## Mathematics : All Publications (in the database)
List most recent publications in the database. :chronological alphabetical combined listing:
%% Abel, Michael
@article{fds317698,
Title = {HOMFLY-PT homology for general link diagrams and braidlike
isotopy},
Year = {2016},
Month = {June},
url = {http://arxiv.org/abs/1607.00314},
Key = {fds317698}
}
@article{fds311722,
Author = {M. Abel and M. Hogancamp},
Title = {Stable homology of torus links via categorified Young
symmetrizers II: one-column partitions},
Year = {2016},
Month = {February},
url = {http://arxiv.org/abs/1510.05330},
Key = {fds311722}
}
@article{fds300045,
Author = {M. Abel and L. Rozansky},
Title = {Virtual crossings and a filtration of the triply graded
homology of a link diagram},
Year = {2015},
Month = {February},
url = {http://arxiv.org/abs/1410.5892},
Key = {fds300045}
}
%% Addington, Nicolas
@article{fds226937,
Author = {N. Addington and W. Donovan and C. Meachan},
Title = {Mukai flops and P-twists},
Year = {2015},
Month = {July},
url = {http://arxiv.org/abs/1507.02595},
Key = {fds226937}
}
@article{fds226938,
Author = {N. Addington and W. Donovan and C. Meachan},
Title = {Moduli spaces of torsion sheaves on K3 surfaces and derived
equivalences},
Year = {2015},
Month = {July},
url = {http://arxiv.org/abs/1507.02597},
Key = {fds226938}
}
@article{fds226939,
Author = {N. Addington and W. Donovan and E. Segal},
Title = {The Pfaffian-Grassmannian equivalence revisited},
Journal = {Alg. Geom.},
Volume = {2},
Number = {3},
Pages = {332-364},
Year = {2015},
url = {http://arxiv.org/abs/1401.3661},
Key = {fds226939}
}
@article{fds225141,
Author = {N. Addington},
Title = {On two rationality conjectures for cubic
fourfolds},
Journal = {Math. Res. Lett.},
Year = {2014},
Month = {May},
url = {http://arxiv.org/abs/1405.4902},
Key = {fds225141}
}
@article{fds225601,
Author = {N. Addington and M. Lehn},
Title = {On the symplectic eightfold associated to a Pfaffian cubic
fourfold},
Journal = {J. Reine Angew. Math.},
Year = {2014},
Month = {April},
url = {http://arxiv.org/abs/1404.5657},
Key = {fds225601}
}
@article{fds224079,
Author = {N. Addington and R. P. Thomas},
Title = {Hodge theory and derived categories of cubic
fourfolds},
Journal = {Duke Math. J.},
Volume = {163},
Number = {10},
Pages = {1885-1927},
Year = {2014},
url = {http://arxiv.org/abs/1211.3758},
Key = {fds224079}
}
@article{fds225760,
Author = {N. Addington and E. Segal and E. Sharpe},
Title = {D-brane probes, branched double covers, and noncommutative
resolutions},
Journal = {Adv. Theor. Math. Phys.},
Volume = {18},
Number = {6},
Pages = {1369-1436},
Year = {2014},
url = {http://arxiv.org/abs/1211.2446},
Key = {fds225760}
}
@article{fds224497,
Author = {N. Addington},
Title = {The Brauer group is not a derived invariant},
Booktitle = {Proceedings of "Brauer groups and obstruction problems:
moduli spaces and arithmetic"},
Year = {2013},
Month = {June},
url = {http://arxiv.org/abs/1306.6538},
Key = {fds224497}
}
@article{fds219852,
Author = {N. Addington and P. Aspinwall},
Title = {Categories of massless D-branes and del Pezzo
surfaces},
Journal = {J. High Energy Phys.},
Volume = {2013},
Number = {7},
Pages = {front matter + 39pp.},
Year = {2013},
url = {http://arxiv.org/abs/1305.5767},
Key = {fds219852}
}
@article{fds223836,
Author = {N. Addington},
Title = {New derived symmetries of some hyperkaehler
varieties},
Year = {2011},
Month = {December},
url = {http://arxiv.org/abs/1112.0487},
Key = {fds223836}
}
@article{fds212453,
Author = {N. Addington},
Title = {Spinor sheaves on singular quadrics},
Journal = {Proc. Amer. Math. Soc.},
Volume = {139},
Number = {11},
Pages = {3867-3879},
Year = {2011},
Month = {November},
url = {http://www.ams.org/journals/proc/2011-139-11/S0002-9939-2011-10819-0/},
Key = {fds212453}
}
@article{fds212452,
Author = {N. Addington},
Title = {The derived category of the complete intersection of four
quadrics},
Year = {2009},
Month = {April},
url = {http://arxiv.org/abs/0904.1764},
Key = {fds212452}
}
%% Agarwal, Pankaj K.
@article{fds333280,
Author = {Agarwal, PK and Fox, K and Nath, A},
Title = {Maintaining reeb graphs of triangulated 2-manifolds},
Journal = {LIPIcs},
Volume = {93},
Year = {2018},
Month = {January},
ISBN = {9783959770552},
url = {http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2017.8},
Abstract = {© Pankaj K. Agarwal, Kyle Fox and Abhinandan Nath. Let M be
a triangulated, orientable 2-manifold of genus g without
boundary, and let h be a height function over M that is
linear within each triangle. We present a kinetic data
structure (KDS) for maintaining the Reeb graph R of h as the
heights of M’s vertices vary continuously with time.
Assuming the heights of two vertices of M become equal only
O(1) times, the KDS processes O((? + g)n polylog n) events;
n is the number of vertices in M, and ? is the number of
external events which change the combinatorial structure of
R. Each event is processed in O(log 2 n) time, and the total
size of our KDS is O(gn). The KDS can be extended to
maintain an augmented Reeb graph as well.},
Doi = {10.4230/LIPIcs.FSTTCS.2017.8},
Key = {fds333280}
}
@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 = {9781450354905},
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
answers.},
Doi = {10.4230/LIPIcs.SEA.2017.7},
Key = {fds328996}
}
@article{fds329182,
Author = {Agarwal, PK and Fox, K and Panigrahi, D and Varadarajan, KR and Xiao,
A},
Title = {Faster algorithms for the geometric transportation
problem},
Journal = {LIPIcs},
Volume = {77},
Pages = {71-716},
Year = {2017},
Month = {June},
ISBN = {9783959770385},
url = {http://dx.doi.org/10.4230/LIPIcs.SoCG.2017.7},
Abstract = {© Pankaj K. Agarwal, Kyle Fox, Debmalya Panigrahi, Kasturi
R. Varadarajan, and Allen Xiao. Let R, B C R d for constant
d, be two point sets with |R| + |B| = n, and let λ: R∪B
→ ℕ such that Σ r∈R λ(r) = Σ b∈B λ (b) be demand
functions over R and B. Let d(·, ·) be a suitable distance
function such as the L p distance. The transportation
problem asks to find a map τ: R × B → ℕ such that Σ
b∈B τ(r, b) = λ(r), Σ r∈R τ(r, b) = λ(b), and σ
r∈Rb∈B τ(r, b)d(r, b) is minimized. We present three
new results for the transportation problem when d(·, ·) is
any L p metric: • For any constant ϵ > 0, an O(n 1+ϵ )
expected time randomized algorithm that returns a
transportation map with expected cost O(log 2 (1/ϵ)) times
the optimal cost. • For any ϵ > 0, a (1 +
ϵ)-approximation in O(n 3/2 ϵ -d polylog(U) polylog(n))
time, where U = max p∈Rcup;B λ (p). •An exact strongly
polynomial O(n 2 polylogn) time algorithm, for d =
2.},
Doi = {10.4230/LIPIcs.SoCG.2017.7},
Key = {fds329182}
}
@article{fds330177,
Author = {Wu, Y and Agarwal, PK and Li, C and Yang, J and Yu, C},
Title = {Computational Fact Checking through Query
Perturbations},
Journal = {ACM Transactions on Database Systems},
Volume = {42},
Number = {1},
Pages = {1-41},
Year = {2017},
Month = {January},
url = {http://dx.doi.org/10.1145/2996453},
Doi = {10.1145/2996453},
Key = {fds330177}
}
@article{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
answers},
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},
url = {http://dx.doi.org/10.1016/j.adhoc.2011.04.011},
Abstract = {Multi-channel wireless networks are increasingly deployed as
infrastructure networks, e.g. in metro areas. Network nodes
frequently employ directional antennas to improve spatial
throughput. In such networks, between two nodes, it is of
interest to compute a path with a channel assignment for the
links such that the path and link bandwidths are the same.
