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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}
}

@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
Year = {2009},
Month = {April},
url = {http://arxiv.org/abs/0904.1764},
Key = {fds212452}
}

%% Agarwal, Pankaj K.
@article{fds332953,
Author = {Rav, M and Lowe, A and Agarwal, PK},
Title = {Flood Risk Analysis on Terrains},
Journal = {GIS: Proceedings of the ACM International Symposium on
Advances in Geographic Information Systems},
Volume = {2017-November},
Year = {2017},
Month = {November},
ISBN = {9781450345897},
url = {http://dx.doi.org/10.1145/3139958.3139985},
Abstract = {© 2017 Copyright held by the owner/author(s). An important
problem in terrain analysis is modeling how water flows
across a terrain and creates floods by filling up
depressions. In this paper we study the flooding query
problem: Given a rain region R and a query point q on the
terrain, quickly determine how much rain has to fall in R so
that q is flooded. Available terrain data is often subject
to uncertainty which must be incorporated into the terrain
analysis. For instance, the digital elevation models of
terrains have to be refined to incorporate underground
pipes, tunnels, and waterways under bridges, but there is
often uncertainty in their existence. By representing the
uncertainty in the terrain data explicitly, we can develop
methods for flood risk analysis that properly incorporate
terrain uncertainty when reporting what areas are at risk of
flooding. We present two results. First, we present a linear
size data structure that given a terrain (with no data
uncertainty) can answer the flooding query in O(m log 2 n)
time, where m is the number of minima of the terrain at
which rain is falling and n is the number of vertices of the
terrain. Next, we extend this data structure to handle
“uncertain” terrains, using a standard Monte Carlo
method. Given a probability distribution on terrains, our
data structure solves the problem of determining the
probability that if a specified amount of rain falls on a
given region a query point is flooded. We implement our data
structures and show that they work very well in
practice.},
Doi = {10.1145/3139958.3139985},
Key = {fds332953}
}

@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
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{fds331366,
Author = {Agarwal, PK and Kumar, N and Sintos, S and Suri, S},
Title = {Range-max queries on uncertain data},
Journal = {Journal of Computer and System Sciences},
Year = {2017},
Month = {January},
url = {http://dx.doi.org/10.1016/j.jcss.2017.09.006},
Abstract = {© 2017. Let P be a set of n uncertain points in Rd, where
each point pi P is associated with a real value vi and
exists with probability αi (0,1] independently of the other
points. 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. Our main contributions include the
following: (i) The first index of sub-quadratic size to
achieve a sub-linear query time in any dimension. (ii) A
conditional lower bound for most-likely range-max queries,
based on the conjectured hardness of the set-intersection
problem. (iii) A near-linear-size index for estimating the
expected range-max value within approximation factor 1/2 in
O(polylog(n)) time. (iv) Extensions of our algorithm to more
general uncertainty models and for computing the top-k
values of the range-max.},
Doi = {10.1016/j.jcss.2017.09.006},
Key = {fds331366}
}

@article{fds330829,
Author = {Wu, Y and Gao, J and Agarwal, PK and Yang, J},
Title = {Finding diverse, high-value representatives on a surface of
Journal = {Proceedings of the VLDB Endowment International Conference
on Very Large Data Bases},
Volume = {10},
Number = {7},
Pages = {793-804},
Year = {2017},
Month = {January},
Abstract = {© 2017 VLDB Endowment. In many applications, the system
needs to selectively present a small subset of answers to
users. The set of all possible answers can be seen as an
elevation surface over a domain, where the elevation
measures the quality of each answer, and the dimensions of
the domain correspond to attributes of the answers with
which similarity between answers can be measured. This paper
considers the problem of finding a diverse set of k
high-quality representatives for such a surface. We show
that existing methods for diversified top-k and weighted
clustering problems are inadequate for this problem. We
propose k-DHR as a better formulation for the problem. We
show that k-DHR has a submodular and monotone objective
function, and we develop efficient algorithms for solving
k-DHR with provable guarantees. We conduct extensive
experiments to demonstrate the usefulness of the results
produced by k-DHR for applications in computational
lead-finding and fact-checking, as well as the efficiency
and effectiveness of our algorithms.},
Key = {fds330829}
}

