
             algorithms for building an index on P so that for a
             d-dimensional query rectangle ρ, the expected maximum value
             or the most-likely maximum value in ρ can be computed
             quickly. The specific contributions of our paper include the
             following: (i) The first index of sub-quadratic size to
             achieve a sub-linear query time in any dimension d ≥ 1. It
             also provides a trade-off between query time and size of the
             index. (ii) A conditional lower bound for the most-likely
             range-max queries, based on the conjectured hardness of the
             set-intersection problem, which suggests that in the worst
             case the product (query time) 2 x (index size) is Ω(n 2
             /polylog (n) ). (iii) A linear-size index for estimating the
             expected range-max value within approximation factor 1/2 in
             O(log c n) time, for some constant c > 0; that is, if the
             expected maximum value is μ then the query procedure
             returns a value μ′ with μ/2 ≤ μ′ ≤ μ. (iv)
             Extensions of our algorithm to more general uncertainty
             models and for computing the top-k values of the
             range-max.},
   Doi = {10.1145/2902251.2902281},
   Key = {fds318111}
}

@article{fds318112,
   Author = {Agarwal, PK and Fox, K and Munagala, K and Nath, A},
   Title = {Parallel algorithms for constructing range and
             nearest-neighbor searching data structures},
   Journal = {Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on
             Principles of Database Systems},
   Volume = {26-June-01-July-2016},
   Pages = {429-440},
   Year = {2016},
   Month = {June},
   ISBN = {9781450341912},
   url = {http://dx.doi.org/10.1145/2902251.2902303},
   Abstract = {© 2016 ACM. With the massive amounts of data available
             today, it is common to store and process data using multiple
             machines. Parallel programming platforms such as MapReduce
             and its variants are popular frameworks for handling such
             large data. We present the first provably efficient
             algorithms to compute, store, and query data structures for
             range queries and approximate nearest neighbor queries in a
             popular parallel computing abstraction that captures the
             salient features of MapReduce and other massively parallel
             communication (MPC) models. In particular, we describe
             algorithms for kd-trees, range trees, and BBD-trees that
             only require O(1) rounds of communication for both
             preprocessing and querying while staying competitive in
             terms of running time and workload to their classical
             counterparts. Our algorithms are randomized, but they can be
             made deterministic at some increase in their running time
             and workload while keeping the number of rounds of
             communication to be constant.},
   Doi = {10.1145/2902251.2902303},
   Key = {fds318112}
}

@article{fds318113,
   Author = {Agarwal, PK and Fox, K and Pan, J and Ying, R},
   Title = {Approximating dynamic time warping and edit distance for a
             pair of point sequences},
   Journal = {LIPIcs},
   Volume = {51},
   Pages = {6.1-6.16},
   Year = {2016},
   Month = {June},
   url = {http://dx.doi.org/10.4230/LIPIcs.SoCG.2016.6},
   Abstract = {© Pankaj K. Agarwal, Kyle Fox, Jiangwei Pan, and Rex Ying.
             We present the first subquadratic algorithms for computing
             similarity between a pair of point sequences in
             double-struck R d , for any fixed d > 1, using dynamic time
             warping (DTW) and edit distance, assuming that the point
             sequences are drawn from certain natural families of curves.
             In particular, our algorithms compute (1 +
             ε)-approximations of DTW and ED in near-linear time for
             point sequences drawn from κ-packed or κ-bounded curves,
             and subquadratic time for backbone sequences. Roughly
             speaking, a curve is κ-packed if the length of its
             intersection with any ball of radius r is at most κ · r,
             and it is κ-bounded if the sub-curve between two curve
             points does not go too far from the two points compared to
             the distance between the two points. In backbone sequences,
             consecutive points are spaced at approximately equal
             distances apart, and no two points lie very close together.
             Recent results suggest that a subquadratic algorithm for DTW
             or ED is unlikely for an arbitrary pair of point sequences
             even for d = 1. The commonly used dynamic programming
             algorithms for these distance measures reduce the problem to
             computing a minimum-weight path in a grid graph. Our
             algorithms work by constructing a small set of rectangular
             regions that cover the grid vertices. The weights of
             vertices inside each rectangle are roughly the same, and we
             develop efficient procedures to compute the approximate
             minimum-weight paths through these rectangles.},
   Doi = {10.4230/LIPIcs.SoCG.2016.6},
   Key = {fds318113}
}

@article{fds314402,
   Author = {Yu, A and Agarwal, PK and Yang, J},
   Title = {Top-$k$ Preferences in High Dimensions},
   Journal = {IEEE Transactions on Knowledge and Data Engineering},
   Volume = {28},
   Number = {2},
   Pages = {311-325},
   Year = {2016},
   Month = {February},
   ISSN = {1041-4347},
   url = {http://dx.doi.org/10.1109/TKDE.2015.2451630},
   Doi = {10.1109/TKDE.2015.2451630},
   Key = {fds314402}
}

@article{fds315094,
   Author = {Agarwal, PK and Fox, K and Salzman, O},
   Title = {An efficient algorithm for computing high-quality paths amid
             polygonal obstacles},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Volume = {2},
   Pages = {1179-1192},
   Year = {2016},
   Month = {January},
   ISBN = {9781510819672},
   Abstract = {© Copyright (2016) by SIAM: Society for Industrial and
             Applied Mathematics. We study a path-planning problem amid a
             set 0 of obstacles in R2, in which we wish to compute a
             short path between two points while also maintaining a high
             clearance from 0; the clearance of a point is its distance
             from a nearest obstacle in 0. Specifically, the problem asks
             for a path minimizing the reciprocal of the clearance
             integrated over the length of the path. We present the first
             polynomial-time approximation scheme for this problem. Let n
             be the total number of obstacle vertices and let ϵ ∈ (0,
             1]. Our algorithm computes in time 0(n2/ϵ2 log n/ϵ) a path
             of total cost at most (1 + ϵ) times the cost of the optimal
             path.},
   Key = {fds315094}
}

@article{fds321561,
   Author = {Pan, J and Rao, V and Agarwal, PK and Gelfand, AE},
   Title = {Markov-modulated marked poisson processes for check-in
             data},
   Journal = {33rd International Conference on Machine Learning, ICML
             2016},
   Volume = {5},
   Pages = {3311-3320},
   Year = {2016},
   Month = {January},
   ISBN = {9781510829008},
   Abstract = {© 2016 by the author(s). We develop continuous-time
             probabilistic models to study trajectory data consisting of
             times and locations of user 'check-ins'. We model the data
             as realizations of a marked point process, with intensity
             and mark-distribution modulated by a latent Markov jump
             process (MJP). We also include user-heterogeneity in our
             model by assigning each user a vector of 'preferred
             locations'. Our model extends latent Dirichlet allocation by
             dropping the bag-of-words assumption and operating in
             continuous time. We show how an appropriate choice of priors
             allows efficient posterior inference. Our experiments
             demonstrate the usefulness of our approach by comparing with
             various baselines on a variety of tasks.copyright},
   Key = {fds321561}
}

@article{fds235347,
   Author = {Agarwal, PK and Gao, J and Guibas, LJ and Kaplan, H and Rubin, N and Sharir, M},
   Title = {Stable Delaunay Graphs},
   Journal = {Discrete & Computational Geometry},
   Volume = {54},
   Number = {4},
   Pages = {905-929},
   Year = {2015},
   Month = {December},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/s00454-015-9730-x},
   Doi = {10.1007/s00454-015-9730-x},
   Key = {fds235347}
}

@article{fds235355,
   Author = {Agarwal, PK and Kaplan, H and Rubin, N and Sharir,
             M},
   Title = {Kinetic Voronoi Diagrams and Delaunay Triangulations under
             Polygonal Distance Functions},
   Journal = {Discrete & Computational Geometry},
   Volume = {54},
   Number = {4},
   Pages = {871-904},
   Year = {2015},
   Month = {December},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/s00454-015-9729-3},
   Doi = {10.1007/s00454-015-9729-3},
   Key = {fds235355}
}

@article{fds313238,
   Author = {Zhang, W and Agarwal, PK and Mukherjee, S},
   Title = {Contour trees of uncertain terrains},
   Journal = {GIS: Proceedings of the ACM International Symposium on
             Advances in Geographic Information Systems},
   Volume = {03-06-November-2015},
   Year = {2015},
   Month = {November},
   ISBN = {9781450339674},
   url = {http://dx.doi.org/10.1145/2820783.2820823},
   Abstract = {We study contour trees of terrains, which encode the
             topological changes of the level set of the height value ℓ
             as we raise ℓ from -∞ to +∞ on the terrains, in the
             presence of uncertainty in data. We assume that the terrain
             is represented by a piecewise-linear height function over a
             planar triangulation M, by specifying the height of each
             vertex. We study the case when M is fixed and the
             uncertainty lies in the height of each vertex in the
             triangulation, which is described by a probability
             distribution. We present efficient sampling-based Monte
             Carlo methods for estimating, with high probability, (i) the
             probability that two points lie on the same edge of the
             contour tree, within additive error; (ii) the expected
             distance of two points p; q and the probability that the
             distance of p; q is at least ℓ on the contour tree, within
             additive error, where the distance of p; q on a contour tree
             is defined to be the difference between the maximum height
             and the minimum height on the unique path from p to q on the
             contour tree. The main technical contribution of the paper
             is to prove that a small number of samples are sufficient to
             estimate these quantities. We present two applications of
             these algorithms, and also some experimental results to
             demonstrate the effectiveness of our approach.},
   Doi = {10.1145/2820783.2820823},
   Key = {fds313238}
}

@article{fds313245,
   Author = {Agarwal, PK and Mølhave, T and Revsbæk, M and Safa, I and Wang, Y and Yang, J},
   Title = {Maintaining Contour Trees of Dynamic Terrains},
   Journal = {LIPIcs},
   Volume = {34},
   Pages = {796-811},
   Year = {2015},
   Month = {June},
   ISSN = {1868-8969},
   url = {http://dx.doi.org/10.4230/LIPIcs.SOCG.2015.796},
   Abstract = {We study the problem of maintaining the contour tree T of a
             terrain σ, represented as a triangulated xy-monotone
             surface, as the heights of its vertices vary continuously
             with time. We characterize the combinatorial changes in T
             and how they relate to topological changes in. We present a
             kinetic data structure (KDS) for maintaining T efficiently.
             It maintains certificates that fail, i.e., an event occurs,
             only when the heights of two adjacent vertices become equal
             or two saddle vertices appear on the same contour. Assuming
             that the heights of two vertices of κ become equal only
             O(1) times and these instances can be computed in O(1) time,
             the KDS processes O(κ + n) events, where n is the number of
             vertices in σ and κ; is the number of events at which the
             combinatorial structure of T changes, and processes each
             event in O(log n) time. The KDS can be extended to maintain
             an augmented contour tree and a join/split
             tree.},
   Doi = {10.4230/LIPIcs.SOCG.2015.796},
   Key = {fds313245}
}

@article{fds313246,
   Author = {Agarwal, PK and Fox, K and Nath, A and Sidiropoulos, A and Wang,
             Y},
   Title = {Computing the Gromov-Hausdorff distance for metric
             trees},
   Journal = {Lecture notes in computer science},
   Volume = {9472},
   Pages = {529-540},
   Year = {2015},
   Month = {January},
   ISSN = {0302-9743},
   url = {http://dx.doi.org/10.1007/978-3-662-48971-0_45},
   Abstract = {© Springer-Verlag Berlin Heidelberg 2015. The
             Gromov-Hausdorff distance is a natural way to measure
             distance between two metric spaces. We give the first proof
             of hardness and first non-trivial approximation algorithm
             for computing the Gromov-Hausdorff distance for geodesic
             metrics in trees. Specifically, we prove it is NP-hard to
             approximate the Gromov-Hausdorff distance better than a
             factor of 3. We complement this result by providing a
             polynomial time O(min{n, √rn})-approximation algorithm
             where r is the ratio of the longest edge length in both
             trees to the shortest edge length. For metric trees with
             unit length edges, this yields an O(√ n)-approximation
             algorithm.},
   Doi = {10.1007/978-3-662-48971-0_45},
   Key = {fds313246}
}

@article{fds235346,
   Author = {Agarwal, PK and Sharathkumar, R},
   Title = {Streaming Algorithms for Extent Problems in High
             Dimensions},
   Journal = {Algorithmica},
   Volume = {72},
   Number = {1},
   Pages = {83-98},
   Year = {2015},
   ISSN = {0178-4617},
   url = {http://dx.doi.org/10.1007/s00453-013-9846-4},
   Abstract = {© 2013, Springer Science+Business Media New York.We present
             (single-pass) streaming algorithms for maintaining extent
             measures of a stream S of n points in $\mathbb{R} ^{d}$. We
             focus on designing streaming algorithms whose working space
             is polynomial in d (poly(d)) and sub-linear in n. For the
             problems of computing diameter, width and minimum enclosing
             ball of S, we obtain lower bounds on the worst-case
             approximation ratio of any streaming algorithm that uses
             poly(d) space. On the positive side, we introduce the notion
             of blurred ball cover and use it for answering approximate
             farthest-point queries and maintaining approximate minimum
             enclosing ball and diameter of S. We describe a streaming
             algorithm for maintaining a blurred ball cover whose working
             space is linear in d and independent of n.},
   Doi = {10.1007/s00453-013-9846-4},
   Key = {fds235346}
}

@article{fds235348,
   Author = {Salzman, O and Shaharabani, D and Agarwal, PK and Halperin,
             D},
   Title = {Sparsification of motion-planning roadmaps by edge
             contraction},
   Journal = {International Journal of Robotics Research},
   Volume = {33},
   Number = {14},
   Pages = {1711-1725},
   Year = {2014},
   Month = {December},
   ISSN = {0278-3649},
   url = {http://dx.doi.org/10.1177/0278364914556517},
   Doi = {10.1177/0278364914556517},
   Key = {fds235348}
}

@article{fds313239,
   Author = {Lebeck, N and Mølhave, T and Agarwal, PK},
   Title = {Computing highly occluded paths using a sparse
             network},
   Journal = {GIS: Proceedings of the ACM International Symposium on
             Advances in Geographic Information Systems},
   Volume = {04-07-November-2014},
   Pages = {3-12},
   Year = {2014},
   Month = {November},
   ISBN = {9781450331319},
   url = {http://dx.doi.org/10.1145/2666310.2666394},
   Abstract = {Copyright 2014 ACM. Computing paths over a terrain that are
             highly occluded with respect to observers is an important
             problem in GIS. Given a fast algorithm for computing the
             visibility map, the path-planning step becomes the
             bottleneck. In this paper, we present an approach for
             quickly computing occluded paths over a terrain using a
             sparse network, a sparse 1-dimensional network over the
             terrain. We present different strategies for constructing
             the sparse network. Experimental results show that our
             approach results in significantly improved time for
             computing highly occluded paths between two query points,
             and that the different strategies offer a tradeoff between
             higher-quality paths and lower preprocessing times. Further-
             more, there are strategies that achieve near-optimal paths
             with small preprocessing cost.},
   Doi = {10.1145/2666310.2666394},
   Key = {fds313239}
}

@article{fds235349,
   Author = {Agarwal, PK and Har-Peled, S and Kaplan, H and Sharir,
             M},
   Title = {Union of Random Minkowski Sums and Network Vulnerability
             Analysis},
   Journal = {Discrete & Computational Geometry},
   Volume = {52},
   Number = {3},
   Pages = {551-582},
   Year = {2014},
   Month = {October},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/s00454-014-9626-1},
   Doi = {10.1007/s00454-014-9626-1},
   Key = {fds235349}
}

@article{fds235356,
   Author = {Wu, Y and Agarwal, PK and Li, C and Yang, J and Yu, C},
   Title = {Toward computational fact-checking},
   Journal = {Proceedings of the VLDB Endowment International Conference
             on Very Large Data Bases},
   Volume = {7},
   Number = {7},
   Pages = {589-600},
   Year = {2014},
   Month = {March},
   ISSN = {2150-8097},
   url = {http://dx.doi.org/10.14778/2732286.2732295},
   Doi = {10.14778/2732286.2732295},
   Key = {fds235356}
}

@article{fds235364,
   Author = {Sankararaman, S and Efrat, A and Ramasubramanian, S and Agarwal,
             PK},
   Title = {On channel-discontinuity-constraint routing in wireless
             networks},
   Journal = {Ad Hoc Networks},
   Volume = {13},
   Number = {PART A},
   Pages = {153-169},
   Year = {2014},
   Month = {February},
   ISSN = {1570-8705},
   url = {http://dx.doi.org/10.1016/j.adhoc.2011.04.011},
   Abstract = {Multi-channel wireless networks are increasingly deployed as
             infrastructure networks, e.g. in metro areas. Network nodes
             frequently employ directional antennas to improve spatial
             throughput. In such networks, between two nodes, it is of
             interest to compute a path with a channel assignment for the
             links such that the path and link bandwidths are the same.
             This is achieved when any two consecutive links are assigned
             different channels, termed as "Channel-Discontinuity-Constraint"
             (CDC). CDC-paths are also useful in TDMA systems, where,
             preferably, consecutive links are assigned different
             time-slots. In the first part of this paper, we develop a
             t-spanner for CDC-paths using spatial properties; a
             sub-network containing O(n/θ) links, for any θ > 0, such
             that CDC-paths increase in cost by at most a factor t = (1 -
             2 sin(θ/2)) -2 . We propose a novel distributed algorithm
             to compute the spanner using an expected number of O(n log
             n) fixed-size messages. In the second part, we present a
             distributed algorithm to find minimum-cost CDC-paths between
             two nodes using O(n 2 ) fixed-size messages, by developing
             an extension of Edmonds' algorithm for minimum-cost perfect
             matching. In a centralized implementation, our algorithm
             runs in O(n 2 ) time improving the previous best algorithm
             which requires O(n 3 ) running time. Moreover, this running
             time improves to O(n/θ) when used in conjunction with the
             spanner developed. © 2011 Elsevier B.V. All rights
             reserved.},
   Doi = {10.1016/j.adhoc.2011.04.011},
   Key = {fds235364}
}

@article{fds235350,
   Author = {Agarwal, PK and Pan, J},
   Title = {Near-linear algorithms for geometric hitting sets and set
             covers},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {271-279},
   Year = {2014},
   Month = {January},
   url = {http://dx.doi.org/10.1145/2582112.2582152},
   Abstract = {Given a finite range space ∑ = (X,R), with N = |X| + |R|,
             we present two simple algorithms, based on the
             multiplicative-weight method, for computing a small-size
             hitting set or set cover of β. The first algorithm is a
             simpler variant of the Brönnimann-Goodrich algorithm but
             more efficient to implement, and the second algorithm can be
             viewed as solving a two-player zero-sum game. These
             algorithms, in conjunction with some standard geometric data
             structures, lead to near-linear algorithms for computing a
             small-size hitting set or set cover for a number of
             geometric range spaces. For example, they lead to
             O(Npolylog(N)) expected-time randomized O(1)-approximation
             algorithms for both hitting set and set cover if X is a set
             of points and R a set of disks in R2. Copyright 2014
             ACM.},
   Doi = {10.1145/2582112.2582152},
   Key = {fds235350}
}

@article{fds235351,
   Author = {Agarwal, PK and Sharathkumar, R},
   Title = {Approximation algorithms for bipartite matching with metric
             and geometric costs},
   Journal = {Proceedings of the Annual ACM Symposium on Theory of
             Computing},
   Pages = {555-564},
   Year = {2014},
   Month = {January},
   ISSN = {0737-8017},
   url = {http://dx.doi.org/10.1145/2591796.2591844},
   Abstract = {Let G = G(A∪B;A×B), with |A| = |B| = n, be a weighted
             bipartite graph, and let d(·, ·) be the cost function on
             the edges. Let w(M) denote the weight of a matching in G,
             and M* a minimum-cost perfect matching in G. We call a
             perfect matching M c-approximate, for c ≥1, if w(M)≤
             c·w(M*). We present three approximation algorithms for
             computing minimum-cost perfect matchings in G. First, we
             consider the case when d(·, ·) is a metric. For any δ >
             0, we present an algorithm that, in O(n 2+δ log n log 2
             (1/δ)) time, computes a O(1/δ α )-approximate matching of
             G, where α = log 3 2 ≈ 0:631. Next, we assume the
             existence of a dynamic data structure for answering
             approximate nearest neighbor (ANN) queries under d(·, ·).
             Given two parameters ε,δ∈2 (0, 1), we present an
             algorithm that, in O(ε -2 n 1+δ τ (n, ε) log 2 (n/ε)
             log(1/δ)) time, computes a O(1/δ α )- approximate
             matching of G, where α = 1 + log 2 (1 +ε) and τ (n, ε)
             is the query and update time of an (ε/2)-ANN data
             structure. Finally, we present an algorithm that works even
             if d((·, ·) is not a metric but admits an ANN data
             structure for d(·, ·). In particular, we present an
             algorithm that computes, in O(ε -1 n 3/2 τ (n, ε) log 4
             (n/ε) log Δ) time, a (1 +ε)- approximate matching of A
             and B; here Δ is the ratio of the largest to the
             smallest-cost edge in G, and τ (n, ε) is the query and
             update time of an (ε/c)-ANN data structure for some
             constant c > 1. We show that our results lead to faster
             matching algorithms for many geometric settings. © 2014
             ACM.},
   Doi = {10.1145/2591796.2591844},
   Key = {fds235351}
}

@article{fds235352,
   Author = {Wu, Y and Walenz, B and Li, P and Shim, A and Sonmez, E and Agarwal, PK and Li, C and Yang, J and Yu, C},
   Title = {ICheck: Computationally combating "lies, D - Ned Lies, and
             statistics"},
   Journal = {Proceedings / ACM-SIGMOD International Conference on
             Management of Data. ACM-Sigmod International Conference on
             Management of Data},
   Pages = {1063-1066},
   Year = {2014},
   Month = {January},
   ISSN = {0730-8078},
   url = {http://dx.doi.org/10.1145/2588555.2594522},
   Abstract = {Are you fed up with "lies, d - ned lies, and statistics"
             made up from data in our media? For claims based on
             structured data, we present a system to automatically assess
             the quality of claims (beyond their correctness) and counter
             misleading claims that cherry-pick data to advance their
             conclusions. The key insight is to model such claims as
             parameterized queries and consider how parameter
             perturbations affect their results. We demonstrate our
             system on claims drawn from U.S. congressional voting
             records, sports statistics, and publication records of
             database researchers.},
   Doi = {10.1145/2588555.2594522},
   Key = {fds235352}
}

@article{fds235353,
   Author = {Agarwal, PK and Har-Peled, S and Suri, S and YIldIz, H and Zhang,
             W},
   Title = {Convex hulls under uncertainty},
   Journal = {Lecture notes in computer science},
   Volume = {8737 LNCS},
   Pages = {37-48},
   Year = {2014},
   Month = {January},
   ISBN = {9783662447765},
   ISSN = {0302-9743},
   url = {http://dx.doi.org/10.1007/978-3-662-44777-2_4},
   Abstract = {We study the convex-hull problem in a probabilistic setting,
             motivated by the need to handle data uncertainty inherent in
             many applications, including sensor databases,
             location-based services and computer vision. In our
             framework, the uncertainty of each input point is described
             by a probability distribution over a finite number of
             possible locations including a null location to account for
             non-existence of the point. Our results include both exact
             and approximation algorithms for computing the probability
             of a query point lying inside the convex hull of the input,
             time-space tradeoffs for the membership queries, a
             connection between Tukey depth and membership queries, as
             well as a new notion of β-hull that may be a useful
             representation of uncertain hulls. © 2014 Springer-Verlag
             Berlin Heidelberg.},
   Doi = {10.1007/978-3-662-44777-2_4},
   Key = {fds235353}
}

@article{fds235354,
   Author = {Yu, A and Agarwal, PK and Yang, J},
   Title = {Top-k preferences in high dimensions},
   Journal = {Proceedings / International Conference on Data Engineering.
             International Conference on Data Engineering},
   Pages = {748-759},
   Year = {2014},
   Month = {January},
   ISSN = {1084-4627},
   url = {http://dx.doi.org/10.1109/ICDE.2014.6816697},
   Abstract = {Given a set of objects O, each with d numeric attributes, a
             top-k preference scores these objects using a linear
             combination of their attribute values, where the weight on
             each attribute reflects the interest in this attribute.
             Given a query preference q, a top-k query finds the k
             objects in O with highest scores with respect to q. Given a
             query object o and a set of preferences Q, a reverse top-k
             query finds all preferences q ∈ Q for which o becomes one
             of the top k objects with respect to q. Previous solutions
             to these problems are effective only in low dimensions. In
             this paper, we develop a solution for much higher dimensions
             (up to high tens), if many preferences exhibit sparsity -
             i.e., each specifies non-zero weights for only a handful
             (say 5-7) of attributes (though the subsets of such
             attributes and their weights can vary greatly). Our idea is
             to select carefully a set of low-dimensional core subspaces
             to 'cover' the sparse preferences in a workload. These
             subspaces allow us to index them more effectively than the
             full-dimensional space. Being multi-dimensional, each
             subspace covers many possible preferences; furthermore,
             multiple subspaces can jointly cover a preference, thereby
             expanding the coverage beyond each subspace's
             dimensionality. Experimental evaluation validates our
             solution's effectiveness and advantages over previous
             solutions. © 2014 IEEE.},
   Doi = {10.1109/ICDE.2014.6816697},
   Key = {fds235354}
}

@article{fds235359,
   Author = {Agarwal, PK and Aronov, B and Van Kreveld and M and Löffler, M and Silveira, RI},
   Title = {Computing correlation between piecewise-linear
             functions},
   Journal = {SIAM Journal on Computing},
   Volume = {42},
   Number = {5},
   Pages = {1867-1887},
   Year = {2013},
   Month = {December},
   ISSN = {0097-5397},
   url = {http://dx.doi.org/10.1137/120900708},
   Abstract = {We study the problem of computing correlation between two
             piecewise-linear bivariate functions defined over a common
             domain, where the surfaces they define in three dimensions -
             polyhedral terrains - can be transformed vertically by a
             linear transformation of the third coordinate (scaling and
             translation). We present a randomized algorithm that
             minimizes the maximum vertical distance between the graphs
             of the two functions, over all linear transformations of one
             of the terrains, in O(n 4/3 polylog n) expected time, where
             n is the total number of vertices in the graphs of the two
             functions. We also present approximation algorithms for
             minimizing the mean distance between the graphs of
             univariate and bivariate functions. For univariate functions
             we present a (1 + ε)-approximation algorithm that runs in
             O(n(1 + log 2 (1/ε))) expected time for any fixed ε > 0.
             The (1 + ε)-approximation algorithm for bivariate functions
             runs in O(n/ε) time, for any fixed ε > 0, provided the two
             functions are defined over the same triangulation of their
             domain. © 2013 Society for Industrial and Applied
             Mathematics.},
   Doi = {10.1137/120900708},
   Key = {fds235359}
}

@article{fds235361,
   Author = {Agarwal, PK and Matoušek, J and Sharir, M},
   Title = {On range searching with semialgebraic sets.
             II},
   Journal = {SIAM Journal on Computing},
   Volume = {42},
   Number = {6},
   Pages = {2039-2062},
   Year = {2013},
   Month = {December},
   ISSN = {0097-5397},
   url = {http://dx.doi.org/10.1137/120890855},
   Abstract = {Let P be a set of n points in ℝd. We present a linear-size
             data structure for answering range queries on P with
             constant-complexity semialgebraic sets as ranges, in time
             close to O(n11/d). It essentially matches the performance of
             similar structures for simplex range searching, and, for d
             ≥ 5, significantly improves earlier solutions by the first
             two authors obtained in 1994. This almost settles a
             long-standing open problem in range searching. The data
             structure is based on a partitioning technique of Guth and
             Katz [On the Erdos distinct distances problem in the plane,
             arXiv:1011.4105, 2010], which shows that for a parameter r,
             1 < r ≤ n, there exists a d-variate polynomial f of degree
             O(r1/d) such that each connected component of ℝd \ Z(f)
             contains at most n/r points of P, where Z(f) is the zero set
             of f. We present an efficient randomized algorithm for
             computing such a polynomial partition, which is of
             independent interest and is likely to have additional
             applications. © 2013 Society for Industrial and Applied
             Mathematics.},
   Doi = {10.1137/120890855},
   Key = {fds235361}
}

@article{fds235357,
   Author = {Lebeck, N and Mølhave, T and Agarwal, PK},
   Title = {Computing highly occluded paths on a terrain},
   Journal = {GIS: Proceedings of the ACM International Symposium on
             Advances in Geographic Information Systems},
   Pages = {14-23},
   Year = {2013},
   Month = {December},
   url = {http://dx.doi.org/10.1145/2525314.2525363},
   Abstract = {Understanding the locations of highly occluded paths on a
             terrain is an important GIS problem. In this paper we
             present a model and a fast algorithm for computing highly
             occluded paths on a terrain. It does not assume the observer
             locations to be known and yields a path likely to be
             occluded under a rational observer strategy. We present
             experimental results that examine several different observer
             strategies. The repeated visibility map computations
             necessary for our model is expedited using a fast algorithm
             for calculating approximate visibility maps that models the
             decrease in observational fidelity as distance increases.
             The algorithm computes a multiresolution approximate
             visibility map and makes use of a graphics processing unit
             (GPU) to speed up computation. We present experimental
             results on terrrain data sets with up to 144 million points.
             © 2013 ACM.},
   Doi = {10.1145/2525314.2525363},
   Key = {fds235357}
}

@article{fds235358,
   Author = {Sankararaman, S and Agarwal, PK and Mølhave, T and Pan, J and Boedihardjo, AP},
   Title = {Model-driven matching and segmentation of
             trajectories},
   Journal = {GIS: Proceedings of the ACM International Symposium on
             Advances in Geographic Information Systems},
   Pages = {234-243},
   Year = {2013},
   Month = {December},
   url = {http://dx.doi.org/10.1145/2525314.2525360},
   Abstract = {A fundamental problem in analyzing trajectory data is to
             identify common patterns between pairs or among groups of
             trajectories. In this paper, we consider the problem of
             matching similar portions between a pair of trajectories,
             each observed as a sequence of points sampled from it. We
             present new measures of trajectory similarity - both local
             and global - between a pair of trajectories to distinguish
             between similar and dissimilar portions. We then use this
             model to perform segmentation of a set of trajectories into
             fragments, contiguous portions of trajectories shared by
             many of them. Our model for similarity is robust under noise
             and sampling rate variations. The model also yields a score
             which can be used to rank multiple pairs of trajectories
             according to similarity, e.g. in clustering applications. We
             present quadratic time algorithms to compute the similarity
             between trajectory pairs under our measures together with
             algorithms to identify fragments in a large set of
             trajectories efficiently using the similarity model.
             Finally, we present an extensive experimental study
             evaluating the effectiveness of our approach on real
             datasets, comparing it with earlier approaches. Our
             experiments show that our model for similarity is highly
             accurate in distinguishing similar and dissimilar portions
             as compared to earlier methods even with sparse sampling.
             Further, our segmentation algorithm is able to identify a
             small set of fragments capturing the common parts of
             trajectories in the dataset. © 2013 ACM.},
   Doi = {10.1145/2525314.2525360},
   Key = {fds235358}
}

@article{fds235360,
   Author = {Agarwal, PK and Cormode, G and Huang, Z and Phillips, JM and Wei, Z and Yi,
             K},
   Title = {Mergeable summaries},
   Journal = {ACM Transactions on Database Systems},
   Volume = {38},
   Number = {4},
   Year = {2013},
   Month = {November},
   ISSN = {0362-5915},
   url = {http://dx.doi.org/10.1145/2500128},
   Abstract = {We study the mergeability of data summaries. Informally
             speaking, mergeability requires that, given two summaries on
             two datasets, there is a way to merge the two summaries into
             a single summary on the two datasets combined together,
             while preserving the error and size guarantees. This
             property means that the summaries can be merged in a way
             akin to other algebraic operators such as sum and max, which
             is especially useful for computing summaries on massive
             distributed data. Several data summaries are trivially
             mergeable by construction, most notably all the sketches
             that are linear functions of the datasets. But some other
             fundamental ones, like those for heavy hitters and
             quantiles, are not (known to be) mergeable. In this article,
             we demonstrate that these summaries are indeed mergeable or
             can be made mergeable after appropriatemodifications.
             Specifically, we show that for e-approximate heavy hitters,
             there is a deterministic mergeable summary of size O(1/e);
             for e-approximate quantiles, there is a deterministic
             summary of size O((1/e) log(en)) that has a restricted form
             of mergeability, and a randomized one of size O((1/e)
             log3/2(1/e)) with full mergeability. We also extend our
             results to geometric summaries such as e-approximations
             which permit approximate multidimensional range counting
             queries. While most of the results in this article are
             theoretical in nature, some of the algorithms are actually
             very simple and even perform better than the previously best
             known algorithms, which we demonstrate through experiments
             in a simulated sensor network. We also achieve two results
             of independent interest: (1) we provide the best known
             randomized streaming bound for ε-approximate quantiles that
             depends only on e, of size O((1/e) log3/2(1/e)), and (2) we
             demonstrate that the MG and the SpaceSaving summaries for
             heavy hitters are isomorphic. © 2013.},
   Doi = {10.1145/2500128},
   Key = {fds235360}
}

@article{fds235362,
   Author = {Agarwal, PK and Efrat, A and Ganjugunte, SK and Hay, D and Sankararaman,
             S and Zussman, G},
   Title = {The resilience of WDM networks to probabilistic geographical
             failures},
   Journal = {IEEE/ACM Transactions on Networking (ACM)},
   Volume = {21},
   Number = {5},
   Pages = {1525-1538},
   Year = {2013},
   Month = {January},
   ISSN = {1063-6692},
   url = {http://dx.doi.org/10.1109/TNET.2012.2232111},
   Abstract = {Telecommunications networks, and in particular optical WDM
             networks, are vulnerable to large-scale failures in their
             physical infrastructure, resulting from physical attacks
             (such as an electromagnetic pulse attack) or natural
             disasters (such as solar flares, earthquakes, and floods).
             Such events happen at specific geographical locations and
             disrupt specific parts of the network, but their effects
             cannot be determined exactly in advance. Therefore, we
             provide a unified framework to model network vulnerability
             when the event has a probabilistic nature, defined by an
             arbitrary probability density function. Our framework
             captures scenarios with a number of simultaneous attacks,
             when network components consist of several dependent
             subcomponents, and in which either a 1+1 or a 1:1 protection
             plan is in place. We use computational geometric tools to
             provide efficient algorithms to identify vulnerable points
             within the network under various metrics. Then, we obtain
             numerical results for specific backbone networks,
             demonstrating the applicability of our algorithms to
             real-world scenarios. Our novel approach allows to identify
             locations that require additional protection efforts (e.g.,
             equipment shielding). Overall, the paper demonstrates that
             using computational geometric techniques can significantly
             contribute to our understanding of network resilience. ©
             1993-2012 IEEE.},
   Doi = {10.1109/TNET.2012.2232111},
   Key = {fds235362}
}

@article{fds235363,
   Author = {Agarwal, PK and Sharathkumar, R and Agarwal, PK and Sharathkumar,
             R},
   Title = {Streaming Algorithms for Extent Problems in High
             DimensionsStreaming Algorithms for Extent Problems in High
             Dimensions},
   Journal = {Algorithmica},
   Pages = {1-16},
   Year = {2013},
   ISSN = {0178-4617},
   url = {http://dx.doi.org/10.1007/s00453-013-9846-4},
   Abstract = {We present (single-pass) streaming algorithms for
             maintaining extent measures of a stream S of n points in
             {Mathematical expression}. We focus on designing streaming
             algorithms whose working space is polynomial in d (poly(d))
             and sub-linear in n. For the problems of computing diameter,
             width and minimum enclosing ball of S, we obtain lower
             bounds on the worst-case approximation ratio of any
             streaming algorithm that uses poly(d) space. On the positive
             side, we introduce the notion of blurred ball cover and use
             it for answering approximate farthest-point queries and
             maintaining approximate minimum enclosing ball and diameter
             of S. We describe a streaming algorithm for maintaining a
             blurred ball cover whose working space is linear in d and
             independent of n. © 2013 Springer Science+Business Media
             New York.},
   Doi = {10.1007/s00453-013-9846-4},
   Key = {fds235363}
}

@article{fds235366,
   Author = {Agarwal, PK and Aronov, B and Har-Peled, S and Phillips, JM and Yi, K and Zhang, W},
   Title = {Nearest neighbor searching under uncertainty
             II},
   Journal = {Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on
             Principles of Database Systems},
   Pages = {115-126},
   Year = {2013},
   url = {http://dx.doi.org/10.1145/2463664.2465219},
   Abstract = {Nearest-neighbor (NN) search, which returns the nearest
             neighbor of a query point in a set of points, is an
             important and widely studied problem in many fields, and it
             has wide range of applications. In many of them, such as
             sensor databases, location-based services, face recognition,
             and mobile data, the location of data is imprecise. We
             therefore study nearest neighbor queries in a probabilistic
             framework in which the location of each input point is
             specified as a probability distribution function. We present
             efficient algorithms for (i) computing all points that are
             nearest neighbors of a query point with nonzero probability;
             (ii) estimating, within a specified additive error, the
             probability of a point being the nearest neighbor of a query
             point; (iii) using it to return the point that maximizes the
             probability being the nearest neighbor, or all the points
             with probabilities greater than some threshold to be the NN.
             We also present some experimental results to demonstrate the
             effectiveness of our approach. Copyright 2013
             ACM.},
   Doi = {10.1145/2463664.2465219},
   Key = {fds235366}
}

@article{fds235367,
   Author = {Agarwal, PK and Kaplan, H and Sharir, M},
   Title = {Union of random minkowski sums and network vulnerability
             analysis},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {177-186},
   Year = {2013},
   Abstract = {Let C = {C1,⋯, Cn} be a set of n pairwise-disjoint convex
             s-gons, for some constant s, and let π be a probability
             density function (pdf) over the non-negative reals. For each
             i, let Ki be the Minkowski sum of Ci with a disk of radius
             ri, where each ri is a random non-negative number drawn
             independently from the distribution determined by π. We
             show that the expected complexity of the union of K1,⋯, Kn
             is O (n log n), for any pdf π; the constant of
             proportionality depends on s, but not on the pdf. Next, we
             consider the following problem that arises in analyzing the
             vulnerability of a network under a physical attack. Let G =
             (V, ε) be a planar geometric graph where ε is a set of n
             line segments with pairwise-disjoint relative interiors. Let
             φ: ℝ≥0 → [0,1] be an edge failure probability
             function, where a physical attack at a location x ∈ ℝ2
             causes an edge e of E at distance r from x to fail with
             probability φ(r); we assume that φ is of the form 1 -
             Π(x), where Π is a cumulative distribution function on the
             non-negative reals. The goal is to compute the most
             vulnerable location for G, i.e., the location of the attack
             that maximizes the expected number of failing edges of G.
             Using our bound on the complexity of the union of random
             Minkowski sums, we present a near-linear Monte-Carlo
             algorithm for computing a location that is an approximately
             most vulnerable location of attack for G. Copyright 2013
             ACM.},
   Key = {fds235367}
}

@article{fds235368,
   Author = {Agarwal, PK and Har-Peled, S and Yu, H},
   Title = {EMBEDDINGS OF SURFACES, CURVES, AND MOVING POINTS IN
             EUCLIDEAN SPACE},
   Journal = {SIAM Journal on Computing},
   Volume = {42},
   Number = {2},
   Pages = {442-458},
   Year = {2013},
   ISSN = {0097-5397},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000318353800002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1137/110830046},
   Key = {fds235368}
}

@article{fds235369,
   Author = {Afshani, P and Agarwal, PK and Arge, L and Larsen, KG and Phillips,
             JM},
   Title = {(Approximate) Uncertain Skylines},
   Journal = {Theory of Computing Systems},
   Volume = {52},
   Number = {3},
   Pages = {342-366},
   Year = {2013},
   ISSN = {1432-4350},
   url = {http://dx.doi.org/10.1007/s00224-012-9382-7},
   Abstract = {Given a set of points with uncertain locations, we consider
             the problem of computing the probability of each point lying
             on the skyline, that is, the probability that it is not
             dominated by any other input point. If each point's
             uncertainty is described as a probability distribution over
             a discrete set of locations, we improve the best known exact
             solution. We also suggest why we believe our solution might
             be optimal. Next, we describe simple, near-linear time
             approximation algorithms for computing the probability of
             each point lying on the skyline. In addition, some of our
             methods can be adapted to construct data structures that can
             efficiently determine the probability of a query point lying
             on the skyline. © 2012 Springer Science+Business Media,
             LLC.},
   Doi = {10.1007/s00224-012-9382-7},
   Key = {fds235369}
}

@article{fds235370,
   Author = {Agarwal, PK and Efrat, A and Ganjugunte, SK and Hay, D and Sankararaman,
             S and Zussman, G},
   Title = {The Resilience of WDM Networks to Probabilistic Geographical
             Failures},
   Journal = {IEEE/ACM Transactions on Networking (ACM)},
   Year = {2013},
   ISSN = {1063-6692},
   url = {http://dx.doi.org/10.1109/TNET.2012.2232111},
   Abstract = {Telecommunications networks, and in particular optical WDM
             networks, are vulnerable to large-scale failures in their
             physical infrastructure, resulting from physical attacks
             (such as an electromagnetic pulse attack) or natural
             disasters (such as solar flares, earthquakes, and floods).
             Such events happen at specific geographical locations and
             disrupt specific parts of the network, but their effects
             cannot be determined exactly in advance. Therefore, we
             provide a unified framework to model network vulnerability
             when the event has a probabilistic nature, defined by an
             arbitrary probability density function. Our framework
             captures scenarios with a number of simultaneous attacks,
             when network components consist of several dependent
             subcomponents, and in which either a 1+1 or a 1:1 protection
             plan is in place. We use computational geometric tools to
             provide efficient algorithms to identify vulnerable points
             within the network under various metrics. Then, we obtain
             numerical results for specific backbone networks,
             demonstrating the applicability of our algorithms to
             real-world scenarios. Our novel approach allows to identify
             locations that require additional protection efforts (e.g.,
             equipment shielding). Overall, the paper demonstrates that
             using computational geometric techniques can significantly
             contribute to our understanding of network
             resilience.},
   Doi = {10.1109/TNET.2012.2232111},
   Key = {fds235370}
}

@article{fds235557,
   Author = {Agarwal, PK and Arge, L and Govindarajan, S and Yang, J and Yi,
             K},
   Title = {Efficient external memory structures for range-aggregate
             queries},
   Journal = {Computational Geometry},
   Volume = {46},
   Number = {3},
   Pages = {358-370},
   Year = {2013},
   ISSN = {0925-7721},
   url = {http://dx.doi.org/10.1016/j.comgeo.2012.10.003},
   Abstract = {We present external memory data structures for efficiently
             answering range-aggregate queries. The range-aggregate
             problem is defined as follows: Given a set of weighted
             points in Rd, compute the aggregate of the weights of the
             points that lie inside a d-dimensional orthogonal query
             rectangle. The aggregates we consider in this paper include
             count, sum, and max. First, we develop a structure for
             answering two-dimensional range-count queries that uses
             O(N/B) disk blocks and answers a query in O( logBN) I/Os,
             where N is the number of input points and B is the disk
             block size. The structure can be extended to obtain a
             near-linear-size structure for answering range-sum queries
             using O( logBN) I/Os, and a linear-size structure for
             answering range-max queries in O(logB2N) I/Os. Our
             structures can be made dynamic and extended to higher
             dimensions. © 2012 Elsevier B.V.},
   Doi = {10.1016/j.comgeo.2012.10.003},
   Key = {fds235557}
}

@article{fds303192,
   Author = {Shaharabani, D and Salzman, O and Agarwal, PK and Halperin,
             D},
   Title = {Sparsification of Motion-Planning Roadmaps by Edge
             Contraction},
   Year = {2012},
   Month = {September},
   url = {http://arxiv.org/abs/1209.4463v1},
   Abstract = {We present Roadmap Sparsification by Edge Contraction
             (RSEC), a simple and effective algorithm for reducing the
             size of a motion-planning roadmap. The algorithm exhibits
             minimal effect on the quality of paths that can be extracted
             from the new roadmap. The primitive operation used by RSEC
             is edge contraction - the contraction of a roadmap edge to a
             single vertex and the connection of the new vertex to the
             neighboring vertices of the contracted edge. For certain
             scenarios, we compress more than 98% of the edges and
             vertices at the cost of degradation of average shortest path
             length by at most 2%.},
   Key = {fds303192}
}

@article{fds303193,
   Author = {Agarwal, PK and Avraham, RB and Kaplan, H and Sharir,
             M},
   Title = {Computing the Discrete Fréchet Distance in Subquadratic
             Time},
   Year = {2012},
   Month = {April},
   url = {http://arxiv.org/abs/1204.5333v1},
   Abstract = {The Fr\'echet distance is a similarity measure between two
             curves $A$ and $B$: Informally, it is the minimum length of
             a leash required to connect a dog, constrained to be on $A$,
             and its owner, constrained to be on $B$, as they walk
             without backtracking along their respective curves from one
             endpoint to the other. The advantage of this measure on
             other measures such as the Hausdorff distance is that it
             takes into account the ordering of the points along the
             curves. The discrete Fr\'echet distance replaces the dog and
             its owner by a pair of frogs that can only reside on $n$ and
             $m$ specific pebbles on the curves $A$ and $B$,
             respectively. These frogs hop from a pebble to the next
             without backtracking. The discrete Fr\'echet distance can be
             computed by a rather straightforward quadratic dynamic
             programming algorithm. However, despite a considerable
             amount of work on this problem and its variations, there is
             no subquadratic algorithm known, even for approximation
             versions of the problem. In this paper we present a
             subquadratic algorithm for computing the discrete Fr\'echet
             distance between two sequences of points in the plane, of
             respective lengths $m\le n$. The algorithm runs in
             $O(\dfrac{mn\log\log n}{\log n})$ time and uses $O(n+m)$
             storage. Our approach uses the geometry of the problem in a
             subtle way to encode legal positions of the frogs as states
             of a finite automata.},
   Key = {fds303193}
}

@article{fds235381,
   Author = {Agarwal, PK and Matoušek, J and Sharir, M},
   Title = {On range searching with semialgebraic sets
             II},
   Journal = {Annual Symposium on Foundations of Computer
             Science},
   Pages = {420-429},
   Year = {2012},
   ISSN = {0272-5428},
   url = {http://dx.doi.org/10.1109/FOCS.2012.32},
   Abstract = {Let P be a set of n points in ℝd. We present a linear-size
             data structure for answering range queries on P with
             constant-complexity semi algebraic sets as ranges, in time
             close to O(n1-1/d). It essentially matches the performance
             of similar structures for simplex range searching, and, for
             d ≥ 5, significantly improves earlier solutions by the
             first two authors obtained in~1994. This almost settles a
             long-standing open problem in range searching. The data
             structure is based on the polynomial-partitioning technique
             of Guth and Katz [arXiv:1011.4105], which shows that for a
             parameter r, 1 &lt; r ≤ n, there exists a d-variate
             polynomial f of degree O(r1/d) such that each connected
             component of ℝd \ Z(f) contains at most n/r points of P,
             where Z(f) is the zero set of f. We present an ef?cient
             randomized algorithm for computing such a polynomial
             partition, which is of independent interest and is likely to
             have additional applications. © 2012 IEEE.},
   Doi = {10.1109/FOCS.2012.32},
   Key = {fds235381}
}

@article{fds235545,
   Author = {Afshani, P and Agarwal, PK and Arge, L and Larsen, KG and Phillips,
             JM},
   Title = {(Approximate) Uncertain Skylines},
   Journal = {Theory of Computing Systems},
   Pages = {1-25},
   Year = {2012},
   ISSN = {1432-4350},
   url = {http://dx.doi.org/10.1007/s00224-012-9382-7},
   Abstract = {Given a set of points with uncertain locations, we consider
             the problem of computing the probability of each point lying
             on the skyline, that is, the probability that it is not
             dominated by any other input point. If each point's
             uncertainty is described as a probability distribution over
             a discrete set of locations, we improve the best known exact
             solution. We also suggest why we believe our solution might
             be optimal. Next, we describe simple, near-linear time
             approximation algorithms for computing the probability of
             each point lying on the skyline. In addition, some of our
             methods can be adapted to construct data structures that can
             efficiently determine the probability of a query point lying
             on the skyline. © 2012 Springer Science+Business Media,
             LLC.},
   Doi = {10.1007/s00224-012-9382-7},
   Key = {fds235545}
}

@article{fds235546,
   Author = {Sharathkumar, R and Agarwal, PK},
   Title = {Algorithms for the transportation problem in geometric
             settings},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Pages = {306-317},
   Year = {2012},
   Abstract = {For A, B ⊂ ℝ d, |A| + |B| = n, let a ∈ A have a demand
             d a ∈ ℤ + and b ∈ B have a supply s b ∈ ℤ +, Σ
             a∈A d a = Σ b∈B s b = U and let d(·,·) be a distance
             function. Suppose the diameter of A ∪ B is Δ under
             d(·,·), and ε &gt; 0 is a parameter. We present an
             algorithm that in O((n√U log 2 n + U log
             U)Φ(n)log(ΔU/ε)) time computes a solution to the
             transportation problem on A, B which is within an additive
             error ε from the optimal solution. Here Φ(n) is the query
             and update time of a dynamic weighted nearest neighbor data
             structure under distance function d(·,·). Note that the
             (1/ε) appears only in the log term. As among various
             consequences we obtain, • For A, B ⊂ ℝ d and for the
             case where d(·,·) is a metric, an ε-approximation
             algorithm for the transportation problem in O((n√U log 2 n
             + U log U)Φ(n)log(ΔU/ε)) time. • For A, B ⊂ [Δ] d
             and the L 1 and L ∞, distance, exact algorithm for
             computing an optimal bipartite matching of A, B that runs in
             O(n 3/2 log d+O(1) n log Δ) time. • For A, B ⊂ [Δ] 2
             and RMS distance, exact algorithm for computing an optimal
             bipartite matching of A, B that runs in O(n 3/2+δ log Δ)
             time, for an arbitrarily small constant δ &gt; 0. For point
             sets, A, B ⊂ [Δ] d, for the L p norm and for O &lt; α,β
             &lt; 1, we present a randomized dynamic data structure that
             maintains a partial solution to the transportation problem
             under insertions and deletions of points in which at least
             (1 - α) U of the demands are satisfied and whose cost is
             within (1 + β) of that of the optimal (complete) solution
             to the transportation problem with high probability. The
             insertion, deletion and update times are
             O(poly(log(nΔ)/αβ)), provided U = n O(1). Copyright ©
             SIAM.},
   Key = {fds235546}
}

@article{fds235547,
   Author = {Agarwal, PK and Arge, L and Kaplan, H and Molad, E and Tarjan, RE and Yi,
             K},
   Title = {An optimal dynamic data structure for stabbing-semigroup
             queries},
   Journal = {SIAM Journal on Computing},
   Volume = {41},
   Number = {1},
   Pages = {104-127},
   Year = {2012},
   ISSN = {0097-5397},
   url = {http://dx.doi.org/10.1137/10078791X},
   Abstract = {Let S be a set of n intervals in ℝ, and let (S,+) be any
             commutative semigroup. We assign a weight ω(s) ε S to each
             interval in S. For a point x ε ℝ, let S(x) C S be the set
             of intervals that contain x. Given a point q ε ℝ, the
             stabbing-semigroup query asks for computing ΣsεS(q) ω(s).
             We propose a linear-size dynamic data structure, under the
             pointer-machine model, that answers queries in worst-case
             O(log n) time and supports both insertions and deletions of
             intervals in amortized O(log n) time. It is the first data
             structure that attains the optimal O(log n) bound for all
             three operations. Furthermore, our structure can easily be
             adapted to external memory, where we obtain a linear-size
             structure that answers queries and supports updates in O(log
             Bn) I/Os, where B is the disk block size. For the restricted
             case of a nested family of intervals (either every pair of
             intervals is disjoint or one contains the other), we present
             a simpler solution based on dynamic trees. © 2012 Society
             for Industrial and Applied Mathematics.},
   Doi = {10.1137/10078791X},
   Key = {fds235547}
}

@article{fds235548,
   Author = {Agarwal, PK and Cormode, G and Huang, Z and Phillips, J and Wei, Z and Yi,
             K},
   Title = {Mergeable summaries},
   Journal = {Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on
             Principles of Database Systems},
   Pages = {23-34},
   Year = {2012},
   url = {http://dx.doi.org/10.1145/2213556.2213562},
   Abstract = {We study the mergeability of data summaries. Informally
             speaking, mergeability requires that, given two summaries on
             two data sets, there is a way to merge the two summaries
             into a single summary on the union of the two data sets,
             while preserving the error and size guarantees. This
             property means that the summaries can be merged in a way
             like other algebraic operators such as sum and max, which is
             especially useful for computing summaries on massive
             distributed data. Several data summaries are trivially
             mergeable by construction, most notably all the sketches
             that are linear functions of the data sets. But some other
             fundamental ones like those for heavy hitters and quantiles,
             are not (known to be) mergeable. In this paper, we
             demonstrate that these summaries are indeed mergeable or can
             be made mergeable after appropriate modifications.
             Specifically, we show that for ε-approximate heavy hitters,
             there is a deterministic mergeable summary of size O(1/ε)
             for ε-approximate quantiles, there is a deterministic
             summary of size O(1/ε log(εn))that has a restricted form
             of mergeability, and a randomized one of size O(1/ε log
             3/21/ε) with full mergeability. We also extend our results
             to geometric summaries such as ε-approximations and
             εkernels. We also achieve two results of independent
             interest: (1) we provide the best known randomized streaming
             bound for ε-approximate quantiles that depends only on ε,
             of size O(1/ε log 3/21/ε, and (2) we demonstrate that the
             MG and the SpaceSaving summaries for heavy hitters are
             isomorphic. © 2012 ACM.},
   Doi = {10.1145/2213556.2213562},
   Key = {fds235548}
}

@article{fds235549,
   Author = {Agarwal, PK and Efrat, A and Sankararaman, S and Zhang,
             W},
   Title = {Nearest-neighbor searching under uncertainty},
   Journal = {Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on
             Principles of Database Systems},
   Pages = {225-236},
   Year = {2012},
   url = {http://dx.doi.org/10.1145/2213556.2213588},
   Abstract = {Nearest-neighbor queries, which ask for returning the
             nearest neighbor of a query point in a set of points, are
             important and widely studied in many fields because of a
             wide range of applications. In many of these applications,
             such as sensor databases, location based services, face
             recognition, and mobile data, the location of data is
             imprecise. We therefore study nearest neighbor queries in a
             probabilistic framework in which the location of each input
             point and/or query point is specified as a probability
             density function and the goal is to return the point that
             minimizes the expected distance, which we refer to as the
             expected nearest neighbor (ENN). We present methods for
             computing an exact ENN or an ε-approximate ENN, for a given
             error parameter 0 &lt; ε &lt; 1, under dierent distance
             functions. These methods build an index of near-linear size
             and answer ENN queries in polylogarithmic or sublinear time,
             depending on the underlying function. As far as we know,
             these are the first nontrivial methods for answering exact
             or ε-approximate ENN queries with provable performance
             guarantees. © 2012 ACM.},
   Doi = {10.1145/2213556.2213588},
   Key = {fds235549}
}

@article{fds235550,
   Author = {Sharathkumar, R and Agarwal, PK},
   Title = {A near-linear time ε-approximation algorithm for geometric
             bipartite matching},
   Journal = {Proceedings of the Annual ACM Symposium on Theory of
             Computing},
   Pages = {385-394},
   Year = {2012},
   ISSN = {0737-8017},
   url = {http://dx.doi.org/10.1145/2213977.2214014},
   Abstract = {For point sets A,B ⊂ ℝ d, |A|=|B|=n, and for a parameter
             ε &gt; 0, we present an algorithm that computes, in O(n
             poly(log n, 1/ε)) time, an ε-approximate perfect matching
             of A and B with high probability; the previously best known
             algorithm takes Ω(n 3/2) time. We approximate the L p-norm
             using a distance function, d(·,·) based on a randomly
             shifted quad-tree. The algorithm iteratively generates an
             approximate minimum-cost augmenting path under d(·,·) in
             time proportional to the length of the path. We show that
             the total length of the augmenting paths generated by the
             algorithm is O((n/ε)log n), implying that the running time
             of our algorithm is O(n poly(log n,1/ε)). © 2012
             ACM.},
   Doi = {10.1145/2213977.2214014},
   Key = {fds235550}
}

@article{fds235551,
   Author = {Yu, A and Agarwal, PK and Yang, J},
   Title = {Processing a large number of continuous preference top-k
             queries},
   Journal = {Proceedings / ACM-SIGMOD International Conference on
             Management of Data. ACM-Sigmod International Conference on
             Management of Data},
   Pages = {397-408},
   Year = {2012},
   ISSN = {0730-8078},
   url = {http://dx.doi.org/10.1145/2213836.2213882},
   Abstract = {Given a set of objects, each with multiple numeric
             attributes, a (preference) top-k query retrieves the k
             objects with the highest scores according to a user
             preference, defined as a linear combination of attribute
             values. We consider the problem of processing a large number
             of continuous top-k queries, each with its own preference.
             When objects or user preferences change, the query results
             must be updated. We present a dynamic index that supports
             the reverse top k query, which is of independent interest.
             Combining this index with another one for top-k queries, we
             develop a scalable solution for processing many continuous
             top-k queries that exploits the clusteredness in user
             preferences. We also define an approximate version of the
             problem and present a solution significantly more efficient
             than the exact one with little loss in accuracy. © 2012
             ACM.},
   Doi = {10.1145/2213836.2213882},
   Key = {fds235551}
}

@article{fds235552,
   Author = {Yu, A and Agarwal, PK and Yang, J},
   Title = {Processing and notifying range top-k subscriptions},
   Journal = {Proceedings / International Conference on Data Engineering.
             International Conference on Data Engineering},
   Pages = {810-821},
   Year = {2012},
   ISSN = {1084-4627},
   url = {http://dx.doi.org/10.1109/ICDE.2012.67},
   Abstract = {We consider how to support a large number of users over a
             wide-area network whose interests are characterised by range
             top-k continuous queries. Given an object update, we need to
             notify users whose top-k results are affected. Simple
             solutions include using a content-driven network to notify
             all users whose interest ranges contain the update (ignoring
             top-k), or using a server to compute only the affected
             queries and notifying them individually. The former solution
             generates too much network traffic, while the latter
             overwhelms the server. We present a geometric framework for
             the problem that allows us to describe the set of affected
             queries succinctly with messages that can be efficiently
             disseminated using content-driven networks. We give fast
             algorithms to reformulate each update into a set of messages
             whose number is provably optimal, with or without knowing
             all user interests. We also present extensions to our
             solution, including an approximate algorithm that trades off
             between the cost of server-side reformulation and that of
             user-side post-processing, as well as efficient techniques
             for batch updates. © 2012 IEEE.},
   Doi = {10.1109/ICDE.2012.67},
   Key = {fds235552}
}

@article{fds235553,
   Author = {Yu, A and Agarwal, PK and Yang, J},
   Title = {Subscriber assignment for wide-area content-based
             publish/subscribe},
   Journal = {IEEE Transactions on Knowledge and Data Engineering},
   Volume = {24},
   Number = {10},
   Pages = {1833-1847},
   Year = {2012},
   ISSN = {1041-4347},
   url = {http://dx.doi.org/10.1109/TKDE.2012.65},
   Abstract = {We study the problem of assigning subscribers to brokers in
             a wide-area content-based publish/subscribe system. A good
             assignment should consider both subscriber interests in the
             event space and subscriber locations in the network space,
             and balance multiple performance criteria including
             bandwidth, delay, and load balance. The resulting
             optimization problem is NP-complete, so systems have turned
             to heuristics and/or simpler algorithms that ignore some
             performance criteria. Evaluating these approaches has been
             challenging because optimal solutions remain elusive for
             realistic problem sizes. To enable proper evaluation, we
             develop a Monte Carlo approximation algorithm with good
             theoretical properties and robustness to workload
             variations. To make it computationally feasible, we combine
             the ideas of linear programming, randomized rounding,
             coreset, and iterative reweighted sampling. We demonstrate
             how to use this algorithm as a yardstick to evaluate other
             algorithms, and why it is better than other choices of
             yardsticks. With its help, we show that a simple greedy
             algorithm works well for a number of workloads, including
             one generated from publicly available statistics on Google
             Groups. We hope that our algorithms are not only useful in
             their own right, but our principled approach toward
             evaluation will also be useful in future evaluation of
             solutions to similar problems in content-based
             publish/subscribe. © 2012 IEEE.},
   Doi = {10.1109/TKDE.2012.65},
   Key = {fds235553}
}

@article{fds235554,
   Author = {Agarwal, PK and Avraham, RB and Sharir, M},
   Title = {The 2-center problem in three dimensions},
   Journal = {Computational Geometry},
   Year = {2012},
   ISSN = {0925-7721},
   url = {http://dx.doi.org/10.1016/j.comgeo.2012.11.005},
   Abstract = {Let P be a set of n points in R 3. The 2-center problem for
             P is to find two congruent balls of minimum radius whose
             union covers P. We present a randomized algorithm for
             computing a 2-center of P that runs in O (β (r *) n 2 log 4
             n log log n) expected time; here β (r) = 1 / (1 - r / r 0)
             3, r * is the radius of the 2-center balls of P, and r 0 is
             the radius of the smallest enclosing ball of P. The
             algorithm is near quadratic as long as r * is not too close
             to r 0, which is equivalent to the condition that the
             centers of the two covering balls be not too close to each
             other. This improves an earlier slightly super-cubic
             algorithm of Agarwal, Efrat, and Sharir (2000) [2] (at the
             cost of making the algorithm performance depend on the
             center separation of the covering balls). © 2012 Elsevier
             B.V. All rights reserved.},
   Doi = {10.1016/j.comgeo.2012.11.005},
   Key = {fds235554}
}

@article{fds235555,
   Author = {Agarwal, PK and Ezra, E and Sharir, M},
   Title = {Near-linear approximation algorithms for geometric hitting
             sets},
   Journal = {Algorithmica},
   Volume = {63},
   Number = {1-2},
   Pages = {1-25},
   Year = {2012},
   ISSN = {0178-4617},
   url = {http://dx.doi.org/10.1007/s00453-011-9517-2},
   Abstract = {Given a range space (X,R), where R § 2 X, the hitting set
             problem is to find a smallest-cardinality subset H § X that
             intersects each set in R. We present near-linear-time
             approximation algorithms for the hitting set problem in the
             following geometric settings: (i) R is a set of planar
             regions with small union complexity. (ii) R is a set of
             axis-parallel d-dimensional boxes in Rd . In both cases X is
             either the entire R d , or a finite set of points in R d .
             The approximation factors yielded by the algorithm are
             small; they are either the same as, or within very small
             factors off the best factors known to be computable in
             polynomial time. © Springer Science+Business Media, LLC
             2011.},
   Doi = {10.1007/s00453-011-9517-2},
   Key = {fds235555}
}

@article{fds235556,
   Author = {Agarwal, PK and Cheng, S-W and Yi, K},
   Title = {Range searching on uncertain data},
   Journal = {ACM Transactions on Algorithms},
   Volume = {8},
   Number = {4},
   Year = {2012},
   ISSN = {1549-6325},
   url = {http://dx.doi.org/10.1145/2344422.2344433},
   Abstract = {Querying uncertain data has emerged as an important problem
             in data management due to the imprecise nature of many
             measurement data. In this article, we study answering range
             queries over uncertain data. Specifically, we are given a
             collection P of n uncertain points in ℝ, each represented
             by its one-dimensional probability density function (pdf).
             The goal is to build a data structure on P such that, given
             a query interval I and a probability threshold τ , we can
             quickly report all points of P that lie in I with
             probability at least τ . We present various structures with
             linear or near-linear space and (poly)logarithmic query
             time. Our structures support pdf's that are either
             histograms or more complex ones such as Gaussian or
             piecewise algebraic. © 2012 ACM.},
   Doi = {10.1145/2344422.2344433},
   Key = {fds235556}
}

@article{fds235620,
   Author = {Wu, Y and Agarwal, PK and Li, C and Yang, J and Yu, C},
   Title = {On "one of the few" objects},
   Journal = {Proceedings of the ACM SIGKDD International Conference on
             Knowledge Discovery and Data Mining},
   Pages = {1487-1495},
   Year = {2012},
   url = {http://dx.doi.org/10.1145/2339530.2339762},
   Abstract = {Objects with multiple numeric attributes can be compared
             within any "subspace" (subset of attributes). In
             applications such as computational journalism, users are
             interested in claims of the form: Karl Malone is one of the
             only two players in NBA history with at least 25,000 points,
             12,000 rebounds, and 5,000 assists in one's career. One
             challenge in identifying such "one-of-the-k" claims (k = 2
             above) is ensuring their "interestingness". A small k is not
             a good indicator for interestingness, as one can often make
             such claims for many objects by increasing the
             dimensionality of the subspace considered. We propose a
             uniqueness-based interestingness measure for one-of-the-few
             claims that is intuitive for non-technical users, and we
             design algorithms for finding all interesting claims (across
             all subspaces) from a dataset. Sometimes, users are
             interested primarily in the objects appearing in these
             claims. Building on our notion of interesting claims, we
             propose a scheme for ranking objects and an algorithm for
             computing the top-ranked objects. Using real-world datasets,
             we evaluate the efficiency of our algorithms as well as the
             advantage of our object-ranking scheme over popular methods
             such as Kemeny optimal rank aggregation and weighted-sum
             ranking. © 2012 ACM.},
   Doi = {10.1145/2339530.2339762},
   Key = {fds235620}
}

@article{fds235544,
   Author = {Clark, JS and Agarwal, P and Bell, DM and Flikkema, PG and Gelfand, A and Nguyen, X and Ward, E and Yang, J},
   Title = {Inferential ecosystem models, from network data to
             prediction.},
   Journal = {Ecological Applications},
   Volume = {21},
   Number = {5},
   Pages = {1523-1536},
   Year = {2011},
   Month = {July},
   ISSN = {1051-0761},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/21830699},
   Abstract = {Recent developments suggest that predictive modeling could
             begin to play a larger role not only for data analysis, but
             also for data collection. We address the example of
             efficient wireless sensor networks, where inferential
             ecosystem models can be used to weigh the value of an
             observation against the cost of data collection.
             Transmission costs make observations "expensive"; networks
             will typically be deployed in remote locations without
             access to infrastructure (e.g., power). The capacity to
             sample intensively makes sensor networks valuable, but
             high-frequency data are informative only at specific times
             and locations. Sampling intervals will range from meters and
             seconds to landscapes and years, depending on the process,
             the current states of the system, the uncertainty about
             those states, and the perceived potential for rapid change.
             Given that intensive sampling is sometimes critical, but
             more often wasteful, how do we develop tools to control the
             measurement and transmission processes? We address the
             potential of data collection controlled and/or supplemented
             by inferential ecosystem models. In a given model, the value
             of an observation can be evaluated in terms of its
             contribution to estimates of state variables and important
             parameters. There will be more than one model applied to
             network data that will include as state variables water,
             carbon, energy balance, biogeochemistry, tree ecophysiology,
             and forest demographic processes. The value of an
             observation will depend on the application. Inference is
             needed to weigh the contributions against transmission cost.
             Network control must be dynamic and driven by models capable
             of learning about both the environment and the network. We
             discuss application of Bayesian inference to model data from
             a developing sensor network as a basis for controlling the
             measurement and transmission processes. Our examples involve
             soil moisture and sap flux, but we discuss broader
             application of the approach, including its implications for
             network design.},
   Key = {fds235544}
}

@article{fds235536,
   Author = {Afshani, P and Agarwal, PK and Arge, L and Larsen, KG and Phillips,
             JM},
   Title = {(Approximate) uncertain skylines},
   Journal = {ACM International Conference Proceeding Series},
   Pages = {186-196},
   Year = {2011},
   url = {http://dx.doi.org/10.1145/1938551.1938576},
   Abstract = {Given a set of points with uncertain locations, we consider
             the problem of computing the probability of each point lying
             on the skyline, that is, the probability that it is not
             dominated by any other input point. If each point's
             uncertainty is described as a probability distribution over
             a discrete set of locations, we improve the best known exact
             solution. We also suggest why we believe our solution might
             be optimal. Next, we describe simple, near-linear time
             approximation algorithms for computing the probability of
             each point lying on the skyline. In addition, some of our
             methods can be adapted to construct data structures that can
             efficiently determine the probability of a query point lying
             on the skyline. © 2011 ACM.},
   Doi = {10.1145/1938551.1938576},
   Key = {fds235536}
}

@article{fds235537,
   Author = {Agarwal, PK and Mølhave, T and Sadri, B},
   Title = {I/O-efficieiit contour queries on terrains},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Pages = {268-284},
   Year = {2011},
   Abstract = {A terrain M can be represented as a triangulation of the
             plane along with a height function associated with the
             vertices (and linearly interpolated within the edges and
             triangles) of M. We investigate the problem of answering
             contour queries on M: Given a height l aud a triangle of M
             that intersects the level set of M at height l, report the
             list of the edges of the connected component of this level
             set that intersect f, sorted in clockwise or
             counterclockwise order. Contour queries are different from
             level-set queries in that only one contour (connected
             component of the level set) out of all those that may exist
             is expected to be reported. We present an I/O-efficient data
             structure of linear size that answers a contour query in
             0(logB N + T/B) I/Os, where N is the number of triangles in
             the terrain and T is the number of edges in the output
             contour. The data structure can be constructed using
             O(Sort(N)) I/Os.},
   Key = {fds235537}
}

@article{fds235538,
   Author = {Yu, A and Agarwal, PK and Yang, J},
   Title = {Subscriber assignment for wide-area content-based
             publish/subscribe},
   Journal = {Proceedings / International Conference on Data Engineering.
             International Conference on Data Engineering},
   Pages = {267-278},
   Year = {2011},
   ISSN = {1084-4627},
   url = {http://dx.doi.org/10.1109/ICDE.2011.5767882},
   Abstract = {We study the problem of assigning subscribers to brokers in
             a wide-area content-based publish/subscribe system. A good
             assignment should consider both subscriber interests in the
             event space and subscriber locations in the network space,
             and balance multiple performance criteria including
             bandwidth, delay, and load balance. The resulting
             optimization problem is NP-complete, so systems have turned
             to heuristics and/or simpler algorithms that ignore some
             performance criteria. Evaluating these approaches has been
             challenging because optimal solutions remain elusive for
             realistic problem sizes. To enable proper evaluation, we
             develop a Monte Carlo approximation algorithm with good
             theoretical properties and robustness to workload
             variations. To make it computationally feasible, we combine
             the ideas of linear programming, randomized rounding,
             coreset, and iterative reweighted sampling. We demonstrate
             how to use this algorithm as a yardstick to evaluate other
             algorithms, and why it is better than other choices of
             yardsticks. With its help, we show that a simple greedy
             algorithm works well for a number of workloads, including
             one generated from publicly available statistics on Google
             Groups. We hope that our algorithms are not only useful in
             their own right, but our principled approach toward
             evaluation will also be useful in future evaluation of
             solutions to similar problems in content-based
             publish/subscribe. © 2011 IEEE.},
   Doi = {10.1109/ICDE.2011.5767882},
   Key = {fds235538}
}

@article{fds235539,
   Author = {Agarwal, PK and Mølhave, T and Yu, H and Clark, JS},
   Title = {Exploiting temporal coherence in forest dynamics
             simulation},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {77-86},
   Year = {2011},
   url = {http://dx.doi.org/10.1145/1998196.1998210},
   Abstract = {Understanding the impact of climate and land-use on forest
             ecosystems involves modeling and simulating complex spatial
             interactions at many different scales. With this goal in
             mind, we have developed an individual-based, spatially
             explicit forest simulator, which incorporates fine-scale
             processes that influence forest dynamics. In this paper we
             present new, faster algorithms for computing understory
             light and for dispersal of seeds | the two most
             computationally intensive submodules in our simulator. By
             exploiting temporal coherence, we circumvent the problem of
             doing the entire simulation at each step. We provide
             experimental results that support the efficiency and
             efficacy of our approach. © 2011 ACM.},
   Doi = {10.1145/1998196.1998210},
   Key = {fds235539}
}

@article{fds235540,
   Author = {Agarwal, PK and Efrat, A and Gniady, C and Mitchell, JSB and Polishchuk,
             V and Sabhnani, GR},
   Title = {Distributed localization and clustering using data
             correlation and the Occam's razor principle},
   Journal = {2011 International Conference on Distributed Computing in
             Sensor Systems and Workshops, DCOSS'11},
   Year = {2011},
   url = {http://dx.doi.org/10.1109/DCOSS.2011.5982164},
   Abstract = {We present a distributed algorithm for computing a combined
             solution to three problems in sensor networks: localization,
             clustering, and sensor suspension. Assuming that initially
             only a rough approximation of the sensor positions is known,
             we show how one can use sensor measurements to refine the
             set of possible sensor locations, to group the sensors into
             clusters with linearly correlated measurements, and to
             decide which sensors may suspend transmission without
             jeopardizing the consistency of the collected data. Our
             algorithm applies the "Occam's razor principle" by computing
             a "simplest" explanation for the data gathered from the
             network. We also present centralized algorithms, as well as
             efficient heuristics. © 2011 IEEE.},
   Doi = {10.1109/DCOSS.2011.5982164},
   Key = {fds235540}
}

@article{fds235541,
   Author = {Agarwal, PK and Efrat, A and Ganjugunte, S and Hay, D and Sankararaman,
             S and Zussman, G},
   Title = {The resilience of WDM networks to probabilistic geographical
             failures},
   Journal = {Proceedings - IEEE INFOCOM},
   Pages = {1521-1529},
   Year = {2011},
   ISSN = {0743-166X},
   url = {http://dx.doi.org/10.1109/INFCOM.2011.5934942},
   Abstract = {Telecommunications networks, and in particular optical WDM
             networks, are vulnerable to large-scale failures of their
             physical infrastructure, resulting from physical attacks
             (such as an Electromagnetic Pulse attack) or natural
             disasters (such as solar flares, earthquakes, and floods).
             Such events happen at specific geographical locations and
             disrupt specific parts of the network but their effects are
             not deterministic. Therefore, we provide a unified framework
             to model the network vulnerability when the event has a
             probabilistic nature, defined by an arbitrary probability
             density function. Our framework captures scenarios with a
             number of simultaneous attacks, in which network components
             consist of several dependent subcomponents, and in which
             either a 1+1 or a 1:1 protection plan is in place. We use
             computational geometric tools to provide efficient
             algorithms to identify vulnerable points within the network
             under various metrics. Then, we obtain numerical results for
             specific backbone networks, thereby demonstrating the
             applicability of our algorithms to real-world scenarios. Our
             novel approach allows for identifying locations which
             require additional protection efforts (e.g., equipment
             shielding). Overall, the paper demonstrates that using
             computational geometric techniques can significantly
             contribute to our understanding of network resilience. ©
             2011 IEEE.},
   Doi = {10.1109/INFCOM.2011.5934942},
   Key = {fds235541}
}

@article{fds235542,
   Author = {Beutel, A and Mølhave, T and Agarwal, PK and Boedihardjo, AP and Shine,
             JA},
   Title = {TerraNNI: Natural neighbor interpolation on a 3D grid using
             a GPU},
   Journal = {GIS: Proceedings of the ACM International Symposium on
             Advances in Geographic Information Systems},
   Pages = {64-73},
   Year = {2011},
   url = {http://dx.doi.org/10.1145/2093973.2093984},
   Abstract = {With modern focus on LiDAR technology the amount of
             topographic data, in the form of massive point clouds, has
             increased dramatically. Furthermore, due to the popularity
             of LiDAR, repeated surveys of the same areas are becoming
             more common. This trend will only increase as topographic
             changes prompt surveys over already scanned terrain, in
             which case we obtain large spatio-temporal data sets. In
             dynamic terrains, such as coastal regions, such
             spatio-temporal data can offer interesting insight into how
             the terrain changes over time. An initial step in the
             analysis of such data is to create a digital elevation model
             representing the terrain over time. In the case of
             spatio-temporal data sets those models often represent
             elevation on a 3D volumetric grid. This involves
             interpolating the elevation of LiDAR points on these grid
             points. In this paper we show how to efficiently perform
             natural neighbor interpolation over a 3D volumetric grid.
             Using a graphics processing unit (GPU), we describe
             different algorithms to attain speed and GPU-memory
             trade-offs. Our algorithm extends to higher dimensions. Our
             experimental results demonstrate that the algorithm is
             efficient and scalable. Categories and Subject. © 2011
             ACM.},
   Doi = {10.1145/2093973.2093984},
   Key = {fds235542}
}

@article{fds235543,
   Author = {Abam, MA and Agarwal, PK and Berg, MD and Yu, H},
   Title = {Out-of-order event processing in kinetic data
             structures},
   Journal = {Algorithmica},
   Volume = {60},
   Number = {2},
   Pages = {250-273},
   Year = {2011},
   ISSN = {0178-4617},
   url = {http://dx.doi.org/10.1007/s00453-009-9335-y},
   Abstract = {We study the problem of designing kinetic data structures
             (KDS's for short) when event times cannot be computed
             exactly and events may be processed in a wrong order. In
             traditional KDS's this can lead to major inconsistencies
             from which the KDS cannot recover. We present more robust
             KDS's for the maintenance of several fundamental structures
             such as kinetic sorting and kinetic tournament trees, which
             overcome the difficulty by employing a refined event
             scheduling and processing technique. We prove that the new
             event scheduling mechanism leads to a KDS that is correct
             except for finitely many short time intervals. We analyze
             the maximum delay of events and the maximum error in the
             structure, and we experimentally compare our approach to the
             standard event scheduling mechanism. © 2009 Springer
             Science+Business Media, LLC.},
   Doi = {10.1007/s00453-009-9335-y},
   Key = {fds235543}
}

@article{fds235476,
   Author = {Chen, L and Tang, C and Yang, J and Kitsuregawa, M and Li,
             Q},
   Title = {Lecture Notes in Computer Science (including subseries
             Lecture Notes in Artificial Intelligence and Lecture Notes
             in Bioinformatics): Preface},
   Journal = {Lecture notes in computer science},
   Volume = {6184 LNCS},
   Pages = {V-VI},
   Year = {2010},
   Month = {August},
   ISBN = {3540290087},
   ISSN = {0302-9743},
   Key = {fds235476}
}

@article{fds235521,
   Author = {Agarwal, PK and Sharathkumar, R},
   Title = {Streaming algorithms for extent problems in high
             dimensions},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Pages = {1481-1489},
   Year = {2010},
   Abstract = {We develop (single-pass) streaming algorithms for
             maintaining extent measures of a stream S of n points in
             ℝd. We focus on designing streaming algorithms whose
             working space is polynomial in d (poly(d)) and sub-linear in
             n. For the problems of computing diameter, width and minimum
             enclosing ball of S, we obtain lower bounds on the
             worst-case approximation ratio of any streaming algorithm
             that uses poly(d) space. On the positive side, we introduce
             the notion of blurred ball cover and use it for answering
             approximate farthest-point queries and maintaining
             approximate minimum enclosing ball and diameter of S. We
             describe a streaming algorithm for maintaining a blurred
             ball cover whose working space is linear in d and
             independent of n. Copyright © by SIAM.},
   Key = {fds235521}
}

@article{fds235522,
   Author = {Agarwal, PK and Efrat, A and Sharathkumar, R and Yu,
             H},
   Title = {On approximate geodesic-distance queries amid deforming
             point clouds},
   Journal = {Springer Tracts in Advanced Robotics},
   Volume = {57},
   Pages = {351-365},
   Year = {2010},
   ISSN = {1610-7438},
   url = {http://dx.doi.org/10.1007/978-3-642-00312-7_22},
   Abstract = {We propose data structures for answering a geodesic-distance
             query between two query points in a two-dimensional or
             three-dimensional dynamic environment, in which obstacles
             are deforming continuously. Each obstacle in the environment
             is modeled as the convex hull of a continuously deforming
             point cloud. The key to our approach is to avoid maintaining
             the convex hull of each point cloud explicitly but still
             able to retain sufficient geometric information to estimate
             geodesic distances in the free space. © 2009
             Springer-Verlag.},
   Doi = {10.1007/978-3-642-00312-7_22},
   Key = {fds235522}
}

@article{fds235523,
   Author = {Sankararaman, S and Efrat, A and Ramasubramanian, S and Agarwal,
             PK},
   Title = {On channel-discontinuity-constraint routing in wireless
             networks},
   Journal = {Proceedings - IEEE INFOCOM},
   Year = {2010},
   ISSN = {0743-166X},
   url = {http://dx.doi.org/10.1109/INFCOM.2010.5462188},
   Abstract = {Multi-channel wireless networks are increasingly being
             employed as infrastructure networks, e.g. in metro areas.
             Nodes in these networks frequently employ directional
             antennas to improve spatial throughput. In such networks,
             given a source and destination, it is of interest to compute
             an optimal path and channel assignment on every link in the
             path such that the path bandwidth is the same as that of the
             link bandwidth and such a path satisfies the constraint that
             no two consecutive links on the path are assigned the same
             channel, referred to as "Channel Discontinuity Constraint"
             (CDC). CDC-paths are also quite useful for TDMA system,
             where preferably every consecutive links along a path are
             assigned different time slots. This paper contains several
             contributions. We first present an O(N2) distributed
             algorithm for discovering the shortest CDC-path between
             given source and destination. For use in wireless networks,
             we explain how spatial properties can be used for
             dramatically expedite the algorithm. This improves the
             running time of the O(N3) centralized algorithm of Ahuja et
             al. for finding the minimum-weight CDC-path. Our second
             result is a generalized t-spanner for CDC-path; For any θ
             &gt; 0 we show how to construct a sub-network containing
             only O(N/θ ) edges, such that that length of shortest
             CDC-paths between arbitrary sources and destinations
             increases by only a factor of at most (1-2 sin θ/2 )-2.
             This scheme can be implemented in a distributed manner using
             the ideas of [3] with a message complexity of O(n log n) and
             it is highly dynamic, so addition/deletion of nodes are
             easily handled in a distributed manner. An important
             conclusion of this scheme is in the case of directional
             antennas are used. In this case, it is enough to consider
             only the two closest nodes in each cone.},
   Doi = {10.1109/INFCOM.2010.5462188},
   Key = {fds235523}
}

@article{fds235524,
   Author = {Agarwal, PK and Phillips, JM and Sadri, B},
   Title = {Lipschitz unimodal and isotonic regression on paths and
             trees},
   Journal = {Lecture notes in computer science},
   Volume = {6034 LNCS},
   Pages = {384-396},
   Year = {2010},
   ISSN = {0302-9743},
   url = {http://dx.doi.org/10.1007/978-3-642-12200-2_34},
   Abstract = {We describe algorithms for finding the regression of t, a
             sequence of values, to the closest sequence s by mean
             squared error, so that s is always increasing (isotonicity)
             and so the values of two consecutive points do not increase
             by too much (Lipschitz). The isotonicity constraint can be
             replaced with a unimodular constraint, for exactly one local
             maximum in s. These algorithm are generalized from sequences
             of values to trees of values. For each we describe
             near-linear time algorithms. © 2010 Springer-Verlag.},
   Doi = {10.1007/978-3-642-12200-2_34},
   Key = {fds235524}
}

@article{fds235525,
   Author = {Agarwal, PK and Aronov, B and Kreveld, MV and Löffler, M and Silveira,
             RI},
   Title = {Computing similarity between piecewise-linear
             functions},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {375-383},
   Year = {2010},
   url = {http://dx.doi.org/10.1145/1810959.1811020},
   Abstract = {We study the problem of computing the similarity between two
             piecewise-linear bivariate functions defined over a common
             domain, where the surfaces they define in 3D-polyhedral
             terrains-can be transformed vertically by a linear
             transformation of the third coordinate (scaling and
             translation). We present a randomized algorithm that
             minimizes the maximum vertical distance between the graphs
             of the two functions, over all linear transformations of one
             of the terrains, in O(n4/3 polylog n) expected time, where n
             is the total number of vertices in the graphs of the two
             functions. We also study the computation of similarity
             between two univariate or bivariate functions by minimizing
             the area or volume between their graphs. For univariate
             functions we give a (1+ε)-approximation algorithm for
             minimizing the area that runs in O(n/√ε) time, for any
             fixed ε &gt; 0. The (1 + ε)-approximation algorithm for
             the bivariate version, where volume is minimized, runs in
             O(n/ε2) time, for any fixed ε &gt; 0, provided the two
             functions are defined over the same triangulation of their
             domain.},
   Doi = {10.1145/1810959.1811020},
   Key = {fds235525}
}

@article{fds235526,
   Author = {Agarwal, PK},
   Title = {An improved algorithm for computing the volume of the union
             of cubes},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {230-239},
   Year = {2010},
   url = {http://dx.doi.org/10.1145/1810959.1811000},
   Abstract = {Let c be a set of n axis-aligned cubes in ℝ3, and let u(c)
             denote the union of c. We present an algorithm that computes
             the volume of u(c) in time O(n polylog(n)). The previously
             best known algorithm takes O(n 4/3 log2 n)
             time.},
   Doi = {10.1145/1810959.1811000},
   Key = {fds235526}
}

@article{fds235527,
   Author = {Agarwal, PK and Gao, J and Guibas, LJ and Kaplan, H and Koltun, V and Rubin, N and Sharir, M},
   Title = {Kinetic stable Delaunay graphs},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {127-136},
   Year = {2010},
   url = {http://dx.doi.org/10.1145/1810959.1810984},
   Abstract = {The best known upper bound on the number of topological
             changes in the Delaunay triangulation of a set of moving
             points in ℝ2 is (nearly) cubic, even if each point is
             moving with a fixed velocity. We introduce the notion of a
             stable Delaunay graph (SDG in short), a dynamic subgraph of
             the Delaunay triangulation, that is less volatile in the
             sense that it undergoes fewer topological changes and yet
             retains many useful properties of the full Delaunay
             triangulation. SDG is defined in terms of a parameter α
             &gt; 0, and consists of Delaunay edges pq for which the
             (equal) angles at which p and q see the corresponding
             Voronoi edge epq are at least α. We prove several
             interesting properties of SDG and describe two kinetic data
             structures for maintaining it. Both structures use O*(n)
             storage. They process O* (n2) events during the motion, each
             in O*(1) time, provided that the points of P move along
             algebraic trajectories of bounded degree; the O*(·)
             notation hides multiplicative factors that are polynomial in
             1/α and polylogarithmic in n. The first structure is
             simpler but the dependency on 1/α in its performance is
             higher.},
   Doi = {10.1145/1810959.1810984},
   Key = {fds235527}
}

@article{fds235528,
   Author = {Agarwal, PK and Ben-Avraham, R and Sharir, M},
   Title = {The 2-center problem in three dimensions},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {87-96},
   Year = {2010},
   url = {http://dx.doi.org/10.1145/1810959.1810974},
   Abstract = {Let P be a set of n points in ℝ3. The 2-center problem for
             P is to find two congruent balls of the minimum radius whose
             union covers P. We present two randomized algorithms for
             computing a 2-center of P. The first algorithm runs in O(n3
             log8 n) expected time, and the second algorithm runs in O(n2
             log8 n/(1-r*/r 0)3) expected time, where r* is the radius of
             the 2-center of P and r0 is the radius of the smallest
             enclosing ball of P. The second algorithm is faster than the
             first one as long as r* is not very close to r0, which is
             equivalent to the condition of the centers of the two balls
             in the 2-center of P not being very close to each
             other.},
   Doi = {10.1145/1810959.1810974},
   Key = {fds235528}
}

@article{fds235529,
   Author = {Agarwal, PK and Phillips, JM and Yu, H},
   Title = {Stability of ε-kernels},
   Journal = {Lecture notes in computer science},
   Volume = {6346 LNCS},
   Number = {PART 1},
   Pages = {487-499},
   Year = {2010},
   ISSN = {0302-9743},
   url = {http://dx.doi.org/10.1007/978-3-642-15775-2_42},
   Abstract = {Given a set P of n points in ℝd, an ε-kernel K ⊆ P
             approximates the directional width of P in every direction
             within a relative (1 - ε) factor. In this paper we study
             the stability of ε-kernels under dynamic insertion and
             deletion of points to P and by changing the approximation
             factor ε. In the first case, we say an algorithm for
             dynamically maintaining a ε-kernel is stable if at most
             O(1) points change in K as one point is inserted or deleted
             from P. We describe an algorithm to maintain an ε-kernel of
             size O(1/ε(d - 1)/2) in O(1/ε(d - 1)/2 + logn) time per
             update. Not only does our algorithm maintain a stable
             ε-kernel, its update time is faster than any known
             algorithm that maintains an ε-kernel of size O(1/ε (d -
             1)/2). Next, we show that if there is an ε-kernel of P of
             size κ, which may be dramatically less than O(1/ε (d -
             1)/2), then there is an (ε/2)-kernel of P of size
             O(min{1/ε(d-1)/2, κ⌊d/2⌋ log d-2(1/ε)}).. Moreover,
             there exists a point set P in ℝd and a parameter ε &gt; 0
             such that if every ε-kernel of P has size at least κ, then
             any (ε/2)-kernel of P has size Ω(κ⌊d/2⌋). © 2010
             Springer-Verlag.},
   Doi = {10.1007/978-3-642-15775-2_42},
   Key = {fds235529}
}

@article{fds235530,
   Author = {Mølhave, T and Agarwal, PK and Arge, L and Revsbæk,
             M},
   Title = {Scalable algorithms for large high-resolution terrain
             data},
   Journal = {ACM International Conference Proceeding Series},
   Year = {2010},
   url = {http://dx.doi.org/10.1145/1823854.1823878},
   Abstract = {In this paper we demonstrate that the technology required to
             perform typical GIS computations on very large
             high-resolution terrain models has matured enough to be
             ready for use by practitioners. We also demonstrate the
             impact that high-resolution data has on common problems. To
             our knowledge, some of the computations we present have
             never before been carried out by standard desktop computers
             on data sets of comparable size. © 2010
             ACM.},
   Doi = {10.1145/1823854.1823878},
   Key = {fds235530}
}

@article{fds235531,
   Author = {Beutel, A and Mølhave, T and Agarwal, PK},
   Title = {Natural neighbor interpolation based grid DEM construction
             using a GPU},
   Journal = {GIS: Proceedings of the ACM International Symposium on
             Advances in Geographic Information Systems},
   Pages = {172-181},
   Year = {2010},
   url = {http://dx.doi.org/10.1145/1869790.1869817},
   Abstract = {With modern LiDAR technology the amount of topographic data,
             in the form of massive point clouds, has increased
             dramatically. One of the most fundamental GIS tasks is to
             construct a grid digital elevation model (DEM) from these 3D
             point clouds. In this paper we present a simple yet very
             fast algorithm for constructing a grid DEM from massive
             point clouds using natural neighbor interpolation (NNI). We
             use a graphics processing unit (GPU) to significantly speed
             up the computation. To handle the large data sets and to
             deal with graphics hardware limitations clever blocking
             schemes are used to partition the point cloud. For example,
             using standard desktop computers and graphics hardware, we
             construct a high-resolution grid with 150 million cells from
             two billion points in less than thirty-seven minutes. This
             is about one-tenth of the time required for the same
             computer to perform a standard linear interpolation, which
             produces a much less smooth surface. © 2010
             ACM.},
   Doi = {10.1145/1869790.1869817},
   Key = {fds235531}
}

@article{fds235532,
   Author = {Agarwal, PK and Efrat, A and Ganjugunte, SK and Hay, D and Sankararaman,
             S and Zussman, G},
   Title = {Network vulnerability to single, multiple, and probabilistic
             physical attacks},
   Journal = {Proceedings - IEEE Military Communications Conference
             MILCOM},
   Pages = {1824-1829},
   Year = {2010},
   url = {http://dx.doi.org/10.1109/MILCOM.2010.5679556},
   Abstract = {Telecommunications networks heavily rely on the physical
             infrastructure and, are therefore, vulnerable to natural
             disasters, such as earthquakes or floods, as well as to
             physical attacks, such as an Electromagnetic Pulse (EMP)
             attack. Largescale disasters are likely to destroy network
             equipment and to severely affect interdependent systems such
             as the power-grid. In turn, long-term outage of the
             power-grid might cause additional failures to the
             telecommunication network. In this paper, we model an attack
             as a disk around its epicenter, and provide efficient
             algorithms to find vulnerable points within the network,
             under various metrics. In addition, we consider the case in
             which multiple disasters happen simultaneously and provide
             an approximation algorithm to find the points which cause
             the most significant destruction. Finally, since a network
             element does not always fail, even when it is close to the
             attack's epicenter, we consider a simple probabilistic model
             in which the probability of a network element failure is
             given. Under this model, we tackle the cases of single and
             multiple attacks and develop algorithms that identify
             potential points where an attack is likely to cause a
             significant damage. ©2010 IEEE.},
   Doi = {10.1109/MILCOM.2010.5679556},
   Key = {fds235532}
}

@article{fds235533,
   Author = {Agarwal, PK and Har-Peled, S and Sharir, M and Wang,
             Y},
   Title = {Hausdorff distance under translation for points and
             balls},
   Journal = {ACM Transactions on Algorithms},
   Volume = {6},
   Number = {4},
   Year = {2010},
   ISSN = {1549-6325},
   url = {http://dx.doi.org/10.1145/1824777.1824791},
   Abstract = {We study the shape matching problem under the Hausdorff
             distance and its variants. In the first part of the article,
             we consider two sets A, B of balls in Rd, d = 2, 3,
             andwishtofind a translation t that minimizes the Hausdorff
             distance between A + t, the set of all balls in A shifted by
             t , and B. We consider several variants of this problem.
             First, we extend the notion of Hausdorff distance from sets
             of points to sets of balls, so that each ball has to be
             matched with the nearest ball in the other set. We also
             consider the problem in the standard setting, by computing
             the Hausdorff distance between the unions of the two sets
             (as point sets). Second, we consider either all possible
             translations t (as is the standard approach), or consider
             only translations that keep the balls of Α + t disjoint
             from those of Β. We propose several exact and approximation
             algorithms for these problems. In the second part of the
             article, we note that the Hausdorff distance is sensitive to
             outliers, and thus consider two variants that are more
             robust: the root-mean-square (rms) and the summed Hausdorff
             distance. We propose ef?cient approximation algorithms for
             computing the minimum rms and the minimum summed Hausdorff
             distances under translation, between two point sets in ℝd
             .Inorder to obtain a fast algorithm for the summed Hausdorff
             distance, we propose a deterministic ef?cient dynamic data
             structure for maintaining an ε-approximation of the
             1-median of a set of points in ℝd, under insertions and
             deletions. © 2010 ACM 1549-6325/2010/08-ART71
             $10.00.},
   Doi = {10.1145/1824777.1824791},
   Key = {fds235533}
}

@article{fds235534,
   Author = {Agarwal, PK and Arge, L and Yi, K},
   Title = {I/O-efficient batched union-find and its applications to
             terrain analysis},
   Journal = {ACM Transactions on Algorithms},
   Volume = {7},
   Number = {1},
   Year = {2010},
   ISSN = {1549-6325},
   url = {http://dx.doi.org/10.1145/1868237.1868249},
   Abstract = {In this article we present an I/O-efficient algorithm for
             the batched (off-line) version of the union-find problem.
             Given any sequence of N union and find operations, where
             each union operation joins two distinct sets, our algorithm
             uses O(SORT(N)) = O(N/B logM/B N/B) I/Os, where M is the
             memory size and B is the disk block size. This bound is
             asymptotically optimal in the worst case. If there are union
             operations that join a set with itself, our algorithm uses
             O(SORT(N) + MST(N)) I/Os, where MST(N) is the number of I/Os
             needed to compute the minimum spanning tree of a graph with
             N edges. We also describe a simple and practical O(SORT(N)
             log(N/M ))-I/O algorithm for this problem, which we have
             implemented. We are interested in the union-find problem
             because of its applications in terrain analysis. A terrain
             can be abstracted as a height function defined over ℝ2,
             and many problems that deal with such functions require a
             union-find data structure. With the emergence of modern
             mapping technologies, huge amount of elevation data is being
             generated that is too large to fit in memory, thus
             I/O-efficient algorithms are needed to process this data
             efficiently. In this article, we study two terrain-analysis
             problems that benefit from a union-find data structure: (i)
             computing topological persistence and (ii) constructing the
             contour tree.We give the first O(SORT(N))-I/O algorithms for
             these two problems, assuming that the input terrain is
             represented as a triangular mesh with N vertices. © 2010
             ACM.},
   Doi = {10.1145/1868237.1868249},
   Key = {fds235534}
}

@article{fds235535,
   Author = {Agarwal, PK and Bereg, S and Daescu, O and Kaplan, H and Ntafos, S and Sharir, M and Zhu, B},
   Title = {Guarding a terrain by two watchtowers},
   Journal = {Algorithmica},
   Volume = {58},
   Number = {2},
   Pages = {352-390},
   Year = {2010},
   ISSN = {0178-4617},
   url = {http://dx.doi.org/10.1007/s00453-008-9270-3},
   Abstract = {Given a polyhedral terrain T with n vertices, the
             two-watchtower problem for T asks to find two vertical
             segments, called watchtowers, of smallest common height,
             whose bottom endpoints (bases) lie on T, and whose top
             endpoints guard T, in the sense that each point on T is
             visible from at least one of them. There are three versions
             of the problem, discrete, semi-continuous, and continuous,
             depending on whether two, one, or none of the two bases are
             restricted to be among the vertices of T, respectively. In
             this paper we present the following results for the
             two-watchtower problem in ℝ 2 and ℝ 3: (1) We show that
             the discrete two-watchtowers problem in ℝ 2 can be solved
             in O(n 2log∈ 4 n) time, significantly improving previous
             solutions. The algorithm works, without increasing its
             asymptotic running time, for the semi-continuous version,
             where one of the towers is allowed to be placed anywhere on
             T. (2) We show that the continuous two-watchtower problem in
             ℝ 2 can be solved in O(n 3 α(n)log∈ 3 n) time, again
             significantly improving previous results. (3) Still in ℝ
             2, we show that the continuous version of the problem of
             guarding a finite set P⊂T of m points by two watchtowers
             of smallest common height can be solved in O(mnlog∈ 4 n)
             time. (4) We show that the discrete version of the
             two-watchtower problem in ℝ 3 can be solved in O(n
             11/3polylog(n)) time; this is the first nontrivial result
             for this problem in ℝ 3. © 2008 Springer Science+Business
             Media, LLC.},
   Doi = {10.1007/s00453-008-9270-3},
   Key = {fds235535}
}

@article{fds235516,
   Author = {Agarwal, PK and Sharathkumar, R and Yu, H},
   Title = {Approximate Euclidean shortest paths amid convex
             obstacles},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Pages = {283-292},
   Year = {2009},
   Abstract = {We develop algorithms and data structures for the
             approximate Euclidean shortest path problem amid a set P of
             k convex obstacles in ℝ 2 and ℝ 3, with a total of n
             faces. The running time of our algorithms is linear in n,
             and the size and query time of our data structure are
             independent of n. We follow a "core-set" based approach,
             i.e., we quickly compute a small sketch Q of P whose size is
             independent of n and then compute approximate shortest paths
             with respect to Q. Copyright © by SIAM.},
   Key = {fds235516}
}

@article{fds235517,
   Author = {Agarwal, PK and Ezra, E and Ganjugunte, SK},
   Title = {Efficient sensor placement for surveillance
             problems},
   Journal = {Lecture notes in computer science},
   Volume = {5516 LNCS},
   Pages = {301-314},
   Year = {2009},
   ISSN = {0302-9743},
   url = {http://dx.doi.org/10.1007/978-3-642-02085-8_22},
   Abstract = {We study the problem of covering a two-dimensional spatial
             region P, cluttered with occluders, by sensors. A sensor
             placed at a location p covers a point x in P if x lies
             within sensing radius r from p and x is visible from p,
             i.e., the segment px does not intersect any occluder. The
             goal is to compute a placement of the minimum number of
             sensors that cover P. We propose a landmark-based approach
             for covering P. Suppose P has ς holes, and it can be
             covered by h sensors. Given a small parameter ε&gt;∈0,
             let λ:∈=∈λ(h,ε)∈=∈(h/ε) (1∈+∈ln
             (1∈+∈ς)). We prove that one can compute a set L of
             O(λlogλ log(1/ε)) landmarks so that if a set S of sensors
             covers L, then S covers at least (1∈-∈ε)-fraction of P.
             It is surprising that so few landmarks are needed, and that
             the number of landmarks depends only on h, and does not
             directly depend on the number of vertices in P. We then
             present efficient randomized algorithms, based on the greedy
             approach, that, with high probability, compute sensor
             locations to cover L; here is the number sensors needed to
             cover L. We propose various extensions of our approach,
             including: (i) a weight function over P is given and S
             should cover at least (1∈-∈ε) of the weighted area of
             P, and (ii) each point of P is covered by at least t
             sensors, for a given parameter t∈ ∈1. © 2009 Springer
             Berlin Heidelberg.},
   Doi = {10.1007/978-3-642-02085-8_22},
   Key = {fds235517}
}

@article{fds235518,
   Author = {Agarwal, PK and Xie, J and Yang, J and Yu, H},
   Title = {Input-sensitive scalable continuous join query
             processing},
   Journal = {ACM Transactions on Database Systems},
   Volume = {34},
   Number = {3},
   Year = {2009},
   ISSN = {0362-5915},
   url = {http://dx.doi.org/10.1145/1567274.1567275},
   Abstract = {This article considers the problem of scalably processing a
             large number of continuous queries. Our approach, consisting
             of novel data structures and algorithms and a flexible
             processing framework, advances the state-of-the-art in
             several ways. First, our approach is query sensitive in the
             sense that it exploits potential overlaps in query
             predicates for efficient group processing. We partition the
             collection of continuous queries into groups based on the
             clustering patterns of the query predicates, and apply
             specialized processing strategies to heavily clustered
             groups (or hotspots). We show how to maintain the hotspots
             efficiently, and use them to scalably process continuous
             select-join, band-join, and window-join queries. Second, our
             approach is also data sensitive, in the sense that it makes
             cost-based decisions on how to process each incoming tuple
             based on its characteristics. Experiments demonstrate that
             our approach can improve the processing throughput by orders
             of magnitude. © 2009 ACM.},
   Doi = {10.1145/1567274.1567275},
   Key = {fds235518}
}

@article{fds235519,
   Author = {Agarwal, PK and Cheng, S-W and Tao, Y and Yi, K},
   Title = {Indexing uncertain data},
   Journal = {Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on
             Principles of Database Systems},
   Pages = {137-146},
   Year = {2009},
   url = {http://dx.doi.org/10.1145/1559795.1559816},
   Abstract = {Querying uncertain data has emerged as an important problem
             in data management due to the imprecise nature of many
             measurement data. In this paper we study answering range
             queries over uncertain data. Specifically, we are given a
             collection P of n points in ℝ, each represented by its
             one-dimensional probability density function (pdf). The goal
             is to build an index on P such that given a query interval I
             and a probability threshold t , we can quickly report all
             points of P that lie in I with probability at least t . We
             present various indexing schemes with linear or near-linear
             space and logarithmic query time. Our schemes support pdf's
             that are either histograms or more complex ones such as
             Gaussian or piecewise algebraic. They also extend to the
             external memory model in which the goal is to minimize the
             number of disk accesses when querying the index. Copyright
             2009 ACM.},
   Doi = {10.1145/1559795.1559816},
   Key = {fds235519}
}

@article{fds235520,
   Author = {Agarwal, PK and Ezra, E and Sharir, M},
   Title = {Near-linear approximation algorithms for geometric hitting
             sets},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {23-32},
   Year = {2009},
   url = {http://dx.doi.org/10.1145/1542362.1542368},
   Abstract = {Given a set system (X,R), the hitting set problem is to find
             a smallest-cardinality subset H ⊆ X, with the property
             that each range R ∈ R has a non-empty intersection with H.
             We present near-linear time approximation algorithms for the
             hitting set problem, under the following geometric settings:
             (i) R is a set of planar regions with small union
             complexity. (ii) R is a set of axis-parallel d-rectangles in
             ℝd. In both cases X is either the entire d-dimensional
             space or a finite set of points in d-space. The
             approximation factors yielded by the algorithm are small;
             they are either the same as or within an O(log n) factor of
             the best factors known to be computable in polynomial time.
             © 2009 ACM.},
   Doi = {10.1145/1542362.1542368},
   Key = {fds235520}
}

@article{fds235505,
   Author = {Agarwal, PK and Hurtado, F and Toussaint, GT and Trias,
             J},
   Title = {On polyhedra induced by point sets in space},
   Journal = {Discrete Applied Mathematics},
   Volume = {156},
   Number = {1},
   Pages = {42-54},
   Year = {2008},
   ISSN = {0166-218X},
   url = {http://dx.doi.org/10.1016/j.dam.2007.08.033},
   Abstract = {Given a set S of n ≥ 3 points in the plane (not all on a
             line) it is well known that it is always possible to
             polygonize S, i.e., construct a simple polygon P such that
             the vertices of P are precisely the given points in S. For
             example, the shortest circuit through S is a simple polygon.
             In 1994, Grünbaum showed that an analogous theorem holds in
             R3. More precisely, if S is a set of n ≥ 4 points in R3
             (not all of which are coplanar) then it is always possible
             to polyhedronize S, i.e., construct a simple (sphere-like)
             polyhedron P such that the vertices of P are precisely the
             given points in S. Grünbaum's constructive proof may yield
             Schönhardt polyhedra that cannot be triangulated. In this
             paper several alternative algorithms are proposed for
             constructing such polyhedra induced by a set of points,
             which may always be triangulated, and which enjoy several
             other useful properties as well. Such properties include
             polyhedra that are star-shaped, have Hamiltonian skeletons,
             and admit efficient point-location queries. We show that
             polyhedronizations with a variety of such useful properties
             can be computed efficiently in O (n log n) time.
             Furthermore, we show that a tetrahedralized, xy-monotonic,
             polyhedronization of S may be computed in time O (n1 +
             ε{lunate}), for any ε{lunate} &gt; 0. © 2007 Elsevier
             B.V. All rights reserved.},
   Doi = {10.1016/j.dam.2007.08.033},
   Key = {fds235505}
}

@article{fds235506,
   Author = {Chandramouli, B and Yang, J and Agarwal, PK and Yu, A and Zheng,
             Y},
   Title = {ProSem: Scalable wide-area publish/subscribe},
   Journal = {Proceedings / ACM-SIGMOD International Conference on
             Management of Data. ACM-Sigmod International Conference on
             Management of Data},
   Pages = {1315-1317},
   Year = {2008},
   ISSN = {0730-8078},
   url = {http://dx.doi.org/10.1145/1376616.1376764},
   Abstract = {We demonstrate ProSem, a scalable wide-area
             publish/subscribe system that supports complex, stateful
             subscriptions as well as simple ones. One unique feature of
             ProSem is its cost-based joint optimization of both
             subscription processing and notification dissemination,
             ProSem uses novel reformulation techniques to expose new
             alternatives for processing and disseminating data using
             standard stateless content-driven network
             components.},
   Doi = {10.1145/1376616.1376764},
   Key = {fds235506}
}

@article{fds235507,
   Author = {Agarwal, PK and Sadri, B and Yu, H},
   Title = {Untangling triangulations through local explorations},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {288-297},
   Year = {2008},
   url = {http://dx.doi.org/10.1145/1377676.1377726},
   Abstract = {The problem of maintaining a valid mesh (triangulation)
             within a certain domain that deforms over time arises in
             many applications. During a period for which the underlying
             mesh topology remains unchanged, the deformation moves
             vertices of the mesh and thus potentially turns a mesh
             invalid, or as we call it, tangled. We introduce the notion
             of locally removable regions, which are certain tangled
             regions in the mesh that allow for local removal and
             re-meshing. We present an algorithm that is able to quickly
             compute, through local explorations, a minimum locally
             removable region containing a "seed" tangled region in an
             invalid mesh. By re-meshing within this area, the "seed"
             tangled region can then be removed from the mesh without
             introducing any new tangled region. The algorithm is
             output-sensitive in the sense that it never explores outside
             the output region. Copyright 2008 ACM.},
   Doi = {10.1145/1377676.1377726},
   Key = {fds235507}
}

@article{fds235508,
   Author = {Agarwal, PK and Arge, L and Moølhave, T and Sadri,
             B},
   Title = {I/O-efflcient algorithms for computing contours on a
             terrain},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {129-138},
   Year = {2008},
   url = {http://dx.doi.org/10.1145/1377676.1377698},
   Abstract = {A terrain M is the graph of a bivariate function. We assume
             that M is represented as a triangulated surface with N
             vertices. A contour (or isoline) of M is a connected
             component of a level set of M. Generically, each contour is
             a closed polygonal curve; at "critical" levels these curves
             may touch each other or collapse to a point. We present
             I/O-efficient algorithms for the following two problems
             related to computing contours of M: (i) Given a sequence
             ℓ1 &lt; ... &lt; ℓs of real numbers, we present an
             I/O-optimal algorithm that reports all contours of M at
             heights ℓ1,.. . ,ℓs using O(soRT(N) + T/B) I/Os, where T
             is the total number edges in the output contours, B is the
             "block size," and SORT(N) is the number of I/Os needed to
             sort N elements. The algorithm uses O(N/B) disk blocks. Each
             contour is generated individually with its composing
             segments sorted in clockwise or counterclockwise order.
             Moreover, our algorithm generates information on how the
             contours are nested. (ii) We can preprocess M, using
             O(SORT(N)) I/Os, into a linear-size data structure so that
             all contours at a given height can be reported using O(logB
             N + T/B) I/Os, where T is the output size. Each contour is
             generated individually with its composing segments sorted in
             clockwise or counterclockwise order. Copyright 2008
             ACM.},
   Doi = {10.1145/1377676.1377698},
   Key = {fds235508}
}