This is achieved when any two consecutive links are assigned
different channels, termed as "Channel-Discontinuity-Constraint"
(CDC). CDC-paths are also useful in TDMA systems, where,
preferably, consecutive links are assigned different
time-slots. In the first part of this paper, we develop a
t-spanner for CDC-paths using spatial properties; a
sub-network containing O(n/θ) links, for any θ > 0, such
that CDC-paths increase in cost by at most a factor t = (1 -
2 sin(θ/2)) -2 . We propose a novel distributed algorithm
to compute the spanner using an expected number of O(n log
n) fixed-size messages. In the second part, we present a
distributed algorithm to find minimum-cost CDC-paths between
two nodes using O(n 2 ) fixed-size messages, by developing
an extension of Edmonds' algorithm for minimum-cost perfect
matching. In a centralized implementation, our algorithm
runs in O(n 2 ) time improving the previous best algorithm
which requires O(n 3 ) running time. Moreover, this running
time improves to O(n/θ) when used in conjunction with the
spanner developed. © 2011 Elsevier B.V. All rights
reserved.},
Doi = {10.1016/j.adhoc.2011.04.011},
Key = {fds235364}
}
@article{fds235350,
Author = {Agarwal, PK and Pan, J},
Title = {Near-linear algorithms for geometric hitting sets and set
covers},
Journal = {Proceedings of the Annual Symposium on Computational
Geometry},
Pages = {271-279},
Year = {2014},
Month = {January},
url = {http://dx.doi.org/10.1145/2582112.2582152},
Abstract = {Given a finite range space ∑ = (X,R), with N = |X| + |R|,
we present two simple algorithms, based on the
multiplicative-weight method, for computing a small-size
hitting set or set cover of β. The first algorithm is a
simpler variant of the Brönnimann-Goodrich algorithm but
more efficient to implement, and the second algorithm can be
viewed as solving a two-player zero-sum game. These
algorithms, in conjunction with some standard geometric data
structures, lead to near-linear algorithms for computing a
small-size hitting set or set cover for a number of
geometric range spaces. For example, they lead to
O(Npolylog(N)) expected-time randomized O(1)-approximation
algorithms for both hitting set and set cover if X is a set
of points and R a set of disks in R2. Copyright 2014
ACM.},
Doi = {10.1145/2582112.2582152},
Key = {fds235350}
}
@article{fds235351,
Author = {Agarwal, PK and Sharathkumar, R},
Title = {Approximation algorithms for bipartite matching with metric
and geometric costs},
Journal = {Proceedings of the Annual ACM Symposium on Theory of
Computing},
Pages = {555-564},
Year = {2014},
Month = {January},
ISSN = {0737-8017},
url = {http://dx.doi.org/10.1145/2591796.2591844},
Abstract = {Let G = G(A∪B;A×B), with |A| = |B| = n, be a weighted
bipartite graph, and let d(·, ·) be the cost function on
the edges. Let w(M) denote the weight of a matching in G,
and M* a minimum-cost perfect matching in G. We call a
perfect matching M c-approximate, for c ≥1, if w(M)≤
c·w(M*). We present three approximation algorithms for
computing minimum-cost perfect matchings in G. First, we
consider the case when d(·, ·) is a metric. For any δ >
0, we present an algorithm that, in O(n 2+δ log n log 2
(1/δ)) time, computes a O(1/δ α )-approximate matching of
G, where α = log 3 2 ≈ 0:631. Next, we assume the
existence of a dynamic data structure for answering
approximate nearest neighbor (ANN) queries under d(·, ·).
Given two parameters ε,δ∈2 (0, 1), we present an
algorithm that, in O(ε -2 n 1+δ τ (n, ε) log 2 (n/ε)
log(1/δ)) time, computes a O(1/δ α )- approximate
matching of G, where α = 1 + log 2 (1 +ε) and τ (n, ε)
is the query and update time of an (ε/2)-ANN data
structure. Finally, we present an algorithm that works even
if d((·, ·) is not a metric but admits an ANN data
structure for d(·, ·). In particular, we present an
algorithm that computes, in O(ε -1 n 3/2 τ (n, ε) log 4
(n/ε) log Δ) time, a (1 +ε)- approximate matching of A
and B; here Δ is the ratio of the largest to the
smallest-cost edge in G, and τ (n, ε) is the query and
update time of an (ε/c)-ANN data structure for some
constant c > 1. We show that our results lead to faster
matching algorithms for many geometric settings. © 2014
ACM.},
Doi = {10.1145/2591796.2591844},
Key = {fds235351}
}
@article{fds235352,
Author = {Wu, Y and Walenz, B and Li, P and Shim, A and Sonmez, E and Agarwal, PK and Li, C and Yang, J and Yu, C},
Title = {ICheck: Computationally combating "lies, D - Ned Lies, and
statistics"},
Journal = {Proceedings / ACM-SIGMOD International Conference on
Management of Data. ACM-Sigmod International Conference on
Management of Data},
Pages = {1063-1066},
Year = {2014},
Month = {January},
ISSN = {0730-8078},
url = {http://dx.doi.org/10.1145/2588555.2594522},
Abstract = {Are you fed up with "lies, d - ned lies, and statistics"
made up from data in our media? For claims based on
structured data, we present a system to automatically assess
the quality of claims (beyond their correctness) and counter
misleading claims that cherry-pick data to advance their
conclusions. The key insight is to model such claims as
parameterized queries and consider how parameter
perturbations affect their results. We demonstrate our
system on claims drawn from U.S. congressional voting
records, sports statistics, and publication records of
database researchers.},
Doi = {10.1145/2588555.2594522},
Key = {fds235352}
}
@article{fds235353,
Author = {Agarwal, PK and Har-Peled, S and Suri, S and YIldIz, H and Zhang,
W},
Title = {Convex hulls under uncertainty},
Journal = {Lecture notes in computer science},
Volume = {8737 LNCS},
Pages = {37-48},
Year = {2014},
Month = {January},
ISBN = {9783662447765},
ISSN = {0302-9743},
url = {http://dx.doi.org/10.1007/978-3-662-44777-2_4},
Abstract = {We study the convex-hull problem in a probabilistic setting,
motivated by the need to handle data uncertainty inherent in
many applications, including sensor databases,
location-based services and computer vision. In our
framework, the uncertainty of each input point is described
by a probability distribution over a finite number of
possible locations including a null location to account for
non-existence of the point. Our results include both exact
and approximation algorithms for computing the probability
of a query point lying inside the convex hull of the input,
time-space tradeoffs for the membership queries, a
connection between Tukey depth and membership queries, as
well as a new notion of β-hull that may be a useful
representation of uncertain hulls. © 2014 Springer-Verlag
Berlin Heidelberg.},
Doi = {10.1007/978-3-662-44777-2_4},
Key = {fds235353}
}
@article{fds235354,
Author = {Yu, A and Agarwal, PK and Yang, J},
Title = {Top-k preferences in high dimensions},
Journal = {Proceedings / International Conference on Data Engineering.