@article{fds330830,
Author = {Garg, N and Sadiq, M and Agarwal, P},
Title = {GOASREP: Goal oriented approach for software requirements
elicitation and prioritization using analytic hierarchy
process},
Journal = {Advances in Intelligent Systems and Computing},
Volume = {516},
Pages = {281-287},
Year = {2017},
Month = {January},
ISBN = {9789811031557},
url = {http://dx.doi.org/10.1007/978-981-10-3156-4_28},
Abstract = {© Springer Nature Singapore Pte Ltd. 2017. Software
requirements elicitation is a valuable process for the
identification of software requirements according to the
need of different types of stake-holders. There are
different methods for the elicitation of software
requirements like traditional methods, group elicitation
methods, goal oriented methods, etc. Among these methods,
goal oriented methods have received much recognition by
software requirements engineering community. On the basis of
our literature review, we identify that “goal oriented
requirements elicitation processes do not support how to
select and prioritize the requirements using analytic
hierarchy process on the basis of the cost and effort
criteria”. Therefore, in-order to address this issue, we
proposed a method, i.e. GOASREP, for the elicitation of
software requirements using “goal oriented approach” and
the prioritization of the elicited requirements using
“analytic hierarchy process”. In the proposed method, we
used function point analysis approach for the estimation of
the cost of each requirement. COCOMO model has been applied
to estimate the effort of each requirement. Finally, the
usage of the GOASREP is explained using Institute
Examination System.},
Doi = {10.1007/978-981-10-3156-4_28},
Key = {fds330830}
}

@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{fds330831,
Author = {Gupta, P and Agarwal, P},
Title = {Experimental study & analysis of genetic operators for
alignment of multiple biological sequences},
Journal = {Conference Proceeding - 2015 International Conference on
Advances in Computer Engineering and Applications, ICACEA
2015},
Pages = {643-648},
Year = {2015},
Month = {January},
ISBN = {9781467369114},
url = {http://dx.doi.org/10.1109/ICACEA.2015.7164770},
Abstract = {© 2015 IEEE. This paper presents an experimental work to
observe the effect of various genetic algorithm (GA)
operators for alignment of multiple biological sequences
which is a classical NP complete problem popularly known as
multiple sequence alignment (MSA) problem with its
application area in computational molecular biology. We have
tried to solve the problem by varying various GA parameters
in multiple ways and observed the effect of these on
alignment. It is to be noted that the purpose of the
presented work is not at all to propose an efficient GA
based method for solving MSA problem but just to observe the
effect of varying GA parameters. The proposed observations
can surely help those who wish to apply GA method to solve
the MSA problem by choosing the correct operators &
parameters.},
Doi = {10.1109/ICACEA.2015.7164770},
Key = {fds330831}
}

@article{fds330832,
Author = {Garg, N and Agarwal, P and Khan, S},
Title = {Recent advancements in requirement elicitation and
prioritization techniques},
Journal = {Conference Proceeding - 2015 International Conference on
Advances in Computer Engineering and Applications, ICACEA
2015},
Pages = {237-240},
Year = {2015},
Month = {January},
ISBN = {9781467369114},
url = {http://dx.doi.org/10.1109/ICACEA.2015.7164702},
Abstract = {© 2015 IEEE. Requirement Elicitation identify as one of the
most crucial knowledge intensive activities of software
development. Most of the system fails due to use of wrong
elicitation practice. A requirement is defined as a demand
or needs. A System may have a dozen to thousands of
requirement. Without the Elicitation technique it is
impossible to find out the requirement and need of
developing system. After Elicitation Technique we need to
prioritize their requirements. This Research paper is based
on understanding technique and their usage in the real time
applications by using the Elicitation Technique and
Prioritization Technique we know that it is important for
knowing the need of the stakeholder so that the system
developer can get a clear view of requirement for the
developing system.},
Doi = {10.1109/ICACEA.2015.7164702},
Key = {fds330832}
}

@article{fds330833,
Author = {Sekhon, A and Agarwal, P},
Title = {Face recognition using back propagation neural network
technique},
Journal = {Conference Proceeding - 2015 International Conference on
Advances in Computer Engineering and Applications, ICACEA
2015},
Pages = {226-230},
Year = {2015},
Month = {January},
ISBN = {9781467369114},
url = {http://dx.doi.org/10.1109/ICACEA.2015.7164700},
Abstract = {© 2015 IEEE. The paper presents a back propagation based
artificial neural network learning algorithm for recognizing
human faces. We have worked on eight features for
recognition. A facial recognition system has been proposed
to recognize registered faces in the database & new faces
that are not part of the database. The basic objective is to
understand the ability of back propagation learning
algorithms for face recognition task. Few experimental
observations have also been provided.},
Doi = {10.1109/ICACEA.2015.7164700},
Key = {fds330833}
}

@article{fds330834,
Author = {Agarwal, P},
Title = {Message from program chair},
Journal = {Conference Proceeding - 2015 International Conference on
Advances in Computer Engineering and Applications, ICACEA
2015},
Year = {2015},
Month = {January},
ISBN = {9781467369114},
url = {http://dx.doi.org/10.1109/ICACEA.2015.7164861},
Doi = {10.1109/ICACEA.2015.7164861},
Key = {fds330834}
}