@article{fds235509,
   Author = {Agarwal, PK and Phillips, JM},
   Title = {An efficient algorithm for 2D Euclidean 2-center with
             outliers},
   Journal = {Lecture notes in computer science},
   Volume = {5193 LNCS},
   Pages = {64-75},
   Year = {2008},
   ISSN = {0302-9743},
   url = {http://dx.doi.org/10.1007/978-3-540-87744-8-6},
   Abstract = {For a set P of n points in ℝ2, the Euclidean 2-center
             problem computes a pair of congruent disks of the minimal
             radius that cover P. We extend this to the (2,k)-center
             problem where we compute the minimal radius pair of
             congruent disks to cover n∈-∈k points of P. We present a
             randomized algorithm with O(n k 7 log3 n) expected running
             time for the (2,k)-center problem. We also study the
             (p,k)-center problem in ℝ2 under the ℓ∞-metric. We
             give solutions for p∈=∈4 in O(k O(1) n logn) time and
             for p = 5 in O(k O(1) n log5 n) time. © 2008
             Springer-Verlag Berlin Heidelberg.},
   Doi = {10.1007/978-3-540-87744-8-6},
   Key = {fds235509}
}

@article{fds235510,
   Author = {Agarwal, PK and Chen, DZ and Ganjugunte, SK and Misiołek, E and Sharir,
             M and Tang, K},
   Title = {Stabbing convex polygons with a segment or a
             polygon},
   Journal = {Lecture notes in computer science},
   Volume = {5193 LNCS},
   Pages = {52-63},
   Year = {2008},
   ISSN = {0302-9743},
   url = {http://dx.doi.org/10.1007/978-3-540-87744-8-5},
   Abstract = {Let O = {O1, . . . , Om} be a set of m convex polygons in
             ℝ2 with a total of n vertices, and let B be another convex
             k-gon. A placement of B, any congruent copy of B (without
             reflection), is called free if B does not intersect the
             interior of any polygon in at this placement. A placement z
             of B is called critical if B forms three "distinct" contacts
             with at z. Let be the number of free critical placements. A
             set of placements of B is called a stabbing set of if each
             polygon in intersects at least one placement of B in this
             set. We develop efficient Monte Carlo algorithms that
             compute a stabbing set of size h = O(h *logm), with high
             probability, where h * is the size of the optimal stabbing
             set of O. We also improve bounds on (B, O) for the following
             three cases, namely, (i) B is a line segment and the
             obstacles in are O pairwise-disjoint, (ii) B is a line
             segment and the obstacles in O may intersect (iii) B is a
             convex k-gon and the obstacles in O are disjoint, and use
             these improved bounds to analyze the running time of our
             stabbing-set algorithm. © 2008 Springer-Verlag Berlin
             Heidelberg.},
   Doi = {10.1007/978-3-540-87744-8-5},
   Key = {fds235510}
}

@article{fds235511,
   Author = {Agarwal, PK and Klein, R and Knauer, C and Langerman, S and Morin, P and Sharir, M and Soss, M},
   Title = {Computing the detour and spanning ratio of paths, trees, and
             cycles in 2D and 3D},
   Journal = {Discrete & Computational Geometry},
   Volume = {39},
   Number = {1-3},
   Pages = {17-37},
   Year = {2008},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/s00454-007-9019-9},
   Abstract = {The detour and spanning ratio of a graph G embedded in d
             measure how well G approximates Euclidean space and the
             complete Euclidean graph, respectively. In this paper we
             describe O(nlog∈n) time algorithms for computing the
             detour and spanning ratio of a planar polygonal path. By
             generalizing these algorithms, we obtain O(nlog∈2 n)-time
             algorithms for computing the detour or spanning ratio of
             planar trees and cycles. Finally, we develop subquadratic
             algorithms for computing the detour and spanning ratio for
             paths, cycles, and trees embedded in 3, and show that
             computing the detour in 3 is at least as hard as Hopcroft's
             problem. © 2007 Springer Science+Business Media,
             LLC.},
   Doi = {10.1007/s00454-007-9019-9},
   Key = {fds235511}
}

@article{fds235512,
   Author = {Agarwal, PK and Har-Peled, S and Yu, H},
   Title = {Robust shape fitting via peeling and grating
             coresets},
   Journal = {Discrete & Computational Geometry},
   Volume = {39},
   Number = {1-3},
   Pages = {38-58},
   Year = {2008},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/s00454-007-9013-2},
   Abstract = {Let P be a set of n points in ℝ d. A subset S of P is
             called a (k,ε)-kernel if for every direction, the
             directional width of S ε-approximates that of P, when k
             "outliers" can be ignored in that direction. We show that a
             (k,ε)-kernel of P of size O(k/ε (d-1)/2) can be computed
             in time O(n+k 2/ε d-1). The new algorithm works by
             repeatedly "peeling" away (0,ε)-kernels from the point set.
             We also present a simple ε-approximation algorithm for
             fitting various shapes through a set of points with at most
             k outliers. The algorithm is incremental and works by
             repeatedly "grating" critical points into a working set,
             till the working set provides the required approximation. We
             prove that the size of the working set is independent of n,
             and thus results in a simple and practical, near-linear
             ε-approximation algorithm for shape fitting with outliers
             in low dimensions. We demonstrate the practicality of our
             algorithms by showing their empirical performance on various
             inputs and problems. © 2007 Springer Science+Business
             Media, LLC.},
   Doi = {10.1007/s00454-007-9013-2},
   Key = {fds235512}
}

@article{fds235513,
   Author = {Yu, H and Agarwal, PK and Poreddy, R and Varadarajan,
             KR},
   Title = {Practical methods for shape fitting and kinetic data
             structures using coresets},
   Journal = {Algorithmica},
   Volume = {52},
   Number = {3},
   Pages = {378-402},
   Year = {2008},
   ISSN = {0178-4617},
   url = {http://dx.doi.org/10.1007/s00453-007-9067-9},
   Abstract = {The notion of ε-kernel was introduced by Agarwal et al. (J.
             ACM 51:606-635, 2004) to set up a unified framework for
             computing various extent measures of a point set P
             approximately. Roughly speaking, a subset Q ⊆ P is an
             ε-kernel of P if for every slab W containing Q, the
             expanded slab (1+ε)W contains P. They illustrated the
             significance of ε-kernel by showing that it yields
             approximation algorithms for a wide range of geometric
             optimization problems. We present a simpler and more
             practical algorithm for computing the ε-kernel of a set P
             of points in ℝ d . We demonstrate the practicality of our
             algorithm by showing its empirical performance on various
             inputs. We then describe an incremental algorithm for
             fitting various shapes and use the ideas of our algorithm
             for computing ε-kernels to analyze the performance of this
             algorithm. We illustrate the versatility and practicality of
             this technique by implementing approximation algorithms for
             minimum enclosing cylinder, minimum-volume bounding box, and
             minimum-width annulus. Finally, we show that ε-kernels can
             be effectively used to expedite the algorithms for
             maintaining extents of moving points. © 2007 Springer
             Science+Business Media, LLC.},
   Doi = {10.1007/s00453-007-9067-9},
   Key = {fds235513}
}

@article{fds235514,
   Author = {Agarwal, PK and Kaplan, H and Sharir, M},
   Title = {Kinetic and dynamic data structures for closest pair and all
             nearest neighbors},
   Journal = {ACM Transactions on Algorithms},
   Volume = {5},
   Number = {1},
   Year = {2008},
   ISSN = {1549-6325},
   url = {http://dx.doi.org/10.1145/1435375.1435379},
   Abstract = {We present simple, fully dynamic and kinetic data
             structures, which are variants of a dynamic two-dimensional
             range tree, for maintaining the closest pair and all nearest
             neighbors for a set of n moving points in the plane;
             insertions and deletions of points are also allowed. If no
             insertions or deletions take place, the structure for the
             closest pair uses O(n log n) space, and processes
             O(n2Βs+2(n)log n) critical events, each in O(log2n) time.
             Here s is the maximum number of times where the distances
             between any two specific pairs of points can become equal,
             Βs(q) = s(q)/q, and s(q) is the maximum length of
             Davenport-Schinzel sequences of order s on q symbols. The
             dynamic version of the problem incurs a slight degradation
             in performance: If m n insertions and deletions are
             performed, the structure still uses O(n log n) space, and
             processes O(mnΒs+2(n)log3 n) events, each in O(log3n) time.
             Our kinetic data structure for all nearest neighbors uses
             O(n log2 n) space, and processes O(n 2Β2s+2(n)log3 n)
             critical events. The expected time to process all events is
             O(n2Β s+22(n) log4n), though processing a single event may
             take Θ(n) expected time in the worst case. If m n
             insertions and deletions are performed, then the expected
             number of events is O(mnΒ2s+2(n) log3n) and processing them
             all takes O(mnΒ2s+2(n) log4n). An insertion or deletion
             takes O(n) expected time. © 2008 ACM.},
   Doi = {10.1145/1435375.1435379},
   Key = {fds235514}
}

@article{fds235515,
   Author = {Agarwal, PK and Sharir, M and Welzl, E},
   Title = {Algorithms for center and Tverberg points},
   Journal = {ACM Transactions on Algorithms},
   Volume = {5},
   Number = {1},
   Year = {2008},
   ISSN = {1549-6325},
   url = {http://dx.doi.org/10.1145/1435375.1435380},
   Abstract = {Given a set S of n points in R3, a point x in R3 is called
             center point of S if every closed halfspace whose bounding
             hyperplane passes through x contains at least ⌈n/4⌉
             points from S. We present a near-quadratic algorithm for
             computing the center region, that is the set of all center
             points, of a set of n points in R3. This is nearly tight in
             the worst case since the center region can have (n2)
             complexity. We then consider sets S of 3n points in the
             plane which are the union of three disjoint sets consisting
             respectively of n red, n blue, and n green points. A point x
             in R2 is called a colored Tverberg point of S if there is a
             partition of S into n triples with one point of each color,
             so that x lies in all triangles spanned by these triples. We
             present a first polynomial-time algorithm for recognizing
             whether a given point is a colored Tverberg point of such a
             3-colored set S. © 2008 ACM.},
   Doi = {10.1145/1435375.1435380},
   Key = {fds235515}
}

@article{fds235500,
   Author = {Clark, JS and Dietze, M and Chakraborty, S and Agarwal, PK and Ibanez,
             I and LaDeau, S and Wolosin, M},
   Title = {Resolving the biodiversity paradox.},
   Journal = {Ecology Letters},
   Volume = {10},
   Number = {8},
   Pages = {647-659},
   Year = {2007},
   Month = {August},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/17594418},
   Abstract = {The paradox of biodiversity involves three elements, (i)
             mathematical models predict that species must differ in
             specific ways in order to coexist as stable ecological
             communities, (ii) such differences are difficult to
             identify, yet (iii) there is widespread evidence of
             stability in natural communities. Debate has centred on two
             views. The first explanation involves tradeoffs along a
             small number of axes, including 'colonization-competition',
             resource competition (light, water, nitrogen for plants,
             including the 'successional niche'), and life history (e.g.
             high-light growth vs. low-light survival and few large vs.
             many small seeds). The second view is neutrality, which
             assumes that species differences do not contribute to
             dynamics. Clark et al. (2004) presented a third explanation,
             that coexistence is inherently high dimensional, but still
             depends on species differences. We demonstrate that neither
             traditional low-dimensional tradeoffs nor neutrality can
             resolve the biodiversity paradox, in part by showing that
             they do not properly interpret stochasticity in statistical
             and in theoretical models. Unless sample sizes are small,
             traditional data modelling assures that species will appear
             different in a few dimensions, but those differences will
             rarely predict coexistence when parameter estimates are
             plugged into theoretical models. Contrary to standard
             interpretations, neutral models do not imply functional
             equivalence, but rather subsume species differences in
             stochastic terms. New hierarchical modelling techniques for
             inference reveal high-dimensional differences among species
             that can be quantified with random individual and temporal
             effects (RITES), i.e. process-level variation that results
             from many causes. We show that this variation is large, and
             that it stands in for species differences along unobserved
             dimensions that do contribute to diversity. High dimensional
             coexistence contrasts with the classical notions of
             tradeoffs along a few axes, which are often not found in
             data, and with 'neutral models', which mask, rather than
             eliminate, tradeoffs in stochastic terms. This mechanism can
             explain coexistence of species that would not occur with
             simple, low-dimensional tradeoff scenarios.},
   Doi = {10.1111/j.1461-0248.2007.01041.x},
   Key = {fds235500}
}

@article{fds235501,
   Author = {Agarwal, PK and Mustafa, NH and Wang, Y},
   Title = {Fast molecular shape matching using contact
             maps.},
   Journal = {Journal of Computational Biology},
   Volume = {14},
   Number = {2},
   Pages = {131-143},
   Year = {2007},
   Month = {March},
   ISSN = {1066-5277},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/17456012},
   Abstract = {In this paper, we study the problem of computing the
             similarity of two protein structures by measuring their
             contact-map overlap. Contact-map overlap abstracts the
             problem of computing the similarity of two polygonal chains
             as a graph-theoretic problem. In R3, we present the first
             polynomial time algorithm with any guarantee on the
             approximation ratio for the 3-dimensional problem. More
             precisely, we give an algorithm for the contact-map overlap
             problem with an approximation ratio of sigma where sigma =
             min{sigma(P1), sigma(P2)} <or= O(n(1/2)) is a decomposition
             parameter depending on the input polygonal chains P1 and P2.
             In R2, we improve the running time of the previous best
             known approximation algorithm from O(n(6)) to O(n(3) log n)
             at the cost of decreasing the approximation ratio by half.
             We also give hardness results for the problem in three
             dimensions, suggesting that approximating it better than
             O(n(epsilon)), for some epsilon > 0, is hard.},
   Doi = {10.1089/cmb.2007.0004},
   Key = {fds235501}
}

@article{fds235493,
   Author = {Agarwal, PK and Yu, H},
   Title = {A space-optimal data-stream algorithm for coresets in the
             plane},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {1-10},
   Year = {2007},
   url = {http://dx.doi.org/10.1145/1247069.1247071},
   Abstract = {Given a point set PR 2, a subset Q P is an -kernel of P if
             for every slab W containing Q, the (1+)-expansion of W also
             contains P. We present a data-stream algorithm for
             maintaining an -kernel of a stream of points in R 2 that
             uses O(1/ ) space and takes O(log (1/)) amortized time to
             process each point. This is the first space-optimal
             data-stream algorithm for this problem. Copyright 2007
             ACM.},
   Doi = {10.1145/1247069.1247071},
   Key = {fds235493}
}

@article{fds235494,
   Author = {Agarwal, PK and Kaplan, H and Sharir, M},
   Title = {Computing the volume of the union of cubes},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {294-301},
   Year = {2007},
   url = {http://dx.doi.org/10.1145/1247069.1247121},
   Abstract = {Let C be a set of n axis-aligned cubes in R 3, and let U(C)
             denote the union of C. We present an algorithmthat can
             compute the volume of U(C) in time O(n 4/3 log n). The
             previously best known algorithm, by Overmars and Yap,
             computes the volume of the union ofany n axis-aligned boxes
             in R 3 in O(n 3/2log n) time. Copyright 2007
             ACM.},
   Doi = {10.1145/1247069.1247121},
   Key = {fds235494}
}

@article{fds235495,
   Author = {Agarwal, PK and Har-Peled, S and Yu, H},
   Title = {Embeddings of surfaces, curves, and moving points in
             euclidean space},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {381-389},
   Year = {2007},
   url = {http://dx.doi.org/10.1145/1247069.1247135},
   Abstract = {In this paper we show that dimensionality reduction (i.e.,
             Johnson-Lindenstrauss lemma) preserves not only the
             distances between static points, but also between moving
             points, and more generally between low-dimensional flats,
             polynomial curves, curves with low winding degree, and
             polynomial surfaces. We also show that surfaces with bounded
             doubling dimension can be embedded into low dimension with
             small additive error. Finally, we show that for points with
             polynomial motion, the radius of the smallest enclosing ball
             can be preserved under dimensionality reduction. Copyright
             2007 ACM.},
   Doi = {10.1145/1247069.1247135},
   Key = {fds235495}
}

@article{fds235496,
   Author = {Agarwal, PK and Apfelbaum, R and Purdy, G and Sharir,
             M},
   Title = {Similar simplices in a d-dimensional point
             set},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {232-238},
   Year = {2007},
   url = {http://dx.doi.org/10.1145/1247069.1247112},
   Abstract = {We consider the problem of bounding the maximum possible
             number f k,d(n) of k-simplices that are spanned by a set of
             n pointsin R d and are similar to a given simplex. We first
             show that f 2,3(n) = O(n 13/6), and then tacklethe general
             case, and show that f d-2, d(n) = O(n d-8/5) and f d-1,d(n)
             = O *(n d-72/55), for any d.Our technique extends to derive
             bounds for other valuesof k and d, and we illustrate this by
             showing that f 2,5(n)=O(n 8/3). Copyright 2007
             ACM.},
   Doi = {10.1145/1247069.1247112},
   Key = {fds235496}
}

@article{fds235497,
   Author = {Danner, A and Mølhave, T and Yi, K and Agarwal, PK and Arge, L and Mitasova, H},
   Title = {TerraStream: From elevation data to watershed
             hierarchies},
   Journal = {GIS: Proceedings of the ACM International Symposium on
             Advances in Geographic Information Systems},
   Pages = {212-219},
   Year = {2007},
   url = {http://dx.doi.org/10.1145/1341012.1341049},
   Abstract = {We consider the problem of extracting a river network and a
             watershed hierarchy from a terrain given as a set of
             irregularly spaced points. We describe TERRASTREAM, a
             "pipelined" solution that consists of four main stages:
             construction of a digital elevation model (DEM),
             hydrological conditioning, extraction of river networks, and
             construction of a watershed hierarchy. Our approach has
             several advantages over existing methods. First, we design
             and implement the pipeline so that each stage is scalable to
             massive data sets; a single non-scalable stage would create
             a bottleneck and limit overall scalability. Second, we
             develop the algorithms in a general framework so that they
             work for both TIN and grid DEMs. Furthermore, TERRASTREAM is
             flexible and allows users to choose from various models and
             parameters, yet our pipeline is designed to reduce (or
             eliminate) the need for manual intervention between stages.
             We have implemented TERRASTREAM and we present experimental
             results on real elevation point sets, which show that our
             approach handles massive multi-gigabyte terrain data sets.
             For example, we can process a data set containing over 300
             million points - -over 20GB of raw data - -in under 26
             hours, where most of the time (76%) is spent in the initial
             CPU-intensive DEM construction stage. © 2007
             ACM.},
   Doi = {10.1145/1341012.1341049},
   Key = {fds235497}
}

@article{fds235498,
   Author = {Agarwal, PK},
   Title = {Modeling and analyzing massive terrain data
             sets},
   Journal = {Lecture notes in computer science},
   Volume = {4835 LNCS},
   Pages = {1-},
   Year = {2007},
   ISSN = {0302-9743},
   Abstract = {With recent advances in terrain-mapping technologies such as
             Laser altimetry (LIDAR) and ground based laser scanning,
             millions of georeferenced points can be acquired within
             short periods of time. However, while acquiring and
             georeferencing the data has become extremely efficient,
             transforming the resulting massive amounts of heterogeneous
             data to useful information for different types of users and
             applications is lagging behind, in large part because of the
             scarcity of robust, efficient algorithms for terrain
             modeling and analysis that can handle massive data sets
             acquired by different technologies and that can rapidly
             detect and predict changes in the model as the new data is
             acquired. This talk will review our on-going work on
             developing efficient algorithms for terrain modeling and
             analysis that work with massive data sets. It will focus on
             algorithms for constructing digital elevation models of
             terrains, handling noise in elevation models, and for
             computing watershed regions and stream-networks. The talk
             will also discuss some of the challenges that we face in
             this area. © Springer-Verlag Berlin Heidelberg
             2007.},
   Key = {fds235498}
}

@article{fds235499,
   Author = {Flikkema, PG and Agarwal, PK and Clark, JS and Ellis, C and Gelfand, A and Munagala, K and Yang, J},
   Title = {From data reverence to data relevance: Model-mediated
             wireless sensing of the physical environment},
   Journal = {Lecture notes in computer science},
   Volume = {4487 LNCS},
   Pages = {988-994},
   Year = {2007},
   ISSN = {0302-9743},
   Abstract = {Wireless sensor networks can be viewed as the integration of
             three subsystems: a low-impact in situ data acquisition and
             collection system, a system for inference of process models
             from observed data and a priori information, and a system
             that controls the observation and collection. Each of these
             systems is connected by feedforward and feedback signals
             from the others; moreover, each subsystem is formed from
             behavioral components that are distributed among the sensors
             and out-of-network computational resources. Crucially, the
             overall performance of the system is constrained by the
             costs of energy, time, and computational complexity. We are
             addressing these design issues in the context of monitoring
             forest environments with the objective of inferring
             ecosystem process models. We describe here our framework of
             treating data and models jointly, and its application to
             soil moisture processes. © Springer-Verlag Berlin
             Heidelberg 2007.},
   Key = {fds235499}
}

@article{fds235502,
   Author = {Clark, JS and Agarwal, PK},
   Title = {Rejoinder to Clark et al. (2007): Response to Chesson and
             Rees},
   Journal = {Ecology Letters},
   Volume = {10},
   Number = {8},
   Pages = {661-662},
   Year = {2007},
   ISSN = {1461-023X},
   url = {http://dx.doi.org/10.1111/j.1461-0248.2007.01071.x},
   Doi = {10.1111/j.1461-0248.2007.01071.x},
   Key = {fds235502}
}

@article{fds235503,
   Author = {Govindarajan, S and Dietze, MC and Agarwal, PK and Clark,
             JS},
   Title = {A scalable algorithm for dispersing population},
   Journal = {Journal of Intelligent Information Systems},
   Volume = {29},
   Number = {1},
   Pages = {39-61},
   Year = {2007},
   ISSN = {0925-9902},
   url = {http://dx.doi.org/10.1007/s10844-006-0030-z},
   Abstract = {Models of forest ecosystems are needed to understand how
             climate and land-use change can impact biodiversity. In this
             paper we describe an ecological dispersal model developed
             for the specific case of predicting seed dispersal by trees
             on a landscape for use in a forest simulation model. We
             present efficient approximation algorithms for computing
             seed dispersal. These algorithms allow us to simulate large
             landscapes for long periods of time. We also present
             experimental results that (1) quantify the inherent
             uncertainty in the dispersal model and (2) describe the
             variation of the approximation error as a function of the
             approximation parameters. Based on these experiments, we
             provide guidelines for choosing the right approximation
             parameters, for a given model simulation. © 2007 Springer
             Science+Business Media, LLC.},
   Doi = {10.1007/s10844-006-0030-z},
   Key = {fds235503}
}

@article{fds235504,
   Author = {Zheng, Y and Brady, DJ and Agarwal, PK},
   Title = {Localization using boundary sensors: An analysis based on
             graph theory},
   Journal = {ACM Transactions on Sensor Networks},
   Volume = {3},
   Number = {4},
   Year = {2007},
   ISSN = {1550-4859},
   url = {http://dx.doi.org/10.1145/1281492.1281496},
   Abstract = {We consider sensors, such as fibers, lasers, and
             pyroelectric motion detectors, that fire when objects cross
             a boundary. A moving object can be localized by analyzing
             sequences of boundary crossings. We consider the number of
             distinct sequences and object positions that can be achieved
             using boundary sensors in one- and two-dimensional spaces.
             For 1D systems we use representations of sensor sequences on
             graphs to derive limits on the number of object locations
             that can be monitored by a given sensor population and
             sequence length. For 2D systems we show that in certain
             circumstances the ratio of the number of unique sensor
             sequences to the number of unique object paths is
             exponential in the sequence length and we argue that the
             probability of unique identification is high for
             sufficiently large sequences. We also prove the triangle
             grid can track an object with error limited to a small
             neighborhood. © 2007 ACM.},
   Doi = {10.1145/1281492.1281496},
   Key = {fds235504}
}

@article{fds235365,
   Author = {Agarwal, PK and Arge, L and Danner, A},
   Title = {From point cloud to grid DEM: A scalable
             approach},
   Journal = {Progress in Spatial Data Handling - 12th International
             Symposium on Spatial Data Handling, SDH 2006},
   Pages = {771-788},
   Year = {2006},
   Month = {December},
   url = {http://dx.doi.org/10.1007/3-540-35589-8_48},
   Abstract = {Given a set S of points in ℝ 3 sampled from an elevation
             function H : ℝ 2 → ℝ, we present a scalable algorithm
             for constructing a grid digital elevation model (DEM). Our
             algorithm consists of three stages: First, we construct a
             quad tree on S to partition the point set into a set of
             non-overlapping segments. Next, for each segment q, we
             compute the set of points in q and all segments neighboring
             q. Finally, we interpolate each segment independently using
             points within the segment and its neighboring segments. Data
             sets acquired by LIDAR and other modern mapping technologies
             consist of hundreds of millions of points and are too large
             to fit in main memory. When processing such massive data
             sets, the transfer of data between disk and main memory
             (also called I/O), rather than the CPU time, becomes the
             performance bottleneck. We therefore present an
             I/O-efficient algorithm for constructing a grid DEM. Our
             experiments show that the algorithm scales to data sets much
             larger than the size of main memory, while existing
             algorithms do not scale. For example, using a machine with
             1GB RAM, we were able to construct a grid DEM containing 1.3
             billion cells (occupying 1.2GB) from a LIDAR data set of
             over 390 million points (occupying 20GB) in about 53 hours.
             Neither ArcGIS nor GRASS, two popular GIS products, were
             able to process this data set. © 2006 Springer-Verlag
             Berlin Heidelberg.},
   Doi = {10.1007/3-540-35589-8_48},
   Key = {fds235365}
}

@article{fds235371,
   Author = {Agarwal, PK and Xie, J and Yang, J and Yu, H},
   Title = {Scalable continuous query processing by tracking
             hotspots},
   Journal = {VLDB 2006 - Proceedings of the 32nd International Conference
             on Very Large Data Bases},
   Pages = {31-42},
   Publisher = {ACM},
   Editor = {Dayal, U and Whang, K-Y and Lomet, DB and Alonso, G and Lohman, GM and Kersten, ML and Cha, SK and Kim, Y-K},
   Year = {2006},
   Month = {December},
   ISBN = {1595933859},
   url = {http://dl.acm.org/citation.cfm?id=1182635},
   Abstract = {This paper considers the problem of scalably processing a
             large number of continuous queries. We propose a flexible
             framework with novel data structures and algorithms for
             group-processing and indexing continuous queries by
             exploiting potential overlaps in query Predicates. Our
             approach partitions the collection of continuous queries
             into groups based on the clustering patterns of the query
             ranges, and then applies specialized processing strategies
             to those heavily-clustered groups (or hotspots). To maintain
             the partition dynamically, we present efficient algorithms
             that maintain a nearly optimal partition in nearly amortized
             logarithmic time. We show how to use the hotspots to
             scalably process large numbers of continuous select-join and
             band-join queries, which are much more chal-lenging than
             simple range selection queries. Experiments demonstrate that
             this approach can improve the processing throughput by
             orders of magnitude. As another application of hotspots, we
             show how to use them to build a high-quality histogram for
             intervals in linear time. Copyright 2006 VLDB Endowment,
             ACM.},
   Key = {fds235371}
}

@article{fds235488,
   Author = {Bilu, Y and Agarwal, PK and Kolodny, R},
   Title = {Faster algorithms for optimal multiple sequence alignment
             based on pairwise comparisons.},
   Journal = {IEEE/ACM Transactions on Computational Biology and
             Bioinformatics (ACM)},
   Volume = {3},
   Number = {4},
   Pages = {408-422},
   Year = {2006},
   Month = {October},
   ISSN = {1545-5963},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/17085849},
   Abstract = {Multiple Sequence Alignment (MSA) is one of the most
             fundamental problems in computational molecular biology. The
             running time of the best known scheme for finding an optimal
             alignment, based on dynamic programming, increases
             exponentially with the number of input sequences. Hence,
             many heuristics were suggested for the problem. We consider
             a version of the MSA problem where the goal is to find an
             optimal alignment in which matches are restricted to
             positions in predefined matching segments. We present
             several techniques for making the dynamic programming
             algorithm more efficient, while still finding an optimal
             solution under these restrictions. We prove that it suffices
             to find an optimal alignment of the predefined sequence
             segments, rather than single letters, thereby reducing the
             input size and thus improving the running time. We also
             identify "shortcuts" that expedite the dynamic programming
             scheme. Empirical study shows that, taken together, these
             observations lead to an improved running time over the basic
             dynamic programming algorithm by 4 to 12 orders of
             magnitude, while still obtaining an optimal solution. Under
             the additional assumption that matches between segments are
             transitive, we further improve the running time for finding
             the optimal solution by restricting the search space of the
             dynamic programming algorithm.},
   Doi = {10.1109/TCBB.2006.53},
   Key = {fds235488}
}

@article{fds235481,
   Author = {Agarwal, PK and Har-Peled, S and Yu, H},
   Title = {Robust shape fitting via peeling and grating
             coresets},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Pages = {182-191},
   Year = {2006},
   url = {http://dx.doi.org/10.1145/1109557.1109579},
   Abstract = {Let P be a set of n points in ℝd. We show that a (k,
             ε)-kernel of P of size O(k/ε(d-1)/2) can be computed in
             time O(n + k2/εd-1), where a (k, ε)-kernel is a subset of
             P that ε-approximates the directional width of P, for any
             direction, when k outliers can be ignored in that direction.
             A (k, ε)-kernel is instrumental in solving shape fitting
             problems with k outliers, like computing the minimum-width
             annulus covering all but k of the input points. The size of
             the new kernel improves over the previous known upper bound
             O(k/εd-1) [17], and is tight in the worst case. The new
             algorithm works by repeatedly "peeling" away (0,
             ε)-kernels. We demonstrate the practicality of our
             algorithm by showing its empirical performance on various
             inputs. We also present a simple incremental algorithm for
             (1 + ε)-fitting various shapes through a set of points with
             at most k outliers. The algorithm works by repeatedly
             "grating" critical points into a working set, till the
             working set provides the required approximation. We prove
             that the size of the working set is independent of n, and
             thus results in a simple and practical, near-linear-time
             algorithm for shape fitting with outliers. We illustrate the
             versatility and practicality of this technique by
             implementing approximation algorithms for minimum enclosing
             circle and minimum-width annulus.},
   Doi = {10.1145/1109557.1109579},
   Key = {fds235481}
}

@article{fds235482,
   Author = {Flikkema, PG and Agarwal, PK and Clark, JS and Ellis, C and Gelfand, A and Munagala, K and Yang, J},
   Title = {Model-driven dynamic control of embedded wireless sensor
             networks},
   Journal = {Lecture notes in computer science},
   Volume = {3993 LNCS - III},
   Pages = {409-416},
   Year = {2006},
   ISSN = {0302-9743},
   url = {http://dx.doi.org/10.1007/11758532_55},
   Abstract = {Next-generation wireless sensor networks may revolutionize
             understanding of environmental change by assimilating
             heterogeneous data, assessing the relative value and costs
             of data collection, and scheduling activities accordingly.
             Thus, they are dynamic, data-driven distributed systems that
             integrate sensing with modeling and prediction in an
             adaptive framework. Integration of a range of technologies
             will allow estimation of the value of future data in terms
             of its contribution to understanding and cost. This balance
             is especially important for environmental data, where
             sampling intervals will range from meters and seconds to
             landscapes and years. In this paper, we first describe a
             general framework for dynamic data-driven wireless network
             control that combines modeling of the sensor network and its
             embedding environment, both in and out of the network. We
             then describe a range of challenges that must be addressed,
             and an integrated suite of solutions for the design of
             dynamic sensor networks. © Springer-Verlag Berlin
             Heildelberg 2006.},
   Doi = {10.1007/11758532_55},
   Key = {fds235482}
}

@article{fds235483,
   Author = {Agarwal, PK and Arge, L and Yi, K},
   Title = {I/O-efficient batched union-find and its applications to
             terrain analysis},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Volume = {2006},
   Pages = {167-176},
   Year = {2006},
   Abstract = {Despite extensive study over the last four decades and
             numerous applications, no I/O-efficient algorithm is known
             for the union-find problem. In this paper we present an
             I/O-efficient algorithm for the batched (off-line) version
             of the union-find problem. Given any sequence of N union and
             find operations, where each union operation joins two
             distinct sets, our algorithm uses O(SORT(N)) = O(N/B logM/B
             N/B) I/Os, where M is the memory size and B is the disk
             block size. This bound is asymptotically optimal in the
             worst case. If there are union operations that join a set
             with itself, our algorithm uses O(SORT(N) + MST(N)) I/Os,
             where MST(N) is the number of I/Os needed to compute the
             minimum spanning tree of a graph with N edges. We also
             describe a simple and practical O(SORT(N)log(N/M))-I/O
             algorithm for this problem, which we have implemented. We
             are interested in the union-find problem because of its
             applications in terrain analysis. A terrain can be
             abstracted as a height function defined over ℝ2, and many
             problems that deal with such functions require a union-find
             data structure. With the emergence of modem mapping
             technologies, huge amount of elevation data is being
             generated that is too large to fit in memory, thus
             I/O-efficient algorithms are needed to process this data
             efficiently. In this paper, we study two terrain analysis
             problems that benefit from a unionfind data structure: (i)
             computing topological persistence and (ii) constructing the
             contour tree. We give the first O(SORT(N))-I/O algorithms
             for these two problems, assuming that the input terrain is
             represented as a triangular mesh with N vertices. Finally,
             we report some preliminary experimental results, showing
             that our algorithms give order-of-magnitude improvement over
             previous methods on large data sets that do not fit in
             memory. Copyright 2006 ACM.},
   Key = {fds235483}
}

@article{fds235484,
   Author = {Phillips, JM and Rudolph, J and Agarwal, PK},
   Title = {Segmenting motifs in protein-protein interface
             surfaces},
   Journal = {Lecture notes in computer science},
   Volume = {4175 LNBI},
   Pages = {207-218},
   Year = {2006},
   ISSN = {0302-9743},
   Abstract = {Protein-protein interactions form the basis for many
             intercellular events. In this paper we develop a tool for
             understanding the structure of these interactions.
             Specifically, we define a method for identifying a set of
             structural motifs on protein-protein interface surface.
             These motifs are secondary structures, akin to α-helices
             and β-sheets in protein structure; they describe how
             multiple residues form knob-into hole features across the
             interface. These motifs are generated entirely from
             geometric properties and are easily annotated with
             additional biological data. We point to the use of these
             motifs in analyzing hotspot residues. © Springer-Verlag
             Berlin Heidelberg 2006.},
   Key = {fds235484}
}

@article{fds235485,
   Author = {Agarwal, PK and Aronov, B and Koltun, V},
   Title = {Efficient algorithms for bichromatic separability},
   Journal = {ACM Transactions on Algorithms},
   Volume = {2},
   Number = {2},
   Pages = {209-227},
   Year = {2006},
   ISSN = {1549-6325},
   url = {http://dx.doi.org/10.1145/1150334.1150338},
   Abstract = {A closed solid body separates one point set from another if
             it contains the former and the closure of its complement
             contains the latter. We present a near-linear algorithm for
             deciding whether two sets of n points in ℝ 3 can be
             separated by a prism, near-quadratic algorithms for
             separating by a slab or a wedge, and a near-cubic algorithm
             for separating by a double wedge. The latter three
             algorithms improve the previous best known results by an
             order of magnitude, while the prism separability algorithm
             constitutes an improvement of two orders of magnitude. ©
             2006 ACM.},
   Doi = {10.1145/1150334.1150338},
   Key = {fds235485}
}

@article{fds235486,
   Author = {Agarwal, PK and Overmars, M and Sharir, M},
   Title = {Computing maximally separated sets in the
             plane},
   Journal = {SIAM Journal on Computing},
   Volume = {36},
   Number = {3},
   Pages = {815-834},
   Year = {2006},
   ISSN = {0097-5397},
   url = {http://dx.doi.org/10.1137/S0097539704446591},
   Abstract = {Let S be a set of n points in ℝ2. Given an integer 1 ≤ k
             ≤ n, we wish to find a maximally separated subset I ⊆ S
             of size k; this is a subset for which the minimum among the
             (2k) pairwise distances between its points is as large as
             possible. The decision problem associated with this problem
             is to determine whether there exists I ⊆ S, |I| = k, so
             that all (2k) pairwise distances in I are at least 2. This
             problem can also be formulated in terms of disk-intersection
             graphs: Let D be the set of unit disks centered at the
             points of S. The disk-intersection graph G of D has as edges
             all pairs of disks with nonempty intersection. Any set I
             with the above properties is then the set of centers of
             disks that form an independent set in the graph G. This
             problem is known to be NP-complete if k is part of the
             input. In this paper we first present a linear-time
             ε-approximation algorithm for any constant k. Next we give
             exact algorithms for the cases k = 3 and k = 4 that run in
             time O(n 4/3polylog(n)). We also present a simpler nO(√k)-
             time exact algorithm (as compared with the recent algorithm
             in [J. Alber and J. Fiala, J. Algorithms, 52 (2004), pp.
             134-151]) for arbitrary values of k. © 2006 Society for
             Industrial and Applied Mathematics.},
   Doi = {10.1137/S0097539704446591},
   Key = {fds235486}
}

@article{fds235487,
   Author = {Abam, MA and Agarwal, PK and Berg, MD and Yu, H},
   Title = {Out-of-order event processing in kinetic data
             structures},
   Journal = {Lecture notes in computer science},
   Volume = {4168 LNCS},
   Pages = {624-635},
   Year = {2006},
   ISSN = {0302-9743},
   Abstract = {We study the problem of designing kinetic data structures
             (KDS's for short) when event times cannot be computed
             exactly and events may be processed in a wrong order. In
             traditional KDS's this can lead to major inconsistencies
             from which the KDS cannot recover. We present more robust
             KDS's for the maintenance of two fundamental structures,
             kinetic sorting and tournament trees, which overcome the
             difficulty by employing a refined event scheduling and
             processing technique. We prove that the new event scheduling
             mechanism leads to a KDS that is correct except for finitely
             many short time intervals. We analyze the maximum delay of
             events and the maximum error in the structure, and we
             experimentally compare our approach to the standard event
             scheduling mechanism. © Springer-Verlag Berlin Heidelberg
             2006.},
   Key = {fds235487}
}

@article{fds235489,
   Author = {Agarwal, PK and Mustafa, NH},
   Title = {Independent set of intersection graphs of convex objects in
             2D},
   Journal = {Computational Geometry},
   Volume = {34},
   Number = {2},
   Pages = {83-95},
   Year = {2006},
   ISSN = {0925-7721},
   url = {http://dx.doi.org/10.1016/j.comgeo.2005.12.001},
   Abstract = {The intersection graph of a set of geometric objects is
             defined as a graph G=(S,E) in which there is an edge between
             two nodes s i, s j∈S if s i∩s j≠ ∅. The problem of
             computing a maximum independent set in the intersection
             graph of a set of objects is known to be NP-complete for
             most cases in two and higher dimensions. We present
             approximation algorithms for computing a maximum independent
             set of intersection graphs of convex objects in ℝ 2.
             Specifically, given (i) a set of n line segments in the
             plane with maximum independent set of size α, we present
             algorithms that find an independent set of size at least
             (α/(2log(2n/α))) 1/2 in time O(n 3) and (α/(2log(2n/α)))
             1/4 in time O(n 4/3log cn), (ii) a set of n convex objects
             with maximum independent set of size α, we present an
             algorithm that finds an independent set of size at least
             (α/(2log(2n/α))) 1/3 in time O(n 3+τ (S)), assuming that
             S can be preprocessed in time τ(S) to answer certain
             primitive operations on these convex sets, and (iii) a set
             of n rectangles with maximum independent set of size βn,
             for β≤1, we present an algorithm that computes an
             independent set of size Ω( β 2n) . All our algorithms use
             the notion of partial orders that exploit the geometric
             structure of the convex objects. © 2006 Elsevier B.V. All
             rights reserved.},
   Doi = {10.1016/j.comgeo.2005.12.001},
   Key = {fds235489}
}

@article{fds235490,
   Author = {Agarwal, PK and Brady, D and Matoušek, J},
   Title = {Segmenting object space by geometric reference
             structures},
   Journal = {ACM Transactions on Sensor Networks},
   Volume = {2},
   Number = {4},
   Pages = {455-465},
   Year = {2006},
   ISSN = {1550-4859},
   url = {http://dx.doi.org/10.1145/1218556.1218557},
   Abstract = {A model for segmentation of an object space by an array of
             binary, radiation-field sensors and geometric reference
             structures is described. Given a family of binary,
             radiation-field sensors and a geometric reference structure,
             we refer to the set of sensor states induced by a source at
             point p as the signature of p. We study the segmentation of
             an object space into signature cells and prove near optimal
             bounds on the number of distinct signatures induced by a
             point source, as a function of sensor and reference
             structure complexity. We also show that almost any family of
             signatures can be implemented under this model. © 2006
             ACM.},
   Doi = {10.1145/1218556.1218557},
   Key = {fds235490}
}

@article{fds235491,
   Author = {Agarwal, PK and Wang, Y and Yu, H},
   Title = {A two-dimensional kinetic triangulation with near-quadratic
             topological changes},
   Journal = {Discrete & Computational Geometry},
   Volume = {36},
   Number = {4},
   Pages = {573-592},
   Year = {2006},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/s00454-006-1266-7},
   Abstract = {A triangulation of a set S of points in the plane is a
             subdivision of the convex hull of S into triangles whose
             vertices are points of S. Given a set S of n points in ℝ2,
             each moving independently, we wish to maintain a
             triangulation of S. The triangulation needs to be updated
             periodically as the points in S move, so the goal is to
             maintain a triangulation with a small number of topological
             events, each being the insertion or deletion of an edge. We
             propose a kinetic data structure (KDS) that processes n22
             O(√log n · log log n) topological events with high
             probability if the trajectories of input points are
             algebraic curves of fixed degree. Each topological event can
             be processed in O(log n) time. This is the first known KDS
             for maintaining a triangulation that processes a
             near-quadratic number of topological events, and almost
             matches the Ωn2 lower bound [1]. The number of topological
             events can be reduced to nk2 O(√log k · log log n) if
             only k of the points are moving. © Springer
             2006.},
   Doi = {10.1007/s00454-006-1266-7},
   Key = {fds235491}
}

@article{fds235492,
   Author = {Agarwal, PK and Edelsbrunner, H and Harer, J and Wang,
             Y},
   Title = {Extreme elevation on a 2-manifold},
   Journal = {Discrete & Computational Geometry},
   Volume = {36},
   Number = {4},
   Pages = {553-572},
   Year = {2006},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/s00454-006-1265-8},
   Abstract = {Given a smoothly embedded 2-manifold in ℝ3, we define the
             elevation of a point as the height difference to a
             canonically defined second point on the same manifold. Our
             definition is invariant under rigid motions and can be used
             to define features such as lines of discontinuous or
             continuous but non-smooth elevation. We give an algorithm
             for finding points of locally maximum elevation, which we
             suggest mark cavities and protrusions and are useful in
             matching shapes as for example in protein docking. ©
             Springer 2006.},
   Doi = {10.1007/s00454-006-1265-8},
   Key = {fds235492}
}

@article{fds328053,
   Author = {Agarwal, PK and Cabello, S and Sellarès, JA and Sharir,
             M},
   Title = {Computing a Center-Transversal Line.},
   Journal = {FSTTCS},
   Volume = {4337},
   Pages = {93-104},
   Publisher = {Springer},
   Editor = {Arun-Kumar, S and Garg, N},
   Year = {2006},
   ISBN = {3-540-49994-6},
   url = {http://dx.doi.org/10.1007/11944836_11},
   Doi = {10.1007/11944836_11},
   Key = {fds328053}
}

@article{fds235467,
   Author = {Wang, Y and Agarwal, PK and Brown, P and Edelsbrunner, H and Rudolph,
             J},
   Title = {Coarse and reliable geometric alignment for protein
             docking.},
   Journal = {Pacific Symposium on Biocomputing. Pacific Symposium on
             Biocomputing},
   Pages = {64-75},
   Year = {2005},
   ISSN = {2335-6936},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/15759614},
   Abstract = {We present an efficient algorithm for generating a small set
             of coarse alignments between interacting proteins using
             meaningful features on their surfaces. The proteins are
             treated as rigid bodies, but the results are more generally
             useful as the produced configurations can serve as input to
             local improvement algorithms that allow for protein
             flexibility. We apply our algorithm to a diverse set of
             protein complexes from the Protein Data Bank, demonstrating
             the effectivity of our algorithm, both for bound and for
             unbound protein docking problems.},
   Key = {fds235467}
}

@article{fds235469,
   Author = {Agarwal, PK and Wang, Y and Yin, P},
   Title = {Lower bound for sparse Euclidean spanners},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Pages = {670-671},
   Year = {2005},
   Abstract = {Given a one-dimensional graph G such that any two
             consecutive nodes are unit distance away, and such that the
             minimum number of links between any two nodes (the diameter
             of G) is O(log n), we prove an Ω(n log n/log log n) lower
             bound on the sum of lengths of all the edges (i.e., the
             weight of G). The problem is a variant of the widely studied
             partial sum problem. This in turn provides a lower bound on
             Euclidean spanner graphs with small diameter and low weight,
             showing that the upper bound from [1] is almost
             tight.},
   Key = {fds235469}
}

@article{fds235470,
   Author = {Agarwal, PK and Arge, L and Yi, K},
   Title = {An optimal dynamic interval stabbing-max data
             structure?},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Pages = {803-812},
   Year = {2005},
   Abstract = {In this paper we consider the dynamic stabbing-max problem,
             that is, the problem of dynamically maintaining a set S of n
             axis-parallel hyper-rectangles in ℝd, where each rectangle
             s ∈ S has a weight w(s) ∈ ℝ, so that the rectangle
             with the maximum weight containing a query point can be
             determined efficiently. We develop a linear-size structure
             for the one-dimensional version of the problem, the interval
             stabbing-max problem, that answers queries in worst-case
             O(log n) time and supports updates in amortized O(log n)
             time. Our structure works in the pointer-machine model of
             computation and utilizes many ingredients from recently
             developed external memory structures. Using standard
             techniques, our one-dimensional structure can be extended to
             higher dimensions, while paying a logarithmic factor in
             space, update time, and query time per dimension.
             Furthermore, our structure can easily be adapted to external
             memory, where we obtain a linear-size structure that answers
             queries and supports updates in O(logB n) I/Os, where B is
             the disk block size.},
   Key = {fds235470}
}

@article{fds235471,
   Author = {Agarwal, PK and Sharir, M},
   Title = {Pseudo-line arrangements: Duality, algorithms, and
             applications},
   Journal = {SIAM Journal on Computing},
   Volume = {34},
   Number = {3},
   Pages = {526-552},
   Year = {2005},
   ISSN = {0097-5397},
   url = {http://dx.doi.org/10.1137/S0097539703433900},
   Abstract = {A finite collection of x-monotone unbounded Jordan curves in
             the plane is called a family of pseudo-lines if every pair
             of curves intersect in at most one point, and the two curves
             cross each other there. Let L be such a collection of n
             pseudo-lines, and let P be a set of m points in R 2.
             Extending a result of Goodman [Discrete Math., 32 (1980),
             pp. 27-35], we define a duality transform that maps L to a
             set L* of points in R 2 and P to a set P* of (x-monotone)
             pseudo-lines in R 2, so that the incidence and the
             "above-below" relations between the points and the
             pseudo-lines are preserved. We present an efficient
             algorithm for computing the dual arrangement A(P*) under an
             appropriate model of computation. We also present a dynamic
             data structure for reporting, in O(m ε+k) time, all k
             points of P that lie below a query arc, which is either a
             circular arc or a portion of the graph of a polynomial of
             fixed degree. This result is needed for computing the dual
             arrangement for certain classes of pseudo-lines arising in
             several applications, but is also interesting in its own
             right. We present a few applications of our dual arrangement
             algorithm, such as computing incidences between points and
             pseudo-lines and computing a subset of faces in a
             pseudo-line arrangement. Next, we present an efficient
             algorithm for cutting a set of circles into arcs so that
             every pair of arcs intersect in at most one point, i.e., the
             resulting arcs constitute a collection of pseudo-segments.
             By combining this algorithm with our algorithm for computing
             the dual arrangement of pseudo-lines, we obtain efficient
             algorithms for several problems involving arrangements of
             circles or circular arcs, such as reporting or counting
             incidences between points and circles and computing a set of
             marked faces in arrangements of circles. © 2005 Society for
             Industrial and Applied Mathematics.},
   Doi = {10.1137/S0097539703433900},
   Key = {fds235471}
}

@article{fds235472,
   Author = {Agarwal, PK and Bereg, S and Daescu, O and Kaplan, H and Ntafos, S and Zhu,
             B},
   Title = {Guarding a terrain by two watchtowers},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {346-355},
   Year = {2005},
   url = {http://dx.doi.org/10.1145/1064092.1064145},
   Abstract = {Given a polyhedral terrain T with n vertices, the
             two-watchtower problem for T calls for finding two vertical
             segments, called watchtowers, of smallest common height,
             whose bottom endpoints (bases) lie on T, and whose top
             endpoints guard T, in the sense that each point on T is
             visible from at least one of them. In this paper we present
             the following results for the two-watchtower problem in ℝ2
             and ℝ3: (1) We show that the discrete two-watchtowers
             problem in ℝ2, where the bases are constrained to lie at
             vertices of T, can be solved in O(n2 log4 n) time,
             significantly improving previous solutions. The algorithm
             works, without increasing its asymptotic running time, even
             if one of the towers is allowed to be placed anywhere on T.
             (2) We show that the continuous two-watchtower problem in
             R2, where the bases can lie anywhere on T, can be solved in
             O(n 3a(n) log3 n) time, again significantly improving
             previous results. (3) Still in R2, we show that the
             continuous version of the problem of guarding a finite set P
             C T of m points by two watchtowers of smallest height can be
             solved in O(mn log4 n) time. (4) The discrete version of the
             two-watchtower problem in ℝ3 can be solved in O(n11/3
             polylog(n)) time; this is the first nontrivial result for
             this problem in ℝ3. Copyright 2005 ACM.},
   Doi = {10.1145/1064092.1064145},
   Key = {fds235472}
}

@article{fds235473,
   Author = {Agarwal, PK and Arge, L and Yi, K},
   Title = {I/O-efficient construction of constrained delaunay
             triangulations},
   Journal = {Lecture notes in computer science},
   Volume = {3669},
   Pages = {355-366},
   Year = {2005},
   ISSN = {0302-9743},
   Abstract = {In this paper, we designed and implemented an I/O-efficient
             algorithm for constructing constrained Delaunay
             triangulations. If the number of constraining segments is
             smaller than the memory size, our algorithm runs in expected
             O(N/B logM/B N/B) I/Os for triangulating N points in the
             plane, where M is the memory size and B is the disk block
             size. If there are more constraining segments, the
             theoretical bound does not hold, but in practice the
             performance of our algorithm degrades gracefully. Through an
             extensive set of experiments with both synthetic and real
             data, we show that our algorithm is significantly faster
             than existing implementations. © Springer-Verlag Berlin
             Heidelberg 2005.},
   Key = {fds235473}
}

@article{fds235474,
   Author = {Agarwal, PK and Xie, J and Yang, J and Yu, H},
   Title = {Monitoring continuous band-join queries over dynamic
             data},
   Journal = {Lecture notes in computer science},
   Volume = {3827 LNCS},
   Pages = {349-359},
   Year = {2005},
   ISSN = {0302-9743},
   url = {http://dx.doi.org/10.1007/11602613_36},
   Abstract = {A continuous query is a standing query over a dynamic data
             set whose query result needs to be constantly updated as new
             data arrive. We consider the problem of constructing a data
             structure on a set of continuous band-join queries over two
             data sets R and S, where each band-join query asks for
             reporting the set {(r, s) ∈R × S | a ≤r - s ≤ b} for
             some parameters a and b, so that given a data update in R or
             S, one can quickly identify the subset of continuous queries
             whose results are affected by the update, and compute
             changes to these results. We present the first nontrivial
             data structure for this problem that simultaneously achieves
             subquadratic space and sublinear query time. This is
             achieved by first decomposing the original problem into two
             independent subproblems, and then carefully designing data
             structures suitable for each case, by exploiting the
             particular structure in each subproblem. A key step in the
             above construction is a data structure whose performance
             increases with the degree of clusteredness of the band-joins
             being indexed. We believe that this structure is of
             independent interest and should have broad impact in
             practice. We present the details in [1]. © Springer-Verlag
             Berlin Heidelberg 2005.},
   Doi = {10.1007/11602613_36},
   Key = {fds235474}
}

@article{fds235475,
   Author = {Agarwal, PK and Bilu, Y and Kolodny, R},
   Title = {Faster algorithms for optimal Multiple Sequence Alignment
             based on pairwise comparisons},
   Journal = {Lecture notes in computer science},
   Volume = {3692 LNBI},
   Pages = {315-327},
   Year = {2005},
   ISSN = {0302-9743},
   url = {http://dx.doi.org/10.1007/11557067_26},
   Abstract = {Multiple Sequence Alignment (MSA) is one of the most
             fundamental problems in computational molecular biology. The
             running time of (he best known scheme for finding an optimal
             alignment, based on dynamic programming, increases
             exponentially with the number of input sequences. Hence,
             many heuristics were suggested for the problem. We consider
             the following version of the MSA problem: In a preprocessing
             stage pairwisc alignments are found for every pair of
             sequences. The goal is to find an optimal alignment in which
             matches arc restricted to positions that wore matched at the
             preprocessing stage. We present several techniques for
             making the dynamic programming algorithm more efficient,
             while still finding an optimal solution under these
             restrictions. Namely, in our formulation the MSA must
             conform with pairwisc (local) alignments, and in return can
             he solved more efficiently. We prove that it stiffices to
             find an optimal alignment of sequence segments, rallier than
             single letters, thereby reducing the input size and thus
             improving the running time. © Springer-Verlag Berlin
             Heidelberg 2005.},
   Doi = {10.1007/11557067_26},
   Key = {fds235475}
}

@article{fds235477,
   Author = {Agarwal, PK and Berretty, R-P and Collins, AD},
   Title = {A near-quadratic algorithm for fence design},
   Journal = {Discrete and Computanional Geometry},
   Volume = {33},
   Number = {3},
   Pages = {463-481},
   Year = {2005},
   url = {http://dx.doi.org/10.1007/s00454-004-1148-9},
   Abstract = {A part feeder is a mechanism that receives a stream of
             identical parts in arbitrary orientations and outputs them
             oriented the same way. Various sensorless part feeders have
             been proposed in the literature. The feeder we consider
             consists of a sequence of fences that extend partway across
             a conveyor belt; a polygonal part P carried by the belt is
             reoriented by each fence it encounters. We present an O(m +
             n2 log3n)-time algorithm to compute a sequence of fences
             that uniquely orients P, if one exists, where m is the total
             number of vertices and n is the number of stable edges of P.
             We reduce the problem to searching for a path in a state
             graph that has O(n 3) edges. By exploiting various geometric
             properties of this graph, we show that it can be represented
             implicitly and that a desired path can be computed in O(m +
             n2 log3n) time. We believe that our technique is quite
             general and could be applicable to other part-manipulation
             problems as well. © 2004 Springer-Verlag New York,
             LLC.},
   Doi = {10.1007/s00454-004-1148-9},
   Key = {fds235477}
}

@article{fds235478,
   Author = {Agarwal, PK and Har-Peled, S and Mustafa, NH and Wang,
             Y},
   Title = {Near-linear time approximation algorithms for curve
             simplification},
   Journal = {Algorithmica (New York)},
   Volume = {42},
   Number = {3-4},
   Pages = {203-219},
   Year = {2005},
   url = {http://dx.doi.org/10.1007/s00453-005-1165-y},
   Abstract = {We consider the problem of approximating a polygonal curve P
             under a given error criterion by another polygonal curve P'
             whose vertices are a subset of the vertices of P. The goal
             is to minimize the number of vertices of P' while ensuring
             that the error between P' and P is below a certain
             threshold. We consider two different error measures:
             Hausdorff and Frechet. For both error criteria, we present
             near-linear time approximation algorithms that, given a
             parameter ε &gt; 0, compute a simplified polygonal curve P'
             whose error is less than ε and size at most the size of an
             optimal simplified polygonal curve with error ε/2. We
             consider monotone curves in ℝ2 in the case of the
             Hausdorff error measure under the uniform distance metric
             and arbitrary curves in any dimension for the Frechet error
             measure under L p metrics. We present experimental results
             demonstrating that our algorithms are simple and fast, and
             produce close to optimal simplifications in practice. ©
             2005 Springer Science+Business Media, Inc.},
   Doi = {10.1007/s00453-005-1165-y},
   Key = {fds235478}
}

@article{fds235479,
   Author = {Agarwal, PK and Aronov, B and Koltun, V and Sharir,
             M},
   Title = {Lines avoiding unit balls in three dimensions},
   Journal = {Discrete and Computanional Geometry},
   Volume = {34},
   Number = {2},
   Pages = {231-250},
   Year = {2005},
   url = {http://dx.doi.org/10.1007/s00454-005-1166-2},
   Abstract = {Let B be a set of n unit balls in ℝ3. We show that the
             combinatorial complexity of the space of lines in ℝ3 that
             avoid all the balls of B is O(n3+ε), for any ε &gt; 0.
             This result has connections to problems in visibility, ray
             shooting, motion planning, and geometric optimization. ©
             Springer 2005.},
   Doi = {10.1007/s00454-005-1166-2},
   Key = {fds235479}
}

@article{fds235480,
   Author = {Agarwal, PK and Procopiuc, CM and Varadarajan,
             KR},
   Title = {Approximation algorithms for a k-line center},
   Journal = {Algorithmica (New York)},
   Volume = {42},
   Number = {3-4},
   Pages = {221-230},
   Year = {2005},
   url = {http://dx.doi.org/10.1007/s00453-005-1166-x},
   Abstract = {Given a set P of n points in ℝd and an integer k &gt; 1,
             let w* denote the minimum value so that P can be covered by
             k congruent cylinders of radius w*. We describe a randomized
             algorithm that, given P and an ε &gt; 0, computes k
             cylinders of radius (1 + ε) w* that cover P. The expected
             running time of the algorithm is O(n log n), with the
             constant of proportionality depending on k, d, and ε. We
             first show that there exists a small "certificate" Q ⊆ P,
             whose size does not depend on n, such that for any k
             congruent cylinders that cover Q, an expansion of these
             cylinders by a factor of (1 + ε) covers P. We then use a
             well-known scheme based on sampling and iterated
             re-weighting for computing the cylinders. © 2005 Springer
             Science+Business Media, Inc.},
   Doi = {10.1007/s00453-005-1166-x},
   Key = {fds235480}
}

@article{fds22921,
   Author = {P.K. Agarwal},
   Title = {Reporting all intersecting pairs of polytopes in two and
             three dimensions},
   Year = {2004},
   Abstract = {\," with M. de , and J. Vahrenhold, in Seventh Workshop on
             Algorithms and Data Structures, 2001.},
   Key = {fds22921}
}

@article{fds235455,
   Author = {Agarwal, PK and Aronov, B and Koltun, V},
   Title = {Efficient Algorithms for Bichromatic Separability},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Volume = {15},
   Pages = {675-683},
   Year = {2004},
   Abstract = {A closed solid body separates one point set from another if
             it contains the former and the closure of its complement
             contains the latter. We present a near-linear algorithm for
             deciding whether two sets of n points in 3-space can be
             separated by a prism, near-quadratic algorithms for
             separating by a slab or a wedge, and a near-cubic algorithm
             for separating by a double-wedge. The latter three
             algorithms improve the previous best known results by an
             order of magnitude, while the prism separability algorithm
             constitutes an improvement of two orders of
             magnitude.},
   Key = {fds235455}
}

@article{fds235456,
   Author = {Agarwal, PK and Overmars, M and Sharir, M},
   Title = {Computing Maximally Separated Sets in the Plane and
             Independent Sets in the Intersection Graph of Unit
             Disks},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Volume = {15},
   Pages = {509-518},
   Year = {2004},
   Abstract = {Let S be a set of n points in ℝ2. Given an integer 1 ≤ k
             ≤ n, we wish to find a maximally separated subset I ⊆ S
             of size k; this is a subset for which the minimum among the
             (k/2) pairwise distances between its points is as large as
             possible. The decision problem associated with this problem
             is to determine whether there exists I ⊆ S, |I| = k, so
             that all (k/2) pairwise distances in I are at least 2, say.
             This problem can also be formulated in terms of
             disk-intersection graphs: Let D be the set of unit disks
             centered at the points of S. The disk-intersection graph G
             of D connects pairs of disks by an edge if they have
             nonempty intersection. I is then the set of centers of disks
             that form an independent set in the graph G. This problem is
             known to be NP-Complete if k is part of the input. In this
             paper we first present a linear-time approximation algorithm
             for any constant k. Next we give O(n4/3polylog(n)) exact
             algorithms for the cases k = 3 and k = 4. We also present a
             simpler nO(√k))-time algorithm (as compared with the
             recent algorithm in [5]) for arbitrary values of
             k.},
   Key = {fds235456}
}

@article{fds235457,
   Author = {Yu, H and Agarwal, PK and Poreddy, R and Varadarajan,
             KR},
   Title = {Practical methods for shape fitting and kinetic data
             structures using core sets},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {263-272},
   Year = {2004},
   Abstract = {The notion of ε-kernel was introduced by Agarwal et al. to
             set up a unified framework for computing various extent
             measures of a point set P approximately. Roughly speaking, a
             subset Q ⊆ P is an ε-kernel of P if for every slab W
             containing Q, the expanded slab (1 + ε)W contains P. They
             illustrated the significance of an ε-kernel by showing that
             it yields approximation algorithms for a wide range of
             problems. We present a simpler and more practical algorithm
             for computing the ε-kernel of a set P of points in ℝd. We
             demonstrate the practicality of our algorithm by showing its
             empirical performance on various inputs. We then describe an
             incremental algorithm for fitting various shapes and use the
             ideas of our algorithm for computing ε-kernels to analyze
             the performance of this algorithm. We illustrate the
             versatility and practicality of this technique by
             implementing approximation algorithms for minimum enclosing
             cylinder, minimum-volume bounding box, and minimum-width
             annulus. Finally, we show that ε-kernels can be effectively
             used to expedite the algorithms for maintaining extents of
             moving points.},
   Key = {fds235457}
}

@article{fds235458,
   Author = {Agarwal, PK and Edelsbrunner, H and Harer, J and Wang,
             Y},
   Title = {Extreme elevation on a 2-manifold},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {357-365},
   Year = {2004},
   Abstract = {Given a smoothly embedded 2-manifold in ℝ 3, we define the
             elevation of a point as the height difference to a
             canonically defined second point on the same manifold. Our
             definition is invariant under rigid motions and can be used
             to define features such as lines of discontinuous or
             continuous but non-smooth elevation. We give an algorithm
             for finding points of locally maximum elevation, which we
             suggest mark cavities and protrusions and are useful in
             matching shapes as for example in protein
             docking.},
   Key = {fds235458}
}

@article{fds235459,
   Author = {Govindarajan, S and Dietze, M and Agarwal, PK and Clark,
             JS},
   Title = {A scalable simulator for forest dynamics},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {106-115},
   Year = {2004},
   Abstract = {Models of forest ecosystems are needed to understand how
             climate and land-use change can impact biodiversity. In this
             paper we describe an individual-based, spatially-explicit
             forest simulator with full accounting of both landscape
             context and the fine-scale processes that influence forest
             dynamics. Unfortunately, performing realistic forest
             simulations of such models is computationally infeasible. We
             design efficient algorithms for computing seed dispersal and
             light, using a plethora of techniques. These include
             hierarchical spatial decomposition, monopole approximation
             and utilizing the graphics hardware for fast geometric
             computations. These algorithms allow us to simulate large
             landscapes for long periods of time.},
   Key = {fds235459}
}

@article{fds235460,
   Author = {Agarwal, PK and Aronov, B and Koltun, V and Sharir,
             M},
   Title = {On lines avoiding unit balls in three dimensions},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {36-45},
   Year = {2004},
   Abstract = {Let B be a set of n unit balls in ℝ3. We show that the
             combinatorial complexity of the space of lines in ℝ3 that
             avoid all the balls of B is O(n3+ε), for any ε &gt; 0.
             This result has connections to problems in visibility, ray
             shooting, motion planning and geometric optimization.},
   Key = {fds235460}
}

@article{fds235461,
   Author = {Agarwal, PK and Varadarajan, KR},
   Title = {A near-linear constant-factor approximation for euclidean
             bipartite matching?},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {247-252},
   Year = {2004},
   Abstract = {In the Euclidean bipartite matching problem, we are given a
             set R of "red" points and a set B of "blue" points in ℝ d
             where |R|= |B| = n, and we want to pair up each red point
             with a distinct blue point so that the sum of distances
             between the paired points is minimized. We present an
             approximation algorithm that given any parameter 0 &lt; ε
             &lt; 1 runs in O(n 1+ε) expected time and returns a
             matching whose expected cost is within a multiplicative
             factor O(log(1/ε)) of the optimal. The dimension d is
             considered to be a fixed constant.},
   Key = {fds235461}
}

@article{fds235462,
   Author = {Agarwal, PK and Sharir, M and Welzl, E},
   Title = {Algorithms for center and tverberg points},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {61-67},
   Year = {2004},
   Abstract = {We present a near-quadratic algorithm for computing the
             center region of a set of n points in three dimensions. This
             is nearly tight in the worst case since the center region
             can have ω(n 2) complexity. We then consider the problem of
             recognizing whether a given point q is a colored Tverberg
             point of a set of n colored points in the plane, and present
             the first polynomial-time algorithm for this
             problem.},
   Key = {fds235462}
}

@article{fds235463,
   Author = {Choi, V and Agarwal, PK and Edelsbrunner, H and Rudolph,
             J},
   Title = {Local search heuristic for rigid protein
             docking},
   Journal = {Lecture notes in computer science},
   Volume = {3240},
   Pages = {218-229},
   Year = {2004},
   ISSN = {0302-9743},
   Abstract = {We give an algorithm that locally improves the fit between
             two proteins modeled as space-filling diagrams. The
             algorithm defines the fit in purely geometric terms and
             improves by applying a rigid motion to one of the two
             proteins. Our implementation of the algorithm takes between
             three and ten seconds and converges with high likelihood to
             the correct docked configuration, provided it starts at a
             position away from the correct one by at most 18 degrees of
             rotation and at most 3.0Å of translation. The speed and
             convergence radius make this an attractive algorithm to use
             in combination with a coarse sampling of the six-dimensional
             space of rigid motions. © Springer-Verlag
             2004.},
   Key = {fds235463}
}

@article{fds235464,
   Author = {Agarwal, PK and Nevo, E and Pach, J and Pinchasi, R and Sharir, M and Smorodinsky, S},
   Title = {Lenses in arrangements of pseudo-circles and their
             applications},
   Journal = {Journal of the ACM},
   Volume = {51},
   Number = {2},
   Pages = {139-186},
   Year = {2004},
   ISSN = {0004-5411},
   url = {http://dx.doi.org/10.1145/972639.972641},
   Abstract = {A collection of simple closed Jordan curves in the plane is
             called a family of pseudo-circles if any two of its members
             intersect at most twice. A closed curve composed of two
             subarcs of distinct pseudo-circles is said to be an empty
             lens if the closed Jordan region that it bounds does not
             intersect any other member of the family. We establish a
             linear upper bound on the number of empty lenses in an
             arrangement of n pseudo-circles with the property that any
             two curves intersect precisely twice. We use this bound to
             show that any collection of n x-monotone pseudo-circles can
             be cut into O(n 8/5) arcs so that any two intersect at most
             once; this improves a previous bound of O(n 5/3) due to
             Tamaki and Tbkuyama. If, in addition, the given collection
             admits an algebraic representation by three real parameters
             that satisfies some simple conditions, then the number of
             cuts can be further reduced to O(n 3/2(log n) O(αs(n))),
             where α(n) is the inverse Ackermann function, and s is a
             constant that depends on the the representation of the
             pseudo-circles. For arbitrary collections of pseudo-circles,
             any two of which intersect exactly twice, the number of
             necessary cuts reduces still further to O(n 4/3). As
             applications, we obtain improved bounds for the number of
             incidences, the complexity of a single level, and the
             complexity of many faces in arrangements of circles, of
             pairwise intersecting pseudo-circles, of arbitrary
             x-monotone pseudo-circles, of parabolas, and of homothetic
             copies of any fixed simply shaped convex curve. We also
             obtain a variant of the Gallai-Sylvester theorem for
             arrangements of pairwise intersecting pseudo-circles, and a
             new lower bound on the number of distinct distances under
             any well-behaved norm.},
   Doi = {10.1145/972639.972641},
   Key = {fds235464}
}

@article{fds235465,
   Author = {Agarwal, PK and Edelsbrunner, H and Wang, Y},
   Title = {Computing the writhing number of a polygonal
             knot},
   Journal = {Discrete and Computanional Geometry},
   Volume = {32},
   Number = {1},
   Pages = {37-53},
   Year = {2004},
   url = {http://dx.doi.org/10.1007/s00454-004-2864-x},
   Abstract = {The writhing number measures the global geometry of a closed
             space curve or knot. We show that this measure is related to
             the average winding number of its Gauss map. Using this
             relationship, we give an algorithm for computing the
             writhing number for a polygonal knot with n edges in time
             roughly proportional to n1.6. We also implement a different,
             simple algorithm and provide experimental evidence for its
             practical efficiency.},
   Doi = {10.1007/s00454-004-2864-x},
   Key = {fds235465}
}

@article{fds235466,
   Author = {Agarwal, P and Guibas, L and Nguyen, A and Russel, D and Zhang,
             L},
   Title = {Collision detection for deforming necklaces},
   Journal = {Computational Geometry},
   Volume = {28},
   Number = {2-3 SPEC. ISS.},
   Pages = {137-163},
   Year = {2004},
   ISSN = {0925-7721},
   url = {http://dx.doi.org/10.1016/j.comgeo.2004.03.008},
   Abstract = {In this paper, we propose to study deformable necklaces -
             flexible chains of balls, called beads, in which only
             adjacent balls may intersect. Such objects can be used to
             model macro-molecules, muscles, ropes, and other linear
             objects in the physical world. We exploit this linearity to
             develop geometric structures associated with necklaces that
             are useful for collision detection in physical simulations.
             We show how these structures can be implemented efficiently
             and maintained under necklace deformation. In particular, we
             study a bounding volume hierarchy based on spheres which can
             be used for collision and self-collision detection of
             deforming and moving necklaces. As our theoretical and
             experimental results show, such a hierarchy is easy to
             compute and, more importantly, is also easy to maintain when
             the necklace deforms. Using this hierarchy, we achieve a
             collision detection upper bound of O(nlogn) in two
             dimensions and O(n 2-2/d) in d-dimensions, d3. To our
             knowledge, this is the first subquadratic bound proved for a
             collision detection algorithm using predefined hierarchies.
             In addition, we show that the power diagram, with the help
             of some additional mechanisms, can be used to detect
             self-collisions of a necklace in a way that is complementary
             to the sphere hierarchy. © 2004 Elsevier
             B.V.},
   Doi = {10.1016/j.comgeo.2004.03.008},
   Key = {fds235466}
}

@article{fds235468,
   Author = {Agarwal, PK and Har-Peled, S and Varadarajan, KR},
   Title = {Approximating extent measures of points},
   Journal = {Journal of the ACM},
   Volume = {51},
   Number = {4},
   Pages = {606-635},
   Year = {2004},
   ISSN = {0004-5411},
   url = {http://dx.doi.org/10.1145/1008731.1008736},
   Abstract = {We present a general technique for approximating various
             descriptors of the extent of a set P of n points in R d when
             the dimension d is an arbitrary fixed constant. For a given
             extent measure μ and a parameter ε &gt; 0, it computes in
             time 0(n + l/ε o(1) a subset Q ⊆P of size l/ε o(1), with
             the property that (1 - ε)μ,(P) ≤ μ(Q) ≤ μ(P). The
             specific applications of our technique include
             ε-approximation algorithms for (i) computing diameter,
             width, and smallest bounding box, ball, and cylinder of P,
             (ii) maintaining all the previous measures for a set of
             moving points, and (iii) fitting spheres and cylinders
             through a point set P. Our algorithms are considerably
             simpler, and faster in many cases, than previously known
             algorithms.},
   Doi = {10.1145/1008731.1008736},
   Key = {fds235468}
}

@article{fds235615,
   Author = {Agarwal, PK and Mustafa, NH},
   Title = {K-means projective clustering},
   Journal = {Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on
             Principles of Database Systems},
   Volume = {23},
   Pages = {155-165},
   Year = {2004},
   Abstract = {In many applications it is desirable to cluster high
             dimensional data along various subspaces, which we refer to
             as projective clustering. We propose a new objective
             function for projective clustering, taking into account the
             inherent trade-off between the dimension of a subspace and
             the induced clustering error. We then present an extension
             of the k-means clustering algorithm for projective
             clustering in arbitrary subspaces, and also propose
             techniques to avoid local minima. Unlike previous
             algorithms, ours can choose the dimension of each cluster
             independently and automatically. Furthermore, experimental
             results show that our algorithm is significantly more
             accurate than the previous approaches.},
   Key = {fds235615}
}

@article{fds235616,
   Author = {Agarwal, PK and Wang, Y and Yu, H},
   Title = {A 2D kinetic triangulation with near-quadratic topological
             changes},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {180-189},
   Year = {2004},
   Abstract = {A triangulation of a set S of points in the plane is a
             subdivision of the convex hull of S into triangles whose
             vertices are points of S. Given a set S of n points in ℝ2,
             each moving independently, we wish to maintain a
             triangulation of S. The triangulation needs to be updated
             periodically as the points in S move, so the goal is to
             maintain a triangulation with small number of topological
             events, each being the insertion or deletion of an edge. We
             propose a kinetic data structure (KDS) that processes
             n22O(√log n·log log n) topological events, with high
             probability, if the trajectories of input points are
             algebraic curves of fixed degree. Each topological event can
             be processed in O(log n) time. This is the first known KDS
             for maintaining a triangulation that processes
             near-quadratic number of topological events, and almost
             matches the Ω(n2) lower bound [1]. The number of
             topological events can be reduced to nk · 2O(√log k·log
             log n) if only k of the points are moving.},
   Key = {fds235616}
}

@article{fds235617,
   Author = {Agarwal, PK and Mustafa, NH},
   Title = {Independent set of intersection graphs of convex objects in
             2D},
   Journal = {Lecture notes in computer science},
   Volume = {3111},
   Pages = {127-137},
   Year = {2004},
   ISSN = {0302-9743},
   Abstract = {The intersection graph of a set of geometric objects is
             defined as a graph G = (S, E) in which there is an edge
             between two nodes si, sj ∈ S if si ∩ sj ≠ ∅. The
             problem of computing a maximum independent set in the
             intersection graph of a set of objects is known to be
             NP-complete for most cases in two and higher dimensions. We
             present approximation algorithms for computing a maximum
             independent set of intersection graphs of convex objects in
             ℝ2. Specifically, given a set of n line segments in the
             plane with maximum independent set of size κ, we present
             algorithms that find an independent set of size at least (i)
             (κ/2 log(2n/κ))1/2 in time O(n3) and (ii) (κ/2
             log(2n/κ))1/4 in time O(n4/3 logc n). For a set of n convex
             objects with maximum independent set of size κ, we present
             an algorithm that finds an independent set of size at least
             (κ/2 log(2n/κ))1/3 in time O(n3+τ(S)), assuming that S
             can be preprocessed in time τ(S) to answer certain
             primitive operations on these convex sets. ©
             Springer-Verlag Berlin Heidelberg 2004.},
   Key = {fds235617}
}

@article{fds235618,
   Author = {Agarwal, PK and Berretty, R-P and Collins, AD},
   Title = {A near-quadratic algorithm for fence design},
   Journal = {Springer Tracts in Advanced Robotics},
   Volume = {7 STAR},
   Pages = {347-362},
   Year = {2004},
   ISSN = {1610-7438},
   url = {http://dx.doi.org/10.1007/978-3-540-45058-0_21},
   Abstract = {A part feeder is a mechanism that receives a stream of
             identical parts in arbitrary orientations and putputs them
             oriented the same way. Various sensorless part feeders have
             been proposed in the literature. The feeder we consider
             consists of a sequence of fences that extend partway across
             a conveyor belt; a polygonal part P carried by the belt is
             reoriented by each fence it encounters. We present an O(m +
             n 2log 3 n)-time algorithm to compute a sequence of fences
             that uniquely orients P, if one exists, where m is the total
             number of vertices and n is the number of stable edges of P.
             As in [3], we reduce the problem to searching for a path in
             a state graph that has O(n 3) edges. By exploiting various
             geometric properties of the state graph, we show that it can
             be represented implicitly and a desired path can be found in
             O(m + n 2log 3 n) time. Our technique is quite general and
             is applicable to other part manipulation problems. © 2004
             Springer-Verlag.},
   Doi = {10.1007/978-3-540-45058-0_21},
   Key = {fds235618}
}

@article{fds235619,
   Author = {Agarwal, PK and Arge, L and Erickson, J and Yu, H},
   Title = {Efficient tradeoff schemes in data structures for querying
             moving objects},
   Journal = {Lecture notes in computer science},
   Volume = {3221},
   Pages = {4-15},
   Year = {2004},
   ISSN = {0302-9743},
   Abstract = {The ability to represent and query continuously moving
             objects is important in many applications of spatio-temporal
             database systems. In this paper we develop data structures
             for answering various queries on moving objects, including
             range and proximity queries, and study tradeoffs between
             various performance measures-query time, data structure
             size, and accuracy of results. © Springer-Verlag
             2004.},
   Key = {fds235619}
}

@article{fds235451,
   Author = {Agarwal, PK and Arge, L and Yang, J and Yi, K},
   Title = {I/O-efficient structures for orthogonal range-max and
             stabbing-max queries},
   Journal = {Lecture notes in computer science},
   Volume = {2832},
   Pages = {7-18},
   Year = {2003},
   ISSN = {0302-9743},
   Abstract = {We develop several linear or near-linear space and
             I/O-efficient dynamic data structures for orthogonal
             range-max queries and stabbing-max queries. Given a set of N
             weighted points in ℝd, the range-max problem asks for the
             maximum-weight point in a query hyperrectangle. In the dual
             stabbing-max problem, we are given N weighted
             hyper-rectangles, and we wish to find the maximum-weight
             rectangle containing a query point. Our structures improve
             on previous structures in several important ways. ©
             Springer-Verlag 2003.},
   Key = {fds235451}
}

@article{fds235452,
   Author = {Collins, AD and Agarwal, PK and Harer, JL},
   Title = {HPRM: A hierarchical PRM},
   Journal = {Proceedings - IEEE International Conference on Robotics and
             Automation},
   Volume = {3},
   Pages = {4433-4438},
   Year = {2003},
   Abstract = {We introduce a hierarchical variant of the probabilistic
             roadmap method for motion planning. By recursively refining
             an initially sparse sampling in neighborhoods of the
             C-obstacle boundary, our algorithm generates a smaller
             roadmap that is more likely to find narrow passages than
             uniform sampling. We analyze the failure probability and
             computation time, relating them to path length, path
             clearance, roadmap size, recursion depth, and a local
             property of the free space. The approach is general, and can
             be tailored to any variety of robots. In particular, we
             describe algorithmic details for a planar articulated
             arm.},
   Key = {fds235452}
}

@article{fds235453,
   Author = {Agarwal, PK and Procopiuc, CM and Varadarajan,
             KR},
   Title = {A (1+ε)-approximation algorithm for 2-line-center},
   Journal = {Computational Geometry},
   Volume = {26},
   Number = {2},
   Pages = {119-128},
   Year = {2003},
   ISSN = {0925-7721},
   url = {http://dx.doi.org/10.1016/S0925-7721(03)00017-8},
   Abstract = {We consider the following instance of projective clustering,
             known as the 2-line-center problem: Given a set S of n
             points in ℝ2, cover S by two congruent strips of minimum
             width. Algorithms that find the optimal solution for this
             problem have near-quadratic running time. In this paper we
             present an algorithm that, for any ε &gt; 0, computes in
             time O(n(logn+ε -2log(1/ε))+ε -7/2log(1/ε)) a cover of S
             by two strips of width at most (1+ε)w(*). © 2003 Elsevier
             B.V. All rights reserved.},
   Doi = {10.1016/S0925-7721(03)00017-8},
   Key = {fds235453}
}

@article{fds235454,
   Author = {Agarwal, PK and Arge, L},
   Title = {Editorial},
   Journal = {Computational Geometry},
   Volume = {24},
   Number = {2},
   Pages = {49-},
   Year = {2003},
   ISSN = {0925-7721},
   url = {http://dx.doi.org/10.1016/S0925-7721(02)00090-1},
   Doi = {10.1016/S0925-7721(02)00090-1},
   Key = {fds235454}
}

@article{fds235608,
   Author = {Agarwal, PK and Har-Peled, S and Sharir, M and Wang,
             Y},
   Title = {Hausdorff distance under translation for points and
             balls},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {282-291},
   Year = {2003},
   Abstract = {We study the shape matching problem under the Hausdorff
             distance and its variants. Specifically, we consider two
             sets A, B of balls in ℝd, d = 2, 3, and wish to find a
             translation t that minimizes the Hausdorff distance between
             A + t, the set of all balls in A shifted by t, and B. We
             consider several variants of this problem. First, we extend
             the notion of Hausdorff distance from sets of points to sets
             of balls, so that each ball has to be matched with the
             nearest ball in the other set. We also consider the problem
             in the standard setting, by computing the Hausdorff distance
             between the unions of the two sets (as point sets). Second,
             we consider either all possible translates t (as is the
             standard approach), or consider only translations that keep
             the balls of A + t disjoint from those of B. We propose
             several exact and approximation algorithms for these
             problems. Since the Hausdorff distance is sensitive to
             outliers, we also propose efficient approximation algorithms
             for computing the minimum root-mean-square (rms) and the
             minimum summed Hausdorff distance, under translation,
             between two point sets in Rd. In order to obtain a fast
             algorithm for the summed Hausdorff distance, we propose a
             deterministic efficient dynamic data structure for
             maintaining an ε-approximation of the 1-median of a set of
             points, under insertion and deletion.},
   Key = {fds235608}
}

@article{fds235610,
   Author = {Agarwal, PK and Arge, L and Danner, A and Holland-Minkley,
             B},
   Title = {Cache-oblivious data structures for orthogonal range
             searching},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {237-245},
   Year = {2003},
   Abstract = {We develop cache-oblivious data structures for orthogonal
             range searching, the problem of finding all T points in a
             set of N points in ℝd lying in a query hyper-rectangle.
             Cache-oblivious data structures are designed to be efficient
             in arbitrary memory hierarchies. We describe a dynamic
             linear-size data structure that answers d-dimensional
             queries in O((N/B)1-1/d+T/B) memory transfers, where B is
             the block size of any two levels of a multilevel memory
             hierarchy. A point can be inserted into or deleted from this
             data structure in O(logB2 N) memory transfers. We also
             develop a static structure for the two-dimensional case that
             answers queries in O(logB N + T/B) memory transfers using
             O(N log22 N) space. The analysis of the latter structure
             requires that B = 22c for some non-negative integer constant
             c.},
   Key = {fds235610}
}

@article{fds235611,
   Author = {Agarwal, PK and Krishnan, S and Mustafa, NH and Venkatasubramanian,
             S},
   Title = {Streaming geometric optimization using graphics
             hardware},
   Journal = {Lecture notes in computer science},
   Volume = {2832},
   Pages = {544-555},
   Year = {2003},
   ISSN = {0302-9743},
   Abstract = {In this paper we propose algorithms for solving a variety of
             geometric optimization problems on a stream of points in
             ℝ2 or ℝ3. These problems include various extent measures
             (e.g. diameter, width, smallest enclosing disk), collision
             detection (penetration depth and distance between poly
             topes), and shape fitting (minimum width annulus,
             circle/line fitting). The main contribution of this paper is
             a unified approach to solving all of the above problems
             efficiently using modern graphics hardware. All the above
             problems can be approximated using a constant number of
             passes over the data stream. Our algorithms are easily
             implemented, and our empirical study demonstrates that the
             running times of our programs are comparable to the best
             implementations for the above problems. Another significant
             property of our results is that although the best known
             implementations for the above problems are quite different
             from each other, our algorithms all draw upon the same set
             of tools, making their implementation significantly easier.
             © Springer-Verlag 2003.},
   Key = {fds235611}
}

@article{fds235613,
   Author = {Govindarajan, S and Agarwal, PK and Arge, L},
   Title = {CRB-tree: An efficient indexing scheme for range-aggregate
             queries},
   Journal = {Lecture notes in computer science},
   Volume = {2572},
   Pages = {143-157},
   Year = {2003},
   ISSN = {0302-9743},
   Abstract = {We propose a new indexing scheme, called the CRB-tree, for
             efficiently answering range-aggregate queries. The
             range-aggregate problem is defined as follows: Given a set
             of weighted points in ℝd, compute the aggregate of weights
             of points that lie inside a d-dimensional query rectangle.
             In this paper we focus on range-COUNT, SUM, AVG aggregates.
             First, we develop an indexing scheme for answering
             two-dimensional range-COUNT queries that uses O(N/B) disk
             blocks and answers a query in O(logB N) I/Os, where N is the
             number of input points and B is the disk block size. This is
             the first optimal index structure for the 2D range-COUNT
             problem. The index can be extended to obtain a
             near-linear-size structure for answering range-SUM queries
             using O(logB N) I/Os. We also obtain similar bounds for
             rectangle-intersection aggregate queries, in which the input
             is a set of weighted rectangles and a query asks to compute
             the aggregate of the weights of those input rectangles that
             overlap with the query rectangle. This result immediately
             improves a recent result on temporal-aggregate queries. Our
             indexing scheme can be dynamized and extended to higher
             dimensions. Finally, we demonstrate the practical efficiency
             of our index by comparing its performance against kdB-tree.
             For a dataset of around 100 million points, the CRB-tree
             query time is 8-10 times faster than the kdB-tree query
             time. Furthermore, unlike other indexing schemes, the query
             performance of CRB-tree is oblivious to the distribution of
             the input points and placement, shape and size of the query
             rectangle. © Springer-Verlag Berlin Heidelberg
             2003.},
   Key = {fds235613}
}

@article{fds235609,
   Author = {Agarwal, PK and Arge, L and Erickson, J},
   Title = {Indexing moving points},
   Journal = {Journal of Computer and System Sciences},
   Volume = {66},
   Number = {1},
   Pages = {207-243},
   Year = {2003},
   url = {http://dx.doi.org/10.1016/S0022-0000(02)00035-1},
   Abstract = {We propose three indexing schemes for storing a set S of N
             points in the plane, each moving along a linear trajectory,
             so that any query of the following form can be answered
             quickly: Given a rectangle R and a real value t, report all
             K points of S that lie inside R at time t. We first present
             an indexing structure that, for any given constant ε &gt;
             0, uses O(N/B) disk blocks and answers a query in
             O((N/B)1/2+ε + K/B) I/Os, where B is the block size. It can
             also report all the points of S that lie inside R during a
             given time interval. A point can be inserted or deleted, or
             the trajectory of a point can be changed, in O(logB2 N)
             I/Os. Next, we present a general approach that improves the
             query time if the queries arrive in chronological order, by
             allowing the index to evolve over time. We obtain a tradeoff
             between the query time and the number of times the index
             needs to be updated as the points move. We also describe an
             indexing scheme in which the number of I/Os required to
             answer a query depends monotonically on the difference
             between the query time stamp t and the current time.
             Finally, we develop an efficient indexing scheme to answer
             approximate nearest-neighbor queries among moving points. ©
             2003 Published by Elsevier Science (USA).},
   Doi = {10.1016/S0022-0000(02)00035-1},
   Key = {fds235609}
}

@article{fds235614,
   Author = {Agarwal, PK and Procopiuc, CM},
   Title = {Approximation algorithms for projective clustering},
   Journal = {Journal of Algorithms},
   Volume = {46},
   Number = {2},
   Pages = {115-139},
   Year = {2003},
   url = {http://dx.doi.org/10.1016/S0196-6774(02)00295-X},
   Abstract = {We consider the following two instances of the projective
             clustering problem: Given a set S of n points in ℝd and an
             integer k &gt; 0, cover S by k slabs (respectively
             d-cylinders) so that the maximum width of a slab
             (respectively the maximum diameter of a d-cylinder) is
             minimized. Let w* be the smallest value so that S can be
             covered by k slabs (respectively d-cylinders), each of width
             (respectively diameter) at most w*. This paper contains
             three main results: (i) For d = 2, we present a randomized
             algorithm that computes O(k log k) strips of width almost w*
             that cover S. Its expected running time is O(nk2log4n) if k2
             log k ≤ n; for larger values of k, the expected running
             time is O(n2/3k8/3log14/3n). (ii) For d = 3, a cover of S by
             O(k log k) slabs of width at most w* can be computed in
             expected time O(n3/2k9/4 polylog(n)). (iii) We compute a
             cover of S ⊂ ℝd by O(dk log k) d-cylinders of diameter
             at most 8w* in expected time O(dnk3log4n). We also present a
             few extensions of this result. © 2003 Elsevier Science
             (USA). All rights reserved.},
   Doi = {10.1016/S0196-6774(02)00295-X},
   Key = {fds235614}
}

@article{fds235612,
   Author = {Procopiuc, O and Agarwal, PK and Arge, L and Vitter,
             JS},
   Title = {Bkd-tree: A dynamic scalable kd-tree},
   Journal = {Lecture notes in computer science},
   Volume = {2750},
   Pages = {46-65},
   Year = {2003},
   ISSN = {0302-9743},
   Abstract = {In this paper we propose a new index structure, called the
             Bkd-tree, for indexing large multi-dimensional point data
             sets. The Bkd-tree is an I/O-efficient dynamic data
             structure based on the kd-tree. We present the results of an
             extensive experimental study showing that unlike previous
             attempts on making external versions of the kd-tree dynamic,
             the Bkd-tree maintains its high space utilization and
             excellent query and update performance regardless of the
             number of updates performed on it. © Springer-Verlag Berlin
             Heidelberg 2003.},
   Key = {fds235612}
}

@article{fds325422,
   Author = {Agarwal, P and Nevo, E and Pach, J and Pinchasi, R and Pinchasi, R and Smorodinsky, S},
   Title = {Lenses in arrangements of pseudo-circles and their
             applications},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {123-132},
   Year = {2002},
   Month = {January},
   Abstract = {A collection of simple closed Jordan curves in the plane is
             called a family of pseudo-circles if any two of its members
             intersect at most twice. A closed curve composed of two
             sub-arcs of distinct pseudo-circles is said to be an empty
             lens if it does not intersect any other member of the
             family. We establish a linear upper bound on the number of
             empty lenses in an arrangement of n pseudo-circles with the
             property that any two curves intersect precisely twice.
             Enhancing this bound in several ways, and combining it with
             the technique of Tamaki and Tokuyama [16], we show that any
             collection of n pseudo-circles can be cut into O(n 3/2 (log
             n) O(α(s)(n)) ) arcs so that any two intersect at most
             once, provided that the given pseudo-circles are x-monotone
             and admit an algebraic representation by three real
             parameters; here α(n) is the inverse Ackermann function,
             and s is a constant that depends on the algebraic degree of
             the representation of the pseudo-circles (s = 2 for circles
             and parabolas). For arbitrary collections of pseudo-circles,
             any two of which intersect twice, the number of necessary
             cuts reduces to O(n 4/3 ). As applications, we obtain
             improved bounds for the number of point-curve incidences,
             the complexity of a single level, and the complexity of many
             faces in arrangements of circles, pairwise intersecting
             pseudo-circles, parabolas, and families of homothetic copies
             of a fixed convex curve. We also obtain a variant of the
             Gallai-Sylvester theorem for arrangements of pairwise
             intersecting pseudo-circles, and a new lower bound for the
             number of distinct distances among n points in the plane
             under any simply-defined norm or convex distance
             function.},
   Key = {fds325422}
}

@article{fds22775,
   Author = {P.K. Agarwal and B. Bhattacharya and S. Sen},
   Title = {Output-sensitive algorithms for uniform partitions of
             points},
   Booktitle = {Algorithmica, in press},
   Year = {2002},
   Key = {fds22775}
}

@article{fds22780,
   Author = {P.K. Agarwal and M. Sharir},
   Title = {On the numbers of congruent simplices in a point
             set},
   Journal = {to appear in Discrete and Computational Geometry},
   Year = {2002},
   Key = {fds22780}
}

@article{fds22783,
   Author = {P.K. Agarwal (invited) and J. Basch and L.J. Guibas and J.
             Hershberger and L. Zhang},
   Title = {Deformable free space tiling for kinetic collision
             detection},
   Journal = {submitted to International Journal of Robotics},
   Year = {2002},
   Key = {fds22783}
}

@article{fds22785,
   Author = {P.K. Agarwal and C. M. Procopiuc and andand K. R.
             Varadarajan},
   Title = {An approximation algorithm for computing the two-line
             center},
   Journal = {submitted to Computational Geometry: Theory and
             Applications},
   Year = {2002},
   Key = {fds22785}
}

@article{fds22786,
   Author = {P.K. Agarwal and M. de Berg and S. Har-Peled and M. Overmars and M.
             Sharir and J. Vahrenhold},
   Title = {Reporting all intersecting pairs of polytopes in two and
             three dimensions},
   Journal = {submitted to Computational Geometry: Theory and
             Applications},
   Year = {2002},
   Key = {fds22786}
}

@article{fds23103,
   Author = {P.K. Agarwal and M. Bern and D. Eppstein and N. Amenta and P. Chew and K.
             Clarkson, T. Dey and D. P. Dobkin and H. Edelsbrunner and C. Grimm and L. P. Guibas and J. Harer and J. Hass and A. Hicks and C. K. Johnson and G.
             Lerman, D. Letscher and P. Plassmann and E. Sedgwick and J. Snoeyink and J. Weeks and C. Y},
   Title = {Emerging challenges in computational topology},
   Year = {2002},
   Key = {fds23103}
}

@article{fds22928,
   Author = {P.K. Agarwal and C. M. Procopiuc and S. Har-Peled},
   Title = {STAR-tree: An efficent self-adjusting index for moving
             points},
   Booktitle = {Fourth Workshop on Algorithms Engineering and
             Experiments},
   Year = {2002},
   Key = {fds22928}
}

@article{fds22929,
   Author = {P.K. Agarwal and C. M. Procopiuc and M. Jones and T.M.
             Murali},
   Title = {Classifcation using projective clustering},
   Journal = {ACM SIGMOD International Conference on Management of
             Data},
   Year = {2002},
   Key = {fds22929}
}

@article{fds22931,
   Author = {P.K. Agarwal and S. Govindarajan and L. Arge},
   Title = {CRB-tree: An eÆcient indexing scheme for range aggregate
             queries},
   Year = {2002},
   Key = {fds22931}
}

@article{fds22932,
   Author = {P.K. Agarwal and R. Klein and C. Knauer and M.
             Sharir},
   Title = {Computing the detour of polygonal curves},
   Year = {2002},
   Key = {fds22932}
}

@article{fds235372,
   Author = {Agarwal, PK and Hagerup, T and Ray, R and Sharir, M and Smid, MHM and Welzl, E},
   Title = {Translating a Planar Object to Maximize Point
             Containment.},
   Journal = {ESA},
   Volume = {2461},
   Pages = {42-53},
   Booktitle = {T. Hagerup, R. Ray, M. Sharir, and M. Smid},
   Publisher = {Springer},
   Editor = {Möhring, RH and Raman, R},
   Year = {2002},
   ISBN = {3-540-44180-8},
   url = {http://www.informatik.uni-trier.de/~ley/db/conf/esa/esa2002.html},
   Doi = {10.1007/3-540-45749-6_8},
   Key = {fds235372}
}

@article{fds235441,
   Author = {Procopiuc, CM and Jones, M and Agarwal, PK and Murali,
             TM},
   Title = {A Monte Carlo algorithm for fast projective
             clustering},
   Journal = {Proceedings / ACM-SIGMOD International Conference on
             Management of Data. ACM-Sigmod International Conference on
             Management of Data},
   Pages = {418-427},
   Year = {2002},
   ISSN = {0730-8078},
   Abstract = {We propose a mathematical formulation for the notion of
             optimal projective cluster, starting from natural
             requirements on the density of points in subspaces. This
             allows us to develop a Monte Carlo algorithm for iteratively
             computing projective clusters. We prove that the computed
             clusters are good with high probability. We implemented a
             modified version of the algorithm, using heuristics to speed
             up computation. Our extensive experiments show that our
             method is significantly more accurate than previous
             approaches. In particular, we use our techniques to build a
             classifier for detecting rotated human faces in cluttered
             images.},
   Key = {fds235441}
}

@article{fds235444,
   Author = {Agarwal, PK and Bhattacharya, BK and Sen, S},
   Title = {Improved algorithms for uniform partitions of
             points},
   Journal = {Algorithmica (New York)},
   Volume = {32},
   Number = {4},
   Pages = {521-539},
   Year = {2002},
   Abstract = {We consider the following one- and two-dimensional bucketing
             problems: Given a set 5 of n points in R1 or R2 and a
             positive integer b, distribute the points of S into b
             equal-size buckets so that the maximum number of points in a
             bucket is minimized. Suppose at most (n/b) + Δ points lie
             in each bucket in an optimal solution. We present algorithms
             whose time complexities depend on b and Δ No prior
             knowledge of Δ is necessary for our algorithms. For the
             one-dimensional problem, we give a deterministic algorithm
             that achieves a running time of O(b4(Δ2 + logn) + n). For
             the two-dimensional problem, we present a Monte Carlo
             algorithm that runs in subquadratic time for small values of
             b and Δ. The previous algorithms, by Asano and Tokuyama
             [1], searched the entire parameterized space and required Ω
             (n2) time in the worst case even for constant values of b
             and Δ. We also present a subquadratic algorithm for the
             special case of the two-dimensional problem when b =
             2.},
   Key = {fds235444}
}

@article{fds235445,
   Author = {Agarwal, PK and Berg, MD and Har-Peled, S and Overmars, MH and Sharir,
             M and Vahrenhold, J},
   Title = {Reporting intersecting pairs of convex polytopes in two and
             three dimensions},
   Journal = {Computational Geometry},
   Volume = {23},
   Number = {2},
   Pages = {195-207},
   Year = {2002},
   ISSN = {0925-7721},
   Abstract = {Let P= {Pi,..., Pm} be äset of m convex polytopes in Rd,
             ford = 2,3, with a total of n vertices. We present
             output-sensitive algorithms for reporting all k pairs of
             indices (i, j) such that Pj intersects Pj. For the planar
             case we describe a simple algorithm with running time
             OC/i4β Iog2+e n + k), for any constant e &gt; 0, and an
             improved randomized algorithm with expected running time
             O((/ilog;/i + £)&lt;(»)log«) (which is faster for small
             values of k). For d = 3, we present an O(«8/5+e +
             &amp;)-time algorithm, for any £&gt; 0. Our algorithms can
             be modified to count the number of intersecting pairs in
             O(/i4β log2+£ n) time for the planar case, and in
             O(/i8/5+e) time for the three-dimensional case. ©2002
             Elsevier Science B.V. All rights reserved.},
   Key = {fds235445}
}

@article{fds235446,
   Author = {Agarwal, PK and Sharir, M},
   Title = {The number of congruent simplices in a point
             set},
   Journal = {Discrete & Computational Geometry},
   Volume = {28},
   Number = {2},
   Pages = {123-150},
   Year = {2002},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/s00454-002-0727-x},
   Abstract = {For 1 ≤ k ≤ d -1, let fk(d) (n) be the maximum possible
             number of k-simplices spanned by a set of n points in ℝd
             that are congruent to a given k-simplex. We prove that f2(3)
             = O(n5/3 2O(α2(n))), f2(4)(n) = O(n2+ε), for any ε &gt;
             0, f2(5)(n) = Θ(n7/3), and f3(4) (n) = O(n20/9+ε), for any
             ε &gt; 0. We also derive a recurrence to bound fk(d)(n) for
             arbitrary values of k and d, and use it to derive the bound
             fk(d) (n) = O(nd/2+ε), for any ε &gt; 0, for d ≤ 7 and k
             ≤ d - 2. Following Erdos and Purdy, we conjecture that
             this bound holds for larger values of d as well, and for k
             ≤ d - 2.},
   Doi = {10.1007/s00454-002-0727-x},
   Key = {fds235446}
}

@article{fds235447,
   Author = {Agarwal, PK and Flato, E and Halperin, D},
   Title = {Polygon decomposition for efficient construction of
             Minkowski sums},
   Journal = {Computational Geometry},
   Volume = {21},
   Number = {1-2},
   Pages = {39-61},
   Year = {2002},
   ISSN = {0925-7721},
   Abstract = {Several algorithms for computing the Minkowski sum of two
             polygons in the plane begin by decomposing each polygon into
             convex subpolygons. We examine different methods for
             decomposing polygons by their suitability for efficient
             construction of Minkowski sums. We study and experiment with
             various well-known decompositions as well as with several
             new decomposition schemes. We report on our experiments with
             various decompositions and different input polygons. Among
             our findings are that in general: (i) triangulations are too
             costly, (ii) what constitutes a good decomposition for one
             of the input polygons depends on the other input polygon -
             consequently, we develop a procedure for simultaneously
             decomposing the two polygons such that a "mixed" objective
             function is minimized, (iii) there are optimal decomposition
             algorithms that significantly expedite the Minkowski-sum
             computation, but the decomposition itself is expensive to
             compute - in such cases simple heuristics that approximate
             the optimal decomposition perform very well. ©2002 Elsevier
             Science B.V. All rights reserved.},
   Key = {fds235447}
}

@article{fds235448,
   Author = {Agarwal, PK and Basch, J and Guibas, LJ and Hershberger, J and Zhang,
             L},
   Title = {Deformable free-space tilings for kinetic collision
             detection},
   Journal = {International Journal of Robotics Research},
   Volume = {21},
   Number = {3},
   Pages = {179-197},
   Year = {2002},
   url = {http://dx.doi.org/10.1177/027836402320556395},
   Abstract = {We present kinetic data structures for detecting collisions
             between a set of polygons that are moving continuously.
             Unlike classical collision detection methods that rely on
             bounding volume hierarchies, our method is based on
             deformable tilings of the free space surrounding the
             polygons. The basic shape of our tiles is that of a
             pseudo-triangle, a shape sufficiently flexible to allow
             extensive deformation, yet structured enough to make
             detection of self-collisions easy. We show different schemes
             for maintaining pseudo-triangulations as a kinetic data
             structure, and we analyze their performance. Specifically,
             we first describe an algorithm for maintaining a
             pseudo-triangulation of a point set, and show that the
             pseudo-triangulation changes only quadratically many times
             if points move along algebraic arcs of constant degree. In
             addition, by refining the pseudo-triangulation, we show
             triangulations of points that only change about O (n7/3)
             times for linear motion. We then describe an algorithm for
             maintaining a pseudo-triangulation of a set of convex
             polygons. Finally, we extend our algorithm to the general
             case of maintaining a pseudo-triangulation of a set of
             moving or deforming simple polygons.},
   Doi = {10.1177/027836402320556395},
   Key = {fds235448}
}

@article{fds235442,
   Author = {Agarwal, PK and Procopiuc, CM},
   Title = {Exact and approximation algorithms for clustering},
   Journal = {Algorithmica (New York)},
   Volume = {33},
   Number = {2},
   Pages = {201-226},
   Year = {2002},
   Abstract = {In this paper we present an nO(k1-1/d)-time algorithm for
             solving the k-center problem in ℝd, under L∞- and
             L2-metrics. The algorithm extends to other metrics, and to
             the discrete k-center problem. We also describe a simple (1
             + ε)-approximation algorithm for the k-center problem, with
             running time O(n log k) + (k/ε)O(k1-1/d). Finally, we
             present an nO(k1-1/d)-time algorithm for solving the
             L-capacitated k-center problem, provided that L =
             Ω(n/k1-1/d) or L = O(1).},
   Key = {fds235442}
}

@article{fds235443,
   Author = {Agarwal, PK and Har-Peled, S and Karia, M},
   Title = {Computing approximate shortest paths on convex
             polytopes},
   Journal = {Algorithmica (New York)},
   Volume = {33},
   Number = {2},
   Pages = {227-242},
   Publisher = {to appear in Algorithmica},
   Year = {2002},
   Abstract = {The algorithms for computing a shortest path on a polyhedral
             surface are slow, complicated, and numerically unstable. We
             have developed and implemented a robust and efficient
             algorithm for computing approximate shortest paths on a
             convex polyhedral surface. Given a convex polyhedral surface
             P in ℝ3, two points s, t ε P, and a parameter ε &gt; 0,
             it computes a path between s and t on P whose length is at
             most (1 + ε) times the length of the shortest path between
             those points. It constructs in time O(n/√ε) a graph of
             size O(1/ε4), computes a shortest path on this graph, and
             projects the path onto the surface in O(n/ε) time, where n
             is the number of vertices of P. In the postprocessing step
             we have added a heuristic that considerably improves the
             quality of the resulting path.},
   Key = {fds235443}
}

@article{fds235449,
   Author = {Agarwal, PK and Biedl, T and Lazard, S and Robbins, S and Suri, S and Whitesides, S},
   Title = {Curvature-constrained shortest paths in a convex
             polygon},
   Journal = {SIAM Journal on Computing},
   Volume = {31},
   Number = {6},
   Pages = {1814-1851},
   Year = {2002},
   url = {http://dx.doi.org/10.1137/S0097539700374550},
   Abstract = {Let B be a point robot moving in the plane, whose path is
             constrained to have curvature at most 1, and let P be a
             convex polygon with n vertices. We study the collision-free,
             optimal path-planning problem for B moving between two
             configurations inside P. (A configuration specifies both a
             location and a direction of travel.) We present an O(n2 log
             n) time algorithm for determining whether a collision-free
             path exists for B between two given configurations. If such
             a path exists, the algorithm returns a shortest one. We
             provide a detailed classification of curvature-constrained
             shortest paths inside a convex polygon and prove several
             properties of them, which are interesting in their own
             right. For example, we prove that any such shortest path is
             comprised of at most eight segments, each of which is a
             circular arc of unit radius or a straight-line segment. Some
             of the properties are quite general and shed some light on
             curvature-constrained shortest paths amid
             obstacles.},
   Doi = {10.1137/S0097539700374550},
   Key = {fds235449}
}

@article{fds235450,
   Author = {Agarwal, PK and Guibas, LJ and Edelsbrunner, H and Erickson, J and Isard, M and Har-Peled, S and Hershberger, J and Jensen, C and Kavraki,
             L and Koehl, P and Lin, M and Manocha, D and Metaxas, D and Mirtich, B and Mount, D and Muthukrishnan, S and Pai, D and Sacks, E and Snoeyink, J and Suri, S and Wolefson, O},
   Title = {Algorithmic issues in modeling motion},
   Journal = {ACM Computing Surveys},
   Volume = {34},
   Number = {4},
   Pages = {550-572},
   Year = {2002},
   ISSN = {0360-0300},
   url = {http://dx.doi.org/10.1145/592642.592647},
   Abstract = {This article is a survey of research areas in which motion
             plays a pivotal role. The aim of the article is to review
             current approaches to modeling motion together with related
             data structures and algorithms, and to summarize the
             challenges that lie ahead in producing a more unified theory
             of motion representation that would be useful across several
             disciplines. © 2002 ACM.},
   Doi = {10.1145/592642.592647},
   Key = {fds235450}
}

@article{fds235607,
   Author = {Agarwal, PK and Berg, MD and Gudmundsson, J and Hammar, M and Haverkort,
             HJ},
   Title = {Box-trees and R-trees with near-optimal query
             time},
   Journal = {Discrete & Computational Geometry},
   Volume = {28},
   Number = {3},
   Pages = {291-312},
   Year = {2002},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/s00454-002-2817-1},
   Abstract = {A box-tree is a bounding-volume hierarchy that uses
             axis-aligned boxes as bounding volumes. The query complexity
             of a box-tree with respect to a given type of query is the
             maximum number of nodes visited when answering such a query.
             We describe several new algorithms for constructing
             box-trees with small worst-case query complexity with
             respect to queries with axis-parallel boxes and with points.
             We also prove lower bounds on the worst-case query
             complexity for box-trees, which show that our results are
             optimal or close to optimal. Finally, we present algorithms
             to convert box-trees to R-trees, resulting in R-trees with
             (almost) optimal query complexity.},
   Doi = {10.1007/s00454-002-2817-1},
   Key = {fds235607}
}