International Conference on Data Engineering},
Pages = {748-759},
Year = {2014},
Month = {January},
ISSN = {1084-4627},
url = {http://dx.doi.org/10.1109/ICDE.2014.6816697},
Abstract = {Given a set of objects O, each with d numeric attributes, a
top-k preference scores these objects using a linear
combination of their attribute values, where the weight on
each attribute reflects the interest in this attribute.
Given a query preference q, a top-k query finds the k
objects in O with highest scores with respect to q. Given a
query object o and a set of preferences Q, a reverse top-k
query finds all preferences q ∈ Q for which o becomes one
of the top k objects with respect to q. Previous solutions
to these problems are effective only in low dimensions. In
this paper, we develop a solution for much higher dimensions
(up to high tens), if many preferences exhibit sparsity -
i.e., each specifies non-zero weights for only a handful
(say 5-7) of attributes (though the subsets of such
attributes and their weights can vary greatly). Our idea is
to select carefully a set of low-dimensional core subspaces
to 'cover' the sparse preferences in a workload. These
subspaces allow us to index them more effectively than the
full-dimensional space. Being multi-dimensional, each
subspace covers many possible preferences; furthermore,
multiple subspaces can jointly cover a preference, thereby
expanding the coverage beyond each subspace's
dimensionality. Experimental evaluation validates our
solution's effectiveness and advantages over previous
solutions. © 2014 IEEE.},
Doi = {10.1109/ICDE.2014.6816697},
Key = {fds235354}
}
@article{fds235359,
Author = {Agarwal, PK and Aronov, B and Van Kreveld and M and Löffler, M and Silveira, RI},
Title = {Computing correlation between piecewise-linear
functions},
Journal = {SIAM Journal on Computing},
Volume = {42},
Number = {5},
Pages = {1867-1887},
Year = {2013},
Month = {December},
ISSN = {0097-5397},
url = {http://dx.doi.org/10.1137/120900708},
Abstract = {We study the problem of computing correlation between two
piecewise-linear bivariate functions defined over a common
domain, where the surfaces they define in three dimensions -
polyhedral terrains - can be transformed vertically by a
linear transformation of the third coordinate (scaling and
translation). We present a randomized algorithm that
minimizes the maximum vertical distance between the graphs
of the two functions, over all linear transformations of one
of the terrains, in O(n 4/3 polylog n) expected time, where
n is the total number of vertices in the graphs of the two
functions. We also present approximation algorithms for
minimizing the mean distance between the graphs of
univariate and bivariate functions. For univariate functions
we present a (1 + ε)-approximation algorithm that runs in
O(n(1 + log 2 (1/ε))) expected time for any fixed ε > 0.
The (1 + ε)-approximation algorithm for bivariate functions
runs in O(n/ε) time, for any fixed ε > 0, provided the two
functions are defined over the same triangulation of their
domain. © 2013 Society for Industrial and Applied
Mathematics.},
Doi = {10.1137/120900708},
Key = {fds235359}
}
@article{fds235361,
Author = {Agarwal, PK and Matoušek, J and Sharir, M},
Title = {On range searching with semialgebraic sets.
II},
Journal = {SIAM Journal on Computing},
Volume = {42},
Number = {6},
Pages = {2039-2062},
Year = {2013},
Month = {December},
ISSN = {0097-5397},
url = {http://dx.doi.org/10.1137/120890855},
Abstract = {Let P be a set of n points in ℝd. We present a linear-size
data structure for answering range queries on P with
constant-complexity semialgebraic sets as ranges, in time
close to O(n11/d). It essentially matches the performance of
similar structures for simplex range searching, and, for d
≥ 5, significantly improves earlier solutions by the first
two authors obtained in 1994. This almost settles a
long-standing open problem in range searching. The data
structure is based on a partitioning technique of Guth and
Katz [On the Erdos distinct distances problem in the plane,
arXiv:1011.4105, 2010], which shows that for a parameter r,
1 < r ≤ n, there exists a d-variate polynomial f of degree
O(r1/d) such that each connected component of ℝd \ Z(f)
contains at most n/r points of P, where Z(f) is the zero set
of f. We present an efficient randomized algorithm for
computing such a polynomial partition, which is of
independent interest and is likely to have additional
applications. © 2013 Society for Industrial and Applied
Mathematics.},
Doi = {10.1137/120890855},
Key = {fds235361}
}
@article{fds235357,
Author = {Lebeck, N and Mølhave, T and Agarwal, PK},
Title = {Computing highly occluded paths on a terrain},
Journal = {GIS: Proceedings of the ACM International Symposium on
Advances in Geographic Information Systems},
Pages = {14-23},
Year = {2013},
Month = {December},
url = {http://dx.doi.org/10.1145/2525314.2525363},
Abstract = {Understanding the locations of highly occluded paths on a
terrain is an important GIS problem. In this paper we
present a model and a fast algorithm for computing highly
occluded paths on a terrain. It does not assume the observer
locations to be known and yields a path likely to be
occluded under a rational observer strategy. We present
experimental results that examine several different observer
strategies. The repeated visibility map computations
necessary for our model is expedited using a fast algorithm
for calculating approximate visibility maps that models the
decrease in observational fidelity as distance increases.
The algorithm computes a multiresolution approximate
visibility map and makes use of a graphics processing unit
(GPU) to speed up computation. We present experimental
results on terrrain data sets with up to 144 million points.
© 2013 ACM.},
Doi = {10.1145/2525314.2525363},
Key = {fds235357}
}
@article{fds235358,
Author = {Sankararaman, S and Agarwal, PK and Mølhave, T and Pan, J and Boedihardjo, AP},
Title = {Model-driven matching and segmentation of
trajectories},
Journal = {GIS: Proceedings of the ACM International Symposium on
Advances in Geographic Information Systems},
Pages = {234-243},
Year = {2013},
Month = {December},
url = {http://dx.doi.org/10.1145/2525314.2525360},
Abstract = {A fundamental problem in analyzing trajectory data is to
identify common patterns between pairs or among groups of
trajectories. In this paper, we consider the problem of
matching similar portions between a pair of trajectories,
each observed as a sequence of points sampled from it. We
present new measures of trajectory similarity - both local
and global - between a pair of trajectories to distinguish
between similar and dissimilar portions. We then use this
model to perform segmentation of a set of trajectories into
fragments, contiguous portions of trajectories shared by
many of them. Our model for similarity is robust under noise
and sampling rate variations. The model also yields a score
which can be used to rank multiple pairs of trajectories
according to similarity, e.g. in clustering applications. We
present quadratic time algorithms to compute the similarity
between trajectory pairs under our measures together with
algorithms to identify fragments in a large set of
trajectories efficiently using the similarity model.
Finally, we present an extensive experimental study
evaluating the effectiveness of our approach on real
datasets, comparing it with earlier approaches. Our
experiments show that our model for similarity is highly
accurate in distinguishing similar and dissimilar portions
as compared to earlier methods even with sparse sampling.
Further, our segmentation algorithm is able to identify a
small set of fragments capturing the common parts of
trajectories in the dataset. © 2013 ACM.},
Doi = {10.1145/2525314.2525360},
Key = {fds235358}
}
@article{fds235360,
Author = {Agarwal, PK and Cormode, G and Huang, Z and Phillips, JM and Wei, Z and Yi,
K},
Title = {Mergeable summaries},
Journal = {ACM Transactions on Database Systems},
Volume = {38},
Number = {4},
Year = {2013},
Month = {November},
ISSN = {0362-5915},
url = {http://dx.doi.org/10.1145/2500128},
Abstract = {We study the mergeability of data summaries. Informally
speaking, mergeability requires that, given two summaries on
two datasets, there is a way to merge the two summaries into
a single summary on the two datasets combined together,
while preserving the error and size guarantees. This
property means that the summaries can be merged in a way
akin to other algebraic operators such as sum and max, which
is especially useful for computing summaries on massive
distributed data. Several data summaries are trivially
mergeable by construction, most notably all the sketches
that are linear functions of the datasets. But some other
fundamental ones, like those for heavy hitters and
quantiles, are not (known to be) mergeable. In this article,
we demonstrate that these summaries are indeed mergeable or
can be made mergeable after appropriatemodifications.