@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},
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.},
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.
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},
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{fds330835,
Author = {Agarwal, P and Gupta, R and Maheswari, T and Agarwal, P and Yadav, S and Bali, V},
Title = {A genetic algorithm for alignment of multiple DNA
sequences},
Journal = {Lecture Notes of the Institute for Computer Sciences,
Social-Informatics and Telecommunications
Engineering},
Volume = {108 LNICST},
Pages = {437-443},
Year = {2012},
Month = {December},
ISBN = {9783642356148},
url = {http://dx.doi.org/10.1007/978-3-642-35615-5_71},
Abstract = {This paper presents a new genetic algorithm based solution
to obtain alignment of multiple DNA molecular sequences.
Multiple Sequence alignment is one of the most active
ongoing research problems in the field of computational
molecular biology. Sequence alignment is important because
it allows scientists to analyze protein strands (such as DNA
and RNA) and determine where there are overlaps. These
overlaps can show commonalities in evolution and they also
allow scientists to better prepare vaccines against viruses,
which are made of protein strands. We have proposed new
genetic operations for crossover, mutation, fitness
calculation, population initialization. Proposed scheme
generates new populations with better fitness value. We have
also reviewed the some of the popular works by different
researchers towards solving the MSA problem w.r.t various
phases involved in general GA procedure. A working example
is presented to validate the proposed scheme. Improvement in
the overall population fitness is also calculated. © 2012
ICST Institute for Computer Science, Social Informatics and
Telecommunications Engineering.},
Doi = {10.1007/978-3-642-35615-5_71},
Key = {fds330835}
}