@article{fds235375,
   Author = {Agarwal, PK and Har-Peled, S and Mustafa, NH and Wang,
             Y},
   Title = {Near-Linear Time Approximation Algorithms for Curve
             Simplification.},
   Journal = {ESA},
   Volume = {2461},
   Pages = {29-41},
   Publisher = {Springer},
   Editor = {Möhring, RH and Raman, R},
   Year = {2002},
   ISBN = {3-540-44180-8},
   url = {http://www.informatik.uni-trier.de/~ley/db/conf/esa/esa2002.html},
   Doi = {10.1007/3-540-45749-6_7},
   Key = {fds235375}
}

@article{fds235376,
   Author = {Procopiuc, CM and Agarwal, PK and Har-Peled, S},
   Title = {STAR-Tree: An Efficient Self-Adjusting Index for Moving
             Objects.},
   Journal = {ALENEX},
   Volume = {2409},
   Pages = {178-193},
   Publisher = {Springer},
   Editor = {Mount, DM and Stein, C},
   Year = {2002},
   ISBN = {3-540-43977-3},
   url = {http://www.informatik.uni-trier.de/~ley/db/conf/alenex/alenex2002.html},
   Doi = {10.1007/3-540-45643-0_14},
   Key = {fds235376}
}

@article{fds235377,
   Author = {Agarwal, PK and Govindarajan, S and Muthukrishnan,
             S},
   Title = {Range Searching in Categorical Data: Colored Range Searching
             on Grid.},
   Journal = {ESA},
   Volume = {2461},
   Pages = {17-28},
   Publisher = {Springer},
   Editor = {Möhring, RH and Raman, R},
   Year = {2002},
   ISBN = {3-540-44180-8},
   url = {http://www.informatik.uni-trier.de/~ley/db/conf/esa/esa2002.html},
   Doi = {10.1007/3-540-45749-6_6},
   Key = {fds235377}
}

@article{fds235378,
   Author = {Agarwal, PK and Gao, J and Guibas, LJ},
   Title = {Kinetic Medians and kd-Trees.},
   Journal = {ESA},
   Volume = {2461},
   Pages = {5-16},
   Publisher = {Springer},
   Editor = {Möhring, RH and Raman, R},
   Year = {2002},
   ISBN = {3-540-44180-8},
   url = {http://www.informatik.uni-trier.de/~ley/db/conf/esa/esa2002.html},
   Doi = {10.1007/3-540-45749-6_5},
   Key = {fds235378}
}

@article{fds235379,
   Author = {Agarwal, PK and Procopiuc, CM and Varadarajan,
             KR},
   Title = {Approximation Algorithms for k-Line Center.},
   Journal = {ESA},
   Volume = {2461},
   Pages = {54-63},
   Publisher = {Springer},
   Editor = {Möhring, RH and Raman, R},
   Year = {2002},
   ISBN = {3-540-44180-8},
   url = {http://www.informatik.uni-trier.de/~ley/db/conf/esa/esa2002.html},
   Doi = {10.1007/3-540-45749-6_9},
   Key = {fds235379}
}

@article{fds316733,
   Author = {Agarwal, PK and Sharir, M},
   Title = {Pseudo-line arrangements: duality, algorithms, and
             applications.},
   Journal = {SODA},
   Pages = {800-809},
   Booktitle = {Thirteenth Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Publisher = {ACM/SIAM},
   Editor = {Eppstein, D},
   Year = {2002},
   ISBN = {0-89871-513-X},
   url = {http://dl.acm.org/citation.cfm?id=545381},
   Key = {fds316733}
}

@article{fds316127,
   Author = {Agarwal, PK and Edelsbrunner, H and Wang, Y},
   Title = {Computing the writhing number of a polygonal
             knot.},
   Journal = {SODA},
   Pages = {791-799},
   Booktitle = {Thirteenth Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Publisher = {ACM/SIAM},
   Editor = {Eppstein, D},
   Year = {2002},
   ISBN = {0-89871-513-X},
   url = {http://dl.acm.org/citation.cfm?id=545381},
   Key = {fds316127}
}

@article{fds1159,
   Author = {L. Guibas and J. Hershberger and E. Veach and P.K.
             Agarwal},
   Title = {Maintaining structures for moving points},
   Journal = {Discrete and Computational Geometry},
   Volume = {26},
   Pages = {253-374},
   Year = {2001},
   Key = {fds1159}
}

@article{fds1161,
   Author = {K. R. Varadarajan and P.K. Agarwal},
   Title = {Approximating shortest paths on polyhedral
             terrains},
   Journal = {SIAM Journal on Computing},
   Volume = {30},
   Pages = {1321-1340},
   Year = {2001},
   Key = {fds1161}
}

@article{fds1162,
   Author = {H. Wang and P.K. Agarwal},
   Title = {Approximation algorithms for shortest paths with bounded
             curvature},
   Journal = {SIAM Journal on Computing},
   Volume = {30},
   Pages = {1739-1772},
   Year = {2001},
   Key = {fds1162}
}

@article{fds1781,
   Author = {J. Basch and L. J. Guibas and J. Hershberger and L. Zhang and P.K.
             Agarwal},
   Title = {Deformable free space tiling for kinetic collision
             detection},
   Pages = {83-96},
   Booktitle = {Algorithmic Foundations of Robotics},
   Publisher = {A.K. Peters, Natick, MA,},
   Editor = {B. Donald and K. Lynch and D. Russ},
   Year = {2001},
   Key = {fds1781}
}

@article{fds1782,
   Author = {S. Sen and P.K. Agarwal},
   Title = {Randomized algorithms for geometric optimization},
   Pages = {151-201},
   Booktitle = {Handbook of Randomized Computation},
   Publisher = {Kluwar Academic Press, The Netherlands},
   Editor = {J. Pardalos and S. Rajasekaran and J. Reif and J.
             Rolim},
   Year = {2001},
   Key = {fds1782}
}

@article{fds22920,
   Author = {P.K. Agarwal and L. Arge and J. Vahrenhold},
   Title = {Time responsive indexing schemes for moving
             points},
   Booktitle = {Seventh Workshop on Algorithms and Data Structures},
   Year = {2001},
   Key = {fds22920}
}

@article{fds23101,
   Author = {P.K. Agarwal and D. Halperin and R. Pollack},
   Title = {Guest editors' foreword},
   Journal = {Discrete and Computational Geometry},
   Volume = {25},
   Pages = {505-506},
   Year = {2001},
   Key = {fds23101}
}

@article{fds23102,
   Author = {P.K. Agarwal},
   Title = {Guest editors' foreword},
   Journal = {Discrete and Computational Geometry},
   Volume = {26},
   Pages = {185-186},
   Year = {2001},
   Key = {fds23102}
}

@article{fds22917,
   Author = {P.K. Agarwal},
   Title = {On the numbers of congruent simplices in a point
             set},
   Booktitle = {Seventeenth Annual Symposium on Computational
             Geometry},
   Year = {2001},
   Key = {fds22917}
}

@article{fds22922,
   Author = {P.K. Agarwal and M. de Berg and S. Har-Peled and M. Overmars and M.
             Sharir and J. Vahrenhold},
   Title = {Reporting all intersecting pairs of polytopes in two and
             three dimensions},
   Booktitle = {Seventh Workshop on Algorithms and Data Structures},
   Year = {2001},
   Key = {fds22922}
}

@article{fds22923,
   Author = {P.K. Agarwal and S. Har-Peled and Y.Wang},
   Title = {Occlusion culling for fast walkthrough in urban
             areas},
   Booktitle = {Eurographics},
   Year = {2001},
   Key = {fds22923}
}

@article{fds22924,
   Author = {P.K. Agarwal and M. Dietze and S. Govindarajan and J.
             Clark},
   Title = {The extinction debt revisited: population dynamics in a
             continuous space model},
   Booktitle = {Ecological Society of America Annual Meeting},
   Year = {2001},
   Key = {fds22924}
}

@article{fds235435,
   Author = {Agarwal, PK and Sharir, M},
   Title = {On the number of congruent simplices in a point
             set},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {1-9},
   Year = {2001},
   Abstract = {We derive improved bounds on the number of k-dimensional
             simplices spanned by a set of n points in Rd that are
             congruent to a given k-simplex, for k ≤ d - 1. Let
             fk(d)(n) be the maximum number of k-simplices spanned by a
             set of n points in Rd that are congruent to a given
             k-simplex. We prove that f2(3)(n) = O(n5/3 · 2O(α(2)(n))),
             f2(4) (n) = O(n2+ε), f2(5) (n) = Θ(n7/3), and f3(4) (n) =
             O(n9/4+ε). We also derive a recurrence to bound fk(d)(n)
             for arbitrary values of k and d, and use it to derive the
             bound fk(d) (n) = O(nd/2+ε for d ≤ 7 and k ≤ d - 2.
             Following Erdös and Purdy, we conjecture that this bound
             holds for larger values of d as well, and for k ≤ d -
             2.},
   Key = {fds235435}
}

@article{fds235439,
   Author = {Agarwal, PK and Aronov, B and Sharir, M},
   Title = {Exact and approximation algorithms for minimum-width
             cylindrical shells},
   Journal = {Discrete and Computanional Geometry},
   Volume = {26},
   Number = {3},
   Pages = {307-320},
   Year = {2001},
   Abstract = {Let S be a set of n points in ℝ3. Let ω* be the width
             (i.e., thickness) of a minimum-width infinite cylindrical
             shell (the region between two co-axial cylinders) containing
             S. We first present an O(n5)-time algorithm for computing
             ω*, which as far as we know is the first nontrivial
             algorithm for this problem. We then present an O(n2+δ)-time
             algorithm, for any δ &gt; 0, that computes a cylindrical
             shell of width at most 56ω* containing S.},
   Key = {fds235439}
}

@article{fds235440,
   Author = {Agarwal, PK and Guibas, LJ and Hershberger, J and Veach,
             E},
   Title = {Maintaining the extent of a moving point
             set},
   Journal = {Discrete and Computanional Geometry},
   Volume = {26},
   Number = {3},
   Pages = {353-374},
   Year = {2001},
   Abstract = {Let S be a set of n moving points in the plane. We give new
             efficient and compact kinetic data structures for
             maintaining the diameter, width, and smallest area or
             perimeter bounding rectangle of S. If the points in S move
             with algebraic motions, these structures process O(n2+δ)
             events. We also give constructions showing that Ω(n2)
             combinatorial changes are possible for these extent
             functions even if each point is moving with constant
             velocity. We give a similar construction and upper bound for
             the convex hull, improving known results.},
   Key = {fds235440}
}

@article{fds235373,
   Author = {Agarwal, PK and Arge, L and Procopiuc, O and Vitter,
             JS},
   Title = {A Framework for Index Bulk Loading and Dynamization.},
   Journal = {ICALP},
   Volume = {2076},
   Pages = {115-127},
   Booktitle = {Twenty-Eighth International Colloquium on Automata,
             Languages, and Programming},
   Publisher = {Springer},
   Editor = {Orejas, F and Spirakis, PG and Leeuwen, JV},
   Year = {2001},
   ISBN = {3-540-42287-0},
   url = {http://www.informatik.uni-trier.de/~ley/db/conf/icalp/icalp2001.html},
   Doi = {10.1007/3-540-48224-5_10},
   Key = {fds235373}
}

@article{fds235436,
   Author = {Agarwal, PK and Hal-Peled, S},
   Title = {Maintaining approximate extent measures of moving
             points},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Pages = {148-157},
   Booktitle = {Twelfth Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Year = {2001},
   Abstract = {We present approximation algorithms for maintaining various
             descriptors of the extent of moving points in R d. We first
             describe a data structure for maintaining the smallest
             orthogonal rectangle containing the point set. We then use
             this data structure to maintain the approximate diameter,
             smallest enclosing disk, width, and smallest area or
             perimeter bounding rectangle of a set of moving points in R
             2 so that the number of events is only a constant. This
             contrasts with &amp;OHgr;(n 2) events that data structures
             for the maintenance of those exact properties have to
             handle. Copyright © 2009 ACM, Inc.},
   Key = {fds235436}
}

@article{fds235437,
   Author = {Agarwal, PK and Berg, MD and Gudmundsson, J and Hammar, M and Haverkort,
             HJ},
   Title = {Box-trees and R-trees with near-optimal query
             time},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {124-133},
   Booktitle = {Seventeenth Annual Symposium on Computational
             Geometry},
   Year = {2001},
   Abstract = {A box-tree is a bounding-volume hierarchy that uses
             axis-aligned boxes as bounding volumes. The query complexity
             of a box-tree with respect to a given type of query is the
             maximum number of nodes visited when answering such a query.
             We describe several new algorithms for constructing
             box-trees with small worst-case query complexity with
             respect to queries with axis-parallel boxes and with points.
             We also prove lower bounds on the worst-case query
             complexity for box-trees, which show that our results are
             optimal or close to optimal. Finally, we present algorithms
             to convert box-trees to R-trees, resulting in R-trees with
             (almost) optimal query complexity.},
   Key = {fds235437}
}

@article{fds235438,
   Author = {Agarwal, PK and Collins, AD and Harer, JL},
   Title = {Minimal trap design},
   Journal = {Proceedings - IEEE International Conference on Robotics and
             Automation},
   Volume = {3},
   Pages = {2243-2248},
   Booktitle = {IEEE Conference on Robotics and Automation},
   Year = {2001},
   Abstract = {This paper addresses the issue of trap design for sensorless
             automated assembly. First, we present a simple algorithm
             that determines in O(nm α(nm) log(nm)) time whether an
             n-sided polygonal part will fall through an m-sided
             polygonal trap. We then introduce the notion of a minimal
             trap for a polygonal part, and develop an algorithm to
             design a family of minimal feeders built from these traps.
             The algorithm runs in O(kn3+ε) time, where k is the number
             of stable orientations of P. Moreover, it is complete in the
             sense that we can always find a feeder, provided that one
             exists that rejects and supports the appropriate poses of
             the part.},
   Key = {fds235438}
}

@article{fds235606,
   Author = {Agarwal, PK and Aronov, B and Sharir, M},
   Title = {On the complexity of many faces in arrangements of
             circles},
   Journal = {Annual Symposium on Foundations of Computer Science -
             Proceedings},
   Pages = {74-83},
   Booktitle = {Forty Second Annual Symposium on Foundations of Computer
             Science},
   Year = {2001},
   Abstract = {The many-faces problem for arrangements of circles in the
             plane was studied. The complexity of many faces and the
             algorithmic problem arised in a variety of problems
             including three-dimensional arrangements. The improved
             bounds on the complexity of m distinct faces in an
             arrangement of n circles were obtained. The bounds coincide
             with the best known bounds for the number of incidences
             between m points and n circles.},
   Key = {fds235606}
}

@article{fds313243,
   Author = {Agarwal, PK and Arge, L and Vahrenhold, J},
   Title = {Time Responsive External Data Structures for Moving
             Points.},
   Journal = {WADS},
   Volume = {2125},
   Pages = {50-61},
   Publisher = {Springer},
   Editor = {Dehne, FKHA and Sack, J-R and Tamassia, R},
   Year = {2001},
   ISBN = {3-540-42423-7},
   url = {http://www.informatik.uni-trier.de/~ley/db/conf/wads/wads2001.html},
   Doi = {10.1007/3-540-44634-6_6},
   Key = {fds313243}
}

@article{fds313241,
   Author = {Agarwal, PK and Berg, MD and Har-Peled, S and Overmars, MH and Sharir,
             M and Vahrenhold, J},
   Title = {Reporting Intersecting Pairs of Polytopes in Two and Three
             Dimensions.},
   Journal = {WADS},
   Volume = {2125},
   Pages = {122-134},
   Publisher = {Springer},
   Editor = {Dehne, FKHA and Sack, J-R and Tamassia, R},
   Year = {2001},
   ISBN = {3-540-42423-7},
   url = {http://www.informatik.uni-trier.de/~ley/db/conf/wads/wads2001.html},
   Doi = {10.1007/3-540-44634-6_12},
   Key = {fds313241}
}

@article{fds313237,
   Author = {Agarwal, PK and Guibas, LJ and Har-Peled, S and Rabinovitch, A and Sharir, M},
   Title = {Computing the penetration depth of two convex polytopes in
             3d},
   Journal = {Lecture notes in computer science},
   Volume = {1851},
   Pages = {328-338},
   Booktitle = {Seventh Scandinavian Workshop on Algorithm
             Theory},
   Year = {2000},
   Month = {January},
   ISBN = {3540676902},
   ISSN = {0302-9743},
   url = {http://dx.doi.org/10.1007/3-540-44985-X},
   Abstract = {© Springer-Verlag Berlin Heidelberg 2000. Let A and B be
             two convex polytopes in R 3 with m and n facets,
             respectively. The penetration depth of A and B, denoted as
             π(A, B), is the minimum distance by which A has to be
             translated so that A and B do not intersect. We present a
             randomized algorithm that computes π(A,B) in O(m 3/4+ɛ n
             3/4+ɛ + m 1+ɛ + n 1+ɛ ) expected time, for any constant
             ɛ > 0. It also computes a vector t such that ||t|| =
             π(A,B) and int(A + t) ⊓ B = θ. We show that if the
             Minkowski sum B ⊗ (—A) has K facets, then the expected
             running time of our algorithm is O (K 1/2+ɛ m 1/4 n 1/4 + m
             1+ɛ + n 1+ɛ ), for any ɛ > 0. We also present an
             approximation algorithm for computing π(A,B). For any δ >
             0, we can compute, in time O(m + n + (log 2 (m + n))/δ), a
             vector t such that ||t|| < (1 + δ)π(A, B) and int(A +t)
             ⊓ B = θ. Our result also gives a δ-approximation
             algorithm for computing the width of A in time O(n + (log 2
             n)/δ), which is simpler and slightly faster than the recent
             algorithm by Chan.},
   Doi = {10.1007/3-540-44985-X},
   Key = {fds313237}
}

@article{fds1163,
   Author = {L. J. Guibas and S. Har-Peled and A. Rabinovitch and M. Sharir and P.K. Agarwal},
   Title = {Computing the penetration depth of two convex polytopes in
             3D},
   Journal = {Nordic J. Computing},
   Volume = {7},
   Pages = {227-240},
   Year = {2000},
   Key = {fds1163}
}

@article{fds1164,
   Author = {B. Aronov and S. Har-Peled and M. Sharir and P.K.
             Agarwal},
   Title = {Exact and approximation algorithms for the minimum width
             annuli and shells},
   Journal = {Discrete and Computational Geometry},
   Volume = {24},
   Pages = {687-705},
   Year = {2000},
   Key = {fds1164}
}

@article{fds1777,
   Author = {M. Sharir and P.K. Agarwal},
   Title = {Davenport-Schinzel sequences and their geometric
             applications},
   Pages = {1-47},
   Booktitle = {Handbook of Computational Geometry},
   Publisher = {North-Holland, New York},
   Editor = {J.-R. Sack and J. Urrutia},
   Year = {2000},
   Key = {fds1777}
}

@article{fds1779,
   Author = {M. Sharir and P.K. Agarwal},
   Title = {Arrangements and their applications},
   Pages = {49-119},
   Booktitle = {Handbook of Computational Geometry},
   Publisher = {North-Holland, New York},
   Editor = {J.-R. Sack and J. Urrutia},
   Year = {2000},
   Key = {fds1779}
}

@article{fds1780,
   Author = {L. Knipping and M. van Kreveld and T. Strijk and A. Wolff and P.K.
             Agarwal},
   Title = {A simple and eÆcient algorithm for high quality line
             labeling},
   Pages = {147-159},
   Booktitle = {Innovations in GIS VII: GeoComputation},
   Publisher = {Taylor and Francis, London},
   Editor = {P. M. Atkinson and D. Martin},
   Year = {2000},
   Key = {fds1780}
}

@article{fds1792,
   Author = {K. R. Varadarajan and P.K. Agarwal},
   Title = {Efficient algorithms for polygon simplification},
   Journal = {Discrete and Computational Geometry},
   Volume = {23},
   Pages = {273-291},
   Year = {2000},
   Key = {fds1792}
}

@article{fds22909,
   Author = {P.K. Agarwal and J. Basch and L. J. Guibas and J. Hershberger and L.
             Zhang},
   Title = {Deformable free space tiling for kinetic collision
             detection},
   Booktitle = {Fourth Workshop on Algorithmic Foundations of
             Robotics},
   Year = {2000},
   Key = {fds22909}
}

@article{fds235380,
   Author = {Agarwal, PK and Basch, J and Berg, MD and Guibas, LJ and Hershberger,
             J},
   Title = {Lower Bounds for Kinetic Planar Subdivisions.},
   Journal = {Discrete & Computational Geometry},
   Volume = {24},
   Pages = {721-733},
   Year = {2000},
   url = {http://dx.doi.org/10.1007/s004540010060},
   Doi = {10.1007/s004540010060},
   Key = {fds235380}
}

@article{fds235427,
   Author = {Varadarajan, KR and Agarwal, PK},
   Title = {Approximating shortest paths on a nonconvex
             polyhedron},
   Journal = {SIAM Journal on Computing},
   Volume = {30},
   Number = {4},
   Pages = {1321-1340},
   Year = {2000},
   ISSN = {0097-5397},
   Abstract = {We present an approximation algorithm that, given the
             boundary P of a simple, nonconvex polyhedron in ℝ3 and two
             points s and t on P, constructs a path on P between s and t
             whose length is at most 7(1 + ε)dP(s, t), where dP(s, t) is
             the length of the shortest path between s and t on P, and ε
             &gt; 0 is an arbitrarily small positive constant. The
             algorithm runs in O(n5/3 log5/3 n) time, where n is the
             number of vertices in P. We also present a slightly faster
             algorithm that runs in O(n8/5 log8/5 n) time and returns a
             path whose length is at most 15(1 + ε)dP(s, t). © 2000
             Society for Industrial and Applied Mathematics.},
   Key = {fds235427}
}

@article{fds235428,
   Author = {Agarwal, PK and Wanq, H},
   Title = {Approximation algorithms for curvature-constrained shortest
             paths},
   Journal = {SIAM Journal on Computing},
   Volume = {30},
   Number = {6},
   Pages = {1739-1772},
   Year = {2000},
   ISSN = {0097-5397},
   Abstract = {Let B be a point robot in the plane, whose path is
             constrained to have curvature of at most 1, and let fi be a
             set of polygonal obstacles with n vertices. We study the
             collision-free, optimal path-planning problem for D. Given a
             parameter e, we present an O((n2/e4)logn)-time algorithm for
             computing a collision-free, curvature-constrained path
             between two given positions, whose length is at most (l+s)
             times the length of an optimal path, provided it is robust.
             (Roughly speaking, a path is robust if it remains
             collision-free even if certain positions on the path are
             perturbed). Our algorithm thus runs significantly faster
             than the previously best known algorithm by Jacobs and Canny
             whose running time is O((2;)2 + rc2("L)logn), where L is the
             total edge length of the obstacles. More importantly, the
             running time of our algorithm does not depend on the size of
             obstacles. The path returned by this algorithm is not
             necessarily robust. We present an O((n2-5/e4) logn)-time
             algorithm that returns a robust path whose length is at most
             (1 + s) times the length of an optimal path, provided it is
             robust. We also give a stronger characterization of
             curvature-constrained shortest paths, which, apart from
             being crucial for our algorithm, is interesting in its own
             right. Roughly speaking, we prove that, except in some
             special cases, a shortest path touches obstacles at points
             that have a visible vertex nearby. © 2001 Society for
             Industrial and Applied Mathematics.},
   Key = {fds235428}
}

@article{fds235429,
   Author = {Agarwal, PK and Varadarajan, KR},
   Title = {Efficient algorithms for approximating polygonal
             chains},
   Journal = {Discrete and Computanional Geometry},
   Volume = {23},
   Number = {2},
   Pages = {273-291},
   Year = {2000},
   Abstract = {We consider the problem of approximating a polygonal chain C
             by another polygonal chain C′ whose vertices are
             constrained to be a subset of the set of vertices of C. The
             goal is to minimize the number of vertices needed in the
             approximation C′. Based on a framework introduced by Imai
             and Iri [25], we define an error criterion for measuring the
             quality of an approximation. We consider two problems. (1)
             Given a polygonal chain C and a parameter ε ≥ 0, compute
             an approximation of C, among all approximations whose error
             is at most ε, that has the smallest number of vertices. We
             present an O(n4/3+δ)-time algorithm to solve this problem,
             for any δ &gt; 0; the constant of proportionality in the
             running time depends on δ. (2) Given a polygonal chain C
             and an integer k, compute an approximation of C with at most
             k vertices whose error is the smallest among all
             approximations with at most k vertices. We present a simple
             randomized algorithm, with expected running time O(n4/3+δ),
             to solve this problem.},
   Key = {fds235429}
}

@article{fds235430,
   Author = {Agarwal, PK and Guibas, LJ and Murali, TM and Vitter,
             JS},
   Title = {Cylindrical static and kinetic binary space
             partitions},
   Journal = {Computational Geometry: Theory and Applications},
   Volume = {16},
   Number = {2},
   Pages = {103-127},
   Year = {2000},
   Abstract = {We describe the first known algorithm for efficiently
             maintaining a Binary Space Partition (BSP) for n
             continuously moving segments in the plane, whose interiors
             remain disjoint throughout the motion. Under reasonable
             assumptions on the motion, we show that the total number of
             times this BSP changes is O(n2), and that we can update the
             BSP in O(log n) expected time per change. Throughout the
             motion, the expected size of the BSP is O(n log n). We also
             consider the problem of constructing a BSP for n static
             triangles with pairwise-disjoint interiors in ℝ3. We
             present a randomized algorithm that constructs a BSP of size
             O(n2) in O(n2log2 n) expected time. We also describe a
             deterministic algorithm that constructs a BSP of size O((n +
             k) log2 n) and height O(log n) in O((n + k) log3 n) time,
             where k is the number of intersection points between the
             edges of the projections of the triangles onto the xy-plane.
             This is the first known algorithm that constructs a BSP of
             O(log n) height for disjoint triangles in ℝ3. © 2000
             Elsevier Science B.V. All rights reserved.},
   Key = {fds235430}
}

@article{fds235431,
   Author = {Agarwal, PK and Grove, EF and Murali, TM and Vitter,
             JS},
   Title = {Binary space partitions for fat rectangles},
   Journal = {SIAM Journal on Computing},
   Volume = {29},
   Number = {5},
   Pages = {1422-1448},
   Year = {2000},
   url = {http://dx.doi.org/10.1137/S0097539797320578},
   Abstract = {We consider the practical problem of constructing binary
             space partitions (BSPs) for a set S of n orthogonal,
             nonintersecting, two-dimensional rectangles in R3 such that
             the aspect ratio of each rectangle in S is at most α, for
             some constant α≥1. We present an n2O(√log n)-time
             algorithm to build a binary space partition of size
             n2O(√log n) for S. We also show that if m of the n
             rectangles in S have aspect ratios greater than α, we can
             construct a BSP of size n√m2O(√log n) for S in
             n√m2O(√log n) time. The constants of proportionality in
             the big-oh terms are linear in log α. We extend these
             results to cases in which the input contains nonorthogonal
             or intersecting objects.},
   Doi = {10.1137/S0097539797320578},
   Key = {fds235431}
}

@article{fds235432,
   Author = {Agarwal, PK and Sharir, M},
   Title = {Pipes, Cigars, and Kreplach: The Union of Minkowski Sums in
             Three Dimensions},
   Journal = {Discrete and Computanional Geometry},
   Volume = {24},
   Number = {4},
   Pages = {645-685},
   Year = {2000},
   Abstract = {Let Ω be a set of pairwise-disjoint polyhedral obstacles in
             ℝ3 with a total of n vertices, and let B be a ball in
             ℝ3. We show that the combinatorial complexity of the free
             configuration space ℱ of B amid Ω, i.e., (the closure of)
             the set of all placements of B at which B does not intersect
             any obstacle, is O(n2+ε), for any ε &gt; 0; the constant
             of proportionality depends on ε. This upper bound almost
             matches the known quadratic lower bound on the maximum
             possible complexity of ℱ. The special case in which Ω is
             a set of lines is studied separately. We also present a few
             extensions of this result, including a randomized algorithm
             for computing the boundary of ℱ whose expected running
             time is O(n2+ε), for any ε &gt; 0.},
   Key = {fds235432}
}

@article{fds235433,
   Author = {Agarwal, PK and Arge, L and Erickson, J and Franciosa, PG and Vitter,
             JS},
   Title = {Efficient searching with linear constraints},
   Journal = {Journal of Computer and System Sciences},
   Volume = {61},
   Number = {2},
   Pages = {194-216},
   Year = {2000},
   url = {http://dx.doi.org/10.1006/jcss.2000.1709},
   Abstract = {We show how to preprocess a set S of points in Rd into an
             external memory data structure that efficiently supports
             linear-constraint queries. Each query is the form of linear
             constraints xd≤a0+Σi = 1d-1 aixi; the data structure must
             report all the points of S that satisfy, the constraint.
             This problem is called halfspace range searching in the
             computational geometry literature. Our goal is to minimize
             the number of disk blocks required to store the data
             structure and the number of disk accesses (I/Os) required to
             answer a query. For d = 2, we present the first data
             structure that uses linear space and answers
             linear-constraint queries using an optimal number of I/Os in
             the worst case. For d = 3, we present a near-linear-size
             data structure that answers queries using an optimal number
             of I/Os on the average. We present linear-size data
             structures that can answer d-dimensional linear-constraint
             queries (and even more general d-dimensional simplex
             queries) efficiently in the worst case. For the d = 3 case,
             we also show how to obtain trade-offs between space and
             query time.},
   Doi = {10.1006/jcss.2000.1709},
   Key = {fds235433}
}

@article{fds235434,
   Author = {Agarwal, PK and Aronov, B and Har-Peled, S and Sharir,
             M},
   Title = {Approximation Algorithms for Minimum-Width Annuli and
             Shells},
   Journal = {Discrete and Computanional Geometry},
   Volume = {24},
   Number = {4},
   Pages = {687-705},
   Year = {2000},
   Abstract = {Let S be a set of n points in ℝd. The "roundness" of S can
             be measured by computing the width ωz.ast; = ω*(S) of the
             thinnest spherical shell (or annulus in ℝ2) that contains
             S. This paper contains two main results related to computing
             an approximation of ω*: (i) For d = 2, we can compute in
             O(n log n) time an annulus containing S whose width is at
             most 2ω*(S). We extend this algorithm, so that, for any
             given parameter ε &gt; 0, an annulus containing S whose
             width is at most (1 + ε)ω* is computed in time O(n log n +
             n/ε2). (ii) For d ≥ 3, given a parameter ε &gt; 0, we
             can compute a shell containing S of width at most (1 +
             ε)ω* either in time O((n/εd) log(Δ/ω*ε)) or in time
             O((n/εd-2)(log n + 1/ε) log(Δ/ω*ε)), where Δ is the
             diameter of S.},
   Key = {fds235434}
}

@article{fds235382,
   Author = {Agarwal, PK and Flato, E and Halperin, D},
   Title = {Polygon Decomposition for Efficient Construction of
             Minkowski Sums.},
   Journal = {ESA},
   Volume = {1879},
   Pages = {20-31},
   Booktitle = {Eighth European Symposium on Algorithms},
   Publisher = {Springer},
   Editor = {Paterson, M},
   Year = {2000},
   ISBN = {3-540-41004-X},
   url = {http://www.informatik.uni-trier.de/~ley/db/conf/esa/esa2000.html},
   Doi = {10.1007/3-540-45253-2_3},
   Key = {fds235382}
}

@article{fds235422,
   Author = {Agarwal, PK and Arge, L and Erickson, J},
   Title = {Indexing moving points},
   Journal = {Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on
             Principles of Database Systems},
   Pages = {175-186},
   Booktitle = {Nineteenth Annual Symposium on Principles of Database
             Systems},
   Year = {2000},
   Abstract = {We propose three indexing schemes for storing a set S of N
             points in the plane, each moving along a linear trajectory,
             so that a query of the following form can be answered
             quickly: Given a rectangle R and a real value tq, report all
             K points of S that lie inside R at time tq. We first present
             an indexing structure that, for any given constant εGRT0,
             uses O(N/B) disk blocks, where B is the block size, and
             answers a query in O((N/B)1/2+ε+K/B) I/Os. It can also
             report all the points of S that lie inside R during a given
             time interval. A point can be inserted or deleted, or the
             trajectory of a point can be changed, in O(logB2 N) I/Os.
             Next, we present a general approach that improves the query
             time if the queries arrive in chronological order, by
             allowing the index to evolve over time. We obtain a tradeoff
             between the query time and the number of times the index
             needs to be updated as the points move. We also describe an
             indexing scheme in which the number of I/Os required to
             answer a query depends monotonically on the difference
             between tq and the current time. Finally, we develop an
             efficient indexing scheme to answer approximate
             nearest-neighbor queries among moving points.},
   Key = {fds235422}
}

@article{fds235423,
   Author = {Agarwal, PK and Har-Peled, S and Karia, M},
   Title = {Computing approximate shortest paths on convex
             polytopes},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {270-279},
   Booktitle = {Sixteenth Annual Symposium on Computational
             Geometry},
   Year = {2000},
   Abstract = {The algorithms for computing a shortest path on a polyhedral
             surface are slow, complicated, and numerically unstable. We
             have developed and implemented a robust and efficient
             algorithm for computing approximate shortest paths on a
             convex polyhedral surface. Given a convex polyhedral surface
             P in R3, two points s, t∈P, and a parameter ε&gt;0, it
             computes a path between s and t on P whose length is at most
             (1+ε) times the length of the shortest path between those
             points. It first constructs in time O(n/√ε) a graph of
             size O(1/ε4), computes a shortest path on this graph, and
             projects the path onto the surface in O(n/ε) time, where n
             is the number of vertices of P. In the post-processing we
             have added a heuristic that considerably improves the
             quality of the resulting path.},
   Key = {fds235423}
}

@article{fds235424,
   Author = {Agarwal, PK and Procopiuc, CM},
   Title = {Approximation algorithms for projective clustering},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Pages = {538-547},
   Booktitle = {Eleventh Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Year = {2000},
   Abstract = {We consider the following two instances of the projective
             clustering problem: Given a set S of n points in Rd and an
             integer k&gt;0, cover S by k hyper-strips (resp.
             hyper-cylinders) so that the maximum width of a hyper-strip
             (resp., the maximum diameter of a hyper-cylinder) is
             minimized. Let w* be the smallest value so that S can be
             covered by k hyper-strips (resp. hyper-cylinders), each of
             width (resp. diameter) at most w*. It is NP-hard to compute
             k planar strips of width even at most Cw*, for any constant
             C&gt;0. This paper contains four main results related to
             projective clustering: (i) For d = 2, we present a
             randomized algorithm that computes O(k log k) strips of
             width at most 6 w* that cover S. Its expected running time
             is O(nk2 log4 n) if k2 log k≤n; for larger values of k,
             the expected running time is O(n2/3 k8/3 log4 n). We also
             propose another algorithm that computes a cover of S by O(k
             log k) strips of width at most w* in expected running time
             O(n4/3k4/3 log11/3 n) if k2 log k≤n. (ii) For d = 3, a
             cover of S by O(k log k) hyper-strips of width at most 24 w*
             can be computed in expected time O(n3/2k11/4poly log n).
             (iii) We compute a cover of S⊂Rd by O(dk log k)
             hyper-cylinders of diameter at most 8 w* in expected time
             O(dnk3 log4 n). We also present some extensions of this
             result. (iv) Finally, we present an O(n log n) algorithm
             that covers S by two strips of width at most 3
             w*.},
   Key = {fds235424}
}

@article{fds235425,
   Author = {Agarwal, PK and Desikan, PK},
   Title = {Approximation algorithms for layered manufacturing},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Pages = {528-537},
   Booktitle = {Eleventh Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Year = {2000},
   Abstract = {An important problem in layered manufacturing is the choice
             of a good build direction, which influences the quality and
             the cost of manufacturing the object. We present efficient
             algorithms for computing a build direction that optimizes
             the total area of faces that are in contact with supports.
             For a given convex polytope with n faces and for a parameter
             ε&gt;0, we present an O((n/ε3)polylog n) algorithm that
             computes a build direction so that the total area of faces
             in contact with supports is at most (1+ε)A*, where A* is
             the minimum area of contact with supports for all build
             directions. For non-convex polyhedra, we provide evidence
             that the lower bound for any algorithm computing the optimal
             direction might be Ω(n4). We also present a faster
             algorithm for some special cases. Our technique for convex
             polyhedra involves computing approximate levels in
             arrangement of lines with weights. For given parameters
             ω,ε&gt;0, we present an algorithm that computes a
             (1+ε)-approximate weighted ω-level in an arrangement of n
             weighted lines in time O((n/ε3) polylog
             n).},
   Key = {fds235425}
}

@article{fds235426,
   Author = {Agarwal, PK and Aronov, B and Sharir, M},
   Title = {Exact and approximation algorithms for minimum-width
             cylindrical shells},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Pages = {510-517},
   Booktitle = {Eleventh Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Year = {2000},
   Abstract = {Let S be a set of n points in R3. Let ω* = ω*(S) be the
             width (i.e., thickness) of a minimum-width infinite
             cylindrical shell (the region between two co-axial
             cylinders) containing S. We first present an O(n5)-time
             algorithm for computing ω*, which as far as we know is the
             first nontrivial algorithm for this problem. We then present
             an O(n2+δ)-time algorithm, for any δ&gt;0, that computes a
             cylindrical shell of width at most 26(1+1/n4/9)ω*
             containing S.},
   Key = {fds235426}
}

@article{fds22871,
   Author = {P.K. Agarwal and L. Arge and G. Brodal and J. S.
             Vitter},
   Title = {I/O-efficient dynamic point location in monotone
             subdivisions},
   Booktitle = {Tenth Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Year = {1999},
   Key = {fds22871}
}

@article{fds23099,
   Author = {P.K. Agarwal and S. A. Cook},
   Title = {Guest editors' foreword},
   Journal = {Journal of Computer and Systems Sciences},
   Volume = {58},
   Pages = {259},
   Year = {1999},
   Key = {fds23099}
}

@article{fds23100,
   Author = {P.K. Agarwal},
   Title = {Guest editors' foreword},
   Journal = {International Journal of Computational Geometry and
             Applications},
   Volume = {9},
   Pages = {325},
   Year = {1999},
   Key = {fds23100}
}

@article{fds22782,
   Author = {P.K. Agarwal and P. K. Desikan},
   Title = {Fast algorithms for surface simpli cation and other related
             problems},
   Journal = {submitted to Discrete and Computational Geometry},
   Year = {1999},
   Key = {fds22782}
}

@article{fds22875,
   Author = {P.K. Agarwal and L. Knipping and M. van Kreveld and T. Strijk and A.Wolff},
   Title = {A simple and efficient algorithm for high quality line
             labeling},
   Booktitle = {GIS Research UK: 7th National Conference},
   Year = {1999},
   Key = {fds22875}
}

@article{fds22877,
   Author = {P.K. Agarwal and B. Aronov and S. Har-Peled and M.
             Sharir},
   Title = {Exact and approximation algorithms for the minimum width
             annuli and shells},
   Booktitle = {Fifteenth Annual Symposium on Computational
             Geometry},
   Year = {1999},
   Key = {fds22877}
}

@article{fds235412,
   Author = {Agarwal, PK and Aronov, B and Har-Peled, S and Sharir,
             M},
   Title = {Approximation and exact algorithms for minimum-width annuli
             and shells},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {380-389},
   Year = {1999},
   Abstract = {The approximation and the exact algorithms to compute the
             minimum-width shell or annulus are discussed. To measure the
             S or the roundness of a set of n points in Rd, the S can be
             approximated with a sphere (Γ) so that the maximum distance
             between a point of S and Γ is minimized. It was found that
             the problem of measuring the roundness of S is equivalent to
             computing a shell of the smallest width that contains
             S.},
   Key = {fds235412}
}

@article{fds235416,
   Author = {Agarwal, PK and Arge, L and Brodal, GS and Vitter,
             JS},
   Title = {I/O-efficient dynamic point location in monotone planar
             subdivisions},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Pages = {11-20},
   Year = {1999},
   Abstract = {We present an efficient external-memory dynamic data
             structure for point location in monotone planar
             subdivisions. Our data structure uses O(N/B) disk blocks to
             store a monotone subdivision of size N, where B is the size
             of a disk block. It supports queries in O(logB2 N) I/Os
             (worst-case) and updates in O(logB2 N) I/Os (amortized). We
             also propose a new variant of B-trees, called level-balanced
             B-trees, which allow insert, delete, merge, and split
             operations in O((1+b/BlogM/BN/B)logbN) I/Os (amortized),
             2≤b≤B/2, even if each node stores a pointer to its
             parent. Here M is the size of main memory. Besides being
             essential to our point-location data structure, we believe
             that level-balanced B-trees are of significant independent
             interest. They can, for example, be used to dynamically
             maintain a planar st-graph using O((1+b/BlogM/BN/B) logb N)
             = O(logb2 N) I/Os (amortized) per update, so that
             reachability queries can be answered in O(logB N) I/Os
             (worst case).},
   Key = {fds235416}
}

@article{fds235417,
   Author = {Agarwal, PK and O'Rourke, J},
   Title = {Open Problems Presented at SCG'98},
   Journal = {Journal of Algorithms},
   Volume = {30},
   Number = {2},
   Pages = {449-453},
   Year = {1999},
   Abstract = {A subset of the problems presented at the open-problem
             session of the 14th Annual ACM Symposium on Computational
             Geometry, held on June 7-10, 1998, is listed. © 1999
             Academic Press.},
   Key = {fds235417}
}

@article{fds235419,
   Author = {Agarwal, PK and Aronov, B and Sharir, M},
   Title = {Line transversals of balls and smallest enclosing cylinders
             in three dimensions},
   Journal = {Discrete & Computational Geometry},
   Volume = {21},
   Number = {3},
   Pages = {373-388},
   Year = {1999},
   ISSN = {0179-5376},
   Abstract = {We establish a near-cubic upper bound on the complexity of
             the space of line transversals of a collection of n balls in
             three dimensions, and show that the bound is almost tight,
             in the worst case. We apply this bound to obtain a
             near-cubic algorithm for computing a smallest infinite
             cylinder enclosing a given set of points or balls in
             3-space. We also present an approximation algorithm for
             computing a smallest enclosing cylinder.},
   Key = {fds235419}
}

@article{fds235420,
   Author = {Agarwal, PK and Efrat, A and Sharir, M},
   Title = {Vertical decomposition of shallow levels in 3-dimensional
             arrangements and its applications},
   Journal = {SIAM Journal on Computing},
   Volume = {29},
   Number = {3},
   Pages = {912-953},
   Year = {1999},
   Abstract = {Let F be a collection of n bivariate algebraic functions of
             constant maximum degree. We show that the combinatorial
             complexity of the vertical decomposition of the (≤k)-level
             of the arrangement A(F) is O(k3+ε ψ(n/k)) for any ε &gt;
             0, where ψ(r) is the maximum complexity of the lower
             envelope of a subset of at most r functions of F. This bound
             is nearly optimal in the worst case and implies the
             existence of shallow cuttings, in the sense of [J. Matousek,
             Comput. Geom., 2 (1992), pp. 169-186], of small size in
             arrangements of bivariate algebraic functions. We also
             present numerous applications of these results, including
             (i) data structures for several generalized 3-dimensional
             range-searching problems; (ii) dynamic data structures for
             planar nearest- and farthest-neighbor searching under
             various fairly general distance functions; (iii) an improved
             (near-quadratic) algorithm for minimum-weight bipartite
             Euclidean matching in the plane; and (iv) efficient
             algorithms for certain geometric optimization problems in
             static and dynamic settings.},
   Key = {fds235420}
}

@article{fds235421,
   Author = {Agarwal, PK and Aronov, B and Sharir, M},
   Title = {Motion planning for a convex polygon in a polygonal
             environment},
   Journal = {Discrete & Computational Geometry},
   Volume = {22},
   Number = {2},
   Pages = {201-221},
   Year = {1999},
   ISSN = {0179-5376},
   Abstract = {We study the motion-planning problem for a convex m-gon P in
             a planar polygonal environment Q bounded by n edges. We give
             the first algorithm that constructs the entire free
             configuration space (the three-dimensional space of all free
             placements of P in Q) in time that is near-quadratic in mn,
             which is nearly optimal in the worst case. The algorithm is
             also conceptually simple. Previous solutions were
             incomplete, more expensive, or produced only part of the
             free configuration space. Combining our solution with
             parametric searching, we obtain an algorithm that finds the
             largest placement of P in Q in time that is also
             near-quadratic in mn. In addition, we describe an algorithm
             that preprocesses the computed free configuration space so
             that reachability queries can be answered in polylogarithmic
             time.},
   Key = {fds235421}
}

@article{fds235413,
   Author = {Agarwal, PK and Sharir, M},
   Title = {Pipes, cigars, and kreplach: The union of Minkowski sums in
             three dimensions},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {143-153},
   Booktitle = {Fifteenth Annual Symposium on Computational
             Geometry},
   Year = {1999},
   Abstract = {Let Ω be a set of pairwise-disjoint polyhedral obstacles in
             R3 with a total of n vertices, and let B be a ball. We show
             that the combinatorial complexity of the free configuration
             space F of B amid Ω, i.e., the set of all placements of B
             at which B does not intersect any obstacle, is O(n2+ε), for
             any ε&gt;0; the constant of proportionality depends on ε.
             This upper bound almost matches the known quadratic lower
             bound on the maximum possible complexity of F. We also
             present a randomized algorithm to compute the boundary of F
             whose expected running time is O(n2+ε), for any
             ε&gt;0.},
   Key = {fds235413}
}

@article{fds235414,
   Author = {Agarwal, PK and Basch, J and Berg, MD and Guibas, LJ and Hershberger,
             J},
   Title = {Lower bounds for kinetic planar subdivisions},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {247-254},
   Booktitle = {Fifteenth Annual Symposium on Computational
             Geometry},
   Year = {1999},
   Abstract = {We revisit the notion of kinetic efficiency for
             non-canonically-defined discrete attributes of moving data,
             like binary space partitions and triangulations. Under very
             general computational models, we obtain lower bounds on the
             minimum amount of work required to maintain any binary space
             partition of moving segments in the plane or any Steiner
             triangulation of moving points in the plane. Such lower
             bounds - the first to be obtained in the kinetic context -
             are necessary to evaluate the efficiency of kinetic data
             structures when the attribute to be maintained is not
             canonically defined.},
   Key = {fds235414}
}

@article{fds235415,
   Author = {Varadarajan, KR and Agarwal, PK},
   Title = {Approximation algorithms for bipartite and non-bipartite
             matching in the plane},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Pages = {805-814},
   Booktitle = {Tenth Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Year = {1999},
   Abstract = {In the approximate Euclidean min-cost perfect matching
             problem, we are a given a set V of 2n points in the plane,
             and a real number ε&lt;0, and we want to pair up the points
             (into n pairs) so that the sum of the distances between the
             paired points is within a multiplicative factor of (1+ε) of
             the optimal. We present a Monte-Carlo algorithm that
             returns, with probability at least 1/2, a solution within
             (1+ε) of the optimal; the running time of our algorithm is
             O((n/ε3) log6 n). In the bipartite version of this problem,
             we are given a set R of n red points, a set B of n blue
             points in the plane, and a real number ε&gt;0. We want to
             match each red point with a blue point so that the sum of
             the distances between paired points is within (1+ε) times
             that of an optimal matching. We present an algorithm for
             this problem that runs in O((n/ε)3/2 log5 n)
             time.},
   Key = {fds235415}
}

@article{fds235418,
   Author = {Agarwal, PK and Sharir, M},
   Title = {Motion planning of a ball amid segments in three
             dimensions},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Pages = {21-30},
   Booktitle = {Tenth Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Year = {1999},
   Abstract = {Let S be a set of n pairwise disjoint segments in R3, and
             let B be a ball of radius 1. The free configuration space F
             of B amid S is the set of all placements of B at which (the
             interior of) B does not intersect any segment of S. We show
             that the combinatorial complexity of F is O(n5/2+ε), for
             any ε&gt;0, with the constant of proportionality depending
             on ε. This is the first subcubic bound on the complexity of
             the free configuration space even when S is a set of lines
             in R3. We also present a randomized algorithm that can
             compute the boundary o the free configuration space in
             O(n5/2+ε) expected time.},
   Key = {fds235418}
}

@article{fds313244,
   Author = {Agarwal, PK and Bhattacharya, BK and Sen, S},
   Title = {Output-Sensitive Algorithms for Uniform Partitions of
             Points.},
   Journal = {ISAAC},
   Volume = {1741},
   Pages = {403-414},
   Booktitle = {Tenth Annual International Symposium on Algorithms and
             Computation},
   Publisher = {Springer},
   Editor = {Aggarwal, A and Rangan, CP},
   Year = {1999},
   ISBN = {3-540-66916-7},
   url = {http://www.informatik.uni-trier.de/~ley/db/conf/isaac/isaac99.html},
   Doi = {10.1007/3-540-46632-0_41},
   Key = {fds313244}
}

@book{fds1432,
   Author = {P.K. Agarwal},
   Title = {Robotics: The Algorithmic Perspective},
   Publisher = {A. K. Peters, Wellesley},
   Editor = {L. Kavraki and M. Mason},
   Year = {1998},
   Key = {fds1432}
}

@article{fds1776,
   Author = {J. Erickson and P.K. Agarwal},
   Title = {Geometric range searching and its relatives},
   Pages = {1-56},
   Booktitle = {Advances in Discrete and Computational Geometry},
   Publisher = {American Mathematical Society, Providence},
   Editor = {B. Chazelle and J. Goodman and R. Pollack},
   Year = {1998},
   Key = {fds1776}
}

@article{fds22869,
   Author = {P.K. Agarwal and T. M. Murali and J. S. Vitter},
   Title = {A new algorithm for constructing binary space partitions for
             orthogonal rectangles},
   Booktitle = {Sixth European Symposium on Algorithms},
   Year = {1998},
   Key = {fds22869}
}

@article{fds235408,
   Author = {Agarwal, PK and Sharir, M and Welzl, E},
   Title = {The discrete 2-center problem},
   Journal = {Discrete & Computational Geometry},
   Volume = {20},
   Number = {3},
   Pages = {287-305},
   Year = {1998},
   ISSN = {0179-5376},
   Abstract = {We present an algorithm for computing the discrete 2-center
             of a set P of n points in the plane; that is, computing two
             congruent disks of smallest possible radius, centered at two
             points of P, whose union covers P. Our algorithm runs in
             time O(n4/3 log5 n).},
   Key = {fds235408}
}

@article{fds235409,
   Author = {Agarwal, PK and Aronov, B and Chan, TM and Sharir,
             M},
   Title = {On levels in arrangements of lines, segments, planes, and
             triangles},
   Journal = {Discrete & Computational Geometry},
   Volume = {19},
   Number = {3},
   Pages = {315-331},
   Year = {1998},
   ISSN = {0179-5376},
   Abstract = {We consider the problem of bounding the complexity of the
             kth level in an arrangement of n curves or surfaces, a
             problem dual to, and an extension of, the well-known k-set
             problem. Among other results, we prove a new bound,
             O(nk5/3), on the complexity of the kth level in an
             arrangement of n planes in ℝ3, or on the number of k-sets
             in a set of n points in three dimensions, and we show that
             the complexity of the kth level in an arrangement of n line
             segments in the plane is O(n-√kα(n/k)), and that the
             complexity of the kth level in an arrangement of n triangles
             in 3-space is O(n2k5/6α(n/k)).},
   Key = {fds235409}
}

@article{fds235410,
   Author = {Agarwal, PK and O'Rourke, J},
   Title = {Computational geometry column 34},
   Journal = {International Journal of Computational Geometry and
             Applications},
   Volume = {8},
   Number = {5-6},
   Pages = {637-642},
   Year = {1998},
   Abstract = {Problems presented at the open-problem session of the 14th
             Annual ACM Symposium on Computational Geometry are
             listed.},
   Key = {fds235410}
}

@article{fds235411,
   Author = {Agarwal, PK and Kreveld, MV and Suri, S},
   Title = {Label placement by maximum independent set in
             rectangles},
   Journal = {Computational Geometry: Theory and Applications},
   Volume = {11},
   Number = {3-4},
   Pages = {209-218},
   Year = {1998},
   Abstract = {Motivated by the problem of labeling maps, we investigate
             the problem of computing a large non-intersecting subset in
             a set of n rectangles in the plane. Our results are as
             follows. In O(n log n) time, we can find an O(log n)-factor
             approximation of the maximum subset in a set of n arbitrary
             axis-parallel rectangles in the plane. If all rectangles
             have unit height, we can find a 2-approximation in O(n log
             n) time. Extending this result, we obtain a (1 +
             1/k)-approximationin time O(n log n + n2k-1) time, for any
             integer k ≥ 1. © 1998 Elsevier Science B.V. All rights
             reserved.},
   Key = {fds235411}
}

@article{fds235597,
   Author = {Agarwal, PK and Matoušek, J and Schwarzkopf, O},
   Title = {Computing many faces in arrangements of lines and
             segments},
   Journal = {SIAM Journal on Computing},
   Volume = {27},
   Number = {2},
   Pages = {491-505},
   Year = {1998},
   Abstract = {We present randomized algorithms for computing many faces in
             an arrangement of lines or of segments in the plane, which
             are considerably simpler and slightly faster than the
             previously known ones. The main new idea is a simple
             randomized O(n log n) expected time algorithm for computing
             √n cells in an arrangement of n lines.},
   Key = {fds235597}
}

@article{fds235598,
   Author = {Agarwal, PK},
   Title = {Surface approximation and geometric partitions},
   Journal = {SIAM Journal on Computing},
   Volume = {27},
   Number = {4},
   Pages = {1016-1035},
   Year = {1998},
   Abstract = {Motivated by applications in computer graphics,
             visualization, and scientific computation, we study the
             computational complexity of the following problem: given a
             set S of n points sampled from a bivariate function f(x, y)
             and an input parameter ε &gt; 0, compute a piecewise-linear
             function ∑(x, y) of minimum complexity (that is, an
             xy-monotone polyhedral surface, with a minimum number of
             vertices, edges, or faces) such that |∑(xp,yp) - zp| ≤
             ε for all (xp, yp, zp) ∈ S. We give hardness evidence for
             this problem, by showing that a closely related problem is
             NP-hard. The main result of our paper is a polynomial-time
             approximation algorithm that computes a piecewise-linear
             surface of size O(Ko log Ko), where Ko is the complexity of
             an optimal surface satisfying the constraints of the
             problem. The technique developed in our paper is more
             general and applies to several other problems that deal with
             partitioning of points (or other objects) subject to certain
             geometric constraints. For instance, we get the same
             approximation bound for the following problem arising in
             machine learning: given n "red" and m "blue" points in the
             plane, find a minimum number of pairwise disjoint triangles
             such that each blue point is covered by some triangle and no
             red point lies in any of the triangles. © 1998 Society for
             Industrial and Applied Mathematics.},
   Key = {fds235598}
}

@article{fds235599,
   Author = {Agarwal, PK and Berg, MD and Matoušek, J and Schwarzkopf,
             O},
   Title = {Constructing Levels in Arrangements and Higher Order Voronoi
             Diagrams},
   Journal = {SIAM Journal on Computing},
   Volume = {27},
   Number = {3},
   Pages = {654-667},
   Year = {1998},
   Abstract = {We give simple randomized incremental algorithms for
             computing the ≤κ-level in an arrangement of n lines in
             the plane or in an arrangement of n planes in ℝ3. The
             expected running time of our algorithms is O(nκ + nα(n)
             logn) for the planar case and O(nκ2 + nlog3n) for the
             three-dimensional case. Both bounds are optimal unless κ is
             very small. The algorithm generalizes to computing the
             ≤κ-level in an arrangement of discs or x-monotone Jordan
             curves in the plane. Our approach can also compute the
             κ-level; this yields a randomized algorithm for computing
             the order-κ Voronoi diagram of n points in the plane in
             expected time O(κ(n - κ) log n + n log3
             n).},
   Key = {fds235599}
}

@article{fds235603,
   Author = {Agarwal, PK and Sharir, M},
   Title = {Efficient algorithms for geometric optimization},
   Journal = {ACM Computing Surveys},
   Volume = {30},
   Number = {4},
   Pages = {448-458},
   Year = {1998},
   ISSN = {0360-0300},
   Abstract = {We review the recent progress in the design of efficient
             algorithms for various problems in geometric optimization.
             We present several techniques used to attack these problems,
             such as parametric searching, geometric alternatives to
             parametric searching, prune-and-search techniques for linear
             programming and related problems, and LP-type problems and
             their efficient solution. We then describe a wide range of
             applications of these and other techniques to numerous
             problems in geometric optimization, including facility
             location, proximity problems, statistical estimators and
             metrology, placement and intersection of polygons and
             polyhedra, and ray shooting and other query-type problems.
             © 1999 ACM.},
   Key = {fds235603}
}

@article{fds235604,
   Author = {Agarwal, PK and Amenta, N and Sharir, M},
   Title = {Largest placement of one convex polygon inside
             another},
   Journal = {Discrete & Computational Geometry},
   Volume = {19},
   Number = {1},
   Pages = {95-104},
   Year = {1998},
   ISSN = {0179-5376},
   Abstract = {We show that the largest similar copy of a convex polygon P
             with m edges inside a convex polygon Q with n edges can be
             computed in O(mn2 log n) time. We also show that the
             combinatorial complexity of the space of all similar copies
             of P inside Q is O(mn2), and that it can also be computed in
             O(mn2 log n) time.},
   Key = {fds235604}
}

@article{fds235374,
   Author = {Murali, TM and Agarwal, PK and Vitter, JS},
   Title = {Constructing Binary Space Partitions for Orthogonal
             Rectabgles in Practice.},
   Journal = {ESA},
   Volume = {1461},
   Pages = {211-222},
   Publisher = {Springer},
   Editor = {Bilardi, G and Italiano, GF and Pietracaprina, A and Pucci,
             G},
   Year = {1998},
   ISBN = {3-540-64848-8},
   url = {http://www.informatik.uni-trier.de/~ley/db/conf/esa/esa98.html},
   Doi = {10.1007/3-540-68530-8_18},
   Key = {fds235374}
}

@article{fds235406,
   Author = {Agarwal, PK and Biedl, T and Lazard, S and Robbins, S and Suri, S and Whitesides, S},
   Title = {Curvature-constrained shortest paths in a convex
             polygon},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {392-401},
   Booktitle = {Fourteenth Annual Symposium on Computational
             Geometry},
   Year = {1998},
   Abstract = {Let B be a point robot moving in the plane, whose path is
             constrained to have curvature at most 1, and let P be a
             convex polygon with n vertices. We study the collision-free,
             optimal path-planning problem for B moving between two
             configurations inside P (a configuration specifies both a
             location and a direction of travel). We present an O(n2 log
             n) time algorithm for determining whether a collision-free
             path exists for B between two given configurations. If such
             a path exists, the algorithm returns a shortest one. We
             provide a detailed classification of curvature-constrained
             shortest paths inside a convex polygon and prove several
             properties of them, which are interesting in their own
             right. Some of the properties are quite general and shed
             some light on curvature-constrained shortest paths amid
             obstacles.},
   Key = {fds235406}
}

@article{fds235407,
   Author = {Agarwal, PK and Arge, L and Erickson, J and Franciosa, PG and Vitter,
             JS},
   Title = {Efficient searching with linear constraints},
   Journal = {Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on
             Principles of Database Systems},
   Pages = {169-178},
   Booktitle = {Seventeenth Annual Symposium on Principles of Database
             Systems},
   Year = {1998},
   Abstract = {We show how to preprocess a set S of points in Rd into an
             external memory data structure that efficiently supports
             linear-constraint queries. Each query is in the form of a
             linear constraint a·x≤b; the data structure must report
             all the points of S that satisfy the constraint. Our goal is
             to minimize the number of disk blocks required to store the
             data structure and the number of disk accesses (I/Os)
             required to answer a query. For d = 2, we present the first
             near-linear size data structure that can answer
             linear-constraint queries using an optimal number of I/Os.
             We also present a linear-size data structure that can answer
             queries efficiently in the worst case. We combine these two
             approaches to obtain tradeoffs between space and query time.
             Finally, we show that some of our techniques extend to
             higher dimensions.},
   Key = {fds235407}
}

@article{fds235600,
   Author = {Agarwal, PK and Procopiuc, CM},
   Title = {Exact and approximation algorithms for clustering},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Pages = {658-667},
   Booktitle = {Ninth Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Year = {1998},
   Abstract = {In this paper we present an nO(k(1-1/d)) time algorithm for
             solving the k-center problem in Rd, under L∞ and L2
             metrics. The algorithm extends to other metrics, and to the
             discrete k-center problem. We also describe a simple
             (1+ε)-approximation algorithm for the k-center problem,
             with running time O(n log k)+(k/ε)O(k(1-1/d)). Finally, we
             present a nO(k(1-1/d)) time algorithm for solving the
             L-capacitated k-center problem, provided that L =
             Ω(n/k1-1/d) or L = O(1). We conclude with a simple
             approximation algorithm for the L-capacitated k-center
             problem.},
   Key = {fds235600}
}

@article{fds235601,
   Author = {Agarwal, PK and Arge, L and Murali, TM and Varadarajan, KR and Vitter,
             JS},
   Title = {I/O-efficient algorithms for contour-line extraction and
             planar graph blocking},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Pages = {117-126},
   Booktitle = {Ninth Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Year = {1998},
   Abstract = {For a polyhedral terrain Σ, the contour at z-coordinate h,
             denoted Ch, is defined to be the intersection of the plane z
             = h with Σ. In this paper, we study the contour-line
             extraction problem, where we want to preprocess Σ into a
             data structure so that given a query z-coordinate h, we can
             report Ch quickly. This is a central problem that arises in
             geographic information systems (GIS), where terrains are
             often stored as Triangular Irregular Networks (TINs). We
             present an I/O-optimal algorithm for this problem which
             stores a terrain Σ with N vertices using O(N/B) blocks,
             where B is the size of a disk block, so that for any query
             h, the contour Ch can be computed using O(logB N+|Ch|/B) I/O
             operations, where |Ch| denotes the size of Ch. We also
             present an improved algorithm for a more general problem of
             blocking bounded-degree planar graphs such as TINs (i.e.,
             storing them on disk so that any graph traversal algorithm
             can traverse the graph in an I/O-efficient manner), and
             apply it to two problems that arise in GIS.},
   Key = {fds235601}
}

@article{fds235602,
   Author = {Agarwal, PK and Erickson, J and Guibas, LJ},
   Title = {Kinetic binary space partitions for intersecting segments
             and disjoint triangles},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Pages = {107-116},
   Booktitle = {Ninth Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Year = {1998},
   Abstract = {We describe randomized algorithms for efficiently
             maintaining a binary space partition of continuously moving,
             possibly intersecting, line segments in the plane, and of
             continuously moving but disjoint triangles in space. Our
             two-dimensional BSP has depth O(log n) and size O(n log n+k)
             and can be constructed in expected O(n log2 n+k log n) time,
             where k is the number of intersecting pairs. We can detect
             combinatorial changes to our BSP caused by the motion of the
             segments, and we can update our BSP in expected O(log n)
             time per change. Our three-dimensional BSP has depth O(log
             n), size O(n log2 n+k′), construction time O(n log3
             n+k′log n), and update time O(log2 n) (all expected),
             where k′ is the number of intersections between pairs of
             edges in the xy-projection of the triangles. Under
             reasonable assumptions about the motion of the segments or
             triangles, the expected number of number of combinatorial
             changes to either BSP is O(mnλs(n)), where m is the number
             of moving objects and λs(n) is the maximum length of an (n,
             s) Davenport-Schinzel sequence for some constant
             s.},
   Key = {fds235602}
}

@article{fds235605,
   Author = {Agarwal, PK and Eppstein, D and Guibas, LJ and Henzinger,
             MR},
   Title = {Parametric and kinetic minimum spanning trees},
   Journal = {Annual Symposium on Foundations of Computer Science -
             Proceedings},
   Pages = {596-605},
   Booktitle = {Thirty Ninth Annual Symposium on Foundations of Computer
             Science},
   Year = {1998},
   Abstract = {We consider the parametric minimum spanning tree problem, in
             which we are given a graph with edge weights that are linear
             functions of a parameter λ and wish to compute the sequence
             of minimum spanning trees generated as λ varies. We also
             consider the kinetic minimum spanning tree problem, in which
             λ represents time and the graph is subject in addition to
             changes such as edge insertions, deletions, and
             modifications of the weight functions as time progresses. We
             solve both problems in time O(n2/3 log4/3 n) per
             combinatorial change in the tree (or randomized O(n2/3 log
             n) per change). Our time bounds reduce to O(n1/2 log3/2 n)
             per change (O(n1/2log n) randomized) for planar graphs or
             other minor-closed families of graphs, and O(n1/4 log3/2 n)
             per change (O(n1/4 log n) randomized) for planar graphs with
             weight changes but no insertions or deletions.},
   Key = {fds235605}
}

@article{fds1433,
   Author = {N. Amenta and B. Aronov and M. Sharir and P.K.
             Agarwal},
   Title = {Largest placements and motion planning of a convex
             polygon},
   Series = {pp. 143-154},
   Booktitle = {Algorithms for Robotic Motion and Manipulation},
   Publisher = {A. K. Peters, Wellesley},
   Editor = {J.-P. Laumond and M. Overmars},
   Year = {1997},
   Key = {fds1433}
}

@article{fds1775,
   Author = {P.K. Agarwal},
   Title = {Range searching},
   Pages = {575-598},
   Booktitle = {CRC Handbook of Discrete and Computational
             Geometry},
   Publisher = {CRC Press, NewYork},
   Editor = {J. Goodman and J. O'Rourke},
   Year = {1997},
   Key = {fds1775}
}

@article{fds22855,
   Author = {P.K. Agarwal and P. K. Desikan},
   Title = {Fast algorithms for surface simpli cation and other related
             problems},
   Booktitle = {Eighth Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Year = {1997},
   Key = {fds22855}
}

@article{fds22858,
   Author = {P.K. Agarwal and L. Guibas and T. M. Murali and J. S.
             Vitter},
   Title = {Cylindrical kinetic and static binary space
             partitions},
   Booktitle = {Thirteenth Annual Symposium on Computational
             Geometry},
   Year = {1997},
   Key = {fds22858}
}

@article{fds22859,
   Author = {P.K. Agarwal and (short communication) and T. M. Murali and J.
             S. Vitter},
   Title = {Practical techniques for constructing binary space
             partitions of rectangles},
   Booktitle = {Thirteenth Annual Symposium on Computational
             Geometry},
   Year = {1997},
   Key = {fds22859}
}

@article{fds22860,
   Author = {P.K. Agarwal and M. Sharir and E. Welzl},
   Title = {The discrete 2-center problem},
   Booktitle = {Thirteenth Annual Symposium on Computational
             Geometry},
   Year = {1997},
   Key = {fds22860}
}

@article{fds22861,
   Author = {P.K. Agarwal and L. Guibas and J. Hershberger and E.
             Veach},
   Title = {Maintaining structures for moving points},
   Booktitle = {Fifth Workshop on Algorithms and Data Structures},
   Year = {1997},
   Key = {fds22861}
}

@article{fds22862,
   Author = {P.K. Agarwal and M. van Kreveld and S. Suri},
   Title = {Label placement by maximum independent set in
             rectangles},
   Booktitle = {Ninth Canadian Conference on Computational
             Geometry},
   Year = {1997},
   Key = {fds22862}
}

@article{fds22863,
   Author = {P.K. Agarwal and K. R. Varadarajan},
   Title = {Approximating shortest paths on polyhedral
             terrains},
   Booktitle = {Thirty Eighth Annual Symposium on Foundations of Computer
             Science},
   Year = {1997},
   Key = {fds22863}
}

@article{fds235404,
   Author = {Agarwal, PK and Sharir, M and Welzl, E},
   Title = {Discrete 2-center problem},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {147-155},
   Year = {1997},
   Abstract = {We present an algorithm for computing the discrete 2-center
             of a set P of n points in the plane; that is, computing two
             congruent disks of smallest possible radius, centered at two
             points of P, whose union covers P. Our algorithm runs in
             time O(n4/3 log5 n).},
   Key = {fds235404}
}

@article{fds235586,
   Author = {Agarwal, PK and Murali, TM and Vitter, JS},
   Title = {Practical techniques for constructing Binary Space
             Partitions for orthogonal rectangles},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {382-384},
   Year = {1997},
   Abstract = {We present the first systematic comparison of the
             performance of algorithms that construct Binary Space
             Partitions for orthogonal rectangles in R3. We compare known
             algorithms with our implementation of a variant of a recent
             algorithm of Agarwal et al.. We show via an empirical study
             that their algorithm constructs BSPs of near-linear size in
             practice and performs better than most of the other
             algorithms in the literature.},
   Key = {fds235586}
}

@article{fds235587,
   Author = {Agarwal, PK and Guibas, LJ and Murali, TM and Vitter,
             JS},
   Title = {Cylindrical static and kinetic binary space
             partitions},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {39-48},
   Year = {1997},
   Abstract = {We describe the first known algorithm for efficiently
             maintaining a Binary Space Partition (BSP) for n
             continuously moving segments in the plane. Under reasonable
             assumptions on the motion, we show that the total number of
             times the BSP changes is O(n2), and that we can update the
             BSP in O(log n) expected time per change. We also consider
             the problem of constructing a BSP for n triangles in R3. We
             present a randomized algorithm that constructs a BSP of
             expected size O(n2) in O(n2 log2 n) expected time. We also
             describe a deterministic algorithm that constructs a BSP of
             size O((n+k)log n) and height O(log n) in O((n+k)log2 n)
             time, where k is the number of intersection points between
             the edges of the projections of the triangles onto the
             xy-plane.},
   Key = {fds235587}
}

@article{fds235589,
   Author = {Agarwal, PK and Desikan, PK},
   Title = {Efficient algorithm for terrain simplification},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Pages = {139-147},
   Year = {1997},
   Abstract = {Given a set S̄ of n points in R3, sampled from an unknown
             bivariate function f(x, y) (i.e., for each point p ∈ S̄,
             zp = f(xp, yp)), a piecewise-linear function g(x, y) is
             called an ε-approximation of f(x, y) if for every p ∈
             S̄, |f(x,y)-g(x,y)|≤ε. The problem of computing an
             ε-approximation with the minimum number of vertices is
             NP-Hard. We present a randomized algorithm that computes an
             ε-approximation of size O(c2log2 c) in O(n2+δ+c3log2clog
             n/c) expected time, where c is the size of the
             ε-approximation with the minimum number of vertices and δ
             is any arbitrarily small positive number. Under some
             reasonable assumptions, the size of the output is close to
             O(clog c) and the expected running time is O(n2+δ). We have
             implemented a variant of this algorithm and include some
             empirical results.},
   Key = {fds235589}
}

@article{fds235591,
   Author = {Varadarajan, KR and Agarwal, PK},
   Title = {Approximating shortest paths on a nonconvex
             polyhedron},
   Journal = {Annual Symposium on Foundations of Computer Science -
             Proceedings},
   Pages = {182-191},
   Year = {1997},
   Abstract = {We present an approximation algorithm that, given the
             boundary P of a simple, nonconvex polyhedron in R3, and two
             points s and t on P, constructs a path on P between s and t
             whose length is at most 7(1+ε)dP(s,t), where dP(s,t) is the
             length of the shortest path between s and t on P, and
             ε&gt;0 is an arbitrarily small positive constant. The
             algorithm runs in O(n5/3 log5/3 n) time, where n is the
             number of vertices in P. We also present a slightly faster
             algorithm that runs in O(n8/5 log8/5 n) time and returns a
             path whose length is at most 15(1+ε)dp(s,t).},
   Key = {fds235591}
}

@article{fds235592,
   Author = {Agarwal, PK and Aronov, B and Pach, J and Pollack, R and Sharir,
             M},
   Title = {Quasi-planar graphs have a linear number of
             edges},
   Journal = {Combinatorica},
   Volume = {17},
   Number = {1},
   Pages = {1-9},
   Year = {1997},
   Abstract = {A graph is called quasi-planar if it can be drawn in the
             plane so that no three of its edges are pairwise crossing.
             It is shown that the maximum number of edges of a
             quasi-planar graph with n vertices is O(n).},
   Key = {fds235592}
}

@article{fds235593,
   Author = {Agarwal, PK and Har-Peled, S and Sharir, M and Varadarajan,
             KR},
   Title = {Approximating shortest paths on a convex polytope in three
             dimensions},
   Journal = {Journal of the ACM},
   Volume = {44},
   Number = {4},
   Pages = {567-584},
   Year = {1997},
   Abstract = {Given a convex polytope P with n faces in ℝ3, points s, t
             ∈ ∂P, and a parameter 0 &lt; ∈ ≤ 1, we present an
             algorithm that constructs a path on ∂P from s to t whose
             length is at most (1 + ∈)dP(s, t), where dP(s, t) is the
             length of the shortest path between s and t on ∂P. The
             algorithm runs in O(n log 1/∈ + 1/∈3) time, and is
             relatively simple. The running time is O(n + 1/∈3) if we
             only want the approximate shortest path distance and not the
             path itself. We also present an extension of the algorithm
             that computes approximate shortest path distances from a
             given source point on ∂P to all vertices of
             P.},
   Key = {fds235593}
}

@article{fds235594,
   Author = {Varadarajan, KR and Agarwal, PK},
   Title = {Linear approximation of simple objects},
   Journal = {Information Processing Letters},
   Volume = {62},
   Number = {2},
   Pages = {89-94},
   Year = {1997},
   Abstract = {Let P = {P1, P2, . . . , Pm} be a set of m convex polygons
             in the plane with a total number of n vertices, and for 1
             ≤ i ≤ m, let wi ∈ℝ+ be a weight associated with Pi.
             The weighted distance between a line l and a polygon Pi is
             given by d(l, Pi) = minp∈Pi,q∈l d(p, q).wi, where d(p,
             q) is the Euclidean distance between p and q. We want to
             compute a line l that minimizes the maximum distance between
             l and the polygons of P. We present an O(nα(n) log3 n)-time
             algorithm to compute such a line. We also give an
             O(n2+ε)-time algorithm, where ε is an arbitrarily small
             positive constant, to solve the three dimensional version of
             this problem; here, P is a set of convex polytopes in ℝ3,
             and we want to compute a plane h that minimizes the maximum
             weighted distance between h and the polytopes. © 1997
             Published by Elsevier Science B.V.},
   Key = {fds235594}
}

@article{fds235595,
   Author = {Agarwal, PK and Aronov, B and Sharir, M},
   Title = {Computing envelopes in four dimensions with
             applications},
   Journal = {SIAM Journal on Computing},
   Volume = {26},
   Number = {6},
   Pages = {1714-1732},
   Year = {1997},
   Abstract = {Let F ℱe a collection of n d-variate, possibly partially
             defined, functions, all algebraic of some constant maximum
             degree. We present a randomized algorithm that computes the
             vertices, edges, and 2-faces of the lower envelope (i.e.,
             pointwise minimum) of ℱ in expected time O(nd+ε) for any
             ε &gt; 0. For d = 3, by combining this algorithm with the
             point-location technique of Preparata and Tamassia, we can
             compute, in randomized expected time O(n3+ε), for any ε
             &gt; 0, a data structure of size O(n3+ε) that, for any
             query point q, can determine in O(log2 n) time the
             function(s) of ℱ that attain the lower envelope at q. As a
             consequence, we obtain improved algorithmic solutions to
             several problems in computational geometry, including (a)
             computing the width of a point set in 3-space, (b) computing
             the "biggest stick" in a simple polygon in the plane, and
             (c) computing the smallest-width annulus covering a planar
             point set. The solutions to these problems run in randomized
             expected time O(n17/11+ε), for any ε &gt; 0, improving
             previous solutions that run in time O(n8/5+ε). We also
             present data structures for (i) performing nearest-neighbor
             and related queries for fairly general collections of
             objects in 3-space and for collections of moving objects in
             the plane and (ii) performing ray-shooting and related
             queries among n spheres or more general objects in 3-space.
             Both of these data structures require O(n3+ε) storage and
             preprocessing time, for any ε &gt; 0, and support
             polylogarithmic-time queries. These structures improve
             previous solutions to these problems.},
   Key = {fds235595}
}

@article{fds235596,
   Author = {Agarwal, PK and Aronov, B and O'Rourke, J and Schevon,
             CA},
   Title = {Star unfolding of a polytope with applications},
   Journal = {SIAM Journal on Computing},
   Volume = {26},
   Number = {6},
   Pages = {1689-1713},
   Year = {1997},
   Abstract = {We introduce the notion of a star unfolding of the surface P
             of a three-dimensional convex polytope with n vertices, and
             use it to solve several problems related to shortest paths
             on P. The first algorithm computes the edge sequences
             traversed by shortest paths on P in time O(n6β(n) log n),
             where β(n) is an extremely slowly growing function. A much
             simpler O(n6) time algorithm that finds a small superset of
             all such edge sequences is also sketched. The second
             algorithm is an O(n8 log n) time procedure for computing the
             geodesic diameter of P: the maximum possible separation of
             two points on P with the distance measured along P. Finally,
             we describe an algorithm that preprocesses P into a data
             structure that can efficiently answer the queries of the
             following form: "Given two points, what is the length of the
             shortest path connecting them?" Given a parameter 1 ≤ m
             ≤ n2, it can preprocess P in time O(n6m1+δ), for any δ
             &gt; O, into a data structure of size O(n6m1+δ), so that a
             query can be answered in time O((√n/m1/4) log n). If one
             query point always lies on an edge of P, the algorithm can
             be improved to use O(n5m1+δ) preprocessing time and storage
             and guarantee O((n/m)1/3 log n) query time for any choice of
             m between 1 and n.},
   Key = {fds235596}
}

@article{fds235405,
   Author = {Agarwal, PK and Latombe, J-C and Motwani, R and Raghavan,
             P},
   Title = {Nonholonomic path planning for pushing a disk among
             obstacles},
   Journal = {Proceedings - IEEE International Conference on Robotics and
             Automation},
   Volume = {4},
   Pages = {3124-3129},
   Booktitle = {IEEE Conference on Robotics and Automation},
   Year = {1997},
   Abstract = {We consider the path-planning problem for a robot pushing an
             object in an environment containing obstacles. This new
             variant of the classical robot path-planning problem has
             several interesting geometric aspects, which we explore. We
             focus on the setting where the robot makes a point contact
             with the object which is assumed to be a unit disk, while
             the obstacles are assumed to be polygonal.},
   Key = {fds235405}
}

@article{fds235588,
   Author = {Agarwal, PK and Aronov, B and Sharir, M},
   Title = {On levels in arrangements of lines, segments, planes, and
             triangles},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {30-38},
   Booktitle = {Thirteenth Annual Symposium on Computational
             Geometry},
   Year = {1997},
   Abstract = {We consider the problem of bounding the complexity of the
             k-th level in an arrangement of n curves or surfaces, a
             problem dual to, and extending, the well-known k-set
             problem. (a) We review and simplify some old proofs in new
             disguise and give new proofs of the bound O(n√k+1) for the
             complexity of the k-th level in an arrangement of n lines.
             (b) We derive an improved version of Lovasz Lemma in any
             dimension, and use it to prove a new bound, O(n2k2/3), on
             the complexity of the k-th level in an arrangement of n
             planes in R3, or on the number of k-sets in a set of n
             points in three dimensions. (c) We show that the complexity
             of any single level in an arrangement of n line segments in
             the plane is O(n3/2), and that the complexity of any single
             level in an arrangement of n triangles in 3-space is
             O(n17/6).},
   Key = {fds235588}
}

@article{fds235590,
   Author = {Agarwal, PK and Aronov, B and Sharir, M},
   Title = {Line transversals of balls and smallest enclosing cylinders
             in three dimensions},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Pages = {483-492},
   Booktitle = {Eighth Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Year = {1997},
   Abstract = {We establish a near-cubic upper bound on the complexity of
             the space of line transversals of a collection of n balls in
             three dimensions; and show that the bound is almost tight,
             in the worst case. We apply this bound to obtain a
             near-cubic algorithm for computing a smallest infinite
             cylinder enclosing a given set of points or balls in
             3-space. We also present an approximation algorithm for
             computing a smallest enclosing cylinder.},
   Key = {fds235590}
}

@article{fds313240,
   Author = {Agarwal, PK and Guibas, LJ and Hershberger, J and Veach,
             E},
   Title = {Maintaining the Extent of a Moving Point
             Set.},
   Journal = {WADS},
   Volume = {1272},
   Pages = {31-44},
   Publisher = {Springer},
   Editor = {Dehne, FKHA and Rau-Chaplin, A and Sack, J-R and Tamassia,
             R},
   Year = {1997},
   ISBN = {3-540-63307-3},
   url = {http://www.informatik.uni-trier.de/~ley/db/conf/wads/wads97.html},
   Doi = {10.1007/3-540-63307-3_46},
   Key = {fds313240}
}

@article{fds22848,
   Author = {P.K. Agarwal and H. Wang},
   Title = {Approximation algorithms for shortest paths with bounded
             curvature},
   Booktitle = {Seventh Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Year = {1996},
   Key = {fds22848}
}

@article{fds22935,
   Author = {P.K. Agarwal and S. Suri},
   Title = {Simple and practical geometric algorithms},
   Journal = {ACM Computing Surveys},
   Volume = {28},
   Year = {1996},
   Key = {fds22935}
}

@article{fds22936,
   Author = {P.K. Agarwal and S. Suri},
   Title = {Simple and practical geometric algorithms},
   Journal = {ACM Computing Surveys},
   Volume = {28},
   Year = {1996},
   Key = {fds22936}
}

@misc{fds23109,
   Author = {P.K. Agarwal},
   Title = {Range searching},
   Journal = {Technical Report CS-1996-05, Department of Computer Science,
             Duke University},
   Year = {1996},
   Key = {fds23109}
}

@article{fds22849,
   Author = {P.K. Agarwal and M. de Berg and D. Halperin and M.
             Sharir},
   Title = {Computing depth orders in multiple directions},
   Booktitle = {Seventh Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Year = {1996},
   Key = {fds22849}
}

@article{fds22850,
   Author = {P.K. Agarwal and H. Wang},
   Title = {Approximation algorithms for shortest paths with bounded
             curvature},
   Booktitle = {Seventh Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Year = {1996},
   Key = {fds22850}
}

@article{fds22852,
   Author = {P.K. Agarwal and N. Amenta and B. Aronov and M.
             Sharir},
   Title = {Largest placements and motion planning of a convex
             polygon},
   Booktitle = {Second International Workshop on Algorithmic Foundations of
             Robotics},
   Year = {1996},
   Key = {fds22852}
}

@article{fds235398,
   Author = {Frey, HC and Agarwal, P},
   Title = {Probabilistic analysis and optimization of new power
             generation technologies: a case study for the
             externally-fired combined cycle},
   Journal = {Proceedings of the American Power Conference},
   Volume = {1},
   Pages = {52-57},
   Year = {1996},
   Abstract = {A new performance and cost model for the EFCC
             (externally-fired combined cycle) is developed. This model
             is applied in a series of case studies to illustrate a
             variety of methods for technology assessment. The model
             applications also provide insight into the risks and
             potential pay-offs of the EFCC.},
   Key = {fds235398}
}

@article{fds235401,
   Author = {Agarwal, PK and Kreveld, MV},
   Title = {Connected Component and Simple Polygon Intersection
             Searching},
   Journal = {Algorithmica (New York)},
   Volume = {15},
   Number = {6},
   Pages = {626-660},
   Year = {1996},
   Abstract = {Efficient data structures are given for the following two
             query problems: (i) preprocess a set P of simple polygons
             with a total of n edges, so that all polygons of P
             intersected by a query segment can be reported efficiently,
             and (ii) preprocess a set S of n segments, so that the
             connected components of the arrangement of S intersected by
             a query segment can be reported quickly. In these problems
             we do not want to return the polygons or connected
             components explicitly (i.e., we do not wish to report the
             segments defining the polygon, or the segments lying in the
             connected components). Instead, we assume that the polygons
             (or connected components) are labeled and we just want to
             report their labels. We present data structures of size
             O(n1+f) that can answer a query in time O(n1/2+f + k), where
             k is the output size. If the edges of P (or the segments in
             S) are orthogonal, the query time can be improved to O(log n
             + k) using O(n log n) space. We also present data structures
             that can maintain the connected components as we insert new
             segments. For arbitrary segments the amortized update and
             query time are O(n1/2+f) and O(n1/2+f + k), respectively,
             and the space used by the data structure is O(n1+f). If we
             allow O (n4/3+f) space, the amortized update and query time
             can be improved to O(n1/3+f) and O(n1/3+f + k),
             respectively. For orthogonal segments the amortized update
             and query time are O(log2 n) and O(log2 n + k log n), and
             the space used by the data structure is O(n log n). Some
             other related results are also mentioned.},
   Key = {fds235401}
}

@article{fds235402,
   Author = {Agarwal, PK and Schwarzkopf, O and Sharir, M},
   Title = {The overlay of lower envelopes and its applications},
   Journal = {Discrete & Computational Geometry},
   Volume = {15},
   Number = {1},
   Pages = {1-13},
   Year = {1996},
   ISSN = {0179-5376},
   Abstract = {Let ℱ and G be two collections of a total of n (possibly
             partially defined) bivariate, algebraic functions of
             constant maximum degree. The minimization diagrams of ℱ, G
             are the planar maps obtained by the xy-projections of the
             lower envelopes of ℱ, G, respectively. We show that the
             combinatorial complexity of the overlay of the minimization
             diagrams of ℱ and of G is O(n2+ε), for any ε &gt; 0.
             This result has several applications: (i) a near-quadratic
             upper bound on the complexity of the region in 3-space
             enclosed between the lower envelope of one such collection
             of functions and the upper envelope of another collection;
             (ii) an efficient and simple divide-and-conquer algorithm
             for constructing lower envelopes in three dimensions; and
             (iii) a near-quadratic upper bound on the complexity of the
             space of all plane transversals of a collection of simply
             shaped convex sets in three dimensions.},
   Key = {fds235402}
}

@article{fds235403,
   Author = {Agarwal, PK and Sharir, M},
   Title = {Ray shooting amidst convex polyhedra and polyhedral terrains
             in three dimensions},
   Journal = {SIAM Journal on Computing},
   Volume = {25},
   Number = {1},
   Pages = {100-116},
   Year = {1996},
   Abstract = {We consider the problem of ray shooting in a
             three-dimensional scene consisting of m (possibly
             intersecting) convex polyhedra or polyhedral terrains with a
             total of n faces, i.e., we want to preprocess them into a
             data structure, so that the first intersection point of a
             query ray and the given polyhedra can be determined quickly.
             We present a technique that requires O((mn)2+ε)
             preprocessing time and storage, and can answer ray-shooting
             queries in O(log2 n) time. This is a significant improvement
             over previously known techniques (which require O(n4+ε)
             space and preprocessing) if m is much smaller than n, which
             is often the case in practice. Next, we present a variant of
             the technique that requires O(n1+ε) space and
             preprocessing, and answers queries in time O(m1/4n1/2+ε),
             again a significant improvement over previous techniques
             when m ≪ n.},
   Key = {fds235403}
}

@article{fds235581,
   Author = {Frey, HC and Agarwal, P},
   Title = {Probabilistic modeling and optimization of clean coal
             technologies: case studies of the externally-fired combined
             cycle},
   Journal = {Proceedings of the Air & Waste Management Association's
             Annual Meeting & Exhibition},
   Pages = {16pp},
   Year = {1996},
   Abstract = {In previous work, quantitative probabilistic analysis
             techniques have been applied to the evaluation of advanced
             clean coal technologies. Probabilistic evaluations enable
             the consequences of uncertainties in the input parameters to
             detailed engineering-economic models to be displayed and
             evaluated. Risk is the probability of an adverse outcome.
             Probabilistic analysis provides a systematic framework for
             the evaluation of technological risks. These types of risks
             include the possibility of poor performance, high emission,
             and high cost compared to more conventional technologies. By
             identifying the sources of high risk outcomes, it is
             possible to prioritize research on new technologies so as to
             minimize such risks. Furthermore, probabilistic analysis has
             been applied to compare competing technologies under
             uncertainty. The existence of uncertainty poses challenges
             to the optimization of advanced power generation and
             environmental control technologies. Probabilistic modeling
             and mathematical programming techniques for optimization are
             combined to optimize process flowsheets under uncertainty. A
             stochastic optimization capability enables to optimization
             of a flowsheet so as to maximize favorable outcomes and to
             minimize risks. Probabilistic analysis and optimization
             techniques are applied to case studies using an
             engineering-economic model of the Externally-Fired Combined
             Cycle (EFCC) technology. The case studies illustrate the key
             insights obtained from a probabilistic approach to analysis
             and optimization.},
   Key = {fds235581}
}

@article{fds235582,
   Author = {Agarwal, PK and Sen, S},
   Title = {Selection in Monotone Matrices and Computing kth Nearest
             Neighbors},
   Journal = {Journal of Algorithms},
   Volume = {20},
   Number = {3},
   Pages = {581-601},
   Year = {1996},
   url = {http://dx.doi.org/10.1006/jagm.1996.0028},
   Abstract = {An m × n matrix script A sign = (ai, j), 1 ≤ i ≤ m and
             1 &lt; j &lt; n, is called a totally monotone matrix if for
             all i1, i2, j1, j2, satisfying 1 &lt; i1 &lt; i2 &lt; m, 1
             &lt; j1 &lt; j2 &lt; n. ai1, j1 &lt; ai1, j2 ⇒ ai2, j1
             &lt; ai2, j2. We present an O((m + n)√n log n) time
             algorithm to select the kth smallest item from an m × n
             totally monotone matrix for any k ≤ mn. This is the first
             sub-quadratic algorithm for selecting an item from a totally
             monotone matrix. Our method also yields an algorithm of the
             same time complexity for a generalized row-selection problem
             in monotone matrices. Given a set S = {P1,..., Pn} of n
             points in convex position and a vector k = {k1,..., kn}, we
             also present an O(n4/3 logc n) algorithm to compute the kith
             nearest neighbor of pi for every i ≤ n; here c is an
             appropriate constant. This algorithm is considerably faster
             than the one based on a row-selection algorithm for monotone
             matrices. If the points of S are arbitrary, then the kith
             nearest neighbor of pi, for all i ≤ n, can be computed in
             time O(n7/5 logc n), which also improves upon the previously
             best-known result. © 1996 Academic Press,
             Inc.},
   Doi = {10.1006/jagm.1996.0028},
   Key = {fds235582}
}

@article{fds235583,
   Author = {Agarwal, PK and Sharir, M},
   Title = {Ray Shooting Amidst Convex Polygons in 2D},
   Journal = {Journal of Algorithms},
   Volume = {21},
   Number = {3},
   Pages = {508-519},
   Year = {1996},
   url = {http://dx.doi.org/10.1006/jagm.1996.0056},
   Abstract = {We consider the problem of ray shooting in a two-dimensional
             scene consisting of m convex polygons with a total of n
             edges. We present a data structure that requires O(mn log m)
             space and preprocessing time and that answers a ray shooting
             query in O(log2 m log2 n) time. If the polygons are pairwise
             disjoint, the space and preprocessing time can be improved
             to O((m2 + n)log m) and O((m2 + n log n)log m),
             respectively. Our algorithm also works for a collection of
             disjoint simple polygons. We also show that if we allow only
             O(n) space, a ray shooting query among a collection of
             disjoint simple polygons can be answered in time O([m/
             √n]1+ε log2 n) time, for any ε &gt; 0. © 1996 Academic
             Press, Inc.},
   Doi = {10.1006/jagm.1996.0056},
   Key = {fds235583}
}

@article{fds235584,
   Author = {Agarwal, PK and Sharir, M},
   Title = {Efficient randomized algorithms for some geometric
             optimization problems},
   Journal = {Discrete & Computational Geometry},
   Volume = {16},
   Number = {4},
   Pages = {317-337},
   Year = {1996},
   ISSN = {0179-5376},
   Abstract = {In this paper we first prove the following combinatorial
             bound, concerning the complexity of the vertical
             decomposition of the minimization diagram of trivariate
             functions: Let ℱ be a collection of n totally or partially
             defined algebraic trivariate functions of constant maximum
             degree, with the additional property that, for a given pair
             of functions f, f′ ∈ ℱ, the surface f(x, y, z) =
             f′(x, y, z) is xy-monotone (actually, we need a somewhat
             weaker property). We show that the vertical decomposition of
             the minimization diagram of ℱ consists of O(n3+ε) cells
             (each of constant description complexity), for any ε &gt;
             0. In the second part of the paper, we present a general
             technique that yields faster randomized algorithms for
             solving a number of geometric optimization problems,
             including (i) computing the width of a point set in 3-space,
             (ii) computing the minimum-width annulus enClosing a set of
             n Points in the plane, and (iii) computing the "biggest
             stick" inside a simple polygon in the plane. Using the above
             result on vertical decompositions, we show that the expected
             running time of all three algorithms is O(n3/2+ε), for any
             ε &gt; 0. Our algorithm improves and simplifies previous
             solutions of all three problems.},
   Key = {fds235584}
}

@article{fds235585,
   Author = {Tamassia, R and Agarwal, PK and Amato, N and Chen, DZ and Dobkin, D and Drysdale, S and Fortune, S and Goodrich, MT and Hershberger, J and O'Rourke, J and Preparata, FP and Sack, J-R and Suri, S and Tollis, I and Vitter, JS and Whitesides, S},
   Title = {Strategic directions in computational geometry},
   Journal = {ACM Computing Surveys},
   Volume = {28},
   Number = {4},
   Pages = {591-606},
   Year = {1996},
   Key = {fds235585}
}

@article{fds235399,
   Author = {Agarwal, PK and Grove, EF and Murali, TM and Vitter,
             JS},
   Title = {Binary space partitions for fat rectangles},
   Journal = {Annual Symposium on Foundations of Computer Science -
             Proceedings},
   Pages = {482-491},
   Booktitle = {Thirty Seventh Annual Symposium on Foundations of Computer
             Science},
   Year = {1996},
   Abstract = {We consider the practical problem of constructing binary
             space partitions (BSPs) for a set S of n orthogonal,
             non-intersecting, two-dimensional rectangles in IR3 such
             that the aspect ratio of each rectangle in S is at most α,
             for some constant α≥1. We present an n2O(√log n)-time
             algorithm to build a binary space partition of size
             n2O(√log n) for S. We also show that if m of the n
             rectangles in S have aspect ratios greater than α, we can
             construct a BSP of size n√m2O(√log n) for S in
             n√m2O(√log n) time. The constants of proportionality in
             the big-oh terms are linear in log α. We extend these
             results to cases in which the input contains non-orthogonal
             or intersecting objects.},
   Key = {fds235399}
}

@article{fds235400,
   Author = {Cohen, J and Varshney, A and Manocha, D and Turk, G and Weber, H and Agarwal, P and Brooks, F and Wright, W},
   Title = {Simplification envelopes},
   Journal = {Proceedings of the ACM SIGGRAPH Conference on Computer
             Graphics},
   Pages = {119-128},
   Booktitle = {SIGGRAPH},
   Year = {1996},
   Abstract = {We propose the idea of simplification envelopes for
             generating a hierarchy of level-of-detail approximations for
             a given polygonal model. Our approach guarantees that all
             points of an approximation are within a user-specifiable
             distance ε from the original model and that all points of
             the original model are within a distance ε from the
             approximation. Simplification envelopes provide a general
             framework within which a large collection of existing
             simplification algorithms can run. We demonstrate this
             technique in conjunction with two algorithms, one local, the
             other global. The local algorithm provides a fast method for
             generating approximations to large input meshes (at least
             hundreds of thousands of triangles). The global algorithm
             provides the opportunity to avoid local `minima' and
             possibly achieve better simplifications as a result. Each
             approximation attempts to minimize the total number of
             polygons required to satisfy the above ε constraint. The
             key advantages of our approach are: General technique
             providing guaranteed error bounds for genus-preserving
             simplification; Automation of both the simplification
             process and the selection of appropriate viewing distances;
             Prevention of self-intersection; Preservation of sharp
             features; and Allows variation of approximation distance
             across different portions of a model.},
   Key = {fds235400}
}

@article{fds329462,
   Author = {Agarwal, PK and Berg, MD and Halperin, D and Sharir,
             M},
   Title = {Efficient Generation of k-Directional Assembly
             Sequences.},
   Journal = {SODA},
   Pages = {122-131},
   Publisher = {ACM/SIAM},
   Editor = {Tardos, É},
   Year = {1996},
   ISBN = {0-89871-366-8},
   Key = {fds329462}
}

@article{fds329461,
   Author = {Wang, H and Agarwal, PK},
   Title = {Approximation Algorithms for Curvature-Constrained Shortest
             Paths.},
   Journal = {SODA},
   Pages = {409-418},
   Publisher = {ACM/SIAM},
   Editor = {Tardos, É},
   Year = {1996},
   ISBN = {0-89871-366-8},
   Key = {fds329461}
}

@book{fds1430,
   Author = {M. Sharir and P.K. Agarwal},
   Title = {Davenport-Schinzel Sequences and Their Geometric
             Applications},
   Publisher = {Cambridge University Press, Cambridge-New
             York-Melbourne},
   Year = {1995},
   Key = {fds1430}
}

@book{fds1431,
   Author = {J. Pach and P.K. Agarwal},
   Title = {Combinatorial Geometry},
   Publisher = {John Wiley and Sons, New York},
   Year = {1995},
   Key = {fds1431}
}

@article{fds1436,
   Author = {M. Sharir and P.K. Agarwal},
   Title = {Algorithmic techniques for geometric optimization},
   Series = {vol. 1000; pp. 234-253},
   Booktitle = {Computer Science Today: Recent Trends and Developments,
             Lecture Notes in Computer Science},
   Publisher = {Springer-Verlag, Berlin},
   Editor = {J. van Leeuwen},
   Year = {1995},
   Key = {fds1436}
}

@article{fds1833,
   Author = {J. Matousek and P.K. Agarwal},
   Title = {Dynamic half-space searching and its applications},
   Journal = {Algorithmica},
   Volume = {14},
   Pages = {325-345},
   Year = {1995},
   Key = {fds1833}
}

@misc{fds23108,
   Author = {P.K. Agarwal and F. Brooks and A. Varshney and H.Weber and W.
             Wright},
   Title = {Multiresolution hierarchy generation of polygonal
             models},
   Journal = {Technical Report CS-1995-20, Department of Computer Science,
             Duke University},
   Year = {1995},
   Key = {fds23108}
}

@article{fds22840,
   Author = {P.K. Agarwal and P. Raghavan and H. Tamaki},
   Title = {Motion planning for a steering-constrained robot through
             moderate obstacles},
   Booktitle = {Twenty Seventh Annual ACM Symposium on Theory of
             Computing},
   Year = {1995},
   Key = {fds22840}
}

@article{fds22841,
   Author = {P.K. Agarwal and B. Aronov and S. Suri},
   Title = {Line stabbing bounds on triangulations in
             3D},
   Booktitle = {Eleventh Annual Symposium on Computational
             Geometry},
   Year = {1995},
   Key = {fds22841}
}

@article{fds22844,
   Author = {P.K. Agarwal and O. Schwarzkopf and M. Sharir},
   Title = {The overlay of envelopes and their applications},
   Booktitle = {Eleventh Annual Symposium on Computational
             Geometry},
   Year = {1995},
   Key = {fds22844}
}

@article{fds22845,
   Author = {P.K. Agarwal and K. R. Varadarajan},
   Title = {Linear approximation of convex objects},
   Booktitle = {Seventh Canadian Conference on Computational
             Geometry},
   Year = {1995},
   Key = {fds22845}
}

@article{fds235394,
   Author = {Agarwal, P},
   Title = {Cellular segregation and engulfment simulations using the
             cell programming language},
   Journal = {Journal of Theoretical Biology},
   Volume = {176},
   Number = {1},
   Pages = {79-89},
   Year = {1995},
   ISSN = {0022-5193},
   url = {http://dx.doi.org/10.1006/jtbi.1995.0178},
   Abstract = {In developmental biology, modeling and simulation play an
             important role in understanding cellular interactions. In
             this paper a simple language, the Cell Programming Language
             (CPL), is suggested for writing programs that describe this
             behavior. Using these programs, it is possible to simulate
             and visualize intercellular behavior. CPL is used to model
             cellular segregation based upon the differential adhesion
             hypothesis. Results indicate that a high degree of
             segregation can be produced in a mixture of cells by
             allowing random motion. The engulfment of a tissue by a less
             adhesive tissue is also observed when the two tissues are
             placed in contact. Both these simulations utilize only local
             interactions and random motion of cells. Earlier simulations
             used long-range interactions to observe similar effects. The
             present simulations prove that random motion of cells can
             produce long-range effects.},
   Doi = {10.1006/jtbi.1995.0178},
   Key = {fds235394}
}

@article{fds235396,
   Author = {Agarwal, PK and Matoušek, J},
   Title = {Dynamic half-space range reporting and its
             applications},
   Journal = {Algorithmica},
   Volume = {13},
   Number = {4},
   Pages = {325-345},
   Year = {1995},
   ISSN = {0178-4617},
   url = {http://dx.doi.org/10.1007/BF01293483},
   Abstract = {We consider the half-space range-reporting problem: Given a
             set S of n points in ℝd, preprocess it into a data
             structure, so that, given a query half-space γ, all k
             points of S ∩ γ can be reported efficiently. We extend
             previously known static solutions to dynamic ones,
             supporting insertions and deletions of points of S. For a
             given parameter m, n ≤m ≤n⌊d/2⌋ and an arbitrarily
             small positive constant e{open}, we achieve O(m1+e{open})
             space and preprocessing time, O((n/m⌊d/2⌋ log n+k) query
             time, and O(m1+e{open}n) amortized update time (d ≳ 3). We
             present, among others, the following applications: an
             O(n1+e{open})-time algorithm for computing convex layers in
             ℝ3, and an output sensitive algorithm for computing a
             level in an arrangements of planes in ℝ3, whose time
             complexity is O((b+n) ne{open}, where b is the size of the
             level. © 1995 Springer-Verlag New York Inc.},
   Doi = {10.1007/BF01293483},
   Key = {fds235396}
}

@article{fds235397,
   Author = {Agarwal, PK and Katz, MJ and Sharir, M},
   Title = {Computing depth orders for fat objects and related
             problems},
   Journal = {Computational Geometry},
   Volume = {5},
   Number = {4},
   Pages = {187-206},
   Year = {1995},
   ISSN = {0925-7721},
   Abstract = {Let K be a set of n non-intersecting objects in 3-space. A
             depth order of K, if it exists, is a linear order &lt; of
             the objects in K such that if K, L ε{lunate} K and K lies
             vertically below L then K &lt; L. We present a new technique
             for computing depth orders, and apply it to several special
             classes of objects. Our results include: (i) If K is a set
             of n triangles whose xy-projections are all 'fat', then a
             depth order for K can be computed in time O(n log5n). (ii)
             If K is a set of n convex and simply-shaped objects whose
             xy-projections are all 'fat' and their sizes are within a
             constant ratio from one another, then a depth order for K
             can be computed in time O(nλs 1 2(n) log4n), where s is the
             maximum number of intersections between the boundaries of
             the xy-projections of any pair of objects in K, and λs(n)
             is the maximum length of (n,s) Davenport-Schinzel sequences.
             © 1995.},
   Key = {fds235397}
}

@article{fds329365,
   Author = {Agarwal, PK and Schwarzkopf, O and Sharir, M},
   Title = {The Overlay of Lower Envelopes in Three Dimensions and Its
             Applications.},
   Journal = {Symposium on Computational Geometry},
   Pages = {182-189},
   Publisher = {ACM},
   Editor = {Snoeyink, J},
   Year = {1995},
   ISBN = {0-89791-724-3},
   url = {http://dx.doi.org/10.1145/220279.220299},
   Doi = {10.1145/220279.220299},
   Key = {fds329365}
}

@article{fds329366,
   Author = {Agarwal, PK and Efrat, A and Sharir, M},
   Title = {Vertical Decomposition of Shallow Levels in 3-Dimensional
             Arrangements and Its Applications.},
   Journal = {Symposium on Computational Geometry},
   Pages = {39-50},
   Booktitle = {Eleventh Annual Symposium on Computational
             Geometry},
   Publisher = {ACM},
   Editor = {Snoeyink, J},
   Year = {1995},
   ISBN = {0-89791-724-3},
   url = {http://dx.doi.org/10.1145/220279.220284},
   Doi = {10.1145/220279.220284},
   Key = {fds329366}
}

@article{fds329367,
   Author = {Agarwal, PK and Aronov, B and Suri, S},
   Title = {Stabbing Triangulations by Lines in 3D.},
   Journal = {Symposium on Computational Geometry},
   Pages = {267-276},
   Publisher = {ACM},
   Editor = {Snoeyink, J},
   Year = {1995},
   ISBN = {0-89791-724-3},
   url = {http://dx.doi.org/10.1145/220279.220308},
   Doi = {10.1145/220279.220308},
   Key = {fds329367}
}

@article{fds329364,
   Author = {Agarwal, PK and Sharir, M},
   Title = {Efficient Randomized Algorithms for Some Geometric
             Optimization Problems.},
   Journal = {Symposium on Computational Geometry},
   Pages = {326-335},
   Booktitle = {Eleventh Annual Symposium on Computational
             Geometry},
   Publisher = {ACM},
   Editor = {Snoeyink, J},
   Year = {1995},
   ISBN = {0-89791-724-3},
   url = {http://dx.doi.org/10.1145/220279.220314},
   Doi = {10.1145/220279.220314},
   Key = {fds329364}
}

@article{fds313242,
   Author = {Agarwal, PK and Aronov, B and Pach, J and Pollack, R and Sharir,
             M},
   Title = {Quasi-Planar Graphs Have a Linear Number of
             Edges.},
   Journal = {Graph Drawing},
   Volume = {1027},
   Pages = {1-7},
   Booktitle = {Symposium on Graph Drawing},
   Publisher = {Springer},
   Editor = {Brandenburg, F-J},
   Year = {1995},
   ISBN = {3-540-60723-4},
   url = {http://www.informatik.uni-trier.de/~ley/db/conf/gd/gd95.html},
   Doi = {10.1007/BFb0021784},
   Key = {fds313242}
}

@article{fds1834,
   Author = {M. van Kreveld and P.K. Agarwal},
   Title = {Implicit point location in arrangement segments with
             application to motion planning},
   Journal = {International Journal of Computational Geometry and
             Applications},
   Volume = {4},
   Pages = {369-383},
   Year = {1994},
   Key = {fds1834}
}

@article{fds1839,
   Author = {J. Matousek and P.K. Agarwal},
   Title = {Range searching with semialgebraic sets},
   Journal = {Discrete and Computational Geometry},
   Volume = {11},
   Pages = {393-418},
   Year = {1994},
   Key = {fds1839}
}

@article{fds22834,
   Author = {P.K. Agarwal and S. Suri},
   Title = {Surface approximation and disjoint geometric
             covers},
   Booktitle = {Fifth Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Year = {1994},
   Key = {fds22834}
}

@article{fds22839,
   Author = {P.K. Agarwal and S. Sen},
   Title = {Selection in monotone matrices and kth nearest
             neighbors},
   Booktitle = {Fourth Scandinavian Workshop on Algorithm
             Theory},
   Year = {1994},
   Key = {fds22839}
}

@article{fds235388,
   Author = {Agarwal, P},
   Title = {Simulation of aggregation in Dictyostelium using the cell
             programming language},
   Journal = {Computer Applications in the Biosciences},
   Volume = {10},
   Number = {6},
   Pages = {647-655},
   Year = {1994},
   Abstract = {In developmental biology, modeling and simulation play an
             important role in understanding cellular interactions. We
             suggest a simple language, the Cell Programming Language
             (CPL), to write computer programs to describe this behavior.
             Using these programs, it is possible to simulate and
             visualize intercellular behavior. We employ CPL to model
             aggregation in Dictyostelium in response to a chemotactic
             agent. CPL programs are utilized to model a variety of
             aggregation behavior including streaming, spiral formation
             and the effect of amoeba density on aggregation patterns. We
             believe CPL is a useful tool for developing, understanding
             and checking biological models that utilize cellular
             interactions.},
   Key = {fds235388}
}

@article{fds235389,
   Author = {Agarwal, P and Sharir, M},
   Title = {Planar geometric location problems},
   Journal = {Algorithmica (New York)},
   Volume = {11},
   Number = {2},
   Pages = {185-195},
   Year = {1994},
   Abstract = {We present an O(n2 log3 n) algorithm for the two-center
             problem, in which we are given a set S of n points in the
             plane and wish to find two closed disks whose union contains
             S so that the larger of the two radii is as small possible.
             We also give an O(n2log4n) algorithm for solving the
             two-line-center problem, where we want to find two strips
             that cover S whose maximum width is as small as possible.
             The best previous solutions of both problems require O(n3)
             time.},
   Key = {fds235389}
}