Specifically, we show that for e-approximate heavy hitters,
there is a deterministic mergeable summary of size O(1/e);
for e-approximate quantiles, there is a deterministic
summary of size O((1/e) log(en)) that has a restricted form
of mergeability, and a randomized one of size O((1/e)
log3/2(1/e)) with full mergeability. We also extend our
results to geometric summaries such as e-approximations
which permit approximate multidimensional range counting
queries. While most of the results in this article are
theoretical in nature, some of the algorithms are actually
very simple and even perform better than the previously best
known algorithms, which we demonstrate through experiments
in a simulated sensor network. We also achieve two results
of independent interest: (1) we provide the best known
randomized streaming bound for ε-approximate quantiles that
depends only on e, of size O((1/e) log3/2(1/e)), and (2) we
demonstrate that the MG and the SpaceSaving summaries for
heavy hitters are isomorphic. © 2013.},
Doi = {10.1145/2500128},
Key = {fds235360}
}
@article{fds235362,
Author = {Agarwal, PK and Efrat, A and Ganjugunte, SK and Hay, D and Sankararaman,
S and Zussman, G},
Title = {The resilience of WDM networks to probabilistic geographical
failures},
Journal = {IEEE/ACM Transactions on Networking (ACM)},
Volume = {21},
Number = {5},
Pages = {1525-1538},
Year = {2013},
Month = {January},
ISSN = {1063-6692},
url = {http://dx.doi.org/10.1109/TNET.2012.2232111},
Abstract = {Telecommunications networks, and in particular optical WDM
networks, are vulnerable to large-scale failures in their
physical infrastructure, resulting from physical attacks
(such as an electromagnetic pulse attack) or natural
disasters (such as solar flares, earthquakes, and floods).
Such events happen at specific geographical locations and
disrupt specific parts of the network, but their effects
cannot be determined exactly in advance. Therefore, we
provide a unified framework to model network vulnerability
when the event has a probabilistic nature, defined by an
arbitrary probability density function. Our framework
captures scenarios with a number of simultaneous attacks,
when network components consist of several dependent
subcomponents, and in which either a 1+1 or a 1:1 protection
plan is in place. We use computational geometric tools to
provide efficient algorithms to identify vulnerable points
within the network under various metrics. Then, we obtain
numerical results for specific backbone networks,
demonstrating the applicability of our algorithms to
real-world scenarios. Our novel approach allows to identify
locations that require additional protection efforts (e.g.,
equipment shielding). Overall, the paper demonstrates that
using computational geometric techniques can significantly
contribute to our understanding of network resilience. ©
1993-2012 IEEE.},
Doi = {10.1109/TNET.2012.2232111},
Key = {fds235362}
}
@article{fds235363,
Author = {Agarwal, PK and Sharathkumar, R and Agarwal, PK and Sharathkumar,
R},
Title = {Streaming Algorithms for Extent Problems in High
DimensionsStreaming Algorithms for Extent Problems in High
Dimensions},
Journal = {Algorithmica},
Pages = {1-16},
Year = {2013},
ISSN = {0178-4617},
url = {http://dx.doi.org/10.1007/s00453-013-9846-4},
Abstract = {We present (single-pass) streaming algorithms for
maintaining extent measures of a stream S of n points in
{Mathematical expression}. We focus on designing streaming
algorithms whose working space is polynomial in d (poly(d))
and sub-linear in n. For the problems of computing diameter,
width and minimum enclosing ball of S, we obtain lower
bounds on the worst-case approximation ratio of any
streaming algorithm that uses poly(d) space. On the positive
side, we introduce the notion of blurred ball cover and use
it for answering approximate farthest-point queries and
maintaining approximate minimum enclosing ball and diameter
of S. We describe a streaming algorithm for maintaining a
blurred ball cover whose working space is linear in d and
independent of n. © 2013 Springer Science+Business Media
New York.},
Doi = {10.1007/s00453-013-9846-4},
Key = {fds235363}
}
@article{fds235366,
Author = {Agarwal, PK and Aronov, B and Har-Peled, S and Phillips, JM and Yi, K and Zhang, W},
Title = {Nearest neighbor searching under uncertainty
II},
Journal = {Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on
Principles of Database Systems},
Pages = {115-126},
Year = {2013},
url = {http://dx.doi.org/10.1145/2463664.2465219},
Abstract = {Nearest-neighbor (NN) search, which returns the nearest
neighbor of a query point in a set of points, is an
important and widely studied problem in many fields, and it
has wide range of applications. In many of them, such as
sensor databases, location-based services, face recognition,
and mobile data, the location of data is imprecise. We
therefore study nearest neighbor queries in a probabilistic
framework in which the location of each input point is
specified as a probability distribution function. We present
efficient algorithms for (i) computing all points that are
nearest neighbors of a query point with nonzero probability;
(ii) estimating, within a specified additive error, the
probability of a point being the nearest neighbor of a query
point; (iii) using it to return the point that maximizes the
probability being the nearest neighbor, or all the points
with probabilities greater than some threshold to be the NN.
We also present some experimental results to demonstrate the
effectiveness of our approach. Copyright 2013
ACM.},
Doi = {10.1145/2463664.2465219},
Key = {fds235366}
}
@article{fds235367,
Author = {Agarwal, PK and Kaplan, H and Sharir, M},
Title = {Union of random minkowski sums and network vulnerability
analysis},
Journal = {Proceedings of the Annual Symposium on Computational
Geometry},
Pages = {177-186},
Year = {2013},
Abstract = {Let C = {C1,⋯, Cn} be a set of n pairwise-disjoint convex
s-gons, for some constant s, and let π be a probability
density function (pdf) over the non-negative reals. For each
i, let Ki be the Minkowski sum of Ci with a disk of radius
ri, where each ri is a random non-negative number drawn
independently from the distribution determined by π. We
show that the expected complexity of the union of K1,⋯, Kn
is O (n log n), for any pdf π; the constant of
proportionality depends on s, but not on the pdf. Next, we
consider the following problem that arises in analyzing the
vulnerability of a network under a physical attack. Let G =
(V, ε) be a planar geometric graph where ε is a set of n
line segments with pairwise-disjoint relative interiors. Let
φ: ℝ≥0 → [0,1] be an edge failure probability
function, where a physical attack at a location x ∈ ℝ2
causes an edge e of E at distance r from x to fail with
probability φ(r); we assume that φ is of the form 1 -
Π(x), where Π is a cumulative distribution function on the
non-negative reals. The goal is to compute the most
vulnerable location for G, i.e., the location of the attack
that maximizes the expected number of failing edges of G.