@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
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
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
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
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
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{fds330836, Author = {Rizvi, SAM and Agarwal, P}, Title = {A time efficient algorithm for finding longest common subsequence from two molecular sequences}, Journal = {Proceedings of the IEEE ... annual Northeast Bioengineering Conference. IEEE Northeast Bioengineering Conference}, Pages = {302-306}, Year = {2007}, Month = {December}, ISBN = {1424410339}, url = {http://dx.doi.org/10.1109/NEBC.2007.4413398}, Abstract = {This paper presents a new algorithm for finding Longest Common Subsequence from two given sequences of DNA, Proteins etc of interest. We have presented a Sequential Algorithm, which is quite effective. Our method compares the given Database sequence of DNA representing the entire/partial genetic structure of some organism (such sequences are very long), which is assumed to be stored in the database only once with a given query sequence. Although our method can be applied for Protein or RNA Sequences but here we have only taken DNA Sequences. The bucket sorting method where elements are collected in buckets and then collected in some manner to get the sorted list inspires our algorithm. Our algorithm collects the index positions of the database sequence in respective buckets which becomes the input for the main algorithm. Given algorithm is quite effective as far as time complexity is concerned. © 2007 IEEE.}, Doi = {10.1109/NEBC.2007.4413398}, Key = {fds330836} } @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{fds330837, Author = {Rizvi, SAM and Agarwal, P}, Title = {A new bucket-based algorithm for finding LCS from two given molecular sequences}, Journal = {Proceedings - Third International Conference onInformation Technology: New Generations, ITNG 2006}, Volume = {2006}, Pages = {560-561}, Year = {2006}, Month = {November}, ISBN = {0769524974}, url = {http://dx.doi.org/10.1109/ITNG.2006.12}, Abstract = {This paper presents a new algorithm for finding Longest Common Subsequence from two given sequences of DNA, Proteins etc of interest. Given algorithm is quite effective as far as time complexity is concerned Our method compares the given Database sequence of DNA representing the entire/partial genetic structure of some organism (such sequences are very long), which is assumed to be stored in the database only once with a given query sequence. © 2006 IEEE.}, Doi = {10.1109/ITNG.2006.12}, Key = {fds330837} } @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.}, 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 = {© 2017 Wiley Periodicals, Inc. 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 (Figure presented.) of optimal. Our construction provides a direct and natural way for proving the (Figure presented.) -optimality gap. An earlier proof of the same result made crucial use of a key inequality of Bruss and Delbaen [5] 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{fds332857, Author = {Beale, JT and Majda, AJ}, Title = {Explicit smooth velocity kernels for vortex methods.}, Year = {1983}, Month = {January}, Abstract = {The authors showed the convergence of a class of vortex methods for incompressible, inviscid flow in two or three space dimensions. These methods are based on the fact that the velocity can be determined from the vorticity by a singular integral. The accuracy of the method depends on replacing the integral kernel with a smooth approximation. The purpose of this note is to construct smooth kernels of arbitrary order of accuracy which are given by simple, explicit formulae.}, Key = {fds332857} } @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{fds330929, Author = {Tralie, CJ and Smith, A and Borggren, N and Hineman, J and Bendich, P and Zulch, P and Harer, J}, Title = {Geometric Cross-Modal Comparison of Heterogeneous Sensor Data}, Journal = {Proceedings of the 39th IEEE Aerospace Conference}, Year = {2018}, Month = {March}, Abstract = {In this work, we address the problem of cross-modal comparison of aerial data streams. A variety of simulated automobile trajectories are sensed using two different modalities: full-motion video, and radio-frequency (RF) signals received by detectors at various locations. The information represented by the two modalities is compared using self-similarity matrices (SSMs) corresponding to time-ordered point clouds in feature spaces of each of these data sources; we note that these feature spaces can be of entirely different scale and dimensionality. Several metrics for comparing SSMs are explored, including a cutting-edge time-warping technique that can simultaneously handle local time warping and partial matches, while also controlling for the change in geometry between feature spaces of the two modalities. We note that this technique is quite general, and does not depend on the choice of modalities. In this particular setting, we demonstrate that the cross-modal distance between SSMs corresponding to the same trajectory type is smaller than the cross-modal distance between SSMs corresponding to distinct trajectory types, and we formalize this observation via precision-recall metrics in experiments. Finally, we comment on promising implications of these ideas for future integration into multiple-hypothesis tracking systems.}, Key = {fds330929} } @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{fds330930, Author = {Bendich, P and Gasparovic, E and Harer, J and Tralie, C}, Title = {Geometric Models for Musical Audio Data}, Journal = {Proceedings of the 32st International Symposium on Computational Geometry (SOCG)}, Year = {2016}, Month = {June}, Key = {fds330930} } @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{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{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 = {Annals of Applied Statistics}, Volume = {10}, Number = {1}, Pages = {198-218}, Year = {2016}, 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{fds315425, Author = {Tralie, CJ and Bendich, P}, Title = {Cover Song Identification with Timbral Shape Sequences}, Journal = {16th International Society for Music Information Retrieval (ISMIR)}, Pages = {38-44}, Year = {2015}, Month = {October}, 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{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 Frechet mean in (Dp;Wp), the space of persistence diagrams equipped with the p-th Wasserstein metric. In particular, they showed that the Frechet 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 Frechet mean de nition to the realm of vineyards. We x this problem by altering the original de nition 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 the (Frechet mean) persistence diagram of a perturbation of the input diagrams. We show that this new de nition de nes a (Holder) 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{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{fds330841, Author = {Bray, H and Roesch, H}, Title = {Proof of a Null Geometry Penrose Conjecture}, Journal = {Notices of the American Mathematical Society.}, Volume = {65}, Publisher = {American Mathematical Society}, Year = {2018}, Month = {February}, Key = {fds330841} } @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, R 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{fds332945, Author = {Cnaan-On, I and Harms, A and Krolik, JL and Calderbank, AR}, Title = {Run-length limited codes for backscatter communication}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {6110-6114}, Year = {2017}, Month = {June}, ISBN = {9781509041176}, url = {http://dx.doi.org/10.1109/ICASSP.2017.7953330}, Abstract = {© 2017 IEEE. In backscatter communications, ultra-low power devices signal by modulating the reflection of radio frequency signals emitted from an external source. Unlike conventional one-way communication, the backscatter channel experiences unique self-interference and spread Doppler clutter. Run-length limited (RLL) codes provide a method for spectrum shaping that requires no hardware changes to the communicating devices. The proposed coding framework is suitable for any arbitrarily-shaped pulse train or continuous wave reader waveform. It exploits the unique channel Doppler spread statistics to offer a trade-off between interference rejection and data rate. Analysis shows that code rates of 1 and 4/5 are achievable when dealing with low spread Doppler channels, which is an improvement over the current rate 1/2 with current mainstream backscatter communication techniques. Simulation results with realistic channel assumptions are analyzed and discussed to confirm the theoretical analysis.}, Doi = {10.1109/ICASSP.2017.7953330}, Key = {fds332945} } @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], th is work aims to recover the material's spectrum 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 background 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},
Journal = {IEEE J. Select. Topics Signal Processing, vol. 7, no. 2, pp.
284-295, Apr. 2013},
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},
Journal = {IEEE Trans. Signal Processing, vol. 61, no. 3, pp. 707-723,
Feb. 2013},
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
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.
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
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.
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{`