@article{fds235390,
   Author = {Agarwal, PK},
   Title = {On stabbling lines for convex polyhedra in
             3D},
   Journal = {Computational Geometry},
   Volume = {4},
   Number = {4},
   Pages = {177-189},
   Year = {1994},
   ISSN = {0925-7721},
   Abstract = {A line ℓ is called a stabbling line for a set Bof convex
             polyhedra in R3 if it intersects every polyhedron of B. This
             paper presents an upper bound of O(n3log n) on the
             complexity of the space of stabbling lines for B, where n is
             the number of edges in the polyhedra of B. We solve a more
             general problem that counts the number of faces in a set of
             convex polyhedra, which are implicitly defined by a set of
             half-spaces and a set of hyperplanes. We show that the
             former problem is a special case of the latter problem. We
             also apply this technique to obtain an upper bound on the
             number of distinct faces that ever appear on the
             intersection of a set of half-spaces as we insert or delete
             half-spaces dynamically. © 1994.},
   Key = {fds235390}
}

@article{fds235391,
   Author = {Agarwal, PK and Sharir, M and Toledo, S},
   Title = {Applications of Parametric Searching in Geometric
             Optimization},
   Journal = {Journal of Algorithms},
   Volume = {17},
   Number = {3},
   Pages = {292-318},
   Year = {1994},
   ISSN = {0196-6774},
   url = {http://dx.doi.org/10.1006/jagm.1994.1038},
   Abstract = {We present several applications in computational geometry of
             Megiddo′s parametric searching technique. These
             applications include: (1) Finding the minimum Hausdorff
             distance in the Euclidean metric between two polygonal
             regions under translation; (2) Computing the biggest line
             segment that can be placed inside a simple polygon; (3)
             Computing the smallest width annulus that contains a given
             set of given points in the plane; (4) Given a set of n
             points in 3-space, finding the largest radius r such that if
             we place a ball of radius r around each point, no segment
             connecting a pair of points is intersected by a third ball.
             Besides obtaining efficient solutions to all these problems
             (which, in every case, either improve considerably previous
             solutions or are the first nontrivial solutions to these
             problems), our goal is to demonstrate the versatility of the
             parametric searching technique. © 1994 Academic Press. All
             rights reserved.},
   Doi = {10.1006/jagm.1994.1038},
   Key = {fds235391}
}

@article{fds235392,
   Author = {Agarwal, PK and Matousek, J},
   Title = {On range searching with semialgebraic sets},
   Journal = {Discrete & Computational Geometry},
   Volume = {11},
   Number = {1},
   Pages = {393-418},
   Year = {1994},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/BF02574015},
   Abstract = {Let P be a set of n points in ℝ d (where d is a small
             fixed positive integer), and let Γ be a collection of
             subsets of ℝ d, each of which is defined by a constant
             number of bounded degree polynomial inequalities. We
             consider the following Γ-range searching problem: Given P,
             build a data structure for efficient answering of queries of
             the form, "Given a γ∈Γ, count (or report) the points of
             P lying in γ." Generalizing the simplex range searching
             techniques, we give a solution with nearly linear space and
             preprocessing time and with O(n 1-1/b+δ ) query time, where
             d≤b≤2d-3 and δ&gt;0 is an arbitrarily small constant.
             The acutal value of b is related to the problem of
             partitioning arrangements of algebraic surfaces into cells
             with a constant description complexity. We present some of
             the applications of Γ-range searching problem, including
             improved ray shooting among triangles in ℝ3. © 1994
             Springer-Verlag New York Inc.},
   Doi = {10.1007/BF02574015},
   Key = {fds235392}
}

@article{fds235393,
   Author = {Agarwal, PK and Alon, N and Aronov, B and Suri, S},
   Title = {Can visibility graphs Be represented compactly?},
   Journal = {Discrete & Computational Geometry},
   Volume = {12},
   Number = {1},
   Pages = {347-365},
   Year = {1994},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/BF02574385},
   Abstract = {We consider the problem of representing the visibility graph
             of line segments as a union of cliques and bipartite
             cliques. Given a graph G, a family G={G 1, G 2,..., G k } is
             called a clique cover of G if (i) each G i is a clique or a
             bipartite clique, and (ii) the union of G i is G. The size
             of the clique cover G is defined as ∑ i=1 k n i, where n i
             is the number of vertices in G i . Our main result is that
             there are visibility graphs of n nonintersecting line
             segments in the plane whose smallest clique cover has size
             Ω(n 2/log2 n). An upper bound of O(n 2/log n) on the clique
             cover follows from a well-known result in extremal graph
             theory. On the other hand, we show that the visibility graph
             of a simple polygon always admits a clique cover of size
             O(nlog3 n), and that there are simple polygons whose
             visibility graphs require a clique cover of size Ω(n log
             n). © 1994 Springer-Verlag New York Inc.},
   Doi = {10.1007/BF02574385},
   Key = {fds235393}
}

@article{fds235395,
   Author = {Agarwal, PK and Sharir, M},
   Title = {On the number of views of polyhedral terrains},
   Journal = {Discrete & Computational Geometry},
   Volume = {12},
   Number = {1},
   Pages = {177-182},
   Year = {1994},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/BF02574373},
   Abstract = {We show that the number of topologically different
             orthographic views of a polyhedral terrain with n edges is
             O(n 5+e{open} ), and that the number of topologically
             different perspective views of such a terrain is O(n
             8+e{open} ), for any e{open}&gt;0. Both bounds are almost
             tight in the worst case. The proofs are simple consequences
             of the recent almost-tight bounds of [11] on the complexity
             of lower envelopes in higher dimensions. © 1994
             Springer-Verlag New York Inc.},
   Doi = {10.1007/BF02574373},
   Key = {fds235395}
}

@article{fds235580,
   Author = {Agarwal, PK and Suri, S},
   Title = {Surface approximation and geometric partitions},
   Journal = {Proceedings of the Annual ACM SIAM Symposium on Discrete
             Algorithms},
   Pages = {24-33},
   Year = {1994},
   Abstract = {Motivated by applications in scientific computation,
             visualization, and computer graphics, we study the
             computational complexity of the following problem: Given a
             set S of n points sampled from a bivariate function f(x,y)
             and an input parameter ε&lt;0, compute a piecewise linear
             function Σ(x,y) of minimum complexity (that is, a
             xy-monotone polyhedral surface, with a minimum number of
             vertices, edges, or faces) such that |Σ(xp,yp)-zp|≤ε,
             for any (xp,yp,zp) ∈ S. We prove that the decision version
             of this problem is NP-Hard. The main result of our paper is
             a polynomial-time approximation algorithm that computes a
             piecewise linear surface of size O(Ko log Ko), where Ko is
             the complexity of an optimal surface satisfying the
             constraints of the problem. The technique developed in our
             paper is more general and applies to several other problems
             that deal with partitioning of points (or other objects)
             subject to certain geometric constraints. For instance, we
             get the same approximation bound for the following problem,
             which arises in machine learning: given n `red' and m `blue'
             points in the plane, find a minimum number of pairwise
             disjoint triangles such that each blue point is covered by
             some triangle and no red point lies in any of the
             triangles.},
   Key = {fds235580}
}

@article{fds235385,
   Author = {Agarwal, PK and Berg, MD and Matousek, J and Schwarzkopf,
             O},
   Title = {Constructing levels in arrangements and higher order Voronoi
             diagrams},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {67-75},
   Booktitle = {Tenth Annual Symposium on Computational Geometry},
   Year = {1994},
   Abstract = {We give a simple lazy randomized incremental algorithm to
             compute ≤k-levels in arrangements of x-monotone Jordan
             curves in the plane, and in arrangements of planes in
             three-dimensional space. If each pair of curves intersects
             in at most s points, the expected running time of the
             algorithm is O(k2λs(n/k) + min(λs(n) log2 n, k2λs(n/k)
             log n)). For the three-dimensional case the expected running
             time is O(nk2 + min(n log3 n, nk2 log n)). The algorithm
             also works for computing the ≤k-level in a set of discs,
             with an expected running time of O(nk + min(n log2 n, nk log
             n)). Furthermore, we give a simple algorithm for computing
             the order-k Voronoi diagram of a set of n points in the
             plane that runs in expected time O(k(n - k) log n + n log3
             n).},
   Key = {fds235385}
}

@article{fds235386,
   Author = {Agarwal, PK and Aronov, B and Sharir, M},
   Title = {Computing envelopes in four dimensions with
             applications},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {348-358},
   Booktitle = {Tenth Annual Symposium on Computational Geometry},
   Year = {1994},
   Abstract = {Let F be a collection of n d-variate, possibly partially
             defined, functions, all algebraic of some constant maximum
             degree. We present a randomized algorithm that computes the
             vertices, edges, and 2-faces of the lower envelope (i.e.,
             pointwise minimum) of F in expected time O(nd+ε), for any
             ε &gt; 0. For d = 3, by combining this algorithm with the
             point location technique of Preparata and Tamassia, we can
             compute, in randomized expected time O(n3+ε), for any ε
             &gt; 0, a data structure of size O(n3+ε) that, given any
             query point q, can determine in O(log2 n) time whether q
             lies above, below or on the envelope. As a consequence, we
             obtain improved algorithmic solutions to many problems in
             computational geometry, including (a) computing the width of
             a point set in 3-space, (b) computing the biggest stick in a
             simple polygon in the plane, and (c) computing the
             smallest-width annulus covering a planar point set. The
             solutions to these problems run in time O(n17/11+ε), for
             any ε &gt; 0, improving previous solutions that run in time
             O(n8/5+ε). We also present data structures for (i)
             performing nearest-neighbor and related queries for fairly
             general collections of objects in 3-space and for
             collections of moving objects in the plane, and (ii)
             performing ray-shooting and related queries among n spheres
             or more general objects in 3-space. Both of these data
             structures require O(n3+ε) storage and preprocessing time,
             for any ε &gt; 0, and support polylogarithmic-time queries.
             These structures improve previous solutions to these
             problems.},
   Key = {fds235386}
}

@article{fds235387,
   Author = {Agarwal, PK and Matousek, J and Schwarzkopf, O},
   Title = {Computing many faces in arrangements of lines and
             segments},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {76-84},
   Booktitle = {Tenth Annual Symposium on Computational Geometry},
   Year = {1994},
   Abstract = {We present randomized algorithms for computing many faces in
             an arrangement of lines or of segments in the plane, which
             are considerably simpler and slightly faster than the
             previously known ones. The main new idea is a simple
             randomized O(n log n) expected time algorithm for computing
             √n cells in an arrangement of n lines.},
   Key = {fds235387}
}

@article{fds328997,
   Author = {Agarwal, PK and Sen, S},
   Title = {Selection in Monotone Matrices and Computing kth Nearest
             Neighbors.},
   Journal = {SWAT},
   Volume = {824},
   Pages = {13-24},
   Publisher = {Springer},
   Editor = {Schmidt, EM and Skyum, S},
   Year = {1994},
   ISBN = {3-540-58218-5},
   url = {http://dx.doi.org/10.1007/3-540-58218-5_2},
   Doi = {10.1007/3-540-58218-5_2},
   Key = {fds328997}
}

@article{fds328998,
   Author = {Agarwal, PK and Katz, MJ and Sharir, M},
   Title = {Computing Depth Orders and Related Problems.},
   Journal = {SWAT},
   Volume = {824},
   Pages = {1-12},
   Booktitle = {Fourth Scandinavian Workshop on Algorithm
             Theory},
   Publisher = {Springer},
   Editor = {Schmidt, EM and Skyum, S},
   Year = {1994},
   ISBN = {3-540-58218-5},
   url = {http://dx.doi.org/10.1007/3-540-58218-5_1},
   Doi = {10.1007/3-540-58218-5_1},
   Key = {fds328998}
}

@article{fds329183,
   Author = {Agarwal, PK and Van Kreveld and M},
   Title = {Connected component and simple polygon intersection
             searching},
   Journal = {Lecture notes in computer science},
   Volume = {709 LNCS},
   Pages = {37-47},
   Year = {1993},
   Month = {January},
   ISBN = {9783540571551},
   Abstract = {© Springer-Verlag Berlin Heidelberg 1993. Efficient data
             structures are given for the following two query problems:
             (i) Preprocess a set P of simple polygons with a total of n
             edges, so that all polygons of P intersected by a query
             segment can be reported efficiently, and (ii) Preprocess a
             set S of n segments, so that the connected components of the
             arrangement of S intersected by a query segment can be
             reported quickly. In both cases the data structure should
             return the labels of the intersected polygons or components,
             not their complete description. Efficient data structures
             are presented for the static case, the dynamic case, and an
             efficient on-line construction algorithm for the connected
             components is given.},
   Key = {fds329183}
}

@article{fds1846,
   Author = {M. Sharir and P.K. Agarwal},
   Title = {Circular visibility of a simple polygon from a fixed
             point},
   Journal = {International Journal of Computational Geometry and
             Applications},
   Volume = {3},
   Pages = {1-25},
   Year = {1993},
   Key = {fds1846}
}

@misc{fds23107,
   Author = {P.K. Agarwal and M. Sharir and S. Toledo},
   Title = {An efficient multidimensional searching technique and its
             applications},
   Journal = {Technical Report CS-1993-20, Department of Computer Science,
             Duke University},
   Year = {1993},
   Key = {fds23107}
}

@article{fds22830,
   Author = {P.K. Agarwal and M. Sharir},
   Title = {Ray shooting among convex polytopes in 3D},
   Booktitle = {Fourth Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Year = {1993},
   Key = {fds22830}
}

@article{fds22832,
   Author = {P.K. Agarwal and M. van Kreveld},
   Title = {Polygon and connected component intersection
             searching},
   Booktitle = {Third Workshop on Algorithms and Data Structures},
   Year = {1993},
   Key = {fds22832}
}

@article{fds22833,
   Author = {P.K. Agarwal and M. Sharir},
   Title = {On the number of views of polyhedral terrains},
   Booktitle = {Fifth Canadian Conference on Computational
             Geometry},
   Year = {1993},
   Key = {fds22833}
}

@article{fds235571,
   Author = {Agarwal, PK and Sharir, M},
   Title = {Circle Shooting in a Simple Polygon},
   Journal = {Journal of Algorithms},
   Volume = {14},
   Number = {1},
   Pages = {69-87},
   Year = {1993},
   ISSN = {0196-6774},
   url = {http://dx.doi.org/10.1006/jagm.1993.1004},
   Abstract = {Consider the following problem: Given a simple n-gon P,
             preprocess it so that for a query circle π and a point s on
             π, one can quickly compute Φ(P, π, s), the first
             intersection point between P and π as we follow π from s
             in clockwise direction. We show that P can be preprocessed,
             in time O(n log3n), into a data structure of size O(n
             log3n), so that, for a query circle π, Φ(P, π, s) can be
             computed in O(log4n) time. We apply the circle shooting
             algorithm to report all K intersections between a set of m
             circular arcs and another set of n circular arcs in time
             O((m√n + n√m )log2.5(m + n) + (K + m + n)log4(m + n)).
             © 1993 Academic Press. All rights reserved.},
   Doi = {10.1006/jagm.1993.1004},
   Key = {fds235571}
}

@article{fds235572,
   Author = {Agarwal, PK and Sharir, M},
   Title = {Ray shooting amidst convex polytopes in three
             dimensions},
   Journal = {Proceedings of the Fourth Annual ACM-SIAM Symposium on
             Discrete Algorithms},
   Pages = {260-270},
   Year = {1993},
   Abstract = {We consider the problem of ray shooting in a 3-dimensional
             scene consisting of m (possibly intersecting) convex
             polyhedra with a total of n faces, i.e., we want to
             preprocess them into a data structure, so that the first
             intersection point of a query ray and the given polyhedra
             can be determined quickly. We present a technique that
             requires O((mn)2+ε) preprocessing time and storage, and can
             answer ray shooting queries in O(log n) time. This is a
             significant improvement over previously known techniques
             (which require O(n4+ε) space and preprocessing) if m is
             much smaller than n, which is often the case in practice. We
             also present a variant of the technique that requires
             O(n1+ε) space and preprocessing, and answers queries in
             time O(m1/4n1/2+ε), again a significant improvement over
             previous techniques when m≪n. Our algorithms also work
             when the given polyhedra intersect, and also apply to a
             collection of (possibly intersecting) polyhedral
             terrains.},
   Key = {fds235572}
}

@article{fds235574,
   Author = {Agarwal, PK and Matousek, J},
   Title = {Ray shooting and parametric search},
   Journal = {SIAM Journal on Computing},
   Volume = {22},
   Number = {4},
   Pages = {794-806},
   Year = {1993},
   Abstract = {Efficient algorithms for the ray shooting problem are
             presented: Given a collection Γ of objects in Rd, build a
             data structure so that, for a query ray, the first object of
             Γ hit by the ray can be quickly determined. Using the
             parametric search technique, this problem is reduced to the
             segment emptiness problem. For various ray shooting
             problems, space/query-time trade-offs of the following type
             are achieved: For some integer b and a parameter m
             (n≤m≤nb) the queries are answered in time
             O((n/m1/b)logO(1)n), with O(m1+ε) space and preprocessing
             time (ε&gt;0 is arbitrarily small but fixed constant). b =
             [d/2] is obtained for ray shooting in a convex d-polytope
             defined as an intersection of n half spaces, b = d for an
             arrangement of n hyperplanes in Rd, and b = 3 for an
             arrangement of n half planes in R3. This approach also
             yields fast procedures for finding the first k objects hit
             by a query ray, for searching nearest and farthest
             neighbors, and for the hidden surface removal. All the data
             structures can be maintained dynamically in amortized time
             O(m1+ε/n) per insert/delete operation.},
   Key = {fds235574}
}

@article{fds235575,
   Author = {Agarwal, PK and Aronov, B and Sharir, M and Suri,
             S},
   Title = {Selecting distances in the plane},
   Journal = {Algorithmica},
   Volume = {9},
   Number = {5},
   Pages = {495-514},
   Year = {1993},
   ISSN = {0178-4617},
   url = {http://dx.doi.org/10.1007/BF01187037},
   Abstract = {We present a randomized algorithm for computing the kth
             smallest distance in a set of n points in the plane, based
             on the parametric search technique of Megiddo [Mel]. The
             expected running time of our algorithm is O(n4/3 log8/3n).
             The algorithm can also be made deterministic, using a more
             complicated technique, with only a slight increase in its
             running time. A much simpler deterministic version of our
             procedure runs in time O(n3/2 log5/2n). All versions improve
             the previously best-known upper bound of O(@#@ n9/5 log4/5n)
             by Chazelle [Ch]. A simple O(n log n)-time algorithm for
             computing an approximation of the median distance is also
             presented. © 1993 Springer-Verlag New York
             Inc.},
   Doi = {10.1007/BF01187037},
   Key = {fds235575}
}

@article{fds235576,
   Author = {Agarwal, PK and Pellegrini, M and Sharir, M},
   Title = {Counting circular arc intersections},
   Journal = {SIAM Journal on Computing},
   Volume = {22},
   Number = {4},
   Pages = {778-793},
   Year = {1993},
   Abstract = {In this paper efficient algorithms for counting
             intersections in a collection of circles or circular arcs
             are presented. An algorithm for counting intersections in a
             collection of n circles is presented whose running time is
             O(n3/2+ε), for any ε&gt;0 is presented. Using this
             algorithm as a subroutine, it is shown that the
             intersections in a set of n circular arcs can also be
             counted in time O(n3/2+ε). If all arcs have the same
             radius, the running time can be improved to O(n4/3+ε), for
             any ε&gt;0.},
   Key = {fds235576}
}

@article{fds235577,
   Author = {Agarwal, PK and Efrat, A and Sharir, M and Toledo,
             S},
   Title = {Computing a Segment Center for a Planar Point
             Set},
   Journal = {Journal of Algorithms},
   Volume = {15},
   Number = {2},
   Pages = {314-323},
   Year = {1993},
   ISSN = {0196-6774},
   url = {http://dx.doi.org/10.1006/jagm.1993.1043},
   Abstract = {Given a set S of n points in the plane and a segment e, a
             center placement of e is a placement (allowing translation
             and rotation) that minimizes the maximum distance from e to
             the points of S. We present an algorithm for computing a
             center placement for S, whose running time is
             O(n2α(n)log3n), where α(n) is the inverse Ackermann
             function. The algorithm makes use of the parametric
             searching technique of Megiddo. © 1993 Academic Press. All
             rights reserved.},
   Doi = {10.1006/jagm.1993.1043},
   Key = {fds235577}
}

@article{fds235578,
   Author = {Agarwal, PK and Vankreveld, M and Overmars, M},
   Title = {Intersection Queries in Curved Objects},
   Journal = {Journal of Algorithms},
   Volume = {15},
   Number = {2},
   Pages = {229-266},
   Year = {1993},
   ISSN = {0196-6774},
   url = {http://dx.doi.org/10.1006/jagm.1993.1040},
   Abstract = {A number of problems of the following type are studied:
             Given a set of n arcs (disks, circles, circular arcs, Jordan
             arcs) in the plane, preprocess it into a data structure, so
             that for a query line (or segment) one can quickly (i)
             report all arcs intersecting it, or (ii) count the number of
             arcs intersecting it. We also study the ray-shooting problem
             among disjoint Jordan arcs and circular arcs. Most of the
             data structures presented here use close to linear space and
             have query time close to O(√n + K) or O(n2/3 + K), where K
             is the size of the output. © 1993 Academic Press. All
             rights reserved.},
   Doi = {10.1006/jagm.1993.1040},
   Key = {fds235578}
}

@article{fds235579,
   Author = {Agarwal, PK and Sharir, M},
   Title = {Applications of a new space-partitioning
             technique},
   Journal = {Discrete & Computational Geometry},
   Volume = {9},
   Number = {1},
   Pages = {11-38},
   Year = {1993},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/BF02189304},
   Abstract = {We present several applications of a recent
             space-partitioning technique of Chazelle, Sharir, and Welzl
             (Proceedings of the 6th Annual ACM Symposium on
             Computational Geometry, 1990, pp. 23-33). Our results
             include efficient algorithms for output-sensitive hidden
             surface removal, for ray shooting in two and three
             dimensions, and for constructing spanning trees with low
             stabbing number. © 1993 Springer-Verlag New York
             Inc.},
   Doi = {10.1007/BF02189304},
   Key = {fds235579}
}

@article{fds235573,
   Author = {Agarwal, PK and Alon, N and Aronov, B and Suri, S},
   Title = {Can visibility graphs be represented compactly?},
   Journal = {Proceedings of the 9th Annual Symposium on Computational
             Geometry},
   Pages = {338-347},
   Booktitle = {Ninth Annual Symposium on Computational Geometry},
   Year = {1993},
   Abstract = {We consider the problem of representing the visibility graph
             of line segments as a union of cliques and bipartite
             cliques. Given a graph G, a family G = {G1, G2,..., Gk} is
             called a clique cover of G if (i) each Gi is a clique or a
             bipartite clique, and (ii) the union of Gi is G. The size of
             the clique cover G is defined as Σik=1 ni, where ni is the
             number of vertices in Gi. Our main result is that there
             exist visibility graphs of n nonintersecting line segments
             in the plane whose smallest clique cover has size Ω(n2/log2
             n). An upper bound of O(n2/log n) on the clique cover
             follows from a well-known result in extremal graph theory.
             On the other hand, we show that the visibility graph of a
             simple polygon always admits a clique cover a size O(n log3
             n), and that there are simple polygons whose visibility
             graphs require a clique cover of size Ω(n log
             n).},
   Key = {fds235573}
}

@article{fds329184,
   Author = {Agarwal, PK and van Kreveld, M},
   Title = {Implicit point location of line segments, with an
             arrangements an application to motion planning},
   Journal = {Lecture notes in computer science},
   Volume = {652 LNCS},
   Pages = {80-91},
   Year = {1992},
   Month = {January},
   ISBN = {9783540562870},
   Abstract = {© 1992, Springer Verlag. All rights reserved. Let S be a
             set of n (possibly intersecting) line segments in the plane.
             We show that tile arrangement of S can be stored implicitly
             into a data structure of size O(n log 2 n) so that the
             following query can be answered in time O(n 1/2 log 2 n):
             Given two query points, determine whether they lie in the
             same face of the arrangemen t of S and, if so, return a path
             between them that lies within the face. This version of the
             implicit point location problem is motivated by the
             following motion planning problem: Given a polygonal robot R
             with m vertices and a planar region bounded by polygonal
             obstacles with n vertices in total, prcprocess them into a
             data structure so that, glvcn initial and final positions of
             R, one can quickly dctermine whether there exists a
             continuous collision-free translational motion of R from the
             initial to the final position. We show that such a query can
             be answered in time O((mn) 1/2 log 2 mn) using O(mn log 2
             mn) storage.},
   Key = {fds329184}
}

@article{fds1852,
   Author = {P.K. Agarwal},
   Title = {Ray shooting and other applications of spanning trees with
             low stabbing number},
   Journal = {SIAM Journal on Computing},
   Volume = {21},
   Pages = {540-570},
   Year = {1992},
   Key = {fds1852}
}

@article{fds22827,
   Author = {P.K. Agarwal and J. Matousek},
   Title = {Range searching with semialgebraic sets},
   Booktitle = {Seventeenth Symposium on Mathematical Foundations of
             Computer Science},
   Year = {1992},
   Key = {fds22827}
}

@article{fds22828,
   Author = {P.K. Agarwal and D. Eppstein and J. Matousek},
   Title = {Dynamic half-space range searching with applications to
             proximity problems},
   Booktitle = {Thirty Third Annual Symposium on Foundations of Computer
             Science},
   Year = {1992},
   Key = {fds22828}
}

@article{fds22829,
   Author = {P.K. Agarwal and M. van Kreveld},
   Title = {Implicit point location in arrangement segments with
             application to motion planning},
   Booktitle = {Twelfth Conference on Foundations of Software Technology and
             Theoretical Computer Science},
   Year = {1992},
   Key = {fds22829}
}

@article{fds235565,
   Author = {Agarwal, PK and Matoušek, J and Suri, S},
   Title = {Farthest neighbors, maximum spanning trees and related
             problems in higher dimensions},
   Journal = {Computational Geometry},
   Volume = {1},
   Number = {4},
   Pages = {189-201},
   Year = {1992},
   ISSN = {0925-7721},
   Abstract = {We present a randomized algorithm of expected time
             complexity O(m 2 3n 2 3log 4 3m + m log2m + n log2n) for
             computing bi-chromatic farthest neighbors between n red
             points and m blue points in E3. The algorithm can also be
             used to compute all farthest neighbors or external farthest
             neighbors of n points in E3 in O(n 4 3log 4 3n) expected
             time. Using these procedures as building blocks, we can
             compute a Euclidean maximum spanning tree or a
             minimum-diameter two-partition of n points in E3 in O(n 4
             3log 7 3n) expected time. The previous best bound for these
             problems was O(n 3 2log 1 2n). Our algorithms can be
             extended to higher dimensions. We also propose fast and
             simple approximation algorithms for these problems. These
             approximation algorithms produce solutions that approximate
             the true value with a relative accuracy ε and run in time
             O(nε (1-k) 2log n) or O(nε (1-k) 2log2n) in k-dimensional
             space. © 1992.},
   Key = {fds235565}
}

@article{fds235567,
   Author = {Agarwal, PK and Matoušek, J},
   Title = {Relative neighborhood graphs in three dimensions},
   Journal = {Computational Geometry},
   Volume = {2},
   Number = {1},
   Pages = {1-14},
   Year = {1992},
   ISSN = {0925-7721},
   Abstract = {The relative neighborhood graph (RNG) of a set S of n points
             in Rd is a graph (S, E), where (p, q)∈E if and only if
             there is no point z∈S such that max{d(p, z), d(q,
             z)}&lt;d(p, q). We show that in R3, RNG(S) has O(n 4 3)
             edges. We present a randomized algorithm that constructs
             RNG(S) in expected time O(n 3 2+ε) assuming that the points
             of S are in general position. If the points of S are
             arbitrary, the expected running time is O(n 7 4+ε). These
             algorithms can be made deterministic without affecting their
             asymptotic running time. © 1992.},
   Key = {fds235567}
}

@article{fds235568,
   Author = {Kreveld, MV and Overmars, M and Agarwal, PK},
   Title = {Intersection queries in sets of disks},
   Journal = {BIT Numerical Mathematics},
   Volume = {32},
   Number = {2},
   Pages = {268-279},
   Year = {1992},
   ISSN = {0006-3835},
   url = {http://dx.doi.org/10.1007/BF01994881},
   Abstract = {In this paper we develop some new data structures for
             storing a set of disks that can answer different types of
             intersection queries efficiency. If the disks are
             non-intersecting we obtain a linear size data structure that
             can report all k disks intersecting a query line segment in
             time O(nβ+ε+k), where n is the number of disks,
             β=log2(1+√5)-1 ≈ 0.695, and ε is an arbitrarily small
             positive constant. If the segment is a full line, the query
             time becomes O(nβ+k). For intersecting disks we obtain an
             O(n log n) size data structure that can answer an
             intersection query in time O(n2/3 log2n+k). We also present
             a linear size data structure for ray shooting queries, whose
             query time is O(nβ). © 1992 BIT Foundations.},
   Doi = {10.1007/BF01994881},
   Key = {fds235568}
}

@article{fds235569,
   Author = {Agarwal, PK and Aronov, B},
   Title = {Counting facets and incidences},
   Journal = {Discrete & Computational Geometry},
   Volume = {7},
   Number = {1},
   Pages = {359-369},
   Year = {1992},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/BF02187848},
   Abstract = {We show that m distinct cells in an arrangement of n planes
             in ℝ3 are bounded by O(m2/3n+n2) faces, which in turn
             yields a tight bound on the maximum number of facets
             bounding m cells in an arrangement of n hyperplanes in ℝd,
             for every d≥3. In addition, the method is extended to
             obtain tight bounds on the maximum number of faces on the
             boundary of all nonconvex cells in an arrangement of
             triangles in ℝ3. We also present a simpler proof of the
             O(m2/3nd/3+nd-1) bound on the number of incidences between n
             hyperplanes in ℝd and m vertices of their arrangement. ©
             1992 Springer-Verlag New York Inc.},
   Doi = {10.1007/BF02187848},
   Key = {fds235569}
}

@article{fds235570,
   Author = {Agarwal, PK and Shing, M-T},
   Title = {Oriented aligned rectangle packing problem},
   Journal = {European Journal of Operational Research},
   Volume = {62},
   Number = {2},
   Pages = {210-220},
   Year = {1992},
   ISSN = {0377-2217},
   Abstract = {Given a collection R of n (= M × N) rectangles, we wish to
             pack it into M rows and N columns as the elements of an M ×
             N matrix. The height of a row is defined to be the height of
             the tallest rectangle in that row, and the width of a column
             is defined to be the width of the widest rectangle in that
             column. The cost of a packing is the sum of the heights of
             the M rows plus the sum of the widths of the N columns. The
             oriented aligned rectangle packing problem is to find a
             packing with the minimum cost. In this paper we present an
             O(n) time algorithm and an O(n2) time algorithm for two
             non-trivial special cases. We also show how to extend the
             algorithms to handle other cost functions. ©
             1992.},
   Key = {fds235570}
}

@article{fds235566,
   Author = {Agarwal, PK and Matousek, J},
   Title = {Ray shooting and parametric search},
   Journal = {Conference Proceedings of the Annual ACM Symposium on Theory
             of Computing},
   Pages = {517-526},
   Booktitle = {Twenty Fourth Annual ACM Symposium on Theory of
             Computing},
   Year = {1992},
   Abstract = {We present efficient algorithms for the ray shooting
             problem: Given a collection Γ of objects in Rd, build a
             data structure, so that one can quickly determine the first
             object of Γ hit by a query ray. Using the parametric search
             technique, we reduce this problem to the segment emptiness
             problem. For various ray shooting problems, we achieve
             space/query time tradeoffs of the following type: for some
             integer b and a parameter m (n≤m≤nb) the queries are
             answered in time O(n/m1/b logO(1) n), with O(m1+ε) space
             and preprocessing time (ε&gt;0 is arbitrarily small but
             fixed). We get b = [d/2] for ray shooting in a convex
             d-polytope defined as an intersection of n half-spaces, b =
             d for an arrangement of n hyperplanes in Rd and b = 3 for an
             arrangement of n half-planes in R3. Next we apply the ray
             shooting algorithms to several problems including reporting
             k-nearest (or k-farthest) neighbors, hidden surface removal,
             computing convex layers, and computing levels in
             arrangements of planes. All the algorithms described here
             either give the first nontrivial solutions to these
             problems, or improve the previously best known solutions
             significantly.},
   Key = {fds235566}
}

@article{fds329463,
   Author = {Agarwal, PK and Matousek, J},
   Title = {Relative Neighborhood Graphs in Three Dimensions.},
   Journal = {SODA},
   Pages = {58-65},
   Booktitle = {Third Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Publisher = {ACM/SIAM},
   Editor = {Frederickson, GN},
   Year = {1992},
   ISBN = {0-89791-466-X},
   Key = {fds329463}
}

@article{fds329464,
   Author = {Agarwal, PK and Sharir, M and Toledo, S},
   Title = {Applications of Parametric Searching in Geometric
             Optimization.},
   Journal = {SODA},
   Pages = {72-82},
   Booktitle = {Third Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Publisher = {ACM/SIAM},
   Editor = {Frederickson, GN},
   Year = {1992},
   ISBN = {0-89791-466-X},
   Key = {fds329464}
}

@article{fds329185,
   Author = {Agarwal, PK and Matousek, J},
   Title = {On Range Searching with Semialgebraic Sets.},
   Journal = {MFCS},
   Volume = {629},
   Pages = {1-13},
   Publisher = {Springer},
   Editor = {Havel, IM and Koubek, V},
   Year = {1992},
   ISBN = {3-540-55808-X},
   url = {http://dx.doi.org/10.1007/3-540-55808-X_1},
   Doi = {10.1007/3-540-55808-X_1},
   Key = {fds329185}
}

@book{fds1429,
   Author = {P. K. Agarwal},
   Title = {Intersection and Decomposition Algorithms for Planar
             Arrangements,},
   Publisher = {Cambridge University Press, Cambridge-New
             York-Melbourne},
   Year = {1991},
   Key = {fds1429}
}

@article{fds1856,
   Author = {H. Edelsbrunner and O. Schwarzkopf and E. Welzl and P.K.
             Agarwal},
   Title = {Euclidean minimum spanning tree and bichromatic closest
             pairs},
   Journal = {Discrete and Computational Geometry},
   Volume = {6},
   Pages = {407-422},
   Year = {1991},
   Key = {fds1856}
}

@article{fds22774,
   Author = {P.K. Agarwal},
   Title = {Geometric partitioning and its applications},
   Pages = {1-37},
   Booktitle = {Discrete and Computational Geometry: Papers from the DIMACS
             Special Year},
   Publisher = {American Mathematical Society},
   Editor = {J. Goodman and R. Pollack and W. Steiger},
   Year = {1991},
   Key = {fds22774}
}

@article{fds22812,
   Author = {P.K. Agarwal and M. Sharir},
   Title = {Planar geometric location problems and maintaining the width
             of a planar set},
   Booktitle = {Second Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Year = {1991},
   Key = {fds22812}
}

@article{fds22813,
   Author = {P.K. Agarwal and M. Sharir},
   Title = {Counting circular arc intersections},
   Booktitle = {Seventh Annual Symposium on Computational
             Geometry},
   Year = {1991},
   Key = {fds22813}
}

@article{fds22814,
   Author = {P.K. Agarwal and M. Sharir},
   Title = {Applications of a new space partitioning
             technique},
   Booktitle = {Second Workshop on Algorithms and Data Structures},
   Year = {1991},
   Key = {fds22814}
}

@article{fds22818,
   Author = {P.K. Agarwal and M. van Kreveld and M. Overmars},
   Title = {Storing and searching curved objects},
   Booktitle = {Seventh Annual Symposium on Computational
             Geometry},
   Year = {1991},
   Key = {fds22818}
}

@article{fds22824,
   Author = {P.K. Agarwal and J. Matousek and S. Suri},
   Title = {Farthest neighbors, maximum spanning trees and related
             problems in higher dimensions},
   Booktitle = {Second Workshop on Algorithms and Data Structures},
   Year = {1991},
   Key = {fds22824}
}

@article{fds235384,
   Author = {Agarwal, PK and Edelsbrunner, H and Schwarzkopf, O and Welzl,
             E},
   Title = {Euclidean minimum spanning trees and bichromatic closest
             pairs},
   Journal = {Discrete & Computational Geometry},
   Volume = {6},
   Number = {1},
   Pages = {407-422},
   Year = {1991},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/BF02574698},
   Abstract = {We present an algorithm to compute a Euclidean minimum
             spanning tree of a given set S of N points in E d in time
             O(F d (N,N) log d N), where F d (n,m) is the time required
             to compute a bichromatic closest pair among n red and m
             green points in E d . If F d (N,N)=Ω(N 1+ε), for some
             fixed e{open}&gt;0, then the running time improves to O(F d
             (N,N)). Furthermore, we describe a randomized algorithm to
             compute a bichromatic closest pair in expected time O((nm
             log n log m)2/3+m log2 n+n log2 m) in E 3, which yields an
             O(N 4/3 log4/3 N) expected time, algorithm for computing a
             Euclidean minimum spanning tree of N points in E 3. In d≥4
             dimensions we obtain expected time O((nm)1-1/([d/2]+1)+ε+m
             log n+n log m) for the bichromatic closest pair problem and
             O(N 2-2/([d/2]+1)ε) for the Euclidean minimum spanning tree
             problem, for any positive e{open}. © 1991 Springer-Verlag
             New York Inc.},
   Doi = {10.1007/BF02574698},
   Key = {fds235384}
}

@article{fds235563,
   Author = {Agarwal, PK and Aggarwal, A and Aronov, B and Kosaraju, SR and Schieber,
             B and Suri, S},
   Title = {Computing external farthest neighbors for a simple
             polygon},
   Journal = {Discrete Applied Mathematics},
   Volume = {31},
   Number = {2},
   Pages = {97-111},
   Year = {1991},
   ISSN = {0166-218X},
   Abstract = {Let P be (the boundary of) a simple polygon with n vertices.
             For a vertex p of P, let φ{symbol}(p) be the set of points
             on P that are farthest from p, where the distance between
             two points is the length of the (Euclidean) shortest path
             that connects them without intersecting the interior of P.
             In this paper, we present an O(n log n) algorithm to compute
             a member of φ{symbol}(p) for every vertex p of P. As a
             corollary, the external diameter of P can also be computed
             in the same time. © 1991.},
   Key = {fds235563}
}

@article{fds235564,
   Author = {Agarwal, PK and Sharir, M},
   Title = {Off-line dynamic maintenance of the width of a planar point
             set},
   Journal = {Computational Geometry},
   Volume = {1},
   Number = {2},
   Pages = {65-78},
   Year = {1991},
   ISSN = {0925-7721},
   Abstract = {Agarwal, P.K. and M. Sharir, Off-line dynamic maintenance of
             the width of a planar point set, Computational Geometry:
             Theory and Applications 1 (1990) 65-78. In this paper we
             present an efficient algorithm for the off-line dynamic
             maintenance of the width of a planar point set in the
             following restricted case: We are given a real parameter W
             and a sequence Σ=(σ1,...,σn) of n insert and delete
             operations on a set S of points in R2, initially consisting
             of n points, and we want to determine whether there is an i
             such that the width of S the ith operation is less than or
             equal to W. Our algorithm runs in time O(nlog3n) and uses
             O(n) space. © 1991.},
   Key = {fds235564}
}

@article{fds1859,
   Author = {P.K. Agarwal},
   Title = {Partitioning arrangements of lines: I. A deterministic
             algorithm},
   Journal = {Discrete and Computational Geometry},
   Volume = {5},
   Pages = {449-483},
   Year = {1990},
   Key = {fds1859}
}

@article{fds1860,
   Author = {M. T. Shing and P.K. Agarwal},
   Title = {Algorithms for special cases of rectilinear Steiner trees:
             I. Points on the boundary of a rectangle},
   Journal = {Networks},
   Volume = {20},
   Pages = {453-485},
   Year = {1990},
   Key = {fds1860}
}

@article{fds22817,
   Author = {P.K. Agarwal and B. Aronov and J. O'Rourke and C.
             Schevon},
   Title = {Star unfolding of a polytope with applications},
   Booktitle = {Second Scandinavian Workshop on Algorithm
             Theory},
   Year = {1990},
   Key = {fds22817}
}

@article{fds22823,
   Author = {P.K. Agarwal and H. Edelsbrunner and O. Schwarzkopf and E.
             Welzl},
   Title = {Euclidean minimum spanning tree and bichromatic closest
             pairs},
   Booktitle = {Sixth Annual Symposium on Computational Geometry},
   Year = {1990},
   Key = {fds22823}
}

@article{fds235383,
   Author = {Agarwal, PK},
   Title = {Partitioning arrangements of lines I: An efficient
             deterministic algorithm},
   Journal = {Discrete & Computational Geometry},
   Volume = {5},
   Number = {1},
   Pages = {449-483},
   Year = {1990},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/BF02187805},
   Abstract = {In this paper we consider the following problem: Given a set
             ℒ of n lines in the plane, partition the plane into O(r2)
             triangles so that no triangle meets more than O(n/r) lines
             of ℒ. We present a deterministic algorithm for this
             problem with O(nr log n/r) running time, where ω is a
             constant &lt;3.33. © 1990 Springer-Verlag New York
             Inc.},
   Doi = {10.1007/BF02187805},
   Key = {fds235383}
}

@article{fds235558,
   Author = {Agarwal, PK and Edelsbrunner, H and Schwarzkopf, O and Welzl,
             E},
   Title = {Euclidean minimum spanning trees and bichromatic closest
             pairs},
   Pages = {203-210},
   Year = {1990},
   Abstract = {We present an algorithm to compute a Euclidean minimum
             spanning tree of a given set S of n points in Ed in time
             O(Td(N, N) logd N), where Td(n, m) is the time required to
             compute a bichromatic closest pair among n red and m blue
             points in Ed. If Td(N, N) = Ω(N1+ε), for some fixed ε
             &gt; 0, then the running time improves to O(Td(N, N)).
             Furthermore, we describe a randomized algorithm to compute a
             bichromatic closets pair in expected time O((nm log n log
             m)2/3+m log2 n + n log2 m) in E3, which yields an
             O(N4/3log4/3 N) expected time algorithm for computing a
             Euclidean minimum spanning tree of N points in
             E3.},
   Key = {fds235558}
}

@article{fds235560,
   Author = {Agarwal, PK and Sharir, M},
   Title = {Red-blue intersection detection algorithms, with
             applications to motion planning and collision
             detection},
   Journal = {SIAM Journal on Computing},
   Volume = {19},
   Number = {2},
   Pages = {297-321},
   Year = {1990},
   Abstract = {Let Γ be a collection of n (possibly intersecting) 'red'
             Jordan arcs of some simple shape in the plane and let Γ′
             be a similar collection of m 'blue' arcs. Several efficient
             algorithms are presented for detecting an intersection
             between an arc of Γ and arc of Γ′.},
   Key = {fds235560}
}

@article{fds235562,
   Author = {Agarwal, PK},
   Title = {Partitioning arrangements of lines II: Applications},
   Journal = {Discrete & Computational Geometry},
   Volume = {5},
   Number = {1},
   Pages = {533-573},
   Year = {1990},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/BF02187809},
   Abstract = {In this paper we present efficient deterministic algorithms
             for various problems involving lines or segments in the
             plane, using the partitioning algorithm described in a
             companion paper [A3]. These applications include: (i) an
             O(m2/3n2/3 · log2/3n · logω/3 (m/√n)+(m+n) log n)
             algorithm to compute all incidences between m points and n
             lines, where ω is a constant &lt;3.33; (ii) an O(m2/3n2/3
             · log5/3n · logω/3 (m/√n)+(m+n) log n) algorithm to
             compute m faces in an arrangement of n lines; (iii) an
             O(n4/3 log(ω+2)/3n) algorithm to count the number of
             intersections in a set of n segments; (iv) an O(n4/3 log(ω
             + 2)/3n) algorithm to count "red-blue" intersections between
             two sets of segments, and (v) an O(n3/2 logω/3n) algorithm
             to compute spanning trees with low stabbing number for a set
             of n points. We also present an algorithm that, given set of
             n points in the plane, preprocesses it, in time O(n√m
             logω+1/2n), into a data structure of size O(m) for n log
             n≤m≤n2, so that the number of points of S lying inside a
             query triangle can be computed in O((n/√m) log3/2n) time.
             © 1990 Springer-Verlag New York Inc.},
   Doi = {10.1007/BF02187809},
   Key = {fds235562}
}

@article{fds235561,
   Author = {Agarwal, PK and Aronov, B and Sharir, M and Suri,
             S},
   Title = {Selecting distances in the plane},
   Pages = {321-331},
   Booktitle = {Sixth Annual Symposium on Computational Geometry},
   Year = {1990},
   Abstract = {We describe a randomized algorithm for computing the kth
             smallest distance in a set of n points in the plane, based
             on the parametric search technique of Megiddo. The expected
             running time of our algorithm is O(n4/3 log8/3 n). A
             deterministic version of our procedure runs in time O(n3/2
             log5/2 n). Both versions improve the previously best known
             upper bound of O(n9/5 log4/5 n) by Chazelle. A simple O(n
             log n) time algorithm for computing an approximation of the
             median distance is also presented.},
   Key = {fds235561}
}

@article{fds329466,
   Author = {Agarwal, PK and Aronov, B and O'Rourke, J and Schevon,
             CA},
   Title = {Star Unfolding of a Polytope with Applications (Extended
             Abstract).},
   Journal = {SWAT},
   Volume = {447},
   Pages = {251-263},
   Publisher = {Springer},
   Editor = {Gilbert, JR and Karlsson, RG},
   Year = {1990},
   ISBN = {3-540-52846-6},
   url = {http://dx.doi.org/10.1007/3-540-52846-6_94},
   Doi = {10.1007/3-540-52846-6_94},
   Key = {fds329466}
}

@article{fds329465,
   Author = {Kreveld, MJV and Overmars, MH and Agarwal, PK},
   Title = {Intersection Queries in Sets of Disks.},
   Journal = {SWAT},
   Volume = {447},
   Pages = {393-403},
   Booktitle = {Second Scandinavian Workshop on Algorithm
             Theory},
   Publisher = {Springer},
   Editor = {Gilbert, JR and Karlsson, RG},
   Year = {1990},
   ISBN = {3-540-52846-6},
   url = {http://dx.doi.org/10.1007/3-540-52846-6_107},
   Doi = {10.1007/3-540-52846-6_107},
   Key = {fds329465}
}

@article{fds22819,
   Author = {P.K. Agarwal and A. Aggarwal and B. Aronov and S. Kosaraju and B.
             Shieber and S. Suri},
   Title = {Computing all external-farthest neighbors for a simple
             polygon},
   Booktitle = {First Canadian Conference on Computational
             Geometry},
   Year = {1989},
   Key = {fds22819}
}

@article{fds22820,
   Author = {P.K. Agarwal},
   Title = {An efficient algorithm for partitioning arrangements of
             lines and its applications},
   Booktitle = {Fifth Annual Symposium on Computational Geometry},
   Year = {1989},
   Key = {fds22820}
}

@article{fds22821,
   Author = {P.K. Agarwal},
   Title = {Ray shooting and other applications of spanning trees with
             low stabbing number},
   Journal = {Fifth Annual Symposium on Computational Geometry},
   Year = {1989},
   Key = {fds22821}
}

@article{fds235559,
   Author = {Agarwal, PK and Sharir, M and Shor, P},
   Title = {Sharp upper and lower bounds on the length of general
             Davenport-Schinzel sequences},
   Journal = {Journal of Combinatorial Theory, Series A},
   Volume = {52},
   Number = {2},
   Pages = {228-274},
   Year = {1989},
   ISSN = {0097-3165},
   Abstract = {We obtain sharp upper and lower bounds on the maximal length
             λs(n) of (n, s)-Davenport-Schinzel sequences, i.e.,
             sequences composed of n symbols, having no two adjacent
             equal elements and containing no alternating subsequence of
             length s + 2. We show that (i) λ4(n) = Θ(n·2α(n)); (ii)
             for s &gt; 4, λs(n) ≤ n·2(α(n)) (s - 2) 2 + Cs(n) if s
             is even and λs(n) ≤ n·2(α(n)) (s - 3) 2log(α(n)) +
             Cs(n) if s is odd, where Cs(n) is a function of α(n) and s,
             asymptotically smaller than the main term; and finally (iii)
             for even values of s &gt; 4, λs(n) = Ω(n·2Ks(α(n)) (s -
             2) 2 + Qs(n)), where Ks = (( (s - 2) 2)!)-1 and Qs is a
             polynomial in α(n) of degree at most (s - 4) 2. ©
             1989.},
   Key = {fds235559}
}

@article{fds22816,
   Author = {P.K. Agarwal and Micha Sharir},
   Title = {Red-blue intersection detection algorithms, with
             applications to motion planning and collision
             detection},
   Journal = {Fourth Annual Symposium on Computational
             Geometry},
   Year = {1988},
   Key = {fds22816}
}

@article{fds1157,
   Author = {T. Smith and D. Peuquet and S. Menon, and P.K.
             Agarwal},
   Title = {KBGIS-II: A knowledge-based geographic information
             system},
   Journal = {International Journal of Geographical Information
             Systems},
   Volume = {1},
   Pages = {149-172},
   Year = {1987},
   Key = {fds1157}
}

@misc{fds23106,
   Author = {P.K. Agarwal and M. T. Shing},
   Title = {Multiterminal flows in planar networks},
   Journal = {Technical Report TRCS86-07, Department of Computer Science,
             Santa Barbara},
   Year = {1986},
   Key = {fds23106}
}

@misc{fds23105,
   Author = {P.K. Agarwal},
   Title = {Geometric Algorithms},
   Journal = {Technical Report TRCS85-17, Department of Computer Science,
             Santa Barbara},
   Year = {1985},
   Key = {fds23105}
}

@article{fds22815,
   Author = {P.K. Agarwal and A. Choudhary and S. Sengupta},
   Title = {A VME bus compatible FFT Processor},
   Booktitle = {Conference on Signal Processing},
   Year = {1983},
   Key = {fds22815}
}


%% Aguado, Alex   
@misc{fds208064,
   Author = {Alejandro Aguado},
   Title = {A short note on mapping cylinders},
   Journal = {arXiv:1206.1277v2 [math.AT]},
   Year = {2012},
   Month = {June},
   Key = {fds208064}
}

@misc{fds204392,
   Author = {Alejandro Aguado},
   Title = {On the cardinality of the Kuratowski family},
   Journal = {Mathematics Magazine (Problem 1888)},
   Volume = {85 (1) & 86 (1)},
   Year = {2012},
   Month = {February},
   url = {http://www.jstor.org/stable/10.4169/math.mag.85.1.61},
   Key = {fds204392}
}

@misc{fds208066,
   Author = {Alejandro Aguado},
   Title = {On group designs and the social golfer problem},
   Year = {2012},
   Key = {fds208066}
}

@article{fds146627,
   Author = {Alejandro Aguado and Saad I. El-Zanati},
   Title = {On σ-labeling the union of three cycles.},
   Journal = {Journal of Combinatorial Mathematics and Combinatorial
             Computing},
   Volume = {64},
   Pages = {33-48},
   Year = {2008},
   MRNUMBER = {MR2389065},
   url = {http://www.ams.org/mathscinet-getitem?mr=2389065},
   Key = {fds146627}
}

@article{fds146626,
   Author = {Alejandro Aguado and Saad I. El-Zanati and et al.},
   Title = {On ρ-labeling the union of three cycles},
   Journal = {The Australasian Journal of Combinatorics},
   Volume = {37},
   Pages = {155-170},
   Year = {2007},
   MRNUMBER = {MR2284379 (2007k:05190)},
   url = {http://www.ams.org/mathscinet-getitem?mr=2284379},
   Key = {fds146626}
}

@misc{fds146628,
   Author = {Alejandro Aguado},
   Title = {Cantor Sets, Antoine's Necklace and p-Adic
             Numbers},
   Series = {Undergraduate Thesis (unpublished)},
   Publisher = {22 figures, 48 pages},
   Year = {2006},
   Key = {fds146628}
}

@article{fds146625,
   Author = {Alejandro Aguado},
   Title = {A 10 days solution to the social golfer problem},
   Series = {Math games: Social Golfer problem},
   Publisher = {MAA Online},
   Editor = {Ed Pegg Jr.},
   Year = {2004},
   url = {http://www.maa.org/editorial/mathgames/mathgames_08_14_07.html},
   Key = {fds146625}
}


%% Allard, William K.   
@article{fds200674,
   Author = {W.K. Allard and Guanglian Chen and Mauro Maggioni},
   Title = {W.K. Allard, G. Chen, M. Maggioni Multiscale Geometric
             Methods for Data Sets II: Geometric Wavelets},
   Journal = {to appear in ACHA},
   Year = {2011},
   Key = {fds200674}
}

@article{fds167778,
   Author = {W.K. Allard},
   Title = {A boundary approximation algorithm for planar
             domains},
   Year = {2009},
   url = {http://www.math.duke.edu/~wka/bdry.pdf},
   Key = {fds167778}
}

@article{fds243260,
   Author = {Allard, WK},
   Title = {Total variation for image denoising: III.
             Examples},
   Journal = {SIAM Journal on Imaging Sciences},
   Volume = {2},
   Year = {2009},
   url = {http://www.math.duke.edu/~wka/new.pdf},
   Key = {fds243260}
}

@article{fds243262,
   Author = {Allard, WK},
   Title = {Total variation regularization for image denoising: I.
             Geometric theory using total variation regularization; II
             Examples.},
   Journal = {SIAM Journal on Mathematical Analysis},
   Volume = {39},
   Number = {4},
   Year = {2007},
   Month = {November},
   url = {http://www.math.duke.edu/~wka},
   Abstract = {http://www.math.duke.edu/~wka},
   Key = {fds243262}
}

@article{fds243261,
   Author = {Allard, WK},
   Title = {Total variation regularization for image denoising, I.
             Geometric theory},
   Journal = {SIAM Journal on Mathematical Analysis},
   Volume = {39},
   Number = {4},
   Pages = {1150-1190},
   Year = {2007},
   ISSN = {0036-1410},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000253016600006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1137/060662617},
   Key = {fds243261}
}

@article{fds243263,
   Author = {Allard, WK},
   Title = {The reconstruction of surfaces in R3 by reflection},
   Journal = {The Journal of Geometric Analysis},
   Volume = {9},
   Number = {5},
   Year = {1999},
   url = {http://www.math.duke.edu/faculty/allard/papers/allabst.ps},
   Key = {fds243263}
}

@article{fds9254,
   Author = {William K Allard},
   Title = {An Introduction to the Deferred Execution
             Tool},
   Journal = {Proceedings of Ninth SIAM Annual Conference on Parallel
             Processing for Scientific Computing, (SIAM) March
             1999},
   Key = {fds9254}
}

@article{fds9393,
   Author = {William K. Allard and John Trangenstein},
   Title = {On the Performance of a Distributed Object Oriented Adaptive
             Mesh Refinement Code},
   url = {http://www.math.duke.edu/~wka/papers/adaptive.ps},
   Key = {fds9393}
}

@article{fds9392,
   Author = {William K. Allard},
   Title = {Users Guide to the Deferred Execution Tool},
   url = {http://www.math.duke.edu/~wka/papers/deferred.ps},
   Key = {fds9392}
}


%% Allman, Justin   
@article{fds300039,
   Author = {J. Allman},
   Title = {An iterated residue perspective on stable Grothendieck
             polynomials},
   Year = {2015},
   url = {http://arxiv.org/abs/1408.1911v2},
   Abstract = {http://arxiv.org/abs/1408.1911v2},
   Key = {fds300039}
}

@article{fds296252,
   Author = {J Allman},
   Title = {Grothendieck Classes of Quiver Cycles as Iterated
             Residues},
   Journal = {The Michigan Mathematical Journal},
   Volume = {63},
   Number = {4},
   Pages = {865-888},
   Year = {2014},
   Month = {December},
   ISSN = {0026-2285},
   url = {http://dx.doi.org/10.1307/mmj/1417799229},
   Doi = {10.1307/mmj/1417799229},
   Key = {fds296252}
}

@article{fds314708,
   Author = {JM Allman and JE Grabowski},
   Title = {A quantum analogue of the dihedral action on
             Grassmannians},
   Journal = {Journal of Algebra},
   Volume = {359},
   Pages = {49-68},
   Year = {2012},
   Month = {June},
   ISSN = {0021-8693},
   url = {http://hdl.handle.net/10161/11847 Duke open
             access},
   Doi = {10.1016/j.jalgebra.2012.03.016},
   Key = {fds314708}
}


%% Ambrose, David M.   
@article{fds10435,
   Author = {David M. Ambrose},
   Title = {Well-posedness of vortex sheets with surface
             tension},
   Journal = {SIAM J. Math. Analysis},
   Key = {fds10435}
}


%% Anderson, David F.   
@article{fds49074,
   Author = {David F. Anderson and Jonathan C. Mattingly},
   Title = {Propagation of Fluctuations in Biochemical Reaction Systems,
             II: Nonlinear Chains},
   Year = {2006},
   Month = {Fall},
   Abstract = {We consider biochemical reaction chains and investigate how
             random fluctuations, as characterized by variance, propagate
             down the chains. We perform such a study under the
             assumption that the number of molecules is high enough so
             that the behavior of the concentrations of the system is
             well approximated by differential equations. We conclude
             that the variances of the fluxes will decrease as one moves
             down the chain and, through an example, show that there is
             no corresponding result for the variances of the chemical
             species.},
   Key = {fds49074}
}

@article{fds47856,
   Author = {H. Frederik Nijhout and Michael C. Reed and David F. Anderson and Jonathan C. Mattingly and S. Jill james and Cornelia M.
             Ulrich},
   Title = {Long-Range Allosteric Interactions between the Folate and
             Methionine Cycles Stabilize DNA Methylation Reaction
             Rate},
   Journal = {Epigenetics},
   Volume = {1},
   Number = {2},
   Pages = {81-87},
   Year = {2006},
   Month = {April},
   Key = {fds47856}
}

@article{fds52331,
   Author = {David F. Anderson and Jonathan C. Mattingly and H. Frederik
             Nijhout and Michael Reed},
   Title = {Propagation of Fluctuations in Biochemical Systems, I:
             Linear SSC Networks},
   Journal = {Bulletin of Mathematical Biology},
   Year = {2006},
   url = {http://arxiv.org/abs/math/0510642},
   Abstract = {We investigate the propagation of random fluctuations
             through biochemical networks in which the concentrations of
             species are large enough so that the unperturbed problem is
             well-described by ordinary differential equation. We
             characterize the behavior of variance as fluctuations
             propagate down chains, study the effect of side chains and
             feedback loops, and investigate the asymptotic behavior as
             one rate constant gets large. We also describe how the ideas
             can be applied to the study of methionine
             metabolism.},
   Key = {fds52331}
}


%% Aristotelous, Andreas   
@article{fds224099,
   Author = {Aristotelous, A. C. and Durrett, R.},
   Title = {Fingering in Stochastic Growth Models.},
   Journal = {Experimental Mathematics},
   Year = {2014},
   Month = {July},
   Key = {fds224099}
}

@article{fds223440,
   Author = {Andreas C. Aristotelous and Ohannes A. Karakashian and Steven
             M.Wise},
   Title = {Adaptive, Second-Order in Time, Primitive-Variable
             Discontinuous Galerkin Schemes for a Cahn-Hilliard Equation
             with a Mass Source},
   Journal = {IMA Journal of Numerical Analysis},
   Year = {2014},
   Month = {March},
   Key = {fds223440}
}

@article{fds223439,
   Author = {A. C. Aristotelous and M. A. Haider},
   Title = {Evaluation of Diffusive Transport and Cellular Uptake of
             Nutrients in Tissue Engineered Constructs using a Hybrid
             Discrete Model},
   Journal = {Processes},
   Year = {2014},
   Month = {March},
   Key = {fds223439}
}

@article{fds223438,
   Author = {Andreas C. Aristotelous and Richard Durrett},
   Title = {Chemical Evolutionary Games},
   Journal = {Theoretical Population Biology},
   Year = {2014},
   Month = {February},
   Key = {fds223438}
}

@article{fds223441,
   Author = {Andreas C. Aristotelous and Mansoor A. Haider},
   Title = {Use of Hybrid Discrete Cellular Models for Identification of
             Macroscopic Nutrient Loss in Reaction-Diffusion Models of
             Tissues.},
   Journal = {Int. J. Numer. Meth. Biomed. Engng.},
   Year = {2014},
   Month = {February},
   Key = {fds223441}
}

@article{fds219212,
   Author = {Andreas C. Aristotelous and Ohannes A. Karakashian and Steven
             M.Wise},
   Title = {A Mixed Discontinuous Galerkin, Convex Splitting Scheme for
             a Modified Cahn-Hilliard Equation and an Efficient Nonlinear
             Multigrid Solver.},
   Journal = {DCDS-B},
   Volume = {18},
   Number = {9},
   Pages = {2211–2238},
   Year = {2013},
   Month = {November},
   Key = {fds219212}
}

@article{fds219216,
   Author = {A. C. Aristotelous},
   Title = {Adaptive Discontinuous Galerkin Finite Element Methods for a
             Diffuse Interface Model of Biological Growth},
   Journal = {PhD Thesis, The University of Tennessee,
             U.S.A.},
   Year = {2011},
   Month = {August},
   Key = {fds219216}
}


%% Arlotto, Alessandro   
@article{fds330134,
   Author = {Arlotto, A and Wei, Y and Xie, X},
   Title = {An adaptive O(log n)-optimal policy for the online selection
             of a monotone subsequence from a random sample},
   Journal = {Random Structures and Algorithms},
   Volume = {52},
   Number = {1},
   Pages = {41-53},
   Publisher = {Wiley},
   Year = {2018},
   Month = {January},
   url = {http://dx.doi.org/10.1002/rsa.20728},
   Abstract = {Given a sequence of n independent random variables with
             common continuous distribution, we propose a simple adaptive
             online policy that selects a monotone increasing
             subsequence. We show that the expected number of monotone
             increasing selections made by such a policy is within O(log
             n) of optimal. Our construction provides a direct and
             natural way for proving the O(log n)-optimality gap. An
             earlier proof of the same result made crucial use of a key
             inequality of Bruss and Delbaen (2001) and of
             de-Poissonization.},
   Doi = {10.1002/rsa.20728},
   Key = {fds330134}
}

@article{fds330135,
   Author = {Arlotto, A and Frazelle, AE and Wei, Y},
   Title = {Strategic open routing in service networks},
   Journal = {Management Science},
   Publisher = {INFORMS},
   Year = {2018},
   Key = {fds330135}
}

@article{fds330136,
   Author = {Arlotto, A and Steele, JM},
   Title = {A central limit theorem for costs in Bulinskaya’s
             inventory management problem when deliveries face
             delays},
   Journal = {Methodology and Computing in Applied Probability},
   Year = {2018},
   url = {http://dx.doi.org/10.1007/s11009-016-9522-7},
   Doi = {10.1007/s11009-016-9522-7},
   Key = {fds330136}
}

@article{fds330137,
   Author = {Arlotto, A and Gurvich, I},
   Title = {Uniformly bounded regret in the multi-secretary
             problem},
   Year = {2017},
   Month = {October},
   Abstract = {In the secretary problem of Cayley (1875) and Moser (1956),
             $n$ non-negative, independent, random variables with common
             distribution are sequentially presented to a decision maker
             who decides when to stop and collect the most recent
             realization. The goal is to maximize the expected value of
             the collected element. In the $k$-choice variant, the
             decision maker is allowed to make $k \leq n$ selections to
             maximize the expected total value of the selected elements.
             Assuming that the values are drawn from a known distribution
             with finite support, we prove that the best regret---the
             expected gap between the optimal online policy and its
             offline counterpart in which all $n$ values are made visible
             at time $0$---is uniformly bounded in the the number of
             candidates $n$ and the budget $k$. Our proof is
             constructive: we develop an adaptive Budget-Ratio policy
             that achieves this performance. The policy selects or skips
             values depending on where the ratio of the residual budget
             to the remaining time stands relative to multiple thresholds
             that correspond to middle points of the distribution. We
             also prove that being adaptive is crucial: in general, the
             minimal regret among non-adaptive policies grows like the
             square root of $n$. The difference is the value of
             adaptiveness.},
   Key = {fds330137}
}

@article{fds322098,
   Author = {Arlotto, A and Steele, JM},
   Title = {A central limit theorem for temporally nonhomogenous Markov
             chains with applications to dynamic programming},
   Journal = {Mathematics of Operations Research},
   Volume = {41},
   Number = {4},
   Pages = {1448-1468},
   Year = {2016},
   Month = {November},
   url = {http://dx.doi.org/10.1287/moor.2016.0784},
   Doi = {10.1287/moor.2016.0784},
   Key = {fds322098}
}

@article{fds322099,
   Author = {Arlotto, A and Mossel, E and Steele, JM},
   Title = {Quickest online selection of an increasing subsequence of
             specified size},
   Journal = {Random Structures and Algorithms},
   Volume = {49},
   Number = {2},
   Pages = {235-252},
   Year = {2016},
   Month = {September},
   url = {http://dx.doi.org/10.1002/rsa.20634},
   Doi = {10.1002/rsa.20634},
   Key = {fds322099}
}

@article{fds330138,
   Author = {Arlotto, A and Steele, JM},
   Title = {Beardwood–Halton–Hammersley theorem for stationary
             ergodic sequences: a counterexample},
   Journal = {The annals of applied probability : an official journal of
             the Institute of Mathematical Statistics},
   Volume = {26},
   Number = {4},
   Pages = {2141-2168},
   Year = {2016},
   Month = {August},
   url = {http://dx.doi.org/10.1214/15-AAP1142},
   Doi = {10.1214/15-AAP1142},
   Key = {fds330138}
}

@article{fds319303,
   Author = {Arlotto, A and Nguyen, VV and Steele, JM},
   Title = {Optimal online selection of a monotone subsequence: a
             central limit theorem},
   Journal = {Stochastic Processes and their Applications},
   Volume = {125},
   Number = {9},
   Pages = {3596-3622},
   Year = {2015},
   Month = {September},
   url = {http://dx.doi.org/10.1016/j.spa.2015.03.009},
   Doi = {10.1016/j.spa.2015.03.009},
   Key = {fds319303}
}

@article{fds319304,
   Author = {Arlotto, A and Gans, N and Steele, JM},
   Title = {Markov decision problems where means bound
             variances},
   Journal = {Operations Research},
   Volume = {62},
   Number = {4},
   Pages = {864-875},
   Year = {2014},
   Month = {August},
   url = {http://dx.doi.org/10.1287/opre.2014.1281},
   Doi = {10.1287/opre.2014.1281},
   Key = {fds319304}
}

@article{fds330139,
   Author = {Arlotto, A and Steele, JM},
   Title = {Optimal online selection of an alternating subsequence: a
             central limit theorem},
   Journal = {Advances in applied probability},
   Volume = {46},
   Number = {2},
   Pages = {536-559},
   Year = {2014},
   Month = {June},
   url = {http://dx.doi.org/10.1239/aap/1401369706},
   Doi = {10.1239/aap/1401369706},
   Key = {fds330139}
}

@article{fds319305,
   Author = {Arlotto, A and Chick, SE and Gans, N},
   Title = {Optimal hiring and retention policies for heterogeneous
             workers who learn},
   Journal = {Management Science},
   Volume = {60},
   Number = {1},
   Pages = {110-129},
   Year = {2014},
   Month = {January},
   url = {http://dx.doi.org/10.1287/mnsc.2013.1754},
   Doi = {10.1287/mnsc.2013.1754},
   Key = {fds319305}
}

@article{fds319306,
   Author = {Arlotto, A and Chen, RW and Shepp, LA and Steele,
             JM},
   Title = {Online selection of alternating subsequences from a random
             sample},
   Journal = {Journal of applied probability},
   Volume = {48},
   Number = {4},
   Pages = {1114-1132},
   Year = {2011},
   Month = {December},
   url = {http://dx.doi.org/10.1239/jap/1324046022},
   Abstract = {We consider sequential selection of an alternating
             subsequence from a sequence of independent, identically
             distributed, continuous random variables, and we determine
             the exact asymptotic behavior of an optimal sequentially
             selected subsequence. Moreover, we find (in a sense we make
             precise) that a person who is constrained to make sequential
             selections does only about 12 percent worse than a person
             who can make selections with full knowledge of the random
             sequence. © 2011 Applied Probability Trust.},
   Doi = {10.1239/jap/1324046022},
   Key = {fds319306}
}

@article{fds319307,
   Author = {Arlotto, A and Steele, JM},
   Title = {Optimal sequential selection of a unimodal subsequence of a
             random sequence},
   Journal = {Combinatorics, Probability and Computing},
   Volume = {20},
   Number = {06},
   Pages = {799-814},
   Year = {2011},
   Month = {November},
   url = {http://dx.doi.org/10.1017/S0963548311000411},
   Abstract = {We consider the problem of selecting sequentially a unimodal
             subsequence from a sequence of independent identically
             distributed random variables, and we find that a person
             doing optimal sequential selection does so within a factor
             of the square root of two as well as a prophet who knows all
             of the random observations in advance of any selections. Our
             analysis applies in fact to selections of subsequences that
             have d+1 monotone blocks, and, by including the case d=0,
             our analysis also covers monotone subsequences. © 2011
             Cambridge University Press.},
   Doi = {10.1017/S0963548311000411},
   Key = {fds319307}
}

@article{fds319308,
   Author = {Arlotto, A and Gans, N and Chick, S},
   Title = {Optimal employee retention when inferring unknown learning
             curves},
   Journal = {Proceedings - Winter Simulation Conference},
   Pages = {1178-1188},
   Editor = {Johansson, B and Jain, S and Montoya-Torres, J and Hugan, J and Yücesan, E},
   Year = {2010},
   url = {http://dx.doi.org/10.1109/WSC.2010.5679074},
   Abstract = {This paper formulates an employer's hiring and retention
             decisions as an infinite-armed bandit problem and
             characterizes the structure of optimal hiring and retention
             policies. We develop approximations that allow us to
             explicitly calculate these policies and to evaluate their
             benefit. The solution involves a balance of two types of
             learning: the learning that reflects the improvement in
             performance of employees as they gain experience, and the
             Bayesian learning of employers as they infer properties of
             employees' abilities to inform the decision of whether to
             retain or replace employees. Numerical experiments with
             Monte Carlo simulation suggest that the gains to active
             screening and monitoring of employees can be substantial.
             ©2010 IEEE.},
   Doi = {10.1109/WSC.2010.5679074},
   Key = {fds319308}
}

@article{fds319309,
   Author = {Arlotto, A and Scarsini, M},
   Title = {Hessian orders and multinormal distributions},
   Journal = {Journal of Multivariate Analysis},
   Volume = {100},
   Number = {10},
   Pages = {2324-2330},
   Year = {2009},
   Month = {November},
   url = {http://dx.doi.org/10.1016/j.jmva.2009.03.009},
   Abstract = {Several well known integral stochastic orders (like the
             convex order, the supermodular order, etc.) can be defined
             in terms of the Hessian matrix of a class of functions. Here
             we consider a generic Hessian order, i.e., an integral
             stochastic order defined through a convex cone H of Hessian
             matrices, and we prove that if two random vectors are
             ordered by the Hessian order, then their means are equal and
             the difference of their covariance matrices belongs to the
             dual of H. Then we show that the same conditions are also
             sufficient for multinormal random vectors. We study several
             particular cases of this general result. © 2009 Elsevier
             Inc. All rights reserved.},
   Doi = {10.1016/j.jmva.2009.03.009},
   Key = {fds319309}
}


%% Arthurs, Kayne M.   
@article{fds9514,
   Author = {Kayne M. Arthurs and Leon C. Moore and Charles S. Peskin and E. Bruce
             Pitman and H. E. Layton},
   Title = {Modeling Arteriolar Flow and Mass Transport Using the
             Immersed Boundary Method},
   Journal = {Journal of Computational Physics, vol. 147, (1998), pp.
             402-440},
   Key = {fds9514}
}


%% Aspinwall, Paul S.   
@article{fds322464,
   Author = {Aspinwall, PS and Plesser, MR},
   Title = {General mirror pairs for gauged linear sigma
             models},
   Journal = {The Journal of High Energy Physics},
   Volume = {2015},
   Number = {11},
   Year = {2015},
   Month = {November},
   url = {http://dx.doi.org/10.1007/JHEP11(2015)029},
   Doi = {10.1007/JHEP11(2015)029},
   Key = {fds322464}
}

@article{fds243265,
   Author = {Aspinwall, PS},
   Title = {Exoflops in two dimensions},
   Journal = {The Journal of High Energy Physics},
   Volume = {2015},
   Number = {7},
   Year = {2015},
   Month = {July},
   url = {http://dx.doi.org/10.1007/JHEP07(2015)104},
   Doi = {10.1007/JHEP07(2015)104},
   Key = {fds243265}
}

@article{fds243266,
   Author = {Aspinwall, PS and Gaines, B},
   Title = {Rational curves and (0, 2)-deformations},
   Journal = {Journal of Geometry and Physics},
   Volume = {88},
   Pages = {1-15},
   Year = {2015},
   Month = {February},
   ISSN = {0393-0440},
   url = {http://dx.doi.org/10.1016/j.geomphys.2014.09.012},
   Doi = {10.1016/j.geomphys.2014.09.012},
   Key = {fds243266}
}

@article{fds243264,
   Author = {Aspinwall, PS},
   Title = {Some applications of commutative algebra to string
             theory},
   Pages = {25-56},
   Booktitle = {Commutative Algebra: Expository Papers Dedicated to David
             Eisenbud on the Occasion of His 65th Birthday},
   Year = {2013},
   Month = {November},
   ISBN = {9781461452928},
   url = {http://dx.doi.org/10.1007/978-1-4614-5292-8_2},
   Abstract = {© 2013 Springer Science+Business Media New York. All rights
             reserved. String theory was first introduced as a model for
             strong nuclear interactions, then reinterpreted as a model
             for quantum gravity, and then all fundamental
             physics.},
   Doi = {10.1007/978-1-4614-5292-8_2},
   Key = {fds243264}
}

@article{fds303516,
   Author = {Addington, N and Aspinwall, PS},
   Title = {Categories of Massless D-Branes and del Pezzo
             Surfaces},
   Journal = {J. High Energy Phys. 7(176):39pp., 2013},
   Volume = {2013},
   Number = {176},
   Year = {2013},
   Month = {May},
   url = {http://arxiv.org/abs/1305.5767v2},
   Abstract = {In analogy with the physical concept of a massless D-brane,
             we define a notion of "Q-masslessness" for objects in the
             derived category. This is defined in terms of monodromy
             around singularities in the stringy Kahler moduli space and
             is relatively easy to study using spherical functors. We
             consider several examples in which del Pezzo surfaces and
             other rational surfaces in Calabi-Yau threefolds are
             contracted. For precisely the del Pezzo surfaces that can be
             written as hypersurfaces in weighted P3, the category of
             Q-massless objects is a "fractional Calabi-Yau" category of
             graded matrix factorizations.},
   Doi = {10.1007/JHEP07(2013)176},
   Key = {fds303516}
}

@article{fds212419,
   Author = {P.S. Aspinwall and M.R. Plesser},
   Title = {Elusive Worldsheet Instantons in Heterotic String
             Compactifications},
   Volume = {85},
   Pages = {33-52},
   Booktitle = {Proceedings of Symposia in Pure Mathematics},
   Year = {2012},
   url = {http://arxiv.org/abs/1106.2998},
   Key = {fds212419}
}

@article{fds243301,
   Author = {Aspinwall, PS and Melnikov, IV and Plesser, MR},
   Title = {(0,2) elephants},
   Journal = {Journal of High Energy Physics},
   Volume = {2012},
   Number = {1},
   Pages = {060},
   Year = {2012},
   ISSN = {1126-6708},
   url = {http://dx.doi.org/10.1007/JHEP01(2012)060},
   Abstract = {We enumerate massless E6 singlets for (0,2)-compactifications
             of the heterotic string on a Calabi-Yau threefold with the
             \standard embedding" in three distinct ways. In the large
             radius limit of the threefold, these singlets count
             deformations of the Calabi-Yau together with its tangent
             bundle. In the \small-radius" limit we apply Landau-Ginzburg
             methods. In the orbifold limit we use a combination of
             geometry and free field methods. In general these counts
             dier. We show how to identify states between these phases
             and how certain states vanish from the massless spectrum as
             one deforms the complex structure or Kahler form away from
             the Gepner point. The appearance of extra singlets for
             particular values of complex structure is explored in all
             three pictures, and our results suggest that this does not
             depend on the Kähler moduli. © SISSA 2012.},
   Doi = {10.1007/JHEP01(2012)060},
   Key = {fds243301}
}

@article{fds243302,
   Author = {Aspinwall, PS and Morrison, DR},
   Title = {Quivers from Matrix Factorizations},
   Journal = {Communications in Mathematical Physics},
   Volume = {313},
   Number = {3},
   Pages = {607-633},
   Year = {2012},
   ISSN = {0010-3616},
   url = {http://dx.doi.org/10.1007/s00220-012-1520-1},
   Abstract = {We discuss how matrix factorizations offer a practical
             method of computing the quiver and associated superpotential
             for a hypersurface singularity. This method also yields
             explicit geometrical interpretations of D-branes (i. e.,
             quiver representations) on a resolution given in terms of
             Grassmannians. As an example we analyze some non-toric
             singularities which are resolved by a single ℙ 1 but have
             "length" greater than one. These examples have a much richer
             structure than conifolds. A picture is proposed that relates
             matrix factorizations in Landau-Ginzburg theories to the way
             that matrix factorizations are used in this paper to perform
             noncommutative resolutions. © 2012 Springer-Verlag.},
   Doi = {10.1007/s00220-012-1520-1},
   Key = {fds243302}
}

@article{fds303518,
   Author = {Aspinwall, PS},
   Title = {A McKay-Like Correspondence for (0,2)-Deformations},
   Volume = {18},
   Number = {4},
   Pages = {761-797},
   Year = {2011},
   Month = {October},
   url = {http://arxiv.org/abs/1110.2524v3},
   Abstract = {We present a local computation of deformations of the
             tangent bundle for a resolved orbifold singularity C^d/G.
             These correspond to (0,2)-deformations of (2,2)-theories. A
             McKay-like correspondence is found predicting the dimension
             of the space of first-order deformations from simple
             calculations involving the group. This is confirmed in two
             dimensions using the Kronheimer-Nakajima quiver
             construction. In higher dimensions such a computation is
             subject to nontrivial worldsheet instanton corrections and
             some examples are given where this happens. However, we
             conjecture that the special crepant resolution given by the
             G-Hilbert scheme is never subject to such corrections, and
             show this is true in an infinite number of cases. Amusingly,
             for three-dimensional examples where G is abelian, the
             moduli space is associated to a quiver given by the toric
             fan of the blow-up. It is shown that an orbifold of the form
             C^3/Z7 has a nontrivial superpotential and thus an
             obstructed moduli space.},
   Key = {fds303518}
}

@article{fds243303,
   Author = {Aspinwall, PS and Plesser, MR},
   Title = {Decompactifications and massless D-branes in hybrid
             models},
   Journal = {Journal of High Energy Physics},
   Volume = {2010},
   Number = {7},
   Pages = {078},
   Year = {2010},
   ISSN = {1126-6708},
   url = {http://dx.doi.org/10.1007/JHEP07(2010)078},
   Abstract = {A method of determining the mass spectrum of BPS D-branes in
             any phase limit of a gauged linear sigma model is
             introduced. A ring associated to monodromy is defined and
             one considers K-theory to be a module over this ring. A
             simple but interesting class of hybrid models with
             Landau-Ginzburg fibres over ℙ n are analyzed using special
             Kähler geometry and D-brane probes. In some cases the
             hybrid limit is an infinite distance in moduli space and
             corresponds to a decompactification. In other cases the
             hybrid limit is at a finite distance and acquires massless
             D-branes. An example studied appears to correspond to a
             novel theory of supergravity with an SU(2) gauge symmetry
             where the gauge and gravitational couplings are necessarily
             tied to each other. © SISSA 2010.},
   Doi = {10.1007/JHEP07(2010)078},
   Key = {fds243303}
}

@article{fds166462,
   Author = {P.S. Aspinwall},
   Title = {Probing Geometry with Stability Conditions},
   Year = {2009},
   Month = {May},
   url = {http://arxiv.org/abs/0905.3137},
   Key = {fds166462}
}

@book{fds166464,
   Author = {P.S. Aspinwall and Tom Bridgeland and Alastair Craw and Micheal
             Douglas, Mark Gross and Anton Kapustin and Greg Moore and Graeme
             Segal, Balazs Szendroi and Pelham Wilson},
   Title = {Dirichlet Branes and Mirror Symmetry},
   Publisher = {American Mathematical Society},
   Year = {2009},
   Key = {fds166464}
}

@article{fds243304,
   Author = {Aspinwall, PS},
   Title = {Topological D-branes and commutative algebra},
   Journal = {Communications in Number Theory and Physics},
   Volume = {3},
   Number = {3},
   Pages = {445-474},
   Year = {2009},
   ISSN = {1931-4523},
   url = {http://arxiv.org/abs/hep-th/0703279},
   Abstract = {We show that questions concerning the topological B-model on
             a Calabi-Yau manifold in the Landau-Ginzburg phase can be
             rephrased in the language of commutative algebra. This
             yields interesting and very practical methods for analyzing
             the model. We demonstrate how the relevant "Ext" groups and
             superpotentials can be computed efficiently by computer
             algebra packages such as Macaulay. This picture leads us to
             conjecture a general description of D-branes in linear sigma
             models in terms of triangulated categories. Each phase of
             the linear sigma model is associated with a different
             presentation of the category of D-branes.},
   Key = {fds243304}
}

@article{fds152804,
   Author = {P.S. Aspinwall},
   Title = {D-Branes on Toric Calabi-Yau Varieties},
   Year = {2008},
   url = {http://arxiv.org/abs/0806.2612},
   Key = {fds152804}
}

@article{fds152802,
   Author = {P.S. Aspinwall},
   Title = {The Landau-Ginzburg to Calabi-Yau Dictionary for
             D-Branes},
   Journal = {J.Math.Phys.},
   Volume = {48},
   Pages = {082304},
   Year = {2007},
   Key = {fds152802}
}

@article{fds243305,
   Author = {Aspinwall, PS},
   Title = {Landau-Ginzburg to Calabi-Yau dictionary for
             D-branes},
   Journal = {Journal of Mathematical Physics},
   Volume = {48},
   Number = {8},
   Pages = {082304},
   Year = {2007},
   ISSN = {0022-2488},
   url = {http://dx.doi.org/10.1063/1.2768185},
   Abstract = {Based on the work by Orlov (e-print arXiv:math.AG0503632),
             we give a precise recipe for mapping between B-type D-branes
             in a Landau-Ginzburg orbifold model (or Gepner model) and
             the corresponding large radius Calabi-Yau manifold. The
             D-branes in Landau-Ginzburg theories correspond to matrix
             factorizations and the D-branes on the Calabi-Yau manifolds
             are objects in the derived category. We give several
             examples including branes on quotient singularities
             associated with weighted projective spaces. We are able to
             confirm several conjectures and statements in the
             literature. © 2007 American Institute of
             Physics.},
   Doi = {10.1063/1.2768185},
   Key = {fds243305}
}

@article{fds243306,
   Author = {Aspinwall, PS and Maloney, A and Simons, A},
   Title = {Black hole entropy, marginal stability and mirror
             symmetry},
   Journal = {Journal of High Energy Physics},
   Volume = {2007},
   Number = {7},
   Pages = {034},
   Year = {2007},
   ISSN = {1126-6708},
   url = {http://dx.doi.org/10.1088/1126-6708/2007/07/034},
   Abstract = {We consider the superconformal quantum mechanics associated
             to BPS black holes in type IIB Calabi-Yau compactifications.
             This quantum mechanics describes the dynamics of D-branes in
             the near-horizon attractor geometry of the black hole. In
             many cases, the black hole entropy can be found by counting
             the number of chiral primaries in this quantum mechanics.
             Both the attractor mechanism and notions of marginal
             stability play important roles in generating the large
             number of microstates required to explain this entropy. We
             compute the microscopic entropy explicitly in a few
             different cases, where the theory reduces to quantum
             mechanics on the moduli space of special Lagrangians. Under
             certain assumptions, the problem may be solved by
             implementing mirror symmetry as three T-dualities: this is
             essentially the mirror of a calculation by Gaiotto,
             Strominger and Yin. In some simple cases, the calculation
             may be done in greater generality without resorting to
             conjectures about mirror symmetry. For example, the K3 × T2
             case may be studied precisely using the Fourier-Mukai
             transform. © SISSA 2007.},
   Doi = {10.1088/1126-6708/2007/07/034},
   Key = {fds243306}
}

@article{fds51429,
   Author = {P.S. Aspinwall},
   Title = {D-Branes, Pi-Stability and Theta-Stability},
   Volume = {401},
   Series = {Contemporary Mathematics},
   Booktitle = {Snowbird Lectures on String Geometry},
   Publisher = {AMS},
   Year = {2006},
   url = {http://arxiv.org/abs/hep-th/0407123},
   Key = {fds51429}
}

@article{fds243307,
   Author = {Aspinwall, PS and Fidkowski, LM},
   Title = {Superpotentials for quiver gauge theories},
   Journal = {The Journal of High Energy Physics},
   Volume = {2006},
   Number = {10},
   Pages = {047},
   Year = {2006},
   ISSN = {1029-8479},
   url = {http://dx.doi.org/10.1088/1126-6708/2006/10/047},
   Abstract = {We compute superpotentials for quiver gauge theories arising
             from marginal D-Brane decay on collapsed del Pezzo cycles S
             in a Calabi-Yau X. This is done using the machinery of A∞
             products in the derived category of coherent sheaves of X,
             which in turn is related to the derived category of S and
             quiver path algebras. We confirm that the superpotential is
             what one might have guessed from analyzing the moduli space,
             i.e., it is linear in the fields corresponding to the Ext2s
             of the quiver and that each such Ext 2 multiplies a
             polynomial in Ext1s equal to precisely the relation
             represented by the Ext2. © SISSA 2006.},
   Doi = {10.1088/1126-6708/2006/10/047},
   Key = {fds243307}
}

@article{fds243308,
   Author = {Aspinwall, PS and Katz, S},
   Title = {Computation of superpotentials for D-branes},
   Journal = {Communications in Mathematical Physics},
   Volume = {264},
   Number = {1},
   Pages = {227-253},
   Year = {2006},
   ISSN = {0010-3616},
   url = {http://dx.doi.org/10.1007/s00220-006-1527-6},
   Abstract = {We present a general method for the computation of
             tree-level superpotentials for the world-volume theory of
             B-type D-branes. This includes quiver gauge theories in the
             case that the D-brane is marginally stable. The technique
             involves analyzing the A ∞-structure inherent in the
             derived category of coherent sheaves. This effectively gives
             a practical method of computing correlation functions in
             holomorphic Chern-Simons theory. As an example, we give a
             more rigorous proof of previous results concerning 3-branes
             on certain singularities including conifolds. We also
             provide a new example.},
   Doi = {10.1007/s00220-006-1527-6},
   Key = {fds243308}
}

@article{fds303519,
   Author = {Aspinwall, PS and Kallosh, R},
   Title = {Fixing All Moduli for M-Theory on K3xK3},
   Journal = {JHEP},
   Volume = {0510},
   Pages = {001},
   Year = {2005},
   Month = {June},
   url = {http://arxiv.org/abs/hep-th/0506014v1},
   Abstract = {We analyze M-theory compactified on K3xK3 with fluxes
             preserving half the supersymmetry and its F-theory limit,
             which is dual to an orientifold of the type IIB string on
             $K3\times T^2/Z_2$. The geometry of attractive K3 surfaces
             plays a significant role in the analysis. We prove that the
             number of choices for the K3 surfaces is finite and we show
             how they can be completely classified. We list the
             possibilities in one case. We then study the instanton
             effects and see that they will generically fix all of the
             moduli. We also discuss situations where the instanton
             effects might not fix all the moduli.},
   Doi = {10.1088/1126-6708/2005/10/001},
   Key = {fds303519}
}

@article{fds43748,
   Author = {P.S. Aspinwall},
   Title = {An Analysis of Fluxes by Duality},
   Year = {2005},
   url = {http://arxiv.org/abs/hep-th/0504036},
   Key = {fds43748}
}

@article{fds43744,
   Author = {P.S. Aspinwall},
   Title = {D-Branes on Calabi-Yau Manifolds},
   Booktitle = {Progress in String Theory, TASI 2003 Lecture
             Notes},
   Publisher = {World Scientific},
   Year = {2005},
   url = {http://arxiv.org/abs/hep-th/0403166},
   Key = {fds43744}
}

@article{fds243300,
   Author = {Aspinwall, PS and Kallosh, R},
   Title = {Fixing all moduli for M-theory on K3×K3},
   Journal = {Journal of High Energy Physics},
   Number = {10},
   Pages = {1-20},
   Year = {2005},
   url = {http://dx.doi.org/10.1088/1126-6708/2005/10/001},
   Abstract = {We analyze M-theory compactified on K3 × K3 with fluxes
             preserving half the supersymmetry and its F-theory limit,
             which is dual to an orientifold of the type IIB string on K3
             × (T2/ℤ2). The geometry of attractive K3 surfaces plays a
             significant role in the analysis. We prove that the number
             of choices for the K3 surfaces is finite and we show how
             they can be completely classified. We list the possibilities
             in one case. We then study the instanton effects and see
             that they will generically fix all of the moduli. We also
             discuss situations where the instanton effects might not fix
             all the moduli. © SISSA 2005.},
   Doi = {10.1088/1126-6708/2005/10/001},
   Key = {fds243300}
}

@article{fds243309,
   Author = {Aspinwall, PS and Horja, RP and Karp, RL},
   Title = {Massless D-branes on Calabi-Yau threefolds and
             monodromy},
   Journal = {Communications in Mathematical Physics},
   Volume = {259},
   Number = {1},
   Pages = {45-69},
   Year = {2005},
   url = {http://dx.doi.org/10.1007/s00220-005-1378-6},
   Abstract = {We analyze the link between the occurrence of massless
             B-type D-branes for specific values of moduli and monodromy
             around such points in the moduli space. This allows us to
             propose a classification of all massless B-type D-branes at
             any point in the moduli space of Calabi-Yau's. This
             classification then justifies a previous conjecture due to
             Horja for the general form of monodromy. Our analysis is
             based on using monodromies around points in moduli space
             where a single D-brane becomes massless to generate
             monodromies around points where an infinite number become
             massless. We discuss the various possibilities within the
             classification. © Springer-Verlag 2005.},
   Doi = {10.1007/s00220-005-1378-6},
   Key = {fds243309}
}

@article{fds243298,
   Author = {Aspinwall, PS},
   Title = {The breakdown of topology at small scales},
   Journal = {Journal of High Energy Physics},
   Volume = {8},
   Number = {7},
   Pages = {453-463},
   Year = {2004},
   url = {http://arxiv.org/abs/hep-th/0312188v1},
   Abstract = {We discuss how a topology (the Zariski topology) on a space
             can appear to break down at small distances due to D-brane
             decay. The mechanism proposed coincides perfectly with the
             phase picture of Calabi-Yau moduli spaces. The topology
             breaks down as one approaches non-geometric phases. This
             picture is not without its limitations, which are also
             discussed. © SISSA/ISAS 2004.},
   Doi = {10.1088/1126-6708/2004/07/021},
   Key = {fds243298}
}

@article{fds243299,
   Author = {Aspinwall, PS and Melnikov, IV},
   Title = {D-branes on vanishing del Pezzo surfaces},
   Journal = {Journal of High Energy Physics},
   Volume = {8},
   Number = {12},
   Pages = {901-930},
   Year = {2004},
   url = {http://arxiv.org/abs/hep-th/0405134v2},
   Abstract = {We analyze in detail the case of a marginally stable D-Brane
             on a collapsed del Pezzo surface in a Calabi-Yau threefold
             using the derived category of quiver representations and the
             idea of aligned gradings. We show how the derived category
             approach to D-branes provides a straight-forward and
             rigorous construction of quiver gauge theories associated to
             such singularities. Our method shows that a procedure
             involving exceptional collections used elsewhere in the
             literature is only valid if some tachyon-inducing Ext3
             groups are zero. We then analyze in generality a large class
             of Seiberg dualities which arise from tilting equivalences.
             It follows that some (but not all) mutations of exceptional
             collections induce Seiberg duality in this context. The same
             tilting equivalence can also be used to remove unwanted Ext3
             groups and convert an unphysical quiver into a physical one.
             © SISSA/ISAS 2005.},
   Doi = {10.1088/1126-6708/2004/12/042},
   Key = {fds243299}
}

@article{fds243295,
   Author = {Aspinwall, PS},
   Title = {A point's point of view of stringy geometry},
   Journal = {Journal of High Energy Physics},
   Volume = {7},
   Number = {1},
   Pages = {17-31},
   Year = {2003},
   url = {http://arxiv.org/abs/hep-th/0203111v2},
   Abstract = {The notion of a "point" is essential to describe the
             topology of spacetime. Despite this, a point probably does
             not play a particularly distinguished rôle in any intrinsic
             formulation of string theory. We discuss one way to try to
             determine the notion of a point from a worldsheet point of
             view. The derived category description of D-branes is the
             key tool. The case of a flop is analyzed and II-stability in
             this context is tied in to some ideas of Bridgeland.
             Monodromy associated to the flop is also computed via
             II-stability and shown to be consistent with previous
             conjectures. © SISSA/ISAS 2003.},
   Doi = {10.1088/1126-6708/2003/01/002},
   Key = {fds243295}
}

@article{fds243297,
   Author = {Aspinwall, PS and Karp, RL},
   Title = {Solitons in Seiberg-Witten theory and D-branes in the
             derived category},
   Journal = {Journal of High Energy Physics},
   Volume = {7},
   Number = {4},
   Pages = {1119-1137},
   Year = {2003},
   url = {http://arxiv.org/abs/hep-th/0211121v1},
   Abstract = {We analyze the "geometric engineering" limit of a type II
             string on a suitable Calabi-Yau threefold to obtain an N = 2
             pure SU(2) gauge theory. The derived category picture
             together with II-stability of B-branes beautifully
             reproduces the known spectrum of BPS solitons in this case
             in a very explicit way. Much of the analysis is particularly
             easy since it can be reduced to questions about the derived
             category of ℙ1. © SISSA/ISAS 2003.},
   Doi = {10.1088/1126-6708/2003/04/049},
   Key = {fds243297}
}

@article{fds243296,
   Author = {Aspinwall, PS and Douglas, MR},
   Title = {D-brane stability and monodromy},
   Journal = {The Journal of High Energy Physics},
   Volume = {6},
   Number = {5},
   Pages = {739-773},
   Year = {2002},
   ISSN = {1029-8479},
   url = {http://arxiv.org/abs/hep-th/0110071},
   Abstract = {We review the idea of II-stability for B-type D-branes on a
             Calabi-Yau manifold. It is shown that the octahedral axiom
             from the theory of derived categories is an essential
             ingredient in the study of stability. Various examples in
             the context of the quintic Calabi-Yau threefold are studied
             and we plot the lines of marginal stability in several
             cases. We derive the conjecture of Kontsevich, Horja and
             Morrison for the derived category version of monodromy
             around a "conifold" point. Finally, we propose an
             application of these ideas to the study of supersymmetry
             breaking. © SISSA/ISAS 2002.},
   Key = {fds243296}
}

@article{fds243292,
   Author = {Aspinwall, PS and Plesser, MR},
   Title = {D-branes, discrete torsion and the McKay
             correspondence},
   Journal = {The Journal of High Energy Physics},
   Volume = {5},
   Number = {2},
   Pages = {XIX-25},
   Year = {2001},
   ISSN = {1029-8479},
   url = {http://arxiv.org/abs/hep-th/0009042},
   Abstract = {We analyze the D-branes of a type-IIB string theory on an
             orbifold singularity including the possibility of discrete
             torsion following the work of Douglas et al. First we prove
             some general results about the moduli space of a point
             associated to the "regular representation" of the orbifold
             group. This includes some analysis of the "wrapped branes"
             which necessarily appear when the orbifold singularity is
             not isolated. Next we analyze the stringy homology of the
             orbifold using the McKay correspondence and the relationship
             between K-theory and homology. We find that discrete torsion
             and torsion in this stringy homology are closely-related
             concepts but that they differ in general. Lastly we question
             to what extent the D-1 brane may be thought of as being dual
             to a string.},
   Key = {fds243292}
}

@article{fds243293,
   Author = {Aspinwall, PS},
   Title = {Some navigation rules for D-brane monodromy},
   Journal = {Journal of Mathematical Physics},
   Volume = {42},
   Number = {12},
   Pages = {5534-5552},
   Year = {2001},
   url = {http://dx.doi.org/10.1063/1.1409963},
   Abstract = {We explore some aspects of monodromies of D-branes in the
             Kähler moduli space of Calabi-Yau compactifications. Here a
             D-brane is viewed as an object of the derived category of
             coherent sheaves. We compute all the interesting monodromies
             in some nontrivial examples and link our work to recent
             results and conjectures concerning helices and mutations. We
             note some particular properties of the 0-brane. © 2001
             American Institute of Physics.},
   Doi = {10.1063/1.1409963},
   Key = {fds243293}
}

@article{fds243294,
   Author = {Aspinwall, PS and Lawrence, A},
   Title = {Derived categories and zero-brane stability},
   Journal = {The Journal of High Energy Physics},
   Volume = {5},
   Number = {8},
   Pages = {XIV-26},
   Year = {2001},
   ISSN = {1029-8479},
   Abstract = {We define a particular class of topological field theories
             associated to open strings and prove the resulting D-branes
             and open strings form the bounded derived category of
             coherent sheaves. This derivation is a variant of some ideas
             proposed recently by Douglas. We then argue that any 0-brane
             on any Calabi-Yau threefold must become unstable along some
             path in the Kähler moduli space. As a byproduct of this
             analysis we see how the derived category can be invariant
             under a birational transformation between
             Calabi-Yaus.},
   Key = {fds243294}
}

@article{fds243288,
   Author = {Aspinwall, PS and Katz, S and Morrison, DR},
   Title = {Lie groups, Calabi-Yau threefolds, and F-theory},
   Journal = {Advances in Theoretical and Mathematical
             Physics},
   Volume = {4},
   Number = {1},
   Pages = {1-24},
   Year = {2000},
   ISSN = {1095-0761},
   url = {http://arxiv.org/abs/hep-th/0002012},
   Abstract = {The F-theory vacuum constructed from an elliptic Calabi-Yau
             threefold with section yields an effective six-dimensional
             theory. The Lie algebra of the gauge sector of this theory
             and its representation on the space of massless
             hypermultiplets are shown to be determined by the
             intersection theory of the homology of the Calabi-Yau
             threefold. (Similar statements hold for M-theory and the
             type IIA string compactified on the threefold, where there
             is also a dependence on the expectation values of the
             Ramond-Ramond fields.) We describe general rules for
             computing the hypermultiplet spectrum of any F-theory
             vacuum, including vacua with non-simply-laced gauge groups.
             The case of monodromy acting on a curve of Aeven
             singularities is shown to be particularly interesting and
             leads to some unexpected rules for how 2-branes are allowed
             to wrap certain 2-cycles. We also review the peculiar
             numerical predictions for the geometry of elliptic
             Calabi-Yau threefolds with section which arise from anomaly
             cancellation in six dimensions.},
   Key = {fds243288}
}

@article{fds243290,
   Author = {Aspinwall, PS},
   Title = {A note on the equivalence of Vafa's and Douglas's picture of
             discrete torsion},
   Journal = {Journal of High Energy Physics},
   Volume = {4},
   Number = {12},
   Pages = {XXXVIII-6},
   Year = {2000},
   url = {http://arxiv.org/abs/hep-th/0009045},
   Abstract = {For a general non-abelian group action and an arbitrary
             genus worldsheet we show that Vafa's old definition of
             discrete torsion coincides with Douglas's D-brane definition
             of discrete torsion associated to projective
             representations.},
   Key = {fds243290}
}

@article{fds243291,
   Author = {Aspinwall, PS and Plesser, MR},
   Title = {Heterotic string corrections from the dual type-II
             string},
   Journal = {Journal of High Energy Physics},
   Volume = {4},
   Number = {4},
   Pages = {XXXIV-21},
   Year = {2000},
   url = {http://arxiv.org/abs/hep-th/9910248},
   Abstract = {We introduce a method of using the a dual type-IIA string to
             compute α′-corrections to the moduli space of heterotic
             string compactifications. In particular we study the
             hypermultiplet moduli space of a heterotic string on a K3
             surface. One application of this machinery shows that
             type-IIB strings compactified on a Calabi-Yau space suffer
             from worldsheet instantons, spacetime instantons and, in
             addition, "mixed" instantons which in a sense are both
             worldsheet and spacetime. As another application we look at
             the hyperkähler limit of the moduli space in which the K3
             surface becomes an ALE space. This is a variant of the
             "geometric engineering" method used for vector multiplet
             moduli space and should be applicable to a wide range of
             examples. In particular we reproduce Sen and Witten's result
             for the heterotic string on an A1 singularity and a trivial
             bundle and generalize this to a collection of E8 point-like
             instantons on an ALE space.},
   Key = {fds243291}
}

@article{fds303521,
   Author = {Aspinwall, PS},
   Title = {Compactification, Geometry and Duality: N=2},
   Year = {1999},
   Month = {December},
   url = {http://arxiv.org/abs/hep-th/0001001v2},
   Abstract = {These are notes based on lectures given at TASI99. We review
             the geometry of the moduli space of N=2 theories in four
             dimensions from the point of view of superstring
             compactification. The cases of a type IIA or type IIB string
             compactified on a Calabi-Yau threefold and the heterotic
             string compactified on K3xT2 are each considered in detail.
             We pay specific attention to the differences between N=2
             theories and N>2 theories. The moduli spaces of vector
             multiplets and the moduli spaces of hypermultiplets are
             reviewed. In the case of hypermultiplets this review is
             limited by the poor state of our current understanding. Some
             peculiarities such as ``mixed instantons'' and the
             non-existence of a universal hypermultiplet are
             discussed.},
   Key = {fds303521}
}

@article{fds243289,
   Author = {Aspinwall, PS and Plesser, MR},
   Title = {T-duality can fail},
   Journal = {The Journal of High Energy Physics},
   Volume = {3},
   Number = {8},
   Pages = {XI-18},
   Year = {1999},
   ISSN = {1029-8479},
   url = {http://arxiv.org/abs/hep-th/9905036},
   Abstract = {We show that T-duality can be broken by non-perturbative
             effects in string coupling. The T-duality in question is
             that of the 2-torus when the heterotic string is
             compactified on K3xT2. This case is compared carefully to a
             situation where T-duality appears to work. A holonomy
             argument is presented to show that T-dualities (and general
             U-dualities) should only be expected for large amounts of
             supersymmetry. This breaking of R ↔ 1/R symmetry raises
             some interesting questions in string theory which we
             discuss. Finally we discuss how the classical modular group
             of a 2-torus appears to be broken too.},
   Key = {fds243289}
}

@article{fds243284,
   Author = {Aspinwall, PS and Morrison, DR},
   Title = {Non-simply-connected gauge groups and rational points on
             elliptic curves},
   Journal = {The Journal of High Energy Physics},
   Volume = {1998},
   Number = {7},
   Pages = {XXII-15},
   Year = {1998},
   ISSN = {1029-8479},
   url = {http://arxiv.org/abs/hep-th/9805206},
   Abstract = {We consider the F-theory description of non-simply-connected
             gauge groups appearing in the E8 × E8 heterotic string. The
             analysis is closely tied to the arithmetic of torsion points
             on an elliptic curve. The general form of the corresponding
             elliptic fibration is given for all finite subgroups of E8
             which are applicable in this context. We also study the
             closely-related question of point-like instantons on a K3
             surface whose holonomy is a finite group. As an example we
             consider the case of the heterotic string on a K3 surface
             having the E8 gauge symmetry broken to SU(9)/ℤ3 or (E6 ×
             SU(3))/ℤ3 by point-like instantons with ℤ3
             holonomy.},
   Key = {fds243284}
}

@article{fds243286,
   Author = {Aspinwall, PS and Donagi, RY},
   Title = {The heterotic string, The tangent bundle and derived
             categories},
   Journal = {Advances in Theoretical and Mathematical
             Physics},
   Volume = {2},
   Number = {5},
   Pages = {1041-1074},
   Year = {1998},
   ISSN = {1095-0761},
   url = {http://arxiv.org/abs/hep-th/9806094},
   Abstract = {We consider the compactification of the E8×E8 heterotic
             string on a K3 surface with "the spin connection embedded in
             the gauge group" and the dual picture in the type IIA string
             (or F-theory) on a Calabi-Yau threefold X. It turns out that
             the same X arises also as dual to a heterotic
             compactification on 24 point-like instantons. X is
             necessarily singular, and we see that this singularity
             allows the Ramond-Ramond moduli on X to split into distinct
             components, one containing the (dual of the heterotic)
             tangent bundle, while another component contains the
             point-like instantons. As a practical application we derive
             the result that a heterotic string compactified on the
             tangent bundle of a K3 with ADE singularities acquires
             nonperturbatively enhanced gauge symmetry in just the same
             fashion as a type IIA string on a singular K3 surface. On a
             more philosophical level we discuss how it appears to be
             natural to say that the heterotic string is compactified
             using an object in the derived category of coherent sheaves.
             This is necessary to properly extend the notion of T-duality
             to the heterotic string on a K3 surface. © 1998
             International Press.},
   Key = {fds243286}
}

@article{fds243287,
   Author = {Aspinwall, PS},
   Title = {Aspects of the hypermultiplet moduli space in string
             duality},
   Journal = {The Journal of High Energy Physics},
   Volume = {2},
   Number = {4},
   Pages = {XXIX-26},
   Year = {1998},
   ISSN = {1029-8479},
   url = {http://arxiv.org/abs/hep-th/9802194},
   Abstract = {A type IIA string (or F-theory) compactified on a Calabi-Yau
             threefold is believed to be dual to a heterotic string on a
             K3 surface times a 2-torus (or on a K3 surface). We consider
             how the resulting moduli space of hypermultiplets is
             identified between these two pictures in the case of the E8
             × E8 heterotic string. As examples we discuss SU(2)-bundles
             and G2-bundles on the K3 surface and the case of point-like
             instantons. We are lead to a rather beautiful identification
             between the integral cohomology of the Calabi-Yau threefold
             and some integral structures on the heterotic side somewhat
             reminiscent of mirror symmetry. We discuss the consequences
             for probing nonperturbative effects in the both the type IIA
             string and the heterotic string.},
   Key = {fds243287}
}

@article{fds243281,
   Author = {Aspinwall, PS},
   Title = {Point-like instantons and the Spin(32)/ℤ2
             heterotic string},
   Journal = {Nuclear Physics B},
   Volume = {496},
   Number = {1-2},
   Pages = {149-176},
   Year = {1997},
   url = {http://arxiv.org/abs/hep-th/9612108},
   Abstract = {We consider heterotic string theories compactified on a K3
             surface which lead to an unbroken perturbative gauge group
             of Spin(32)/ℤ2. All solutions obtained are combinations of
             two types of point-like instanton - one "simple type" as
             discovered by Witten and a new type associated to the
             "generalized second Stiefel-Whitney class" as introduced by
             Berkooz et al. The new type of instanton is associated to an
             enhancement of the gauge symmetry by Sp(4) and the addition
             of a massless tensor supermultiplet. It is shown that if
             four simple instantons coalesce at an orbifold point in the
             K3 surface then a massless tensor field appears which may be
             used to interpolate between the two types of instanton. By
             allowing various combinations of point-like instantons to
             coalesce, large gauge groups (e.g., rank 128) with many
             massless tensor supermultiplets result. The analysis is done
             in terms of F-theory. © 1997 Elsevier Science
             B.V.},
   Key = {fds243281}
}

@article{fds243285,
   Author = {Aspinwall, PS and Morrison, DR},
   Title = {Point-like instantons on K3 orbifolds},
   Journal = {Nuclear Physics B},
   Volume = {503},
   Number = {3},
   Pages = {533-564},
   Year = {1997},
   Abstract = {The map between the moduli space of F-theory (or type II
             string) compactifications and heterotic string
             compactifications can be considerably simplified by using
             "stable degenerations". We discuss how this method applies
             to both the E8 × E8 and the Spin(32)/ℤ2 heterotic string.
             As a simple application of the method we derive some basic
             properties of the non-perturbative physics of collections of
             E8 or Spin(32)/ℤ2 point-like instantons sitting at ADE
             singularities on a K3 surface. © 1997 Elsevier Science
             B.V.},
   Key = {fds243285}
}

@article{fds303517,
   Author = {Aspinwall, PS and Gross, M},
   Title = {The SO(32) Heterotic String on a K3 Surface},
   Journal = {Phys.Lett. B},
   Volume = {387},
   Pages = {735-742},
   Year = {1996},
   Month = {May},
   url = {http://arxiv.org/abs/hep-th/9605131v2},
   Abstract = {The SO(32) heterotic string on a K3 surface is analyzed in
             terms of the dual theory of a type II string (or F-theory)
             on an elliptically fibred Calabi-Yau manifold. The results
             are in beautiful agreement with earlier work by Witten using
             very different methods. In particular, we find gauge groups
             of SO(32) x Sp(k) appearing at points in the moduli space
             identified with point-like instantons and see
             hypermultiplets in the (32,2k) representation becoming
             massless at the same time. We also discuss some aspects of
             the E8 x E8 case.},
   Doi = {10.1016/0370-2693(96)01095-7},
   Key = {fds303517}
}