Using our bound on the complexity of the union of random
Minkowski sums, we present a near-linear Monte-Carlo
algorithm for computing a location that is an approximately
most vulnerable location of attack for G. Copyright 2013
ACM.},
Key = {fds235367}
}
@article{fds235368,
Author = {Agarwal, PK and Har-Peled, S and Yu, H},
Title = {EMBEDDINGS OF SURFACES, CURVES, AND MOVING POINTS IN
EUCLIDEAN SPACE},
Journal = {SIAM Journal on Computing},
Volume = {42},
Number = {2},
Pages = {442-458},
Year = {2013},
ISSN = {0097-5397},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000318353800002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Doi = {10.1137/110830046},
Key = {fds235368}
}
@article{fds235369,
Author = {Afshani, P and Agarwal, PK and Arge, L and Larsen, KG and Phillips,
JM},
Title = {(Approximate) Uncertain Skylines},
Journal = {Theory of Computing Systems},
Volume = {52},
Number = {3},
Pages = {342-366},
Year = {2013},
ISSN = {1432-4350},
url = {http://dx.doi.org/10.1007/s00224-012-9382-7},
Abstract = {Given a set of points with uncertain locations, we consider
the problem of computing the probability of each point lying
on the skyline, that is, the probability that it is not
dominated by any other input point. If each point's
uncertainty is described as a probability distribution over
a discrete set of locations, we improve the best known exact
solution. We also suggest why we believe our solution might
be optimal. Next, we describe simple, near-linear time
approximation algorithms for computing the probability of
each point lying on the skyline. In addition, some of our
methods can be adapted to construct data structures that can
efficiently determine the probability of a query point lying
on the skyline. © 2012 Springer Science+Business Media,
LLC.},
Doi = {10.1007/s00224-012-9382-7},
Key = {fds235369}
}
@article{fds235370,
Author = {Agarwal, PK and Efrat, A and Ganjugunte, SK and Hay, D and Sankararaman,
S and Zussman, G},
Title = {The Resilience of WDM Networks to Probabilistic Geographical
Failures},
Journal = {IEEE/ACM Transactions on Networking (ACM)},
Year = {2013},
ISSN = {1063-6692},
url = {http://dx.doi.org/10.1109/TNET.2012.2232111},
Abstract = {Telecommunications networks, and in particular optical WDM
networks, are vulnerable to large-scale failures in their
physical infrastructure, resulting from physical attacks
(such as an electromagnetic pulse attack) or natural
disasters (such as solar flares, earthquakes, and floods).
Such events happen at specific geographical locations and
disrupt specific parts of the network, but their effects
cannot be determined exactly in advance. Therefore, we
provide a unified framework to model network vulnerability
when the event has a probabilistic nature, defined by an
arbitrary probability density function. Our framework
captures scenarios with a number of simultaneous attacks,
when network components consist of several dependent
subcomponents, and in which either a 1+1 or a 1:1 protection
plan is in place. We use computational geometric tools to
provide efficient algorithms to identify vulnerable points
within the network under various metrics. Then, we obtain
numerical results for specific backbone networks,
demonstrating the applicability of our algorithms to
real-world scenarios. Our novel approach allows to identify
locations that require additional protection efforts (e.g.,
equipment shielding). Overall, the paper demonstrates that
using computational geometric techniques can significantly
contribute to our understanding of network
resilience.},
Doi = {10.1109/TNET.2012.2232111},
Key = {fds235370}
}
@article{fds235557,
Author = {Agarwal, PK and Arge, L and Govindarajan, S and Yang, J and Yi,
K},
Title = {Efficient external memory structures for range-aggregate
queries},
Journal = {Computational Geometry},
Volume = {46},
Number = {3},
Pages = {358-370},
Year = {2013},
ISSN = {0925-7721},
url = {http://dx.doi.org/10.1016/j.comgeo.2012.10.003},
Abstract = {We present external memory data structures for efficiently
answering range-aggregate queries. The range-aggregate
problem is defined as follows: Given a set of weighted
points in Rd, compute the aggregate of the weights of the
points that lie inside a d-dimensional orthogonal query
rectangle. The aggregates we consider in this paper include
count, sum, and max. First, we develop a structure for
answering two-dimensional range-count queries that uses
O(N/B) disk blocks and answers a query in O( logBN) I/Os,
where N is the number of input points and B is the disk
block size. The structure can be extended to obtain a
near-linear-size structure for answering range-sum queries
using O( logBN) I/Os, and a linear-size structure for
answering range-max queries in O(logB2N) I/Os. Our
structures can be made dynamic and extended to higher
dimensions. © 2012 Elsevier B.V.},
Doi = {10.1016/j.comgeo.2012.10.003},
Key = {fds235557}
}
@article{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 < r ≤ n, there exists a d-variate
polynomial f of degree O(r1/d) such that each connected
component of ℝd \ Z(f) contains at most n/r points of P,
where Z(f) is the zero set of f. We present an ef?cient
randomized algorithm for computing such a polynomial
partition, which is of independent interest and is likely to
have additional applications. © 2012 IEEE.},
Doi = {10.1109/FOCS.2012.32},
Key = {fds235381}
}
@article{fds235545,
Author = {Afshani, P and Agarwal, PK and Arge, L and Larsen, KG and Phillips,
JM},
Title = {(Approximate) Uncertain Skylines},
Journal = {Theory of Computing Systems},
Pages = {1-25},
Year = {2012},
ISSN = {1432-4350},
url = {http://dx.doi.org/10.1007/s00224-012-9382-7},
Abstract = {Given a set of points with uncertain locations, we consider
the problem of computing the probability of each point lying
on the skyline, that is, the probability that it is not
dominated by any other input point. If each point's
uncertainty is described as a probability distribution over
a discrete set of locations, we improve the best known exact
solution. We also suggest why we believe our solution might
be optimal. Next, we describe simple, near-linear time
approximation algorithms for computing the probability of
each point lying on the skyline. In addition, some of our
methods can be adapted to construct data structures that can
efficiently determine the probability of a query point lying
on the skyline. © 2012 Springer Science+Business Media,
LLC.},
Doi = {10.1007/s00224-012-9382-7},
Key = {fds235545}
}
@article{fds235546,
Author = {Sharathkumar, R and Agarwal, PK},
Title = {Algorithms for the transportation problem in geometric
settings},
Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
Algorithms},
Pages = {306-317},
Year = {2012},
Abstract = {For A, B ⊂ ℝ d, |A| + |B| = n, let a ∈ A have a demand
d a ∈ ℤ + and b ∈ B have a supply s b ∈ ℤ +, Σ
a∈A d a = Σ b∈B s b = U and let d(·,·) be a distance
function. Suppose the diameter of A ∪ B is Δ under
d(·,·), and ε > 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 > 0. For point
sets, A, B ⊂ [Δ] d, for the L p norm and for O < α,β
< 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 < ε < 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 > 0, we present an algorithm that computes, in O(n
poly(log n, 1/ε)) time, an ε-approximate perfect matching
of A and B with high probability; the previously best known
algorithm takes Ω(n 3/2) time. We approximate the L p-norm
using a distance function, d(·,·) based on a randomly
shifted quad-tree. The algorithm iteratively generates an
approximate minimum-cost augmenting path under d(·,·) in
time proportional to the length of the path. We show that
the total length of the augmenting paths generated by the
algorithm is O((n/ε)log n), implying that the running time
of our algorithm is O(n poly(log n,1/ε)). © 2012
ACM.},
Doi = {10.1145/2213977.2214014},
Key = {fds235550}
}
@article{fds235551,
Author = {Yu, A and Agarwal, PK and Yang, J},
Title = {Processing a large number of continuous preference top-k
queries},
Journal = {Proceedings / ACM-SIGMOD International Conference on
Management of Data. ACM-Sigmod International Conference on
Management of Data},
Pages = {397-408},
Year = {2012},
ISSN = {0730-8078},
url = {http://dx.doi.org/10.1145/2213836.2213882},
Abstract = {Given a set of objects, each with multiple numeric
attributes, a (preference) top-k query retrieves the k
objects with the highest scores according to a user
preference, defined as a linear combination of attribute
values. We consider the problem of processing a large number
of continuous top-k queries, each with its own preference.
When objects or user preferences change, the query results
must be updated. We present a dynamic index that supports
the reverse top k query, which is of independent interest.
Combining this index with another one for top-k queries, we
develop a scalable solution for processing many continuous
top-k queries that exploits the clusteredness in user
preferences. We also define an approximate version of the
problem and present a solution significantly more efficient
than the exact one with little loss in accuracy. © 2012
ACM.},
Doi = {10.1145/2213836.2213882},
Key = {fds235551}
}
@article{fds235552,
Author = {Yu, A and Agarwal, PK and Yang, J},
Title = {Processing and notifying range top-k subscriptions},
Journal = {Proceedings / International Conference on Data Engineering.
International Conference on Data Engineering},
Pages = {810-821},
Year = {2012},
ISSN = {1084-4627},
url = {http://dx.doi.org/10.1109/ICDE.2012.67},
Abstract = {We consider how to support a large number of users over a
wide-area network whose interests are characterised by range
top-k continuous queries. Given an object update, we need to
notify users whose top-k results are affected. Simple
solutions include using a content-driven network to notify
all users whose interest ranges contain the update (ignoring
top-k), or using a server to compute only the affected
queries and notifying them individually. The former solution
generates too much network traffic, while the latter
overwhelms the server. We present a geometric framework for
the problem that allows us to describe the set of affected
queries succinctly with messages that can be efficiently
disseminated using content-driven networks. We give fast
algorithms to reformulate each update into a set of messages
whose number is provably optimal, with or without knowing
all user interests. We also present extensions to our
solution, including an approximate algorithm that trades off
between the cost of server-side reformulation and that of
user-side post-processing, as well as efficient techniques
for batch updates. © 2012 IEEE.},
Doi = {10.1109/ICDE.2012.67},
Key = {fds235552}
}
@article{fds235553,
Author = {Yu, A and Agarwal, PK and Yang, J},
Title = {Subscriber assignment for wide-area content-based
publish/subscribe},
Journal = {IEEE Transactions on Knowledge and Data Engineering},
Volume = {24},
Number = {10},
Pages = {1833-1847},
Year = {2012},
ISSN = {1041-4347},
url = {http://dx.doi.org/10.1109/TKDE.2012.65},
Abstract = {We study the problem of assigning subscribers to brokers in
a wide-area content-based publish/subscribe system. A good
assignment should consider both subscriber interests in the
event space and subscriber locations in the network space,
and balance multiple performance criteria including
bandwidth, delay, and load balance. The resulting
optimization problem is NP-complete, so systems have turned
to heuristics and/or simpler algorithms that ignore some
performance criteria. Evaluating these approaches has been
challenging because optimal solutions remain elusive for
realistic problem sizes. To enable proper evaluation, we
develop a Monte Carlo approximation algorithm with good
theoretical properties and robustness to workload
variations. To make it computationally feasible, we combine
the ideas of linear programming, randomized rounding,
coreset, and iterative reweighted sampling. We demonstrate
how to use this algorithm as a yardstick to evaluate other
algorithms, and why it is better than other choices of
yardsticks. With its help, we show that a simple greedy
algorithm works well for a number of workloads, including
one generated from publicly available statistics on Google
Groups. We hope that our algorithms are not only useful in
their own right, but our principled approach toward
evaluation will also be useful in future evaluation of
solutions to similar problems in content-based
publish/subscribe. © 2012 IEEE.},
Doi = {10.1109/TKDE.2012.65},
Key = {fds235553}
}
@article{fds235554,
Author = {Agarwal, PK and Avraham, RB and Sharir, M},
Title = {The 2-center problem in three dimensions},
Journal = {Computational Geometry},
Year = {2012},
ISSN = {0925-7721},
url = {http://dx.doi.org/10.1016/j.comgeo.2012.11.005},
Abstract = {Let P be a set of n points in R 3. The 2-center problem for
P is to find two congruent balls of minimum radius whose
union covers P. We present a randomized algorithm for
computing a 2-center of P that runs in O (β (r *) n 2 log 4
n log log n) expected time; here β (r) = 1 / (1 - r / r 0)
3, r * is the radius of the 2-center balls of P, and r 0 is
the radius of the smallest enclosing ball of P. The
algorithm is near quadratic as long as r * is not too close
to r 0, which is equivalent to the condition that the
centers of the two covering balls be not too close to each
other. This improves an earlier slightly super-cubic
algorithm of Agarwal, Efrat, and Sharir (2000) [2] (at the
cost of making the algorithm performance depend on the
center separation of the covering balls). © 2012 Elsevier
B.V. All rights reserved.},
Doi = {10.1016/j.comgeo.2012.11.005},
Key = {fds235554}
}
@article{fds235555,
Author = {Agarwal, PK and Ezra, E and Sharir, M},
Title = {Near-linear approximation algorithms for geometric hitting
sets},
Journal = {Algorithmica},
Volume = {63},
Number = {1-2},
Pages = {1-25},
Year = {2012},
ISSN = {0178-4617},
url = {http://dx.doi.org/10.1007/s00453-011-9517-2},
Abstract = {Given a range space (X,R), where R § 2 X, the hitting set
problem is to find a smallest-cardinality subset H § X that
intersects each set in R. We present near-linear-time
approximation algorithms for the hitting set problem in the
following geometric settings: (i) R is a set of planar
regions with small union complexity. (ii) R is a set of
axis-parallel d-dimensional boxes in Rd . In both cases X is
either the entire R d , or a finite set of points in R d .
The approximation factors yielded by the algorithm are
small; they are either the same as, or within very small
factors off the best factors known to be computable in
polynomial time. © Springer Science+Business Media, LLC
2011.},
Doi = {10.1007/s00453-011-9517-2},
Key = {fds235555}
}
@article{fds235556,
Author = {Agarwal, PK and Cheng, S-W and Yi, K},
Title = {Range searching on uncertain data},
Journal = {ACM Transactions on Algorithms},
Volume = {8},
Number = {4},
Year = {2012},
ISSN = {1549-6325},
url = {http://dx.doi.org/10.1145/2344422.2344433},
Abstract = {Querying uncertain data has emerged as an important problem
in data management due to the imprecise nature of many
measurement data. In this article, we study answering range
queries over uncertain data. Specifically, we are given a
collection P of n uncertain points in ℝ, each represented
by its one-dimensional probability density function (pdf).
The goal is to build a data structure on P such that, given
a query interval I and a probability threshold τ , we can
quickly report all points of P that lie in I with
probability at least τ . We present various structures with
linear or near-linear space and (poly)logarithmic query
time. Our structures support pdf's that are either
histograms or more complex ones such as Gaussian or
piecewise algebraic. © 2012 ACM.},
Doi = {10.1145/2344422.2344433},
Key = {fds235556}
}
@article{fds235620,
Author = {Wu, Y and Agarwal, PK and Li, C and Yang, J and Yu, C},
Title = {On "one of the few" objects},
Journal = {Proceedings of the ACM SIGKDD International Conference on
Knowledge Discovery and Data Mining},
Pages = {1487-1495},
Year = {2012},
url = {http://dx.doi.org/10.1145/2339530.2339762},
Abstract = {Objects with multiple numeric attributes can be compared
within any "subspace" (subset of attributes). In
applications such as computational journalism, users are
interested in claims of the form: Karl Malone is one of the
only two players in NBA history with at least 25,000 points,
12,000 rebounds, and 5,000 assists in one's career. One
challenge in identifying such "one-of-the-k" claims (k = 2
above) is ensuring their "interestingness". A small k is not
a good indicator for interestingness, as one can often make
such claims for many objects by increasing the
dimensionality of the subspace considered. We propose a
uniqueness-based interestingness measure for one-of-the-few
claims that is intuitive for non-technical users, and we
design algorithms for finding all interesting claims (across
all subspaces) from a dataset. Sometimes, users are
interested primarily in the objects appearing in these
claims. Building on our notion of interesting claims, we
propose a scheme for ranking objects and an algorithm for
computing the top-ranked objects. Using real-world datasets,
we evaluate the efficiency of our algorithms as well as the
advantage of our object-ranking scheme over popular methods
such as Kemeny optimal rank aggregation and weighted-sum
ranking. © 2012 ACM.},
Doi = {10.1145/2339530.2339762},
Key = {fds235620}
}
@article{fds235544,
Author = {Clark, JS and Agarwal, P and Bell, DM and Flikkema, PG and Gelfand, A and Nguyen, X and Ward, E and Yang, J},
Title = {Inferential ecosystem models, from network data to
prediction.},
Journal = {Ecological Applications},
Volume = {21},
Number = {5},
Pages = {1523-1536},
Year = {2011},
Month = {July},
ISSN = {1051-0761},
url = {http://www.ncbi.nlm.nih.gov/pubmed/21830699},
Abstract = {Recent developments suggest that predictive modeling could
begin to play a larger role not only for data analysis, but
also for data collection. We address the example of
efficient wireless sensor networks, where inferential
ecosystem models can be used to weigh the value of an
observation against the cost of data collection.