@article{fds243276,
   Author = {Aspinwall, PS},
   Title = {An N = 2 dual pair and a phase transition},
   Journal = {Nuclear Physics B},
   Volume = {460},
   Number = {1},
   Pages = {57-76},
   Year = {1996},
   url = {http://dx.doi.org/10.1016/0550-3213(95)00611-7},
   Abstract = {We carefully analyze the N = 2 dual pair of string theories
             in four dimensions introduced by Ferrara, Harvey, Strominger
             and Vafa. The analysis shows that a second discrete degree
             of freedom must be switched on in addition to the known
             "Wilson line" to achieve a non-perturbatively consistent
             theory. We also identify the phase transition this model
             undergoes into another dual pair via a process analogous to
             a conifold transition. This provides the first known example
             of a phase transition which is understood from both the type
             II and the heterotic string picture.},
   Doi = {10.1016/0550-3213(95)00611-7},
   Key = {fds243276}
}

@article{fds243278,
   Author = {Aspinwall, PS and Louis, J},
   Title = {On the ubiquity of K3 fibrations in string
             duality},
   Journal = {Physics Letters, Section B: Nuclear, Elementary Particle and
             High-Energy Physics},
   Volume = {369},
   Number = {3-4},
   Pages = {233-242},
   Year = {1996},
   Abstract = {We consider the general case of N = 2 dual pairs of type
             IIA/heterotic string theories in four dimensions. We show
             that if the type IIA string in this pair can be viewed as
             having been compactified on a Calabi-Yau manifold in the
             usual way then this manifold must be of the form of a K3
             fibration. We also see how the bound on the rank of the
             gauge group of the perturbative heterotic string has a
             natural interpretation on the type IIA side.},
   Key = {fds243278}
}

@article{fds243279,
   Author = {Aspinwall, PS},
   Title = {Enhanced gauge symmetries and Calabi-Yau
             threefolds},
   Journal = {Physics Letters, Section B: Nuclear, Elementary Particle and
             High-Energy Physics},
   Volume = {371},
   Number = {3-4},
   Pages = {231-237},
   Year = {1996},
   Abstract = {We consider the general case of a type IIA string
             compactified on a Calabi-Yau manifold which has a heterotic
             dual description. It is shown that the nonabelian gauge
             symmetries which can appear nonperturbatively in the type II
             string but which are understood perturbatively in the
             heterotic string are purely a result of string-string
             duality in six dimensions. We illustrate this with some
             examples.},
   Key = {fds243279}
}

@article{fds243280,
   Author = {Aspinwall, PS},
   Title = {Some relationships between dualities in string
             theory},
   Journal = {Nuclear Physics B - Proceedings Supplements},
   Volume = {46},
   Number = {1-3},
   Pages = {30-38},
   Year = {1996},
   url = {http://dx.doi.org/10.1016/0920-5632(96)00004-7},
   Abstract = {Some relationships between string theories and
             eleven-dimensional supergravity are discussed and reviewed.
             We see how some relationships can be derived from others.
             The cases of N = 2 supersymmetry in nine dimensions and N =
             4 supersymmetry in four dimensions are discussed in some
             detail. The latter case leads to consideration of quotients
             of a K3 surface times a torus and to a possible peculiar
             relationship between eleven-dimensional supergravity and the
             heterotic strings in ten dimensions.},
   Doi = {10.1016/0920-5632(96)00004-7},
   Key = {fds243280}
}

@article{fds243282,
   Author = {Aspinwall, PS and Gross, M},
   Title = {Heterotic-heterotic string duality and multiple K3
             fibrations},
   Journal = {Physics Letters, Section B: Nuclear, Elementary Particle and
             High-Energy Physics},
   Volume = {382},
   Number = {1-2},
   Pages = {81-88},
   Year = {1996},
   Abstract = {A type IIA string compactified on a Calabi-Yau manifold
             which admits a K3 fibration is believed to be equivalent to
             a heterotic string in four dimensions. We study cases where
             a Calabi-Yau manifold can have more than one such fibration
             leading to equivalences between perturbatively inequivalent
             heterotic strings. This allows an analysis of an example in
             six dimensions due to Duff, Minasian and Witten and enables
             us to go some way to prove a conjecture by Kachru and Vafa.
             The interplay between gauge groups which arise
             perturbatively and nonperturbatively is seen clearly in this
             example. As an extreme case we discuss a Calabi-Yau manifold
             which admits an infinite number of K3 fibrations leading to
             infinite set of equivalent heterotic strings.},
   Key = {fds243282}
}

@article{fds243283,
   Author = {Aspinwall, PS and Morrison, DR and Gross, M},
   Title = {Stable singularities in string theory},
   Journal = {Communications in Mathematical Physics},
   Volume = {178},
   Number = {1},
   Pages = {115-134},
   Year = {1996},
   Abstract = {We study a topological obstruction of a very stringy nature
             concerned with deforming the target space of an N = 2
             non-linear σ-model. This target space has a singularity
             which may be smoothed away according to the conventional
             rules of geometry, but when one studies the associated
             conformal field theory one sees that such a deformation is
             not possible without a discontinuous change in some of the
             correlation functions. This obstruction appears to come from
             torsion in the homology of the target space (which is seen
             by deforming the theory by an irrelevant operator). We
             discuss the link between this phenomenon and orbifolds with
             discrete torsion as studied by Vafa and Witten.},
   Key = {fds243283}
}

@article{fds243274,
   Author = {Aspinwall, PS and Morrison, DR},
   Title = {U-duality and integral structures},
   Journal = {Physics Letters B},
   Volume = {355},
   Number = {1-2},
   Pages = {141-149},
   Year = {1995},
   ISSN = {0370-2693},
   url = {http://dx.doi.org/10.1016/0370-2693(95)00745-7},
   Abstract = {We analyze the U-duality group of the case of a type II
             superstring compactified to four dimensions on a K3 surface
             times a torus. The various limits of this theory are
             considered which have interpretations as type IIA and IIB
             superstrings, the heterotic string, and eleven-dimensional
             supergravity, allowing all these theories to be directly
             related to each other. The integral structure which appears
             in the Ramond-Ramond sector of the type II superstring is
             related to the quantum cohomology of general Calabi-Yau
             threefolds which allows the moduli space of type II
             superstring compactifications on Calabi-Yau manifolds to be
             analyzed. © 1995.},
   Doi = {10.1016/0370-2693(95)00745-7},
   Key = {fds243274}
}

@article{fds243275,
   Author = {Aspinwall, PS and Greene, BR},
   Title = {On the geometric interpretation of N = 2 superconformal
             theories},
   Journal = {Nuclear Physics B},
   Volume = {437},
   Number = {1},
   Pages = {205-227},
   Year = {1995},
   ISSN = {0550-3213},
   url = {http://dx.doi.org/10.1016/0550-3213(94)00571-U},
   Abstract = {We clarify certain important issues relevant for the
             geometric interpretation of a large class of N= 2
             superconformal theories. By fully exploiting the phase
             structure of these theories (discovered in earlier works) we
             are able to clearly identify their geometric content. One
             application is to present a simple and natural resolution to
             the question of what constitutes the mirror of a rigid
             Calabi-Yau manifold. We also discuss some other models with
             unusual phase diagrams that highlight some subtle features
             regarding the geometric content of conformal theories. ©
             1995 Elsevier Science B.V. All rights reserved.},
   Doi = {10.1016/0550-3213(94)00571-U},
   Key = {fds243275}
}

@article{fds243277,
   Author = {Aspinwall, PS},
   Title = {Enhanced gauge symmetries and K3 surfaces},
   Journal = {Physics Letters B},
   Volume = {357},
   Number = {3},
   Pages = {329-334},
   Year = {1995},
   ISSN = {0370-2693},
   url = {http://dx.doi.org/10.1016/0370-2693(95)00957-M},
   Abstract = {String-string duality dictates that type IIA strings
             compactified on a K3 surface acquire non-abelian gauge
             groups for certain values of the K3 moduli. We argue that,
             contrary to expectation, the theories for which such
             enhanced gauge symmetries appear are not orbifolds in the
             string sense. For a specific example we show that a theory
             with enhanced gauge symmetry and an orbifold theory have the
             same classical K3 surface as a target space but the value of
             the "B-field" differs. This raises the possibility that the
             conformal field theory associated to a string theory with an
             enhanced gauge group is badly behaved in some way. ©
             1995.},
   Doi = {10.1016/0370-2693(95)00957-M},
   Key = {fds243277}
}

@article{fds243269,
   Author = {Aspinwall, PS and Greene, BR and Morrison, DR},
   Title = {Measuring small distances in N = 2 sigma
             models},
   Journal = {Nuclear Physics B},
   Volume = {420},
   Number = {1-2},
   Pages = {184-242},
   Year = {1994},
   ISSN = {0550-3213},
   url = {http://dx.doi.org/10.1016/0550-3213(94)90379-4},
   Abstract = {We analyze global aspects of the moduli space of Kähler
             forms for N = (2,2) conformal σ-models. Using algebraic
             methods and mirror symmetry we study extensions of the
             mathematical notion of length (as specified by a Kähler
             structure) to conformal field theory and calculate the way
             in which lengths change as the moduli fields are varied
             along distinguished paths in the moduli space. We find
             strong evidence supporting the notion that, in the robust
             setting of quantum Calabi-Yau moduli space, string theory
             restricts the set of possible Kähler forms by enforcing
             "minimal length" scales, provided that topology change is
             properly taken into account. Some lengths, however, may
             shrink to zero. We also compare stringy geometry to
             classical general relativity in this context. ©
             1994.},
   Doi = {10.1016/0550-3213(94)90379-4},
   Key = {fds243269}
}

@article{fds243270,
   Author = {Aspinwall, PS and Morrison, DR},
   Title = {Chiral rings do not suffice: N=(2,2) theories with nonzero
             fundamental group},
   Journal = {Physics Letters B},
   Volume = {334},
   Number = {1-2},
   Pages = {79-86},
   Year = {1994},
   ISSN = {0370-2693},
   url = {http://dx.doi.org/10.1016/0370-2693(94)90594-0},
   Abstract = {The Kähler moduli space of a particular
             non-simply-connected Calabi-Yau manifold is mapped out using
             mirror symmetry. It is found that, for the model considered,
             the chiral ring may be identical for different associated
             conformal field theories. This ambiguity is explained in
             terms of both A-model and B-model language. It also provides
             an apparent counterexample to the global Torelli problem for
             Calabi-Yau threefolds. © 1994.},
   Doi = {10.1016/0370-2693(94)90594-0},
   Key = {fds243270}
}

@article{fds243271,
   Author = {Aspinwall, PS},
   Title = {Minimum distances in non-trivial string target
             spaces},
   Journal = {Nuclear Physics B},
   Volume = {431},
   Number = {1-2},
   Pages = {78-96},
   Year = {1994},
   Abstract = {The idea of minimum distance, familiar from R ↔ 1/R
             duality when the string target space is a circle, is
             analyzed for less trivial geometries. The particular
             geometry studied is that of a blown-up quotient singularity
             within a Calabi-Yau space and mirror symmetry is used to
             perform the analysis. It is found that zero distances can
             appear but that in many cases this requires other distances
             within the same target space to be infinite. In other cases
             zero distances can occur without compensating infinite
             distances.},
   Key = {fds243271}
}

@article{fds243272,
   Author = {Aspinwall, PS and Greene, BR and Morrison, DR},
   Title = {Space-time topology change and stringy geometry
             a},
   Journal = {Journal of Mathematical Physics},
   Volume = {35},
   Number = {10},
   Pages = {5321-5337},
   Year = {1994},
   ISSN = {0022-2488},
   Abstract = {Recent work which has significantly honed the geometric
             understanding and interpretation of the moduli space of
             certain N=2 superconformal field theories is reviewed. This
             has resolved some important issues in mirror symmetry and
             has also established that string theory admits physically
             smooth processes which can result in a change in topology of
             the spatial universe. Recent work which illuminates some
             properties of physically related theories associated with
             singular spaces such as orbifolds is described. © 1994
             American Institute of Physics.},
   Key = {fds243272}
}

@article{fds243273,
   Author = {Aspinwall, PS and Greene, BR and Morrison, DR},
   Title = {Calabi-Yau moduli space, mirror manifolds and spacetime
             topology change in string theory},
   Journal = {Nuclear Physics B},
   Volume = {416},
   Number = {2},
   Pages = {414-480},
   Year = {1994},
   Abstract = {We analyze the moduli spaces of Calabi-Yau three-folds and
             their associated conformally invariant nonlinear σ-models
             and show that they are described by an unexpectedly rich
             geometrical structure. Specifically, the Kahler sector of
             the moduli space of such Calabi-Yau conformal theories
             admits a decomposition into adjacent domains some of which
             correspond to the (complexified) Kahler cones of
             topologically distinct manifolds. These domains are
             separated by walls corresponding to singular Calabi-Yau
             spaces in which the spacetime metric has degenerated in
             certain regions. We show that the union of these domains is
             isomorphic to the complex structure moduli space of a single
             topological Calabi-Yau space - the mirror. In this way we
             resolve a puzzle for mirror symmetry raised by the apparent
             asymmetry between the Kahler and complex structure moduli
             spaces of a Calabi-Yau manifold. Furthermore, using mirror
             symmetry, we show that we can interpolate in a physically
             smooth manner between any two theories represented by
             distinct points in the Kahler moduli space, even if such
             points correspond to topologically distinct spaces.
             Spacetime topology change in string theory, therefore, is
             realized by the most basic operation of deformation by a
             truly marginal operator. Finally, this work also yields some
             important insights on the nature of orbifolds in string
             theory.},
   Key = {fds243273}
}

@booklet{Aspinwall93,
   Author = {Aspinwall, PS and Greene, BR and Morrison, DR},
   Title = {The Monomial-Divisor Mirror Map},
   Journal = {Internat. Math. Res. Notices (1993), 319-337},
   Volume = {72},
   Number = {3},
   Pages = {319 -- 337},
   Year = {1993},
   Month = {September},
   url = {http://arxiv.org/abs/alg-geom/9309007v1},
   Abstract = {For each family of Calabi-Yau hypersurfaces in toric
             varieties, Batyrev has proposed a possible mirror partner
             (which is also a family of Calabi-Yau hypersurfaces). We
             explain a natural construction of the isomorphism between
             certain Hodge groups of these hypersurfaces, as predicted by
             mirror symmetry, which we call the monomial-divisor mirror
             map. We indicate how this map can be interpreted as the
             differential of the expected mirror isomorphism between the
             moduli spaces of the two Calabi-Yau manifolds. We formulate
             a very precise conjecture about the form of that mirror
             isomorphism, which when combined with some earlier
             conjectures of the third author would completely specify it.
             We then conclude that the moduli spaces of the nonlinear
             sigma models whose targets are the different birational
             models of a Calabi-Yau space should be connected by analytic
             continuation, and that further analytic continuation should
             lead to moduli spaces of other kinds of conformal field
             theories. (This last conclusion was first drawn by
             Witten.)},
   Key = {Aspinwall93}
}

@article{fds322465,
   Author = {Aspinwall, PS and Morrison, DR and Greene, BR},
   Title = {The monomial-divisor mirror map},
   Journal = {International Mathematics Research Notices},
   Volume = {1993},
   Number = {12},
   Pages = {319-337},
   Year = {1993},
   Month = {January},
   url = {http://dx.doi.org/10.1155/S1073792893000376},
   Doi = {10.1155/S1073792893000376},
   Key = {fds322465}
}

@booklet{Aspinwall93a,
   Author = {Aspinwall, PS and Morrison, DR},
   Title = {Topological field theory and rational curves},
   Journal = {Communications in Mathematical Physics},
   Volume = {151},
   Number = {2},
   Pages = {245-262},
   Year = {1993},
   ISSN = {0010-3616},
   url = {http://dx.doi.org/10.1007/BF02096768},
   Abstract = {We analyze the quantum field theory corresponding to a
             string propagating on a Calabi-Yau threefold. This theory
             naturally leads to the consideration of Witten's topological
             non-linear σ-model and the structure of rational curves on
             the Calabi-Yau manifold. We study in detail the case of the
             world-sheet of the string being mapped to a multiple cover
             of an isolated rational curve and we show that a natural
             compactification of the moduli space of such a multiple
             cover leads to a formula in agreement with a conjecture by
             Candelas, de la Ossa, Green and Parkes. © 1993
             Springer-Verlag.},
   Doi = {10.1007/BF02096768},
   Key = {Aspinwall93a}
}

@booklet{Aspinwall93,
   Author = {Aspinwall, PS and Greene, BR and Morrison, DR},
   Title = {Multiple mirror manifolds and topology change in string
             theory},
   Journal = {Physics Letters B},
   Volume = {303},
   Number = {3-4},
   Pages = {249-259},
   Year = {1993},
   ISSN = {0370-2693},
   url = {http://dx.doi.org/10.1016/0370-2693(93)91428-P},
   Abstract = {We use mirror symmetry to establish the first concrete arena
             of spacetime topology change in string theory. In
             particular, we establish that the quantum theories based on
             certain nonlinear sigma models with topologically distinct
             target spaces can be smoothly connected even though
             classically a physical singularity would be encountered. We
             accomplish this by rephrasing the description of these
             nonlinear sigma models in terms of their mirror manifold
             partners - a description in which the full quantum theory
             can be described exactly using lowest order geometrical
             methods. We establish that, for the known class of mirror
             manifolds, the moduli space of the corresponding conformal
             field theory requires not just two but numerous
             topologically distinct Calabi-Yau manifolds for its
             geometric interpretation. A single family of continously
             connected conformal theories thereby probes a host of
             topologically distinct geometrical spaces giving rise to
             multiple mirror manifolds. © 1993.},
   Doi = {10.1016/0370-2693(93)91428-P},
   Key = {Aspinwall93}
}

@booklet{Aspinwall91a,
   Author = {Aspinwall, PS and Lütken, CA},
   Title = {Geometry of mirror manifolds},
   Journal = {Nuclear Physics B},
   Volume = {353},
   Number = {2},
   Pages = {427-461},
   Year = {1991},
   Abstract = {We analyze the mirror manifold hypothesis in one and three
             dimensions using the simplest available representations of
             the N = 2 superconformai algebra. The symmetries of these
             tensor models can be divided out to give an explicit
             representation of the mirror, and we give a simple group
             theoretical algorithm for determining which symmetries
             should be used. We show that the mirror of a superconformai
             field theory does not always have a geometrical
             interpretation, but when it does, deformations of complex
             structure of one manifold are reflected in deformations of
             the Kähler form of the mirror manifold, and we show how the
             large radius limit of a manifold corresponds to a large
             complex structure limit in the mirror manifold. The mirror
             of the Tian-Yau three generation model is constructed both
             as a conformal field theory and as an algebraic variety with
             Euler number six. The Hodge numbers of this manifold are
             fixed, but the intersection numbers are highly ambiguous,
             presumably reflecting a rich structure of multicritical
             points in the moduli space of the field theory.},
   Key = {Aspinwall91a}
}

@booklet{Aspinwall91,
   Author = {Aspinwall, PS and Lütken, CA},
   Title = {Quantum algebraic geometry of superstring
             compactifications},
   Journal = {Nuclear Physics B},
   Volume = {355},
   Number = {2},
   Pages = {482-510},
   Year = {1991},
   ISSN = {0550-3213},
   url = {http://dx.doi.org/10.1016/0550-3213(91)90123-F},
   Abstract = {We investigate the algebrao-geometric structure which is
             inherent in 2-dimensional conformally invariant quantum
             field theories with N=2 supersymmetry, and its relation to
             the Calabi-Yau manifolds which appear in the so-called
             "large radius limit". Based on a careful comparison of the
             Kähler cone of Calabi-Yau manifolds and the moduli space of
             marginal chiral fields in string theory, we give a precise
             definition of this limit. The possibility of "flopping"
             between manifolds of different topology implies that the
             large radius limit of a given conformal model is ambiguous,
             and that the instantons in string theory could smooth out
             some of the singularities present in the classical moduli
             space. Since the mirror symmetry implies that the duality
             group of the stringy moduli space in a topological basis is
             at least Sp(b-3, Z)×Sp(b13, Z), we are able to identify the
             generalization of the "R → 1/R" symmetry in c=1 models to
             any (2,2) model. © 1991.},
   Doi = {10.1016/0550-3213(91)90123-F},
   Key = {Aspinwall91}
}

@booklet{Aspinwall90,
   Author = {Aspinwall, PS and Lütken, CA and Ross, GG},
   Title = {Construction and couplings of mirror manifolds},
   Journal = {Physics Letters, Section B: Nuclear, Elementary Particle and
             High-Energy Physics},
   Volume = {241},
   Number = {3},
   Pages = {373-380},
   Year = {1990},
   Abstract = {We present an analysis of the conjectured existence of
             Calabi-Yau "mirror manifolds" for the case where the
             starting manifold is Y4,5. We construct mirror pairs with
             equal but opposite values for the Euler characteristic and
             the Hodge numbers h2,1 and h1,1 interchanged. In one
             particular example we show that the couplings of (1,1)-forms
             equal the couplings of (2,1)-forms in the mirror manifold,
             provided that a suitable limit is taken of the complex
             structure which corresponds to the large-radius limit
             appropriate for the mirror manifold. This leads to a
             determination, via deformation theory, of corrections to the
             topologically determined couplings of the
             (1,1)-forms.},
   Key = {Aspinwall90}
}

@article{fds243268,
   Author = {Aspinwall, P},
   Title = {(2, 2)-Superconformal field theories near orbifold
             points},
   Journal = {Communications in Mathematical Physics},
   Volume = {128},
   Number = {3},
   Pages = {593-611},
   Year = {1990},
   ISSN = {0010-3616},
   url = {http://dx.doi.org/10.1007/BF02096875},
   Abstract = {A thorough analysis of the "blowing-up" modes of the ℤ6
             based on the Lie algebra A2⊕D4 is presented. We discover
             that the descriptions of these modes in the language of
             superconformal field theory and Calabi-Yau compactification
             are not immediately in agreement. A solution to this
             apparent inconsistency is offered which leads to the
             possibility of differentiably distinct Calabi-Yau manifolds
             giving isomorphic physics. © 1990 Springer-Verlag.},
   Doi = {10.1007/BF02096875},
   Key = {fds243268}
}

@booklet{Aspinwall87,
   Author = {ASPINWALL, PS and GREENE, BR and KIRKLIN, KH and MIRON,
             PJ},
   Title = {SEARCHING FOR 3-GENERATION CALABI-YAU MANIFOLDS},
   Journal = {Nuclear Physics B},
   Volume = {294},
   Number = {1},
   Pages = {193-222},
   Year = {1987},
   Month = {November},
   ISSN = {0550-3213},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1987K348000010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1016/0550-3213(87)90579-7},
   Key = {Aspinwall87}
}

@article{fds243267,
   Author = {Aspinwall, PS and Greene, BR and Kirklin, KH and Miron,
             PJ},
   Title = {Searching for three-generation Calabi-Yau
             manifolds},
   Journal = {Nuclear Physics B},
   Volume = {294},
   Number = {C},
   Pages = {193-222},
   Year = {1987},
   ISSN = {0550-3213},
   url = {http://dx.doi.org/10.1016/0550-3213(87)90579-7},
   Abstract = {All possible Calabi-Yau manifolds realisable as complete
             intersections and quotients of complete intersections by
             projectively-inherited symmetries are considered. We develop
             a stringent set of criteria with which to exhaustively
             search this huge class for three-generation manifolds. We
             find only one manifold meeting our conditions - namely the
             first manifold discovered by Yau. In addition it is shown
             that all known three-generation Calabi-Yau manifolds are
             either diffeomorphic to this one example or ill-defined. ©
             1987.},
   Doi = {10.1016/0550-3213(87)90579-7},
   Key = {fds243267}
}

@article{fds10130,
   Author = {Paul S. Aspinwall and Albion Lawrence},
   Title = {Derived Categories and 0-Brane Stability},
   Journal = {J. High Energy Phys. 08 (2001) 004},
   url = {http://arxiv.org/abs/hep-th/0104147},
   Key = {fds10130}
}

@article{fds8976,
   Author = {Paul S Aspinwall},
   Title = {String Theory and Duality},
   Journal = {Doc. Math. J. DMV Extra Volume ICM II (1998)
             229-238.},
   url = {http://arxiv.org/abs/math/9809004},
   Key = {fds8976}
}

@article{fds8970,
   Author = {Paul S Aspinwall},
   Title = {K3 Surfaces and String Duality},
   Journal = {in C. Esthimiou and B. Greene, editors, "Fields, Strings and
             Duality, TASI 1996", pages 421-540, World Scientific,
             1997.},
   url = {http://arxiv.org/abs/hep-th/9611137},
   Key = {fds8970}
}

@article{fds8973,
   Author = {Paul S Aspinwall},
   Title = {M-Theory Versus F-Theory Pictures of the Heterotic
             String},
   Journal = {Adv. Theo. Math. Phys. 1 (1997) 127-147,
             hep-th/9707014.},
   Key = {fds8973}
}

@article{fds8954,
   Author = {Paul S Aspinwall and D.R. Morrison},
   Title = {String Theory on K3 Surfaces},
   Journal = {in B. Greene and S.T. Yau, editors, "Mirror Symmetry II",
             pages 703-716, International Press, 1996,
             hep-th/9404151.},
   Key = {fds8954}
}

@article{fds8955,
   Author = {Paul S Aspinwall},
   Title = {Resolution of Orbifold Singularities in String
             Theory},
   Journal = {in B. Greene and S.T. Yau, editors, "Mirror Symmetry II",
             pages 355-426, International Press, 1996,
             hep-th/9403123.},
   Key = {fds8955}
}

@article{fds8957,
   Author = {Paul S Aspinwall and B.R. Greene and D.R. Morrison},
   Title = {Spacetime Topology Change: The Physics of Calabi-Yau Moduli
             Space},
   Journal = {in M.B. Halpern et al., editors, "Strings '93", pages
             241-262, World Scientific, 1995, hep-th/9311186.},
   Key = {fds8957}
}

@article{fds8958,
   Author = {Paul S Aspinwall},
   Title = {The Moduli Space of N = 2 Superconformal Field
             Theories},
   Journal = {in E. Gava et al., editors, "1994 Summer School in High
             Engergy Physics and Cosmology" pages 352-401, World
             Scientific, 1995, hep-th/9412115.},
   Key = {fds8958}
}


%% Bakhtin, Yuri   
@article{Bakhtin-Dinaburg-Sinai-2004,
   Author = {Bakhtin Yu.Yu. and Dinaburg E.I. and Sinai
             Ya.G.},
   Title = {On solutions of the Navier-Stokes system with infinite
             energy and enstrophy. In memory of A.A.Bolibrukh},
   Journal = {Uspekhi Mat. Nauk},
   Volume = {59},
   Number = {6},
   Pages = {in print},
   Year = {2004},
   Key = {Bakhtin-Dinaburg-Sinai-2004}
}

@article{Arnold-Bakhtin-Dinaburg-2004-umn,
   Author = {Arnold M.D.and Bakhtin Yu. Yu. and Dinaburg
             E.I.},
   Title = {Regularity of solutions to the Navier--Stokes system on
             plane},
   Journal = {Uspekhi Mat. Nauk},
   Volume = {59},
   Number = {3},
   Year = {2004},
   Key = {Arnold-Bakhtin-Dinaburg-2004-umn}
}

@article{Arnold-Bakhtin-Dinaburg-2004-cmp,
   Author = {Arnold M.D.and Bakhtin Yu. Yu. and Dinaburg
             E.I.},
   Title = {Regularity of Solutions to Vorticity Navier--Stokes System
             on $\mathbf{R}^2.$},
   Journal = {Accepted for publication in Comm. Math. Phys.},
   Year = {2004},
   Key = {Arnold-Bakhtin-Dinaburg-2004-cmp}
}

@article{Bakhtin-Mattingly-2004,
   Author = {Bakhtin Yu.Yu. and Mattingly J.C.},
   Title = {Stationary solutions of stochastic differential equations
             with memory and stochastic partial differential
             equations},
   Journal = {Accepted for publication in Commun. Contemp.
             Math},
   Year = {2004},
   Key = {Bakhtin-Mattingly-2004}
}

@article{Bakhtin-2004-Cascades,
   Author = {Bakhtin Yu. Yu.},
   Title = {Existence and uniqueness of stationary solutions for 3D
             Navier-Stokes system with small random forcing via
             stochastic cascades},
   Journal = {Submitted to J. Stat. Phys.},
   Year = {2004},
   Key = {Bakhtin-2004-Cascades}
}

@inproceedings{Bakhtin-2003-Kolmogorov,
   Author = {Bakhtin Yu.Yu.},
   Title = {Stationary measures for stochastic Gibbsian
             dynamics},
   Pages = {90},
   Booktitle = {Kolmogorov and contemporary mathematics.
             {A}bstracts},
   Organization = {MSU, Moscow},
   Institution = {MSU, Moscow},
   Year = {2003},
   Key = {Bakhtin-2003-Kolmogorov}
}

@article{Bakhtin-2003-Lyapunov,
   Author = {Bakhtin Yu.Yu.},
   Title = {Lyapunov Exponents for Stochastic Differential Equations
             with Infinite Memory. Applications to Stochastic
             Navier-Stokes system in 2D},
   Journal = {Submitted to Stoch.Processes App.},
   Year = {2003},
   Key = {Bakhtin-2003-Lyapunov}
}

@article{MR2001790,
   Author = {Bakhtin, Yu. Yu.},
   Title = {Existence and uniqueness of the stationary solution of a
             nonlinear stochastic differential equation with
             memory},
   Journal = {Teor. Veroyatnost. i Primenen.},
   Volume = {47},
   Number = {4},
   Pages = {764--768},
   Year = {2002},
   Key = {MR2001790}
}

@inproceedings{Bakhtin-Eger,
   Author = {Bakhtin Yu.},
   Title = {A functional central limit theorem for parabolically
             rescaled random solutions of the Burgers
             equation.},
   Pages = {30-31},
   Booktitle = {Abstracts of XXI Seminar on Stability Problems of Stochastic
             Models, Eger},
   Year = {2001},
   Key = {Bakhtin-Eger}
}

@article{MR1978661,
   Author = {Bakhtin, Yu. Yu.},
   Title = {A functional central limit theorem for transformed solutions
             of the multidimensional {B}urgers equation with random
             initial data},
   Journal = {Teor. Veroyatnost. i Primenen.},
   Volume = {46},
   Number = {3},
   Pages = {427--448},
   Year = {2001},
   Key = {MR1978661}
}

@phdthesis{Bakhtin-Thesis,
   Author = {Bakhtin Yu.Yu.},
   Title = {Limit theorems for random solutions of the {B}urgers
             equation},
   Organization = {Moscow State University},
   Institution = {Moscow State University},
   Year = {2001},
   Key = {Bakhtin-Thesis}
}

@article{MR1843593,
   Author = {Bakhtin, Yu. Yu.},
   Title = {The functional central limit theorem for solutions of the
             multidimensional {B}urgers equation with initial data
             specified by an associated random measure},
   Journal = {Vestnik Moskov. Univ. Ser. I Mat. Mekh.},
   Number = {6},
   Pages = {8--15, 86},
   Year = {2000},
   Key = {MR1843593}
}

@article{MR1776912,
   Author = {Bakhtin, Yu. Yu.},
   Title = {A functional central limit theorem for transformed solutions
             of the multidimensional {B}urgers equation with random
             initial data},
   Journal = {Dokl. Akad. Nauk},
   Volume = {372},
   Number = {6},
   Pages = {727--729},
   Year = {2000},
   Key = {MR1776912}
}

@article{MR1841053,
   Author = {Bakhtin, Yu. Yu. and Danilov, A. V. and Kantsel{\cprime}, A.
             V. and Chervonenkis, A. Ya.},
   Title = {A method for the restoration of a field of conditional
             distributions from empirical data},
   Journal = {Avtomat. i Telemekh.},
   Number = {12},
   Pages = {75--86},
   Year = {2000},
   Key = {MR1841053}
}

@article{Bakhtin-FCLT-1999,
   Author = {Bakhtin Yu.Yu.},
   Title = {A functional central limit theorem for random solutions of
             the {B}urgers equation},
   Journal = {Theory Probab. Appl.},
   Volume = {44},
   Number = {3},
   Pages = {698-699},
   Year = {1999},
   Key = {Bakhtin-FCLT-1999}
}

@inproceedings{Bakhtin-1999-france,
   Author = {Bakhtin Yu.},
   Title = {Asymptotic analysis of the Burgers equation with random
             initial data.},
   Pages = {10-14},
   Booktitle = {Eleventh European Young Statisticians Meeting,Marly-le-Roi},
   Year = {1999},
   Key = {Bakhtin-1999-france}
}

@article{MR1691261,
   Author = {Bakhtin, Yu. Yu.},
   Title = {The law of the iterated logarithm for solutions of the
             {B}urgers equation with random initial data},
   Journal = {Mat. Zametki},
   Volume = {64},
   Number = {6},
   Pages = {812--823},
   Year = {1998},
   Key = {MR1691261}
}

@article{MR1794505,
   Author = {Bakhtin, Yu. Yu. and Bulinski{\u\i}, A. V.},
   Title = {Moment inequalities for sums of dependent multi-indexed
             random variables},
   Journal = {Fundam. Prikl. Mat.},
   Volume = {3},
   Number = {4},
   Pages = {1101--1108},
   Year = {1997},
   Key = {MR1794505}
}


%% Bar-On, Rann   
@misc{fds178687,
   Author = {R. Bar-On},
   Title = {105L-106L Coursepack, Fall 2014 and Spring
             2015},
   Year = {2014},
   Month = {August},
   Key = {fds178687}
}

@article{fds225803,
   Author = {Rann Bar-On and Jack Bookman and Benjamin Cooke and Donna Hall and Sarah
             Schott},
   Title = {(Re)discovering SoTL Through a Fundamental Challenge:
             Helping Students Transition to College Calculus},
   Volume = {83},
   Series = {MAA Notes},
   Pages = {59-66},
   Booktitle = {Doing the Scholarship of Teaching and Learning in
             Mathematics},
   Publisher = {The Mathematical Association of America},
   Editor = {Jacqueline M. Dewar and Curtis D. Bennett},
   Year = {2014},
   ISBN = {9780883851937},
   Keywords = {SoTL calculus undergraduate education},
   Abstract = {Teaching and learning occur both inside and outside of the
             classroom, but undergraduates' transition to college
             mathematics are affected by many factors outside of the
             classroom. A collaboration at Duke between mathematics
             faculty and the Academic Resource Center (ARC) originally
             designed to fill knowledge gaps gradually adapted into a
             tool to help less well-prepared students transition to the
             calculus curriculum. The collaboration to monitor student
             progress and the adaptation of research tools grew initial
             voluntary algebra review sessions into an algebra review and
             study group program that supports students through the two
             course sequence of Laboratory Calculus with Functions I and
             II. The collaborators have applied for an NSF grant proposal
             to transition the program into the structure of the course
             labs to build a formative feedback loop between the
             students, undergraduate TAs, and mathematics and ARC
             instructors. The grant proposal builds on a collaboration
             between the ARC and Chemistry faculty to help pre-med
             students navigate a four-course Chemistry sequence through
             Organic Chemistry, which trains TAs to monitor not only
             content understanding, but self-regulation and metacognitive
             development.},
   Key = {fds225803}
}

@misc{fds145344,
   Author = {Rann Bar-On and Paul Bendich and Benjamin Cooke and Michael Gratton and Timothy Lucas and Michael Nicholas and Nicholas Robbins and Abraham
             Smith, Joseph Spivey},
   Title = {Graduate Calculus Curriculum Review},
   Year = {2007},
   Month = {March},
   url = {http://www.math.duke.edu/~adsmith/proposal.pdf},
   Abstract = {http://fds.duke.edu/db/aas/math/grad/adsmith/publications/139484/},
   Key = {fds145344}
}


%% Basak, Anirban   
@article{fds300033,
   Author = {A. Basak and A. Dembo},
   Title = {Ferromagnetic Ising measures on large locally tree- like
             graphs},
   Journal = {The Annals of Probability},
   Year = {2015},
   Month = {October},
   url = {http://arxiv.org/abs/1205.4749},
   Key = {fds300033}
}

@article{fds300030,
   Author = {A. Basak and S. Mukherjee},
   Title = {Universality of mean-field for the Potts
             model},
   Year = {2015},
   Month = {August},
   url = {http://arxiv.org/abs/1508.03949},
   Key = {fds300030}
}

@article{fds300031,
   Author = {A. Basak and M. Rudelson},
   Title = {Invertibility of sparse non-Hermitian matrices},
   Year = {2015},
   Month = {July},
   url = {http://arxiv.org/abs/1507.03525},
   Key = {fds300031}
}

@article{fds300034,
   Author = {A. Basak and A. Bose and S. S. Mukherjee},
   Title = {Limiting spectral distribution of a class of Hankel type
             random matrices},
   Journal = {Random Matrices: Theory and Applications},
   Year = {2015},
   Month = {April},
   url = {http://arxiv.org/abs/1408.0874},
   Key = {fds300034}
}


%% Beale, J. Thomas   
@article{fds322466,
   Author = {Beale, JT and Ying, W and Wilson, JR},
   Title = {A Simple Method for Computing Singular or Nearly Singular
             Integrals on Closed Surfaces},
   Journal = {Communications in computational physics},
   Volume = {20},
   Number = {03},
   Pages = {733-753},
   Year = {2016},
   Month = {September},
   url = {http://dx.doi.org/10.4208/cicp.030815.240216a},
   Doi = {10.4208/cicp.030815.240216a},
   Key = {fds322466}
}

@article{fds226858,
   Author = {J. t. Beale and W. YIng and J. R. Wilson},
   Title = {A simple method for computing singular or nearly singular
             integrals on closed surfaces},
   Journal = {Commun. Comput. Phys.},
   Year = {2015},
   Month = {August},
   url = {http://www.math.duke.edu/faculty/beale/papers/bywcicp.pdf},
   Key = {fds226858}
}

@article{fds243316,
   Author = {Beale, JT},
   Title = {Uniform Error Estimates for Navier--Stokes Flow with an
             Exact Moving Boundary Using the Immersed Interface
             Method},
   Journal = {SIAM Journal on Numerical Analysis},
   Volume = {53},
   Number = {4},
   Pages = {2097-2111},
   Year = {2015},
   Month = {January},
   ISSN = {0036-1429},
   url = {http://www.math.duke.edu/faculty/beale/papers/nseiim.pdf},
   Doi = {10.1137/151003441},
   Key = {fds243316}
}

@article{fds243354,
   Author = {Tlupova, S and Beale, JT},
   Title = {Nearly singular integrals in 3D stokes flow},
   Journal = {Communications in computational physics},
   Volume = {14},
   Number = {5},
   Pages = {1207-1227},
   Year = {2013},
   ISSN = {1815-2406},
   url = {http://www.math.duke.edu/faculty/beale/papers/stokes3d2.pdf},
   Abstract = {A straightforward method is presented for computing
             three-dimensional Stokes flow, due to forces on a surface,
             with high accuracy at points near the surface. The
             flowquantities arewritten as boundary integrals using the
             free-spaceGreen's function. To evaluate the integrals near
             the boundary, the singular kernels are regularized and a
             simple quadrature is applied in coordinate charts. High
             order accuracy is obtained by adding special corrections for
             the regularization and discretization errors, derived here
             using local asymptotic analysis. Numerical tests demonstrate
             the uniform convergence rates of the method. © 2013
             Global-Science Press.},
   Doi = {10.4208/cicp.020812.080213a},
   Key = {fds243354}
}

@article{fds243355,
   Author = {Ying, W and Beale, JT},
   Title = {A fast accurate boundary integral method for potentials on
             closely packed cells},
   Journal = {Communications in computational physics},
   Volume = {14},
   Number = {4},
   Pages = {1073-1093},
   Year = {2013},
   ISSN = {1815-2406},
   url = {http://www.math.duke.edu/faculty/beale/papers/cpcells2.pdf},
   Abstract = {Boundary integral methods are naturally suited for the
             computation of harmonic functions on a region having
             inclusions or cells with different material properties.
             However, accuracy deteriorates when the cell boundaries are
             close to each other. We present a boundary integralmethod in
             two dimensions which is specially designed tomaintain second
             order accuracy even if boundaries are arbitrarily close.
             Themethod uses a regularization of the integral kernel which
             admits analytically determined corrections to maintain
             accuracy. For boundaries with many components we use the
             fast multipolemethod for efficient summation. We compute
             electric potentials on a domain with cells whose
             conductivity differs from that of the surrounding medium. We
             first solve an integral equation for a source term on the
             cell interfaces and then find values of the potential near
             the interfaces via integrals. Finally we use a Poisson
             solver to extend the potential to a regular grid covering
             the entire region. A number of examples are presented. We
             demonstrate that increased refinement is not needed to
             maintain accuracy as interfaces become very close. © 2013
             Global-Science Press.},
   Doi = {10.4208/cicp.210612.240113a},
   Key = {fds243355}
}

@article{fds243356,
   Author = {Beale, JT},
   Title = {Partially implicit motion of a sharp interface in
             Navier-Stokes flow},
   Journal = {J. Comput. Phys.},
   Volume = {231},
   Pages = {6159-6172},
   Year = {2012},
   url = {http://www.math.duke.edu/faculty/beale/papers/pimpl2.pdf},
   Key = {fds243356}
}

@article{fds243357,
   Author = {Layton, AT and Beale, JT},
   Title = {A partially implicit hybrid method for computing interface
             motion in stokes flow},
   Journal = {Discrete and Continuous Dynamical Systems - Series
             B},
   Volume = {17},
   Number = {4},
   Pages = {1139-1153},
   Year = {2012},
   ISSN = {1531-3492},
   url = {http://www.math.duke.edu/faculty/beale/papers/dcdsb.pdf},
   Abstract = {We present a partially implicit hybrid method for simulating
             the motion of a stiff interface immersed in Stokes flow, in
             free space or in a rectangular domain with boundary
             conditions. We assume the interface is a closed curve which
             remains in the interior of the computational region. The
             implicit time integration is based on the small-scale
             decomposition approach and does not require the iterative
             solution of a system of nonlinear equations. First-order and
             second-order versions of the time-stepping method are
             derived systematically, and numerical results indicate that
             both methods are substantially more stable than explicit
             methods. At each time level, the Stokes equations are solved
             using a hybrid approach combining nearly singular integrals
             on a band of mesh points near the interface and a mesh-based
             solver. The solutions are second-order accurate in space and
             preserve the jump discontinuities across the interface.
             Finally, the hybrid method can be used as an alternative to
             adaptive mesh refinement to resolve boundary layers that are
             frequently present around a stiff immersed
             interface.},
   Doi = {10.3934/dcdsb.2012.17.1139},
   Key = {fds243357}
}

@article{fds243353,
   Author = {Beale, JT and Layton, AT},
   Title = {A velocity decomposition approach for moving interfaces in
             viscous fluids},
   Journal = {Journal of Computational Physics},
   Volume = {228},
   Number = {9},
   Pages = {3358-3367},
   Year = {2009},
   ISSN = {0021-9991},
   url = {http://www.math.duke.edu/faculty/beale/papers/velcomp.pdf},
   Abstract = {We present a second-order accurate method for computing the
             coupled motion of a viscous fluid and an elastic material
             interface with zero thickness. The fluid flow is described
             by the Navier-Stokes equations, with a singular force due to
             the stretching of the moving interface. We decompose the
             velocity into a "Stokes" part and a "regular" part. The
             first part is determined by the Stokes equations and the
             singular interfacial force. The Stokes solution is obtained
             using the immersed interface method, which gives
             second-order accurate values by incorporating known jumps
             for the solution and its derivatives into a finite
             difference method. The regular part of the velocity is given
             by the Navier-Stokes equations with a body force resulting
             from the Stokes part. The regular velocity is obtained using
             a time-stepping method that combines the semi-Lagrangian
             method with the backward difference formula. Because the
             body force is continuous, jump conditions are not necessary.
             For problems with stiff boundary forces, the decomposition
             approach can be combined with fractional time-stepping,
             using a smaller time step to advance the interface quickly
             by Stokes flow, with the velocity computed using boundary
             integrals. The small time steps maintain numerical
             stability, while the overall solution is updated on a larger
             time step to reduce computational cost. © 2009 Elsevier
             Inc. All rights reserved.},
   Doi = {10.1016/j.jcp.2009.01.023},
   Key = {fds243353}
}

@article{fds243358,
   Author = {Beale, JT},
   Title = {Smoothing properties of implicit finite difference methods
             for a diffusion equation in maximum norm},
   Journal = {SIAM Journal on Numerical Analysis},
   Volume = {47},
   Number = {4},
   Pages = {2476-2495},
   Year = {2009},
   ISSN = {0036-1429},
   url = {http://www.math.duke.edu/faculty/beale/papers/parab.pdf},
   Abstract = {We prove a regularity property of finite difference schemes
             for the heat or diffusion equation μ t = δμ in maximum
             norm with large time steps. For a class of time
             discretizations including L-stable single-step methods and
             the second-order backward difference formula, with the usual
             second-order Laplacian, we show that solutions of the scheme
             gai n first spatial differences boundedly, and also second
             differences except for logarithmic factors, with respect to
             nonhomogeneous terms. A weaker property is shown for the
             Crank-Nicolson method. As a consequence we show that the
             numerical solution of a convection-diffusion equation with
             an interface can allow O(h) truncation error near the
             interface and still have a solution with uniform O(h 2)
             accuracy and first differences of uniform accuracy almost
             O(h 2). © 2009 Society for Industrial and Applied
             Mathematics.},
   Doi = {10.1137/080731645},
   Key = {fds243358}
}

@article{fds243359,
   Author = {Beale, JT and Chopp, D and LeVeque, R and Li, Z},
   Title = {Correction to the article A comparison of the extended
             finite element method with the immersed interface method for
             elliptic equations with discontinuous coefficients and
             singular sources by Vaughan et al.},
   Journal = {Commun. Appl. Math. Comput. Sci.},
   Volume = {3},
   Pages = {95-100},
   Year = {2008},
   Month = {August},
   url = {http://www.math.duke.edu/faculty/beale/papers/camcoscorr.pdf},
   Key = {fds243359}
}

@article{fds243360,
   Author = {Beale, JT and Strain, J},
   Title = {Locally corrected semi-Lagrangian methods for Stokes flow
             with moving elastic interfaces},
   Journal = {Journal of Computational Physics},
   Volume = {227},
   Number = {8},
   Pages = {3896-3920},
   Year = {2008},
   ISSN = {0021-9991},
   url = {http://hdl.handle.net/10161/6958 Duke open
             access},
   Abstract = {We present a new method for computing two-dimensional Stokes
             flow with moving interfaces that respond elastically to
             stretching. The interface is moved by semi-Lagrangian
             contouring: a distance function is introduced on a tree of
             cells near the interface, transported by a semi-Lagrangian
             time step and then used to contour the new interface. The
             velocity field in a periodic box is calculated as a
             potential integral resulting from interfacial and body
             forces, using a technique based on Ewald summation with
             analytically derived local corrections. The interfacial
             stretching is found from a surprisingly natural formula. A
             test problem with an exact solution is constructed and used
             to verify the speed, accuracy and robustness of the
             approach. © 2007 Elsevier Inc. All rights
             reserved.},
   Doi = {10.1016/j.jcp.2007.11.047},
   Key = {fds243360}
}

@article{fds243361,
   Author = {Beale, JT},
   Title = {A proof that a discrete delta function is second-order
             accurate},
   Journal = {Journal of Computational Physics},
   Volume = {227},
   Number = {4},
   Pages = {2195-2197},
   Year = {2008},
   ISSN = {0021-9991},
   url = {http://www.math.duke.edu/faculty/beale/papers/ddel.pdf},
   Abstract = {It is proved that a discrete delta function introduced by
             Smereka [P. Smereka, The numerical approximation of a delta
             function with application to level set methods, J. Comput.
             Phys. 211 (2006) 77-90] gives a second-order accurate
             quadrature rule for surface integrals using values on a
             regular background grid. The delta function is found using a
             technique of Mayo [A. Mayo, The fast solution of Poisson's
             and the biharmonic equations on irregular regions, SIAM J.
             Numer. Anal. 21 (1984) 285-299]. It can be expressed
             naturally using a level set function. © 2007 Elsevier Inc.
             All rights reserved.},
   Doi = {10.1016/j.jcp.2007.11.004},
   Key = {fds243361}
}

@article{fds243362,
   Author = {Beale, JT and Layton, AT},
   Title = {On the accuracy of finite difference methods for elliptic
             problems with interfaces},
   Journal = {Commun. Appl. Math. Comput. Sci.},
   Volume = {1},
   Pages = {91-119},
   Year = {2006},
   url = {http://www.math.duke.edu/faculty/beale/papers/alayton.pdf},
   Key = {fds243362}
}

@article{fds243363,
   Author = {Baker, GR and Beale, JT},
   Title = {Vortex blob methods applied to interfacial
             motion},
   Journal = {Journal of Computational Physics},
   Volume = {196},
   Number = {1},
   Pages = {233-258},
   Year = {2004},
   url = {http://www.math.duke.edu/faculty/beale/papers/baker.pdf},
   Abstract = {We develop a boundary integral method for computing the
             motion of an interface separating two incompressible,
             inviscid fluids. The velocity integral is regularized, so
             that the vortex sheet on the interface is replaced by a sum
             of "blobs" of vorticity. The regularization allows control
             of physical instabilities. We design a class of high order
             blob methods and analyze the errors. Numerical tests suggest
             that the blob size should be scaled with the local spacing
             of the interfacial markers. For a vortex sheet in one fluid,
             with a first-order kernel, we obtain a spiral roll-up
             similar to Krasny [J. Comput. Phys. 65 (1986) 292], but the
             higher order kernels lead to more detailed structure. We
             verify the accuracy of the new method by computing a
             liquid-gas interface with Rayleigh-Taylor instability. We
             then apply the method to the more difficult case of
             Rayleigh-Taylor flow separating two fluids of positive
             density, a case for which the regularization appears to be
             essential, as found by Kerr and Tryggvason [both J. Comput.
             Phys. 76 (1988) 48; 75 (1988) 253]. We use a "blob"
             regularization in certain local terms in the evolution
             equations as well as in the velocity integral. We find
             strong evidence that improved spatial resolution with fixed
             blob size leads to a converged, regularized solution without
             numerical instabilities. However, it is not clear that there
             is a weak limit as the regularization is decreased. © 2003
             Elsevier Inc. All rights reserved.},
   Doi = {10.1016/j.jcp.2003.10.023},
   Key = {fds243363}
}

@article{fds243364,
   Author = {Beale, JT},
   Title = {A grid-based boundary integral method for elliptic problems
             in three dimensions},
   Journal = {SIAM Journal on Numerical Analysis},
   Volume = {42},
   Number = {2},
   Pages = {599-620},
   Year = {2004},
   ISSN = {0036-1429},
   url = {http://www.math.duke.edu/faculty/beale/papers/gbbim.pdf},
   Abstract = {We develop a simple, efficient numerical method of boundary
             integral type for solving an elliptic partial differential
             equation in a three-dimensional region using the classical
             formulation of potential theory. Accurate values can be
             found near the boundary using special corrections to a
             standard quadrature. We treat the Dirichlet problem for a
             harmonic function with a prescribed boundary value in a
             bounded three-dimensional region with a smooth boundary. The
             solution is a double layer potential, whose strength is
             found by solving an integral equation of the second kind.
             The boundary surface is represented by rectangular grids in
             overlapping coordinate systems, with the boundary value
             known at the grid points. A discrete form of the integral
             equation is solved using a regularized form of the kernel.
             It is proved that the discrete solution converges to the
             exact solution with accuracy O(h p), p &lt; 5, depending on
             the smoothing parameter. Once the dipole strength is found,
             the harmonic function can be computed from the double layer
             potential. For points close to the boundary, the integral is
             nearly singular, and accurate computation is not routine. We
             calculate the integral by summing over the boundary grid
             points and then adding corrections for the smoothing and
             discretization errors using formulas derived here; they are
             similar to those in the two-dimensional case given by [J. T.
             Beale and M.-C. Lai, SIAM J. Numer. Anal., 38 (2001), pp.
             1902-1925]. The resulting values of the solution are
             uniformly of O(h p) accuracy, p &lt; 3. With a total of N
             points, the calculation could be done in essentially O(N)
             operations if a rapid summation method is used. © 2004
             Society for Industrial and Applied Mathematics.},
   Doi = {10.1137/S0036142903420959},
   Key = {fds243364}
}

@article{fds243329,
   Author = {Beale, JT},
   Title = {Discretization of Layer Potentials and Numerical Methods for
             Water Waves (Tosio Kato's Method and Principle for Evolution
             Equations in Mathematical Physics)},
   Volume = {1234},
   Pages = {18-26},
   Publisher = {Kyoto University},
   Year = {2001},
   Month = {October},
   ISSN = {1880-2818},
   Key = {fds243329}
}

@article{fds243351,
   Author = {Beale, JT},
   Title = {A convergent boundary integral method for three-dimensional
             water waves},
   Journal = {Mathematics of Computation},
   Volume = {70},
   Number = {235},
   Pages = {977-1029},
   Year = {2001},
   url = {http://www.math.duke.edu/faculty/beale/papers/mathcomp.ps},
   Abstract = {We design a boundary integral method for time-dependent,
             three-dimensional, doubly periodic water waves and prove
             that it converges with O(h3) accuracy, without restriction
             on amplitude. The moving surface is represented by grid
             points which are transported according to a computed
             velocity. An integral equation arising from potential theory
             is solved for the normal velocity. A new method is developed
             for the integration of singular integrals, in which the
             Green's function is regularized and an efficient local
             correction to the trapezoidal rule is computed. The sums
             replacing the singular integrals are treated as discrete
             versions of pseudodifferential operators and are shown to
             have mapping properties like the exact operators. The scheme
             is designed so that the error is governed by evolution
             equations which mimic the structure of the original problem,
             and in this way stability can be assured. The wave-like
             character of the exact equations of motion depends on the
             positivity of the operator which assigns to a function on
             the surface the normal derivative of its harmonic extension;
             similarly, the stability of the scheme depends on
             maintaining this property for the discrete operator. With n
             grid points, the scheme can be implemented with essentially
             O(n) operations per time step.},
   Doi = {10.1090/S0025-5718-00-01218-7},
   Key = {fds243351}
}

@article{fds243352,
   Author = {Beale, JT and Lai, M-C},
   Title = {A method for computing nearly singular integrals},
   Journal = {SIAM Journal on Numerical Analysis},
   Volume = {38},
   Number = {6},
   Pages = {1902-1925},
   Year = {2001},
   url = {http://www.math.duke.edu/faculty/beale/papers/nearsing.ps},
   Abstract = {We develop a method for computing a nearly singular
             integral, such as a double layer potential due to sources on
             a curve in the plane, evaluated at a point near the curve.
             The approach is to regularize the singularity and obtain a
             preliminary value from a standard quadrature rule. Then we
             add corrections for the errors due to smoothing and
             discretization, which are found by asymptotic analysis. We
             prove an error estimate for the corrected value, uniform
             with respect to the point of evaluation. One application is
             a simple method for solving the Dirichlet problem for
             Laplace's equation on a grid covering an irregular region in
             the plane, similar to an earlier method of A. Mayo [SIAM J.
             Sci. Statist. Comput., 6 (1985), pp. 144-157]. This approach
             could also be used to compute the pressure gradient due to a
             force on a moving boundary in an incompressible fluid.
             Computational examples are given for the double layer
             potential and for the Dirichlet problem.},
   Doi = {10.1137/S0036142999362845},
   Key = {fds243352}
}

@article{fds243347,
   Author = {Beale, JT and Hou, TY and Lowengrub, J},
   Title = {Stability of boundary integral methods for water
             waves},
   Journal = {AMS-IMS-SIAM Joint Summer Research Conference},
   Pages = {241-245},
   Year = {1996},
   Abstract = {This paper studies the numerical stability of method of
             boundary integral type, in which the free surface is tracked
             explicitly. The focus is on two-dimensional motions,
             periodic in the horizontal direction, so that issues of
             boundary conditions for the free surface can be avoided. The
             case considered is rather special, but analysis has provided
             a definitive answer in this case, and the treatment of this
             case might partially clarify the numerical issues in the
             more realistic problems. The results are presented in
             detail. A calculation of an overturning wave illustrates the
             resolution made possible by a fully stable numerical method.
             A careful study of an overturning wave by method of this
             class was presented previously.},
   Key = {fds243347}
}

@article{fds243349,
   Author = {Beale, JT and Hou, TY and Lowengrub, J},
   Title = {Convergence of a boundary integral method for water
             waves},
   Journal = {SIAM Journal on Numerical Analysis},
   Volume = {33},
   Number = {5},
   Pages = {1797-1843},
   Year = {1996},
   Abstract = {We prove nonlinear stability and convergence of certain
             boundary integral methods for time-dependent water waves in
             a two-dimensional, inviscid, irrotational, incompressible
             fluid, with or without surface tension. The methods are
             convergent as long as the underlying solution remains fairly
             regular (and a sign condition holds in the case without
             surface tension). Thus, numerical instabilities are ruled
             out even in a fully nonlinear regime. The analysis is based
             on delicate energy estimates, following a framework
             previously developed in the continuous case [Beale, Hou, and
             Lowengrub, Comm. Pure Appl. Math., 46 (1993), pp.
             1269-1301]. No analyticity assumption is made for the
             physical solution. Our study indicates that the numerical
             methods must satisfy certain compatibility conditions in
             order to be stable. Violation of these conditions will lead
             to numerical instabilities. A breaking wave is calculated as
             an illustration.},
   Key = {fds243349}
}

@article{fds243350,
   Author = {Lifschitz, A and Suters, WH and Beale, JT},
   Title = {The onset of instability in exact vortex rings with
             swirl},
   Journal = {Journal of Computational Physics},
   Volume = {129},
   Number = {1},
   Pages = {8-29},
   Year = {1996},
   url = {http://dx.doi.org/10.1006/jcph.1996.0230},
   Abstract = {We study the time-dependent behavior of disturbances to
             inviscid vortex rings with swirl, using two different
             approaches. One is a linearized stability analysis for short
             wavelengths, and the other is direct flow simulation by a
             computational vortex method. We begin with vortex rings
             which are exact solutions of the Euler equations of
             inviscid, incompressible fluid flow, axisymmetric, and
             traveling along the axis; swirl refers to the component of
             velocity around the axis. Exact vortex rings with swirl can
             be computed reliably using a variational method.
             Quantitative predictions can then be made for the maximum
             growth rates of localized instabilities of small amplitude,
             using asymptotic analysis as in geometric optics. The
             predicted growth rates are compared with numerical solutions
             of the full, time-dependent Euler equations, starting with a
             small disturbance in an exact ring. These solutions are
             computed by a Lagrangian method, in which the
             three-dimensional flow is represented by a collection of
             vortex elements, moving according to their induced velocity.
             The computed growth rates are typically found to be about
             half of the predicted maximum, and the dependence on
             location and ring parameters qualitatively matches the
             predictions. The comparison of these two very different
             methods for estimating the growth of instabilities serves to
             check the realm of validity of each approach. © 1996
             Academic Press, Inc.},
   Doi = {10.1006/jcph.1996.0230},
   Key = {fds243350}
}

@article{fds243335,
   Author = {Beale, JT and Greengard, C},
   Title = {Convergence of euler-stokes splitting of the navier-stokes
             equations},
   Journal = {Communications on Pure & Applied Mathematics},
   Volume = {47},
   Number = {8},
   Pages = {1083-1115},
   Year = {1994},
   Month = {August},
   ISSN = {0010-3640},
   url = {http://dx.doi.org/10.1002/cpa.3160470805},
   Doi = {10.1002/cpa.3160470805},
   Key = {fds243335}
}

@article{fds243333,
   Author = {Bourgeois, AJ and Beale, JT},
   Title = {Validity of the Quasigeostrophic Model for Large-Scale Flow
             in the Atmosphere and Ocean},
   Journal = {SIAM Journal on Mathematical Analysis},
   Volume = {25},
   Number = {4},
   Pages = {1023-1068},
   Year = {1994},
   Month = {July},
   ISSN = {0036-1410},
   url = {http://dx.doi.org/10.1137/S0036141092234980},
   Doi = {10.1137/S0036141092234980},
   Key = {fds243333}
}

@article{fds243346,
   Author = {Beale, JT and Hou, TY and Lowengrub, JS and Shelley,
             MJ},
   Title = {Spatial and temporal stability issues for interfacial flows
             with surface tension},
   Journal = {Mathematical and Computer Modelling},
   Volume = {20},
   Number = {10-11},
   Pages = {1-27},
   Year = {1994},
   ISSN = {0895-7177},
   Abstract = {Many physically interesting problems involve the propagation
             of free surfaces in fluids with surface tension effects.
             Surface tensions is an ever-present physical effect that is
             often neglected due to the difficulties associated with its
             inclusion in the equations of motion. Accurate simulation of
             these interfaces presents a problem of considerable
             difficulty on several levels. First, even for stably
             stratified flows like water waves, it turns out that
             straightforward spatial discretizations (of the boundary
             integral formulation) generate numerical instability.
             Second, surface tension introduces a large number of
             derivatives through the Laplace-Young boundary condition.
             This induces severe time step restrictions for explicit time
             integration methods. In this paper, we present a class of
             stable spatial discretizations and we present a
             reformulation of the equations of motion that make apparent
             how to remove the high order time step restrictions
             introduced by the surface tension. This paper is a review of
             the results given in [1,2]. © 1994.},
   Key = {fds243346}
}

@article{fds243320,
   Author = {Beale, JT and Hou, TY and Lowengrub, JS},
   Title = {Growth rates for the linearized motion of fluid interfaces
             away from equilibrium},
   Journal = {Communications on Pure & Applied Mathematics},
   Volume = {46},
   Number = {9},
   Pages = {1269-1301},
   Year = {1993},
   Month = {October},
   ISSN = {0010-3640},
   url = {http://dx.doi.org/10.1002/cpa.3160460903},
   Doi = {10.1002/cpa.3160460903},
   Key = {fds243320}
}

@article{fds9208,
   Author = {J. T. Beale and T. Y. Hou and J. S. Lowengrub},
   Title = {On the well-posedness of two-fluid interfacial flows with
             surface tension},
   Journal = {Singularities in Fluids, Plasmas, and Optics, R. Caflisch et
             al., ed., NATO ASI Series, Kluwer},
   Pages = {11-38},
   Year = {1993},
   Key = {fds9208}
}

@article{fds243336,
   Author = {Beale, JT},
   Title = {Exact solitary water waves with capillary ripples at
             infinity},
   Journal = {Communications on Pure & Applied Mathematics},
   Volume = {44},
   Number = {2},
   Pages = {211-257},
   Year = {1991},
   Month = {March},
   ISSN = {0010-3640},
   url = {http://dx.doi.org/10.1002/cpa.3160440204},
   Doi = {10.1002/cpa.3160440204},
   Key = {fds243336}
}

@article{fds243332,
   Author = {Beale, JT and Schaeffer, DG},
   Title = {Nonlinear behavior of model equations which are linearly
             ill-posed},
   Journal = {Communications in Partial Differential Equations},
   Volume = {13},
   Number = {4},
   Pages = {423-467},
   Year = {1988},
   Month = {January},
   ISSN = {0360-5302},
   url = {http://dx.doi.org/10.1080/03605308808820548},
   Doi = {10.1080/03605308808820548},
   Key = {fds243332}
}

@article{fds243330,
   Author = {Beale, JT},
   Title = {Analysis of Vortex Methods for Incompressible
             Flow},
   Journal = {Journal of Statistical Physics},
   Volume = {44},
   Number = {5-6},
   Pages = {1009-1011},
   Year = {1986},
   Month = {September},
   ISSN = {0022-4715},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1986E184600018&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Key = {fds243330}
}

@article{fds243344,
   Author = {Beale, JT},
   Title = {Convergent 3-D vortex method with grid-free
             stretching.},
   Year = {1986},
   Abstract = {This document proves the convergence of a vortex method for
             three dimensional, incompressible, inviscid flow without
             boundaries. This version differs from an earlier one whose
             convergence was shown in another work in that the
             calculation does not depend explicitly on the arrangement of
             the vorticity elements in a Lagrangian frame. Thus, it could
             be used naturally in a more general context in which
             boundaries and viscosity are present. It is also shown that
             previous estimates for the velocity approximation can be
             improved by taking into account the fact that the integral
             kernel has an average value of zero. Implications for the
             design of the method are discussed. (A)},
   Key = {fds243344}
}

@article{fds243348,
   Author = {Beale, JT},
   Title = {Large-time behavior of discrete velocity boltzmann
             equations},
   Journal = {Communications in Mathematical Physics},
   Volume = {106},
   Number = {4},
   Pages = {659-678},
   Year = {1986},
   ISSN = {0010-3616},
   url = {http://dx.doi.org/10.1007/BF01463401},
   Abstract = {We study the asymptotic behavior of equations representing
             one-dimensional motions in a fictitious gas with a discrete
             set of velocities. The solutions considered have finite mass
             but arbitrary amplitude. With certain assumptions, every
             solution approaches a state in which each component is a
             traveling wave without interaction. The techniques are
             similar to those in an earlier treatment of the Broadwell
             model [1]. © 1986 Springer-Verlag.},
   Doi = {10.1007/BF01463401},
   Key = {fds243348}
}

@article{fds243342,
   Author = {Beale, JT and Nishida, T},
   Title = {Large-Time Behavior of Viscous Surface Waves},
   Journal = {North-Holland Mathematics Studies},
   Volume = {128},
   Number = {C},
   Pages = {1-14},
   Year = {1985},
   ISSN = {0304-0208},
   url = {http://dx.doi.org/10.1016/S0304-0208(08)72355-7},
   Doi = {10.1016/S0304-0208(08)72355-7},
   Key = {fds243342}
}

@article{fds243343,
   Author = {Beale, JT and Majda, A},
   Title = {High order accurate vortex methods with explicit velocity
             kernels},
   Journal = {Journal of Computational Physics},
   Volume = {58},
   Number = {2},
   Pages = {188-208},
   Year = {1985},
   ISSN = {0021-9991},
   url = {http://dx.doi.org/10.1016/0021-9991(85)90176-7},
   Abstract = {Vortex methods of high order accuracy are developed for
             inviscid, incompressible fluid flow in two or three space
             dimensions. The velocity kernels are smooth functions given
             by simple, explicit formulas. Numerical results are given
             for test problems with exact solutions in two dimensions. It
             is found that the higher order methods yield a considerably
             more accurate representation of the velocity field than
             those of lower order for moderate integration times. On the
             other hand, the velocity field computed by the point vortex
             method has very poor accuracy at locations other than the
             particle trajectories. © 1985.},
   Doi = {10.1016/0021-9991(85)90176-7},
   Key = {fds243343}
}

@article{fds243345,
   Author = {Beale, JT},
   Title = {Large-time behavior of the Broadwell model of a discrete
             velocity gas},
   Journal = {Communications in Mathematical Physics},
   Volume = {102},
   Number = {2},
   Pages = {217-235},
   Year = {1985},
   ISSN = {0010-3616},
   url = {http://dx.doi.org/10.1007/BF01229378},
   Abstract = {We study the behavior of solutions of the one-dimensional
             Broadwell model of a discrete velocity gas. The particles
             have velocity ±1 or 0; the total mass is assumed finite. We
             show that at large time the interaction is negligible and
             the solution tends to a free state in which all the mass
             travels outward at speed 1. The limiting behavior is stable
             with respect to the initial state. No smallness assumptions
             are made. © 1985 Springer-Verlag.},
   Doi = {10.1007/BF01229378},
   Key = {fds243345}
}

@article{fds243340,
   Author = {Beale, JT and Kato, T and Majda, A},
   Title = {Remarks on the breakdown of smooth solutions for the 3-D
             Euler equations},
   Journal = {Communications in Mathematical Physics},
   Volume = {94},
   Number = {1},
   Pages = {61-66},
   Year = {1984},
   ISSN = {0010-3616},
   url = {http://dx.doi.org/10.1007/BF01212349},
   Abstract = {The authors prove that the maximum norm of the vorticity
             controls the breakdown of smooth solutions of the 3-D Euler
             equations. In other words, if a solution of the Euler
             equations is initially smooth and loses its regularity at
             some later time, then the maximum vorticity necessarily
             grows without bound as the critical time approaches;
             equivalently, if the vorticity remains bounded, a smooth
             solution persists. © 1984 Springer-Verlag.},
   Doi = {10.1007/BF01212349},
   Key = {fds243340}
}

@article{fds243341,
   Author = {Beale, JT},
   Title = {Large-time regularity of viscous surface
             waves},
   Journal = {Archive for Rational Mechanics and Analysis},
   Volume = {84},
   Number = {4},
   Pages = {307-352},
   Year = {1984},
   ISSN = {0003-9527},
   url = {http://dx.doi.org/10.1007/BF00250586},
   Doi = {10.1007/BF00250586},
   Key = {fds243341}
}

@article{fds322467,
   Author = {Beale, JT and Majda, A},
   Title = {Vortex methods. II. Higher order accuracy in two and three
             dimensions},
   Journal = {Mathematics of Computation},
   Volume = {39},
   Number = {159},
   Pages = {29-29},
   Year = {1982},
   Month = {September},
   url = {http://dx.doi.org/10.1090/S0025-5718-1982-0658213-7},
   Doi = {10.1090/S0025-5718-1982-0658213-7},
   Key = {fds322467}
}

@article{fds243323,
   Author = {Beale, JT and MAJDA, A},
   Title = {Vortex Methods 2: Higher-Order Accuracy in 2 and 3
             Dimensions},
   Journal = {Mathematics of Computation},
   Volume = {39},
   Number = {159},
   Pages = {29-52},
   Year = {1982},
   ISSN = {0025-5718},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1982NY40800002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.2307/2007618},
   Key = {fds243323}
}

@article{fds243327,
   Author = {Beale, JT and MAJDA, A},
   Title = {Vortex Methods 1: Convergence in 3 Dimensions},
   Journal = {Mathematics of Computation},
   Volume = {39},
   Number = {159},
   Pages = {1-27},
   Year = {1982},
   ISSN = {0025-5718},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1982NY40800001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Key = {fds243327}
}

@article{fds243328,
   Author = {Beale, JT},
   Title = {The initial value problem for the navier-stokes equations
             with a free surface},
   Journal = {Communications on Pure & Applied Mathematics},
   Volume = {34},
   Number = {3},
   Pages = {359-392},
   Year = {1981},
   Month = {May},
   ISSN = {0010-3640},
   url = {http://dx.doi.org/10.1002/cpa.3160340305},
   Doi = {10.1002/cpa.3160340305},
   Key = {fds243328}
}

@article{fds243326,
   Author = {Beale, JT and MAJDA, A},
   Title = {Rates of Convergence for Viscous Splitting of the
             Navier-Stokes Equations},
   Journal = {Mathematics of Computation},
   Volume = {37},
   Number = {156},
   Pages = {243-259},
   Year = {1981},
   ISSN = {0025-5718},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1981MP67700001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.2307/2007424},
   Key = {fds243326}
}

@article{fds243324,
   Author = {Beale, JT},
   Title = {Water-Waves Generated by a Pressure Disturbance on a Steady
             Stream},
   Journal = {Duke Mathematical Journal},
   Volume = {47},
   Number = {2},
   Pages = {297-323},
   Year = {1980},
   ISSN = {0012-7094},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1980KA08800002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1215/S0012-7094-80-04719-5},
   Key = {fds243324}
}

@article{fds243339,
   Author = {Beale, JT},
   Title = {The existence of cnoidal water waves with surface
             tension},
   Journal = {Journal of Differential Equations},
   Volume = {31},
   Number = {2},
   Pages = {230-263},
   Year = {1979},
   ISSN = {0022-0396},
   Key = {fds243339}
}

@article{fds243325,
   Author = {Beale, JT},
   Title = {The existence of solitary water waves},
   Journal = {Communications on Pure & Applied Mathematics},
   Volume = {30},
   Number = {4},
   Pages = {373-389},
   Year = {1977},
   Month = {July},
   ISSN = {0010-3640},
   url = {http://dx.doi.org/10.1002/cpa.3160300402},
   Doi = {10.1002/cpa.3160300402},
   Key = {fds243325}
}

@article{fds243322,
   Author = {Beale, JT},
   Title = {Eigenfunction expansions for objects floating in an open
             sea},
   Journal = {Communications on Pure & Applied Mathematics},
   Volume = {30},
   Number = {3},
   Pages = {283-313},
   Year = {1977},
   Month = {May},
   ISSN = {0010-3640},
   url = {http://dx.doi.org/10.1002/cpa.3160300303},
   Doi = {10.1002/cpa.3160300303},
   Key = {fds243322}
}

@article{fds243338,
   Author = {Beale, JT},
   Title = {Acoustic Scattering From Locally Reacting
             Surfaces},
   Journal = {Indiana University Mathematics Journal},
   Volume = {26},
   Number = {2},
   Pages = {199-222},
   Year = {1977},
   Abstract = {A theory is developed for scattering from surfaces that are
             nonporous and locally reacting in the sense that wave motion
             along the surface is negligible. It is assumed that a small
             part of the surface reacts to the excess pressure due to the
             wave like a resistive harmonic oscillator. This boundary
             condition differs from others for the acoustic equation in
             that it does not have the so-called coercive property.
             However, with certain assumptions on the parameters
             occurring in the boundary behavior, it is possible to find a
             special class of initial data, dense in the energy norm,
             whose solutions form pre-compact sets with respect to local
             energy. As a consequence, the local decay of arbitrary
             solutions of finite energy is established.},
   Key = {fds243338}
}

@article{fds243337,
   Author = {Beale, JT},
   Title = {Spectral Properties of an Acoustic Boundary
             Condition},
   Journal = {Indiana University Mathematics Journal},
   Volume = {25},
   Number = {9},
   Pages = {895-917},
   Year = {1976},
   Abstract = {A boundary condition is studied for the wave equation
             occurring in theoretical acoustics. The initial value
             problem in a bounded domain is solved by semigroup methods
             in a Hilbert space of data with finite energy. A description
             of the spectrum of the semigroup generator A is then
             obtained. Unlike the generators associated with the usual
             boundary conditions, which have compact resolvent and
             spectrum consisting of discrete eigenvalues, A always has
             essential spectrum. Moreover, if the parameters occurring in
             the boundary condition are constant, there are sequences of
             eigenvalues converging to the essential spectrum.},
   Key = {fds243337}
}

@article{fds243318,
   Author = {Beale, JT and Rosencrans, SI},
   Title = {Acoustic boundary conditions},
   Volume = {80},
   Number = {6},
   Pages = {1276-1279},
   Year = {1974},
   Month = {November},
   ISSN = {0002-9904},
   url = {http://dx.doi.org/10.1090/S0002-9904-1974-13714-6},
   Doi = {10.1090/S0002-9904-1974-13714-6},
   Key = {fds243318}
}

@article{fds243317,
   Author = {Beale, JT},
   Title = {Purely imaginary scattering frequencies for exterior
             domains},
   Journal = {Duke Mathematical Journal},
   Volume = {41},
   Number = {3},
   Pages = {607-637},
   Year = {1974},
   Month = {September},
   ISSN = {0012-7094},
   url = {http://dx.doi.org/10.1215/S0012-7094-74-04165-9},
   Doi = {10.1215/S0012-7094-74-04165-9},
   Key = {fds243317}
}

@article{fds243319,
   Author = {Beale, JT},
   Title = {Scattering frequencies of resonators},
   Journal = {Communications on Pure & Applied Mathematics},
   Volume = {26},
   Number = {4},
   Pages = {549-563},
   Year = {1973},
   Month = {July},
   ISSN = {0010-3640},
   url = {http://dx.doi.org/10.1002/cpa.3160260408},
   Doi = {10.1002/cpa.3160260408},
   Key = {fds243319}
}

@article{fds10348,
   Author = {J. T. Beale},
   Title = {Methods for computing singular and nearly singular
             integrals},
   Journal = {J. Turbulence, vol. 3, (2002), article 041 (4
             pp.)},
   url = {http://www.math.duke.edu/faculty/beale/papers/jot.pdf},
   Key = {fds10348}
}

@article{fds10345,
   Author = {J. T. Beale},
   Title = {Discretization of Layer Potentials and Numerical Methods for
             Water Waves},
   Journal = {Proc. of Workshop on Kato's Method and Principle for
             Evolution Equations in Mathematical Physics, H. Fujita, S.
             T. Kuroda, H.Okamoto, eds., Univ. of Tokyo Press, pp.
             18-26.},
   Key = {fds10345}
}

@article{fds9732,
   Author = {J. T. Beale},
   Title = {Boundary Integral Methods for Three-Dimensional Water
             Waves},
   Journal = {Equadiff 99, Proceedings of the International Conference on
             Differential Equations, Vol. 2, pp. 1369-78},
   url = {http://www.math.duke.edu/faculty/beale/papers/equadiff.ps},
   Key = {fds9732}
}

@article{fds8750,
   Author = {J. T. Beale and T.Y. Hou and J.S. Lowengrub},
   Title = {Stability of Boundary Integral Methods for Water
             Waves},
   Journal = {Nonlinear Evolutionary Partial Differential Equations, X. X.
             Ding and T.P. Liu eds., A.M.S., 1997, 107-27.},
   Key = {fds8750}
}

@article{fds8748,
   Author = {J. T. Beale and T.Y. Hou and J.S. Lowengrub},
   Title = {Stability of Boundary Integral Methods for Water
             Waves},
   Journal = {Advances in Multi-Fluid Flows, Y. Renardy et al., ed., pp.
             241-45, SIAM, Philadelphia, 1996.},
   Key = {fds8748}
}

@article{fds8749,
   Author = {J. T. Beale and A. Lifschitz and W.H. Suters},
   Title = {A Numerical and Analytical Study of Vortex Rings with
             Swirl},
   Journal = {Vortex Flows and Related Numerical Methods, II, ESAIM Proc.
             1, 565-75, Soc. Math. Appl. Indust., Paris,
             1996.},
   Key = {fds8749}
}

@article{fds9209,
   Author = {J. T. Beale and E. Thomann and C. Greengard},
   Title = {Operator splitting for Navier-Stokes and the Chorin-Marsden
             product formula},
   Journal = {Vortex Flows and Related Numerical Methods, J. T. Beale et
             al., ed., pp. 27-38, NATO ASI Series, Kluwer,
             1993.},
   Key = {fds9209}
}

@article{fds9203,
   Author = {J. T. Beale},
   Title = {The approximation of weak solutions to the Euler equations
             by vortex elements},
   Journal = {Multidimensional Hyperbolic Problems and Computations, J.
             Glimm et al., ed., pp. 23-37, Springer-Verlag, New York,
             1991.},
   Key = {fds9203}
}

@article{fds9205,
   Author = {J. T. Beale and A. Eydeland and B. Turkington},
   Title = {Numerical tests of 3-D vortex methods using a vortex ring
             with swirl},
   Journal = {Vortex Dynamics and Vortex Methods, C. Anderson and C.
             Greengard, ed., pp. 1-9, A.M.S., 1991.},
   Key = {fds9205}
}

@article{fds9206,
   Author = {J. T. Beale},
   Title = {Solitary water waves with ripples beyond all
             orders},
   Journal = {Asymptotics beyond All Orders, H. Segur et al., ed., pp.
             293-98, NATO ASI Series, Plenum, 1991.},
   Key = {fds9206}
}

@article{fds9200,
   Author = {J. T. Beale},
   Title = {Large-time behavior of model gases with a discrete set of
             velocities},
   Journal = {Mathematics Applied to Science, J. Goldstein et al., ed. pp.
             1-12, Academic Press, Orlando, 1988.},
   Key = {fds9200}
}

@article{fds9201,
   Author = {J. T. Beale},
   Title = {On the accuracy of vortex methods at large
             times},
   Journal = {Computational Fluid Dynamics and Reacting Gas Flows, B.
             Engquist et al., ed., pp. 19-32, Springer-Verlag, New York,
             1988.},
   Key = {fds9201}
}

@article{fds9195,
   Author = {J. T. Beale},
   Title = {Existence, regularity, and decay of viscous surface
             waves},
   Journal = {Nonlinear Systems of Partial Differential Equations in
             Applied Mathematics, Part 2, Lectures in Applied
             Mathematics, Vol. 23, A.M.S., Providence, 1986,
             137-48.},
   Key = {fds9195}
}

@article{fds9196,
   Author = {J. T. Beale},
   Title = {A convergent three-dimensional vortex method with grid-free
             stretching},
   Journal = {Math. Comp. 46 (1986), 401-24 and S15-S20.},
   Key = {fds9196}
}

@article{fds9191,
   Author = {J. T. Beale},
   Title = {Large-time regularity of viscous surface
             waves},
   Journal = {Arch. Rational Mech. Anal. 84 (1984), 307-52.},
   Key = {fds9191}
}

@article{fds9193,
   Author = {J. T. Beale and A. Majda},
   Title = {Vortex methods for fluid flow in two or three
             dimensions},
   Journal = {Contemp. Math. 28 (1984), 221-29.},
   Key = {fds9193}
}

@article{fds9190,
   Author = {J. T. Beale},
   Title = {Large-time regularity of viscous surface
             waves},
   Journal = {Contemp. Math. 17 (1983), 31-33.},
   Key = {fds9190}
}

@article{fds9187,
   Author = {J. T. Beale and A. Majda},
   Title = {Vortex methods I: Convergence in three dimensions},
   Journal = {Math. Comp. 39 (1982), 1-27.},
   Key = {fds9187}
}

@article{fds9189,
   Author = {J. T. Beale and A. Majda},
   Title = {The design and numerical analysis of vortex
             methods},
   Journal = {Transonic, Shock, and Multidimensional Flows, R. E. Meyer,
             ed., Academic Press, New York, 1982.},
   Key = {fds9189}
}


%% Belov, Sergey   
@article{fds31885,
   Author = {Sergei Belov and Alexei Rybkin},
   Title = {On the existence of WKB-type asymptotics for the generalized
             eigenvectors of discrete string operators},
   Journal = {Bull. London Math. Soc.},
   Volume = {36},
   Number = {2},
   Pages = {241-251},
   Year = {2004},
   MRNUMBER = {2026899},
   url = {http://www.ams.org/mathscinet-getitem?mr=2026899},
   Key = {fds31885}
}

@article{fds31887,
   Author = {S.M. Belov and N.B. Avdonina and Z. Felfli and M. Marletta and A. Z.
             Msezane and S.N. Naboko},
   Title = {Semiclassical approach to Regge poles trajectories
             calculations for nonsingular potentials: Thomas-Fermi
             type},
   Journal = {J. Phys. A},
   Volume = {37},
   Number = {27},
   Pages = {6943–6954},
   Year = {2004},
   MRNUMBER = {2078324},
   url = {http://www.ams.org/mathscinet-getitem?mr=2078324},
   Key = {fds31887}
}

@article{fds31884,
   Author = {S.M. Belov and A.V. Rybkin},
   Title = {Higher order trace formulas of the Buslaev-Faddeev type for
             the half-line Schrodinger operator with long-range
             potentials},
   Journal = {J. Math. Phys.},
   Volume = {44},
   Number = {7},
   Pages = {2748–2761},
   Year = {2003},
   MRNUMBER = {1982789},
   url = {http://www.ams.org/mathscinet-getitem?mr=1982789},
   Key = {fds31884}
}

@article{fds31883,
   Author = {N.B. Avdonina and S. Belov and Z. Felfli and A.Z. Msezane and S.N.
             Naboko},
   Title = {Semiclassical approach for calculating Regge-pole
             trajectories for singular potentials},
   Journal = {Phys. Rev. A (3)},
   Volume = {66},
   Number = {2},
   Pages = {022713},
   Year = {2002},
   MRNUMBER = {1955150},
   url = {http://link.aps.org/abstract/PRA/v66/e022713},
   Key = {fds31883}
}


%% Bendich, Paul L   
@article{fds324396,
   Author = {Bendich, P and Chin, SP and Clark, J and Desena, J and Harer, J and Munch,
             E and Newman, A and Porter, D and Rouse, D and Strawn, N and Watkins,
             A},
   Title = {Topological and statistical behavior classifiers for
             tracking applications},
   Journal = {IEEE Transactions on Aerospace and Electronic
             Systems},
   Volume = {52},
   Number = {6},
   Pages = {2644-2661},
   Year = {2016},
   Month = {December},
   url = {http://dx.doi.org/10.1109/TAES.2016.160405},
   Abstract = {© 1965-2011 IEEE.This paper introduces a method to
             integrate target behavior into the multiple hypothesis
             tracker (MHT) likelihood ratio. In particular, a periodic
             track appraisal based on behavior is introduced. The track
             appraisal uses elementary topological data analysis coupled
             with basic machine-learning techniques, and it adjusts the
             traditional kinematic data association likelihood (i.e.,
             track score) using an established formulation for
             feature-aided data association. The proposed method is
             tested and demonstrated on synthetic vehicular data
             representing an urban traffic scene generated by the
             Simulation of Urban Mobility package. The vehicles in the
             scene exhibit different driving behaviors. The proposed
             method distinguishes those behaviors and shows improved data
             association decisions relative to a conventional, kinematic
             MHT.},
   Doi = {10.1109/TAES.2016.160405},
   Key = {fds324396}
}

@article{fds321986,
   Author = {Bendich, P and Gasparovic, E and Harer, J and Tralie,
             C},
   Title = {Geometric models for musical audio data},
   Journal = {LIPIcs},
   Volume = {51},
   Pages = {65.1-65.5},
   Year = {2016},
   Month = {June},
   ISBN = {9783959770095},
   url = {http://dx.doi.org/10.4230/LIPIcs.SoCG.2016.65},
   Abstract = {© Paul Bendich, Ellen Gasparovic, John Harer, and
             Christopher Tralie. We study the geometry of sliding window
             embeddings of audio features that summarize perceptual
             information about audio, including its pitch and timbre.
             These embeddings can be viewed as point clouds in high
             dimensions, and we add structure to the point clouds using a
             cover tree with adaptive thresholds based on multi-scale
             local principal component analysis to automatically assign
             points to clusters. We connect neighboring clusters in a
             scaffolding graph, and we use knowledge of stratified space
             structure to refine our estimates of dimension in each
             cluster, demonstrating in our music applications that
             choruses and verses have higher dimensional structure, while
             transitions between them are lower dimensional. We showcase
             our technique with an interactive web-based application
             powered by Javascript and WebGL which plays music
             synchronized with a principal component analysis embedding
             of the point cloud down to 3D. We also render the clusters
             and the scaffolding on top of this projection to visualize
             the transitions between different sections of the
             music.},
   Doi = {10.4230/LIPIcs.SoCG.2016.65},
   Key = {fds321986}
}

@article{fds315426,
   Author = {Bendich, P and Marron, JS and Miller, E and Pieloch, A and Skwerer,
             S},
   Title = {Persistent Homology Analysis of Brain Artery
             Trees.},
   Journal = {The annals of applied statistics},
   Volume = {10},
   Number = {1},
   Pages = {198-218},
   Year = {2016},
   Month = {January},
   ISSN = {1932-6157},
   url = {http://hdl.handle.net/10161/11157 Duke open
             access},
   Abstract = {New representations of tree-structured data objects, using
             ideas from topological data analysis, enable improved
             statistical analyses of a population of brain artery trees.
             A number of representations of each data tree arise from
             persistence diagrams that quantify branching and looping of
             vessels at multiple scales. Novel approaches to the
             statistical analysis, through various summaries of the
             persistence diagrams, lead to heightened correlations with
             covariates such as age and sex, relative to earlier analyses
             of this data set. The correlation with age continues to be
             significant even after controlling for correlations from
             earlier significant summaries.},
   Doi = {10.1214/15-AOAS886},
   Key = {fds315426}
}

@article{fds311346,
   Author = {Paul Bendich and Ellen Gasparovic and John Harer and Christopher
             J. Tralie},
   Title = {Scaffoldings and Spines: Organizing High-Dimensional Data
             Using Cover Trees, Local Principal Component Analysis, and
             Persistent Homology},
   Year = {2016},
   url = {http://arxiv.org/abs/1602.06245},
   Key = {fds311346}
}

@article{fds315427,
   Author = {Bendich, P and Gasparovic, E and Harer, J and Izmailov, R and Ness,
             L},
   Title = {Multi-scale local shape analysis and feature selection in
             machine learning applications},
   Journal = {Proceedings of the International Joint Conference on Neural
             Networks},
   Volume = {2015-September},
   Pages = {1-8},
   Year = {2015},
   Month = {September},
   url = {http://hdl.handle.net/10161/12014 Duke open
             access},
   Abstract = {© 2015 IEEE. We introduce a method called multi-scale local
             shape analysis for extracting features that describe the
             local structure of points within a dataset. The method uses
             both geometric and topological features at multiple levels
             of granularity to capture diverse types of local information
             for subsequent machine learning algorithms operating on the
             dataset. Using synthetic and real dataset examples, we
             demonstrate significant performance improvement of
             classification algorithms constructed for these datasets
             with correspondingly augmented features.},
   Doi = {10.1109/IJCNN.2015.7280428},
   Key = {fds315427}
}

@article{fds303522,
   Author = {Munch, E and Turner, K and Bendich, P and Mukherjee, S and Mattingly, J and Harer, J},
   Title = {Probabilistic Fréchet Means for Time Varying Persistence
             Diagrams},
   Volume = {9},
   Number = {1},
   Pages = {1173-1204},
   Year = {2015},
   Month = {January},
   url = {http://arxiv.org/abs/1307.6530v3},
   Abstract = {In order to use persistence diagrams as a true statistical
             tool, it would be very useful to have a good notion of mean
             and variance for a set of diagrams. In 2011, Mileyko and his
             collaborators made the first study of the properties of the
             Fr\'echet mean in $(\mathcal{D}_p,W_p)$, the space of
             persistence diagrams equipped with the p-th Wasserstein
             metric. In particular, they showed that the Fr\'echet mean
             of a finite set of diagrams always exists, but is not
             necessarily unique. The means of a continuously-varying set
             of diagrams do not themselves (necessarily) vary
             continuously, which presents obvious problems when trying to
             extend the Fr\'echet mean definition to the realm of
             vineyards. We fix this problem by altering the original
             definition of Fr\'echet mean so that it now becomes a
             probability measure on the set of persistence diagrams; in a
             nutshell, the mean of a set of diagrams will be a weighted
             sum of atomic measures, where each atom is itself a
             persistence diagram determined using a perturbation of the
             input diagrams. This definition gives for each $N$ a map
             $(\mathcal{D}_p)^N \to \mathbb{P}(\mathcal{D}_p)$. We show
             that this map is H\"older continuous on finite diagrams and
             thus can be used to build a useful statistic on time-varying
             persistence diagrams, better known as vineyards.},
   Doi = {10.1214/15-EJS1030},
   Key = {fds303522}
}

@article{fds321987,
   Author = {Rouse, D and Watkins, A and Porter, D and Harer, J and Bendich, P and Strawn, N and Munch, E and Desena, J and Clarke, J and Gilbert, J and Chin,
             S and Newman, A},
   Title = {Feature-aided multiple hypothesis tracking using topological
             and statistical behavior classifiers},
   Journal = {Proceedings of SPIE - The International Society for Optical
             Engineering},
   Volume = {9474},
   Year = {2015},
   Month = {January},
   ISBN = {9781628415902},
   url = {http://dx.doi.org/10.1117/12.2179555},
   Abstract = {© 2015 SPIE. This paper introduces a method to integrate
             target behavior into the multiple hypothesis tracker (MHT)
             likelihood ratio. In particular, a periodic track appraisal
             based on behavior is introduced that uses elementary
             topological data analysis coupled with basic machine
             learning techniques. The track appraisal adjusts the
             traditional kinematic data association likelihood (i.e.,
             track score) using an established formulation for
             classification-aided data association. The proposed method
             is tested and demonstrated on synthetic vehicular data
             representing an urban traffic scene generated by the
             Simulation of Urban Mobility package. The vehicles in the
             scene exhibit different driving behaviors. The proposed
             method distinguishes those behaviors and shows improved data
             association decisions relative to a conventional, kinematic
             MHT.},
   Doi = {10.1117/12.2179555},
   Key = {fds321987}
}

@article{fds292867,
   Author = {Paul Bendich and Peter Bubenik},
   Title = {Stabilizing the output of persistent homology
             computations},
   Journal = {Proc. 2016 Symposium on Computational Geometry},
   Year = {2015},
   url = {http://arxiv.org/abs/1512.01700},
   Key = {fds292867}
}

@article{fds226628,
   Author = {Liz Munch and Paul Bendich and Kate Turner and Sayan Mukherjee and Jonathan Mattingly and John Harer},
   Title = {Probabalistic Frechet Means and Statistics on
             Vineyards},
   Journal = {Electronic Journal of Statistics},
   Volume = {9},
   Pages = {1173-1204},
   Year = {2015},
   url = {http://arxiv.org/abs/1307.6530},
   Abstract = {In order to use persistence diagrams as a true statistical
             tool, it would be very useful to have a good notion of mean
             and variance for a set of diagrams. In [21], Mileyko and his
             collaborators made the rst study of the properties of the
             Frechet mean in (Dp;Wp), the space of persistence diagrams
             equipped with the p-th Wasserstein metric. In particular,
             they showed that the Frechet mean of a nite set of diagrams
             always exists, but is not necessarily unique. As an
             unfortunate consequence, one sees that the means of a
             continuously-varying set of diagrams do not themselves vary
             continuously, which presents obvious problems when trying to
             extend the Frechet mean de nition to the realm of
             vineyards. We x this problem by altering the original de
             nition of Frechet mean so that it now becomes a probability
             measure on the set of persistence diagrams; in a nutshell,
             the mean of a set of diagrams will be a weighted sum of
             atomic measures, where each atom is itself the (Frechet
             mean) persistence diagram of a perturbation of the input
             diagrams. We show that this new de nition de nes a (Holder)
             continuous map, for each k, from (Dp)k ! P(Dp), and we
             present several examples to show how it may become a useful
             statistic on vineyards.},
   Key = {fds226628}
}

@article{fds227232,
   Author = {Christopher J Tralie and Paul Bendich},
   Title = {Cover Song Identification with Timbral Shape},
   Journal = {Proceedings of the 16th International Society for Music
             Information Retrieval},
   Pages = {38-44},
   Year = {2015},
   url = {http://arxiv.org/abs/1507.05143},
   Abstract = {We introduce a novel low level feature for identifying cover
             songs which quantifies the relative changes in the smoothed
             frequency spectrum of a song. Our key insight is that a
             sliding window representation of a chunk of audio can be
             viewed as a time-ordered point cloud in high dimensions. For
             corresponding chunks of audio between different versions of
             the same song, these point clouds are approximately rotated,
             translated, and scaled copies of each other. If we treat
             MFCC embeddings as point clouds and cast the problem as a
             relative shape sequence, we are able to correctly identify
             42/80 cover songs in the “Covers 80” dataset. By
             contrast, all other work to date on cover songs exclusively
             relies on matching note sequences from Chroma derived
             features.},
   Key = {fds227232}
}

@article{fds315425,
   Author = {Tralie, CJ and Bendich, P},
   Title = {Cover Song Identification with Timbral Shape
             Sequences},
   Journal = {Proc. of Int. Symp. on Music Inf. Retrieval},
   Pages = {38-44},
   Year = {2015},
   url = {http://arxiv.org/abs/1507.05143v1},
   Abstract = {We introduce a novel low level feature for identifying cover
             songs which quantifies the relative changes in the smoothed
             frequency spectrum of a song. Our key insight is that a
             sliding window representation of a chunk of audio can be
             viewed as a time-ordered point cloud in high dimensions. For
             corresponding chunks of audio between different versions of
             the same song, these point clouds are approximately rotated,
             translated, and scaled copies of each other. If we treat
             MFCC embeddings as point clouds and cast the problem as a
             relative shape sequence, we are able to correctly identify
             42/80 cover songs in the "Covers 80" dataset. By contrast,
             all other work to date on cover songs exclusively relies on
             matching note sequences from Chroma derived
             features.},
   Key = {fds315425}
}

@article{fds220713,
   Author = {Paul Bendich and Herbert Edelsbrunner and Dmitriy Morozov and Amit Patel},
   Title = {Homology and Robustness of Level and Interlevel
             Sets},
   Journal = {Homology, Homotopy, and Applications},
   Volume = {15},
   Number = {1},
   Pages = {51-72},
   Editor = {Gunnar Carlsson},
   Year = {2013},
   Month = {March},
   Abstract = {Given a continuous function f : X → R on a topological
             space, we consider the preimages of intervals and their
             homol- ogy groups and show how to read the ranks of these
             groups from the extended persistence diagram of f. In
             addition, we quan- tify the robustness of the homology
             classes under perturbations of f using well groups, and we
             show how to read the ranks of these groups from the same
             extended persistence diagram. The special case X = R^3 has
             ramifications in the fields of medical imaging and
             scientific visualization.},
   Key = {fds220713}
}

@article{fds302435,
   Author = {P.L. Bendich and Bendich, P and Wang, B and Mukherjee, S},
   Title = {Local homology transfer and stratification
             learning},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Pages = {1355-1370},
   Year = {2012},
   Month = {April},
   Abstract = {The objective of this paper is to show that point cloud data
             can under certain circumstances be clustered by strata in a
             plausible way. For our purposes, we consider a stratified
             space to be a collection of manifolds of different
             dimensions which are glued together in a locally trivial
             manner inside some Euclidean space. To adapt this abstract
             definition to the world of noise, we first define a
             multi-scale notion of stratified spaces, providing a
             stratification at different scales which are indexed by a
             radius parameter. We then use methods derived from kernel
             and cokernel persistent homology to cluster the data points
             into different strata. We prove a correctness guarantee for
             this clustering method under certain topological conditions.
             We then provide a probabilistic guarantee for the clustering
             for the point sample setting - we provide bounds on the
             minimum number of sample points required to state with high
             probability which points belong to the same strata. Finally,
             we give an explicit algorithm for the clustering. Copyright
             © SIAM.},
   Key = {fds302435}
}

@article{fds302436,
   Author = {P.L. Bendich and Bendich, P and Cabello, S and Edelsbrunner, H},
   Title = {A point calculus for interlevel set homology},
   Journal = {Pattern Recognition Letters},
   Volume = {33},
   Number = {11},
   Pages = {1436-1444},
   Year = {2012},
   ISSN = {0167-8655},
   url = {http://dx.doi.org/10.1016/j.patrec.2011.10.007},
   Abstract = {The theory of persistent homology opens up the possibility
             to reason about topological features of a space or a
             function quantitatively and in combinatorial terms. We refer
             to this new angle at a classical subject within algebraic
             topology as a point calculus, which we present for the
             family of interlevel sets of a real-valued function. Our
             account of the subject is expository, devoid of proofs, and
             written for non-experts in algebraic topology. © 2011
             Elsevier B.V. All rights reserved.},
   Doi = {10.1016/j.patrec.2011.10.007},
   Key = {fds302436}
}

@article{fds303523,
   Author = {Bendich, P and Edelsbrunner, H and Morozov, D and Patel,
             A},
   Title = {Homology and Robustness of Level and Interlevel
             Sets},
   Year = {2011},
   Month = {February},
   url = {http://arxiv.org/abs/1102.3389v1},
   Abstract = {Given a function $f: \Xspace \to \Rspace$ on a topological
             space, we consider the preimages of intervals and their
             homology groups and show how to read the ranks of these
             groups from the extended persistence diagram of $f$. In
             addition, we quantify the robustness of the homology classes
             under perturbations of $f$ using well groups, and we show
             how to read the ranks of these groups from the same extended
             persistence diagram. The special case $\Xspace = \Rspace^3$
             has ramifications in the fields of medical imaging and
             scientific visualization.},
   Key = {fds303523}
}

@article{fds243365,
   Author = {P.L. Bendich and Bendich, P and Galkovskyi, T and Harer, J},
   Title = {Improving homology estimates with random
             walks},
   Journal = {Inverse Problems},
   Volume = {27},
   Number = {12},
   Year = {2011},
   ISSN = {0266-5611},
   url = {http://dx.doi.org/10.1088/0266-5611/27/12/124002},
   Abstract = {This experimental paper makes the case for a new approach to
             the use of persistent homology in the study of shape and
             feature in datasets. By introducing ideas from diffusion
             geometry and random walks, we discover that homological
             features can be enhanced and more effectively extracted from
             spaces that are sampled densely and evenly, and with a small
             amount of noise. This study paves the way for a more
             theoretical analysis of how random walk metrics affect
             persistence diagrams, and provides evidence that combining
             topological data analysis with techniques inspired by
             diffusion geometry holds great promise for new analyses of a
             wide variety of datasets. © 2011 IOP Publishing
             Ltd.},
   Doi = {10.1088/0266-5611/27/12/124002},
   Key = {fds243365}
}

@article{fds243366,
   Author = {P.L. Bendich and Bendich, P and Harer, J},
   Title = {Persistent Intersection Homology},
   Journal = {Foundations of Computational Mathematics},
   Volume = {11},
   Number = {3},
   Pages = {305-336},
   Year = {2011},
   ISSN = {1615-3375},
   url = {http://dx.doi.org/10.1007/s10208-010-9081-1},
   Abstract = {The theory of intersection homology was developed to study
             the singularities of a topologically stratified space. This
             paper incorporates this theory into the already developed
             framework of persistent homology. We demonstrate that
             persistent intersection homology gives useful information
             about the relationship between an embedded stratified space
             and its singularities. We give an algorithm for the
             computation of the persistent intersection homology groups
             of a filtered simplicial complex equipped with a
             stratification by subcomplexes, and we prove its
             correctness. We also derive, from Poincaré Duality, some
             structural results about persistent intersection homology.
             © 2010 SFoCM.},
   Doi = {10.1007/s10208-010-9081-1},
   Key = {fds243366}
}

@article{fds302432,
   Author = {Bendich, P and Mukherjee, S and Wang, B},
   Title = {Stratification learning through homology
             inference},
   Journal = {AAAI Fall Symposium - Technical Report},
   Volume = {FS-10-06},
   Pages = {10-17},
   Year = {2010},
   Month = {December},
   Abstract = {We develop a topological approach to stratification
             learning. Given point cloud data drawn from a stratified
             space, our objective is to infer which points belong to the
             same strata. First we define a multi-scale notion of a
             stratified space, giving a stratification for each radius
             level. We then use methods derived from kernel and cokernel
             persistent homology to cluster the data points into
             different strata, and we prove a result which guarantees the
             correctness of our clustering, given certain topological
             conditions. We later give bounds on the minimum number of
             sample points required to infer, with probability, which
             points belong to the same strata. Finally, we give an
             explicit algorithm for the clustering and apply it to some
             simulated data. Copyright © 2010, Association for the
             Advancement of Artificial Intelligence. All rights
             reserved.},
   Key = {fds302432}
}

@article{fds302434,
   Author = {P.L. Bendich and Bendich, P and Edelsbrunner, H and Kerber, M},
   Title = {Computing robustness and persistence for
             images.},
   Journal = {IEEE Transactions on Visualization and Computer
             Graphics},
   Volume = {16},
   Number = {6},
   Pages = {1251-1260},
   Year = {2010},
   Month = {November},
   ISSN = {1077-2626},
   url = {http://dx.doi.org/10.1109/tvcg.2010.139},
   Abstract = {We are interested in 3-dimensional images given as arrays of
             voxels with intensity values. Extending these values to a
             continuous function, we study the robustness of homology
             classes in its level and interlevel sets, that is, the
             amount of perturbation needed to destroy these classes. The
             structure of the homology classes and their robustness, over
             all level and interlevel sets, can be visualized by a
             triangular diagram of dots obtained by computing the
             extended persistence of the function. We give a fast
             hierarchical algorithm using the dual complexes of oct-tree
             approximations of the function. In addition, we show that
             for balanced oct-trees, the dual complexes are geometrically
             realized in R³ and can thus be used to construct level and
             interlevel sets. We apply these tools to study 3-dimensional
             images of plant root systems.},
   Doi = {10.1109/tvcg.2010.139},
   Key = {fds302434}
}

@article{fds315428,
   Author = {Bendich, P and Mukherjee, S and Wang, B},
   Title = {Towards Stratification Learning through Homology
             Inference},
   Year = {2010},
   Month = {August},
   url = {http://arxiv.org/abs/1008.3572v1},
   Abstract = {A topological approach to stratification learning is
             developed for point cloud data drawn from a stratified
             space. Given such data, our objective is to infer which
             points belong to the same strata. First we define a
             multi-scale notion of a stratified space, giving a
             stratification for each radius level. We then use methods
             derived from kernel and cokernel persistent homology to
             cluster the data points into different strata, and we prove
             a result which guarantees the correctness of our clustering,
             given certain topological conditions; some geometric
             intuition for these topological conditions is also provided.
             Our correctness result is then given a probabilistic flavor:
             we give bounds on the minimum number of sample points
             required to infer, with probability, which points belong to
             the same strata. Finally, we give an explicit algorithm for
             the clustering, prove its correctness, and apply it to some
             simulated data.},
   Key = {fds315428}
}

@article{fds302431,
   Author = {P.L. Bendich and Bendich, P and Edelsbrunner, H and Morozov, D and Patel,
             A},
   Title = {The robustness of level sets},
   Journal = {Lecture notes in computer science},
   Volume = {6346 LNCS},
   Number = {PART 1},
   Pages = {1-10},
   Year = {2010},
   ISSN = {0302-9743},
   url = {http://dx.doi.org/10.1007/978-3-642-15775-2_1},
   Abstract = {We define the robustness of a level set homology class of a
             function f : double-struck X → ℝ as the magnitude of a
             perturbation necessary to kill the class. Casting this
             notion into a group theoretic framework, we compute the
             robustness for each class, using a connection to extended
             persistent homology. The special case double-struck X = ℝ
             3 has ramifications in medical imaging and scientific
             visualization. © 2010 Springer-Verlag.},
   Doi = {10.1007/978-3-642-15775-2_1},
   Key = {fds302431}
}

@article{fds302433,
   Author = {P.L. Bendich and Bendich, P and Edelsbrunner, H and Kerber, M and Patel,
             A},
   Title = {Persistent homology under non-uniform error},
   Journal = {Lecture notes in computer science},
   Volume = {6281 LNCS},
   Pages = {12-23},
   Year = {2010},
   ISSN = {0302-9743},
   url = {http://dx.doi.org/10.1007/978-3-642-15155-2_2},
   Abstract = {Using ideas from persistent homology, the robustness of a
             level set of a real-valued function is defined in terms of
             the magnitude of the perturbation necessary to kill the
             classes. Prior work has shown that the homology and
             robustness information can be read off the extended
             persistence diagram of the function. This paper extends
             these results to a non-uniform error model in which
             perturbations vary in their magnitude across the domain. ©
             2010 Springer-Verlag.},
   Doi = {10.1007/978-3-642-15155-2_2},
   Key = {fds302433}
}

@article{fds226384,
   Author = {P.L. Bendich and David Cohen-Steiner and Herbert Edelsbrunner and John Harer and Dmitriy Morozov},
   Title = {Inferring Local Homology from Sampled Stratified
             Spaces},
   Journal = {In Proceedings of the 48th Annual IEEE Symposium on
             Foundations of Computer Science, pages 536-546,
             2007.},
   Year = {2007},
   Key = {fds226384}
}


%% Berkesch, Christine   
@article{fds211711,
   Author = {C. Berkesch and D. Erman and M. Kummini},
   Title = {Three flavors of extremal Betti tables},
   Year = {2012},
   url = {http://arxiv.org/abs/1207.5707},
   Key = {fds211711}
}

@article{fds211709,
   Author = {C. Berkesch and J. Burke and D. Erman and C. Gibbons},
   Title = {The cone of Betti diagrams over a hypersurface ring of low
             embedding dimension},
   Journal = {J. Pure Applied Algebra},
   Volume = {216},
   Pages = {2256--2268},
   Year = {2012},
   url = {http://arxiv.org/abs/1109.5198},
   Key = {fds211709}
}

@article{fds197208,
   Author = {C. Berkesch},
   Title = {The rank of a hypergeometric system},
   Journal = {Compos. Math.},
   Volume = {147},
   Number = {1},
   Pages = {284-318},
   Year = {2011},
   url = {http://arxiv.org/abs/0807.0453},
   Key = {fds197208}
}

@article{fds197201,
   Author = {C. Berkesch and D. Erman and M. Kummini and S. V.
             Sam},
   Title = {Shapes of free resolutions over a local ring},
   Journal = {to appear in Math. Ann.},
   Year = {2011},
   url = {http://arxiv.org/abs/1105.2244},
   Key = {fds197201}
}

@article{fds211708,
   Author = {C. Berkesch and D. Erman and M. Kummini and S. V.
             Sam},
   Title = {Tensor complexes: Multilinear free resolutions constructed
             from higher tensors},
   Journal = {J. European Mathematical Society},
   Year = {2011},
   url = {http://arxiv.org/abs/1101.4604},
   Key = {fds211708}
}

@article{fds197203,
   Author = {C. Berkesch and J. Forsgård and M. Passare},
   Title = {Euler--Mellin integrals and A-hypergeometric
             functions},
   Year = {2011},
   url = {http://arxiv.org/abs/1103.6273},
   Key = {fds197203}
}