Transmission costs make observations "expensive"; networks
will typically be deployed in remote locations without
access to infrastructure (e.g., power). The capacity to
sample intensively makes sensor networks valuable, but
high-frequency data are informative only at specific times
and locations. Sampling intervals will range from meters and
seconds to landscapes and years, depending on the process,
the current states of the system, the uncertainty about
those states, and the perceived potential for rapid change.
Given that intensive sampling is sometimes critical, but
more often wasteful, how do we develop tools to control the
measurement and transmission processes? We address the
potential of data collection controlled and/or supplemented
by inferential ecosystem models. In a given model, the value
of an observation can be evaluated in terms of its
contribution to estimates of state variables and important
parameters. There will be more than one model applied to
network data that will include as state variables water,
carbon, energy balance, biogeochemistry, tree ecophysiology,
and forest demographic processes. The value of an
observation will depend on the application. Inference is
needed to weigh the contributions against transmission cost.
Network control must be dynamic and driven by models capable
of learning about both the environment and the network. We
discuss application of Bayesian inference to model data from
a developing sensor network as a basis for controlling the
measurement and transmission processes. Our examples involve
soil moisture and sap flux, but we discuss broader
application of the approach, including its implications for
network design.},
Key = {fds235544}
}
@article{fds235536,
Author = {Afshani, P and Agarwal, PK and Arge, L and Larsen, KG and Phillips,
JM},
Title = {(Approximate) uncertain skylines},
Journal = {ACM International Conference Proceeding Series},
Pages = {186-196},
Year = {2011},
url = {http://dx.doi.org/10.1145/1938551.1938576},
Abstract = {Given a set of points with uncertain locations, we consider
the problem of computing the probability of each point lying
on the skyline, that is, the probability that it is not
dominated by any other input point. If each point's
uncertainty is described as a probability distribution over
a discrete set of locations, we improve the best known exact
solution. We also suggest why we believe our solution might
be optimal. Next, we describe simple, near-linear time
approximation algorithms for computing the probability of
each point lying on the skyline. In addition, some of our
methods can be adapted to construct data structures that can
efficiently determine the probability of a query point lying
on the skyline. © 2011 ACM.},
Doi = {10.1145/1938551.1938576},
Key = {fds235536}
}
@article{fds235537,
Author = {Agarwal, PK and Mølhave, T and Sadri, B},
Title = {I/O-efficieiit contour queries on terrains},
Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
Algorithms},
Pages = {268-284},
Year = {2011},
Abstract = {A terrain M can be represented as a triangulation of the
plane along with a height function associated with the
vertices (and linearly interpolated within the edges and
triangles) of M. We investigate the problem of answering
contour queries on M: Given a height l aud a triangle of M
that intersects the level set of M at height l, report the
list of the edges of the connected component of this level
set that intersect f, sorted in clockwise or
counterclockwise order. Contour queries are different from
level-set queries in that only one contour (connected
component of the level set) out of all those that may exist
is expected to be reported. We present an I/O-efficient data
structure of linear size that answers a contour query in
0(logB N + T/B) I/Os, where N is the number of triangles in
the terrain and T is the number of edges in the output
contour. The data structure can be constructed using
O(Sort(N)) I/Os.},
Key = {fds235537}
}
@article{fds235538,
Author = {Yu, A and Agarwal, PK and Yang, J},
Title = {Subscriber assignment for wide-area content-based
publish/subscribe},
Journal = {Proceedings / International Conference on Data Engineering.
International Conference on Data Engineering},
Pages = {267-278},
Year = {2011},
ISSN = {1084-4627},
url = {http://dx.doi.org/10.1109/ICDE.2011.5767882},
Abstract = {We study the problem of assigning subscribers to brokers in
a wide-area content-based publish/subscribe system. A good
assignment should consider both subscriber interests in the
event space and subscriber locations in the network space,
and balance multiple performance criteria including
bandwidth, delay, and load balance. The resulting
optimization problem is NP-complete, so systems have turned
to heuristics and/or simpler algorithms that ignore some
performance criteria. Evaluating these approaches has been
challenging because optimal solutions remain elusive for
realistic problem sizes. To enable proper evaluation, we
develop a Monte Carlo approximation algorithm with good
theoretical properties and robustness to workload
variations. To make it computationally feasible, we combine
the ideas of linear programming, randomized rounding,
coreset, and iterative reweighted sampling. We demonstrate
how to use this algorithm as a yardstick to evaluate other
algorithms, and why it is better than other choices of
yardsticks. With its help, we show that a simple greedy
algorithm works well for a number of workloads, including
one generated from publicly available statistics on Google
Groups. We hope that our algorithms are not only useful in
their own right, but our principled approach toward
evaluation will also be useful in future evaluation of
solutions to similar problems in content-based
publish/subscribe. © 2011 IEEE.},
Doi = {10.1109/ICDE.2011.5767882},
Key = {fds235538}
}
@article{fds235539,
Author = {Agarwal, PK and Mølhave, T and Yu, H and Clark, JS},
Title = {Exploiting temporal coherence in forest dynamics
simulation},
Journal = {Proceedings of the Annual Symposium on Computational
Geometry},
Pages = {77-86},
Year = {2011},
url = {http://dx.doi.org/10.1145/1998196.1998210},
Abstract = {Understanding the impact of climate and land-use on forest
ecosystems involves modeling and simulating complex spatial
interactions at many different scales. With this goal in
mind, we have developed an individual-based, spatially
explicit forest simulator, which incorporates fine-scale
processes that influence forest dynamics. In this paper we
present new, faster algorithms for computing understory
light and for dispersal of seeds | the two most
computationally intensive submodules in our simulator. By
exploiting temporal coherence, we circumvent the problem of
doing the entire simulation at each step. We provide
experimental results that support the efficiency and
efficacy of our approach. © 2011 ACM.},
Doi = {10.1145/1998196.1998210},
Key = {fds235539}
}
@article{fds235540,
Author = {Agarwal, PK and Efrat, A and Gniady, C and Mitchell, JSB and Polishchuk,
V and Sabhnani, GR},
Title = {Distributed localization and clustering using data
correlation and the Occam's razor principle},
Journal = {2011 International Conference on Distributed Computing in
Sensor Systems and Workshops, DCOSS'11},
Year = {2011},
url = {http://dx.doi.org/10.1109/DCOSS.2011.5982164},
Abstract = {We present a distributed algorithm for computing a combined
solution to three problems in sensor networks: localization,
clustering, and sensor suspension. Assuming that initially
only a rough approximation of the sensor positions is known,
we show how one can use sensor measurements to refine the
set of possible sensor locations, to group the sensors into
clusters with linearly correlated measurements, and to
decide which sensors may suspend transmission without
jeopardizing the consistency of the collected data. Our
algorithm applies the "Occam's razor principle" by computing
a "simplest" explanation for the data gathered from the
network. We also present centralized algorithms, as well as
efficient heuristics. © 2011 IEEE.},
Doi = {10.1109/DCOSS.2011.5982164},
Key = {fds235540}
}
@article{fds235541,
Author = {Agarwal, PK and Efrat, A and Ganjugunte, S and Hay, D and Sankararaman,
S and Zussman, G},
Title = {The resilience of WDM networks to probabilistic geographical
failures},
Journal = {Proceedings - IEEE INFOCOM},
Pages = {1521-1529},
Year = {2011},
ISSN = {0743-166X},
url = {http://dx.doi.org/10.1109/INFCOM.2011.5934942},
Abstract = {Telecommunications networks, and in particular optical WDM
networks, are vulnerable to large-scale failures of their
physical infrastructure, resulting from physical attacks
(such as an Electromagnetic Pulse attack) or natural
disasters (such as solar flares, earthquakes, and floods).