@article{fds197205,
   Author = {C. Berkesch and A. Leykin},
   Title = {Algorithms for Bernstein--Sato polynomials and multiplier
             ideals},
   Journal = {ISSAC},
   Year = {2010},
   url = {http://arxiv.org/abs/1002.1475},
   Key = {fds197205}
}

@article{fds197207,
   Author = {C. Berkesch and D. Erman and M. Kummini and S. V.
             Sam},
   Title = {Poset structures in Boij--Söderberg theory},
   Journal = {to appear in Int. Math. Res. Not.},
   Year = {2010},
   url = {http://arxiv.org/abs/1010.2663},
   Key = {fds197207}
}

@article{fds197206,
   Author = {C. Berkesch and L. F. Matusevich},
   Title = {A-graded methods for monomial ideals},
   Journal = {J. Algebra},
   Volume = {322},
   Pages = {2886-2904},
   Year = {2009},
   url = {http://arxiv.org/abs/0807.4306},
   Key = {fds197206}
}


%% Berman, Peter H   
@article{fds10422,
   Author = {Peter H. Berman},
   Title = {Computing the Galois Group of Y' = AY + B, Y' = AY
             Completely Reducible},
   Journal = {Journal of Symbolic Computation},
   url = {http://www.math.duke.edu/~berman/Y_inhom06.pdf},
   Abstract = {We consider a special case of the problem of computing the
             Galois group of a linear ordinary differential operator L in
             C(x)[D]. We assume that C is a computable,
             characteristic-zero, algebraically closed constant field
             with factorization algorithm. There exists a decision
             procedure, due to Compoint and Singer, to compute the group
             in case L is completely reducible. In ``Calculating the
             Galois group of L_1(L_2(y)) = 0, L_1, L_2 completely
             reducible operators,'' Berman and Singer address the case of
             a product of two completely reducible operators. Their
             article shows how to reduce that case to the case of an
             inhomogeneous equation of the form L(y) = b, L completely
             reducible, b in C(x). Their article further presents a
             decision procedure to reduce that inhomogeneous case to the
             case of the associated homogeneous equation L(y) = 0, using
             an algorithm whose steps include the computation of a
             certain set of factorizations of L; this set is very large
             and difficult to compute in general. In this article, we
             give a new algorithm to compute the Galois group of a system
             of first-order equations Y' = AY + B, A in Mat_n(C(x)), b in
             C(x)^n, in case the associated homogeneous system Y' = AY is
             completely reducible. After the additional step of applying
             a cyclic vector algorithm to translate between operators and
             first-order systems, our algorithm yields a more efficient
             method to compute the group of L(y) = b, L completely
             reducible, b in C(x). The new method's improved efficiency
             comes from replacing the large set of factorizations
             required by the Berman-Singer method with a single
             block-diagonal decomposition of the coefficient matrix
             satisfying certain properties.},
   Key = {fds10422}
}

@article{fds9870,
   Author = {Peter H. Berman and M. F. Singer},
   Title = {Calculating the Galois Group of L_1(L_2(y))=0, L_1, L_2
             Completely Reducible Operators},
   Journal = {Journal of Pure and Applied Algebra, vol. #139 (1999), pp.
             3-24},
   url = {http://www4.ncsu.edu:8030/~singer/papers/12Inhom.ps},
   Abstract = {This article addresses the problem of computing the Galois
             group of a product of two completely reducible linear
             operators with rational function coefficients. It shows how
             to reduce this problem to the case of a single completely
             reducible linear operator, which is addressed in a separate
             article by Compoint and Singer. A decision procedure and
             several examples are provided.},
   Key = {fds9870}
}


%% Bertozzi, Andrea L   
@booklet{Bertozzi04,
   Author = {A. L. Bertozzi and J. B. Greer},
   Title = {Low-curvature image simplifiers: Global regularity of smooth
             solutions and Laplacian limiting schemes},
   Journal = {Communications On Pure And Applied Mathematics},
   Volume = {57},
   Number = {6},
   Pages = {764 -- 790},
   Year = {2004},
   Month = {June},
   Key = {Bertozzi04}
}

@booklet{Witelski04,
   Author = {T. P. Witelski and A. J. Bernoff and A. L.
             Bertozzi},
   Title = {Blowup and dissipation in a critical-case unstable thin film
             equation},
   Journal = {European Journal Of Applied Mathematics},
   Volume = {15},
   Pages = {223 -- 256},
   Year = {2004},
   Month = {April},
   Key = {Witelski04}
}

@article{fds20356,
   Author = {Chad Topaz and Andrea L. Bertozzi},
   Title = {Swarming dynamics and pattern formation in a model for
             biological group motion},
   Journal = {to appear in SIAM J. Appl. Math.},
   Year = {2004},
   Month = {March},
   Key = {fds20356}
}

@booklet{Topaz04,
   Author = {C. M. Topaz and A. L. Bertozzi},
   Title = {Swarming patterns in a two-dimensional kinematic model for
             biological groups},
   Journal = {Siam Journal On Applied Mathematics},
   Volume = {65},
   Number = {1},
   Pages = {152 -- 174},
   Year = {2004},
   Key = {Topaz04}
}

@article{fds24258,
   Author = {Junjie Zhou and B. Dupuy and A.L. Bertozzi and A. E.
             Hosoi},
   Title = {Shock dynamics in particle-laden thin films},
   Year = {2004},
   Key = {fds24258}
}

@article{fds23849,
   Author = {M Kemp and A.L. Bertozzi and D. Marthaler},
   Title = {Multi-UUV perimeter surveillance},
   Editor = {Sebasco Estates and Maine, C. and Brancart, E. An and M.
             Benjamin},
   Year = {2004},
   Key = {fds23849}
}

@article{fds21046,
   Author = {Andrea L. Bertozzi and John B. Greer},
   Title = {Low curvature image simplifiers: global regularity of smooth
             solutions and Laplacian limiting schemes},
   Journal = {Comm. Pure Appl. Math.},
   Volume = {57},
   Number = {6},
   Pages = {764-790},
   Year = {2004},
   Key = {fds21046}
}

@article{fds23552,
   Author = {John B. Greer and Andrea L. Bertozzi},
   Title = {Traveling wave solutions of fourth order PDEs for image
             processing},
   Journal = {SIAM J. Math. Anal.},
   Volume = {36},
   Number = {1},
   Pages = {38-68},
   Year = {2004},
   url = {http://epubs.siam.org/sam-bin/dbq/article/42737},
   Key = {fds23552}
}

@article{fds23086,
   Author = {T.P. Witelski and A. J. Bernoff and A. L. Bertozzi},
   Title = {Blow-up and dissipation in a critical-case unstable thin
             film equation},
   Journal = {European J. Appl. Math.},
   Volume = {15},
   Pages = {223-256},
   Year = {2004},
   Key = {fds23086}
}

@article{fds20708,
   Author = {Mark Bowen and Jeanman Sur and Andrea L. Bertozzi and Robert P.
             Behringer},
   Title = {Nonlinear dynamics of two-dimensional undercompressive
             shocks},
   Journal = {Physica D},
   Year = {2004},
   Key = {fds20708}
}

@article{fds23087,
   Author = {Andrea Bertozzi and John Greer and Stanley Osher and Kevin
             Vixie},
   Title = {Nonlinear regularizations of TV based PDEs for image
             processing},
   Journal = {AMS Series of Contemporary Mathematics, proceedings of the
             2003 Northewestern PDE conference, Gui-Qiang Chen, Joseph
             Jerome, and George Gasper eds.},
   Year = {2004},
   Key = {fds23087}
}

@article{fds18677,
   Author = {Chuang, Y.L. and Oren, R. and Bertozzi, A.L. and Phillips, N. and Katul, G.G.},
   Title = {"The porous media model for the hydraulic system of a tree:
             from sap flux data to transpiration rate"},
   Journal = {Ecological modeling},
   Year = {2004},
   Key = {fds18677}
}

@booklet{Greer04a,
   Author = {J. B. Greer and A. L. Bertozzi},
   Title = {H-1 solutions of a class of fourth order nonlinear equations
             for image processing},
   Journal = {Discrete And Continuous Dynamical Systems},
   Volume = {10},
   Number = {1-2},
   Pages = {349 -- 366},
   Year = {2004},
   Key = {Greer04a}
}

@article{fds12422,
   Author = {A.L. Bertozzi M. Kemp, and D. Marthaler},
   Title = {Determining Environmental Boundaries: Asynchronous
             communication and physical scales},
   Series = {Lecture Notes in Control and Information
             Systems},
   Booktitle = {Proceedings of the Block Island Workshop on Cooperative
             Control 2003},
   Publisher = {Springer-Verlag},
   Editor = {V. Kumar and N. Leonard and S. Morse},
   Year = {2003},
   Month = {September},
   Key = {fds12422}
}

@booklet{Zhornitskaya00,
   Author = {L. Zhornitskaya and A. L. Bertozzi},
   Title = {Positivity-preserving numerical schemes for lubrication-type
             equations},
   Journal = {Siam Journal On Numerical Analysis},
   Volume = {37},
   Number = {2},
   Pages = {523 -- 555},
   Year = {2000},
   Month = {January},
   Key = {Zhornitskaya00}
}

@booklet{Bertozzi99,
   Author = {A. L. Bertozzi and A. Munch and M. Shearer},
   Title = {Undercompressive shocks in thin film flows},
   Journal = {Physica D},
   Volume = {134},
   Number = {4},
   Pages = {431 -- 464},
   Year = {1999},
   Month = {December},
   Key = {Bertozzi99}
}

@booklet{Munch99,
   Author = {A. Munch and A. L. Bertozzi},
   Title = {Rarefaction-undercompressive fronts in driven
             films},
   Journal = {Physics Of Fluids},
   Volume = {11},
   Number = {10},
   Pages = {2812 -- 2814},
   Year = {1999},
   Month = {October},
   Key = {Munch99}
}

@booklet{Bertozzi98,
   Author = {A. L. Bertozzi and A. Munch and X. Fanton and A. M.
             Cazabat},
   Title = {Contact line stability and "undercompressive shocks" in
             driven thin film flow},
   Journal = {Physical Review Letters},
   Volume = {81},
   Number = {23},
   Pages = {5169 -- 5172},
   Year = {1998},
   Month = {December},
   Key = {Bertozzi98}
}

@booklet{Bernoff98,
   Author = {A. J. Bernoff and A. L. Bertozzi and T. P.
             Witelski},
   Title = {Axisymmetric surface diffusion: Dynamics and stability of
             self-similar pinchoff},
   Journal = {Journal Of Statistical Physics},
   Volume = {93},
   Number = {3-4},
   Pages = {725 -- 776},
   Year = {1998},
   Month = {November},
   Key = {Bernoff98}
}

@booklet{Bertozzi96a,
   Author = {A. L. Bertozzi},
   Title = {Symmetric singularity formation in lubrication-type
             equations for interface motion},
   Journal = {Siam Journal On Applied Mathematics},
   Volume = {56},
   Number = {3},
   Pages = {681 -- 714},
   Year = {1996},
   Month = {June},
   Key = {Bertozzi96a}
}

@booklet{Bertozzi96b,
   Author = {A. L. Bertozzi and M. Pugh},
   Title = {The lubrication approximation for thin viscous films:
             Regularity and long-time behavior of weak
             solutions},
   Journal = {Communications On Pure And Applied Mathematics},
   Volume = {49},
   Number = {2},
   Pages = {85 -- 123},
   Year = {1996},
   Month = {February},
   Key = {Bertozzi96b}
}

@booklet{Bertozzi96,
   Author = {A. L. Bertozzi},
   Title = {Lubrication approximations for surface tension driven
             interfaces: Some open problems},
   Journal = {Zeitschrift Fur Angewandte Mathematik Und
             Mechanik},
   Volume = {76},
   Pages = {373 -- 376},
   Year = {1996},
   Key = {Bertozzi96}
}

@booklet{Bernoff95,
   Author = {A. J. Bernoff and A. L. Bertozzi},
   Title = {Singularities in a modified kuramoto-sivashinsky equation
             describing interface motion for phase-transition},
   Journal = {Physica D},
   Volume = {85},
   Number = {3},
   Pages = {375 -- 404},
   Year = {1995},
   Month = {August},
   Key = {Bernoff95}
}

@booklet{Bertozzi94,
   Author = {A. L. Bertozzi and M. Pugh},
   Title = {The lubrication approximation for thin viscous films - the
             moving contact line with a porous-media cutoff of
             van-der-waals interactions},
   Journal = {Nonlinearity},
   Volume = {7},
   Number = {6},
   Pages = {1535 -- 1564},
   Year = {1994},
   Month = {November},
   Key = {Bertozzi94}
}

@booklet{Bertozzi88,
   Author = {A. L. Bertozzi},
   Title = {Heteroclinic orbits and chaotic dynamics in planar
             fluid-flows},
   Journal = {Siam Journal On Mathematical Analysis},
   Volume = {19},
   Number = {6},
   Pages = {1271 -- 1294},
   Year = {1988},
   Month = {November},
   Key = {Bertozzi88}
}

@article{fds15845,
   Author = {John B. Greer and Andrea L. Bertozzi},
   Title = {H1 Solutions of a class of fourth order nonlinear
             equations for image processing},
   Journal = {Discrete and continuous dynamical systems 2004, special
             issue in honor of Mark Vishik, Editors: V. Chepyzhov, M.
             Efendiev, Alain Miranville, and Roger Temam, 
             web page },
   Volume = {1-2},
   Number = {10},
   Pages = {349-366},
   url = {http://www.math.ucla.edu/applied/cam/index.html},
   Abstract = {to appear},
   Key = {fds15845}
}

@article{fds15844,
   Author = {B. A. Wagner and A. L. Bertozzi and L. E. Howle},
   Title = {Positive Feedback Control of Rayleigh-Benard
             Convection},
   Journal = {Discrete and Continuous Dynamical Systems Series B, 2003,
             special issue in honor of David Schaeffer},
   Volume = {3},
   Number = {4},
   Pages = {619-642},
   url = {http://www.math.ucla.edu/applied/cam/index.html},
   Key = {fds15844}
}

@article{fds15523,
   Author = {Daniel Marthaler and Andrea L. Bertozzi},
   Title = {Tracking environmental level sets with autonomous
             vehicles},
   Journal = {S. Butenko, R. Murphey and P.M. Pardalos (editors), ``Recent
             Developments in Cooperative Control and Optimization'',
             Kluwer Academic Publishers, 2003},
   url = {http://www.ise.ufl.edu/cao/cco/announc.htm},
   Key = {fds15523}
}

@article{fds10449,
   Author = {B. Cook and D. Marthaler and C. Topaz and A. Bertozzi and M.
             Kemp},
   Title = {Fractional bandwidth reacquisition algorithms for
             VSW-MCM},
   Journal = {Multi-Robot Systems: From Swarms to Intelligent Automata,
             Volume II, 2003, Kluwer Academic Publishers, Dordrecht, A.C.
             Schultz et al. eds. 77-86},
   url = {http://www.pao.nrl.navy.mil/robots/},
   Key = {fds10449}
}

@article{fds10445,
   Author = {Jeanman Sur and Andrea L. Bertozzi and Robert P.
             Behringer},
   Title = {Reverse undercompressive shock structures in driven thin
             film flow},
   Journal = {Phys. Rev. Lett. 90 (12) 126105, 2003},
   url = {http://ojps.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRLTAO000090000012126105000001&idtype=cvips&gifs=Yes},
   Key = {fds10445}
}

@article{fds10433,
   Author = {R. Buckingham and M. Shearer and A. L. Bertozzi},
   Title = {Thin film traveling waves and the Navier slip
             condition},
   Journal = {SIAM J. Appl. Math.Volume 63, Number 2, pp. 722-744,
             2003},
   url = {http://epubs.siam.org/sam-bin/dbq/article/40140},
   Key = {fds10433}
}

@article{fds18679,
   Author = {Daniel Marthaler and Andrea L. Bertozzi},
   Title = {Collective motion algorithms for determining environmental
             boundaries},
   Key = {fds18679}
}

@article{fds10326,
   Author = {Andrea L. Bertozzi and Mark Bowen},
   Title = {Thin films and moving contact lines},
   Journal = {Modern Methods in Scientific Computing and Applications,
             Proceedings of the Nato Adv. Study Institute, Montreal
             Canada, 2001, pp. 31-79.Anne Bourlioux, Martin J. Gander,
             and Gert Sabidussi, eds., Nato Science Series II, Vol. 75,
             Kluwer, Dordrecht, 2002},
   Key = {fds10326}
}

@book{fds9452,
   Author = {Andrew J. Majda and Andrea L. Bertozzi},
   Title = {Vorticity and Incompressible Flow},
   Journal = {Cambridge Univ. Press, 2002.},
   url = {http://www.cup.org/titles/catalogue.asp?isbn=0521639484},
   Key = {fds9452}
}

@article{fds10158,
   Author = {M. Bertalmio and A. L. Bertozzi and G. Sapiro},
   Title = {Navier-Stokes, Fluid Dynamics, and Image and Video
             Inpainting},
   Journal = {Proceedings of the 
             International Conference on Computer Vision and Pattern
             Recognition , IEEE, Dec. 2001, Kauai, HI, volume I, pp.
             I-355-I362.},
   url = {http://www.math.duke.edu/~bertozzi/inpaint/623A_bertozzi.ps},
   Abstract = {Image inpainting involves filling in part of an image or
             video using information from the surrounding area.
             Applications include the restoration of damaged photographs
             and movies and the removal of selected objects. In this
             paper, we introduce a class of automated methods for digital
             inpainting. The approach uses ideas from classical fluid
             dynamics to propagate isophote lines continuously from the
             exterior into the region to be inpainted. The main idea is
             to think of the image intensity as a `stream function' for a
             two-dimensional incompressible flow. The Laplacian of the
             image intensity plays the role of the vorticity of the
             fluid; it is transported into the region to be inpainted by
             a vector field defined by the stream function. The resulting
             algorithm is designed to continue isophotes while matching
             gradient vectors at the boundary of the inpainting region.
             The method is directly based on the Navier-Stokes equations
             for fluid dynamics, which has the immediate advantage of
             well-developed theoretical and numerical results. This is a
             new approach for introducing ideas from computational fluid
             dynamics into problems in computer vision and image
             analysis.},
   Key = {fds10158}
}

@article{fds9865,
   Author = {Andrea L. Bertozzi and Guenther Gruen and Thomas P.
             Witelski},
   Title = {Dewetting films: bifurcations and concentrations},
   Journal = {Nonlinearity, vol 14, number 6, Nov 2001, pp
             1569-1592.},
   url = {http://www.iop.org/EJ/S/3/133/toc/Non/accel},
   Abstract = {Under the influence of long range attractive and short range
             repulsive forces, thin liquid films rupture and form complex
             dewetting patterns. This paper studies this phenomenon in
             one space dimension in the framework of fourth order
             degenerate parabolic equations of lubrication type. We
             derive the global structure of the bifurcation diagram for
             steady state solutions. A stability analysis of the solution
             branches and numerical simulations suggest coarsening
             occurs. Furthermore, we study the behavior of solutions in
             the limit that short range repulsive forces are neglected.
             Both asymptotic analysis and numerical experiments show that
             this limit can concentrate mass in $\delta$-distributions.},
   Key = {fds9865}
}

@article{fds9830,
   Author = {Andrea Bertozzi and Andreas Munch and Michael Shearer and Kevin
             Zumbrun},
   Title = {Stability of compressive and undercompressive thin film
             travelling waves},
   Journal = {European J. of Appl. Math., 12(3), pp.253-291,
             2001},
   url = {http://www.journals.cup.org/bin/bladerunner?REQUNIQ=997889121&REQSESS=44897&117000REQEVENT=&REQINT1=82548&REQAUTH=0},
   Abstract = {Recent studies of liquid films driven by competing forces
             due to surface tension gradients and gravity reveal that
             undercompressive traveling waves play an important role in
             the dynamics when the competing forces are comparable. In
             this paper we provide a theoretical framework for assessing
             the spectral stability of compressive and undercompressive
             traveling waves in thin film models. Associated with the
             linear stability problem is an Evans function which vanishes
             precisely at eigenvalues of the linearized operator. The
             structure of an index related to the Evans function explains
             computational results for stability of compressive waves. A
             new formula for the index in the undercompressive case
             yields results consistent with stability. <p> In considering
             stability of undercompressive waves to transverse
             perturbations, there is an apparent inconsistency between
             long-wave asymptotics of the largest eigenvalue and its
             actual behavior. We show that this paradox is due to the
             unusual structure of the eigenfunctions and we construct a
             revised long-wave asymptotics. We conclude with numerical
             computations of the largest eigenvalue, comparisons with the
             asymptotic results, and several open problems associated
             with our findings.},
   Key = {fds9830}
}

@article{fds9800,
   Author = {Javier Diez and Lou Kondic and Andrea Bertozzi},
   Title = {Global models for moving contact lines},
   Journal = {Phys. Rev. E. 63, 011208 (January 2001)},
   url = {http://pre.aps.org/},
   Key = {fds9800}
}

@article{fds9761,
   Author = {Andrea L. Bertozzi and Mary C. Pugh},
   Title = {Finite-time blow-up of solutions of some long-wave unstable
             thin film equations},
   Journal = {Indiana Univ. Mathematics J. 49(4), pp. 1323-1366,
             2000},
   url = {http://inca.math.indiana.edu/iumj/index.php},
   Key = {fds9761}
}

@article{fds9631,
   Author = {Andrea L. Bertozzi and Michael Shearer},
   Title = {Existence of undercompressive traveling waves in thin film
             equations},
   Journal = {SIAM J. Math. Anal., vol 32, no. 1, pp. 194-213,
             2000.},
   url = {http://epubs.siam.org/sam-bin/dbq/article/35089},
   Key = {fds9631}
}

@article{fds9526,
   Author = {L. Zhornitskaya and A. L. Bertozzi},
   Title = {Positivity Preserving Numerical Schemes for Lubrication-Type
             Equations},
   Journal = {S.I.A.M. J. Num Anal., Vol. 37, No. 2, pp. 523-555,
             2000.},
   url = {http://epubs.siam.org/sam-bin/dbq/article/33569},
   Key = {fds9526}
}

@article{fds9450,
   Author = {Andrea L Bertozzi and A. Munch and M. Shearer},
   Title = {Undercompressive Shocks in Thin Film Flow},
   Journal = {Physica D, 134(4), 431-464, 1999.},
   url = {http://www.elsevier.nl/inca/publications/store/5/0/5/7/1/4/},
   Key = {fds9450}
}

@article{fds9382,
   Author = {L. Kondic and A. L. Bertozzi},
   Title = {Nonlinear Dynamics and Transient Growth of Driven Contact
             Lines},
   Journal = {Physics of Fluids, vol. 11, number 11, pages 3560-3562,
             1999},
   url = {http://ojps.aip.org/journal_cgi/getabs?KEY=PHFLE6&cvips=PHFLE6000011000011003560000001&gifs=Yes},
   Key = {fds9382}
}

@article{fds9451,
   Author = {L. Kondic and A. L. Bertozzi},
   Title = {Thin Liquid Films: Instabilities of Driven Coating Flows On
             A Rough Surface},
   Journal = {Dynamics in Small Confined Systems IV, ed. J. M. Drake, G.
             S. Grest, J. Klafter, and R. Kopelman, Materials Research
             Society Symposium Proceedings, Vol. 543, pages 213-218,
             1999.},
   Key = {fds9451}
}

@article{fds9054,
   Author = {A. Munch and A. L. Bertozzi},
   Title = {Rarefaction-Undercompressive Fonts in Driven
             Films},
   Journal = {Physics of Fluids (Letters) 11(10), pp. 2812-2814,
             1999},
   url = {http://ojps.aip.org/journal_cgi/dbt?KEY=PHFLE6&Volume=11&Issue=10},
   Key = {fds9054}
}

@article{fds9056,
   Author = {Andrea L. Bertozzi,A. Münch and M. Shearer},
   Title = {Undercompressive waves in driven thin film flow: Theory,
             Computation, and Experiment},
   Journal = {Proceedings of the Conference on Trends in Mathematical
             Physics, Knoxville, TN, Oct. 14-17, 1998. editors:
             V.Alexiades and G.Siopsis, AMS/IP Studies in Advanced
             Mathematics, Volume 13, AMS and International Press, 1999,
             pp. 43-68.},
   Key = {fds9056}
}

@article{fds8752,
   Author = {Andrea L Bertozzi and A. Munch and X. Fanton and A.M.
             Cazabat},
   Title = {Contact Line Stability and 'Undercompressive Shocks' In
             Driven Thin Film Flow},
   Journal = {Physical Review Letters, 81(23), pp. 5169-5l72. December 7,
             1998},
   url = {http://ojps.aip.org/journal_cgi/getabs?KEY=PRLTAO&cvips=PRLTAO000081000023005169000001&gifs=Yes},
   Key = {fds8752}
}

@article{fds8754,
   Author = {Andrew Bernoff and Andrea L Bertozzi and Thomas
             Witelski},
   Title = {Axisymmetric Surface Diffusion: Dynamics and Stability of
             Self-Similar Pinch-Off},
   Journal = {J. Stat. Phys., 93(3/4), November 1998, pp.
             725-776},
   Key = {fds8754}
}

@article{fds8756,
   Author = {Andrea L Bertozzi and M. Pugh},
   Title = {Long-Wave Instabilities and Saturation in Thin Film
             Equations},
   Journal = {Comm. Pur. Appl. Math., Vol. LI, pages 625-651,
             1998.},
   Key = {fds8756}
}

@article{fds8753,
   Author = {Andrea L Bertozzi},
   Title = {The Mathematics of Moving Contact Lines in Thin Liquid
             Films},
   Journal = {Notices Am. Math. Soc., 45(6), pp. 689-697, June/July
             1998},
   Key = {fds8753}
}

@article{fds8781,
   Author = {Andrea L Bertozzi and Michael Brenner},
   Title = {Linear Stability and Transient Growth in Driven Contact
             Lines},
   Journal = {Physics of Fluids 9(3) March 1997, pp. 530-539.},
   url = {http://ojps.aip.org/journal_cgi/dbt?KEY=PHFLE6&Volume=9&Issue=3},
   Key = {fds8781}
}

@article{fds8782,
   Author = {Robert Almgren and Andrea L Bertozzi and Michael
             Brenner},
   Title = {Stable and Unstable Singularities in the Unforced Hele-Shaw
             Cell},
   Journal = {Physics of Fluids 8(6), June 1996.},
   url = {http://ojps.aip.org/journal_cgi/dbt?KEY=PHFLE6&Volume=8&Issue=6},
   Key = {fds8782}
}

@article{fds8783,
   Author = {Andrea L Bertozzi},
   Title = {Lubrication Approximations for Surface Tension Driven
             Interfaces: Some Open Problems},
   Journal = {Z. angew. Math. Mech. 76(1996) S2, pp. 373-376},
   Key = {fds8783}
}

@article{fds8784,
   Author = {Andrea L Bertozzi},
   Title = {Symmetric Singularity Formation in Lubrication-Type
             Equations for Interface Motion, 34 pp},
   Journal = {SIAM J. Applied Math. Vol. 56, No. 3, pp. June 1996, pp.
             681-714},
   Key = {fds8784}
}

@article{fds8785,
   Author = {Andrea L Bertozzi and M. Pugh},
   Title = {The Lubrication Approximation for Thin Viscous Films:
             Regularity and Long Time Behavior of Weak
             Solutions},
   Journal = {Comm. Pure. Appl. Math., February, 49(2), 1996, pp.
             85-123.},
   Key = {fds8785}
}

@article{fds8786,
   Author = {A. J. Bernoff and Andrea L Bertozzi},
   Title = {Singularities in a Modified Kuramoto-Sivashinsky Equation
             Describing Interface Motion for Phase Transition},
   Journal = {Physica D 85 (1995) 375-404.},
   Key = {fds8786}
}

@article{fds8787,
   Author = {Andrea L Bertozzi},
   Title = {Loss and Gain of Regularity in a Lubrication Equation for
             Thin Viscous Films},
   Journal = {Free Boundary Problems: Theory and Applications, pp. 72-85,
             J. I. Diaz, M. Herrero, A. Linan, J. L. Vazquez,
             eds.},
   Key = {fds8787}
}

@article{fds8788,
   Author = {Andrea L Bertozzi and M. Pugh},
   Title = {The Lubrication Approximation for Thin Viscous Films: The
             Moving Contact Line with a 'Porous Media' cut off of Van der
             Waals Interactions},
   Journal = {Nonlinearity. 7(6)November, 1994, pp. 1535-64.},
   Key = {fds8788}
}

@article{fds8789,
   Author = {Andrea L Bertozzi and Michael P. Brenner and Todd F. Dupont and Leo
             P. Kadanoff},
   Title = {Singularities and Similarities in Interface
             Flows},
   Journal = {Trends and Perspectives in Applied Mathematics, pp. 155-208,
             L. Sirovich, ed. volume 100, Springer-Verlag Applied
             Mathematical Sciences, 1994.},
   Key = {fds8789}
}

@article{fds8790,
   Author = {Andrea L Bertozzi and Ashvin B. Chhabra},
   Title = {Cancellation Exponents and Fractal Scaling},
   Journal = {Phys. Rev. E., 49(5) May 1, 1994, pp. 4716-9.},
   Key = {fds8790}
}

@article{fds8791,
   Author = {Michael Brenner and Andrea L. Bertozzi},
   Title = {Spreading of Droplets on a Solid Surface},
   Journal = {Physical Review Letters, 71 No. 4 pp. 593-596, July 26,
             1993.},
   Key = {fds8791}
}

@article{fds8792,
   Author = {Andrea L Bertozzi and James McKenna},
   Title = {Multidimensional Residues, Generating Functions, and Their
             Application To Queueing Networks},
   Journal = {SIAM Review, 35, No. 2, pp. 239-268, June
             1993.},
   Key = {fds8792}
}

@article{fds8793,
   Author = {Andrea L Bertozzi and P. Constantin},
   Title = {Global Regularity for Vortex Patches},
   Journal = {Commun. Math. Phys. 152 19-28 (1993).},
   Key = {fds8793}
}

@article{fds9057,
   Author = {Andrea L. Bertozzi},
   Title = {Heteroclinic orbits and chaotic dynamics in planar fluid
             flows},
   Journal = {SIAM J. Math. Anal., vol. 19, no. 6, November 1988, pp.
             1271-1294. pp 41-76.},
   Key = {fds9057}
}


%% Bi, Zhuoxin   
@article{fds10150,
   Author = {Herbie Lee and David Higdon and Zhuoxin Bi and Marco Ferreira and Mike West},
   Title = {Markov Random Field Models for High Dimensional Parameter in
             Simulations of Fluid Flow in Porous media},
   Journal = {Accepted for publication by Technometrics,
             2001.},
   Key = {fds10150}
}

@article{fds9661,
   Author = {Zhuoxin Bi and John Trangenstein},
   Title = {Mutiscale Iterative Techniques and Adaptive Mesh Refinement
             for Miscible Displacement Simulation},
   Journal = {SPE 75232, SPE/DOE symposium on EOR},
   Key = {fds9661}
}

@article{fds9879,
   Author = {Zhuoxin Bi and John Trangenstein and Davis Higdon and Herbie
             Lee},
   Title = {Upscaling tensorial permeability field based on GMRF models
             and HMFE techniques},
   Journal = {SPE ACET 2002},
   Key = {fds9879}
}

@article{fds9877,
   Author = {Herbie Lee and David Higdon and Zhuoxin Bi},
   Title = {"A Bayesian Approach to Characterizing Uncertainty in
             Inverse Problems Using Coarse and Fine Scale
             Information,},
   Journal = {IEEE on Signal Processing},
   Key = {fds9877}
}

@article{fds9878,
   Author = {John Trangenstein and Zhuoxin Bi},
   Title = {Multiscale Iterative Techniques and Adaptive Mesh Refinement
             for flow in porous media},
   Journal = {Advances in Subsurface Hydrology},
   Key = {fds9878}
}

@article{fds9833,
   Author = {Dean Oliver and A. C. Reynolds and Zhuoxin Bi and Y.
             Abacioglu},
   Title = {Integration of Production Data into Reservoir
             Models},
   Journal = {Petroleum Geoscience, Vol. 7, S65-S73, 2001},
   Key = {fds9833}
}

@article{fds9812,
   Author = {Zhuoxin Bi and Dean Oliver and Albert Reynolds},
   Title = {Conditioning 3D Stochastic Channels to Pressure Data 3D
             Stochastic Channels to Pressure Data},
   Journal = {SPE Journal, vol. 5, No. 4, P474-484, 2000.},
   url = {http://www.spe.org},
   Key = {fds9812}
}

@article{fds9171,
   Author = {Zhuoxin Bi and Dean S. Oliver and Albert C.
             Reynolds},
   Title = {"Conditioning 3D stochastic channels to well-test pressure
             data,"},
   Journal = {SPE 56682 (1999)},
   url = {http://www.spe.org},
   Key = {fds9171}
}

@book{fds9172,
   Author = {Zhuoxin Bi},
   Title = {Production Logging Principles and Applications,Chapter
             7},
   Key = {fds9172}
}


%% Blake, Lewis D.   
@book{fds220485,
   Author = {Lewis Blake and Michael Reed},
   Title = {Laboratory Calculus (2013-2014)},
   Year = {2013},
   Month = {August},
   Key = {fds220485}
}

@book{fds212854,
   Author = {Lewis Blake and Michael Reed},
   Title = {Laboratory Calculus (2012-2013)},
   Year = {2012},
   Month = {August},
   Key = {fds212854}
}

@book{fds199105,
   Author = {Lewis Blake and Michael Reed},
   Title = {Laboratory Calculus (2011-2012)},
   Year = {2011},
   Month = {August},
   Key = {fds199105}
}

@book{fds184108,
   Author = {Lewis Blake and Michael Reed},
   Title = {Laboratory Calculus (2010-2011)},
   Year = {2010},
   Month = {August},
   Key = {fds184108}
}

@book{fds166625,
   Author = {Lewis Blake and Michael Reed},
   Title = {Laboratory Calculus, 2009-2010},
   Year = {2009},
   Month = {August},
   Key = {fds166625}
}

@book{fds152837,
   Author = {Lewis Blake and Michael Reed},
   Title = {Laboratory Calculus, 2008-2009},
   Year = {2008},
   Month = {August},
   Key = {fds152837}
}

@book{fds139615,
   Author = {Lewis Blake and Michael Reed},
   Title = {Laboratory Calculus, 2007-2008},
   Year = {2007},
   Month = {August},
   Key = {fds139615}
}

@book{fds51294,
   Author = {Lewis Blake and Michael Reed},
   Title = {Laboratory Calculus, 2006-2007},
   Year = {2006},
   Month = {June},
   Key = {fds51294}
}

@book{fds43976,
   Author = {Michael Reed},
   Title = {Laboratory Calculus, 2005-2006},
   Year = {2005},
   Key = {fds43976}
}

@book{fds28801,
   Author = {L.D. Blake and Michael Reed},
   Title = {Laboratory Calculus, 2004-2005},
   Year = {2004},
   Month = {Summer},
   Key = {fds28801}
}

@book{fds16194,
   Author = {Lewis D. Blake  and Michael Reed},
   Title = {Laboratory Calculus, 2003-2004},
   Year = {2003},
   Key = {fds16194}
}

@article{fds325140,
   Author = {Bookman, J and Blake, L},
   Title = {SEVEN YEARS OF PROJECT CALC AT DUKE UNIVERSITY APPROACHING
             STEADY STATE?*},
   Journal = {PRIMUS},
   Volume = {6},
   Number = {3},
   Pages = {221-234},
   Year = {1996},
   Month = {January},
   url = {http://dx.doi.org/10.1080/10511979608965825},
   Doi = {10.1080/10511979608965825},
   Key = {fds325140}
}

@book{fds10401,
   Author = {Lewis D. Blake and Michael Reed},
   Title = {Laboratory Calculus, 2001-2002},
   Key = {fds10401}
}

@book{fds9689,
   Author = {Lewis D. Blake and Michael Reed},
   Title = {Laboratory Calculus, 2000-2001},
   Journal = {John Wiley & Sons, Inc.},
   Key = {fds9689}
}

@book{fds9169,
   Author = {Lewis D. Blake and Michael Reed},
   Title = {Laboratory Calculus, 1999-2000},
   Journal = {John Wiley & Sons, Inc.},
   Key = {fds9169}
}

@book{fds9170,
   Author = {Lewis D. Blake and Michael Reed},
   Title = {Laboratory Calculus 1998-1999},
   Journal = {John Wiley & Sons, Inc},
   Key = {fds9170}
}

@book{fds9168,
   Author = {Lewis D. Blake and Lawrence Moore and David Smith},
   Title = {HP48 and HP48GX Calculator Laboratory Manual},
   Journal = {D.C. Heath and Company},
   Key = {fds9168}
}


%% Bobrowski, Omer   
@article{fds311845,
   Author = {O Bobrowski and M Kahle and P Skraba},
   Title = {Maximally Persistent Cycles in Random Geometric
             Complexes},
   Year = {2015},
   Month = {September},
   url = {http://arxiv.org/abs/1509.04347v2},
   Abstract = {We initiate the study of persistent homology of random
             geometric simplicial complexes. Our main interest is in
             maximally persistent cycles of degree-$k$ in persistent
             homology, for a either the \cech or the Vietoris--Rips
             filtration built on a uniform Poisson process of intensity
             $n$ in the unit cube $[0,1]^d$. This is a natural way of
             measuring the largest "$k$-dimensional hole" in a random
             point set. This problem is in the intersection of geometric
             probability and algebraic topology, and is naturally
             motivated by a probabilistic view of topological inference.
             We show that for all $d \ge 2$ and $1 \le k \le d-1$ the
             maximally persistent cycle has (multiplicative) persistence
             of order $$ \Theta \left(\left(\frac{\log n}{\log \log n}
             \right)^{1/k} \right),$$ with high probability,
             characterizing its rate of growth as $n \to \infty$. The
             implied constants depend on $k$, $d$, and on whether we
             consider the Vietoris--Rips or \cech filtration.},
   Key = {fds311845}
}

@article{fds311846,
   Author = {O Bobrowski and S Weinberger},
   Title = {On the Vanishing of Homology in Random Čech
             Complexes},
   Year = {2015},
   Month = {July},
   url = {http://arxiv.org/abs/1507.06945v2},
   Abstract = {We compute the homology of random \v{C}ech complexes over a
             homogeneous Poisson process on the d-dimensional torus, and
             show that there are, coarsely, two phase transitions. The
             first transition is analogous to the Erd\H{o}s-R\'enyi phase
             transition, where the \v{C}ech complex becomes connected.
             The second transition is where all the other homology groups
             are computed correctly (almost simultaneously). Our
             calculations also suggest a finer measurement of scales,
             where there is a further refinement to this picture and
             separation between different homology groups.},
   Key = {fds311846}
}

@article{fds225071,
   Author = {O. Bobrowski and S. Mukherjee},
   Title = {The Topology of Probability Distributions on
             Manifolds},
   Journal = {Probability Theory and Related Fields},
   Volume = {161},
   Number = {3-4},
   Pages = {651-686},
   Year = {2015},
   url = {http://dx.doi.org/10.1007/s00440-014-0556-x},
   Doi = {10.1007/s00440-014-0556-x},
   Key = {fds225071}
}

@article{fds243368,
   Author = {RJ Adler and O Bobrowski and S Weinberger},
   Title = {Crackle: The Homology of Noise},
   Journal = {Discrete & Computational Geometry},
   Volume = {52},
   Number = {4},
   Pages = {680-704},
   Year = {2014},
   Month = {December},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/s00454-014-9621-6},
   Doi = {10.1007/s00454-014-9621-6},
   Key = {fds243368}
}

@article{fds311847,
   Author = {O Bobrowski and M Kahle},
   Title = {Topology of random geometric complexes: a
             survey},
   Journal = {Topology in Statistical Inference, the Proceedings of
             Symposia in Applied Mathematics},
   Year = {2014},
   Month = {September},
   url = {http://arxiv.org/abs/1409.4734v1},
   Abstract = {In this expository article, we survey the rapidly emerging
             area of random geometric simplicial complexes.},
   Key = {fds311847}
}

@article{fds311848,
   Author = {O Bobrowski and S Mukherjee and JE Taylor},
   Title = {Topological Consistency via Kernel Estimation},
   Journal = {Bernoulli},
   Year = {2014},
   Month = {July},
   url = {http://arxiv.org/abs/1407.5272v3},
   Abstract = {We introduce a consistent estimator for the homology (an
             algebraic structure representing connected components and
             cycles) of level sets of both density and regression
             functions. Our method is based on kernel estimation. We
             apply this procedure to two problems: 1) inferring the
             homology structure of manifolds from noisy observations, 2)
             inferring the persistent homology (a multi-scale extension
             of homology) of either density or regression functions. We
             prove consistency for both of these problems. In addition to
             the theoretical results we demonstrate these methods on
             simulated data for binary regression and clustering
             applications.},
   Key = {fds311848}
}

@article{fds287059,
   Author = {RJ Adler and O Bobrowski and S Weinberger},
   Title = {Crackle: The Homology of Noise},
   Journal = {Discrete and Computational Geometry},
   Volume = {52},
   Number = {4},
   Pages = {680-704},
   Year = {2014},
   Month = {January},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/s00454-014-9621-6},
   Abstract = {© 2014, Springer Science+Business Media New York.We study
             the homology of simplicial complexes built via deterministic
             rules from a random set of vertices. In particular, we show
             that, depending on the randomness that generates the
             vertices, the homology of these complexes can either become
             trivial as the number n of vertices grows, or can contain
             more and more complex structures. The different behaviours
             are consequences of different underlying distributions for
             the generation of vertices, and we consider three
             illustrative examples, when the vertices are sampled from
             Gaussian, exponential, and power-law distributions in Rd. We
             also discuss consequences of our results for manifold
             learning with noisy data, describing the topological
             phenomena that arise in this scenario as “crackle”, in
             analogy to audio crackle in temporal signal
             analysis.},
   Doi = {10.1007/s00454-014-9621-6},
   Key = {fds287059}
}

@article{fds305509,
   Author = {O Bobrowski and S Mukherjee},
   Title = {The Topology of Probability Distributions on
             Manifolds},
   Journal = {arxiv},
   Year = {2013},
   Month = {July},
   url = {http://arxiv.org/abs/1307.1123v2},
   Abstract = {Let $P$ be a set of $n$ random points in $R^d$, generated
             from a probability measure on a $m$-dimensional manifold $M
             \subset R^d$. In this paper we study the homology of
             $U(P,r)$ -- the union of $d$-dimensional balls of radius $r$
             around $P$, as $n \to \infty$, and $r \to 0$. In addition we
             study the critical points of $d_P$ -- the distance function
             from the set $P$. These two objects are known to be related
             via Morse theory. We present limit theorems for the Betti
             numbers of $U(P,r)$, as well as for number of critical
             points of index $k$ for $d_P$. Depending on how fast $r$
             decays to zero as $n$ grows, these two objects exhibit
             different types of limiting behavior. In one particular case
             ($n r^m > C \log n$), we show that the Betti numbers of
             $U(P,r)$ perfectly recover the Betti numbers of the original
             manifold $M$, a result which is of significant interest in
             topological manifold learning.},
   Key = {fds305509}
}

@article{fds311850,
   Author = {RJ Adler and O Bobrowski and S Weinberger},
   Title = {Crackle: The Persistent Homology of Noise},
   Year = {2013},
   Month = {January},
   url = {http://arxiv.org/abs/1301.1466v1},
   Abstract = {We study the homology of simplicial complexes built via
             deterministic rules from a random set of vertices. In
             particular, we show that, depending on the randomness that
             generates the vertices, the homology of these complexes can
             either become trivial as the number $n$ of vertices grows,
             or can contain more and more complex structures. The
             different behaviours are consequences of different
             underlying distributions for the generation of vertices, and
             we consider three illustrative examples, when the vertices
             are sampled from Gaussian, exponential, and power-law
             distributions in $\R^d$. We also discuss consequences of our
             results for manifold learning with noisy data, describing
             the topological phenomena that arise in this scenario as
             `crackle', in analogy to audio crackle in temporal signal
             analysis.},
   Key = {fds311850}
}

@article{fds243371,
   Author = {O Bobrowski and MS Borman},
   Title = {Euler integration of Gaussian random fields and persistent
             homology},
   Journal = {Journal of Topology and Analysis},
   Volume = {4},
   Number = {1},
   Pages = {49-70},
   Year = {2012},
   ISSN = {1793-5253},
   url = {http://dx.doi.org/10.1142/S1793525312500057},
   Abstract = {In this paper we extend the notion of the Euler
             characteristic to persistent homology and give the
             relationship between the Euler integral of a function and
             the Euler characteristic of the function's persistent
             homology. We then proceed to compute the expected Euler
             integral of a Gaussian random field using the Gaussian
             kinematic formula and obtain a simple closed form
             expression. This results in the first explicitly computable
             mean of a quantitative descriptor for the persistent
             homology of a Gaussian random field. © 2012 World
             Scientific Publishing Company.},
   Doi = {10.1142/S1793525312500057},
   Key = {fds243371}
}

@article{fds305510,
   Author = {O Bobrowski and RJ Adler},
   Title = {Distance Functions, Critical Points, and the Topology of
             Random Čech Complexes},
   Journal = {arxiv},
   Volume = {16},
   Number = {2},
   Pages = {311-344},
   Year = {2011},
   Month = {July},
   url = {http://arxiv.org/abs/1107.4775v2},
   Abstract = {For a finite set of points $P$ in $R^d$, the function $d_P:
             R^d \to R^+$ measures Euclidean distance to the set $P$. We
             study the number of critical points of $d_P$ when $P$ is a
             Poisson process. In particular, we study the limit behavior
             of $N_k$ - the number of critical points of $d_P$ with Morse
             index $k$ - as the density of points grows. We present
             explicit computations for the normalized, limiting,
             expectations and variances of the $N_k$, as well as
             distributional limit theorems. We link these results to
             recent results in which the Betti numbers of the random
             \v{C}ech complex based on $P$ were studied.},
   Doi = {http://dx.doi.org/10.4310/HHA.2014.v16.n2.a18},
   Key = {fds305510}
}

@article{fds311849,
   Author = {RJ Adler and O Bobrowski and MS Borman and E Subag and S
             Weinberger},
   Title = {Persistent Homology for Random Fields and
             Complexes},
   Journal = {IMS Collections},
   Volume = {6},
   Pages = {124-143},
   Booktitle = {IMS Collections},
   Year = {2010},
   Month = {March},
   url = {http://arxiv.org/abs/1003.1001v2},
   Abstract = {We discuss and review recent developments in the area of
             applied algebraic topology, such as persistent homology and
             barcodes. In particular, we discuss how these are related to
             understanding more about manifold learning from random point
             cloud data, the algebraic structure of simplicial complexes
             determined by random vertices, and, in most detail, the
             algebraic topology of the excursion sets of random
             fields.},
   Doi = {10.1214/10-IMSCOLL609},
   Key = {fds311849}
}

@article{fds243370,
   Author = {O Bobrowski and R Meir and YC Eldar},
   Title = {Bayesian filtering in spiking neural networks: noise,
             adaptation, and multisensory integration.},
   Journal = {Neural Comput},
   Volume = {21},
   Number = {5},
   Pages = {1277-1320},
   Year = {2009},
   Month = {May},
   ISSN = {0899-7667},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/19018706},
   Abstract = {A key requirement facing organisms acting in uncertain
             dynamic environments is the real-time estimation and
             prediction of environmental states, based on which effective
             actions can be selected. While it is becoming evident that
             organisms employ exact or approximate Bayesian statistical
             calculations for these purposes, it is far less clear how
             these putative computations are implemented by neural
             networks in a strictly dynamic setting. In this work, we
             make use of rigorous mathematical results from the theory of
             continuous time point process filtering and show how optimal
             real-time state estimation and prediction may be implemented
             in a general setting using simple recurrent neural networks.
             The framework is applicable to many situations of common
             interest, including noisy observations, non-Poisson spike
             trains (incorporating adaptation), multisensory integration,
             and state prediction. The optimal network properties are
             shown to relate to the statistical structure of the
             environment, and the benefits of adaptation are studied and
             explicitly demonstrated. Finally, we recover several
             existing results as appropriate limits of our general
             setting.},
   Doi = {10.1162/neco.2008.01-08-692},
   Key = {fds243370}
}

@article{fds243369,
   Author = {O Bobrowski and R Meir and S Shoham and YC Eldar},
   Title = {A neural network implementing optimal state estimation based
             on dynamic spike train decoding},
   Journal = {Advances in Neural Information Processing Systems 20 -
             Proceedings of the 2007 Conference},
   Volume = {145-152},
   Booktitle = {Advances in Neural Information Processing Systems (NIPS)
             20},
   Year = {2009},
   url = {http://oldbooks.nips.cc/papers/files/nips20/NIPS2007_0454.pdf},
   Abstract = {It is becoming increasingly evident that organisms acting in
             uncertain dynamical environments often employ exact or
             approximate Bayesian statistical calculations in order to
             continuously estimate the environmental state, integrate
             information from multiple sensory modalities, form
             predictions and choose actions. What is less clear is how
             these putative computations are implemented by cortical
             neural networks. An additional level of complexity is
             introduced because these networks observe the world through
             spike trains received from primary sensory afferents, rather
             than directly. A recent line of research has described
             mechanisms by which such computations can be implemented
             using a network of neurons whose activity directly
             represents a probability distribution across the possible
             "world states". Much of this work, however, uses various
             approximations, which severely restrict the domain of
             applicability of these implementations. Here we make use of
             rigorous mathematical results from the theory of continuous
             time point process filtering, and show how optimal real-time
             state estimation and prediction may be implemented in a
             general setting using linear neural networks. We demonstrate
             the applicability of the approach with several examples, and
             relate the required network properties to the statistical
             nature of the environment, thereby quantifying the
             compatibility of a given network with its
             environment.},
   Key = {fds243369}
}


%% Bookman, Jack   
@article{fds303524,
   Author = {Bookman, J},
   Title = {Why �False Implies False" is True - a Discovery
             Explanation},
   Journal = {The Mathematics Teacher 71 (November 1978):
             675-676.},
   Year = {2014},
   Month = {December},
   Key = {fds303524}
}

@article{fds303525,
   Author = {Bookman, J and Smith, DA},
   Title = {A Review of �The Electronic Study Guide: Precalculus
             Algebra},
   Journal = {College Mathematics Journal, June 1985},
   Year = {2014},
   Month = {December},
   Key = {fds303525}
}

@article{fds303526,
   Author = {Bookman, J},
   Title = {NSF Workshop on Assessment in Calculus Curriculum Reform
             Efforts},
   Journal = {UME Trends, October, 1992},
   Year = {2014},
   Month = {December},
   Key = {fds303526}
}

@article{fds303527,
   Author = {Bookman, J},
   Title = {Evaluation of Calculus Reform at Duke University},
   Journal = {UME Trends, March 1992},
   Year = {2014},
   Month = {December},
   Key = {fds303527}
}

@article{fds303528,
   Author = {Bookman, J and Friedman, C},
   Title = {A Comparison of the Problem Solving Performance of Students
             in Lab Based and Traditional Calculus},
   Journal = {in Dubinsky, E., Schoenfeld, A.H., Kaput, J. (Ed) Research
             in Collegiate Mathematics Education I. , Providence, RI:
             American Mathematical Society, 1994, pp.
             101-116.},
   Year = {2014},
   Month = {December},
   Key = {fds303528}
}

@article{fds303529,
   Author = {Smith, D and Bookman, J},
   Title = {Assessment in a Technological Age},
   Journal = {Proceedings of the Seventh Annual International Conference
             on Technology in Collegiate Mathematics (1996)
             Addison-Wesley 433-437},
   Year = {2014},
   Month = {December},
   Key = {fds303529}
}

@article{fds303531,
   Author = {Bookman, J},
   Title = {There’s Glory For You! - Why We Define Mathematical Terms
             The Way We Do},
   Journal = {Centroid, Spring 1996, 36-39},
   Year = {2014},
   Month = {December},
   Key = {fds303531}
}

@article{fds303532,
   Author = {Bookman, J and Friedman, C},
   Title = {Student Attitudes and Calculus Reform},
   Journal = {School Science and Mathematics, March 1998:
             117-122},
   Year = {2014},
   Month = {December},
   Key = {fds303532}
}

@article{fds303533,
   Author = {Bookman, J and Friedman, C},
   Title = {The Evaluation of Project CALC at Duke University 1989 -
             1994},
   Journal = {in B. Gold, S. Keith, W. Marion, eds., Assessment Practices
             in Undergraduate Mathematics, MAA Notes # 49, Washington DC:
             Mathematical Association of America, 1999: pp.
             253-256.},
   Year = {2014},
   Month = {December},
   Key = {fds303533}
}

@article{fds303534,
   Author = {Bookman, J},
   Title = {Program Evaluation and Undergraduate Mathematics Renewal:
             The impact of calculus reform on student performance in
             subsequent courses},
   Journal = {in Ganter, S. (Ed.) Calculus Renewal: Issues for
             Undergraduate Mathematics Education in the Next Decade, New
             York, NY: Plenum Press, 2000: pp.91 - 102},
   Year = {2014},
   Month = {December},
   Key = {fds303534}
}

@article{fds303535,
   Author = {Bookman, J},
   Title = {Duke University’s Mathematics Department Outreach to
             Secondary Mathematics Teachers: Problems, Potential, and
             Pitfalls},
   Journal = {Conference proceedings from the Invitational Conference on
             K-12 Outreach from University Science Departments, Raleigh,
             NC: North Carolina State University, 2000: pp.143 -
             145},
   Year = {2014},
   Month = {December},
   Key = {fds303535}
}

@article{fds303536,
   Author = {Bookman, J},
   Title = {Learning Mathematics Meaningfully � A Challenge to College
             Faculty},
   Journal = {Proceedings of First Annual Charleston Connections:
             Innovations in Higher Education Conference, Charleston, SC:
             The Citadel, 2001: pp.92 - 100},
   Year = {2014},
   Month = {December},
   Key = {fds303536}
}

@article{fds296254,
   Author = {Narayan, AP and Whicker, SA and Staples, B and Bookman, J and Bartlett,
             K and McGann, KA},
   Title = {The Clinical Skills Fair - An Innovative Curriculum
             Evaluation Tool},
   Journal = {Journal of Graduate Medical Education},
   Year = {2013},
   Month = {April},
   Key = {fds296254}
}

@article{fds296253,
   Author = {Bookman, and Bar-On, R and Cooke, B and Schott, S},
   Title = {(Re)discovering SoTL through a Fundamental Challenge:
             Helping Students Transition to College Calculus},
   Journal = {MAA Notes: Guide to the Scholarship of Teaching and Learning
             in Mathematics},
   Year = {2012},
   Month = {October},
   Key = {fds296253}
}

@article{fds296260,
   Author = {Lardner, ED and Bookman, J},
   Title = {Lessons Learned in Interdisciplinary Professional
             Development Designed to Promote the Teaching of Quantitative
             Literacy},
   Journal = {Journal of Faculty Development},
   Volume = {27},
   Number = {2},
   Year = {2012},
   Key = {fds296260}
}

@article{fds296257,
   Author = {Varsavsky, C and Waldock, J and Harding, A and Jack Bookman and LS and Luaces, VM},
   Title = {Undergraduate mathematics around the world},
   Journal = {Delta Communications, conference proceedings of the Volcanic
             Delta ’11, the eighth Delta conference on the teaching and
             learning of undergraduate mathematics and
             statistics},
   Year = {2011},
   Key = {fds296257}
}

@article{fds296258,
   Author = {Turner, DA and Narayan, AP and Whicker, SA and Bookman, J and McGann,
             KA},
   Title = {Do pediatric residents prefer interactive learning?
             Educational challenges in the duty hours
             era.},
   Journal = {Medical Teacher (Informa)},
   Volume = {33},
   Number = {6},
   Pages = {494-496},
   Year = {2011},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/21355697},
   Abstract = {BACKGROUND: The volume of information that physicians must
             learn is increasing; yet, trainee educational time is
             limited. Many experts propose using trainees' learning
             preferences to guide teaching. However, data regarding
             predominant learning preferences within pediatrics are
             limited. AIM: Identify predominant learning preferences
             among pediatric residents in a Residency Training Program.
             METHODS: The Visual-Aural-Read/Write-Kinesthetic (VARK)
             questionnaire and Kolb Learning Style Inventory (LSI) were
             administered anonymously to 50 pediatric residents. RESULTS:
             Learning style assessments were completed by 50 pediatric
             residents. Residents were significantly more likely to be
             accommodating on the Kolb LSI, which is consistent with an
             interactive learning preference (p < 0.01); 30%
             demonstrated a multimodal preference on the Kolb LSI (Figure
             1). VARK assessments demonstrated that 45 (90%) respondents
             were kinesthetic, which is also consistent with a
             significant preference for interactive learning
             (p < 0.01). Forty (80%) were found to be multimodal on
             the VARK (Figure 1). There was no association between
             learning preference and the residents' anticipated career
             choice or level of training. CONCLUSIONS: The predominant
             learning preferences among a cohort of pediatric residents
             from a single training program were consistent with a
             preference for interactive learning, suggesting that some
             trainees may benefit from supplementation of educational
             curricula with additional interactive experiences. Continued
             investigation is needed in this area to assess the
             effectiveness of adapting teaching techniques to individual
             learning preferences.},
   Doi = {10.3109/0142159X.2010.542524},
   Key = {fds296258}
}

@article{fds296259,
   Author = {Alison Sweeney, MD and Alyssa Stephany, MD and Shari Whicker and M and Jack Bookman and P and David A Turner, MD},
   Title = {"Resident Educators" - Senior Pediatric Residents as
             Teachers for an Innovative Multidisciplinary Mock Code
             Curriculum},
   Journal = {Journal of Graduate Medical Education},
   Volume = {3},
   Number = {2},
   Pages = {188-195},
   Year = {2011},
   Key = {fds296259}
}

@article{fds296261,
   Author = {Bookman, J and Ganter, SL and Morgan, R},
   Title = {Developing Assessment Methodologies for Quantitative
             Literacy: A Formative Study},
   Journal = {American Mathematical Monthly},
   Volume = {115},
   Number = {10},
   Pages = {911-929},
   Year = {2008},
   Month = {December},
   ISSN = {0002-9890},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000261592600004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Key = {fds296261}
}

@article{fds296262,
   Author = {Bookman, J and Malone, D},
   Title = {Negotiating Roles and Meaning While Learning Mathematics in
             Interactive Technology-Rich Environments},
   Journal = {The Journal of the Scholarship of Teaching and
             Learning},
   Volume = {6},
   Number = {2},
   Pages = {41-65},
   Year = {2006},
   Month = {October},
   Key = {fds296262}
}

@article{fds296256,
   Author = {Bookman, J and Malone, D},
   Title = {The Nature of Learning in Interactive Technological
             Environments: A Proposal for a Research Agenda Based on
             Grounded Theory},
   Journal = {Research in Collegiate Mathematics Education},
   Editor = {edited by Selden, A. and Dubinsky, E. and Harel, G. and Hitt,
             F.},
   Year = {2003},
   Key = {fds296256}
}

@article{fds296255,
   Author = {Winter, D and Lemons, P and Bookman, J and Hoese,
             W},
   Title = {Novice Instructors and Student-Centered Instruction:
             Identifying and Addressing Obstacles to Learning in the
             College Science Laboratory},
   Journal = {Journal of Scholarship of Teaching and Learning},
   Volume = {2},
   Number = {1},
   Year = {2001},
   Key = {fds296255}
}

@article{fds303530,
   Author = {Bookman, J and Blake, L},
   Title = {SEVEN YEARS OF PROJECT CALC AT DUKE UNIVERSITY APPROACHING
             STEADY STATE?*},
   Journal = {PRIMUS},
   Volume = {6},
   Number = {3},
   Pages = {221-234},
   Year = {1996},
   Month = {January},
   url = {http://dx.doi.org/10.1080/10511979608965825},
   Doi = {10.1080/10511979608965825},
   Key = {fds303530}
}

@article{fds303010,
   Author = {Bookman, J},
   Title = {AN EXPERT NOVICE STUDY OF METACOGNITIVE BEHAVIOR IN FOUR
             TYPES OF MATHEMATICS PROBLEMS*},
   Journal = {PRIMUS},
   Volume = {3},
   Number = {3},
   Pages = {284-314},
   Year = {1993},
   Month = {January},
   ISSN = {1051-1970},
   url = {http://dx.doi.org/10.1080/10511979308965710},
   Doi = {10.1080/10511979308965710},
   Key = {fds303010}
}

@article{fds325014,
   Author = {BOOKMAN, J and SMITH, D},
   Title = {THE ELECTRONIC STUDY GUIDE - PRE-CALCULUS
             ALGEBRA},
   Volume = {16},
   Number = {3},
   Pages = {218-221},
   Year = {1985},
   url = {http://dx.doi.org/10.2307/2686577},
   Doi = {10.2307/2686577},
   Key = {fds325014}
}


%% Bouvrie, Jake   
@proceedings{fds208779,
   Author = {J. Bouvrie and B. Hamzi},
   Title = {Empirical Estimators for Stochastically Forced Nonlinear
             Systems: Observability, Controllability and the Invariant
             Measure},
   Booktitle = {Proc. American Control Conference (ACC)},
   Year = {2012},
   Key = {fds208779}
}

@article{fds208780,
   Author = {M. Raginsky and J. Bouvrie},
   Title = {Continuous-Time Stochastic Mirror Descent on a Network:
             Variance Reduction, Consensus, Convergence},
   Booktitle = {Proc. IEEE Conference on Decision and Control
             (CDC)},
   Year = {2012},
   Key = {fds208780}
}

@article{fds208781,
   Author = {J. Bouvrie and M. Maggioni},
   Title = {Geometric Multiscale Reduction for Autonomous and Controlled
             Nonlinear Systems},
   Booktitle = {Proc. IEEE Conference on Decision and Control
             (CDC)},
   Year = {2012},
   Key = {fds208781}
}

@article{fds208783,
   Author = {J. Bouvrie and J.-J.E. Slotine},
   Title = {Synchronization can Control Regularization in Neural Systems
             via Correlated Noise Processes},
   Booktitle = {Proc. Advances in Neural Information Processing Systems
             (NIPS) 25},
   Year = {2012},
   Key = {fds208783}
}

@article{fds208784,
   Author = {J. Bouvrie and M. Maggioni},
   Title = {Efficient Solution of Markov Decision Problems with
             Multiscale Representations},
   Booktitle = {Proc. 50th Annual Allerton Conference on Communication,
             Control, and Computing},
   Year = {2012},
   Key = {fds208784}
}

@article{fds199215,
   Author = {J. Bouvrie and J.-J. E. Slotine},
   Title = {Synchronization and Redundancy: Implications for Robustness
             of Neural Learning and Decision Making},
   Journal = {Neural Computation},
   Volume = {23},
   Number = {11},
   Pages = {2915-2941},
   Year = {2011},
   ISSN = {0899-7667},
   Key = {fds199215}
}

@misc{fds184200,
   Author = {J. Bouvrie and T. Poggio and L. Rosasco and S. Smale and A.
             Wibisono},
   Title = {Generalization and Properties of the Neural
             Response},
   Journal = {MIT-CSAIL Tech Report TR-2010-051/CBCL-292},
   Publisher = {Massachusetts Institute of Technology},
   Year = {2010},
   Month = {November},
   Key = {fds184200}
}

@misc{fds184199,
   Author = {A. Wibisono and J. Bouvrie and L. Rosasco and T.
             Poggio},
   Title = {Learning and Invariance in a Family of Hierarchical
             Kernels},
   Journal = {MIT CSAIL Tech Report MIT-CSAIL-TR-2010-035/CBCL Paper
             290},
   Publisher = {Massachusetts Institute of Technology},
   Year = {2010},
   Month = {July},
   Key = {fds184199}
}

@article{fds184196,
   Author = {J. Bouvrie and B. Hamzi},
   Title = {Balanced Reduction of Nonlinear Control Systems in
             Reproducing Kernel Hilbert Space},
   Booktitle = {Proc. 48th Annual Allerton Conference on Communication,
             Control, and Computing},
   Year = {2010},
   Key = {fds184196}
}

@article{Smale:FOCM:09,
   Author = {S. Smale and L. Rosasco and J. Bouvrie and A. Caponnetto and T. Poggio},
   Title = {Mathematics of the Neural Response},
   Journal = {J. Found. Comput. Math.},
   Year = {2009},
   Month = {June},
   Key = {Smale:FOCM:09}
}

@inproceedings{Bouvrie:NIPS:09,
   Author = {J. Bouvrie and L. Rosasco and T. Poggio},
   Title = {On Invariance in Hierarchical Models},
   Booktitle = {Advances in Neural Information Processing Systems (NIPS)
             22},
   Year = {2009},
   Key = {Bouvrie:NIPS:09}
}

@inproceedings{Bouvrie:ICASSP:08,
   Author = {J. Bouvrie and T. Ezzat and T. Poggio},
   Title = {Localized Spectro-Temporal Cepstral Analysis of
             Speech},
   Booktitle = {IEEE International Conference on Acoustics, Speech, and
             Signal Processing},
   Year = {2008},
   Key = {Bouvrie:ICASSP:08}
}

@inproceedings{Ezzat:ICSLP:07,
   Author = {T. Ezzat and J. Bouvrie and T. Poggio},
   Title = {Spectro-Temporal Analysis of Speech Using 2-D Gabor
             Filters},
   Booktitle = {International Conference on Spoken Language Processing
             (Interspeech)},
   Year = {2007},
   Key = {Ezzat:ICSLP:07}
}

@inproceedings{Knoblich:WImBI:06,
   Author = {U. Knoblich and J. Bouvrie and T. Poggio},
   Title = {Biophysical Models of Neural Computation: Max and Tuning
             Circuits},
   Volume = {4845},
   Series = {Lecture Notes in Artificial Intelligence},
   Booktitle = {Web Intelligence Meets Brain Informatics (WImBI
             2006)},
   Publisher = {Springer},
   Year = {2007},
   Key = {Knoblich:WImBI:06}
}

@inproceedings{Ezzat:ICASSP:07,
   Author = {T. Ezzat and J. Bouvrie and T. Poggio},
   Title = {AM-FM Demodulation of Spectrograms Using Localized 2D
             Max-Gabor Analysis},
   Booktitle = {IEEE International Conference on Acoustics, Speech, and
             Signal Processing},
   Year = {2007},
   Key = {Ezzat:ICASSP:07}
}

@article{Bouvrie:Neucom:07,
   Author = {J. Bouvrie and P. Sinha},
   Title = {Visual object concept discovery: Observations in
             congenitally blind children, and a computational
             approach},
   Journal = {Neurocomputing},
   Volume = {70},
   Number = {13},
   Pages = {2218--2233},
   Year = {2007},
   Key = {Bouvrie:Neucom:07}
}

@inproceedings{rif07,
   Author = {R. Rifkin and K. Schutte and D. Saad and J. Bouvrie and J.
             Glass},
   Title = {Noise Robust Phonetic Classification with Linear Regularized
             Least Squares and Second-Order Features},
   Booktitle = {IEEE International Conference on Acoustics, Speech, and
             Signal Processing},
   Year = {2007},
   Key = {rif07}
}

@techreport{Rifkin:MEMO:ModelPhoneme,
   Author = {R. Rifkin and J.Bouvrie and K. Schutte and S. Chikkerur and M. Kouh and T. Ezzat and T. Poggio},
   Title = {Phonetic Classification Using Hierarchical, Feed-forward,
             Spectro-temporal Patch-based Architectures},
   Organization = {Massachusetts Institute of Technology},
   Institution = {Massachusetts Institute of Technology},
   Address = {Cambridge, MA},
   Year = {2007},
   Key = {Rifkin:MEMO:ModelPhoneme}
}

@inproceedings{Bouvrie:ICSLP:06,
   Author = {J. Bouvrie and T. Ezzat},
   Title = {An Incremental Algorithm for Signal Reconstruction from
             Short-Time Fourier Transform Magnitude},
   Booktitle = {International Conference on Spoken Language Processing
             (Interspeech)},
   Year = {2006},
   Key = {Bouvrie:ICSLP:06}
}

@inproceedings{Ezzat:ICSLP:06,
   Author = {T. Ezzat and J. Bouvrie and T. Poggio},
   Title = {Max-Gabor Analysis and Synthesis of Spectrograms},
   Booktitle = {International Conference on Spoken Language Processing
             (Interspeech)},
   Year = {2006},
   Key = {Ezzat:ICSLP:06}
}


%% Bouzarth, Elizabeth L.   
@article{fds172887,
   Author = {E.L. Bouzarth and M.L. Minion},
   Title = {A multirate time integrator for regularized
             Stokeslets},
   Journal = {Journal of Computational Physics},
   Volume = {229},
   Number = {11},
   Pages = {4208-4224},
   Year = {2010},
   Month = {June},
   url = {http://dx.doi.org/doi:10.1016/j.jcp.2010.02.006},
   Abstract = {The method of regularized Stokeslets is a numerical approach
             to approximating solutions of fluid–structure interaction
             problems in the Stokes regime. Regularized Stokeslets are
             fundamental solutions to the Stokes equations with a
             regularized point-force term that are used to represent
             forces generated by a rigid or elastic object interacting
             with the fluid. Due to the linearity of the Stokes
             equations, the velocity at any point in the fluid can be
             computed by summing the contributions of regularized
             Stokeslets, and the time evolution of positions can be
             computed using standard methods for ordinary differential
             equations. Rigid or elastic objects in the flow are usually
             treated as immersed boundaries represented by a collection
             of regularized Stokeslets coupled together by virtual
             springs which determine the forces exerted by the boundary
             in the fluid. For problems with boundaries modeled by
             springs with large spring constants, the resulting ordinary
             differential equations become stiff, and hence the time step
             for explicit time integration methods is severely
             constrained. Unfortunately, the use of standard implicit
             time integration methods for the method of regularized
             Stokeslets requires the solution of dense nonlinear systems
             of equations for many relevant problems. Here, an alternate
             strategy using an explicit multirate time integration scheme
             based on spectral deferred corrections is incorporated that
             in many cases can significantly decrease the computational
             cost of the method. The multirate methods are higher-order
             methods that treat different portions of the ODE explicitly
             with different time steps depending on the stiffness of each
             component. Numerical examples on two nontrivial
             three-dimensional problems demonstrate the increased
             efficiency of the multi-explicit approach with no
             significant increase in numerical error.},
   Doi = {doi:10.1016/j.jcp.2010.02.006},
   Key = {fds172887}
}

@article{fds181414,
   Author = {E.L. Bouzarth and A.T. Layton and Y.-N. Young},
   Title = {Modeling a Semi-Flexible Filament in Cellular Stokes Flow
             Using Regularized Stokeslets},
   Year = {2010},
   Key = {fds181414}
}

@article{fds181416,
   Author = {E.L. Bouzarth and M.L. Minion},
   Title = {Modeling Non-Slender Bodies with the Method of Regularized
             Stokeslets},
   Year = {2010},
   Key = {fds181416}
}

@article{fds181417,
   Author = {E.L. Bouzarth and M.L. Minion},
   Title = {Modeling Slender Bodies with the Method of Regularized
             Stokeslets},
   Year = {2010},
   Key = {fds181417}
}

@misc{fds166442,
   Author = {E.L. Bouzarth},
   Title = {Regularized Singularities and Spectral Deferred Correction
             Methods: A Mathematical Study of Numerically Modeling Stokes
             Fluid Flow},
   Year = {2008},
   url = {http://search.lib.unc.edu/search?R=UNCb5803305},
   Key = {fds166442}
}

@article{fds166441,
   Author = {E.L. Bouzarth and A. Brooks and R. Camassa and H. Jing and T.J.
             Leiterman, R.M. McLaughlin and R. Superfine and J. Toledo and L.
             Vicci.},
   Title = {Epicyclic orbits in a viscous fluid about a precessing rod:
             Theory and experiments at the micro and macro
             scales},
   Journal = {Physical Review E},
   Volume = {76},
   Pages = {016313},
   Year = {2007},
   url = {http://dx.doi.org/10.1103/PhysRevE.76.016313},
   Abstract = {We present experimental observations and quantified
             theoretical predictions of the nanoscale hydrodynamics
             induced by nanorod precession emulating primary cilia motion
             in developing embryos. We observe phenomena including micron
             size particles which exhibit epicyclic orbits with coherent
             fluctuations distinguishable from comparable amplitude
             thermal noise. Quantifying the mixing and transport physics
             of such motions on small scales is critical to understanding
             fundamental biological processes such as extracellular
             redistribution of nutrients. We present experiments designed
             to quantify the trajectories of these particles, which are
             seen to consist of slow orbits about the rod, with secondary
             epicycles quasicommensurate with the precession rate. A
             first-principles theory is developed to predict trajectories
             in such time-varying flows. The theory is further tested
             using a dynamically similar macroscale experiment to remove
             thermal noise effects. The excellent agreement between our
             theory and experiments confirms that the continuum
             hypothesis applies all the way to the scales of such
             submicron biological motions.},
   Doi = {10.1103/PhysRevE.76.016313},
   Key = {fds166441}
}

@article{fds166444,
   Author = {E.L. Bouzarth and H. Pfister},
   Title = {Helicity conservation under Reidemeister
             Moves},
   Journal = {American Journal of Physics},
   Volume = {74},
   Number = {2},
   Pages = {141-144},
   Year = {2006},
   Month = {February},
   url = {http://dx.doi.org/10.1119/1.2142691},
   Abstract = {We discuss a connection between two fields that appear to
             have little in common: plasma physics and mathematical knot
             theory. Plasma physicists are interested in studying
             helicity conservation in magnetic flux ropes and knot
             theorists commonly consider “Reidemeister moves,”
             transformations that preserve a property called
             “knottedness.” To study the tangling, twisting, and
             untwisting of magnetic flux ropes, it is helpful to know
             which topological transformations conserve helicity.
             Although the second and third types of Reidemeister moves
             applied to a magnetic flux rope clearly conserve the
             helicity of the flux rope, the first type of Reidemeister
             move appears to be in conflict with helicity conservation.We
             show that all three Reidemeister moves conserve helicity in
             magnetic flux ropes.},
   Doi = {10.1119/1.2142691},
   Key = {fds166444}
}

@article{fds166446,
   Author = {E.L. Bouzarth and D. Richeson},
   Title = {Topological Helicity for Framed Links},
   Journal = {Journal of Knot Theory and its Ramifications},
   Volume = {13},
   Number = {8},
   Pages = {1007-1019},
   Year = {2004},
   url = {http://dx.doi.org/10.1142/S0218216504003664},
   Abstract = {We introduce topological helicity, an invariant for oriented
             framed links. Topological helicity provides an elementary
             means of computing helicity for a magnetic flux rope by
             measuring its knotting, linking, and twisting. We present an
             equivalence relation, reconnection-equivalence, for framed
             links and prove that topological helicity is a complete
             invariant for the resulting equivalence classes. We conclude
             by showing that one can use magnetic reconnection to
             transform one collection of linked flux ropes into another
             collection if and only if they have the same
             helicity.},
   Doi = {10.1142/S0218216504003664},
   Key = {fds166446}
}


%% Bowen, Mark   
@article{fds9848,
   Author = {M. Bowen and J. R. King and J. Hulshof},
   Title = {Anomalous exponents and dipole solutions for the thin film
             equation},
   Journal = {SIAM J. Appl. Math., (2001), 62:149-179},
   url = {http://www.math.duke.edu/~bowen/dippap.ps},
   Abstract = {Also available as Leiden Preprint MI 01-2000. We investigate
             similarity solutions of the second kind (in that they
             feature an anomalous exponent) for a fourth order degenerate
             diffusion equation on the half-line $x\ge0$. These
             self-similar solutions are termed dipole solutions and,
             using a combination of phase space analysis and numerical
             simulations, we numerically construct trajectories
             representing these solutions, at the same time obtaining
             broader insight into the nature of the four-dimensional
             phase space. Additional asymptotic analysis provides further
             information concerning the evolution to self-similarity.},
   Key = {fds9848}
}

@article{fds9846,
   Author = {J. R. King and M. Bowen},
   Title = {Moving boundary problems and non-uniqueness for the thin
             film equation},
   Journal = {Euro. J. Appl. Math. (2001), 12:321-356},
   url = {http://www.math.duke.edu/~bowen/ejampap.ps},
   Abstract = {Also avalaiable as Leiden preprint MI 28-99. A variety of
             mass preserving moving boundary problems for the thin film
             equation, $u_{t}=-(u^{n}u_{xxx})_{x}$, are derived (by
             formal asymptotics) from a number of regularisations, the
             case in which the substrate is covered by a very thin
             pre-wetting film being discussed in most detail. Some of the
             properties of the solutions selected in this fashion are
             described and the full range of possible mass preserving
             non-negative solutions is outlined.},
   Key = {fds9846}
}

@article{fds9847,
   Author = {J. Hulshof and J. R. King and M. Bowen},
   Title = {Intermediate asymptotics of the porous medium equation with
             sign changes},
   Journal = {Adv. Diff. Eq. (2001), 6:1115-1152},
   url = {http://www.math.duke.edu/~bowen/scpap.ps},
   Abstract = {Also available as Leiden preprint W98-20 (1998). We study
             the porous medium equation with sign changes and examine the
             way sign changes disappear. We give a formal classification
             of selfsimilar and non-selfsimilar scenarios for their
             disappearance, for N>1 restricting attention to the radial
             case. The results we present on the classification of
             similarity solutions are rigorous except where indicated
             otherwise.},
   Key = {fds9847}
}

@article{fds9845,
   Author = {T. P. Witelski and Mark Bowen},
   Title = {ADI schemes for higher-order nonlinear diffusion
             equations},
   Journal = {Appl. Num. Math.},
   Key = {fds9845}
}

@article{fds9820,
   Author = {M. Bowen and J. R. King},
   Title = {Asymptotic behaviour of the thin film equation in bounded
             domains},
   Journal = {Euro. J. Appl. Math. (2001), 12:135-157},
   url = {http://www.math.duke.edu/~bowen/drpap.ps},
   Abstract = {Also available as Leiden Preprint MI 29-99. We investigate
             the extinction behaviour of a fourth order degenerate
             diffusion equation in a bounded domain, the model
             representing the flow of a viscous fluid over edges at which
             zero contact angle conditions hold. The extinction time may
             be finite or infinite and we distinguish between the two
             cases by identification of appropriate similarity solutions.
             In certain cases an unphysical mass increase may occur for
             early time and the solution may become negative; an
             appropriate remedy for this is noted. Numerical simulations
             supporting the analysis are included.},
   Key = {fds9820}
}


%% Braley, Emily L.   
@article{fds299955,
   Author = {Lindsay D. Waldrop and Stephen C. Adolph and Cecilia G. Diniz
             Behn and Emily Braley and Joshua A. Drew and Robert J. Full and Louis J.
             Gross and John A. Jungck and Brynja Kohler and Jennifer C. Prairie and Blerta Shtylla and Laura A. Miller},
   Title = {Using Active Learning to Teach Concepts and Methods in
             Quantitative Biology},
   Journal = {Integrative and Comparative Biology},
   Volume = {55},
   Number = {5},
   Pages = {933-948},
   Publisher = {Oxford University Press},
   Year = {2015},
   url = {http://icb.oxfordjournals.org/content/55/5/933.full.pdf?keytype=ref&ijkey=nSisiIyjS2Dqt85},
   Abstract = {This article provides a summary of the ideas discussed at
             the 2015 Annual Meeting of the Society for Integrative and
             Comparative Biology society-wide symposium on Leading
             Students and Faculty to Quantitative Biology through Active
             Learning. It also includes a brief review of the recent
             advancements in incorporating active learning approaches
             into quantitative biology classrooms. We begin with an
             overview of recent literature that shows that active
             learning can improve students’ outcomes in Science,
             Technology, Engineering and Math Education disciplines. We
             then discuss how this approach can be particularly useful
             when teaching topics in quantitative biology. Next, we
             describe some of the recent initiatives to develop hands-on
             activities in quantitative biology at both the graduate and
             the undergraduate levels. Throughout the article we provide
             resources for educators who wish to integrate active
             learning and technology into their classrooms.},
   Doi = {10.1093/icb/icv097},
   Key = {fds299955}
}


%% Bray, Clark   
@book{fds163009,
   Author = {C.B. Bray},
   Title = {Multivariable Calculus},
   Pages = {468},
   Publisher = {CreateSpace, Inc.},
   Address = {www.createspace.com},
   Year = {2009},
   Abstract = {This is a textbook on multivariable calculus.},
   Key = {fds163009}
}


%% Bray, Hubert   
@article{fds300017,
   Author = {Bray, HL and Jauregui, JL and Mars, M},
   Title = {Time Flat Surfaces and the Monotonicity of the Spacetime
             Hawking Mass II},
   Journal = {Annales Henri Poincaré},
   Volume = {17},
   Number = {6},
   Pages = {1457-1475},
   Publisher = {Springer Basel},
   Year = {2016},
   Month = {June},
   ISSN = {1424-0637},
   url = {http://arxiv.org/abs/1402.3287},
   Abstract = {In this sequel paper we give a shorter, second proof of the
             monotonicity of the Hawking mass for time flat surfaces
             under spacelike uniformly area expanding flows in spacetimes
             that satisfy the dominant energy condition. We also include
             a third proof which builds on a known formula and describe a
             class of sufficient conditions of divergence type for the
             monotonicity of the Hawking mass. These flows of surfaces
             may have connections to the problem in general relativity of
             bounding the total mass of a spacetime from below by the
             quasi-local mass of spacelike 2-surfaces in the
             spacetime.},
   Doi = {10.1007/s00023-015-0420-2},
   Key = {fds300017}
}

@article{fds303060,
   Author = {Martinez-Medina, LA and Bray, HL and Matos, T},
   Title = {On wave dark matter in spiral and barred
             galaxies},
   Journal = {Journal of Cosmology and Astroparticle Physics},
   Volume = {2015},
   Number = {12},
   Pages = {025-025},
   Year = {2015},
   Month = {December},
   url = {http://arxiv.org/abs/1505.07154},
   Doi = {10.1088/1475-7516/2015/12/025},
   Key = {fds303060}
}

@article{fds287065,
   Author = {Bray, HL and Jauregui, JL},
   Title = {On curves with nonnegative torsion},
   Journal = {Archiv der Mathematik},
   Volume = {104},
   Number = {6},
   Pages = {561-575},
   Year = {2015},
   Month = {June},
   ISSN = {0003-889X},
   url = {http://www.springer.com/-/0/c8d239381b86496b96d95ff26f1061eb},
   Doi = {10.1007/s00013-015-0767-0},
   Key = {fds287065}
}

@article{fds300016,
   Author = {Bray, HL and Jauregui, JL},
   Title = {Time Flat Surfaces and the Monotonicity of the Spacetime
             Hawking Mass},
   Journal = {Communications in Mathematical Physics},
   Volume = {335},
   Number = {1},
   Pages = {285-307},
   Year = {2015},
   Month = {April},
   ISSN = {0010-3616},
   url = {http://arxiv.org/abs/1310.8638},
   Doi = {10.1007/s00220-014-2162-2},
   Key = {fds300016}
}

@article{fds287070,
   Author = {Bray, HL and Parry, AR},
   Title = {Modeling wave dark matter in dwarf spheroidal
             galaxies},
   Journal = {Journal of Physics},
   Volume = {615},
   Year = {2015},
   ISSN = {1742-6588},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000358144800001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1088/1742-6596/615/1/012001},
   Key = {fds287070}
}

@article{fds287066,
   Author = {Bray, H and Goetz, AS},
   Title = {Wave Dark Matter and the Tully-Fisher Relation},
   Year = {2014},
   Month = {September},
   url = {http://arxiv.org/abs/1409.7347},
   Abstract = {Preprint},
   Key = {fds287066}
}

@article{fds287074,
   Author = {Bray, HL},
   Title = {On Dark Matter, Spiral Galaxies, and the Axioms of General
             Relativity},
   Journal = {AMS Contemporary Mathematics Volume},
   Volume = {599},
   Number = {Geometric Analysis, Mathematical Relativ},
   Publisher = {American Mathematical Society},
   Year = {2013},
   url = {http://www.math.duke.edu/~bray/darkmatter/darkmatter.html},
   Key = {fds287074}
}

@article{fds287075,
   Author = {Bray, HL and Jauregui, JL},
   Title = {A geometric theory of zero area singularities in general
             relativity},
   Journal = {Asian Journal of Mathematics},
   Volume = {17},
   Number = {3},
   Pages = {525-560},
   Year = {2013},
   ISSN = {1093-6106},
   url = {http://dx.doi.org/10.4310/AJM.2013.v17.n3.a6},
   Abstract = {The Schwarzschild spacetime metric of negative mass is
             well-known to contain a naked singularity. In a spacelike
             slice, this singularity of the metric is characterized by
             the property that nearby surfaces have arbitrarily small
             area. We develop a theory of such \zero area singularities"
             in Riemannian manifolds, generalizing far beyond the
             Schwarzschild case (for example, allowing the singularities
             to have nontrivial topology). We also dene the mass of such
             singularities. The main result of this paper is a lower
             bound on the ADM mass of an asymptotically at manifold of
             nonnegative scalar curvature in terms of the masses of its
             singularities, assuming a certain conjecture in conformal
             geometry. The proof relies on the Riemannian Penrose
             inequality [9]. Equality is attained in the inequality by
             the Schwarzschild metric of negative mass. An immediate
             corollary is a version of the positive mass theorem that
             allows for certain types of incomplete metrics. © 2013
             International Press.},
   Doi = {10.4310/AJM.2013.v17.n3.a6},
   Key = {fds287075}
}

@article{fds287064,
   Author = {Bray, H},
   Title = {On Wave Dark Matter, Shells in Elliptical Galaxies, and the
             Axioms of General Relativity},
   Year = {2012},
   Month = {December},
   url = {http://www.math.duke.edu/~bray/darkmatter/DMEG.pdf},
   Abstract = {Preprint},
   Key = {fds287064}
}

@article{fds287068,
   Author = {Bray, H},
   Title = {On the Positive Mass, Penrose, and ZAS Inequalities in
             General Dimension},
   Booktitle = {Surveys in Geometric Analysis and Relativity in Honor of
             Richard Schoen’s 60th Birthday},
   Publisher = {Higher Education Press and International
             Press},
   Address = {Beijing and Boston},
   Editor = {Bray, H and Minicozzi, W},
   Year = {2011},
   url = {http://arxiv.org/abs/1101.2230},
   Key = {fds287068}
}

@article{fds287073,
   Author = {Bray, HL and Khuri, MA},
   Title = {P. D. E. 'S which imply the penrose conjecture},
   Journal = {Asian Journal of Mathematics},
   Volume = {15},
   Number = {4},
   Pages = {557-610},
   Publisher = {International Press},
   Year = {2011},
   ISSN = {1093-6106},
   url = {http://www.math.duke.edu/~bray/PE/euclid.ajm.1331583349.pdf},
   Abstract = {In this paper, we show how to reduce the Penrose conjecture
             to the known Riemannian Penrose inequality case whenever
             certain geometrically motivated systems of equations can be
             solved. Whether or not these special systems of equations
             have general existence theories is therefore an important
             open problem. The key tool in our method is the derivation
             of a new identity which we call the generalized Schoen-Yau
             identity, which is of independent interest. Using a
             generalized Jang equation, we use this identity to propose
             canonical embeddings of Cauchy data into corresponding
             static spacetimes. In addition, we discuss the Carrasco-Mars
             counterexample to the Penrose conjecture for generalized
             apparent horizons (added since the first version of this
             paper was posted on the arXiv) and instead conjecture the
             Penrose inequality for time-independent apparent horizons,
             which we define. © 2011 International Press.},
   Key = {fds287073}
}

@article{fds287076,
   Author = {Bray, H and Brendle, S and Neves, A},
   Title = {Rigidity of area-minimizing two-spheres in
             three-manifolds},
   Journal = {Communications in Analysis and Geometry},
   Volume = {18},
   Number = {4},
   Pages = {821-830},
   Year = {2010},
   ISSN = {1019-8385},
   url = {http://arxiv.org/abs/1002.2814},
   Abstract = {We give a sharp upper bound for the area of a minimal
             two-sphere in a three-manifold (M,g) with positive scalar
             curvature. If equality holds, we show that the universal
             cover of (M,g) is isometric to a cylinder.},
   Key = {fds287076}
}

@article{fds287080,
   Author = {Bray, H and Brendle, S and Eichmair, M and Neves,
             A},
   Title = {Area-Minimizing Projective Planes in 3-Manifolds},
   Journal = {Communications on Pure & Applied Mathematics},
   Volume = {63},
   Number = {9},
   Pages = {1237-1247},
   Year = {2010},
   ISSN = {0010-3640},
   url = {http://dx.doi.org/10.1002/cpa.20319},
   Abstract = {Let (M, g) be a compact Riemannian manifold of dimension 3,
             and let F denote the collection of all embedded surfaces
             homeomorphic to R{double-struck}P{double-struck}2. We study
             the infimum of the areas of all surfaces in F . This
             quantity is related to the systole of .M; g/. It makes sense
             whenever F is nonempty. In this paper, we give an upper
             bound for this quantity in terms of the minimum of the
             scalar curvature of (M, g) Moreover, we show that equality
             holds if and only if (M, g) is isometric to
             R{double-struck}P{double-struck}3 up to scaling. The proof
             uses the formula for the second variation of area and
             Hamilton's Ricci flow. © 2010 Wiley Periodicals,
             Inc.},
   Doi = {10.1002/cpa.20319},
   Key = {fds287080}
}

@article{fds287081,
   Author = {Bray, HL and Khuri, MA},
   Title = {A jang equation approach to the penrose inequality},
   Journal = {Discrete and Continuous Dynamical Systems},
   Volume = {27},
   Number = {2},
   Pages = {741-766},
   Year = {2010},
   ISSN = {1078-0947},
   url = {http://dx.doi.org/10.3934/dcds.2010.27.741},
   Abstract = {We introduce a generalized version of the Jang equation,
             designed for the general case of the Penrose Inequality in
             the setting of an asymptotically flat space-like
             hypersurface of a spacetime satisfying the dominant energy
             condition. The appropriate existence and regularity results
             are established in the special case of spherically symmetric
             Cauchy data, and are applied to give a new proof of the
             general Penrose Inequality for these data sets. When
             appropriately coupled with an inverse mean curvature flow,
             analogous existence and regularity results for the
             associated system of equations in the nonspherical setting
             would yield a proof of the full Penrose Conjecture. Thus it
             remains as an important and challenging open problem to
             determine whether this system does indeed admit the desired
             solutions.},
   Doi = {10.3934/dcds.2010.27.741},
   Key = {fds287081}
}

@article{fds287077,
   Author = {Bray, HL and Lee, DA},
   Title = {On the Riemannian Penrose inequality in dimensions less than
             eight},
   Journal = {Duke Mathematical Journal},
   Volume = {148},
   Number = {1},
   Pages = {81-106},
   Year = {2009},
   ISSN = {0012-7094},
   url = {http://www.math.duke.edu/~bray/PE/euclid.dmj.1240432192.pdf},
   Abstract = {The positive mass theorem states that a complete
             asymptotically flat manifold of nonnegative scalar curvature
             has nonnegative mass and that equality is achieved only for
             the Euclidean metric. The Riemannian Penrose inequality
             provides a sharp lower bound for the mass when black holes
             are present. More precisely, this lower bound is given in
             terms of the area of an outermost minimal hypersurface, and
             equality is achieved only for Schwarzschild metrics. The
             Riemannian Penrose inequality was first proved in three
             dimensions in 1997 by G. Huisken and T. Ilmanen for the case
             of a single black hole (see [HI]). In 1999, Bray extended
             this result to the general case of multiple black holes
             using a different technique (see [Br]). In this article, we
             extend the technique of [Br] to dimensions less than eight.
             Part of the argument is contained in a companion article by
             Lee [L]. The equality case of the theorem requires the added
             assumption that the manifold be spin. 2009 © Duke
             University Press.},
   Doi = {10.1215/00127094-2009-020},
   Key = {fds287077}
}

@article{fds287083,
   Author = {Bray, H and Miao, P},
   Title = {On the capacity of surfaces in manifolds with nonnegative
             scalar curvature},
   Journal = {Inventiones mathematicae},
   Volume = {172},
   Number = {3},
   Pages = {459-475},
   Year = {2008},
   ISSN = {0020-9910},
   url = {http://dx.doi.org/10.1007/s00222-007-0102-x},
   Abstract = {Given a surface in an asymptotically flat 3-manifold with
             nonnegative scalar curvature, we derive an upper bound for
             the capacity of the surface in terms of the area of the
             surface and the Willmore functional of the surface. The
             capacity of a surface is defined to be the energy of the
             harmonic function which equals 0 on the surface and goes to
             1 at ∞. Even in the special case of ℝ3, this is a new
             estimate. More generally, equality holds precisely for a
             spherically symmetric sphere in a spatial Schwarzschild
             3-manifold. As applications, we obtain inequalities relating
             the capacity of the surface to the Hawking mass of the
             surface and the total mass of the asymptotically flat
             manifold. © 2008 Springer-Verlag.},
   Doi = {10.1007/s00222-007-0102-x},
   Key = {fds287083}
}

@article{fds287084,
   Author = {Bray, H and Hayward, S and Mars, M and Simon, W},
   Title = {Generalized inverse mean curvature flows in
             spacetime},
   Journal = {Communications in Mathematical Physics},
   Volume = {272},
   Number = {1},
   Pages = {119-138},
   Year = {2007},
   ISSN = {0010-3616},
   url = {http://dx.doi.org/10.1007/s00220-007-0203-9},
   Abstract = {Motivated by the conjectured Penrose inequality and by the
             work of Hawking, Geroch, Huisken and Ilmanen in the null and
             the Riemannian case, we examine necessary conditions on
             flows of two-surfaces in spacetime under which the Hawking
             quasilocal mass is monotone. We focus on a subclass of such
             flows which we call uniformly expanding, which can be
             considered for null as well as for spacelike directions. In
             the null case, local existence of the flow is guaranteed. In
             the spacelike case, the uniformly expanding condition leaves
             a 1-parameter freedom, but for the whole family, the
             embedding functions satisfy a forward-backward parabolic
             system for which local existence does not hold in general.
             Nevertheless, we have obtained a generalization of the weak
             (distributional) formulation of this class of flows,
             generalizing the corresponding step of Huisken and Ilmanen's
             proof of the Riemannian Penrose inequality. ©
             Springer-Verlag 2007.},
   Doi = {10.1007/s00220-007-0203-9},
   Key = {fds287084}
}

@article{fds303538,
   Author = {Bray, HL},
   Title = {A family of quasi-local mass functionals with monotone
             flows},
   Pages = {323-329},
   Editor = {JC Zambrini},
   Year = {2006},
   Month = {January},
   ISBN = {9789812704016},
   url = {http://dx.doi.org/10.1142/9789812704016_0030},
   Abstract = {© 2005 by World Scientific Publishing Co. Pte. Ltd. All
             rights reserved. We define a one parameter family of
             quasi-local mass functionals m c (Σ), 0 ≤ c ≤ ∞,
             which are nondecreasing on surfaces in 3-manifolds with
             nonnegative scalar curvature with respect to a one parameter
             family of flows. In the case that c = 0, m 0 (Σ) equals the
             Hawking mass of Σ 2 and the corresponding flow is inverse
             mean curvature flow. Then, following the arguments of Geroch
             [8], Jang and Wald [12] , and Huisken and Ilmanen [9], we
             note that the generalization of their results for inverse
             mean curvature flow would imply that if m ADM is the total
             mass of the complete, asymptotically flat 3-manifold with
             nonnegative scalar curvature, then m ADM ≥ m c (Σ) for
             all nonnegative c and all connected surfaces Σ which are
             not enclosed by surfaces with less area.},
   Doi = {10.1142/9789812704016_0030},
   Key = {fds303538}
}

@article{fds51387,
   Author = {H.L. Bray},
   Title = {The Positve Energy Theorem and Other Inequalities in
             GR},
   Booktitle = {The Encyclopedia of Mathematical Physics},
   Year = {2005},
   Key = {fds51387}
}

@article{fds287061,
   Author = {Bray, H},
   Title = {The Positve Energy Theorem and Other Inequalities},
   Booktitle = {The Encyclopedia of Mathematical Physics},
   Year = {2005},
   Key = {fds287061}
}

@article{MR2052359,
   Author = {Bray, HL and Neves, A},
   Title = {Classification of Prime 3-Manifolds with Yamabe Invariant
             Greater than RP^3},
   Journal = {Annals of Mathematics},
   Volume = {159},
   Number = {1},
   Pages = {407-424},
   Year = {2004},
   Month = {January},
   url = {http://annals.math.princeton.edu/2004/159-1/p09},
   Abstract = {In this paper we compute the σ-invariants (sometimes also
             called the smooth Yamabe invariants) of RP3 and RP2×S1
             (which are equal) and show that the only prime 3-manifolds
             with larger σ-invariants are S3, S2×S1, and S2×~S1 (the
             nonorientable S2 bundle over S1). More generally, we show
             that any 3-manifold with σ-invariant greater than RP3 is
             either S3, a connect sum with an S2 bundle over S1, or has
             more than one nonorientable prime component. A corollary is
             the Poincaré conjecture for 3-manifolds with σ-invariant
             greater than RP3. Surprisingly these results follow from the
             same inverse mean curvature flow techniques which were used
             by Huisken and Ilmanen in [7] to prove the Riemannian
             Penrose Inequality for a black hole in a spacetime. Richard
             Schoen made the observation [18] that since the constant
             curvature metric (which is extremal for the Yamabe problem)
             on RP3 is in the same conformal class as the Schwarzschild
             metric (which is extremal for the Penrose inequality) on RP3
             minus a point, there might be a connection between the two
             problems. The authors found a strong connection via inverse
             mean curvature flow.},
   Key = {MR2052359}
}

@article{fds287060,
   Author = {Bray, H and Chrusciel, PT},
   Title = {The Penrose Inequality},
   Booktitle = {The Einstein Equations and the Large Scale Behavior of
             Gravitational Fields (50 Years of the Cauchy Problem in
             General Relativity)},
   Publisher = {Birkhauser},
   Editor = {Chrusciel, PT and Friedrich, HF},
   Year = {2004},
   url = {arxiv:gr-qc/0312047v2},
   Key = {fds287060}
}

@article{fds43695,
   Author = {H.L. Bray},
   Title = {A Family of Quasi-local Mass Functionals with Monotone
             Flows},
   Booktitle = {Proceedings of the 14th International Congress on
             Mathematical Physics, Lisbon, Portugal, 2003},
   Editor = {Jean-Claude Zambrini},
   Year = {2003},
   url = {http://books.google.com/books?hl=en&lr=&id=KMJlC6hizIEC&oi=fnd&pg=PA323&dq=A+Family+of+Quasi-local+Mass+Functionals+with+Monotone+Flows&ots=brVkWiZvsE&sig=ovai4UODn6UJqPYkg030nn2tkFM#v=onepage&q=A},
   Key = {fds43695}
}

@article{fds287063,
   Author = {Bray, H},
   Title = {Black Holes and the Penrose Inequality in General
             Relativity},
   Journal = {Proceedings of the International Congress of
             Mathematicians},
   Volume = {2},
   Pages = {257-272},
   Booktitle = {Proceedings of the International Congress of Mathematicians,
             Beijing, China, 2002},
   Year = {2002},
   url = {http://arxiv.org/abs/math/0304261v1},
   Key = {fds287063}
}

@article{MR2002i:53073,
   Author = {Bray, H and Morgan, F},
   Title = {An isoperimetric comparison theorem for schwarzschild space
             and other manifolds},
   Journal = {Proceedings of the American Mathematical
             Society},
   Volume = {130},
   Number = {5},
   Pages = {1467-1472},
   Year = {2002},
   url = {http://www.ams.org/journals/proc/2002-130-05/S0002-9939-01-06186-X/S0002-9939-01-06186-X.pdf},
   Abstract = {We give a very general isoperimetric comparison theorem
             which, as an important special case, gives hypotheses under
             which the spherically symmetric (n - 1)-spheres of a
             spherically symmetric n-manifold are isoperimetric
             hypersurfaces, meaning that they minimize (n -
             1)-dimensional area among hypersurfaces enclosing the same
             n-volume. This result greatly generalizes the result of Bray
             (Ph.D. thesis, 1997), which proved that the spherically
             symmetric 2-spheres of 3-dimensional Schwarzschild space
             (which is defined to be a totally geodesic, space-like slice
             of the usual (3 + 1)-dimensional Schwarzsehild metric) are
             isoperimetric. We also note that this Schwarzschild result
             has applications to the Penrose inequality in general
             relativity, as described by Bray.},
   Doi = {10.1090/S0002-9939-01-06186-X},
   Key = {MR2002i:53073}
}

@article{MR2003c:53047,
   Author = {Bray, H and Finster, F},
   Title = {Curvature estimates and the Positive Mass
             Theorem},
   Journal = {Communications in Analysis and Geometry},
   Volume = {10},
   Number = {2},
   Pages = {291-306},
   Year = {2002},
   url = {http://arxiv.org/abs/math/9906047v3},
   Abstract = {The Positive Mass Theorem implies that any smooth, complete,
             asymptotically flat 3-manifold with non-negative scalar
             curvature which has zero total mass is isometric to (ℝ3
             δij). In this paper, we quantify this statement using
             spinors and prove that if a complete, asymptotically flat
             manifold with non-negative scalar curvature has small mass
             and bounded isoperimetric constant, then the manifold must
             be close to (ℝ3, δij), in the sense that there is an
             upper bound for the L2 norm of the Riemannian curvature
             tensor over the manifold except for a set of small measure.
             This curvature estimate allows us to extend the case of
             equality of the Positive Mass Theorem to include non-smooth
             manifolds with generalized non-negative scalar curvature,
             which we define.},
   Key = {MR2003c:53047}
}

@article{MR2003j:83052,
   Author = {Bray, HL},
   Title = {Black Holes, Geometric Flows, and the Penrose Inequality in
             General Relativity},
   Journal = {Notices of the American Mathematical Society},
   Volume = {49},
   Number = {11},
   Pages = {1372-1381},
   Year = {2002},
   url = {http://www.ams.org/notices/200211/fea-bray.pdf},
   Key = {MR2003j:83052}
}

@article{MR2003k:83066,
   Author = {Bray, HL and Iga, K},
   Title = {Superharmonic Functions in R^n and the Penrose Inequality in
             General Relativity},
   Journal = {Communications in Analysis and Geometry},
   Volume = {10},
   Number = {5},
   Pages = {999-1016},
   Year = {2002},
   Key = {MR2003k:83066}
}

@article{MR2004j:53046,
   Author = {Bray, HL},
   Title = {Proof of the Riemannian Penrose inequality using the
             positive mass theorem},
   Journal = {Journal of Differential Geometry},
   Volume = {59},
   Number = {2},
   Pages = {177-267},
   Year = {2001},
   url = {http://www.math.duke.edu/~bray/PE/euclid.jdg.1090349428.pdf},
   Abstract = {We prove the Riemannian Penrose Conjecture, an important
             case of a conjecture [41] made by Roger Penrose in 1973, by
             defining a new flow of metrics. This flow of metrics stays
             inside the class of asymptotically flat Riemannian
             3-manifolds with nonnegative scalar curvature which contain
             minimal spheres. In particular, if we consider a Riemannian
             3-manifold as a totally geodesic submanifold of a space-time
             in the context of general relativity, then outermost minimal
             spheres with total area A correspond to apparent horizons of
             black holes contributing a mass √A/16π, scalar curvature
             corresponds to local energy density at each point, and the
             rate at which the metric becomes flat at infinity
             corresponds to total mass (also called the ADM mass). The
             Riemannian Penrose Conjecture then states that the total
             mass of an asymptotically flat 3-manifold with nonnegative
             scalar curvature is greater than or equal to the mass
             contributed by the black holes. The flow of metrics we
             define continuously evolves the original 3-metric to a
             Schwarzschild 3-metric, which represents a spherically
             symmetric black hole in vacuum. We define the flow such that
             the area of the minimal spheres (which flow outward) and
             hence the mass contributed by the black holes in each of the
             metrics in the flow is constant, and then use the Positive
             Mass Theorem to show that the total mass of the metrics is
             nonincreasing. Then since the total mass equals the mass of
             the black hole in a Schwarzschild metric, the Riemannian
             Penrose Conjecture follows. We also refer the reader to the
             beautiful work of Huisken and Ilmanen [30], who used inverse
             mean curvature flows of surfaces to prove that the total
             mass is at least the mass contributed by the largest black
             hole.},
   Key = {MR2004j:53046}
}

@incollection{MR2004j:53047,
   Author = {Bray, H and Schoen, RM},
   Title = {Recent Proofs of the Riemannian Penrose Conjecture},
   Pages = {1-36},
   Booktitle = {Current Developments in Mathematics},
   Publisher = {International Press},
   Year = {1999},
   Key = {MR2004j:53047}
}

@misc{fds287067,
   Author = {Bray, H},
   Title = {The Penrose Inequality in General Relativity and Volume
             Comparison Theorems Involving Scalar Curvature},
   Year = {1997},
   url = {arxiv:0902.3241v1},
   Key = {fds287067}
}

@article{fds287082,
   Author = {Bray, H and McCormick, K and Jr, ROW and Zhou, X-D},
   Title = {Wavelet variations on the Shannon sampling
             theorem},
   Journal = {BioSystems},
   Volume = {34},
   Number = {1-3},
   Pages = {249-257},
   Publisher = {Elsevier Science Ireland},
   Year = {1995},
   ISSN = {0303-2647},
   url = {http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T2K-3YMWJCP-J&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1119554323&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=00e2987e0823dfb6839780e7c7af56ec},
   Abstract = {The Shannon sampling theorem asserts that a continuous
             square-integrable function on the real line which has a
             compactly supported Fourier transform is uniquely determined
             by its restriction to a uniform lattice of points whose
             density is determined by the support of the Fourier
             transform. This result can be extended to the wavelet
             representation of functions in two ways. First, under the
             same type of conditions as for the Shannon theorem, the
             scaling coefficients of a wavelet expansion will determine
             uniquely the given square-integrable function. Secondly, for
             a more general function, there is a unique extension from a
             given set of scaling coefficients to a full wavelet
             expansion which minimizes the local obstructions to
             translation invariance in a variational sense. ©
             1995.},
   Doi = {10.1016/0303-2647(94)01457-I},
   Key = {fds287082}
}


%% Bryant, Robert   
@article{fds325462,
   Author = {Bryant, RL and Huang, L and Mo, X},
   Title = {On Finsler surfaces of constant flag curvature with a
             Killing field},
   Journal = {Journal of Geometry and Physics},
   Volume = {116},
   Pages = {345-357},
   Year = {2017},
   Month = {June},
   url = {http://dx.doi.org/10.1016/j.geomphys.2017.02.012},
   Doi = {10.1016/j.geomphys.2017.02.012},
   Key = {fds325462}
}

@article{fds320294,
   Author = {Bryant, RL},
   Title = {On the convex Pfaff-Darboux Theorem of Ekeland and
             Nirenberg},
   Year = {2015},
   Month = {December},
   url = {http://arxiv.org/abs/1512.07100},
   Abstract = {The classical Pfaff-Darboux Theorem, which provides local
             `normal forms' for 1-forms on manifolds, has applications in
             the theory of certain economic models. However, the normal
             forms needed in these models come with an additional
             requirement of convexity, which is not provided by the
             classical proofs of the Pfaff-Darboux Theorem. (The
             appropriate notion of `convexity' is a feature of the
             economic model. In the simplest case, when the economic
             model is formulated in a domain in n-space, convexity has
             its usual meaning. In 2002, Ekeland and Nirenberg were able
             to characterize necessary and sufficient conditions for a
             given 1-form to admit a convex local normal form (and to
             show that some earlier attempts at this characterization had
             been unsuccessful). In this article, after providing some
             necessary background, I prove a strengthened and generalized
             convex Pfaff-Darboux Theorem, one that covers the case of a
             Legendrian foliation in which the notion of convexity is
             defined in terms of a torsion-free affine connection on the
             underlying manifold. (The main result in Ekeland and
             Nirenberg's paper concerns the case in which the affine
             connection is flat.)},
   Key = {fds320294}
}

@article{fds320295,
   Author = {Bryant, RL},
   Title = {On the conformal volume of 2-tori},
   Year = {2015},
   Month = {July},
   url = {http://arxiv.org/abs/1507.01485},
   Keywords = {conformal volume},
   Abstract = {This note provides a proof of a 1985 conjecture of Montiel
             and Ros about the conformal volume of tori. (This material
             is not really new; I'm making it available now because of
             requests related to recent interest in the
             conjecture.)},
   Key = {fds320295}
}

@article{fds320296,
   Author = {Bryant, RL},
   Title = {S.-S. Chern's study of almost-complex structures on the
             six-sphere},
   Year = {2014},
   Month = {May},
   url = {http://arxiv.org/abs/1405.3405},
   Keywords = {6-sphere complex structure exceptional geometry},
   Abstract = {In 2003, S.-s. Chern began a study of almost-complex
             structures on the 6-sphere, with the idea of exploiting the
             special properties of its well-known almost-complex
             structure invariant under the exceptional group $G_2$. While
             he did not solve the (currently still open) problem of
             determining whether there exists an integrable
             almost-complex structure on the 6-sphere, he did prove a
             significant identity that resolves the question for an
             interesting class of almost-complex structures on the
             6-sphere.},
   Key = {fds320296}
}

@article{fds320297,
   Author = {Bryant, RL},
   Title = {Notes on exterior differential systems},
   Year = {2014},
   Month = {May},
   url = {http://arxiv.org/abs/1405.3116},
   Keywords = {exterior differential systems Lie theory differential
             geometry},
   Abstract = {These are notes for a very rapid introduction to the basics
             of exterior differential systems and their connection with
             what is now known as Lie theory, together with some typical
             and not-so-typical applications to illustrate their
             use.},
   Key = {fds320297}
}

@article{fds320298,
   Author = {Bryant, RL and Eastwood, MG and Gover, AR and Neusser,
             K},
   Title = {Some differential complexes within and beyond parabolic
             geometry},
   Year = {2012},
   Month = {March},
   Abstract = {For smooth manifolds equipped with various geometric
             structures, we construct complexes that replace the de Rham
             complex in providing an alternative fine resolution of the
             sheaf of locally constant functions. In case that the
             geometric structure is that of a parabolic geometry, our
             complexes coincide with the Bernstein-Gelfand-Gelfand
             complex associated with the trivial representation. However,
             at least in the cases we discuss, our constructions are
             relatively simple and avoid most of the machinery of
             parabolic geometry. Moreover, our method extends to certain
             geometries beyond the parabolic realm.},
   Key = {fds320298}
}

@book{fds318258,
   Author = {R. Bryant and Bryant, RL and Chern, SS and Gardner, RB and Goldschmidt, HL and Griffiths, PA},
   Title = {Exterior Differential Systems},
   Pages = {475 pages},
   Publisher = {Springer},
   Year = {2011},
   Month = {December},
   ISBN = {1461397162},
   MRNUMBER = {92h:58007},
   url = {http://www.ams.org/mathscinet-getitem?mr=92h:58007},
   Abstract = {This book gives a treatment of exterior differential
             systems.},
   Key = {fds318258}
}

@article{fds216495,
   Author = {R. Bryant and Michael G. Eastwood and A. Rod. Gover and Katharina
             Neusser},
   Title = {Some differential complexes within and beyond parabolic
             geometry},
   Year = {2011},
   Month = {December},
   url = {http://arxiv.org/abs/1112.2142v2},
   Abstract = {For smooth manifolds equipped with various geometric
             structures, we construct complexes that replace the de Rham
             complex in providing an alternative fine resolution of the
             sheaf of locally constant functions. In case that the
             geometric structure is that of a parabolic geometry, our
             complexes coincide with the Bernstein- Gelfand-Gelfand
             complex associated with the trivial representation. However,
             at least in the cases we discuss, our constructions are
             relatively simple and avoid most of the machinery of
             parabolic geometry. Moreover, our method extends to certain
             geometries beyond the parabolic realm.},
   Key = {fds216495}
}

@article{fds320299,
   Author = {Bryant, R and Xu, F},
   Title = {Laplacian Flow for Closed $G_2$-Structures: Short Time
             Behavior},
   Year = {2011},
   Month = {January},
   Abstract = {We prove short time existence and uniqueness of solutions to
             the Laplacian flow for closed $G_2$ structures on a compact
             manifold $M^7$. The result was claimed in \cite{BryantG2},
             but its proof has never appeared.},
   Key = {fds320299}
}

@article{fds225242,
   Author = {R.L. Bryant and Feng Xu},
   Title = {Laplacian flow for closed G2-structures: short
             time behavior},
   Year = {2011},
   Month = {January},
   url = {http://arxiv.org/abs/1101.2004},
   Abstract = {We prove short time existence and uniqueness of solutions to
             the Laplacian flow for closed G2 structures on a compact
             manifold M7. The result was claimed in \cite{BryantG2}, but
             its proof has never appeared.},
   Key = {fds225242}
}

@article{fds243372,
   Author = {Bryant, RL},
   Title = {Nonembedding and nonextension results in special
             holonomy},
   Pages = {346-367},
   Booktitle = {The Many Facets of Geometry: A Tribute to Nigel
             Hitchin},
   Publisher = {Oxford University Press},
   Address = {Oxford},
   Editor = {Garcia-Prada, O and Bourguignon, JP and Salamon,
             S},
   Year = {2010},
   Month = {Fall},
   ISBN = {0199534926},
   MRCLASS = {53C29},
   MRNUMBER = {MR2681703},
   url = {http://dx.doi.org/10.1093/acprof:oso/9780199534920.003.0017},
   Abstract = {Constructions of metrics with special holonomy by methods of
             exterior differential systems are reviewed and the
             interpretations of these construction as `flows' on
             hypersurface geometries are considered. It is shown that
             these hypersurface 'flows' are not generally well-posed for
             smooth initial data and counterexamples to existence are
             constructed.},
   Doi = {10.1093/acprof:oso/9780199534920.003.0017},
   Key = {fds243372}
}

@article{fds243377,
   Author = {Bryant, RL},
   Title = {Commentary},
   Journal = {Bulletin of the American Mathematical Society},
   Volume = {46},
   Number = {2},
   Pages = {177-178},
   Year = {2009},
   ISSN = {0273-0979},
   url = {http://dx.doi.org/10.1090/S0273-0979-09-01248-8},
   Doi = {10.1090/S0273-0979-09-01248-8},
   Key = {fds243377}
}

@article{fds243378,
   Author = {R. Bryant and Bryant, RL and Dunajski, M and Eastwood, M},
   Title = {Metrisability of two-dimensional projective
             structures},
   Volume = {83},
   Number = {3},
   Pages = {465-499},
   Year = {2009},
   ISSN = {0022-040X},
   MRCLASS = {53},
   MRNUMBER = {MR2581355},
   url = {http://arxiv.org/abs/0801.0300v1},
   Abstract = {We carry out the programme of R. Liouville \cite{Liouville}
             to construct an explicit local obstruction to the existence
             of a Levi--Civita connection within a given projective
             structure $[\Gamma]$ on a surface. The obstruction is of
             order 5 in the components of a connection in a projective
             class. It can be expressed as a point invariant for a second
             order ODE whose integral curves are the geodesics of
             $[\Gamma]$ or as a weighted scalar projective invariant of
             the projective class. If the obstruction vanishes we find
             the sufficient conditions for the existence of a metric in
             the real analytic case. In the generic case they are
             expressed by the vanishing of two invariants of order 6 in
             the connection. In degenerate cases the sufficient
             obstruction is of order at most 8.},
   Key = {fds243378}
}

@article{fds243385,
   Author = {R. Bryant and Bryant, RL and Manno, G and Matveev, VS},
   Title = {A solution of a problem of Sophus Lie: Normal forms of
             two-dimensional metrics admitting two projective vector
             fields},
   Journal = {Mathematische Annalen},
   Volume = {340},
   Number = {2},
   Pages = {437-463},
   Year = {2008},
   Month = {Spring},
   url = {http://www.arxiv.org/abs/0705.3592},
   Abstract = {We give a complete list of normal forms for the
             two-dimensional metrics that admit a transitive Lie
             pseudogroup of geodesic-preserving transformations and we
             show that these normal forms are mutually non-isometric.
             This solves a problem posed by Sophus Lie. © 2007
             Springer-Verlag.},
   Doi = {10.1007/s00208-007-0158-3},
   Key = {fds243385}
}

@article{fds320198,
   Author = {Bryant, RL},
   Title = {Gradient Kähler Ricci solitons},
   Journal = {Asterisque},
   Volume = {321},
   Series = {Astérisque},
   Number = {321},
   Pages = {51-97},
   Booktitle = {Géométrie différentielle, physique mathématique,
             mathématiques et société. I.},
   Publisher = {Soc. Math. France},
   Year = {2008},
   Month = {Spring},
   ISBN = {978-285629-258-7},
   MRCLASS = {53C55 (53C21)},
   MRNUMBER = {2010i:53138},
   url = {http://arxiv.org/abs/math/0407453},
   Abstract = {Some observations about the local and global generality of
             gradient Kahler Ricci solitons are made, including the
             existence of a canonically associated holomorphic volume
             form and vector field, the local generality of solutions
             with a prescribed holomorphic volume form and vector field,
             and the existence of Poincaré coordinates in the case that
             the Ricci curvature is positive and the vector field has a
             fixed point. © Asterisque 321.},
   Key = {fds320198}
}

@book{fds318259,
   Author = {R. Bryant and Gu, C and Berger, M and Bryant, RL},
   Title = {Differential Geometry and Differential Equations Proceedings
             of a Symposium, held in Shanghai, June 21 - July 6,
             1985},
   Pages = {246 pages},
   Publisher = {Springer},
   Year = {2006},
   Month = {November},
   ISBN = {3540478833},
   Abstract = {The DD6 Symposium was, like its predecessors DD1 to DD5 both
             a research symposium and a summer seminar and concentrated
             on differential geometry. This volume contains a selection
             of the invited papers and some additional
             contributions.},
   Key = {fds318259}
}

@article{fds243386,
   Author = {Bryant, RL},
   Title = {On the geometry of almost complex 6-manifolds},
   Journal = {The Asian Journal of Mathematics},
   Volume = {10},
   Number = {3},
   Pages = {561-606},
   Year = {2006},
   Month = {September},
   url = {http://arxiv.org/abs/math/0508428},
   Keywords = {almost complex manifolds quasi-integrable Nijenhuis
             tensor},
   Abstract = {This article is mostly a writeup of two talks, the first
             given in the Besse Seminar at the Ecole Polytechnique in
             1998 and the second given at the 2000 International Congress
             on Differential Geometry in memory of Alfred Gray in Bilbao,
             Spain. It begins with a discussion of basic geometry of
             almost complex 6-manifolds. In particular, I define a 2-
             parameter family of intrinsic first-order functionals on
             almost complex structures on 6-manifolds and compute their
             Euler-Lagrange equations. It also includes a discussion of a
             natural generalization of holomorphic bundles over complex
             manifolds to the almost complex case. The general almost
             complex manifold will not admit any nontrivial bundles of
             this type, but there is a large class of nonintegrable
             almost complex manifolds for which there are such nontrivial
             bundles. For example, the standard almost complex structure
             on the 6-sphere admits such nontrivial bundles. This class
             of almost complex manifolds in dimension 6 will be referred
             to as quasi-integrable. Some of the properties of
             quasi-integrable structures (both almost complex and
             unitary) are developed and some examples are given. However,
             it turns out that quasi-integrability is not an involutive
             condition, so the full generality of these structures in
             Cartan's sense is not well-understood.},
   Key = {fds243386}
}

@article{fds318260,
   Author = {BRYANT, RL},
   Title = {Conformal geometry and 3-plane fields on
             6-manifolds},
   Volume = {1502 (Developments of Cartan Geometry an},
   Series = {RIMS Symposium Proceedings},
   Pages = {1-15},
   Booktitle = {Developments of Cartan Geometry and Related Mathematical
             Problems},
   Publisher = {Kyoto University},
   Year = {2006},
   Month = {July},
   url = {http://arxiv.org/abs/math/0511110},
   Keywords = {differential invariants},
   Abstract = {The purpose of this note is to provide yet another example
             of the link between certain conformal geometries and
             ordinary differential equations, along the lines of the
             examples discussed by Nurowski in math.DG/0406400. In this
             particular case, I consider the equivalence problem for
             3-plane fields D on 6-manifolds M that satisfy the
             nondegeneracy condition that D+[D,D]=TM I give a solution of
             the equivalence problem for such D (as Tanaka has
             previously), showing that it defines a so(4,3)- valued
             Cartan connection on a principal right H-bundle over M where
             H is the subgroup of SO(4,3) that stabilizes a null 3-plane
             in R^{4,3}. Along the way, I observe that there is
             associated to each such D a canonical conformal structure of
             split type on M, one that depends on two derivatives of the
             plane field D. I show how the primary curvature tensor of
             the Cartan connection associated to the equivalence problem
             for D can be interpreted as the Weyl curvature of the
             associated conformal structure and, moreover, show that the
             split conformal structures in dimension 6 that arise in this
             fashion are exactly the ones whose so(4,4)-valued Cartan
             connection admits a reduction to a spin(4,3)-connection. I
             also discuss how this case has features that are analogous
             to those of Nurowski's examples.},
   Key = {fds318260}
}

@article{fds243387,
   Author = {Bryant, RL},
   Title = {SO(n)-invariant special Lagrangian submanifolds of C^{n+1}
             with fixed loci},
   Journal = {Chinese Annals of Mathematics, Series B},
   Volume = {27},
   Number = {1},
   Pages = {95-112},
   Year = {2006},
   Month = {January},
   MRNUMBER = {MR2209954},
   url = {http://arxiv.org/abs/math/0402201},
   Keywords = {calibrations, special Lagrangian submanifolds},
   Abstract = {Let SO(n) act in the standard way on C^n and extend this
             action in the usual way to C^{n+1}. It is shown that
             nonsingular special Lagrangian submanifold L in C^{n+1} that
             is invariant under this SO(n)-action intersects the fixed
             line C in a nonsingular real-analytic arc A (that may be
             empty). If n>2, then A has no compact component. Conversely,
             an embedded, noncompact nonsingular real-analytic arc A in C
             lies in an embedded nonsingular special Lagrangian
             submanifold that is SO(n)-invariant. The same existence
             result holds for compact A if n=2. If A is connected, there
             exist n distinct nonsingular SO(n)- invariant special
             Lagrangian extensions of A such that any embedded
             nonsingular SO(n)-invariant special Lagrangian extension of
             A agrees with one of these n extensions in some open
             neighborhood of A. The method employed is an analysis of a
             singular nonlinear PDE and ultimately calls on the work of
             Gerard and Tahara to prove the existence of the
             extension.},
   Key = {fds243387}
}

@article{fds318261,
   Author = {Bryant, R and Freed, D},
   Title = {Shiing-Shen Chern - Obituary},
   Journal = {Physics today},
   Volume = {59},
   Number = {1},
   Pages = {70-72},
   Year = {2006},
   Month = {January},
   url = {http://dx.doi.org/10.1063/1.2180187},
   Doi = {10.1063/1.2180187},
   Key = {fds318261}
}

@article{fds318262,
   Author = {Bryant, RL},
   Title = {Second order families of special Lagrangian
             3-folds},
   Journal = {Perspectives in Riemannian Geometry, CRM Proceedings and
             Lecture Notes, edited by Vestislav Apostolov, Andrew Dancer,
             Nigel Hitchin, and McKenzie Wang, vol. 40 (2006), American
             Mathematical Society},
   Volume = {40},
   Series = {CRM Proceedings and Lecture Notes},
   Pages = {63-98},
   Booktitle = {Perspectives in Riemannian Geometry},
   Publisher = {American Mathematical Society},
   Editor = {Vestislav Apostolov and Andrew Dancer and Nigel Hitchin and McKenzie Wang},
   Year = {2006},
   ISBN = {0-8218-3852-0},
   url = {http://arxiv.org/abs/math/0007128},
   Abstract = {A second order family of special Lagrangian submanifolds of
             complex m-space is a family characterized by the
             satisfaction of a set of pointwise conditions on the second
             fundamental form. For example, the set of ruled special
             Lagrangian submanifolds of complex 3-space is characterized
             by a single algebraic equation on the second fundamental
             form. While the `generic' set of such conditions turns out
             to be incompatible, i.e., there are no special Lagrangian
             submanifolds that satisfy them, there are many interesting
             sets of conditions for which the corresponding family is
             unexpectedly large. In some cases, these geometrically
             defined families can be described explicitly, leading to new
             examples of special Lagrangian submanifolds. In other cases,
             these conditions characterize already known families in a
             new way. For example, the examples of Lawlor-Harvey
             constructed for the solution of the angle conjecture and
             recently generalized by Joyce turn out to be a natural and
             easily described second order family.},
   Key = {fds318262}
}

@article{fds318263,
   Author = {Bryant, RL},
   Title = {Geometry of manifolds with special holonomy: "100 years of
             holonomy"},
   Journal = {Contemporary Mathematics},
   Volume = {395},
   Series = {Contemporary Mathematics},
   Pages = {29-38},
   Booktitle = {150 years of mathematics at Washington University in St.
             Louis},
   Publisher = {AMS},
   Year = {2006},
   ISBN = {0-8218-3603-X},
   MRNUMBER = {MR2206889},
   url = {http://www.ams.org/mathscinet-getitem?mr=2206889},
   Keywords = {53C29 (70F25)},
   Key = {fds318263}
}

@article{fds318264,
   Author = {Bryant, RL},
   Title = {Geodesically reversible Finsler 2-spheres of constant
             curvature},
   Volume = {11},
   Series = {Nankai Tracts in Mathematics},
   Pages = {95-111},
   Booktitle = {Inspired by S. S. Chern---A Memorial Volume in Honor of a
             Great Mathematician},
   Publisher = {World Scientific Publishers},
   Editor = {Griffiths, PA},
   Year = {2006},
   Month = {Winter},
   url = {http://arxiv.org/abs/math/0407514},
   Abstract = {A Finsler space is said to be geodesically reversible if
             each oriented geodesic can be reparametrized as a geodesic
             with the reverse orientation. A reversible Finsler space is
             geodesically reversible, but the converse need not be true.
             In this note, building on recent work of LeBrun and Mason,
             it is shown that a geodesically reversible Finsler metric of
             constant flag curvature on the 2-sphere is necessarily
             projectively flat. As a corollary, using a previous result
             of the author, it is shown that a reversible Finsler metric
             of constant flag curvature on the 2-sphere is necessarily a
             Riemannian metric of constant Gauss curvature, thus settling
             a long-standing problem in Finsler geometry.},
   Key = {fds318264}
}

@article{fds318265,
   Author = {Bryant, RL},
   Title = {Some remarks on G_2-structures},
   Pages = {75-109},
   Booktitle = {Proceedings of Gökova Geometry-Topology Conference
             2005},
   Publisher = {International Press},
   Editor = {Akbulut, S and Onder, T and Stern, R},
   Year = {2006},
   ISBN = {1-57146-152-3},
   url = {http://arxiv.org/abs/math/0305124},
   Abstract = {This article consists of some loosely related remarks about
             the geometry of G_2-structures on 7-manifolds and is partly
             based on old unpublished joint work with two other people:
             F. Reese Harvey and Steven Altschuler. Much of this work has
             since been subsumed in the work of Hitchin
             \cite{MR02m:53070} and Joyce \cite{MR01k:53093}. I am making
             it available now mainly because of interest expressed by
             others in seeing these results written up since they do not
             seem to have all made it into the literature. A formula is
             derived for the scalar curvature and Ricci curvature of a
             G_2-structure in terms of its torsion. When the fundamental
             3-form of the G_2-structure is closed, this formula implies,
             in particular, that the scalar curvature of the underlying
             metric is nonpositive and vanishes if and only if the
             structure is torsion-free. This version contains some new
             results on the pinching of Ricci curvature for metrics
             associated to closed G_2-structures. Some formulae are
             derived for closed solutions of the Laplacian flow that
             specify how various related quantities, such as the torsion
             and the metric, evolve with the flow. These may be useful in
             studying convergence or long-time existence for given
             initial data.},
   Key = {fds318265}
}

@article{fds318266,
   Author = {Bryant, R},
   Title = {Holonomy and Special Geometries},
   Series = {Conference Proceedings and Lecture Notes in Geometry and
             Topology},
   Pages = {71-90},
   Booktitle = {Dirac Operators: Yesterday and Today},
   Publisher = {International Press},
   Editor = {Bourguinon, JP and Branson, T and Chamseddine, A and Hijazi, O and Stanton, R},
   Year = {2005},
   ISBN = {1-57146-175-2},
   MRNUMBER = {MR2205367},
   url = {http://www.ams.org/mathscinet-getitem?mr=2205367},
   Key = {fds318266}
}

@book{fds318267,
   Author = {R. Bryant and David Bao and S.-S. Chern and Zhongmin Shen},
   Title = {A Sampler of Riemann-Finsler Geometry},
   Volume = {50},
   Series = {Mathematical Sciences Research Institute
             Publications},
   Pages = {363 pages},
   Publisher = {Cambridge University Press},
   Editor = {Bao, D and Bryant, RL and Chern, S-S and Shen, Z},
   Year = {2004},
   Month = {November},
   ISBN = {0521831814},
   MRNUMBER = {MR2132655(2005j:53003)},
   url = {http://www.ams.org/mathscinet-getitem?mr=2132655},
   Abstract = {These expository accounts treat issues in Finsler geometry
             related to volume, geodesics, curvature and mathematical
             biology, with instructive examples.},
   Key = {fds318267}
}

@article{fds320300,
   Author = {Bryant, RL},
   Title = {Real hypersurfaces in unimodular complex
             surfaces},
   Year = {2004},
   Month = {July},
   url = {http://arxiv.org/abs/math/0407472},
   Abstract = {A unimodular complex surface is a complex 2-manifold X
             endowed with a holomorphic volume form. A strictly
             pseudoconvex real hypersurface M in X inherits not only a
             CR-structure but a canonical coframing as well. In this
             article, this canonical coframing on M is defined, its
             invariants are discussed and interpreted geometrically, and
             its basic properties are studied. A natural evolution
             equation for strictly pseudoconvex real hypersurfaces in
             unimodular complex surfaces is defined, some of its
             properties are discussed, and several examples are computed.
             The locally homogeneous examples are determined and used to
             illustrate various features of the geometry of the induced
             structure on the hypersurface.},
   Key = {fds320300}
}

@article{fds243379,
   Author = {R. Bryant and Bryant, R and Edelsbrunner, H and Koehl, P and Levitt,
             M},
   Title = {The area derivative of a space-filling diagram},
   Journal = {Discrete and Computanional Geometry},
   Volume = {32},
   Number = {3},
   Pages = {293-308},
   Year = {2004},
   MRNUMBER = {2005k:92077},
   url = {http://dx.doi.org/10.1007/s00454-004-1099-1},
   Abstract = {The motion of a biomolecule greatly depends on the engulfing
             solution, which is mostly water. Instead of representing
             individual water molecules, it is desirable to develop
             implicit solvent models that nevertheless accurately
             represent the contribution of the solvent interaction to the
             motion. In such models, hydrophobicity is expressed as a
             weighted sum of atomic surface areas. The derivatives of
             these weighted areas contribute to the force that drives the
             motion. In this paper we give formulas for the weighted and
             unweighted area derivatives of a molecule modeled as a
             space-filling diagram made up of balls in motion. Other than
             the radii and the centers of the balls, the formulas are
             given in terms of the sizes of circular arcs of the boundary
             and edges of the power diagram. We also give
             inclusion-exclusion formulas for these sizes.},
   Doi = {10.1007/s00454-004-1099-1},
   Key = {fds243379}
}

@book{fds318268,
   Author = {R. Bryant and Bryant, RL and Griffiths, PA and Grossman, DA},
   Title = {Exterior Differential Systems and Euler-Lagrange Partial
             Differential Equations},
   Series = {Chicago Lectures in Mathematics},
   Pages = {213 pages},
   Publisher = {University of Chicago Press},
   Year = {2003},
   Month = {July},
   ISBN = {0226077934},
   MRNUMBER = {MR1985469},
   url = {http://arxiv.org/abs/math/0207039},
   Abstract = {We use methods from exterior differential systems (EDS) to
             develop a geometric theory of scalar, first-order Lagrangian
             functionals and their associated Euler-Lagrange PDEs,
             subject to contact transformations. The first chapter
             contains an introduction of the classical Poincare-Cartan
             form in the context of EDS, followed by proofs of classical
             results, including a solution to the relevant inverse
             problem, Noether's theorem on symmetries and conservation
             laws, and several aspects of minimal hypersurfaces. In the
             second chapter, the equivalence problem for Poincare-Cartan
             forms is solved, giving the differential invariants of such
             a form, identifying associated geometric structures
             (including a family of affine hypersurfaces), and exhibiting
             certain "special" Euler-Lagrange equations characterized by
             their invariants. In the third chapter, we discuss a
             collection of Poincare-Cartan forms having a naturally
             associated conformal geometry, and exhibit the conservation
             laws for non-linear Poisson and wave equations that result
             from this. The fourth and final chapter briefly discusses
             additional PDE topics from this viewpoint--Euler-Lagrange
             PDE systems, higher order Lagrangians and conservation laws,
             identification of local minima for Lagrangian functionals,
             and Backlund transformations. No previous knowledge of
             exterior differential systems or of the calculus of
             variations is assumed.},
   Key = {fds318268}
}

@book{fds43013,
   Title = {Selected works of Phillip A. Griffiths with commentary. Part
             4. Differential systems.},
   Publisher = {American Mathematical Society, Providence, RI; International
             Press, Somerville, MA},
   Editor = {R. L. Bryant and David R. Morrison},
   Year = {2003},
   MRNUMBER = {2005e:01025d},
   url = {http://www.ams.org/mathscinet-getitem?mr=2005e:01025d},
   Key = {fds43013}
}

@article{fds10364,
   Title = {Levi-flat minimal hypersurfaces in two-dimensional complex
             space forms},
   Volume = {37},
   Series = {Adv. Stud. Pure Math.},
   Pages = {1--44},
   Booktitle = {Lie groups, geometric structures and differential
             equations---one hundred years after Sophus Lie (Kyoto/Nara,
             1999)},
   Publisher = {Math. Soc. Japan},
   Year = {2002},
   MRNUMBER = {MR1980895},
   url = {http://arxiv.org/abs/math/9909159},
   Abstract = {The purpose of this article is to classify the real
             hypersurfaces in complex space forms of dimension 2 that are
             both Levi-flat and minimal. The main results are as follows:
             When the curvature of the complex space form is nonzero,
             there is a 1-parameter family of such hypersurfaces.
             Specifically, for each one-parameter subgroup of the
             isometry group of the complex space form, there is an
             essentially unique example that is invariant under this
             one-parameter subgroup. On the other hand, when the
             curvature of the space form is zero, i.e., when the space
             form is complex 2-space with its standard flat metric, there
             is an additional `exceptional' example that has no
             continuous symmetries but is invariant under a lattice of
             translations. Up to isometry and homothety, this is the
             unique example with no continuous symmetries.},
   Key = {fds10364}
}

@article{fds243380,
   Author = {Bryant, RL},
   Title = {Some remarks on Finsler manifolds with constant flag
             curvature},
   Journal = {Houston Journal of Mathematics},
   Volume = {28},
   Number = {2},
   Pages = {221-262},
   Year = {2002},
   MRNUMBER = {2003h:53102},
   url = {HJM},
   Abstract = {This article is an exposition of four loosely related
             remarks on the geometry of Finsler manifolds with constant
             positive flag curvature. The first remark is that there is a
             canonical Kahler structure on the space of geodesics of such
             a manifold. The second remark is that there is a natural way
             to construct a (not necessarily complete) Finsler n-manifold
             of constant positive flag curvature out of a hypersurface in
             suitably general position in complex projective n-space. The
             third remark is that there is a description of the Finsler
             metrics of constant curvature on the 2-sphere in terms of a
             Riemannian metric and 1-form on the space of its geodesics.
             In particular, this allows one to use any (Riemannian) Zoll
             metric of positive Gauss curvature on the 2-sphere to
             construct a global Finsler metric of constant positive
             curvature on the 2-sphere. The fourth remark concerns the
             generality of the space of (local) Finsler metrics of
             constant positive flag curvature in dimension n+1>2 . It is
             shown that such metrics depend on n(n+1) arbitrary functions
             of n+1 variables and that such metrics naturally correspond
             to certain torsion- free S^1 x GL(n,R)-structures on
             2n-manifolds. As a by- product, it is found that these
             groups do occur as the holonomy of torsion-free affine
             connections in dimension 2n, a hitherto unsuspected
             phenomenon.&nbsp;},
   Key = {fds243380}
}

@book{fds320301,
   Author = {Bryant, RL},
   Title = {Rigidity and quasi-rigidity of extremal cycles in Hermitian
             symmetric spaces},
   Year = {2001},
   Month = {March},
   url = {http://arxiv.org/abs/math/0006186},
   Abstract = {I use local differential geometric techniques to prove that
             the algebraic cycles in certain extremal homology classes in
             Hermitian symmetric spaces are either rigid (i.e.,
             deformable only by ambient motions) or quasi-rigid (roughly
             speaking, foliated by rigid subvarieties in a nontrivial
             way). These rigidity results have a number of applications:
             First, they prove that many subvarieties in Grassmannians
             and other Hermitian symmetric spaces cannot be smoothed
             (i.e., are not homologous to a smooth subvariety). Second,
             they provide characterizations of holomorphic bundles over
             compact Kahler manifolds that are generated by their global
             sections but that have certain polynomials in their Chern
             classes vanish (for example, c_2 = 0, c_1c_2 - c_3 = 0, c_3
             = 0, etc.).},
   Key = {fds320301}
}

@article{MR2002i:53010,
   Author = {Bryant, RL},
   Title = {On surfaces with prescribed shape operator},
   Journal = {Results Math. 40 (2001), no. 1-4, 88--121},
   Volume = {40},
   Number = {1--4},
   Pages = {88-121},
   Year = {2001},
   MRNUMBER = {2002i:53010},
   url = {http://arxiv.org/abs/math/0107083},
   Abstract = {The problem of immersing a simply connected surface with a
             prescribed shape operator is discussed. From classical and
             more recent work, it is known that, aside from some special
             degenerate cases, such as when the shape operator can be
             realized by a surface with one family of principal curves
             being geodesic, the space of such realizations is a convex
             set in an affine space of dimension at most 3. The cases
             where this maximum dimension of realizability is achieved
             have been classified and it is known that there are two such
             families of shape operators, one depending essentially on
             three arbitrary functions of one variable (called Type I in
             this article) and another depending essentially on two
             arbitrary functions of one variable (called Type II in this
             article). In this article, these classification results are
             rederived, with an emphasis on explicit computability of the
             space of solutions. It is shown that, for operators of
             either type, their realizations by immersions can be
             computed by quadrature. Moreover, explicit normal forms for
             each can be computed by quadrature together with, in the
             case of Type I, by solving a single linear second order ODE
             in one variable. (Even this last step can be avoided in most
             Type I cases.) The space of realizations is discussed in
             each case, along with some of their remarkable geometric
             properties. Several explicit examples are constructed
             (mostly already in the literature) and used to illustrate
             various features of the problem.},
   Key = {MR2002i:53010}
}

@article{fds243382,
   Author = {Bryant, RL},
   Title = {Bochner-Kähler metrics},
   Journal = {Journal of the AMS},
   Volume = {14},
   Number = {3},
   Pages = {623-715},
   Year = {2001},
   MRNUMBER = {2002i:53096},
   url = {http://arxiv.org/abs/math/0003099},
   Abstract = {A Kahler metric is said to be Bochner-Kahler if its Bochner
             curvature vanishes. This is a nontrivial condition when the
             complex dimension of the underlying manifold is at least 2.
             In this article it will be shown that, in a certain well-
             defined sense, the space of Bochner-Kahler metrics in
             complex dimension n has real dimension n+1 and a recipe for
             an explicit formula for any Bochner-Kahler metric is given.
             It is shown that any Bochner-Kahler metric in complex
             dimension n has local (real) cohomogeneity at most~n. The
             Bochner-Kahler metrics that can be `analytically continued'
             to a complete metric, free of singularities, are identified.
             In particular, it is shown that the only compact Bochner-
             Kahler manifolds are the discrete quotients of the known
             symmetric examples. However, there are compact Bochner-
             Kahler orbifolds that are not locally symmetric. In fact,
             every weighted projective space carries a Bochner-Kahler
             metric. The fundamental technique is to construct a
             canonical infinitesimal torus action on a Bochner-Kahler
             metric whose associated momentum mapping has the orbits of
             its symmetry pseudo-groupoid as fibers.},
   Key = {fds243382}
}

@article{fds243383,
   Author = {Bryant, RL},
   Title = {Recent advances in the theory of holonomy},
   Journal = {Asterisque},
   Volume = {266},
   Number = {5},
   Pages = {351-374},
   Publisher = {Centre National de la Recherche Scientifique},
   Year = {2000},
   MRNUMBER = {2001h:53067},
   url = {http://www.dmi.ens.fr/bourbaki/Prog_juin99.html},
   Key = {fds243383}
}

@article{fds243384,
   Author = {Bryant, RL},
   Title = {Harmonic morphisms with fibers of dimension
             one},
   Journal = {Communications in Analysis and Geometry},
   Volume = {8},
   Number = {2},
   Pages = {219-265},
   Year = {2000},
   MRNUMBER = {2001i:53101},
   url = {http://arxiv.org/abs/dg-ga/9701002},
   Abstract = {I prove three classification results about harmonic
             morphisms whose fibers have dimension one. All are valid
             when the domain is at least of dimension 4. (The character
             of this overdetermined problem is very different when the
             dimension of the domain is 3 or less.) The first result is a
             local classification for such harmonic morphisms with
             specified target metric, the second is a finiteness theorem
             for such harmonic morphisms with specified domain metric,
             and the third is a complete classification of such harmonic
             morphisms when the domain is a space form of constant
             sectional curvature. The methods used are exterior
             differential systems and the moving frame. The basic results
             are local, but, because of the rigidity of the solutions,
             they allow a complete global classification.},
   Key = {fds243384}
}

@article{fds243409,
   Author = {Bryant, RL},
   Title = {Calibrated Embeddings in the Special Lagrangian and
             Coassociative Cases},
   Journal = {Annals of Global Analysis and Geometry},
   Volume = {18},
   Number = {3-4},
   Pages = {405-435},
   Year = {2000},
   MRNUMBER = {2002j:53063},
   url = {http://arxiv.org/abs/math/9912246},
   Abstract = {Every closed, oriented, real analytic Riemannian 3-manifold
             can be isometrically embedded as a special Lagrangian
             submanifold of a Calabi-Yau 3-fold, even as the real locus
             of an antiholomorphic, isometric involution. Every closed,
             oriented, real analytic Riemannian 4-manifold whose bundle
             of self-dual 2-forms is trivial can be isometrically
             embedded as a coassociative submanifold in a G2-manifold,
             even as the fixed locus of an anti-G2 involution. These
             results, when coupled with McLean's analysis of the moduli
             spaces of such calibrated sub-manifolds, yield a plentiful
             supply of examples of compact calibrated submanifolds with
             nontrivial deformation spaces.},
   Key = {fds243409}
}

@article{fds318269,
   Author = {Bryant, R},
   Title = {Élie Cartan and geometric duality},
   Journal = {Journées Élie Cartan 1998 et 1999},
   Volume = {16},
   Pages = {5-20},
   Booktitle = {Journées Élie Cartan 1998 et 1999},
   Publisher = {Institut Élie Cartan},
   Year = {2000},
   url = {http://www.math.duke.edu/~bryant/Cartan.pdf},
   Key = {fds318269}
}

@article{fds318270,
   Author = {Bryant, RL},
   Title = {Pseudo-Riemannian metrics with parallel spinor fields and
             vanishing Ricci tensor},
   Volume = {4},
   Series = {Séminaires & Congrès},
   Pages = {53-94},
   Booktitle = {Global analysis and harmonic analysis (Marseille-Luminy,
             1999)},
   Publisher = {Société Mathématique de France},
   Editor = {Bourguinon, JP and Branson, T and Hijazi, O},
   Year = {2000},
   ISBN = {2-85629-094-9},
   MRNUMBER = {2002h:53082},
   url = {http://arxiv.org/abs/math/0004073},
   Abstract = {I discuss geometry and normal forms for pseudo-Riemannian
             metrics with parallel spinor fields in some interesting
             dimensions. I also discuss the interaction of these
             conditions for parallel spinor fields with the condition
             that the Ricci tensor vanish (which, for pseudo-Riemannian
             manifolds, is not an automatic consequence of the existence
             of a nontrivial parallel spinor field).},
   Key = {fds318270}
}

@article{fds243402,
   Author = {Bryant, RL},
   Title = {Some examples of special Lagrangian tori},
   Journal = {Adv. Theor. Math. Phys.},
   Volume = {3},
   Number = {1},
   Pages = {83-90},
   Year = {1999},
   MRNUMBER = {2000f:32033},
   url = {http://arxiv.org/abs/math/9902076},
   Abstract = {A short paper giving some examples of smooth hypersurfaces M
             of degree n+1 in complex projective n-space that are defined
             by real polynomial equations and whose real slice contains a
             component diffeomorphic to an n-1 torus, which is then
             special Lagrangian with respect to the Calabi-Yau metric on
             M.},
   Key = {fds243402}
}

@article{fds243408,
   Author = {R. Bryant and Sharpe, E and Bryant, RL},
   Title = {D-branes and Spin^c-structures},
   Journal = {Physics Letters, Section B: Nuclear, Elementary Particle and
             High-Energy Physics},
   Volume = {450},
   Number = {4},
   Pages = {353-357},
   Year = {1999},
   MRNUMBER = {2000c:53054},
   url = {http://arxiv.org/abs/hep-th/98l2084},
   Abstract = {It was recently pointed out by E. Witten that for a D-brane
             to consistently wrap a submanifold of some manifold, the
             normal bundle must admit a Spin^c structure. We examine this
             constraint in the case of type II string compactifications
             with vanishing cosmological constant and argue that, in all
             such cases, the normal bundle to a sypersymmetric cycle is
             automatically Spin^c.},
   Key = {fds243408}
}

@article{fds10011,
   Author = {Russell, Thomas and Farris, Frank},
   Title = {Integrability, Gorman systems, and the Lie bracket structure
             of the real line (with an appendix by –––)},
   Journal = {J. Math. Econom.},
   Volume = {29},
   Number = {2},
   Pages = {183–209},
   Year = {1998},
   MRNUMBER = {99f:90029},
   url = {http://www.ams.org/mathscinet-getitem?mr=99f:90029},
   Key = {fds10011}
}

@article{fds243403,
   Author = {Bryant, RL},
   Title = {Projectively flat Finsler 2-spheres of constant
             curvature},
   Journal = {Selecta Math. (N.S.)},
   Volume = {3},
   Number = {2},
   Pages = {161-203},
   Year = {1997},
   MRNUMBER = {98i:53101},
   url = {http://arxiv.org/abs/dg-ga/9611010},
   Key = {fds243403}
}

@article{fds8915,
   Title = {Finsler structures on the 2-sphere satisfying
             K=1},
   Volume = {196},
   Series = {Contemporary Mathematics},
   Pages = {27–41},
   Booktitle = {Finsler geometry (Seattle, WA, 1995)},
   Publisher = {Amer. Math. Soc., Providence, RI},
   Editor = {David Bao and Shiing-shen Chern and Zhongmin
             Shen},
   Year = {1996},
   MRNUMBER = {97e:53128},
   url = {http://www.math.duke.edu/preprints/95-11.dvi},
   Key = {fds8915}
}

@article{fds318271,
   Author = {Bryant, RL},
   Title = {On extremals with prescribed Lagrangian densities},
   Volume = {36},
   Series = {Symposia Mathematica},
   Pages = {86-111},
   Booktitle = {Manifolds and geometry (Pisa, 1993)},
   Publisher = {Cambridge University Press},
   Editor = {Bartolomeis, P and Tricerri, F and Vesentini, E},
   Year = {1996},
   ISBN = {0-521-56216-3},
   MRNUMBER = {99a:58043},
   url = {http://arxiv.org/abs/dg-ga/9406001},
   Abstract = {Consider two manifolds~$M^m$ and $N^n$ and a first-order
             Lagrangian $L(u)$ for mappings $u:M\to N$, i.e., $L$ is an
             expression involving $u$ and its first derivatives whose
             value is an $m$-form (or more generally, an $m$-density)
             on~$M$. One is usually interested in describing the extrema
             of the functional $\Cal L(u) = \int_M L(u)$, and these are
             characterized locally as the solutions of the Euler-Lagrange
             equation~$E_L(u)=0$ associated to~$L$. In this note I will
             discuss three problems which can be understood as trying to
             determine how many solutions exist to the Euler-Lagrange
             equation which also satisfy $L(u) = \Phi$, where $\Phi$ is a
             specified $m$-form or $m$-density on~$M$. The first problem,
             which is solved completely, is to determine when two minimal
             graphs over a domain in the plane can induce the same area
             form without merely differing by a vertical translation or
             reflection. The second problem, described more fully below,
             arose in Professor Calabi's study of extremal isosystolic
             metrics on surfaces. The third problem, also solved
             completely, is to determine the (local) harmonic maps
             between spheres which have constant energy
             density.},
   Key = {fds318271}
}

@article{fds318272,
   Author = {Bryant, R},
   Title = {Classical, exceptional, and exotic holonomies: a status
             report},
   Volume = {1},
   Series = {Sémin. Congr.},
   Pages = {93-165},
   Booktitle = {Actes de la Table Ronde de Géométrie Différentielle},
   Publisher = {Société Mathématique de France},
   Editor = {Besse, A},
   Year = {1996},
   ISBN = {2-85629-047-7},
   MRNUMBER = {98c:53037},
   url = {http://www.math.duke.edu/preprints/95-10.dvi},
   Abstract = {A survey paper on the status of the holonomy problem as of
             1995.},
   Key = {fds318272}
}

@article{fds243407,
   Author = {R. Bryant and Bryant, RL and Griffiths, PA},
   Title = {Characteristic cohomology of differential systems. I.
             General theory},
   Journal = {The Journal of the American Mathematical
             Society},
   Volume = {8},
   Number = {3},
   Pages = {507-507},
   Year = {1995},
   Month = {September},
   MRNUMBER = {96c:58183},
   url = {http://www.math.duke.edu/preprints/93-01.dvi},
   Doi = {10.1090/S0894-0347-1995-1311820-X},
   Key = {fds243407}
}

@article{fds243404,
   Author = {R. Bryant and Griffiths, PA and Hsu, L and Bryant, RL},
   Title = {Hyperbolic exterior differential systems and their
             conservation laws, Part II},
   Journal = {Selecta Math. (N.S.)},
   Volume = {1},
   Number = {2},
   Pages = {265-323},
   Year = {1995},
   MRNUMBER = {97d:580009},
   url = {http://www.math.duke.edu/preprints/94-13.dvi},
   Key = {fds243404}
}

@article{fds243405,
   Author = {R. Bryant and Griffiths, PA and Hsu, L and Bryant, RL},
   Title = {Hyperbolic exterior differential systems and their
             conservation laws, Part I},
   Journal = {Selecta Math. (N.S.)},
   Volume = {1},
   Number = {1},
   Pages = {21-112},
   Year = {1995},
   MRNUMBER = {97d:580008},
   url = {http://www.math.duke.edu/preprints/94-13.dvi},
   Key = {fds243405}
}

@article{fds243406,
   Author = {R. Bryant and Bryant, RL and Griffiths, PA},
   Title = {Characteristic cohomology of differential systems, II:
             Conservation laws for a class of parabolic
             equations},
   Journal = {Duke Math. Journal},
   Volume = {78},
   Number = {3},
   Pages = {531-676},
   Year = {1995},
   MRNUMBER = {96d:58158},
   url = {http://www.math.duke.edu/preprints/93-02.dvi},
   Key = {fds243406}
}

@article{fds318273,
   Author = {R. Bryant and BRYANT, R and GRIFFITHS, P and HSU, L},
   Title = {Toward a geometry of differential equations},
   Journal = {GEOMETRY, TOPOLOGY & PHYSICS},
   Volume = {4},
   Series = {Conf. Proc. Lecture Notes Geom. Topology},
   Pages = {1-76},
   Booktitle = {Geometry, Topology, & Physics},
   Publisher = {Internat. Press, Cambridge, MA},
   Editor = {S.-T. Yau},
   Year = {1995},
   ISBN = {1-57146-024-1},
   MRNUMBER = {97b:58005},
   url = {http://www.math.duke.edu/preprints/94-12.dvi},
   Key = {fds318273}
}

@article{fds318274,
   Author = {R. Bryant and Bryant, R and Gardner, RB},
   Title = {Control Structures},
   Volume = {12},
   Series = {Banach Center Publications},
   Pages = {111-121},
   Booktitle = {Geometry in nonlinear control and differential inclusions
             (Warsaw, 1993)},
   Publisher = {Polish Academy of Sciences},
   Editor = {Jakubczyk, B and Respondek, W and Rzezuchowski,
             T},
   Year = {1995},
   MRNUMBER = {96h:93024},
   url = {http://www.math.duke.edu/preprints/94-11.dvi},
   Key = {fds318274}
}

@article{fds318275,
   Author = {Bryant, R},
   Title = {An introduction to Lie groups and symplectic
             geometry},
   Volume = {1},
   Series = {IAS/Park City Mathematics},
   Pages = {5-181},
   Booktitle = {Geometry and quantum field theory (Park City, UT,
             1991)},
   Publisher = {American Mathematical Society},
   Editor = {Freed, D and Uhlenbeck, K},
   Year = {1995},
   ISBN = {0-8218-0400-6},
   MRNUMBER = {96i:58002},
   url = {http://www.ams.org/mathscinet-getitem?mr=96i:58002},
   Abstract = {A series of lectures on Lie groups and symplectic geometry,
             aimed at the beginning graduate student level.},
   Key = {fds318275}
}

@article{fds243401,
   Author = {R. Bryant and Bryant, RL and Hsu, L},
   Title = {Rigidity of integral curves of rank 2 distributions},
   Journal = {Inventiones mathematicae},
   Volume = {114},
   Number = {1},
   Pages = {435-461},
   Year = {1993},
   ISSN = {0020-9910},
   MRNUMBER = {94j:58003},
   url = {http://www.math.duke.edu/~bryant/Rigid.dvi},
   Doi = {10.1007/BF01232676},
   Key = {fds243401}
}

@article{fds243400,
   Author = {Bryant, RL},
   Title = {Some remarks on the geometry of austere manifolds},
   Journal = {Bol. Soc. Brasil. Mat. (N.S.)},
   Volume = {21},
   Number = {2},
   Pages = {133-157},
   Year = {1991},
   MRNUMBER = {92k:53112},
   url = {http://www.math.duke.edu/preprints/90-03.dvi},
   Key = {fds243400}
}

@article{fds318276,
   Author = {Bryant, R},
   Title = {Two exotic holonomies in dimension four, path geometries,
             and twistor theory},
   Volume = {53},
   Series = {Proc. Sympos. Pure Math.},
   Pages = {33-88},
   Booktitle = {Complex geometry and Lie theory (Sundance, UT,
             1989)},
   Publisher = {American Mathematical Society},
   Editor = {Carlson, J and Clemens, H and Morrison, D},
   Year = {1991},
   ISBN = {0-8218-1492-3},
   MRNUMBER = {93e:53030},
   url = {http://www.math.duke.edu/~bryant/ExoticHol.dvi},
   Key = {fds318276}
}

@article{fds243398,
   Author = {R. Bryant and Harvey, FR and Bryant, RL},
   Title = {Submanifolds in hyper-Kähler geometry},
   Journal = {J. Amer. Math. Soc.},
   Volume = {2},
   Number = {1},
   Pages = {1-31},
   Year = {1989},
   MRNUMBER = {89m:53090},
   url = {http://www.ams.org/mathscinet-getitem?mr=89m:53090},
   Key = {fds243398}
}

@article{fds243399,
   Author = {R. Bryant and Salamon, S and Bryant, RL},
   Title = {On the construction of some complete metrics with
             exceptional holonomy},
   Journal = {Duke Math. J.},
   Volume = {58},
   Number = {3},
   Pages = {829-850},
   Year = {1989},
   MRNUMBER = {90i:53055},
   url = {http://www.ams.org/mathscinet-getitem?mr=90i:53055},
   Key = {fds243399}
}

@article{fds318277,
   Author = {Bryant, R},
   Title = {Surfaces in conformal geometry},
   Volume = {48},
   Series = {Proc. Sympos. Pure Math.},
   Pages = {227-240},
   Booktitle = {The mathematical heritage of Hermann Weyl (Durham, NC,
             1987)},
   Publisher = {American Mathematical Society},
   Editor = {Wells, RO},
   Year = {1988},
   ISBN = {0-8218-1482-6},
   MRNUMBER = {89m:53102},
   url = {http://www.ams.org/mathscinet-getitem?mr=89m:53102},
   Abstract = {A survey paper. However, there are some new results.
             Building on the results in A duality theorm for Willmore
             surfaces, I use the Klein correspondance to determine the
             moduli space of Willmore critical spheres for low critical
             values and also determine the moduli space of Willmore
             minima for the real projective plane in 3-space.},
   Key = {fds318277}
}

@article{fds318278,
   Author = {Bryant, R},
   Title = {Surfaces of mean curvature one in hyperbolic
             space},
   Volume = {154-155},
   Series = {Astérisque},
   Pages = {321-347},
   Booktitle = {Théorie des variétés minimales et applications
             (Palaiseau, 1983–1984)},
   Publisher = {Société Mathématique de France},
   Year = {1988},
   MRNUMBER = {955072},
   url = {http://www.ams.org/mathscinet-getitem?mr=955072},
   Key = {fds318278}
}

@book{fds318279,
   Author = {R. Bryant and Victor Guillemin and Sigurdur Helgason and R. O. Wells, Jr.},
   Title = {Integral Geometry},
   Volume = {63},
   Pages = {350 pages},
   Publisher = {American Mathematical Society},
   Editor = {Bryant, R and Guillemin, V and Helgason, S and Wells,
             RO},
   Year = {1987},
   ISBN = {0-8218-5071-7},
   MRNUMBER = {87j:53003},
   url = {http://www.ams.org/mathscinet-getitem?mr=87j:53003},
   Abstract = {Proceedings of the AMS-IMS-SIAM joint summer research
             conference held in Brunswick, Maine, August 12–18,
             1984},
   Key = {fds318279}
}

@article{fds243397,
   Author = {Bryant, RL},
   Title = {Metrics with exceptional holonomy},
   Journal = {Ann. of Math. (2)},
   Volume = {126},
   Number = {3},
   Pages = {525-576},
   Year = {1987},
   MRNUMBER = {89b:53084},
   url = {http://www.ams.org/mathscinet-getitem?mr=89b:53084},
   Key = {fds243397}
}

@article{fds318280,
   Author = {Bryant, R},
   Title = {On notions of equivalence of variational problems with one
             independent variable},
   Volume = {68},
   Series = {Contemporary Mathematics},
   Pages = {65-76},
   Booktitle = {Differential geometry: the interface between pure and
             applied mathematics (San Antonio, Tex., 1986)},
   Publisher = {American Mathematical Society},
   Editor = {Luksic, M and Martin, C and Shadwick, W},
   Year = {1987},
   ISBN = {0-8218-5075-X},
   MRNUMBER = {89f:58037},
   url = {http://www.ams.org/mathscinet-getitem?mr=89f:58037},
   Key = {fds318280}
}

@article{fds318281,
   Author = {Bryant, R},
   Title = {A survey of Riemannian metrics with special holonomy
             groups},
   Pages = {505-514},
   Booktitle = {Proceedings of the International Congress of Mathematicians.
             Vol. 1, 2. (Berkeley, Calif., 1986)},
   Publisher = {American Mathematical Society},
   Editor = {Gleason, A},
   Year = {1987},
   ISBN = {0-8218-0110-4},
   MRNUMBER = {89f:53068},
   url = {http://www.ams.org/mathscinet-getitem?mr=89f:53068},
   Key = {fds318281}
}

@article{fds318282,
   Author = {Bryant, R},
   Title = {Minimal Lagrangian submanifolds of Kähler-Einstein
             manifolds},
   Volume = {1255},
   Series = {Lecture Notes in Math.},
   Pages = {1-12},
   Booktitle = {Differential geometry and differential equations (Shanghai,
             1985)},
   Publisher = {Springer Verlag},
   Editor = {Gu, C and Berger, M and Bryant, RL},
   Year = {1987},
   ISBN = {3-540-17849-X},
   MRNUMBER = {88j:53061},
   url = {http://www.ams.org/mathscinet-getitem?mr=88j:53061},
   Key = {fds318282}
}

@article{fds243396,
   Author = {R. Bryant and Griffiths, PA and Bryant, RL},
   Title = {Reduction for constrained variational problems and
             $\int{1\over 2}k\sp 2\,ds$},
   Journal = {Amer. J. Math.},
   Volume = {108},
   Number = {3},
   Pages = {525-570},
   Year = {1986},
   MRNUMBER = {88a:58044},
   url = {http://www.ams.org/mathscinet-getitem?mr=88a:58044},
   Key = {fds243396}
}

@article{fds243394,
   Author = {Bryant, RL},
   Title = {Minimal surfaces of constant curvature in
             S^n},
   Journal = {Trans. Amer. Math. Soc.},
   Volume = {290},
   Number = {1},
   Pages = {259-271},
   Year = {1985},
   MRNUMBER = {87c:53110},
   url = {http://www.ams.org/mathscinet-getitem?mr=87c:53110},
   Key = {fds243394}
}

@article{fds243395,
   Author = {Bryant, RL},
   Title = {Lie groups and twistor spaces},
   Journal = {Duke Math. J.},
   Volume = {52},
   Number = {1},
   Pages = {223-261},
   Year = {1985},
   MRNUMBER = {87d:58047},
   url = {http://www.ams.org/mathscinet-getitem?mr=87d:58047},
   Key = {fds243395}
}

@article{fds318283,
   Author = {Bryant, R},
   Title = {Metrics with holonomy G2 or Spin(7)},
   Volume = {1111},
   Series = {Lecture Notes in Math.},
   Pages = {269-277},
   Booktitle = {Workshop Bonn 1984 (Bonn, 1984)},
   Publisher = {Springer},
   Editor = {Hirzebruch, F and Schwermer, J and Suter, S},
   Year = {1985},
   MRNUMBER = {87a:53082},
   url = {http://www.ams.org/mathscinet-getitem?mr=87a:53082},
   Key = {fds318283}
}

@article{fds243393,
   Author = {Bryant, RL},
   Title = {A duality theorem for Willmore surfaces},
   Journal = {J. Differential Geom.},
   Volume = {20},
   Number = {1},
   Pages = {23-53},
   Year = {1984},
   MRNUMBER = {86j:58029},
   url = {http://www.ams.org/mathscinet-getitem?mr=86j:58029},
   Key = {fds243393}
}

@article{fds243391,
   Author = {R. Bryant and Griffiths, P and Yang, D},
   Title = {Characteristics and existence of isometric
             embeddings},
   Journal = {Duke Math. J.},
   Volume = {50},
   Number = {4},
   Pages = {893-994},
   Year = {1983},
   MRNUMBER = {85d:53027},
   url = {http://www.ams.org/mathscinet-getitem?mr=85d:53027},
   Key = {fds243391}
}

@article{fds243392,
   Author = {R. Bryant and Berger, E and Griffiths, P},
   Title = {The Gauss equations and rigidity of isometric
             embeddings},
   Journal = {Duke Math. J.},
   Volume = {50},
   Number = {3},
   Pages = {803-892},
   Year = {1983},
   MRNUMBER = {85k:53056},
   url = {http://www.ams.org/mathscinet-getitem?mr=85k:53056},
   Key = {fds243392}
}

@article{fds318284,
   Author = {R. Bryant and Bryant, R and Griffiths, PA},
   Title = {Some observations on the infinitesimal period relations for
             regular threefolds with trivial canonical
             bundle},
   Volume = {36},
   Series = {Progress in Mathematics},
   Pages = {77-102},
   Booktitle = {Arithmetic and geometry, Vol. II},
   Publisher = {Birkhäuser Boston},
   Editor = {Artin, M and Tate, J},
   Year = {1983},
   ISBN = {3-7643-3133-X},
   MRNUMBER = {86a:32044},
   url = {http://www.ams.org/mathscinet-getitem?mr=86a:32044},
   Key = {fds318284}
}

@article{fds243389,
   Author = {Bryant, RL},
   Title = {Holomorphic curves in Lorentzian CR-manifolds},
   Journal = {Trans. Amer. Math. Soc.},
   Volume = {272},
   Number = {1},
   Pages = {203-221},
   Year = {1982},
   MRNUMBER = {83i:32029},
   url = {http://www.ams.org/mathscinet-getitem?mr=83i:32029},
   Abstract = {When can a real hypersurface in complex n-space contain any
             complex curves? Since the tangent spaces to such a curve
             would have to be null vectors for the Levi form, a necessary
             condition is that the Levi form have zeros. The simplest way
             this can happen in the non-degenerate case is for the Levi
             form to have the Lorentzian signature. In this paper, I show
             that a Lorentzian CR-manifold M has at most a finite
             parameter family of holomorphic curves, in fact, at most an
             n2 parameter family if the dimension of M is 2n+1. This
             maximum is attained, as I show by example. When n=2, the
             only way it can be reached is for M to be CR-flat. In higher
             dimensions, where the CR-flat model does not achieve the
             maximum, it is still unknown whether or not there is more
             than one local model with the maximal dimension family of
             holomorphic curves. The technique used is exterior
             differential systems together with the Chern-Moser theory in
             the n=2 case. Reprints are available, but can also be
             downloaded from the AMS or from JSTOR},
   Key = {fds243389}
}

@article{fds243390,
   Author = {Bryant, RL},
   Title = {Submanifolds and special structures on the
             octonians},
   Journal = {J. Differential Geom.},
   Volume = {17},
   Number = {2},
   Pages = {185-232},
   Year = {1982},
   MRNUMBER = {84h:53091},
   url = {http://www.ams.org/mathscinet-getitem?mr=84h:53091},
   Abstract = {A study of the geometry of submanifolds of real 8-space
             under the group of motions generated by translations and
             rotations in the subgroup Spin(7) instead of the full SO(8).
             I call real 8-space endowed with this group O or octonian
             space. The fact that the stabilizer of an oriented 2-plane
             in Spin(7) is U(3) implies that any oriented 6-manifold in O
             inherits a U(3)-structure. The first part of the paper
             studies the generality of the 6-manifolds whose inherited
             U(3)-structure is symplectic, complex, or K&auml;hler, etc.
             by applying the theory of exterior differential systems. I
             then turn to the study of the standard 6-sphere in O as an
             almost complex manifold and study the space of what are now
             called pseudo-holomorphic curves in the 6-sphere. I prove
             that every compact Riemann surface occurs as a (possibly
             ramified) pseudo-holomorphic curve in the 6-sphere. I also
             show that all of the genus zero pseudo-holomorphic curves in
             the 6-sphere are algebraic as surfaces. Reprints are
             available.},
   Key = {fds243390}
}

@article{fds243410,
   Author = {Bryant, RL},
   Title = {Conformal and minimal immersions of compact surfaces into
             the 4-sphere},
   Journal = {J. Differential Geom.},
   Volume = {17},
   Number = {3},
   Pages = {455-473},
   Year = {1982},
   MRNUMBER = {84a:53062},
   url = {http://www.ams.org/mathscinet-getitem?mr=84a:53062},
   Key = {fds243410}
}

@article{fds318285,
   Author = {R. Bryant and Bryant, R and Chern, SS and Griffiths, PA},
   Title = {Exterior Differential Systems},
   Volume = {1},
   Pages = {219-338},
   Booktitle = {Proceedings of the 1980 Beijing Symposium on Differential
             Geometry and Differential Equations (Beijing,
             1980)},
   Publisher = {Science Press; Gordon & Breach Science Publishers},
   Editor = {Chern, SS and Wu, WT},
   Year = {1982},
   ISBN = {0-677-16420-3},
   MRNUMBER = {85k:58005},
   url = {http://www.ams.org/mathscinet-getitem?mr=85k:58005},
   Key = {fds318285}
}

@article{fds243388,
   Author = {R. Bryant and Berger, E and Griffiths, P},
   Title = {Some isometric embedding and rigidity results for Riemannian
             manifolds},
   Journal = {Proc. Nat. Acad. Sci. U.S.A.},
   Volume = {78},
   Number = {8},
   Pages = {4657-4660},
   Year = {1981},
   MRNUMBER = {82h:53074},
   url = {http://www.ams.org/mathscinet-getitem?mr=82h:53074},
   Key = {fds243388}
}

@book{fds10113,
   Author = {R. Bryant and Marcel Berger and Chao Hao Gu},
   Title = {Differential Geometry and Differential Equations},
   Journal = {Proceedings of the sixth symposium held at Fudan University,
             Shanghai, June 21--July 6, 1985, pp. xii+243, 1987,
             Springer-Verlag, Berlin},
   MRNUMBER = {88b:53002},
   url = {http://www.ams.org/mathscinet-getitem?mr=88b:53002},
   Key = {fds10113}
}


%% Cahill, Jameson   
@article{fds225806,
   Author = {Jameson Cahill and Dustin G. Mixon},
   Title = {Robust width: A characterization of uniformly stable and
             robust compressed sensing},
   Year = {2014},
   url = {http://arxiv.org/abs/1408.4409},
   Abstract = {http://arxiv.org/abs/1408.4409},
   Key = {fds225806}
}

@article{fds225807,
   Author = {Saeid Bahmanpour and Jameson Cahill and Peter G. Casazza and John
             Jasper, Lindsey M. Woodland},
   Title = {Phase retrieval and norm retrieval},
   Year = {2014},
   url = {http://arxiv.org/abs/1409.8266},
   Key = {fds225807}
}

@article{fds221006,
   Author = {J. Cahill and P.G. Casazza and M. Ehler and S. Li},
   Title = {Tight and random nonorthogonal fusion frames},
   Year = {2013},
   url = {http://http://arxiv.org/abs/1309.0532},
   Abstract = {First we show that tight nonorthogonal fusion frames are
             relatively easy to com by. In order to do this we need to
             establish a classification of how to to wire a self adjoint
             operator as a product of (nonorthogonal) projection
             operators. We also discuss the link between nonorthogonal
             fusion frames and positive operator valued measures, we
             define and study a nonorthogonal fusion frame potential, and
             we introduce the idea of random nonorthogonal fusion
             frames.},
   Key = {fds221006}
}

@article{fds221008,
   Author = {J. Cahill and D.G. Mixon and N. Strawn},
   Title = {Connectivity and Irreducibility of Algebraic Varieties of
             Finite Unit Norm Tight Frames},
   Year = {2013},
   url = {http://arxiv.org/abs/1311.4748},
   Abstract = {In this paper, we settle a long-standing problem on the
             connectivity of spaces of finite unit norm tight frames
             (FUNTFs), essentially affirming a conjecture first appearing
             in Dykema and Strawn (2003). Our central technique involves
             continuous liftings of paths from the polytope of eigensteps
             (see Cahill et al. (2012)) to spaces of FUNTFs. After
             demonstrating this connectivity result, we refine our
             analysis to show that the set of nonsingular points on these
             spaces is also connected, and we use this result to show
             that spaces of FUNTFs are irreducible in the
             algebro-geometric sense, and that generic FUNTFs are full
             spark.},
   Key = {fds221008}
}


%% Cain, John   
@misc{fds32393,
   Author = {D.G. Schaeffer and J.W. Cain and D.J. Gauthier and S.S. Kalb and W.
             Krassowska, R.A. Oliver and E.G. Tolkacheva and W.
             Ying},
   Title = {An ionically based mapping model with memory for cardiac
             restitution},
   Year = {2005},
   Month = {February},
   Key = {fds32393}
}

@article{fds38248,
   Author = {J.W. Cain and D.G. Schaeffer},
   Title = {Two-term asymptotic approximation of a cardiac restitution
             curve},
   Year = {2005},
   Key = {fds38248}
}

@misc{fds36954,
   Author = {J. Cain},
   Title = {Issues in the one-dimensional dynamics of a paced cardiac
             fiber},
   Journal = {Ph.D. Dissertation, Duke University},
   Year = {2005},
   Key = {fds36954}
}

@misc{fds26554,
   Author = {J.W. Cain and E.G. Tolkacheva and D.G. Schaeffer and D.J.
             Gauthier},
   Title = {Rate-dependent waveback velocity of cardiac action
             potentials in a one-dimensional cable},
   Journal = {International Conference for Mathematics in Biology and
             Medicine: Annual Meeting for the Society for Mathematical
             Biology},
   Year = {2004},
   Month = {July},
   Key = {fds26554}
}

@article{fds26048,
   Author = {D.G. Schaeffer and J.W. Cain and D.J. Gauthier and S.S. Kalb and W.
             Krassowska, R.A. Oliver and E.G. Tolkacheva},
   Title = {An ionically based mapping model with memory for cardiac
             restitution},
   Journal = {Bull. Math. Bio.},
   Year = {2004},
   Key = {fds26048}
}

@article{fds30212,
   Author = {J.W. Cain and E.G. Tolkacheva and D.G. Schaeffer and D.J.
             Gauthier},
   Title = {Rate-dependent propagation of cardiac action potentials in a
             one-dimensional fiber},
   Journal = {Phys. Rev. E.},
   Volume = {70},
   Number = {6},
   Pages = {061906},
   Year = {2004},
   Key = {fds30212}
}

@misc{fds26555,
   Author = {J.W. Cain},
   Title = {Simulating discordant alternans with a two-current
             model},
   Journal = {International School on Biomathematics, Bioengineering and
             Clinical Aspects of Blood Flow, MSRI},
   Year = {2002},
   Month = {August},
   Key = {fds26555}
}


%% Calderbank, Robert   
@article{fds326748,
   Author = {Wang, L and Chen, M and Rodrigues, M and Wilcox, D and Calderbank, R and Carin, L},
   Title = {Information-Theoretic Compressive Measurement
             Design.},
   Journal = {IEEE Transactions on Pattern Analysis and Machine
             Intelligence},
   Volume = {39},
   Number = {6},
   Pages = {1150-1164},
   Year = {2017},
   Month = {June},
   url = {http://dx.doi.org/10.1109/tpami.2016.2568189},
   Abstract = {An information-theoretic projection design framework is
             proposed, of interest for feature design and compressive
             measurements. Both Gaussian and Poisson measurement models
             are considered. The gradient of a proposed
             information-theoretic metric (ITM) is derived, and a
             gradient-descent algorithm is applied in design; connections
             are made to the information bottleneck. The fundamental
             solution structure of such design is revealed in the case of
             a Gaussian measurement model and arbitrary input statistics.
             This new theoretical result reveals how ITM parameter
             settings impact the number of needed projection
             measurements, with this verified experimentally. The ITM
             achieves promising results on real data, for both signal
             recovery and classification.},
   Doi = {10.1109/tpami.2016.2568189},
   Key = {fds326748}
}

@article{fds326881,
   Author = {Hadani, R and Rakib, S and Tsatsanis, M and Monk, A and Goldsmith, AJ and Molisch, AF and Calderbank, R},
   Title = {Orthogonal time frequency space modulation},
   Journal = {IEEE Wireless Communications and Networking
             Conference},
   Year = {2017},
   Month = {May},
   ISBN = {9781509041831},
   url = {http://dx.doi.org/10.1109/WCNC.2017.7925924},
   Abstract = {© 2017 IEEE. A new two-dimensional modulation technique
             called Orthogonal Time Frequency Space (OTFS) modulation
             designed in the delay-Doppler domain is introduced. Through
             this design, which exploits full diversity over time and
             frequency, OTFS coupled with equalization converts the
             fading, time-varying wireless channel experienced by
             modulated signals such as OFDM into a time-independent
             channel with a complex channel gain that is roughly constant
             for all symbols. Thus, transmitter adaptation is not needed.
             This extraction of the full channel diversity allows OTFS to
             greatly simplify system operation and significantly improves
             performance, particular in systems with high Doppler, short
             packets, and large antenna arrays. Simulation results
             indicate at least several dB of block error rate performance
             improvement for OTFS over OFDM in all of these settings. In
             addition these results show that even at very high Dopplers
             (500 km/h), OTFS approaches channel capacity through linear
             scaling of throughput with the MIMO order, whereas the
             performance of OFDM under typical design parameters breaks
             down completely.},
   Doi = {10.1109/WCNC.2017.7925924},
   Key = {fds326881}
}

@article{fds326749,
   Author = {Campbell, K and Carpenter, KLH and Espinosa, S and Hashemi, J and Qiu,
             Q and Tepper, M and Calderbank, R and Sapiro, G and Egger, HL and Baker,
             JP and Dawson, G},
   Title = {Use of a Digital Modified Checklist for Autism in Toddlers -
             Revised with Follow-up to Improve Quality of Screening for
             Autism.},
   Journal = {The Journal of Pediatrics},
   Volume = {183},
   Pages = {133-139.e1},
   Year = {2017},
   Month = {April},
   url = {http://dx.doi.org/10.1016/j.jpeds.2017.01.021},
   Abstract = {To assess changes in quality of care for children at risk
             for autism spectrum disorders (ASD) due to process
             improvement and implementation of a digital screening
             form.The process of screening for ASD was studied in an
             academic primary care pediatrics clinic before and after
             implementation of a digital version of the Modified
             Checklist for Autism in Toddlers - Revised with Follow-up
             with automated risk assessment. Quality metrics included
             accuracy of documentation of screening results and
             appropriate action for positive screens (secondary screening
             or referral). Participating physicians completed pre- and
             postintervention surveys to measure changes in attitudes
             toward feasibility and value of screening for ASD. Evidence
             of change was evaluated with statistical process control
             charts and χ2 tests.Accurate documentation in the
             electronic health record of screening results increased from
             54% to 92% (38% increase, 95% CI 14%-64%) and appropriate
             action for children screening positive increased from 25% to
             85% (60% increase, 95% CI 35%-85%). A total of 90% of
             participating physicians agreed that the transition to a
             digital screening form improved their clinical assessment of
             autism risk.Implementation of a tablet-based digital version
             of the Modified Checklist for Autism in Toddlers - Revised
             with Follow-up led to improved quality of care for children
             at risk for ASD and increased acceptability of screening for
             ASD. Continued efforts towards improving the process of
             screening for ASD could facilitate rapid, early diagnosis of
             ASD and advance the accuracy of studies of the impact of
             screening.},
   Doi = {10.1016/j.jpeds.2017.01.021},
   Key = {fds326749}
}

@article{fds326882,
   Author = {Reboredo, H and Renna, F and Calderbank, R and Rodrigues,
             MRD},
   Title = {Bounds on the Number of Measurements for Reliable
             Compressive Classification},
   Journal = {IEEE Transactions on Signal Processing},
   Volume = {64},
   Number = {22},
   Pages = {5778-5793},
   Year = {2016},
   Month = {November},
   url = {http://dx.doi.org/10.1109/TSP.2016.2599496},
   Doi = {10.1109/TSP.2016.2599496},
   Key = {fds326882}
}

@article{fds326883,
   Author = {Thompson, A and Robles, FE and Wilson, JW and Deb, S and Calderbank, R and Warren, WS},
   Title = {Dual-wavelength pump-probe microscopy analysis of melanin
             composition.},
   Journal = {Scientific Reports},
   Volume = {6},
   Pages = {36871},
   Year = {2016},
   Month = {November},
   url = {http://dx.doi.org/10.1038/srep36871},
   Abstract = {Pump-probe microscopy is an emerging technique that provides
             detailed chemical information of absorbers with
             sub-micrometer spatial resolution. Recent work has shown
             that the pump-probe signals from melanin in human skin
             cancers correlate well with clinical concern, but it has
             been difficult to infer the molecular origins of these
             differences. Here we develop a mathematical framework to
             describe the pump-probe dynamics of melanin in human
             pigmented tissue samples, which treats the ensemble of
             individual chromophores that make up melanin as Gaussian
             absorbers with bandwidth related via Frenkel excitons. Thus,
             observed signals result from an interplay between the
             spectral bandwidths of the individual underlying
             chromophores and spectral proximity of the pump and probe
             wavelengths. The model is tested using a dual-wavelength
             pump-probe approach and a novel signal processing method
             based on gnomonic projections. Results show signals can be
             described by a single linear transition path with different
             rates of progress for different individual pump-probe
             wavelength pairs. Moreover, the combined dual-wavelength
             data shows a nonlinear transition that supports our
             mathematical framework and the excitonic model to describe
             the optical properties of melanin. The novel gnomonic
             projection analysis can also be an attractive generic tool
             for analyzing mixing paths in biomolecular and analytical
             chemistry.},
   Doi = {10.1038/srep36871},
   Key = {fds326883}
}

@article{fds326750,
   Author = {Renna, F and Wang, L and Yuan, X and Yang, J and Reeves, G and Calderbank,
             R and Carin, L and Rodrigues, MRD},
   Title = {Classification and Reconstruction of High-Dimensional
             Signals From Low-Dimensional Features in the Presence of
             Side Information},
   Journal = {IEEE Transactions on Information Theory},
   Volume = {62},
   Number = {11},
   Pages = {6459-6492},
   Year = {2016},
   Month = {November},
   url = {http://dx.doi.org/10.1109/TIT.2016.2606646},
   Doi = {10.1109/TIT.2016.2606646},
   Key = {fds326750}
}

@article{fds326751,
   Author = {Kumar, S and Calderbank, R and Pfister, HD},
   Title = {Beyond double transitivity: Capacity-achieving cyclic codes
             on erasure channels},
   Journal = {2016 IEEE Information Theory Workshop, ITW
             2016},
   Pages = {241-245},
   Year = {2016},
   Month = {October},
   ISBN = {9781509010905},
   url = {http://dx.doi.org/10.1109/ITW.2016.7606832},
   Abstract = {© 2016 IEEE. Recently, sequences of error-correcting codes
             with doubly-transitive permutation groups were shown to
             achieve capacity on erasure channels under symbol-wise
             maximum a posteriori (MAP) decoding. From this, it follows
             that Reed-Muller and primitive narrow-sense BCH codes
             achieve capacity in the same setting. In this article, we
             extend this result to a large family of cyclic codes by
             considering codes whose permutation groups satisfy a
             condition weaker than double transitivity. The article
             combines two simple technical contributions. First, we show
             that the transition width of a monotone boolean function is
             O(1/log k), where k is the size of the smallest orbit
             induced by its symmetry group. The proof is based on
             Talagrand's lower bound on influences for monotone boolean
             functions. Second, we consider the extrinsic information
             transfer (EXIT) function of an Fq-linear cyclic code whose
             blocklength N divides q t -1 and is coprime with q-1. We
             show that this EXIT function is a monotone boolean function
             whose symmetry group contains no orbits of size smaller than
             the smallest prime divisor of t. Combining these, we show
             that sequences of cyclic codes, whose blocklengths satisfy
             the above conditions, achieve capacity on the q-ary erasure
             channel if all prime divisors of t tend to
             infinity.},
   Doi = {10.1109/ITW.2016.7606832},
   Key = {fds326751}
}

@article{fds326752,
   Author = {Mappouras, G and Vahid, A and Calderbank, R and Sorin,
             DJ},
   Title = {Methuselah flash: Rewriting codes for extra long storage
             lifetime},
   Journal = {Proceedings - 46th Annual IEEE/IFIP International Conference
             on Dependable Systems and Networks, DSN 2016},
   Pages = {180-191},
   Year = {2016},
   Month = {September},
   ISBN = {9781467388917},
   url = {http://dx.doi.org/10.1109/DSN.2016.25},
   Abstract = {© 2016 IEEE. Motivated by embedded systems and datacenters
             that require long-life components, we extend the lifetime of
             Flash memory using rewriting codes that allow for multiple
             writes to a page before it needs to be erased. Although
             researchers have previously explored rewriting codes for
             this purpose, we make two significant contributions beyond
             prior work. First, we remove the assumption of idealized -
             and unrealistically optimistic - Flash cells used in prior
             work on endurance codes. Unfortunately, current Flash
             technology has a non-ideal interface, due to its underlying
             physical design, and does not, for example, allow all
             seemingly possible increases in a cell's level. We show how
             to provide the ideal multi-level cell interface, by
             developing a virtual Flash cell, and we evaluate its impact
             on existing endurance codes. Our second contribution is our
             development of novel endurance codes, called Methuselah
             Flash Codes (MFC), that provide better cost/lifetime
             trade-offs than previously studied codes.},
   Doi = {10.1109/DSN.2016.25},
   Key = {fds326752}
}

@article{fds326884,
   Author = {Vahid, A and Calderbank, R},
   Title = {Two-User Erasure Interference Channels With Local Delayed
             CSIT},
   Journal = {IEEE Transactions on Information Theory},
   Volume = {62},
   Number = {9},
   Pages = {4910-4923},
   Year = {2016},
   Month = {September},
   url = {http://dx.doi.org/10.1109/TIT.2016.2594224},
   Doi = {10.1109/TIT.2016.2594224},
   Key = {fds326884}
}

@article{fds326885,
   Author = {Nokleby, M and Beirami, A and Calderbank, R},
   Title = {Rate-distortion bounds on Bayes risk in supervised
             learning},
   Journal = {IEEE International Symposium on Information Theory -
             Proceedings},
   Volume = {2016-August},
   Pages = {2099-2103},
   Year = {2016},
   Month = {August},
   ISBN = {9781509018062},
   url = {http://dx.doi.org/10.1109/ISIT.2016.7541669},
   Abstract = {© 2016 IEEE. An information-theoretic framework is
             presented for estimating the number of labeled samples
             needed to train a classifier in a parametric Bayesian
             setting. Ideas from rate-distortion theory are used to
             derive bounds for the average L 1 or L ∞ distance between
             the learned classifier and the true maximum a posteriori
             classifier in terms of familiar information-theoretic
             quantities and the number of training samples available. The
             maximum a posteriori classifier is viewed as a random
             source, labeled training data are viewed as a finite-rate
             encoding of the source, and the L 1 or L ∞ Bayes risk is
             viewed as the average distortion. The result is a framework
             dual to the well-known probably approximately correct (PAC)
             framework. PAC bounds characterize worst-case learning
             performance of a family of classifiers whose complexity is
             captured by the Vapnik-Chervonenkis (VC) dimension. The
             rate-distortion framework, on the other hand, characterizes
             the average-case performance of a family of data
             distributions in terms of a quantity called the
             interpolation dimension, which represents the complexity of
             the family of data distributions. The resulting bounds do
             not suffer from the pessimism typical of the PAC framework,
             particularly when the training set is small.},
   Doi = {10.1109/ISIT.2016.7541669},
   Key = {fds326885}
}

@article{fds326886,
   Author = {Vahid, A and Calderbank, R},
   Title = {When does spatial correlation add value to delayed channel
             state information?},
   Journal = {IEEE International Symposium on Information Theory -
             Proceedings},
   Volume = {2016-August},
   Pages = {2624-2628},
   Year = {2016},
   Month = {August},
   ISBN = {9781509018062},
   url = {http://dx.doi.org/10.1109/ISIT.2016.7541774},
   Abstract = {© 2016 IEEE. Fast fading wireless networks with delayed
             knowledge of the channel state information have received
             significant attention in recent years. An exception is
             networks where channels are spatially correlated. This paper
             characterizes the capacity region of two-user erasure
             interference channels with delayed knowledge of the channel
             state information and spatially correlated channels. There
             are instances where spatial correlation eliminates any
             potential gain from delayed channel state information and
             instances where it enables the same performance that is
             possible with instantaneous knowledge of channel state. The
             key is an extremal entropy inequality for spatially
             correlated channels that separates the two types of
             instances. It is also shown that to achieve the capacity
             region, each transmitter only needs to rely on the delayed
             knowledge of the channels to which it is
             connected.},
   Doi = {10.1109/ISIT.2016.7541774},
   Key = {fds326886}
}

@article{fds326887,
   Author = {Sokolic, J and Renna, F and Calderbank, R and Rodrigues,
             MRD},
   Title = {Mismatch in the Classification of Linear Subspaces:
             Sufficient Conditions for Reliable Classification},
   Journal = {IEEE Transactions on Signal Processing},
   Volume = {64},
   Number = {12},
   Pages = {3035-3050},
   Year = {2016},
   Month = {June},
   url = {http://dx.doi.org/10.1109/TSP.2016.2537272},
   Doi = {10.1109/TSP.2016.2537272},
   Key = {fds326887}
}

@article{fds326753,
   Author = {Wang, L and Renna, F and Yuan, X and Rodrigues, M and Calderbank, R and Carin, L},
   Title = {A general framework for reconstruction and classification
             from compressive measurements with side information},
   Journal = {IEEE International Conference on Acoustics Speech and Signal
             Processing},
   Volume = {2016-May},
   Pages = {4239-4243},
   Year = {2016},
   Month = {May},
   ISBN = {9781479999880},
   url = {http://dx.doi.org/10.1109/ICASSP.2016.7472476},
   Abstract = {© 2016 IEEE. We develop a general framework for compressive
             linear-projection measurements with side information. Side
             information is an additional signal correlated with the
             signal of interest. We investigate the impact of side
             information on classification and signal recovery from
             low-dimensional measurements. Motivated by real
             applications, two special cases of the general model are
             studied. In the first, a joint Gaussian mixture model is
             manifested on the signal and side information. The second
             example again employs a Gaussian mixture model for the
             signal, with side information drawn from a mixture in the
             exponential family. Theoretical results on recovery and
             classification accuracy are derived. The presence of side
             information is shown to yield improved performance, both
             theoretically and experimentally.},
   Doi = {10.1109/ICASSP.2016.7472476},
   Key = {fds326753}
}

@article{fds326888,
   Author = {Beirami, A and Calderbank, R and Christiansen, M and Duffy, K and Makhdoumi, A and Medard, M},
   Title = {A geometric perspective on guesswork},
   Journal = {2015 53rd Annual Allerton Conference on Communication,
             Control, and Computing, Allerton 2015},
   Pages = {941-948},
   Year = {2016},
   Month = {April},
   ISBN = {9781509018239},
   url = {http://dx.doi.org/10.1109/ALLERTON.2015.7447109},
   Abstract = {© 2015 IEEE. Guesswork is the position at which a random
             string drawn from a given probability distribution appears
             in the list of strings ordered from the most likely to the
             least likely. We define the tilt operation on probability
             distributions and show that it parametrizes an exponential
             family of distributions, which we refer to as the tilted
             family of the source. We prove that two sources result in
             the same guesswork, i.e., the same ordering from most likely
             to least likely on all strings, if and only if they belong
             to the same tilted family. We also prove that the strings
             whose guesswork is smaller than a given string are
             concentrated on the tilted family. Applying Laplace's
             method, we derive precise approximations on the distribution
             of guesswork on i.i.d. sources. The simulations show a good
             match between the approximations and the actual guesswork
             for i.i.d. sources.},
   Doi = {10.1109/ALLERTON.2015.7447109},
   Key = {fds326888}
}

@article{fds326889,
   Author = {Vahid, A and Shomorony, I and Calderbank, R},
   Title = {Informational bottlenecks in two-unicast wireless networks
             with delayed CSIT},
   Journal = {2015 53rd Annual Allerton Conference on Communication,
             Control, and Computing, Allerton 2015},
   Pages = {1256-1263},
   Year = {2016},
   Month = {April},
   ISBN = {9781509018239},
   url = {http://dx.doi.org/10.1109/ALLERTON.2015.7447152},
   Abstract = {© 2015 IEEE. We study the impact of delayed channel state
             information at the transmitters (CSIT) in two-unicast
             wireless networks with a layered topology and arbitrary
             connectivity. We introduce a technique to obtain outer
             bounds to the degrees-of-freedom (DoF) region through the
             new graph-theoretic notion of bottleneck nodes. Such nodes
             act as informational bottlenecks only under the assumption
             of delayed CSIT, and imply asymmetric DoF bounds of the form
             mD1 + D2 ≤ m. Combining this outer-bound technique with
             new achievability schemes, we characterize the sum DoF of a
             class of two-unicast wireless networks, which shows that,
             unlike in the case of instantaneous CSIT, the DoF of
             two-unicast networks with delayed CSIT can take an infinite
             set of values.},
   Doi = {10.1109/ALLERTON.2015.7447152},
   Key = {fds326889}
}

@article{fds326890,
   Author = {Huang, J and Qiu, Q and Calderbank, R},
   Title = {The Role of Principal Angles in Subspace
             Classification},
   Journal = {IEEE Transactions on Signal Processing},
   Volume = {64},
   Number = {8},
   Pages = {1933-1945},
   Year = {2016},
   Month = {April},
   url = {http://dx.doi.org/10.1109/TSP.2015.2500889},
   Doi = {10.1109/TSP.2015.2500889},
   Key = {fds326890}
}

@article{fds326754,
   Author = {Qiu, Q and Thompson, A and Calderbank, R and Sapiro,
             G},
   Title = {Data Representation Using the Weyl Transform},
   Journal = {IEEE Transactions on Signal Processing},
   Volume = {64},
   Number = {7},
   Pages = {1844-1853},
   Year = {2016},
   Month = {April},
   url = {http://dx.doi.org/10.1109/TSP.2015.2505661},
   Doi = {10.1109/TSP.2015.2505661},
   Key = {fds326754}
}

@article{fds326891,
   Author = {Goparaju, S and Rouayheb, SE and Calderbank, R},
   Title = {Can linear minimum storage regenerating codes be universally
             secure?},
   Journal = {Conference Record of the Asilomar Conference on Signals,
             Systems and Computers},
   Volume = {2016-February},
   Pages = {549-553},
   Year = {2016},
   Month = {February},
   ISBN = {9781467385763},
   url = {http://dx.doi.org/10.1109/ACSSC.2015.7421189},
   Abstract = {© 2015 IEEE. We study the problem of making a distributed
             storage system information-theoretically secure against a
             passive eavesdropper, and aim to characterize coding schemes
             that are universally secure for up to a given number of
             eavesdropped nodes. Specifically, we consider minimum
             storage regenerating (MSR) codes and ask the following
             question: For an MSR code where a failed node is repaired
             using all the remaining nodes, is it possible to
             simultaneously be optimally secure using a single linear
             coding scheme? We define a pareto-optimality associated with
             this simultaneity and show that there exists at least one
             linear coding scheme that is pareto-optimal.},
   Doi = {10.1109/ACSSC.2015.7421189},
   Key = {fds326891}
}

@article{fds326756,
   Author = {Carpenter, KLH and Sprechmann, P and Calderbank, R and Sapiro, G and Egger, HL},
   Title = {Quantifying Risk for Anxiety Disorders in Preschool
             Children: A Machine Learning Approach.},
   Journal = {PloS one},
   Volume = {11},
   Number = {11},
   Pages = {e0165524},
   Year = {2016},
   Month = {January},
   url = {http://dx.doi.org/10.1371/journal.pone.0165524},
   Abstract = {Early childhood anxiety disorders are common, impairing, and
             predictive of anxiety and mood disorders later in childhood.
             Epidemiological studies over the last decade find that the
             prevalence of impairing anxiety disorders in preschool
             children ranges from 0.3% to 6.5%. Yet, less than 15% of
             young children with an impairing anxiety disorder receive a
             mental health evaluation or treatment. One possible reason
             for the low rate of care for anxious preschoolers is the
             lack of affordable, timely, reliable and valid tools for
             identifying young children with clinically significant
             anxiety. Diagnostic interviews assessing psychopathology in
             young children require intensive training, take hours to
             administer and code, and are not available for use outside
             of research settings. The Preschool Age Psychiatric
             Assessment (PAPA) is a reliable and valid structured
             diagnostic parent-report interview for assessing
             psychopathology, including anxiety disorders, in 2 to 5 year
             old children. In this paper, we apply machine-learning tools
             to already collected PAPA data from two large community
             studies to identify sub-sets of PAPA items that could be
             developed into an efficient, reliable, and valid screening
             tool to assess a young child's risk for an anxiety disorder.
             Using machine learning, we were able to decrease by an order
             of magnitude the number of items needed to identify a child
             who is at risk for an anxiety disorder with an accuracy of
             over 96% for both generalized anxiety disorder (GAD) and
             separation anxiety disorder (SAD). Additionally, rather than
             considering GAD or SAD as discrete/binary entities, we
             present a continuous risk score representing the child's
             risk of meeting criteria for GAD or SAD. Identification of a
             short question-set that assesses risk for an anxiety
             disorder could be a first step toward development and
             validation of a relatively short screening tool feasible for
             use in pediatric clinics and daycare/preschool
             settings.},
   Doi = {10.1371/journal.pone.0165524},
   Key = {fds326756}
}

@article{fds326892,
   Author = {Thompson, A and Calderbank, R},
   Title = {Compressive imaging using fast transform
             coding},
   Journal = {Proceedings of SPIE - The International Society for Optical
             Engineering},
   Volume = {9992},
   Year = {2016},
   Month = {January},
   ISBN = {9781510603882},
   url = {http://dx.doi.org/10.1117/12.2239999},
   Abstract = {© 2016 SPIE. We propose deterministic sampling strategies
             for compressive imaging based on Delsarte-Goethals frames.
             We show that these sampling strategies result in multi-scale
             measurements which can be related to the 2D Haar wavelet
             transform. We demonstrate the effectiveness of our proposed
             strategies through numerical experiments.},
   Doi = {10.1117/12.2239999},
   Key = {fds326892}
}

@article{fds326893,
   Author = {Nokleby, M and Beirami, A and Calderbank, R},
   Title = {A rate-distortion framework for supervised
             learning},
   Journal = {IEEE International Workshop on Machine Learning for Signal
             Processing : [proceedings]. IEEE International Workshop on
             Machine Learning for Signal Processing},
   Volume = {2015-November},
   Year = {2015},
   Month = {November},
   ISBN = {9781467374545},
   url = {http://dx.doi.org/10.1109/MLSP.2015.7324319},
   Abstract = {© 2015 IEEE. An information-theoretic framework is
             presented for bounding the number of samples needed for
             supervised learning in a parametric Bayesian setting. This
             framework is inspired by an analogy with rate-distortion
             theory, which characterizes tradeoffs in the lossy
             compression of random sources. In a parametric Bayesian
             environment, the maximum a posteriori classifier can be
             viewed as a random function of the model parameters. Labeled
             training data can be viewed as a finite-rate encoding of
             that source, and the excess loss due to using the learned
             classifier instead of the MAP classifier can be viewed as
             distortion. A strict bound on the loss-measured in terms of
             the expected total variation-is derived, providing a minimum
             number of training samples needed to drive the expected
             total variation to within a specified tolerance. The
             tightness of this bound is demonstrated on the
             classification of Gaus-sians, for which one can derive
             closed-form expressions for the bound.},
   Doi = {10.1109/MLSP.2015.7324319},
   Key = {fds326893}
}

@article{fds326757,
   Author = {Eslami, A and Velasco, A and Vahid, A and Mappouras, G and Calderbank,
             R and Sorin, DJ},
   Title = {Writing without disturb on phase change memories by
             integrating coding and layout design},
   Journal = {ACM International Conference Proceeding Series},
   Volume = {05-08-October-2015},
   Pages = {71-77},
   Year = {2015},
   Month = {October},
   ISBN = {9781450336048},
   url = {http://dx.doi.org/10.1145/2818950.2818962},
   Abstract = {© 2015 ACM. We integrate coding techniques and layout
             design to elimi- nate write-disturb in phase change memories
             (PCMs), while enhancing lifetime and host-visible capacity.
             We first pro- pose a checkerboard confguration for cell
             layout to elimi- nate write-disturb while doubling the
             memory lifetime. We then introduce two methods to jointly
             design Write-Once- Memory (WOM) codes and layout. The first
             WOM-layout design improves the lifetime by more than double
             without compromising the host-visible capacity. The second
             design applies WOM codes to even more dense layouts to
             achieve both lifetime and capacity gains. The constructions
             demon- strate that substantial improvements to lifetime and
             host- visible capacity are possible by co-designing coding
             and cell layout in PCM.},
   Doi = {10.1145/2818950.2818962},
   Key = {fds326757}
}

@article{fds326894,
   Author = {Vahid, A and Calderbank, R},
   Title = {Impact of local delayed CSIT on the capacity region of the
             two-user interference channel},
   Journal = {IEEE International Symposium on Information Theory -
             Proceedings},
   Volume = {2015-June},
   Pages = {2421-2425},
   Year = {2015},
   Month = {September},
   ISBN = {9781467377041},
   url = {http://dx.doi.org/10.1109/ISIT.2015.7282890},
   Abstract = {© 2015 IEEE. The coherence time of a wireless channel is
             often smaller than the delay with which channel state
             information is available at transmitters. In this paper, we
             aim to find the most important subset of the channel state
             information that transmitters need to learn with delay. We
             characterize the capacity region of the two-user
             interference channel with local delayed channel state
             information at transmitters. We propose a transmission
             strategy that only relies on the delayed knowledge of the
             outgoing links at each transmitter and achieves the
             outer-bound for the scenario in which transmitters learn the
             entire channel state with delay. We also show that the
             delayed knowledge of the outgoing links is the minimum
             delayed knowledge that is required to outperform the no
             knowledge assumption.},
   Doi = {10.1109/ISIT.2015.7282890},
   Key = {fds326894}
}

@article{fds326895,
   Author = {Sokolić, J and Renna, F and Calderbank, R and Rodrigues,
             MRD},
   Title = {Mismatch in the classification of linear subspaces: Upper
             bound to the probability of error},
   Journal = {IEEE International Symposium on Information Theory -
             Proceedings},
   Volume = {2015-June},
   Pages = {2201-2205},
   Year = {2015},
   Month = {September},
   ISBN = {9781467377041},
   url = {http://dx.doi.org/10.1109/ISIT.2015.7282846},
   Abstract = {© 2015 IEEE. This paper studies the performance associated
             with the classification of linear subspaces corrupted by
             noise with a mismatched classifier. In particular, we
             consider a problem where the classifier observes a noisy
             signal, the signal distribution conditioned on the signal
             class is zero-mean Gaussian with low-rank covariance matrix,
             and the classifier knows only the mismatched parameters in
             lieu of the true parameters. We derive an upper bound to the
             misclassification probability of the mismatched classifier
             and characterize its behaviour. Specifically, our
             characterization leads to sharp sufficient conditions that
             describe the absence of an error floor in the low-noise
             regime, and that can be expressed in terms of the principal
             angles and the overlap between the true and the mismatched
             signal subspaces.},
   Doi = {10.1109/ISIT.2015.7282846},
   Key = {fds326895}
}

@article{fds326896,
   Author = {Beirami, A and Calderbank, R and Duffy, K and Medard,
             M},
   Title = {Quantifying computational security subject to source
             constraints, guesswork and inscrutability},
   Journal = {IEEE International Symposium on Information Theory -
             Proceedings},
   Volume = {2015-June},
   Pages = {2757-2761},
   Year = {2015},
   Month = {September},
   ISBN = {9781467377041},
   url = {http://dx.doi.org/10.1109/ISIT.2015.7282958},
   Abstract = {© 2015 IEEE. Guesswork forms the mathematical framework for
             quantifying computational security subject to brute-force
             determination by query. In this paper, we consider guesswork
             subject to a per-symbol Shannon entropy budget. We introduce
             inscrutability rate as the asymptotic rate of increase in
             the exponential number of guesses required of an adversary
             to determine one or more secret strings. We prove that the
             inscrutability rate of any string-source supported on a
             finite alphabet χ, if it exists, lies between the
             per-symbol Shannon entropy constraint and log χ. We further
             prove that the inscrutability rate of any finite-order
             Markov string-source with hidden statistics remains the same
             as the unhidden case, i.e., the asymptotic value of hiding
             the statistics per each symbol is vanishing. On the other
             hand, we show that there exists a string-source that
             achieves the upper limit on the inscrutability rate, i.e.,
             log χ, under the same Shannon entropy budget.},
   Doi = {10.1109/ISIT.2015.7282958},
   Key = {fds326896}
}

@article{fds326897,
   Author = {Tamo, I and Barg, A and Goparaju, S and Calderbank,
             R},
   Title = {Cyclic LRC codes and their subfield subcodes},
   Journal = {IEEE International Symposium on Information Theory -
             Proceedings},
   Volume = {2015-June},
   Pages = {1262-1266},
   Year = {2015},
   Month = {September},
   ISBN = {9781467377041},
   url = {http://dx.doi.org/10.1109/ISIT.2015.7282658},
   Abstract = {© 2015 IEEE. We consider linear cyclic codes with the
             locality property, or locally recoverable codes (LRC codes).
             A family of LRC codes that generalizes the classical
             construction of Reed-Solomon codes was constructed in a
             recent paper by I. Tamo and A. Barg (IEEE Trans. IT, no. 8,
             2014). In this paper we focus on the optimal cyclic codes
             that arise from the general construction. We give a
             characterization of these codes in terms of their zeros, and
             observe that there are many equivalent ways of constructing
             optimal cyclic LRC codes over a given field. We also study
             subfield subcodes of cyclic LRC codes (BCH-like LRC codes)
             and establish several results about their locality and
             minimum distance.},
   Doi = {10.1109/ISIT.2015.7282658},
   Key = {fds326897}
}

@article{fds326758,
   Author = {Renna, F and Wang, L and Yuan, X and Yang, J and Reeves, G and Calderbank,
             R and Carin, L and Rodrigues, MRD},
   Title = {Classification and reconstruction of compressed GMM signals
             with side information},
   Journal = {IEEE International Symposium on Information Theory -
             Proceedings},
   Volume = {2015-June},
   Pages = {994-998},
   Year = {2015},
   Month = {September},
   ISBN = {9781467377041},
   url = {http://dx.doi.org/10.1109/ISIT.2015.7282604},
   Abstract = {© 2015 IEEE. This paper offers a characterization of
             performance limits for classification and reconstruction of
             high-dimensional signals from noisy compressive
             measurements, in the presence of side information. We assume
             the signal of interest and the side information signal are
             drawn from a correlated mixture of distributions/components,
             where each component associated with a specific class label
             follows a Gaussian mixture model (GMM). We provide sharp
             sufficient and/or necessary conditions for the phase
             transition of the misclassification probability and the
             reconstruction error in the low-noise regime. These
             conditions, which are reminiscent of the well-known
             Slepian-Wolf and Wyner-Ziv conditions, are a function of the
             number of measurements taken from the signal of interest,
             the number of measurements taken from the side information
             signal, and the geometry of these signals and their
             interplay.},
   Doi = {10.1109/ISIT.2015.7282604},
   Key = {fds326758}
}

@article{fds235746,
   Author = {Bajwa, WU and Duarte, MF and Calderbank, R},
   Title = {Conditioning of Random Block Subdictionaries With
             Applications to Block-Sparse Recovery and
             Regression},
   Journal = {IEEE Transactions on Information Theory},
   Volume = {61},
   Number = {7},
   Pages = {4060-4079},
   Year = {2015},
   Month = {July},
   ISSN = {0018-9448},
   url = {http://dx.doi.org/10.1109/TIT.2015.2429632},
   Doi = {10.1109/TIT.2015.2429632},
   Key = {fds235746}
}

@article{fds235747,
   Author = {Harms, A and Bajwa, WU and Calderbank, R},
   Title = {Identification of Linear Time-Varying Systems Through
             Waveform Diversity},
   Journal = {IEEE Transactions on Signal Processing},
   Volume = {63},
   Number = {8},
   Pages = {2070-2084},
   Year = {2015},
   Month = {April},
   ISSN = {1053-587X},
   url = {http://dx.doi.org/10.1109/TSP.2015.2407319},
   Doi = {10.1109/TSP.2015.2407319},
   Key = {fds235747}
}

@article{fds235748,
   Author = {Nokleby, M and Rodrigues, M and Calderbank, R},
   Title = {Discrimination on the Grassmann Manifold: Fundamental Limits
             of Subspace Classifiers},
   Journal = {IEEE Transactions on Information Theory},
   Volume = {61},
   Number = {4},
   Pages = {2133-2147},
   Year = {2015},
   Month = {April},
   ISSN = {0018-9448},
   url = {http://dx.doi.org/10.1109/TIT.2015.2407368},
   Doi = {10.1109/TIT.2015.2407368},
   Key = {fds235748}
}

@article{fds326755,
   Author = {Huang, J and Qiu, Q and Calderbank, R and Sapiro,
             G},
   Title = {Geometry-aware deep transform},
   Journal = {Proceedings / IEEE International Conference on Computer
             Vision. IEEE International Conference on Computer
             Vision},
   Volume = {2015 International Conference on Compute},
   Pages = {4139-4147},
   Year = {2015},
   Month = {February},
   ISBN = {9781467383912},
   url = {http://dx.doi.org/10.1109/ICCV.2015.471},
   Abstract = {© 2015 IEEE. Many recent efforts have been devoted to
             designing sophisticated deep learning structures, obtaining
             revolutionary results on benchmark datasets. The success of
             these deep learning methods mostly relies on an enormous
             volume of labeled training samples to learn a huge number of
             parameters in a network, therefore, understanding the
             generalization ability of a learned deep network cannot be
             overlooked, especially when restricted to a small training
             set, which is the case for many applications. In this paper,
             we propose a novel deep learning objective formulation that
             unifies both the classification and metric learning
             criteria. We then introduce a geometry-aware deep transform
             to enable a non-linear discriminative and robust feature
             transform, which shows competitive performance on small
             training sets for both synthetic and real-world data. We
             further support the proposed framework with a formal
             (K)-robustness analysis.},
   Doi = {10.1109/ICCV.2015.471},
   Key = {fds326755}
}

@article{fds290773,
   Author = {Wang, L and Huang, J and Yuan, X and Krishnamurthy, K and Greenberg, J and Cevher, V and Rodrigues, MRD and Brady, D and Calderbank, R and Carin,
             L},
   Title = {Signal Recovery and System Calibration from Multiple
             Compressive Poisson Measurements},
   Journal = {SIAM Journal on Imaging Sciences},
   Volume = {8},
   Number = {3},
   Pages = {1923-1954},
   Year = {2015},
   Month = {January},
   url = {http://dx.doi.org/10.1137/140998779},
   Doi = {10.1137/140998779},
   Key = {fds290773}
}

@article{fds235744,
   Author = {Harms, A and Bajwa, W and Calderbank, R},
   Title = {Efficient linear time-varying system identification using
             chirp waveforms},
   Journal = {Conference Record of the Asilomar Conference on Signals,
             Systems and Computers},
   Volume = {2015-April},
   Pages = {854-858},
   Year = {2015},
   Month = {January},
   ISBN = {9781479982974},
   ISSN = {1058-6393},
   url = {http://dx.doi.org/10.1109/ACSSC.2014.7094572},
   Abstract = {© 2014 IEEE. Linear, time-varying (LTV) systems are
             operators composed of time shifts, frequency shifts, and
             complex amplitude scalings that act on continuous
             finite-energy waveforms. This paper builds upon a novel,
             resource-efficient method previously proposed by the authors
             for identifying the parametric description of such systems
             from the sampled response to linear frequency modulated
             (LFM) waveforms. If the LTV operator is probed with a
             sufficiently diverse set of LFM pulses, more LFM pulses than
             reflectors, then the system can be identified with high
             accuracy. The accuracy is shown to be proportional to the
             uncertainty in the estimated frequencies and confirmed with
             numerical experiments.},
   Doi = {10.1109/ACSSC.2014.7094572},
   Key = {fds235744}
}

@article{fds322362,
   Author = {Xian, Y and Thompson, A and Qiu, Q and Nolte, L and Nowacek, D and Lu, J and Calderbank, R},
   Title = {Classification of whale vocalizations using the Weyl
             transform},
   Journal = {IEEE International Conference on Acoustics Speech and Signal
             Processing},
   Volume = {2015-August},
   Pages = {773-777},
   Year = {2015},
   Month = {January},
   ISBN = {9781467369978},
   url = {http://dx.doi.org/10.1109/ICASSP.2015.7178074},
   Abstract = {© 2015 IEEE. In this paper, we apply the Weyl transform to
             represent the vocalization of marine mammals. In contrast to
             other popular representation methods, such as the MFCC and
             the Chirplet transform, the Weyl transform captures the
             global information of signals. This is especially useful
             when the signal has low order polynomial phase. We can
             reconstruct the signal from the coefficients obtained from
             the Weyl transform, and perform classification based on
             these coefficients. Experimental results show that
             classification using features extracted from the Weyl
             transform outperforms the MFCC and the Chirplet transform on
             our collected whales data.},
   Doi = {10.1109/ICASSP.2015.7178074},
   Key = {fds322362}
}

@article{fds322363,
   Author = {Huang, J and Qiu, Q and Calderbank, R and Rodrigues, M and Sapiro,
             G},
   Title = {Alignment with intra-class structure can improve
             classification},
   Journal = {IEEE International Conference on Acoustics Speech and Signal
             Processing},
   Volume = {2015-August},
   Pages = {1921-1925},
   Year = {2015},
   Month = {January},
   ISBN = {9781467369978},
   url = {http://dx.doi.org/10.1109/ICASSP.2015.7178305},
   Abstract = {© 2015 IEEE. High dimensional data is modeled using
             low-rank subspaces, and the probability of misclassification
             is expressed in terms of the principal angles between
             subspaces. The form taken by this expression motivates the
             design of a new feature extraction method that enlarges
             inter-class separation, while preserving intra-class
             structure. The method can be tuned to emphasize different
             features shared by members within the same class.
             Classification performance is compared to that of
             state-of-the-art methods on synthetic data and on the real
             face database. The probability of misclassification is
             decreased when intra-class structure is taken into
             account.},
   Doi = {10.1109/ICASSP.2015.7178305},
   Key = {fds322363}
}

@article{fds322364,
   Author = {Huang, J and Yuan, X and Calderbank, R},
   Title = {Multi-scale Bayesian reconstruction of compressive X-ray
             image},
   Journal = {IEEE International Conference on Acoustics Speech and Signal
             Processing},
   Volume = {2015-August},
   Pages = {1618-1622},
   Year = {2015},
   Month = {January},
   ISBN = {9781467369978},
   url = {http://dx.doi.org/10.1109/ICASSP.2015.7178244},
   Abstract = {© 2015 IEEE. A novel multi-scale dictionary based Bayesian
             reconstruction algorithm is proposed for compressive X-ray
             imaging, which encodes the material's spectrum by Poisson
             measurements. Inspired by recently developed compressive
             X-ray imaging systems [1], this work aims to recover the
             material's spectru m from the compressive coded image by
             leveraging a reference spectrum library. Instead of directly
             using the huge and redundant library as a dictionary, which
             is cumbersome in computation and difficult for selecting
             those active dictionary atoms, a multi-scale tree structured
             dictionary is refined from the spectrum library, and
             following this a Bayesian reconstruction algorithm is
             developed. Experimental results on real data demonstrate
             superior performance in comparison with traditional
             methods.},
   Doi = {10.1109/ICASSP.2015.7178244},
   Key = {fds322364}
}

@article{fds322365,
   Author = {Yuan, X and Huang, J and Calderbank, R},
   Title = {Polynomial-phase signal direction-finding and
             source-tracking with a single acoustic vector
             sensor},
   Journal = {IEEE International Conference on Acoustics Speech and Signal
             Processing},
   Volume = {2015-August},
   Pages = {2559-2563},
   Year = {2015},
   Month = {January},
   ISBN = {9781467369978},
   url = {http://dx.doi.org/10.1109/ICASSP.2015.7178433},
   Abstract = {© 2015 IEEE. This paper introduces a new ESPRIT-based
             algorithm to estimate the direction-of-arrival of an
             arbitrary degree polynomial-phase signal with a single
             acoustic vector-sensor. The proposed time-invariant ESPRIT
             algorithm is based on a matrix-pencil pair derived from the
             time-delayed data-sets collected by a single acoustic
             vector-sensor. This approach requires neither a prior
             knowledge of the polynomial-phase signal's coefficients nor
             a prior knowledge of the polynomial-phase signal's
             frequency-spectrum. Furthermore, a preprocessing technique
             is proposed to incorporate the single-forgetting-factor
             algorithm and multiple-forgetting-factor adaptive tracking
             algorithm to track a polynomial-phase signal using one
             acoustic vector sensor. Simulation results verify the
             efficacy of the proposed direction finding and source
             tracking algorithms.},
   Doi = {10.1109/ICASSP.2015.7178433},
   Key = {fds322365}
}

@article{fds322366,
   Author = {Huang, J and Yuan, X and Calderbank, R},
   Title = {Collaborative compressive X-ray image reconstruction},
   Journal = {IEEE International Conference on Acoustics Speech and Signal
             Processing},
   Volume = {2015-August},
   Pages = {3282-3286},
   Year = {2015},
   Month = {January},
   ISBN = {9781467369978},
   url = {http://dx.doi.org/10.1109/ICASSP.2015.7178578},
   Abstract = {© 2015 IEEE. The Poisson Factor Analysis (PFA) is applied
             to recover signals from a Poisson compressive sensing
             system. Motivated by the recently developed compressive
             X-ray imaging system, Coded Aperture Coherent Scatter
             Spectral Imaging (CACSSI) [1], we propose a new Bayesian
             reconstruction algorithm. The proposed Poisson-Gamma (PG)
             approach uses multiple measurements to refine our knowledge
             on both sensing matrix and b ackground noise to overcome the
             uncertainties and inaccuracy of the hardware system.
             Therefore, a collaborative compressive X-ray image
             reconstruction algorithm is proposed under a Bayesian
             framework. Experimental results on real data show
             competitive performance in comparison with point estimation
             based methods.},
   Doi = {10.1109/ICASSP.2015.7178578},
   Key = {fds322366}
}

@article{fds326898,
   Author = {Michelusi, N and Nokleby, M and Mitra, U and Calderbank,
             R},
   Title = {Dynamic spectrum estimation with minimal overhead via
             multiscale information exchange},
   Journal = {2015 IEEE Global Communications Conference, GLOBECOM
             2015},
   Year = {2015},
   Month = {January},
   ISBN = {9781479959525},
   url = {http://dx.doi.org/10.1109/GLOCOM.2014.7417532},
   Abstract = {© 2015 IEEE. In this paper, a multiscale approach to
             spectrum sensing in cognitive cellular networks is analyzed.
             Observing that wireless interference decays with distance,
             and that estimating the entire spectrum occupancy across the
             network entails substantial energy cost and communication
             overhead, a protocol for distributed spectrum estimation is
             defined by which secondary users maintain fine-grained
             estimates of the spectrum occupancy of nearby cells, but
             coarse-grained estimates of that of distant cells. This is
             accomplished by arranging the cellular network into a
             hierarchy of increasingly coarser macro-cells and having
             secondary users fuse local spectrum estimates up the
             hierarchy. The spectrum occupancy is modeled as a Markov
             process, and the system is optimized by defining a
             probabilistic framework for spectrum sensing and information
             exchange that balances improvements in spectrum estimation
             against energy costs. The performance of the multiscale
             scheme is evaluated numerically, showing that it offers
             substantial improvements in energy efficiency over local
             estimation. On the other hand, it is shown that schemes that
             attempt to estimate the state of the whole network perform
             poorly, due to the excessive cost of performing information
             exchange with far away cells, and to the fact that, knowing
             the spectrum occupancy of distant cells, which experience
             low interference levels, results in a small increase in
             reward.},
   Doi = {10.1109/GLOCOM.2014.7417532},
   Key = {fds326898}
}

@article{fds235760,
   Author = {Liming Wang, and Carlson, DE and Rodrigues, MRD and Calderbank, R and Carin, L},
   Title = {A Bregman Matrix and the Gradient of Mutual Information for
             Vector Poisson and Gaussian Channels},
   Journal = {IEEE Transactions on Information Theory},
   Volume = {60},
   Number = {5},
   Pages = {2611-2629},
   Year = {2014},
   Month = {May},
   ISSN = {0018-9448},
   url = {http://dx.doi.org/10.1109/TIT.2014.2307068},
   Doi = {10.1109/TIT.2014.2307068},
   Key = {fds235760}
}

@article{fds235759,
   Author = {Bennatan, A and Shamai, S and Calderbank, AR},
   Title = {Soft-Decoding-Based Strategies for Relay and Interference
             Channels: Analysis and Achievable Rates Using LDPC
             Codes},
   Journal = {IEEE Transactions on Information Theory},
   Volume = {60},
   Number = {4},
   Pages = {1977-2009},
   Year = {2014},
   Month = {April},
   ISSN = {0018-9448},
   url = {http://dx.doi.org/10.1109/TIT.2013.2294373},
   Doi = {10.1109/TIT.2013.2294373},
   Key = {fds235759}
}

@article{fds235749,
   Author = {Calderbank, R and Thompson, A and Xie, Y},
   Title = {On block coherence of frames},
   Journal = {Applied and Computational Harmonic Analysis},
   Volume = {38},
   Number = {1},
   Pages = {50-71},
   Year = {2014},
   Month = {January},
   ISSN = {1063-5203},
   url = {http://dx.doi.org/10.1016/j.acha.2014.03.003},
   Abstract = {© 2014 Elsevier Inc. All rights reserved. Block coherence
             of matrices plays an important role in analyzing the
             performance of block compressed sensing recovery algorithmns
             (Bajwa and Mixon, 2012). In this paper, we characterize two
             block coheremice metrics: worst-case and average block
             coherence. First, we present lower bounds on worst-case
             block coherence, in both the general case and also when the
             mnatrix is constrained to be a union of orthobases. We then
             present determninistic mnatrix constructions based upon
             Kronecker products which obtain these lower bounds. We also
             characterize the worst-case block coherence of randomn
             suibspaces. Finally, we present a flipping algorithmn that
             can imnprove the average block coherence of a mnatrix, w}ule
             mnaintaining the worst- case block coherence of the original
             mnatrix. We provide nuimnerical examnples which demnonstrate
             that our proposed determninistic mnatrix construction
             performns well in block comnpressed sensing.},
   Doi = {10.1016/j.acha.2014.03.003},
   Key = {fds235749}
}

@article{fds235751,
   Author = {Goparaju, S and El Rouayheb and S and Calderbank,
             R},
   Title = {New codes and inner bounds for exact repair in distributed
             storage systems},
   Journal = {IEEE International Symposium on Information Theory -
             Proceedings},
   Pages = {1036-1040},
   Year = {2014},
   Month = {January},
   ISSN = {2157-8095},
   url = {http://dx.doi.org/10.1109/ISIT.2014.6874990},
   Abstract = {We study the exact-repair tradeoff between storage and
             repair bandwidth in distributed storage systems. We give new
             inner bounds for the tradeoff region and provide code
             constructions that achieve these bounds. © 2014
             IEEE.},
   Doi = {10.1109/ISIT.2014.6874990},
   Key = {fds235751}
}

@article{fds235752,
   Author = {Nokleby, M and Rodrigues, M and Calderbank, R},
   Title = {Discrimination on the grassmann manifold: Fundamental limits
             of subspace classifiers},
   Journal = {IEEE International Symposium on Information Theory -
             Proceedings},
   Pages = {3012-3016},
   Year = {2014},
   Month = {January},
   ISSN = {2157-8095},
   url = {http://dx.doi.org/10.1109/ISIT.2014.6875387},
   Abstract = {Repurposing tools and intuitions from Shannon theory, we
             derive fundamental limits on the reliable classification of
             high-dimensional signals from low-dimensional features. We
             focus on the classification of linear and affine subspaces
             and suppose the features to be noisy linear projections.
             Leveraging a syntactic equivalence of discrimination between
             subspaces and communications over vector wireless channels,
             we derive asymptotic bounds on classifier performance.
             First, we define the classification capacity, which
             characterizes necessary and sufficient relationships between
             the signal dimension, the number of features, and the number
             of classes to be discriminated, as all three quantities
             approach infinity. Second, we define the
             diversitydiscrimination tradeoff, which characterizes
             relationships between the number of classes and the
             misclassification probability as the signal-to-noise ratio
             approaches infinity. We derive inner and outer bounds on
             these measures, revealing precise relationships between
             signal dimension and classifier performance. © 2014
             IEEE.},
   Doi = {10.1109/ISIT.2014.6875387},
   Key = {fds235752}
}

@article{fds235753,
   Author = {Goparaju, S and Calderbank, R},
   Title = {Binary cyclic codes that are locally repairable},
   Journal = {IEEE International Symposium on Information Theory -
             Proceedings},
   Pages = {676-680},
   Year = {2014},
   Month = {January},
   ISSN = {2157-8095},
   url = {http://dx.doi.org/10.1109/ISIT.2014.6874918},
   Abstract = {Codes for storage systems aim to minimize the repair
             locality, which is the number of disks (or nodes) that
             participate in the repair of a single failed disk.
             Simultaneously, the code must sustain a high rate, operate
             on a small finite field to be practically significant and be
             tolerant to a large number of erasures. To this end, we
             construct new families of binary linear codes that have an
             optimal dimension (rate) for a given minimum distance and
             locality. Specifically, we construct cyclic codes that are
             locally repairable for locality 2 and distances 2, 6 and 10.
             In doing so, we discover new upper bounds on the code
             dimension, and prove the optimality of enabling local repair
             by provisioning disjoint groups of disks. Finally, we extend
             our construction to build codes that have multiple repair
             sets for each disk. © 2014 IEEE.},
   Doi = {10.1109/ISIT.2014.6874918},
   Key = {fds235753}
}

@article{fds235754,
   Author = {Nokleby, M and Rodrigues, M and Calderbank, R},
   Title = {Information-theoretic criteria for the design of compressive
             subspace classifiers},
   Journal = {IEEE International Conference on Acoustics Speech and Signal
             Processing},
   Pages = {3067-3071},
   Year = {2014},
   Month = {January},
   ISSN = {1520-6149},
   url = {http://dx.doi.org/10.1109/ICASSP.2014.6854164},
   Abstract = {Using Shannon theory, we derive fundamental, asymptotic
             limits on the classification of low-dimensional subspaces
             from compressive measurements. We identify a syntactic
             equivalence between the classification of subspaces and the
             communication of codewords over non-coherent,
             multiple-antenna channels, from which we derive sharp bounds
             on the number of classes that can be discriminated with low
             misclassification probability as a function of the signal
             dimensionality and the signal-to-noise ratio. While the
             bounds are asymptotic in the limit of high dimension, they
             provide intuition for classifier design at finite dimension.
             We validate this intuition via an application to face
             recognition. © 2014 IEEE.},
   Doi = {10.1109/ICASSP.2014.6854164},
   Key = {fds235754}
}

@article{fds235755,
   Author = {Carpenter, K and Sprechmann, P and Fiori, M and Calderbank, R and Egger,
             H and Sapiro, G},
   Title = {Questionnaire simplification for fast risk analysis of
             children's mental health},
   Journal = {IEEE International Conference on Acoustics Speech and Signal
             Processing},
   Pages = {6009-6013},
   Year = {2014},
   Month = {January},
   ISSN = {1520-6149},
   url = {http://dx.doi.org/10.1109/ICASSP.2014.6854757},
   Abstract = {Early detection and treatment of psychiatric disorders on
             children has shown significant impact in their subsequent
             development and quality of life. The assessment of
             psychopathology in childhood is commonly carried out by
             performing long comprehensive interviews such as the widely
             used Preschool Age Psychiatric Assessment (PAPA).
             Unfortunately, the time required to complete a full
             interview is too long to apply it at the scale of the actual
             population at risk, and most of the population goes
             undiagnosed or is diagnosed significantly later than
             desired. In this work, we aim to learn from unique and very
             rich previously collected PAPA examples the
             inter-correlations between different questions in order to
             provide a reliable risk analysis in the form of a much
             shorter interview. This helps to put such important risk
             analysis at the hands of regular practitioners, including
             teachers and family doctors. We use for this purpose the
             alternating decision trees algorithm, which combines
             decision trees with boosting to produce small and
             interpretable decision rules. Rather than a binary
             prediction, the algorithm provides a measure of confidence
             in the classification outcome. This is highly desirable from
             a clinical perspective, where it is preferable to abstain a
             decision on the low-confidence cases and recommend further
             screening. In order to prevent over-fitting, we propose to
             use network inference analysis to predefine a set of
             candidate question with consistent high correlation with the
             diagnosis. We report encouraging results with high levels of
             prediction using two independently collected datasets. The
             length and accuracy of the developed method suggests that it
             could be a valuable tool for preliminary evaluation in
             everyday care. © 2014 IEEE.},
   Doi = {10.1109/ICASSP.2014.6854757},
   Key = {fds235755}
}

@article{fds235756,
   Author = {Goparaju, S and Rouayheb, SE and Calderbank, R},
   Title = {New codes and inner bounds for exact repair in distributed
             storage systems},
   Journal = {2014 48th Annual Conference on Information Sciences and
             Systems, CISS 2014},
   Year = {2014},
   Month = {January},
   url = {http://dx.doi.org/10.1109/CISS.2014.6814148},
   Abstract = {We study the exact-repair tradeoff between storage and
             repair bandwidth in distributed storage systems (DSS). We
             give new inner bounds for the tradeoff region and provide
             code constructions that achieve these bounds. © 2014
             IEEE.},
   Doi = {10.1109/CISS.2014.6814148},
   Key = {fds235756}
}

@article{fds235750,
   Author = {Wang, L and Razi, A and Dias Rodrigues and M and Calderbank, R and Carin,
             L},
   Title = {Nonlinear information-theoretic compressive measurement
             design},
   Journal = {31st International Conference on Machine Learning, ICML
             2014},
   Volume = {4},
   Pages = {2896-2907},
   Year = {2014},
   Month = {January},
   ISBN = {9781634393973},
   Abstract = {Copyright © (2014) by the International Machine Learning
             Society (IMLS) All rights reserved. We investigate design of
             general nonlinear functions for mapping high-dimensional
             data into a lower-dimensional (compressive) space. The
             nonlinear measurements are assumed contaminated by additive
             Gaussian noise. Depending on the application, we are either
             interested in recovering the high-dimensional data from the
             nonlinear compressive measurements, or performing
             classification directly based on these measurements. The
             latter case corresponds to classification based on
             nonlinearly constituted and noisy features. The nonlinear
             measurement functions are designed based on constrained
             mutual- information optimization. New analytic results are
             developed for the gradient of mutual information in this
             setting, for arbitrary input-signal statistics. We make
             connections to kernel-based methods, such as the support
             vector machine. Encouraging results are presented on
             multiple datasets, for both signal recovery and
             classification. The nonlinear approach is shown to be
             particularly valuable in high-noise scenarios.},
   Key = {fds235750}
}

@article{fds235776,
   Author = {Goparaju, S and Calderbank, R},
   Title = {A new sub-packetization bound for minimum storage
             regenerating codes},
   Journal = {IEEE International Symposium on Information Theory -
             Proceedings},
   Pages = {1616-1620},
   Year = {2013},
   Month = {December},
   ISSN = {2157-8095},
   url = {http://dx.doi.org/10.1109/ISIT.2013.6620500},
   Abstract = {Codes for distributed storage systems are often designed to
             sustain failure of multiple storage disks. Specifically, an
             (n, k) MDS code stores k symbols in n disks such that the
             overall system is tolerant to a failure of up to n - k
             disks. However, access to at least k disks is still required
             to repair a single erasure. To reduce repair bandwidth,
             array codes are used where the stored symbols or packets are
             vectors of length ℓ. MDS array codes can potentially
             repair a single erasure using a fraction l/(n - k) of data
             stored in the surviving nodes. We ask the following
             question: for a given (n, k), what is the minimum
             vector-length or sub-packetization factor ℓ required to
             achieve this optimal fraction? For exact recovery of
             systematic disks in an MDS code of low redundancy, i.e. k/n
             > 1/2, the best known explicit codes [1] have a
             sub-packetization factor I which is exponential in k. It has
             been conjectured [2] that for a fixed number of parity
             nodes, it is in fact necessary for ℓ to be exponential in
             k. In this paper, we provide new converse bounds on k for a
             given ℓ We prove that k ≤ ℓ 2 for an arbitrary but
             fixed number of parity nodes r = n ™ k. For the practical
             case of 2 parity nodes, we prove a stronger result that k
             ≤ 4ℓ. © 2013 IEEE.},
   Doi = {10.1109/ISIT.2013.6620500},
   Key = {fds235776}
}

@article{fds235764,
   Author = {Xie, Y and Chi, Y and Calderbank, R},
   Title = {Low-rank matrix recovery with poison noise},
   Journal = {2013 IEEE Global Conference on Signal and Information
             Processing, GlobalSIP 2013 - Proceedings},
   Pages = {622},
   Year = {2013},
   Month = {December},
   url = {http://dx.doi.org/10.1109/GlobalSIP.2013.6736959},
   Abstract = {Estimating an image M* + m 1 ×m 2 from its linear
             measurements under Poisson noise is an important problem
             arises from applications such as optical imaging, nuclear
             medicine and x-ray imaging [1]. When the image M* has a
             low-rank structure, we can use a small number of linear
             measurements to recover M*, also known as low-rank matrix
             recovery. This is related to compressed sensing, where the
             goal is to develop efficient data acquisition systems by
             exploiting sparsity of underlying signals. © 2013
             IEEE.},
   Doi = {10.1109/GlobalSIP.2013.6736959},
   Key = {fds235764}
}

@article{fds235765,
   Author = {Wu, T and Polatkan, G and Steel, D and Brown, W and Daubechies, I and Calderbank, R},
   Title = {Painting analysis using wavelets and probabilistic topic
             models},
   Journal = {2013 IEEE International Conference on Image Processing, ICIP
             2013 - Proceedings},
   Pages = {3264-3268},
   Year = {2013},
   Month = {December},
   url = {http://dx.doi.org/10.1109/ICIP.2013.6738672},
   Abstract = {In this paper, computer-based techniques for stylistic
             analysis of paintings are applied to the five panels of the
             14th century Peruzzi Altarpiece by Giotto di Bondone.
             Features are extracted by combining a dual-tree complex
             wavelet transform with a hidden Markov tree (HMT) model.
             Hierarchical clustering is used to identify stylistic
             keywords in image patches, and keyword frequencies are
             calculated for sub-images that each contains many patches. A
             generative hierarchical Bayesian model learns stylistic
             patterns of keywords; these patterns are then used to
             characterize the styles of the sub-images; this in turn,
             permits to discriminate between paintings. Results suggest
             that such unsupervised probabilistic topic models can be
             useful to distill characteristic elements of style. © 2013
             IEEE.},
   Doi = {10.1109/ICIP.2013.6738672},
   Key = {fds235765}
}

@article{fds235766,
   Author = {Renna, F and Calderbank, R and Carin, L and Rodrigues,
             MRD},
   Title = {Reconstruction of Gaussian mixture models from compressive
             measurements: A phase transition view},
   Journal = {2013 IEEE Global Conference on Signal and Information
             Processing, GlobalSIP 2013 - Proceedings},
   Pages = {628},
   Year = {2013},
   Month = {December},
   url = {http://dx.doi.org/10.1109/GlobalSIP.2013.6736965},
   Abstract = {We characterize the minimum number of measurements needed to
             drive to zero the minimum mean squared error (MMSE) of
             Gaussian mixture model (GMM) input signals in the low-noise
             regime. The result also hints at almost phase-transition
             optimal recovery procedures based on a classification and
             reconstruction approach. © 2013 IEEE.},
   Doi = {10.1109/GlobalSIP.2013.6736965},
   Key = {fds235766}
}

@article{fds235767,
   Author = {Reboredo, H and Renna, F and Calderbank, R and Rodrigues,
             MRD},
   Title = {Projections designs for compressive classification},
   Journal = {2013 IEEE Global Conference on Signal and Information
             Processing, GlobalSIP 2013 - Proceedings},
   Pages = {1029-1032},
   Year = {2013},
   Month = {December},
   url = {http://dx.doi.org/10.1109/GlobalSIP.2013.6737069},
   Abstract = {This paper puts forth projections designs for compressive
             classification of Gaussian mixture models. In particular, we
             capitalize on the asymptotic characterization of the
             behavior of an (upper bound to the) misclassification
             probability associated with the optimal Maximum-A-Posteriori
             (MAP) classifier, which depends on quantities that are dual
             to the concepts of the diversity gain and coding gain in
             multi-antenna communications, to construct measurement
             designs that maximize the diversity-order of the measurement
             model. Numerical results demonstrate that the new
             measurement designs substantially outperform random
             measurements. Overall, the analysis and the designs cast
             geometrical insight about the mechanics of compressive
             classification problems. © 2013 IEEE.},
   Doi = {10.1109/GlobalSIP.2013.6737069},
   Key = {fds235767}
}

@article{fds235770,
   Author = {Nokleby, M and Calderbank, R and Rodrigues, MRD},
   Title = {Information-theoretic limits on the classification of
             Gaussian mixtures: Classification on the Grassmann
             manifold},
   Journal = {2013 IEEE Information Theory Workshop, ITW
             2013},
   Year = {2013},
   Month = {December},
   url = {http://dx.doi.org/10.1109/ITW.2013.6691253},
   Abstract = {Motivated by applications in high-dimensional signal
             processing, we derive fundamental limits on the performance
             of compressive linear classifiers. By analogy with Shannon
             theory, we define the classification capacity, which
             quantifies the maximum number of classes that can be
             discriminated with low probability of error, and the
             diversity-discrimination tradeoff, which quantifies the
             tradeoff between the number of classes and the probability
             of classification error. For classification of Gaussian
             mixture models, we identify a duality between classification
             and communications over non-coherent multiple-antenna
             channels. This duality allows us to characterize the
             classification capacity and diversity-discrimination
             tradeoff using existing results from multiple-antenna
             communication. We also identify the easiest possible
             classification problems, which correspond to low-dimensional
             subspaces drawn from an appropriate Grassmann manifold. ©
             2013 IEEE.},
   Doi = {10.1109/ITW.2013.6691253},
   Key = {fds235770}
}

@article{fds235773,
   Author = {Renna, F and Rodrigues, MRD and Chen, M and Calderbank, R and Carin,
             L},
   Title = {Compressive sensing for incoherent imaging systems with
             optical constraints},
   Journal = {IEEE International Conference on Acoustics Speech and Signal
             Processing},
   Pages = {5484-5488},
   Year = {2013},
   Month = {October},
   ISSN = {1520-6149},
   url = {http://dx.doi.org/10.1109/ICASSP.2013.6638712},
   Abstract = {We consider the problem of linear projection design for
             incoherent optical imaging systems. We propose a
             computationally efficient method to obtain effective
             measurement kernels that satisfy the physical constraints
             imposed by an optical system, starting first from arbitrary
             kernels, including those that satisfy a less demanding power
             constraint. Performance is measured in terms of mutual
             information between the source input and the projection
             measurement, as well as reconstruction error for real world
             images. A clear improvement in the quality of image
             reconstructions is shown with respect to both random and
             adaptive projection designs in the literature. © 2013
             IEEE.},
   Doi = {10.1109/ICASSP.2013.6638712},
   Key = {fds235773}
}

@article{fds235774,
   Author = {Wang, M and Xu, W and Calderbank, R},
   Title = {Compressed sensing with corrupted participants},
   Journal = {IEEE International Conference on Acoustics Speech and Signal
             Processing},
   Pages = {4653-4657},
   Year = {2013},
   Month = {October},
   ISSN = {1520-6149},
   url = {http://dx.doi.org/10.1109/ICASSP.2013.6638542},
   Abstract = {Compressed sensing (CS) theory promises one can recover
             real-valued sparse signal from a small number of linear
             measurements. Motivated by network monitoring with link
             failures, we for the first time consider the problem of
             recovering signals that contain both real-valued entries and
             corruptions, where the real entries represent transmission
             delays on normal links and the corruptions represent failed
             links. Unlike conventional CS, here a measurement is
             real-valued only if it does not include a failed link, and
             it is corrupted otherwise. We prove that O((d + 1)max(d, k)
             log n) nonadaptive measurements are enough to recover all
             n-dimensional signals that contain k nonzero real entries
             and d corruptions. We provide explicit constructions of
             measurements and recovery algorithms. We also analyze the
             performance of signal recovery when the measurements contain
             errors. © 2013 IEEE.},
   Doi = {10.1109/ICASSP.2013.6638542},
   Key = {fds235774}
}

@article{fds235775,
   Author = {Chi, Y and Calderbank, R},
   Title = {Knowledge-enhanced matching pursuit},
   Journal = {IEEE International Conference on Acoustics Speech and Signal
             Processing},
   Pages = {6576-6580},
   Year = {2013},
   Month = {October},
   ISSN = {1520-6149},
   url = {http://dx.doi.org/10.1109/ICASSP.2013.6638933},
   Abstract = {Compressive Sensing is possible when the sensing matrix acts
             as a near isometry on signals of interest that can be
             sparsely or compressively represented. The attraction of
             greedy algorithms such as Orthogonal Matching Pursuit is
             their simplicity. However they fail to take advantage of
             both the structure of the sensing matrix and any prior
             information about the sparse signal. This paper introduces
             an oblique projector to matching pursuit algorithms to
             enhance detection of a component that is present in the
             signal by reducing interference from other candidate
             components based on prior information about the signal as
             well as the structure of the sensing matrix. Numerical
             examples demonstrate that performance as a function of SNR
             is superior to conventional matching pursuit. © 2013
             IEEE.},
   Doi = {10.1109/ICASSP.2013.6638933},
   Key = {fds235775}
}

@article{fds303195,
   Author = {Calderbank, R and Thompson, A and Xie, Y},
   Title = {On block coherence of frames},
   Year = {2013},
   Month = {July},
   url = {http://arxiv.org/abs/1307.7544v4},
   Abstract = {Block coherence of matrices plays an important role in
             analyzing the performance of block compressed sensing
             recovery algorithms (Bajwa and Mixon, 2012). In this paper,
             we characterize two block coherence metrics: worst-case and
             average block coherence. First, we present lower bounds on
             worst-case block coherence, in both the general case and
             also when the matrix is constrained to be a union of
             orthobases. We then present deterministic matrix
             constructions based upon Kronecker products which obtain
             these lower bounds. We also characterize the worst-case
             block coherence of random subspaces. Finally, we present a
             flipping algorithm that can improve the average block
             coherence of a matrix, while maintaining the worst-case
             block coherence of the original matrix. We provide numerical
             examples which demonstrate that our proposed deterministic
             matrix construction performs well in block compressed
             sensing.},
   Key = {fds303195}
}

@article{fds303196,
   Author = {Renna, F and Calderbank, R and Carin, L and Rodrigues,
             MRD},
   Title = {Reconstruction of Signals Drawn from a Gaussian Mixture from
             Noisy Compressive Measurements},
   Year = {2013},
   Month = {July},
   url = {http://arxiv.org/abs/1307.0861v2},
   Abstract = {This paper determines to within a single measurement the
             minimum number of measurements required to successfully
             reconstruct a signal drawn from a Gaussian mixture model in
             the low-noise regime. The method is to develop upper and
             lower bounds that are a function of the maximum dimension of
             the linear subspaces spanned by the Gaussian mixture
             components. The method not only reveals the existence or
             absence of a minimum mean-squared error (MMSE) error floor
             (phase transition) but also provides insight into the MMSE
             decay via multivariate generalizations of the MMSE dimension
             and the MMSE power offset, which are a function of the
             interaction between the geometrical properties of the kernel
             and the Gaussian mixture. These results apply not only to
             standard linear random Gaussian measurements but also to
             linear kernels that minimize the MMSE. It is shown that
             optimal kernels do not change the number of measurements
             associated with the MMSE phase transition, rather they
             affect the sensed power required to achieve a target MMSE in
             the low-noise regime. Overall, our bounds are tighter and
             sharper than standard bounds on the minimum number of
             measurements needed to recover sparse signals associated
             with a union of subspaces model, as they are not asymptotic
             in the signal dimension or signal sparsity.},
   Doi = {10.1109/TSP.2014.2309560},
   Key = {fds303196}
}

@article{fds303197,
   Author = {Goparaju, S and Tamo, I and Calderbank, R},
   Title = {An Improved Sub-Packetization Bound for Minimum Storage
             Regenerating Codes},
   Year = {2013},
   Month = {May},
   url = {http://arxiv.org/abs/1305.3498v1},
   Abstract = {Distributed storage systems employ codes to provide
             resilience to failure of multiple storage disks.
             Specifically, an $(n, k)$ MDS code stores $k$ symbols in $n$
             disks such that the overall system is tolerant to a failure
             of up to $n-k$ disks. However, access to at least $k$ disks
             is still required to repair a single erasure. To reduce
             repair bandwidth, array codes are used where the stored
             symbols or packets are vectors of length $\ell$. MDS array
             codes have the potential to repair a single erasure using a
             fraction $1/(n-k)$ of data stored in the remaining disks. We
             introduce new methods of analysis which capitalize on the
             translation of the storage system problem into a geometric
             problem on a set of operators and subspaces. In particular,
             we ask the following question: for a given $(n, k)$, what is
             the minimum vector-length or sub-packetization factor $\ell$
             required to achieve this optimal fraction? For \emph{exact
             recovery} of systematic disks in an MDS code of low
             redundancy, i.e. $k/n > 1/2$, the best known explicit codes
             \cite{WTB12} have a sub-packetization factor $\ell$ which is
             exponential in $k$. It has been conjectured \cite{TWB12}
             that for a fixed number of parity nodes, it is in fact
             necessary for $\ell$ to be exponential in $k$. In this
             paper, we provide a new log-squared converse bound on $k$
             for a given $\ell$, and prove that $k \le
             2\log_2\ell\left(\log_{\delta}\ell+1\right)$, for an
             arbitrary number of parity nodes $r = n-k$, where $\delta =
             r/(r-1)$.},
   Key = {fds303197}
}

@article{fds303198,
   Author = {Goparaju, S and Rouayheb, SE and Calderbank, R and Poor,
             HV},
   Title = {Data Secrecy in Distributed Storage Systems under Exact
             Repair},
   Year = {2013},
   Month = {April},
   url = {http://arxiv.org/abs/1304.3156v2},
   Abstract = {The problem of securing data against eavesdropping in
             distributed storage systems is studied. The focus is on
             systems that use linear codes and implement exact repair to
             recover from node failures.The maximum file size that can be
             stored securely is determined for systems in which all the
             available nodes help in repair (i.e., repair degree $d=n-1$,
             where $n$ is the total number of nodes) and for any number
             of compromised nodes. Similar results in the literature are
             restricted to the case of at most two compromised nodes.
             Moreover, new explicit upper bounds are given on the maximum
             secure file size for systems with $d<n-1$. The key
             ingredients for the contribution of this paper are new
             results on subspace intersection for the data downloaded
             during repair. The new bounds imply the interesting fact
             that the maximum data that can be stored securely decreases
             exponentially with the number of compromised
             nodes.},
   Key = {fds303198}
}

@article{fds303199,
   Author = {Reboredo, H and Renna, F and Calderbank, R and Rodrigues,
             MRD},
   Title = {Compressive Classification},
   Year = {2013},
   Month = {February},
   url = {http://arxiv.org/abs/1302.4660v1},
   Abstract = {This paper derives fundamental limits associated with
             compressive classification of Gaussian mixture source
             models. In particular, we offer an asymptotic
             characterization of the behavior of the (upper bound to the)
             misclassification probability associated with the optimal
             Maximum-A-Posteriori (MAP) classifier that depends on
             quantities that are dual to the concepts of diversity gain
             and coding gain in multi-antenna communications. The
             diversity, which is shown to determine the rate at which the
             probability of misclassification decays in the low noise
             regime, is shown to depend on the geometry of the source,
             the geometry of the measurement system and their interplay.
             The measurement gain, which represents the counterpart of
             the coding gain, is also shown to depend on geometrical
             quantities. It is argued that the diversity order and the
             measurement gain also offer an optimization criterion to
             perform dictionary learning for compressive classification
             applications.},
   Key = {fds303199}
}

@article{fds235761,
   Author = {Wang, L and Carlson, D and Rodrigues, MD and Wilcox, D and Calderbank,
             R and Carin, L},
   Title = {Designed measurements for vector count data},
   Journal = {Advances in Neural Information Processing
             Systems},
   Year = {2013},
   Month = {January},
   ISSN = {1049-5258},
   Abstract = {We consider design of linear projection measurements for a
             vector Poisson signal model. The projections are performed
             on the vector Poisson rate,X ∈ ℝ + n , and the observed
             data are a vector of counts, Y ∈ ℤ + m . The projection
             matrix is designed by maximizing mutual information between
             Y and X, I(Y;X). When there is a latent class label C ∈
             {1; : : : ;L} associated with X, we onsider the mutual
             information with respect to Y and C, I(Y ;C). New analytic
             expressions for the gradient of I(Y ;X) and I(Y ;C) are
             presented, with gradient performed with respect to the
             measurement matrix. Connections are made to the more widely
             studied Gaussian measurement model. Example results are
             presented for compressive topic modeling of a document
             corpora (word counting), and hyperspectral compressive
             sensing for chemical classification (photon
             counting).},
   Key = {fds235761}
}

@article{fds322367,
   Author = {Nokleby, M and Bajwa, WU and Calderbank, R and Aazhang,
             B},
   Title = {Toward resource-optimal consensus over the wireless
             medium},
   Journal = {IEEE Journal of Selected Topics in Signal
             Processing},
   Volume = {7},
   Number = {2},
   Pages = {284-295},
   Year = {2013},
   Month = {January},
   url = {http://dx.doi.org/10.1109/JSTSP.2013.2246765},
   Abstract = {We carry out a comprehensive study of the resource cost of
             averaging consensus in wireless networks. Most previous
             approaches suppose a graphical network, which abstracts away
             crucial features of the wireless medium, and measure
             resource consumption only in terms of the total number of
             transmissions required to achieve consensus. Under a
             path-loss model, we study the resource requirements of
             consensus with respect to three wireless- appropriate
             metrics: total transmit energy, elapsed time, and
             time-bandwidth product. First, we characterize the
             performance of several popular gossip algorithms, showing
             that they may be order-optimal with respect to transmit
             energy but are strictly suboptimal with respect to elapsed
             time and time-bandwidth product. Further, we propose a new
             consensus scheme, termed hierarchical averaging, and show
             that it is nearly order-optimal with respect to all three
             metrics. Finally, we examine the effects of quantization,
             showing that hierarchical averaging provides a nearly
             orderoptimal tradeoff between resource consumption and
             quantization error. © 2013 IEEE.},
   Doi = {10.1109/JSTSP.2013.2246765},
   Key = {fds322367}
}

@article{fds235778,
   Author = {Jacobvitz, AN and Calderbank, R and Sorin, DJ},
   Title = {Coset coding to extend the lifetime of memory},
   Journal = {Proceedings - International Symposium on High-Performance
             Computer Architecture},
   Pages = {222-233},
   Year = {2013},
   ISSN = {1530-0897},
   url = {http://dx.doi.org/10.1109/HPCA.2013.6522321},
   Abstract = {Some recent memory technologies, including phase change
             memory (PCM), have lifetime reliabilities that are affected
             by write operations. We propose the use of coset coding to
             extend the lifetimes of these memories. The key idea of
             coset coding is that it performs a one-to-many mapping from
             each dataword to a coset of vectors, and having multiple
             possible vectors provides the flexibility to choose the
             vector to write that optimizes lifetime. Our technique,
             FlipMin, uses coset coding and, for each write, selects the
             vector that minimizes the number of bits that must flip. We
             also show how FlipMin can be synergistically combined with
             the ability to tolerate bit erasures. Thus, our techniques
             help to prevent bits from wearing out and can then tolerate
             those bits that do wear out. © 2013 IEEE.},
   Doi = {10.1109/HPCA.2013.6522321},
   Key = {fds235778}
}

@article{fds235782,
   Author = {Duarte, MF and Jafarpour, S and Calderbank, AR},
   Title = {Performance of the Delsarte-Goethals frame on clustered
             sparse vectors},
   Journal = {IEEE Transactions on Signal Processing},
   Volume = {61},
   Number = {8},
   Pages = {1998-2008},
   Year = {2013},
   ISSN = {1053-587X},
   url = {http://dx.doi.org/10.1109/TSP.2013.2242064},
   Abstract = {The Delsarte-Goethals frame (DGF) has been proposed for
             deterministic compressive sensing of sparse and compressible
             signals. Results in compressive sensing theory show that the
             DGF enables successful recovery of an overwhelming majority
             of sufficiently sparse signals. However, these results do
             not give a characterization of the sparse vectors for which
             the recovery procedure fails. In this paper, we present a
             formal analysis of the DGF that highlights the presence of
             clustered sparse vectors within its null space. This in turn
             implies that sparse recovery performance is diminished for
             sparse vectors that have their nonzero entries clustered
             together. Such clustered structure is present in compressive
             imaging applications, where commonly-used raster scannings
             of 2-D discrete wavelet transform representations yield
             clustered sparse representations for natural images. Prior
             work leverages this structure by proposing specially
             tailored sparse recovery algorithms that partition the
             recovery of the input vector into known clustered and
             unclustered portions. Alternatively, we propose new
             randomized and deterministic raster scannings for clustered
             coefficient vectors that improve recovery performance.
             Experimental results verify the aforementioned analysis and
             confirm the predicted improvements for both noiseless and
             noisy measurement regimes. © 1991-2012 IEEE.},
   Doi = {10.1109/TSP.2013.2242064},
   Key = {fds235782}
}

@article{fds326899,
   Author = {Harms, A and Bajwa, WU and Calderbank, R and IEEE},
   Title = {Shaping the Power Spectra of Bipolar Sequences with
             Application to Sub-Nyquist Sampling},
   Journal = {2013 IEEE 5TH INTERNATIONAL WORKSHOP ON COMPUTATIONAL
             ADVANCES IN MULTI-SENSOR ADAPTIVE PROCESSING (CAMSAP
             2013)},
   Pages = {236-+},
   Year = {2013},
   ISBN = {978-1-4673-3144-9},
   Key = {fds326899}
}

@article{fds326900,
   Author = {Harms, A and Bajwa, WU and Calderbank, R and IEEE},
   Title = {Resource-Efficient Parametric Recovery of Linear
             Time-Varying Systems},
   Journal = {2013 IEEE 5TH INTERNATIONAL WORKSHOP ON COMPUTATIONAL
             ADVANCES IN MULTI-SENSOR ADAPTIVE PROCESSING (CAMSAP
             2013)},
   Pages = {200-+},
   Year = {2013},
   ISBN = {978-1-4673-3144-9},
   Key = {fds326900}
}

@article{fds303203,
   Author = {Chi, Y and Calderbank, R},
   Title = {Coherence-Based Performance Guarantees of Orthogonal
             Matching Pursuit},
   Year = {2012},
   Month = {September},
   url = {http://arxiv.org/abs/1209.6267v1},
   Abstract = {In this paper, we present coherence-based performance
             guarantees of Orthogonal Matching Pursuit (OMP) for both
             support recovery and signal reconstruction of sparse signals
             when the measurements are corrupted by noise. In particular,
             two variants of OMP either with known sparsity level or with
             a stopping rule are analyzed. It is shown that if the
             measurement matrix $X\in\mathbb{C}^{n\times p}$ satisfies
             the strong coherence property, then with
             $n\gtrsim\mathcal{O}(k\log p)$, OMP will recover a
             $k$-sparse signal with high probability. In particular, the
             performance guarantees obtained here separate the properties
             required of the measurement matrix from the properties
             required of the signal, which depends critically on the
             minimum signal to noise ratio rather than the power profiles
             of the signal. We also provide performance guarantees for
             partial support recovery. Comparisons are given with other
             performance guarantees for OMP using worst-case analysis and
             the sorted one step thresholding algorithm.},
   Key = {fds303203}
}

@article{fds303200,
   Author = {Nokleby, M and Bajwa, WU and Calderbank, R and Aazhang,
             B},
   Title = {Toward Resource-Optimal Consensus over the Wireless
             Medium},
   Year = {2012},
   Month = {August},
   url = {http://arxiv.org/abs/1208.3251v2},
   Abstract = {We carry out a comprehensive study of the resource cost of
             averaging consensus in wireless networks. Most previous
             approaches suppose a graphical network, which abstracts away
             crucial features of the wireless medium, and measure
             resource consumption only in terms of the total number of
             transmissions required to achieve consensus. Under a
             path-loss dominated model, we study the resource
             requirements of consensus with respect to three
             wireless-appropriate metrics: total transmit energy, elapsed
             time, and time-bandwidth product. First we characterize the
             performance of several popular gossip algorithms, showing
             that they may be order-optimal with respect to transmit
             energy but are strictly suboptimal with respect to elapsed
             time and time-bandwidth product. Further, we propose a new
             consensus scheme, termed hierarchical averaging, and show
             that it is nearly order-optimal with respect to all three
             metrics. Finally, we examine the effects of quantization,
             showing that hierarchical averaging provides a nearly
             order-optimal tradeoff between resource consumption and
             quantization error.},
   Doi = {10.1109/JSTSP.2013.2246765},
   Key = {fds303200}
}

@article{fds303201,
   Author = {Chi, Y and Eldar, YC and Calderbank, R},
   Title = {PETRELS: Parallel Subspace Estimation and Tracking by
             Recursive Least Squares from Partial Observations},
   Year = {2012},
   Month = {July},
   url = {http://arxiv.org/abs/1207.6353v2},
   Abstract = {Many real world data sets exhibit an embedding of
             low-dimensional structure in a high-dimensional manifold.
             Examples include images, videos and internet traffic data.
             It is of great significance to reduce the storage
             requirements and computational complexity when the data
             dimension is high. Therefore we consider the problem of
             reconstructing a data stream from a small subset of its
             entries, where the data is assumed to lie in a
             low-dimensional linear subspace, possibly corrupted by
             noise. We further consider tracking the change of the
             underlying subspace, which can be applied to applications
             such as video denoising, network monitoring and anomaly
             detection. Our problem can be viewed as a sequential
             low-rank matrix completion problem in which the subspace is
             learned in an on-line fashion. The proposed algorithm,
             dubbed Parallel Estimation and Tracking by REcursive Least
             Squares (PETRELS), first identifies the underlying
             low-dimensional subspace via a recursive procedure for each
             row of the subspace matrix in parallel with discounting for
             previous observations, and then reconstructs the missing
             entries via least-squares estimation if required. Numerical
             examples are provided for direction-of-arrival estimation
             and matrix completion, comparing PETRELS with state of the
             art batch algorithms.},
   Doi = {10.1109/TSP.2013.2282910},
   Key = {fds303201}
}

@article{fds303202,
   Author = {Harms, A and Bajwa, WU and Calderbank, R},
   Title = {A Constrained Random Demodulator for Sub-Nyquist
             Sampling},
   Year = {2012},
   Month = {April},
   url = {http://arxiv.org/abs/1204.0839v3},
   Abstract = {This paper presents a significant modification to the Random
             Demodulator (RD) of Tropp et al. for sub-Nyquist sampling of
             frequency-sparse signals. The modification, termed
             constrained random demodulator, involves replacing the
             random waveform, essential to the operation of the RD, with
             a constrained random waveform that has limits on its
             switching rate because fast switching waveforms may be hard
             to generate cleanly. The result is a relaxation on the
             hardware requirements with a slight, but manageable,
             decrease in the recovery guarantees. The paper also
             establishes the importance of properly choosing the
             statistics of the constrained random waveform. If the power
             spectrum of the random waveform matches the distribution on
             the tones of the input signal (i.e., the distribution is
             proportional to the power spectrum), then recovery of the
             input signal tones is improved. The theoretical guarantees
             provided in the paper are validated through extensive
             numerical simulations and phase transition
             plots.},
   Doi = {10.1109/TSP.2012.2231077},
   Key = {fds303202}
}

@article{fds235779,
   Author = {Nokleby, M and Bajwa, WU and Calderbank, R and Aazhang,
             B},
   Title = {Toward resource-optimal averaging consensus over the
             wireless medium},
   Journal = {Conference Record of the Asilomar Conference on Signals,
             Systems and Computers},
   Pages = {1197-1201},
   Year = {2012},
   ISSN = {1058-6393},
   url = {http://dx.doi.org/10.1109/ACSSC.2012.6489211},
   Abstract = {We carry out a comprehensive study of the resource costs of
             distributed averaging consensus in wireless sensor networks.
             In particular, we consider two metrics appropriate to the
             wireless medium: total transmit energy and time-bandwidth
             product. Most previous approaches, such as gossip
             algorithms, suppose a graphical network, which abstracts
             away crucial features of the wireless medium, and measure
             resource consumption only in terms of the total number of
             transmissions required to achieve consensus. Under a
             path-loss dominated protocol interference model, we study
             the performance of several popular gossip algorithms,
             showing that they are nearly order-optimal with respect to
             transmit energy but strictly sub-optimal with respect to
             time-bandwidth product. We also propose a new scheme, termed
             hierarchical averaging, which is tailored to the wireless
             medium, and show that in general this approach is nearly
             order-optimal with respect to time-bandwidth product but
             strictly sub-optimal with respect to transmit energy. For
             the special case of free-space propagation, however, the
             proposed hierarchical scheme is approximately order-optimal
             with respect to both metrics. © 2012 IEEE.},
   Doi = {10.1109/ACSSC.2012.6489211},
   Key = {fds235779}
}

@article{fds235780,
   Author = {Harms, A and Bajwa, WU and Calderbank, R},
   Title = {Rapid sensing of underutilized, wideband spectrum using the
             Random Demodulator},
   Journal = {Conference Record of the Asilomar Conference on Signals,
             Systems and Computers},
   Pages = {1940-1944},
   Year = {2012},
   ISSN = {1058-6393},
   url = {http://dx.doi.org/10.1109/ACSSC.2012.6489377},
   Abstract = {Efficient spectrum sensing is an important problem given the
             large and increasing demand for wireless spectrum and the
             need to protect incumbent users. We can more efficiently use
             large swaths of underutilized spectrum by designing spectrum
             sensors that can quickly, and power-efficiently, find and
             opportunistically communicate over unused (or underutilized)
             pieces of spectrum, such as television bands. In this paper,
             we concentrate on a particular sensing architecture, the
             Random Demodulator (RD), and look at two aspects of the
             problem. First, we offer fundamental limits on how
             efficiently any algorithm can perform the sensing operation
             with the RD. Second, we analyze a very simple,
             low-complexity algorithm called one-step thresholding that
             has been shown to work near-optimally for certain
             measurement classes in a low SNR setting or when the
             non-zero input coefficients are nearly equal. We rigorously
             establish that the RD architecture is well-suited for
             near-optimal recovery of the locations of the non-zero
             frequency coefficients in similar settings using one-step
             thresholding and perform numerical experiments to offer some
             confirmation of our results. © 2012 IEEE.},
   Doi = {10.1109/ACSSC.2012.6489377},
   Key = {fds235780}
}

@article{fds235781,
   Author = {Jacobvitz, AN and Calderbank, R and Sorin, DJ},
   Title = {Writing cosets of a convolutional code to increase the
             Lifetime of Flash memory},
   Journal = {2012 50th Annual Allerton Conference on Communication,
             Control, and Computing, Allerton 2012},
   Pages = {308-318},
   Year = {2012},
   url = {http://dx.doi.org/10.1109/Allerton.2012.6483234},
   Abstract = {The goal of this paper is to extend the lifetime of Flash
             memory by reducing the frequency with which a given page of
             memory is erased. This is accomplished by increasing the
             number of writes that are possible before erasure is
             necessary. Redundancy is introduced into the write process
             to decrease the number of memory cells that are impacted by
             a given write, and to even out the impact of writing across
             an entire page of memory. Improvements are expressed in
             terms of write efficiency and lifetime gain. Write
             efficiency is the ratio of cells written to cells available,
             and lifetime gain is the ratio of coded writes to the
             baseline of uncoded writing. We use a physical model that
             allows multiple writes to a given region of memory. This can
             be realized with single level cells or with multi-level
             cells. Data is written to memory in the form of a coset of a
             convolutional code. The coset is represented by a binary
             vector that is selected by the Viterbi algorithm to minimize
             the number of cells impacted by the write (Hamming weight)
             and to even out the number of writes to each cell within a
             given page. Several different Viterbi metrics are evaluated.
             It is shown that page write efficiencies of over 85% and
             lifetime gains of over 500% are possible with only modest
             encoding and decoding complexity. It is also straightforward
             to integrate lifetime extension with standard methods of
             error correction by requiring that the coset representative
             be drawn from an error correcting code. An example is
             provided where single error correction is provided using a
             Hamming code. © 2012 IEEE.},
   Doi = {10.1109/Allerton.2012.6483234},
   Key = {fds235781}
}

@article{fds235783,
   Author = {Wu, Y and Jia, T and Calderbank, R and Duel-Hallen, A and Hallen,
             H},
   Title = {Enabling code diversity for mobile radio channels using
             long-range fading prediction},
   Journal = {IEEE Transactions on Wireless Communications},
   Volume = {11},
   Number = {12},
   Pages = {4362-4371},
   Year = {2012},
   ISSN = {1536-1276},
   url = {http://dx.doi.org/10.1109/TWC.2012.101712.111884},
   Abstract = {Code diversity integrates space-time coding with beamforming
             by using a small number of feedback bits to select from a
             family of space-time codes. Different codes lead to
             different induced channels at the receiver, where Channel
             State Information (CSI) is used to instruct the transmitter
             how to choose the code. Feedback can be combined with
             sub-optimal low complexity decoding of the component codes
             to match Maximum-Likelihood (ML) decoding performance of any
             individual code in the family. It can also be combined with
             ML decoding of the component codes to improve performance
             beyond ML decoding performance of any individual code. Prior
             analysis of code diversity did not take into account the
             effect of the mobile speed and the delay in the feedback
             channel. This paper demonstrates the practicality of code
             diversity in space-time coded systems by showing that
             performance gains based on instantaneous feedback are
             largely preserved when long-range prediction of time-varying
             correlated fading channels is employed to compensate for the
             effect of the feedback delay. To maintain prediction
             accuracy for realistic SNR, noise reduction that employs
             oversampled pilots is used prior to fading prediction. We
             also propose a robust low pilot rate method that utilizes
             interleaving to improve the spectral efficiency. Simulations
             are presented for two channel models: the conventional Jakes
             model and a realistic physical channel model where the
             parameters associated with the reflectors vary in time and
             the arrival rays have different strengths and asymmetric
             arrival angles. © 2002-2012 IEEE.},
   Doi = {10.1109/TWC.2012.101712.111884},
   Key = {fds235783}
}

@article{fds235786,
   Author = {Carson, WR and Chen, M and Rodrigues, MRD and Calderbank, R and Carin,
             L},
   Title = {Communications-inspired projection design with application
             to compressive sensing},
   Journal = {SIAM Journal on Imaging Sciences},
   Volume = {5},
   Number = {4},
   Pages = {1182-1212},
   Year = {2012},
   ISSN = {1936-4954},
   url = {http://hdl.handle.net/10161/8952 Duke open
             access},
   Abstract = {We consider the recovery of an underlying signal x ∈ ℂm
             based on projection measurements of the form y = Mx+w, where
             y ∈ ℂℓ and w is measurement noise; we are interested
             in the case ℓ ≪ m. It is assumed that the signal model
             p(x) is known and that w ~ CN(w; 0,Σw) for known Σ w. The
             objective is to design a projection matrix M ∈ ℂℓ×m
             to maximize key information-theoretic quantities with
             operational significance, including the mutual information
             between the signal and the projections I(x; y) or the Rényi
             entropy of the projections hα (y) (Shannon entropy is a
             special case). By capitalizing on explicit characterizations
             of the gradients of the information measures with respect to
             the projection matrix, where we also partially extend the
             well-known results of Palomar and Verdu ́ from the mutual
             information to the Rényi entropy domain, we reveal the key
             operations carried out by the optimal projection designs:
             mode exposure and mode alignment. Experiments are considered
             for the case of compressive sensing (CS) applied to imagery.
             In this context, we provide a demonstration of the
             performance improvement possible through the application of
             the novel projection designs in relation to conventional
             ones, as well as justification for a fast online projection
             design method with which state-of-the-art adaptive CS signal
             recovery is achieved. © 2012 Society for Industrial and
             Applied Mathematics.},
   Doi = {10.1137/120878380},
   Key = {fds235786}
}

@article{fds236001,
   Author = {Jafarpour, S and Duarte, MF and Calderbank, R},
   Title = {Beyond worst-case reconstruction in deterministic compressed
             sensing},
   Journal = {IEEE International Symposium on Information Theory -
             Proceedings},
   Pages = {1852-1856},
   Year = {2012},
   url = {http://dx.doi.org/10.1109/ISIT.2012.6283601},
   Abstract = {The role of random measurement in compressive sensing is
             analogous to the role of random codes in coding theory. In
             coding theory, decoders that can correct beyond the minimum
             distance of a code allow random codes to achieve the Shannon
             limit. In compressed sensing, the counterpart of minimum
             distance is the spark of the measurement matrix, i.e., the
             size of the smallest set of linearly dependent columns. This
             paper constructs a family of measurement matrices where the
             columns are formed by exponentiating codewords from a
             classical binary error-correcting code of block length M.
             The columns can be partitioned into mutually unbiased bases,
             and the spark of the corresponding measurement matrix is
             shown to be O(√M) by identifying a configuration of
             columns that plays a role similar to that of the Dirac comb
             in classical Fourier analysis. Further, an explicit basis
             for the null space of these measurement matrices is given in
             terms of indicator functions of binary self-dual codes.
             Reliable reconstruction of k-sparse inputs is shown for k of
             order M/log(M) which is best possible and far beyond the
             worst case lower bound provided by the spark. © 2012
             IEEE.},
   Doi = {10.1109/ISIT.2012.6283601},
   Key = {fds236001}
}

@article{fds236002,
   Author = {Zeng, M and Calderbank, R and Cui, S},
   Title = {On design of rateless codes over dying binary erasure
             channel},
   Journal = {IEEE Transactions on Communications},
   Volume = {60},
   Number = {4},
   Pages = {889-894},
   Year = {2012},
   ISSN = {0090-6778},
   url = {http://dx.doi.org/10.1109/TCOMM.2012.022712.110038},
   Abstract = {In this paper, we study a practical coding scheme for the
             dying binary erasure channel (DBEC), which is a binary
             erasure channel (BEC) subject to a random fatal failure. We
             consider the rateless codes and optimize the degree
             distribution to maximize the average recovery probability.
             In particular, we first study the upper bound of the average
             recovery probability, based on which we define the objective
             function as the gap between the upper bound and the average
             recovery probability achieved by a particular degree
             distribution. We then seek the optimal degree distribution
             by minimizing the objective function. A simple and heuristic
             approach is also proposed to provide a suboptimal but good
             degree distribution. Simulation results are presented to
             show the significant performance gain over the conventional
             LT codes. © 2012 IEEE.},
   Doi = {10.1109/TCOMM.2012.022712.110038},
   Key = {fds236002}
}

@article{fds236003,
   Author = {Applebaum, L and Bajwa, WU and Duarte, MF and Calderbank,
             R},
   Title = {Asynchronous code-division random access using convex
             optimization},
   Journal = {Physical Communication},
   Volume = {5},
   Number = {2},
   Pages = {129-147},
   Year = {2012},
   ISSN = {1874-4907},
   url = {http://dx.doi.org/10.1016/j.phycom.2011.09.006},
   Abstract = {Many applications in cellular systems and sensor networks
             involve a random subset of a large number of users
             asynchronously reporting activity to a base station. This
             paper examines the problem of multiuser detection (MUD) in
             random access channels for such applications. Traditional
             orthogonal signaling ignores the random nature of user
             activity in this problem and limits the total number of
             users to be on the order of the number of signal space
             dimensions. Contention-based schemes, on the other hand,
             suffer from delays caused by colliding transmissions and the
             hidden node problem. In contrast, this paper presents a
             novel pairing of an asynchronous non-orthogonal
             code-division random access scheme with a convex
             optimization-based MUD algorithm that overcomes the issues
             associated with orthogonal signaling and contention-based
             methods. Two key distinguishing features of the proposed MUD
             algorithm are that it does not require knowledge of the
             delay or channel state information of every user and it has
             polynomial-time computational complexity. The main
             analytical contribution of this paper is the relationship
             between the performance of the proposed MUD algorithm in the
             presence of arbitrary or random delays and two simple
             metrics of the set of user codewords. The study of these
             metrics is then focused on two specific sets of codewords,
             random binary codewords and specially constructed algebraic
             codewords, for asynchronous random access. The ensuing
             analysis confirms that the proposed scheme together with
             either of these two codeword sets significantly outperforms
             the orthogonal signaling-based random access in terms of the
             total number of users in the system. © 2011 Elsevier
             B.V.},
   Doi = {10.1016/j.phycom.2011.09.006},
   Key = {fds236003}
}

@article{fds236004,
   Author = {Bajwa, WU and Calderbank, R and Mixon, DG},
   Title = {Two are better than one: Fundamental parameters of frame
             coherence},
   Journal = {Applied and Computational Harmonic Analysis},
   Volume = {33},
   Number = {1},
   Pages = {58-78},
   Year = {2012},
   ISSN = {1063-5203},
   url = {http://dx.doi.org/10.1016/j.acha.2011.09.005},
   Abstract = {This paper investigates two parameters that measure the
             coherence of a frame: worst-case and average coherence. We
             first use worst-case and average coherence to derive
             near-optimal probabilistic guarantees on both sparse signal
             detection and reconstruction in the presence of noise. Next,
             we provide a catalog of nearly tight frames with small
             worst-case and average coherence. Later, we find a new lower
             bound on worst-case coherence; we compare it to the Welch
             bound and use it to interpret recently reported signal
             reconstruction results. Finally, we give an algorithm that
             transforms frames in a way that decreases average coherence
             without changing the spectral norm or worst-case coherence.
             © 2011 Elsevier Inc. All rights reserved.},
   Doi = {10.1016/j.acha.2011.09.005},
   Key = {fds236004}
}

@article{fds236005,
   Author = {Wu, Y and Jia, T and Calderbank, R and Duel-Hallen, A and Hallen,
             H},
   Title = {Enabling Code Diversity for Mobile Radio Channels using
             Long-Range Fading Prediction},
   Journal = {IEEE Transactions on Wireless Communications},
   Year = {2012},
   ISSN = {1536-1276},
   url = {http://dx.doi.org/10.1109/TWC.2012.101712.111884},
   Abstract = {Code diversity integrates space-time coding with beamforming
             by using a small number of feedback bits to select from a
             family of space-time codes. Different codes lead to
             different induced channels at the receiver, where Channel
             State Information (CSI) is used to instruct the transmitter
             how to choose the code. Feedback can be combined with
             sub-optimal low complexity decoding of the component codes
             to match Maximum-Likelihood (ML) decoding performance of any
             individual code in the family. It can also be combined with
             ML decoding of the component codes to improve performance
             beyond ML decoding performance of any individual code. Prior
             analysis of code diversity did not take into account the
             effect of the mobile speed and the delay in the feedback
             channel. This paper demonstrates the practicality of code
             diversity in space-time coded systems by showing that
             performance gains based on instantaneous feedback are
             largely preserved when long-range prediction of time-varying
             correlated fading channels is employed to compensate for the
             effect of the feedback delay. To maintain prediction
             accuracy for realistic SNR, noise reduction that employs
             oversampled pilots is used prior to fading prediction. We
             also propose a robust low pilot rate method that utilizes
             interleaving to improve the spectral efficiency. Simulations
             are presented for two channel models: the conventional Jakes
             model and a realistic physical channel model where the
             parameters associated with the reflectors vary in time and
             the arrival rays have different strengths and asymmetric
             arrival angles.},
   Doi = {10.1109/TWC.2012.101712.111884},
   Key = {fds236005}
}

@article{fds236077,
   Author = {Chen, M and Carson, W and Rodrigues, M and Calderbank, R and Carin,
             L},
   Title = {Communications inspired linear discriminant
             analysis},
   Journal = {Proceedings of the 29th International Conference on Machine
             Learning, ICML 2012},
   Volume = {1},
   Pages = {919-926},
   Year = {2012},
   url = {http://hdl.handle.net/10161/8956 Duke open
             access},
   Abstract = {We study the problem of supervised linear dimensionality
             reduction, taking an information-theoretic viewpoint. The
             linear projection matrix is designed by maximizing the
             mutual information between the projected signal and the
             class label. By harnessing a recent theoretical result on
             the gradient of mutual information, the above optimization
             problem can be solved directly using gradient descent,
             without requiring simplification of the objective function.
             Theoretical analysis and empirical comparison are made
             between the proposed method and two closely related methods,
             and comparisons are also made with a method in which Rényi
             entropy is used to define the mutual information (in this
             case the gradient may be computed simply, under a special
             parameter setting). Relative to these alternative
             approaches, the proposed method achieves promising results
             on real datasets. Copyright 2012 by the author(s)/owner(s).},
   Key = {fds236077}
}

@article{fds236078,
   Author = {Chi, Y and Eldar, YC and Calderbank, R},
   Title = {PETRELS: Subspace estimation and tracking from partial
             observations},
   Journal = {IEEE International Conference on Acoustics Speech and Signal
             Processing},
   Pages = {3301-3304},
   Year = {2012},
   ISSN = {1520-6149},
   url = {http://dx.doi.org/10.1109/ICASSP.2012.6288621},
   Abstract = {We consider the problem of reconstructing a data stream from
             a small subset of its entries, where the data stream is
             assumed to lie in a low-dimensional linear subspace,
             possibly corrupted by noise. It is also important to track
             the change of underlying subspace for many applications.
             This problem can be viewed as a sequential low-rank matrix
             completion problem in which the subspace is learned in an
             online fashion. The proposed algorithm, called Parallel
             Estimation and Tracking by REcursive Least Squares
             (PETRELS), identifies the underlying low-dimensional
             subspace via a recursive procedure for each row of the
             subspace matrix in parallel, and then reconstructs the
             missing entries via least-squares estimation if required.
             PETRELS outperforms previous approaches by discounting
             observations in order to capture long-term behavior of the
             data stream and be able to adapt to it. Numerical examples
             are provided for direction-of-arrival estimation and matrix
             completion, comparing PETRELS with state of the art batch
             algorithms. © 2012 IEEE.},
   Doi = {10.1109/ICASSP.2012.6288621},
   Key = {fds236078}
}

@article{fds236079,
   Author = {Qureshi, TR and Zoltowski, MD and Calderbank, R},
   Title = {A novel approach to Doppler compensation and estimation for
             multiple targets in MIMO radar with unitary waveform matrix
             scheduling},
   Journal = {IEEE International Conference on Acoustics Speech and Signal
             Processing},
   Pages = {2473-2476},
   Year = {2012},
   ISSN = {1520-6149},
   url = {http://dx.doi.org/10.1109/ICASSP.2012.6288417},
   Abstract = {In this paper, we present a method of detecting the range
             and Doppler phase of a point target using multiple antennas.
             As a key illustrative example, we consider a 4 x 4 system
             employing a unitary matrix waveform set, e.g., formed from
             Golay complementary sequences. When a non-negligible Doppler
             shift is induced by the target motion, the waveform matrix
             formed from the complementary sequences is no longer
             unitary, resulting in significantly degraded target range
             estimates. To solve this problem, we adopt a subspace based
             approach exploiting the observation that the receive matrix
             formed from matched filtering of the reflected waveforms has
             a (non-trivial) null-space. Through processing of the
             waveforms with the appropriate vector from the null-space,
             we can significantly improve the range detection
             performance. Also, another very important target aspect is
             the velocity with which the target is moving, and to
             determine that, the exact Doppler phase shift induced by the
             target motion needs to be estimated with reasonable
             accuracy. To accomplish this task, we develop a strategy
             that uses the MUSIC algorithm to estimate the Doppler phase,
             and we use simulations to show that the phase estimates
             obtained are reasonably accurate even at low SNRs. © 2012
             IEEE.},
   Doi = {10.1109/ICASSP.2012.6288417},
   Key = {fds236079}
}

@article{fds236080,
   Author = {Carson, WR and Rodrigues, MRD and Chen, M and Carin, L and Calderbank,
             R},
   Title = {How to focus the discriminative power of a
             dictionary},
   Journal = {IEEE International Conference on Acoustics Speech and Signal
             Processing},
   Pages = {1365-1368},
   Year = {2012},
   ISSN = {1520-6149},
   url = {http://dx.doi.org/10.1109/ICASSP.2012.6288144},
   Abstract = {This paper is motivated by the challenge of high fidelity
             processing of images using a relatively small set of
             projection measurements. This is a problem of great interest
             in many sensing applications, for example where high
             photodetector counts are precluded by a combination of
             available power, form factor and expense. The emerging
             methods of dictionary learning and compressive sensing offer
             great potential for addressing this challenge. Combining
             these methods requires that the signals of interest be
             representable as a sparse combination of elements of some
             dictionary. This paper develops a method that aligns the
             discriminative power of such a dictionary with the physical
             limitations of the imaging system. Alignment is accomplished
             by designing a projection matrix that exposes and then
             aligns the modes of the noise with those of the dictionary.
             The design algorithm is obtained by modifying an algorithm
             for designing the pre-filter to maximize the rate and
             reliability of a Multiple Input Multiple Output (MIMO)
             communications channel. The difference is that in the
             communications problem a source is being matched to a
             channel, whereas in the imaging problem a channel, or
             equivalently the noise covariance, is being matched to a
             source. Our results shown that using the proposed
             communications design framework we can reduce reconstruction
             error between 20%, after only 20 projections of a 28 x 28
             image, and 10% after 100 projections. Furthermore, we
             noticeably see the superior quality of the reconstructed
             images. © 2012 IEEE.},
   Doi = {10.1109/ICASSP.2012.6288144},
   Key = {fds236080}
}

@article{fds236081,
   Author = {Nokleby, M and Bajwa, WU and Calderbank, R and Aazhang,
             B},
   Title = {Hierarchical averaging over wireless sensor
             networks},
   Journal = {IEEE International Conference on Acoustics Speech and Signal
             Processing},
   Pages = {3121-3124},
   Year = {2012},
   ISSN = {1520-6149},
   url = {http://dx.doi.org/10.1109/ICASSP.2012.6288576},
   Abstract = {We introduce an approach to gossip algorithms that exploits
             three aspects of the wireless medium: superposition,
             broadcast, and power control. Instead of sending pairwise
             messages between neighbors on a fixed network topology, we
             construct gossip algorithms in which nodes can
             simultaneously recover multiple neighbors' messages and in
             which nodes can adjust the set of their neighbors by
             adjusting transmit power. We present two averaging
             algorithms, each based on a hierarchical clustering of the
             network. In the first algorithm, clusters of nodes transmit
             their estimates locally and randomly select a representative
             node for communications at the next level. In the second,
             each cluster mutually averages and then cooperatively
             transmits at the next level. For path-loss environments,
             these schemes achieve order-optimal or near order-optimal
             performance. © 2012 IEEE.},
   Doi = {10.1109/ICASSP.2012.6288576},
   Key = {fds236081}
}

@article{fds236082,
   Author = {Xie, Y and Chi, Y and Applebaum, L and Calderbank,
             R},
   Title = {Compressive demodulation of mutually interfering
             signals},
   Journal = {2012 IEEE Statistical Signal Processing Workshop, SSP
             2012},
   Pages = {592-595},
   Year = {2012},
   url = {http://dx.doi.org/10.1109/SSP.2012.6319768},
   Abstract = {The challenge of Multiuser Detection (MUD) is that of
             demodulating mutually interfering signals given that at any
             time instant the number of active users is typically small.
             The promise of compressed sensing is the demodulation of
             sparse superpositions of signature waveforms from very few
             measurements. This paper considers signature waveforms that
             are are drawn from a Gabor frame. It describes a MUD
             architecture that uses subsampling to convert analog input
             to a digital signal, and then uses iterative matching
             pursuit to recover the active users. Compressive
             demodulation requires K logN samples to recover K active
             users whereas standard MUD requires N samples. The paper
             provides theoretical performance guarantees and consistent
             numerical simulations. © 2012 IEEE.},
   Doi = {10.1109/SSP.2012.6319768},
   Key = {fds236082}
}

@article{fds236083,
   Author = {Calderbank, R and Jafarpour, S},
   Title = {Finding needles in compressed haystacks},
   Journal = {IEEE International Conference on Acoustics Speech and Signal
             Processing},
   Pages = {3441-3444},
   Year = {2012},
   ISSN = {1520-6149},
   url = {http://dx.doi.org/10.1109/ICASSP.2012.6288656},
   Abstract = {In this paper, we investigate the problem of compressed
             learning, i.e. learning directly in the compressed domain.
             In particular, we provide tight bounds demonstrating that
             the linear kernel SVMs classifier in the measurement domain,
             with high probability, has true accuracy close to the
             accuracy of the best linear threshold classifier in the data
             domain. Furthermore, we indicate that for a family of
             well-known deterministic compressed sensing matrices,
             compressed learning is provided on the fly. Finally, we
             support our claims with experimental results in the texture
             analysis application. © 2012 IEEE.},
   Doi = {10.1109/ICASSP.2012.6288656},
   Key = {fds236083}
}

@article{fds236084,
   Author = {Duarte, MF and Matthews, TE and Warren, WS and Calderbank,
             R},
   Title = {Melanoma classification from hidden Markov tree
             features},
   Journal = {IEEE International Conference on Acoustics Speech and Signal
             Processing},
   Pages = {685-688},
   Year = {2012},
   ISSN = {1520-6149},
   url = {http://dx.doi.org/10.1109/ICASSP.2012.6287976},
   Abstract = {Melanoma detection relies on visual inspection of skin
             samples under the microscope via a qualitative set of
             indicators, causing large discordance among pathologists.
             New developments in pump-probe imaging enable the extraction
             of melanin intensity levels from skin samples and provide
             baseline qualitative figures for melanoma detection and
             classification. However, such basic figures do not capture
             the diverse types of cellular structure that distinguish
             different stages of melanoma. In this paper, we propose an
             initial approach for feature extraction for classification
             purposes via Hidden Markov Tree models trained on skin
             sample melanin intensity images. Our experimental results
             show that the proposed features provide a mathematical
             microscope that is able to better discriminate cellular
             structure, enabling successful classification of skin
             samples that are mislabeled when the baseline melanin
             intensity qualitative figures are used. © 2012
             IEEE.},
   Doi = {10.1109/ICASSP.2012.6287976},
   Key = {fds236084}
}

@article{fds235768,
   Author = {Simpson, MJ and Wilson, JW and Matthews, TE and Duarte, M and Calderbank, R and Warren, WS},
   Title = {Imaging the distribution of melanin in human skin lesions
             with pump-probe microscopy},
   Journal = {Optics InfoBase Conference Papers},
   Year = {2011},
   Month = {December},
   Key = {fds235768}
}

@article{fds235977,
   Author = {Wolff, J and Martens, M and Jafarpour, S and Daubechies, I and Calderbank, R},
   Title = {Uncovering elements of style},
   Journal = {IEEE International Conference on Acoustics Speech and Signal
             Processing},
   Pages = {1017-1020},
   Year = {2011},
   ISSN = {1520-6149},
   url = {http://dx.doi.org/10.1109/ICASSP.2011.5946579},
   Abstract = {This paper relates the style of 16th century Flemish
             paintings by Goossen van der Weyden (GvdW) to the style of
             preliminary sketches or underpaintings made prior to
             executing the painting. Van der Weyden made underpaintings
             in markedly different styles for reasons as yet not
             understood by art historians. The analysis presented here
             starts from a classification of the underpaintings into four
             distinct styles by experts in art history. Analysis of the
             painted surfaces by a combination of wavelet analysis,
             hidden Markov trees and boosting algorithms can distinguish
             the four underpainting styles with greater than 90%
             cross-validation accuracy. On a subsequent blind test this
             classifier provided insight into the hypothesis by art
             historians that different patches of the finished painting
             were executed by different hands. © 2011
             IEEE.},
   Doi = {10.1109/ICASSP.2011.5946579},
   Key = {fds235977}
}

@article{fds235978,
   Author = {Goparaju, S and Calderbank, AR and Carson, WR and Rodrigues, MRD and Perez-Cruz, F},
   Title = {When to add another dimension when communicating over MIMO
             channels},
   Journal = {IEEE International Conference on Acoustics Speech and Signal
             Processing},
   Pages = {3100-3103},
   Year = {2011},
   ISSN = {1520-6149},
   url = {http://dx.doi.org/10.1109/ICASSP.2011.5946351},
   Abstract = {This paper introduces a divide and conquer approach to the
             design of transmit and receive filters for communication
             over a Multiple Input Multiple Output (MIMO) Gaussian
             channel subject to an average power constraint. It involves
             conversion to a set of parallel scalar channels, possibly
             with very different gains, followed by coding per
             sub-channel (i.e. over time) rather than coding across
             sub-channels (i.e. over time and space). The loss in
             performance is negligible at high signal-to-noise ratio
             (SNR) and not significant at medium SNR. The advantages are
             reduction in signal processing complexity and greater
             insight into the SNR thresholds at which a channel is first
             allocated power. This insight is a consequence of
             formulating the optimal power allocation in terms of an
             upper bound on error rate that is determined by parameters
             of the input lattice such as the minimum distance and
             kissing number. The resulting thresholds are given
             explicitly in terms of these lattice parameters. By
             contrast, when the optimization problem is phrased in terms
             of maximizing mutual information, the solution is mercury
             waterfilling, and the thresholds are implicit. © 2011
             IEEE.},
   Doi = {10.1109/ICASSP.2011.5946351},
   Key = {fds235978}
}

@article{fds235979,
   Author = {Wu, Y and Zheng, H and Calderbank, R and Kulkarni, S and Poor,
             HV},
   Title = {On optimal precoding in wireless multicast
             systems},
   Journal = {IEEE International Conference on Acoustics Speech and Signal
             Processing},
   Pages = {3068-3071},
   Year = {2011},
   ISSN = {1520-6149},
   url = {http://dx.doi.org/10.1109/ICASSP.2011.5946306},
   Abstract = {Precoding has been extensively studied for point-to-point
             communications, including the problems of constructing the
             precoding codebook and selecting the best precoder. This
             paper investigates precoding for a multicast channel in
             which a base station is sending the same information to all
             users and each user sends back the index of its best
             precoding matrix. It is assumed that users do not
             collaborate and that no channel state information is known
             at the base station. Optimization problems are formulated to
             reduce the packet drop rate. A set of probabilistic
             algorithms that effectively reduce the average package drop
             rate are presented. It is shown numerically that these new
             schemes lead to significant improvements. © 2011
             IEEE.},
   Doi = {10.1109/ICASSP.2011.5946306},
   Key = {fds235979}
}

@article{fds235980,
   Author = {Kostina, V and Duarte, MF and Jafarpour, S and Calderbank,
             R},
   Title = {The value of redundant measurement in compressed
             sensing},
   Journal = {IEEE International Conference on Acoustics Speech and Signal
             Processing},
   Pages = {3656-3659},
   Year = {2011},
   ISSN = {1520-6149},
   url = {http://dx.doi.org/10.1109/ICASSP.2011.5947143},
   Abstract = {The aim of compressed sensing is to recover attributes of
             sparse signals using very few measurements. Given an overall
             bit budget for quantization, this paper demonstrates that
             there is value to redundant measurement. The measurement
             matrices considered here are required to have the property
             that signal recovery is still possible even after dropping
             certain subsets of D measurements. It introduces the concept
             of a measurement matrix that is weakly democratic in the
             sense that the amount of information about the signal
             carried by each of the designated D-subsets is the same.
             Examples of deterministic measurement matrices that are
             weakly democratic are constructed by exponentiating
             codewords from the binary second order Reed Muller code. The
             value in rejecting D measurements that are on average
             larger, is to be able to provide a finer grid for vector
             quantization of the remaining measurements, even after
             discounting the original budget by the bits used to identify
             the reject set. Simulation results demonstrate that
             redundancy improves recovery SNR, sometimes by a wide
             margin. Optimum performance occurs when a significant
             fraction of measurements are rejected. © 2011
             IEEE.},
   Doi = {10.1109/ICASSP.2011.5947143},
   Key = {fds235980}
}

@article{fds235981,
   Author = {Krishnamurthy, K and Bajwa, WU and Willett, R and Calderbank,
             R},
   Title = {Fast level set estimation from projection
             measurements},
   Journal = {IEEE Workshop on Statistical Signal Processing
             Proceedings},
   Pages = {585-588},
   Year = {2011},
   url = {http://dx.doi.org/10.1109/SSP.2011.5967766},
   Abstract = {Estimation of the level set of a function (i.e., regions
             where the function exceeds some value) is an important
             problem with applications in digital elevation maps, medical
             imaging, and astronomy. In many applications, however, the
             function of interest is acquired through indirect
             measurements, such as tomographic projections,
             coded-aperture measurements, or pseudo-random projections
             associated with compressed sensing. This paper describes a
             new methodology and associated theoretical analysis for
             rapid and accurate estimation of the level set from such
             projection measurements. The proposed method estimates the
             level set from projection measurements without an
             intermediate function reconstruction step, thereby leading
             to significantly faster computation. In addition, the
             coherence of the projection operator and McDiarmid's
             inequality are used to characterize the estimator's
             performance. © 2011 IEEE.},
   Doi = {10.1109/SSP.2011.5967766},
   Key = {fds235981}
}

@article{fds235982,
   Author = {Harms, A and Bajwa, WU and Calderbank, R},
   Title = {Beating Nyquist through correlations: A constrained random
             demodulator for sampling of sparse bandlimited
             signals},
   Journal = {IEEE International Conference on Acoustics Speech and Signal
             Processing},
   Pages = {5968-5971},
   Year = {2011},
   ISSN = {1520-6149},
   url = {http://dx.doi.org/10.1109/ICASSP.2011.5947721},
   Abstract = {Technological constraints severely limit the rate at which
             analog-to-digital converters can reliably sample signals.
             Recently, Tropp et al. proposed an architecture, termed the
             random demodulator (RD), that attempts to overcome this
             obstacle for sparse bandlimited signals. One integral
             component of the RD architecture is a white noise-like,
             bipolar modulating waveform that changes polarity at a rate
             equal to the signal bandwidth. Since there is a hardware
             limitation to how fast analog waveforms can change polarity
             without undergoing shape distortion, this leads to the RD
             also having a constraint on the maximum allowable bandwidth.
             In this paper, an extension of the RD, termed the
             constrained random demodulator (CRD), is proposed that
             bypasses this bottleneck by replacing the original
             modulating waveform with a run-length limited (RLL)
             modulating waveform that changes polarity at a slower rate
             than the signal bandwidth. One of the main contributions of
             the paper is establishing that the CRD, despite employing a
             modulating waveform with correlations, enjoys some
             theoretical guarantees for certain RLL waveforms. In
             addition, for a given sampling rate and rate of change in
             the modulating waveform polarity, numerical simulations
             confirm that the CRD, using an appropriate RLL waveform, can
             sample a signal with an even wider bandwidth without a
             significant loss in performance. © 2011
             IEEE.},
   Doi = {10.1109/ICASSP.2011.5947721},
   Key = {fds235982}
}

@article{fds235983,
   Author = {Applebaum, L and Bajwa, WU and Calderbank, AR and Haupt, J and Nowak,
             R},
   Title = {Deterministic pilot sequences for sparse channel estimation
             in OFDM systems},
   Journal = {17th DSP 2011 International Conference on Digital Signal
             Processing, Proceedings},
   Year = {2011},
   url = {http://dx.doi.org/10.1109/ICDSP.2011.6005024},
   Abstract = {This paper examines the problem of multipath channel
             estimation in single-antenna orthogonal frequency division
             multiplexing (OFDM) systems. In particular, we study the
             problem of pilot assisted channel estimation in wideband
             OFDM systems, where the time-domain (discrete) channel is
             approximately sparse. Existing works on this topic
             established that techniques from the compressed sensing
             literature can yield accurate channel estimates using a
             relatively small number of pilot tones, provided the pilots
             are selected randomly. Here, we describe a general purpose
             procedure for deterministic selection of pilot tones to be
             used for channel estimation, and establish guarantees for
             channel estimation accuracy using these sequences along with
             recovery techniques from the compressed sensing literature.
             Simulation results are presented to demonstrate the
             effectiveness of the proposed procedure in practice. © 2011
             IEEE.},
   Doi = {10.1109/ICDSP.2011.6005024},
   Key = {fds235983}
}

@article{fds235984,
   Author = {Mixon, DG and Bajwa, WU and Calderbank, R},
   Title = {Frame coherence and sparse signal processing},
   Journal = {IEEE International Symposium on Information Theory -
             Proceedings},
   Pages = {663-667},
   Year = {2011},
   url = {http://dx.doi.org/10.1109/ISIT.2011.6034214},
   Abstract = {The sparse signal processing literature often uses random
             sensing matrices to obtain performance guarantees.
             Unfortunately, in the real world, sensing matrices do not
             always come from random processes. It is therefore desirable
             to evaluate whether an arbitrary matrix, or frame, is
             suitable for sensing sparse signals. To this end, the
             present paper investigates two parameters that measure the
             coherence of a frame: worst-case and average coherence. We
             first provide several examples of frames that have small
             spectral norm, worst-case coherence, and average coherence.
             Next, we present a new lower bound on worst-case coherence
             and compare it to the Welch bound. Later, we propose an
             algorithm that decreases the average coherence of a frame
             without changing its spectral norm or worst-case coherence.
             Finally, we use worst-case and average coherence, as opposed
             to the Restricted Isometry Property, to garner near-optimal
             probabilistic guarantees on both sparse signal detection and
             reconstruction in the presence of noise. This contrasts with
             recent results that only guarantee noiseless signal recovery
             from arbitrary frames, and which further assume independence
             across the nonzero entries of the signalin a sense,
             requiring small average coherence replaces the need for such
             an assumption. © 2011 IEEE.},
   Doi = {10.1109/ISIT.2011.6034214},
   Key = {fds235984}
}

@article{fds235985,
   Author = {Calderbank, R and Jafarpour, S and Nastasescu,
             M},
   Title = {Covering radius and the Restricted Isometry
             Property},
   Journal = {2011 IEEE Information Theory Workshop, ITW
             2011},
   Pages = {558-562},
   Year = {2011},
   url = {http://dx.doi.org/10.1109/ITW.2011.6089564},
   Abstract = {The Restricted Isometry Property or RIP introduced by Candes
             and Tao requires an n × p dictionary to act as a near
             isometry on all k-sparse signals. This paper provides a very
             simple condition under which a dictionary Φ (C) obtained by
             exponentiating codewords from a binary linear code C
             satisfies the RIP with high probability. The method is to
             bound the difference between the dictionary Φ(C) and a
             second dictionary A generated by a random Bernoulli process
             which is known to satisfy the RIP with high probability. The
             difference Δ-Φ (C) is controlled by the covering radius of
             C, a fundamental parameter that is bounded above by the
             number of weights in the dual code C ⊥ (the external
             distance of C). The main result complements a more
             sophisticated asymptotic analysis by Babadi and Tarokh of
             the distribution of eigenvalues of random submatrices of
             Φ(C). In this analysis, divergence from the distribution
             corresponding to the full Bernoulli matrix depends on a
             different fundamental parameter of C, namely the minimum
             distance of the dual code C ⊥. © 2011
             IEEE.},
   Doi = {10.1109/ITW.2011.6089564},
   Key = {fds235985}
}

@article{fds235986,
   Author = {Gomaa, A and Chi, Y and Al-Dhahir, N and Calderbank,
             R},
   Title = {On training signal design for multi-user MIMO-OFDM:
             Performance analysis and tradeoffs},
   Journal = {IEEE VTS ... Vehicular Technology Conference : VTC :
             [proceedings]},
   Year = {2011},
   ISSN = {1550-2252},
   url = {http://dx.doi.org/10.1109/VETECF.2011.6092844},
   Abstract = {This paper addresses spectrally-efficient multiantenna
             multi-carrier uplink transmission scenarios where the users
             overlap in time and frequency and are separated using
             spatial processing at the base station. The robustness of
             the proposed training sequences to residual carrier
             frequency offset and phase noise is evaluated analytically.
             This analysis reveals an interesting design tradeoff between
             the Peak-to-Average Power Ratio of a training sequence and
             the increase in channel estimation mean squared error over
             the ideal case when these two impairments are not present.
             © 2011 IEEE.},
   Doi = {10.1109/VETECF.2011.6092844},
   Key = {fds235986}
}

@article{fds235987,
   Author = {Applebaum, L and Bajwa, WU and Calderbank, R and Howard,
             S},
   Title = {Choir codes: Coding for full duplex interference
             management},
   Journal = {2011 49th Annual Allerton Conference on Communication,
             Control, and Computing, Allerton 2011},
   Pages = {1-8},
   Year = {2011},
   url = {http://dx.doi.org/10.1109/Allerton.2011.6120141},
   Abstract = {Communication networks conventionally operate with
             half-duplex methods and interference avoiding schemes to
             manage multiple transceivers. Here we consider a method in
             which nodes transmit and receive in concert to achieve full
             duplex communication without transmitter coordination. We
             build on a recent framework for full-duplex communication in
             ad-hoc wireless networks recently proposed by Zhang, Luo and
             Guo. An individual node in the wireless network either
             transmits or it listens to transmissions from other nodes
             but it cannot do both at the same time. There might be as
             many nodes as there are MAC addresses but we assume that
             only a small subset of nodes contribute to the superposition
             received at any given node in the network. We develop
             deterministic algebraic coding methods that allow
             simultaneous communication across the entire network. We
             call such codes choir codes. Users are assigned subspaces of
             F 2m to define their transmit and listen times. Codewords on
             these subspaces are designed and proven to adhere to bounds
             on worst-case coherence and the associated matrix spectral
             norm. This in turn provides guarantees for multi-user
             detection using convex optimization. Further, we show that
             matrices for each receiver's listening times can be related
             by permutations, thus guaranteeing fairness between
             receivers. Compared with earlier work using random codes,
             our methods have significant improvements including reduced
             decoding/detection error and non-asymptotic results.
             Simulation results verify that, as a method to manage
             interference, our scheme has significant advantages over
             seeking to eliminate or align interference through extensive
             exchange of fine-grained channel state information. © 2011
             IEEE.},
   Doi = {10.1109/Allerton.2011.6120141},
   Key = {fds235987}
}

@article{fds235988,
   Author = {Nokleby, M and Bajwa, WU and Calderbank, R and Aazhang,
             B},
   Title = {Gossiping in groups: Distributed averaging over the wireless
             medium},
   Journal = {2011 49th Annual Allerton Conference on Communication,
             Control, and Computing, Allerton 2011},
   Pages = {1242-1249},
   Year = {2011},
   url = {http://dx.doi.org/10.1109/Allerton.2011.6120310},
   Abstract = {We present an approach to gossip algorithms tailored to the
             practical considerations of wireless communications.
             Traditional gossip algorithms operate via the pairwise
             exchange of estimates, which fails to capture the broadcast
             and superposition nature of the wireless medium. Adapting
             the virtual full-duplex framework of Guo and Zhang, we
             construct a communications scheme in which each node can
             broadcast its estimate to its neighbors while simultaneously
             receiving its neighbors' estimates. This full-duplex scheme
             gives rise to group gossip, a more flexible family of gossip
             algorithms built on multilateral, rather than pairwise,
             exchanges. Our approach obviates the need for
             orthogonalization or medium access; only local information
             and synchronization are necessary. Additionally, group
             gossip has better convergence properties than does
             randomized gossip. Group gossip permits a tighter bound on
             the convergence speed than randomized gossip, and in general
             the upper bound on the convergence time is at most one-third
             that of randomized gossip. © 2011 IEEE.},
   Doi = {10.1109/Allerton.2011.6120310},
   Key = {fds235988}
}

@article{fds235989,
   Author = {Dang, W and Pezeshki, A and Howard, S and Moran, W and Calderbank,
             R},
   Title = {Coordinating complementary waveforms for sidelobe
             suppression},
   Journal = {Conference Record of the Asilomar Conference on Signals,
             Systems and Computers},
   Pages = {2096-2100},
   Year = {2011},
   ISSN = {1058-6393},
   url = {http://dx.doi.org/10.1109/ACSSC.2011.6190398},
   Abstract = {We present a general method for constructing radar transmit
             pulse trains and receive filters for which the radar
             point-spread function in delay and Doppler, given by the
             cross-ambiguity function of the transmit pulse train and the
             pulse train used in the receive filter, is essentially free
             of range sidelobes inside a Doppler interval around the
             zero-Doppler axis. The transmit pulse train is constructed
             by coordinating the transmission of a pair of Golay
             complementary waveforms across time according to zeros and
             ones in a binary sequence P. The pulse train used to filter
             the received signal is constructed in a similar way, in
             terms of sequencing the Golay waveforms, but each waveform
             in the pulse train is weighted by an element from another
             sequence Q. We show that a spectrum jointly determined by P
             and Q sequences controls the size of the range sidelobes of
             the cross-ambiguity function and by properly choosing P and
             Q we can clear out the range sidelobes inside a Doppler
             interval around the zero-Doppler axis. The joint design of P
             and Q enables a tradeoff between the order of the spectral
             null for range sidelobe suppression and the signal-to-noise
             ratio at the receiver output. We establish this trade-off
             and derive a necessary and sufficient condition for the
             construction of P and Q sequences that produce a null of a
             desired order. © 2011 IEEE.},
   Doi = {10.1109/ACSSC.2011.6190398},
   Key = {fds235989}
}

@article{fds235990,
   Author = {Wu, Y and Viswanathan, H and Klein, T and Haner, M and Calderbank,
             R},
   Title = {Capacity optimization in networks with heterogeneous radio
             access technologies},
   Journal = {GLOBECOM - IEEE Global Telecommunications
             Conference},
   Year = {2011},
   url = {http://dx.doi.org/10.1109/GLOCOM.2011.6134226},
   Abstract = {As it becomes common for wireless service providers (WSP) to
             employ multiple heterogeneous radio access technologies
             (RAT), the management of the combined resources across
             multiple RATs arises as an important issue. The WSP's
             objective is to assign different users to the different RATs
             so as to maximize network capacity (or total utility) while
             ensuring that individual users' quality of service (QoS)
             requirements are met. In this paper, we consider this
             resource allocation problem for two scenarios: voice
             communication and video communication. For voice
             communication, we propose a stable and optimal assignment
             scheme based on the deferred acceptance algorithm for both
             static and online cases. For video communication,
             identifying the NP-hardness of the problem, we propose and
             compare a set of heuristic algorithms including a
             low-complexity, high-performance scheme. © 2011
             IEEE.},
   Doi = {10.1109/GLOCOM.2011.6134226},
   Key = {fds235990}
}

@article{fds235991,
   Author = {Li, Y and Papachristodoulou, A and Chiang, M and Calderbank,
             AR},
   Title = {Congestion control and its stability in networks with delay
             sensitive traffic},
   Journal = {Computer Networks},
   Volume = {55},
   Number = {1},
   Pages = {20-32},
   Year = {2011},
   ISSN = {1389-1286},
   url = {http://dx.doi.org/10.1016/j.comnet.2010.07.001},
   Abstract = {We consider congestion control in a network with delay
             sensitive/ insensitive traffic, modelled by adding explicit
             delay terms to the utility function measuring user's
             happiness on the Quality of Service (QoS). A new Network
             Utility Maximization (NUM) problem is formulated and solved
             in a decentralized way via appropriate algorithms
             implemented at the users (primal) and/or links (dual). For
             the dual algorithm, delay-independent and delay-dependent
             stability conditions are derived when propagation delays are
             taken into account. A system with voice and data traffic is
             considered as example and the properties of the congestion
             control algorithm are assessed. © 2010 Elsevier B.V. All
             rights reserved.},
   Doi = {10.1016/j.comnet.2010.07.001},
   Key = {fds235991}
}

@article{fds235992,
   Author = {Chi, Y and Gomaa, A and Al-Dhahir, N and Calderbank,
             R},
   Title = {MMSE-optimal training sequences for spectrally-efficient
             Multi-User MIMO-OFDM systems},
   Journal = {European Signal Processing Conference},
   Pages = {634-638},
   Year = {2011},
   ISSN = {2219-5491},
   Abstract = {This paper proposes a new family of optimal training
             sequences in terms of minimizing the mean-square channel
             estimation error for spectrally-efficient Multi-User
             MIMO-OFDM systems with an arbitrary number of transmit
             antennas and an arbitrary number of training symbols. It
             addresses uplink transmission scenarios where the users
             overlap in time and frequency and are separated using
             spatial processing at the base station. In particular,
             optimal training sequences can be obtained easily from
             standard signal constellations such as QPSK with desired low
             PAPR, making it appealing for practical use. © 2011
             EURASIP.},
   Key = {fds235992}
}

@article{fds235993,
   Author = {Sirinaunpiboon, S and Calderbank, AR and Howard,
             SD},
   Title = {Fast essentially maximum likelihood decoding of the Golden
             code},
   Journal = {IEEE Transactions on Information Theory},
   Volume = {57},
   Number = {6},
   Pages = {3537-3541},
   Year = {2011},
   ISSN = {0018-9448},
   url = {http://dx.doi.org/10.1109/TIT.2011.2136870},
   Abstract = {The Golden code is a full-rate full-diversity space-time
             code which has been incorporated in the IEEE 802.16 (WiMAX)
             standard. The worst case complexity of a tree-based sphere
             decoder for a square QAM constellation is O(N 3), where n is
             the size of the underlying QAM constellation; the worst case
             will dominate average decoding complexity on any channel
             with a significant line of sight component. In this paper,
             we present a simple algorithm with quadratic complexity for
             decoding the Golden code that can be employed by mobile
             terminals with either one or two receive antennas, that is
             resilient to near singularity of the channel matrix, and
             that gives essentially maximum likelihood (ML) performance.
             Dual use is an advantage, since there will likely be some
             IEEE 802.16 mobile terminals with one receive antenna and
             some with two antennas. The key to the quadratic algorithm
             is a maximization of the likelihood function with respect to
             one of the pair of signal points conditioned on the other.
             This choice is made by comparing the determinants of two
             covariance matrices, and the underlying geometry of the
             Golden code guarantees that one of these choices is good
             with high probability. © 2011 IEEE.},
   Doi = {10.1109/TIT.2011.2136870},
   Key = {fds235993}
}

@article{fds235994,
   Author = {Chi, Y and Scharf, LL and Pezeshki, A and Calderbank,
             AR},
   Title = {Sensitivity to basis mismatch in compressed
             sensing},
   Journal = {IEEE Transactions on Signal Processing},
   Volume = {59},
   Number = {5},
   Pages = {2182-2195},
   Year = {2011},
   ISSN = {1053-587X},
   url = {http://dx.doi.org/10.1109/TSP.2011.2112650},
   Abstract = {The theory of compressed sensing suggests that successful
             inversion of an image of the physical world (broadly defined
             to include speech signals, radar/sonar returns, vibration
             records, sensor array snapshot vectors, 2-D images, and so
             on) for its source modes and amplitudes can be achieved at
             measurement dimensions far lower than what might be expected
             from the classical theories of spectrum or modal analysis,
             provided that the image is sparse in an apriori known basis.
             For imaging problems in spectrum analysis, and passive and
             active radar/sonar, this basis is usually taken to be a DFT
             basis. However, in reality no physical field is sparse in
             the DFT basis or in any apriori known basis. No matter how
             finely we grid the parameter space the sources may not lie
             in the center of the grid cells and consequently there is
             mismatch between the assumed and the actual bases for
             sparsity. In this paper, we study the sensitivity of
             compressed sensing to mismatch between the assumed and the
             actual sparsity bases. We start by analyzing the effect of
             basis mismatch on the best k-term approximation error, which
             is central to providing exact sparse recovery guarantees. We
             establish achievable bounds for the ℓ1 error of the best
             k-term approximation and show that these bounds grow
             linearly with the image (or grid) dimension and the mismatch
             level between the assumed and actual bases for sparsity. We
             then derive bounds, with similar growth behavior, for the
             basis pursuit ℓ1 recovery error, indicating that the
             sparse recovery may suffer large errors in the presence of
             basis mismatch. Although, we present our results in the
             context of basis pursuit, our analysis applies to any sparse
             recovery principle that relies on the accuracy of best
             k-term approximations for its performance guarantees. We
             particularly highlight the problematic nature of basis
             mismatch in Fourier imaging, where spillage from off-grid
             DFT components turns a sparse representation into an
             incompressible one. We substantiate our mathematical
             analysis by numerical examples that demonstrate a
             considerable performance degradation for image inversion
             from compressed sensing measurements in the presence of
             basis mismatch, for problem sizes common to radar and sonar.
             © 2011 IEEE.},
   Doi = {10.1109/TSP.2011.2112650},
   Key = {fds235994}
}

@article{fds235995,
   Author = {Thejaswi, PSC and Bennatan, A and Zhang, J and Calderbank, AR and Cochran, D},
   Title = {Layered coding for interference channels with partial
             transmitter side information},
   Journal = {IEEE Transactions on Information Theory},
   Volume = {57},
   Number = {5},
   Pages = {2765-2780},
   Year = {2011},
   ISSN = {0018-9448},
   url = {http://dx.doi.org/10.1109/TIT.2011.2119670},
   Abstract = {A two-user interference channel is considered where each
             transmitter has access to a part of the information intended
             to the other destination. A primary objective is to maximize
             the information rates, by exploring the cooperation between
             the transmitters for interference mitigation, based on the
             partial side information. It is clear that full cooperation
             between the transmitters is not possible since each
             transmitter has only a part of the side information. With
             this insight, several "layered coding" schemes, consisting
             of binning and superposition at different stages, are
             developed. These schemes are are carefully built on coding
             strategies for the classical interference channel and node
             cooperation mechanisms. In particular, two layered coding
             schemes, which are based on a combination of MIMO broadcast
             coding and the HanKobayashi (HK) coding, are thoroughly
             studied : The first one, namely layered coding with binning,
             makes heavy use of the GelfandPinsker binning and the HK
             coding and the second one, namely layered superposition
             coding, involves superposition coding over different tiers.
             Rate regions corresponding to the proposed schemes are
             derived. Then the application of these coding schemes are
             illustrated for the Gaussian case and numerical results
             corroborate that the proposed layered coding schemes yield
             substantial gains at high SNR. © 2011 IEEE.},
   Doi = {10.1109/TIT.2011.2119670},
   Key = {fds235995}
}

@article{fds235996,
   Author = {Calderbank, R and Casazza, PG and Heinecke, A and Kutyniok, G and Pezeshki, A},
   Title = {Sparse fusion frames: Existence and construction},
   Journal = {Advances in Computational Mathematics},
   Volume = {35},
   Number = {1},
   Pages = {1-31},
   Year = {2011},
   ISSN = {1019-7168},
   url = {http://dx.doi.org/10.1007/s10444-010-9162-3},
   Abstract = {Fusion frame theory is an emerging mathematical theory that
             provides a natural framework for performing hierarchical
             data processing. A fusion frame can be regarded as a
             frame-like collection of subspaces in a Hilbert space, and
             thereby generalizes the concept of a frame for signal
             representation. However, when the signal and/or subspace
             dimensions are large, the decomposition of the signal into
             its fusion frame measurements through subspace projections
             typically requires a large number of additions and
             multiplications, and this makes the decomposition
             intractable in applications with limited computing budget.
             To address this problem, in this paper, we introduce the
             notion of a sparse fusion frame, that is, a fusion frame
             whose subspaces are generated by orthonormal basis vectors
             that are sparse in a 'uniform basis' over all subspaces,
             thereby enabling low-complexity fusion frame decompositions.
             We study the existence and construction of sparse fusion
             frames, but our focus is on developing simple algorithmic
             constructions that can easily be adopted in practice to
             produce sparse fusion frames with desired (given) operators.
             By a desired (or given) operator we simply mean one that has
             a desired (or given) set of eigenvalues for the fusion frame
             operator. We start by presenting a complete characterization
             of Parseval fusion frames in terms of the existence of
             special isometries defined on an encompassing Hilbert space.
             We then introduce two general methodologies to generate new
             fusion frames from existing ones, namely the Spatial
             Complement Method and the Naimark Complement Method, and
             analyze the relationship between the parameters of the
             original and the new fusion frame. We proceed by
             establishing existence conditions for 2-sparse fusion frames
             for any given fusion frame operator, for which the
             eigenvalues are greater than or equal to two. We then
             provide an easily implementable algorithm for computing such
             2-sparse fusion frames. © 2010 Springer Science+Business
             Media, LLC.},
   Doi = {10.1007/s10444-010-9162-3},
   Key = {fds235996}
}

@article{fds235997,
   Author = {Chi, Y and Gomaa, A and Al-Dhahir, N and Calderbank,
             AR},
   Title = {Training signal design and tradeoffs for
             spectrally-efficient multi-user MIMO-OFDM
             systems},
   Journal = {IEEE Transactions on Wireless Communications},
   Volume = {10},
   Number = {7},
   Pages = {2234-2245},
   Year = {2011},
   ISSN = {1536-1276},
   url = {http://dx.doi.org/10.1109/TWC.2011.042211.101100},
   Abstract = {In this paper, we design MMSE-optimal training sequences for
             multi-user MIMO-OFDM systems with an arbitrary number of
             transmit antennas and an arbitrary number of training
             symbols. It addresses spectrally-efficient uplink
             transmission scenarios where the users overlap in time and
             frequency and are separated using spatial processing at the
             base station. The robustness of the proposed training
             sequences to residual carrier frequency offset and phase
             noise is evaluated. This analysis reveals an interesting
             design tradeoff between the peak-to-average power ratio of a
             training sequence and the increase in channel estimation
             mean squared error over the ideal case when these two
             impairments are not present. © 2011 IEEE.},
   Doi = {10.1109/TWC.2011.042211.101100},
   Key = {fds235997}
}

@article{fds235998,
   Author = {Qureshi, TR and Zoltowski, MD and Calderbank, R and Pezeshki,
             A},
   Title = {Unitary design of radar waveform diversity
             sets},
   Journal = {Digital Signal Processing},
   Volume = {21},
   Number = {5},
   Pages = {552-567},
   Year = {2011},
   ISSN = {1051-2004},
   url = {http://dx.doi.org/10.1016/j.dsp.2010.09.006},
   Abstract = {In this work, multiple radar waveforms are simultaneously
             transmitted, emitted from different antennas. The goal is to
             process the returns in such a way that the overall ambiguity
             function is a sum of individual ambiguity functions, such
             that the sum better approximates the ideal thumbtack shape.
             A unitary design for the illustrative 4×4 example
             prescribes the scheduling of the waveforms over four
             transmit antennas over four PRIs. Further, it dictates how
             the matched filtering of the returns over four PRIs is
             combined in such a way so as to achieve both perfect
             separation (of the superimposed returns) AND perfect
             reconstruction. Perfect reconstruction implies that the sum
             of the time-autocorrelations associated with each of the
             four waveforms is a delta function. The net result of the
             processing of four PRIs over four virtual antennas yields 16
             cross-correlations all of which ideally exhibit a sharp peak
             at the target delay. Conditions for both perfect separation
             and perfect reconstruction are developed, and a variety of
             waveform sets satisfying both are presented. Doppler
             compensation is achieved by a data-dependent weighting of
             the different PRI matched-filtered outputs prior to summing.
             Simulations are presented verifying the efficacy of the
             proposed unitary waveform matrix designs in conjunction with
             the proposed Doppler compensation technique. © 2010
             Elsevier Inc. All rights reserved.},
   Doi = {10.1016/j.dsp.2010.09.006},
   Key = {fds235998}
}

@article{fds235999,
   Author = {Goel, S and Aggarwal, V and Yener, A and Calderbank,
             AR},
   Title = {The effect of eavesdroppers on network connectivity: A
             secrecy graph approach},
   Journal = {IEEE Transactions on Information Forensics and
             Security},
   Volume = {6},
   Number = {3 PART 1},
   Pages = {712-724},
   Year = {2011},
   ISSN = {1556-6013},
   url = {http://dx.doi.org/10.1109/TIFS.2011.2148714},
   Abstract = {This paper investigates the effect of eavesdroppers on
             network connectivity, using a wiretap model and percolation
             theory. The wiretap model captures the effect of
             eavesdroppers on link security. A link exists between two
             nodes only if the secrecy capacity of that link is positive.
             Network connectivity is defined in a percolation sense,
             i.e., connectivity exists if an infinite connected component
             exists in the corresponding secrecy graph. We consider
             uncertainty in location of eavesdroppers, which is modeled
             directly at the network level as correlated failures in the
             secrecy graph. Our approach attempts to bridge the gap
             between physical layer security under uncertain channel
             state information and network level connectivity under
             secrecy constraints. For square and triangular lattice
             secrecy graphs, we obtain bounds on the percolation
             threshold, which is the critical value of the probability of
             occurrence of an eavesdropper, above which network
             connectivity does not exist. For Poisson secrecy graphs,
             degree distribution and mean value of upper and lower bounds
             on node degree are obtained. Further, inner and outer bounds
             on the achievable region for network connectivity are
             obtained. Both analytic and simulation results show that
             uncertainty in location of eavesdroppers has a dramatic
             effect on network connectivity in a secrecy graph. © 2011
             IEEE.},
   Doi = {10.1109/TIFS.2011.2148714},
   Key = {fds235999}
}

@article{fds236000,
   Author = {Raginsky, M and Jafarpour, S and Harmany, ZT and Marcia, RF and Willett,
             RM and Calderbank, R},
   Title = {Performance bounds for expander-based compressed sensing in
             poisson noise},
   Journal = {IEEE Transactions on Signal Processing},
   Volume = {59},
   Number = {9},
   Pages = {4139-4153},
   Year = {2011},
   ISSN = {1053-587X},
   url = {http://dx.doi.org/10.1109/TSP.2011.2157913},
   Abstract = {This paper provides performance bounds for compressed
             sensing in the presence of Poisson noise using expander
             graphs. The Poisson noise model is appropriate for a variety
             of applications, including low-light imaging and digital
             streaming, where the signal-independent and/or bounded noise
             models used in the compressed sensing literature are no
             longer applicable. In this paper, we develop a novel sensing
             paradigm based on expander graphs and propose a maximum a
             posteriori (MAP) algorithm for recovering sparse or
             compressible signals from Poisson observations. The geometry
             of the expander graphs and the positivity of the
             corresponding sensing matrices play a crucial role in
             establishing the bounds on the signal reconstruction error
             of the proposed algorithm. We support our results with
             experimental demonstrations of reconstructing average packet
             arrival rates and instantaneous packet counts at a router in
             a communication network, where the arrivals of packets in
             each flow follow a Poisson process. © 2011
             IEEE.},
   Doi = {10.1109/TSP.2011.2157913},
   Key = {fds236000}
}

@article{fds235777,
   Author = {Zoltowski, MD and Qureshi, TR and Calderbank, R and Moran,
             B},
   Title = {Unitary Design of Radar Waveform Diversity
             Sets},
   Journal = {Handbook on Array Processing and Sensor Networks},
   Pages = {211-230},
   Year = {2010},
   url = {http://dx.doi.org/10.1002/9780470487068.ch7},
   Doi = {10.1002/9780470487068.ch7},
   Key = {fds235777}
}

@article{fds235952,
   Author = {Li, Y and Li, Z and Chiang, M and Calderbank, AR},
   Title = {Intelligent video network engineering with distributed
             optimization: Two case studies},
   Journal = {Studies in Computational Intelligence},
   Volume = {280},
   Pages = {253-290},
   Year = {2010},
   ISSN = {1860-949X},
   url = {http://dx.doi.org/10.1007/978-3-642-11686-5_8},
   Abstract = {Video is becoming the dominant traffic over the Internet. To
             provide better Quality of Service (QoS) to the end users,
             while also achieve network resource efficiency, is an
             important problem for both network operators, content
             providers and consumers. In this work, we present
             intelligent video networking solutions for IPTV and
             Peer-to-Peer (P2P) systems that optimizes the users' QoS
             experiences while under network resource constraints. Given
             the limited network bandwidth resources, how to provide
             Internet users with good video playback Quality of Service
             (QoS) is a key problem. For IPTV systems video clips
             competing bandwidth, we propose an approach of Content-Aware
             distortion-Fair (CAF) video delivery scheme, which is aware
             of the characteristics of video frames and ensures max-min
             distortion fair sharing among video flows. Different from
             bandwidth fair sharing, CAF targets end-to-end video
             playback quality fairness among users when bandwidth is
             insufficient, based on the fact that users directly care
             about video quality rather than bandwidth. The proposed CAF
             approach does not require rate-distortion modeling of the
             source, which is difficult to estimate, but instead, it
             exploits the temporal prediction structure of the video
             sequences along with a frame drop distortion metric to guide
             resource allocations and coordination. Experimental results
             show that the proposed approach operates with limited
             overhead in computation and communication, and yields better
             QoS, especially when the network is congested. For Internet
             based video broadcasting applications such as IPTV, the
             Peer-to-Peer (P2P) streaming scheme has been found to be an
             effective solution. An important issue in live broadcasting
             is to avoid playback buffer underflow. How to utilize the
             playback buffer and upload bandwidth of peers to minimize
             the freeze-ups in playback, is the problem we try to solve.
             We propose a successive water-filling (SWaF) algorithm for
             the video transmission scheduling in P2P live streaming
             system, to minimize the playback freeze-ups among peers.
             SWaF algorithm only needs each peer to optimally transmit
             (within its uploading bandwidth) part of its available video
             segments in the buffer to other peers requiring the content
             and pass small amount message to some other peers. Moreover,
             SWaF has low complexity and provable optimality. Numerical
             results demonstrated the effectiveness of the proposed
             algorithm. © 2010 Springer-Verlag Berlin
             Heidelberg.},
   Doi = {10.1007/978-3-642-11686-5_8},
   Key = {fds235952}
}

@article{fds235953,
   Author = {Hande, P and Chiang, M and Calderbank, R and Zhang,
             J},
   Title = {Pricing under constraints in access networks: Revenue
             maximization and congestion management},
   Journal = {Proceedings - IEEE INFOCOM},
   Year = {2010},
   ISSN = {0743-166X},
   url = {http://dx.doi.org/10.1109/INFCOM.2010.5461954},
   Abstract = {This paper investigates pricing of Internet connectivity
             services in the context of a monopoly ISP selling broadband
             access to consumers. We first study the optimal combination
             of flat-rate and usage-based access price components for
             maximization of ISP revenue, subject to a capacity
             constraint on the datarate demand. Next, we consider
             time-varying consumer utilities for broadband data rates
             that can result in uneven demand for data-rate over time.
             Practical considerations limit the viability of altering
             prices over time to smoothen out the demanded datarate.
             Despite such constraints on pricing, our analysis reveals
             that the ISP can retain the revenue by setting a low usage
             fee and dropping packets of consumer demanded data that
             exceed capacity. Regulatory attention on ISP congestion
             management discourages such "technical" practices and
             promotes economics based approaches. We characterize the
             loss in ISP revenue from an economics based approach.
             Regulatory requirements further impose limitations on price
             discrimination across consumers, and we derive the revenue
             loss to the ISP from such restrictions. We then develop
             partial recovery of revenue loss through non-linear pricing
             that does not explicitly discriminate across consumers.
             While determination of the access price is ultimately based
             on additional considerations beyond the scope of this paper,
             the analysis here can serve as a benchmark to structure
             access price in broadband access networks. ©2010
             IEEE.},
   Doi = {10.1109/INFCOM.2010.5461954},
   Key = {fds235953}
}

@article{fds235954,
   Author = {Raginsky, M and Jafarpour, S and Willett, R and Calderbank,
             R},
   Title = {Fishing in poisson streams: Focusing on the whales, ignoring
             the minnows},
   Journal = {2010 44th Annual Conference on Information Sciences and
             Systems, CISS 2010},
   Year = {2010},