Such events happen at specific geographical locations and
disrupt specific parts of the network but their effects are
not deterministic. Therefore, we provide a unified framework
to model the network vulnerability when the event has a
probabilistic nature, defined by an arbitrary probability
density function. Our framework captures scenarios with a
number of simultaneous attacks, in which network components
consist of several dependent subcomponents, and in which
either a 1+1 or a 1:1 protection plan is in place. We use
computational geometric tools to provide efficient
algorithms to identify vulnerable points within the network
under various metrics. Then, we obtain numerical results for
specific backbone networks, thereby demonstrating the
applicability of our algorithms to real-world scenarios. Our
novel approach allows for identifying locations which
require additional protection efforts (e.g., equipment
shielding). Overall, the paper demonstrates that using
computational geometric techniques can significantly
contribute to our understanding of network resilience. ©
2011 IEEE.},
Doi = {10.1109/INFCOM.2011.5934942},
Key = {fds235541}
}
@article{fds235542,
Author = {Beutel, A and Mølhave, T and Agarwal, PK and Boedihardjo, AP and Shine,
JA},
Title = {TerraNNI: Natural neighbor interpolation on a 3D grid using
a GPU},
Journal = {GIS: Proceedings of the ACM International Symposium on
Advances in Geographic Information Systems},
Pages = {64-73},
Year = {2011},
url = {http://dx.doi.org/10.1145/2093973.2093984},
Abstract = {With modern focus on LiDAR technology the amount of
topographic data, in the form of massive point clouds, has
increased dramatically. Furthermore, due to the popularity
of LiDAR, repeated surveys of the same areas are becoming
more common. This trend will only increase as topographic
changes prompt surveys over already scanned terrain, in
which case we obtain large spatio-temporal data sets. In
dynamic terrains, such as coastal regions, such
spatio-temporal data can offer interesting insight into how
the terrain changes over time. An initial step in the
analysis of such data is to create a digital elevation model
representing the terrain over time. In the case of
spatio-temporal data sets those models often represent
elevation on a 3D volumetric grid. This involves
interpolating the elevation of LiDAR points on these grid
points. In this paper we show how to efficiently perform
natural neighbor interpolation over a 3D volumetric grid.
Using a graphics processing unit (GPU), we describe
different algorithms to attain speed and GPU-memory
trade-offs. Our algorithm extends to higher dimensions. Our
experimental results demonstrate that the algorithm is
efficient and scalable. Categories and Subject. © 2011
ACM.},
Doi = {10.1145/2093973.2093984},
Key = {fds235542}
}
@article{fds235543,
Author = {Abam, MA and Agarwal, PK and Berg, MD and Yu, H},
Title = {Out-of-order event processing in kinetic data
structures},
Journal = {Algorithmica},
Volume = {60},
Number = {2},
Pages = {250-273},
Year = {2011},
ISSN = {0178-4617},
url = {http://dx.doi.org/10.1007/s00453-009-9335-y},
Abstract = {We study the problem of designing kinetic data structures
(KDS's for short) when event times cannot be computed
exactly and events may be processed in a wrong order. In
traditional KDS's this can lead to major inconsistencies
from which the KDS cannot recover. We present more robust
KDS's for the maintenance of several fundamental structures
such as kinetic sorting and kinetic tournament trees, which
overcome the difficulty by employing a refined event
scheduling and processing technique. We prove that the new
event scheduling mechanism leads to a KDS that is correct
except for finitely many short time intervals. We analyze
the maximum delay of events and the maximum error in the
structure, and we experimentally compare our approach to the
standard event scheduling mechanism. © 2009 Springer
Science+Business Media, LLC.},
Doi = {10.1007/s00453-009-9335-y},
Key = {fds235543}
}
@article{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
> 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 > 0. The (1 + ε)-approximation algorithm for
the bivariate version, where volume is minimized, runs in
O(n/ε2) time, for any fixed ε > 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
> 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 > 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>∈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{fds333282,
Author = {Agarwal, P and Rizvi, SAM},
Title = {A technique based on neural network for predicting the
secondary structure of proteins},
Journal = {Proceedings - International Conference on Computational
Intelligence and Multimedia Applications, ICCIMA
2007},
Volume = {2},
Pages = {382-386},
Year = {2008},
Month = {March},
ISBN = {0769530508},
url = {http://dx.doi.org/10.1109/ICCIMA.2007.47},
Abstract = {This paper presents a neural network approach for predicting
the secondary structure of proteins from amino acid
sequences. We have assumed a simple neural network with one
input & output layer. Single hidden layer is also
considered. Our neural network can be trained to predict the
secondary structure of proteins by studying proteins with
already known secondary structure by modifying the weight
matrix function. Like other existing methods, our method is
also an approximation method and its accuracy depends on the
careful study and training of network. The significance of
the method is its simplicity and applicability. © 2007
IEEE.},
Doi = {10.1109/ICCIMA.2007.47},
Key = {fds333282}
}
@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} > 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 < ... < 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{fds235476,
Author = {Agarwal, PK and Akutsu, T and Amihood, A and Apostolico, A and Benham,
C and Benson, G and Blanchette, M and El-Mabrouk, N and Gascuel, O and Giancarlo, R and Guigo, R and Hallet, M and Huson, D and Kucherov, G and Lacey, M and Lagergren, J and Lancia, G and Landau, GM and Lecroq, T and Moret, B and Morishita, S and Mossel, E and Moulton, V and Pachter, L and Reinert, K and Rigoutsos, I and Sagot, M-F and Sankoff, D and Schbath,
S and Segal, E and Semple, C and Setubal, JC and Sharan, R and Skiena, S and Stoye, J and Ukkonen, E and Vawter, L and Valencia, A and Warnow, T and Wang, L and Casadio, R and Myers, G},
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 = {3692 LNBI},
Pages = {V-VI},
Year = {2005},
ISBN = {3540290087},
ISSN = {0302-9743},
Key = {fds235476}
}
@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 > 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 > 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 > 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 > 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 > 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 < ε
< 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 > 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 > 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 >
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 > 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 > 0, and an
improved randomized algorithm with expected running time
O((/ilog;/i + £)<(»)log«) (which is faster for small
values of k). For d = 3, we present an O(«8/5+e +
&)-time algorithm, for any £> 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 >
0, f2(5)(n) = Θ(n7/3), and f3(4) (n) = O(n20/9+ε), for any
ε > 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 > 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 > 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 > 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 &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
> 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 > 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 > 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 > 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 > 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 > 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>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>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>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>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>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>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 >
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>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>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<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>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>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 > 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>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 < ∈ ≤ 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 > 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
> 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 > 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 > 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
> 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 > 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 < j < n, is called a totally monotone matrix if for
all i1, i2, j1, j2, satisfying 1 < i1 < i2 < m, 1
< j1 < j2 < n. ai1, j1 < ai1, j2 ⇒ ai2, j1
< 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 > 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 >
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 > 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 < of
the objects in K such that if K, L ε{lunate} K and K lies
vertically below L then K < 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>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}>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<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 > 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
> 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 > 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 > 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>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>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>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)}<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>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}>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 <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
> 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 <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 > 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 > 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)/ℤ_{2}
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 < 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 < 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
Frechet mean in (Dp;Wp), the space of persistence diagrams
equipped with the p-th Wasserstein metric. In particular,
they showed that the Frechet mean of a nite set of diagrams
always exists, but is not necessarily unique. As an
unfortunate consequence, one sees that the means of a
continuously-varying set of diagrams do not themselves vary
continuously, which presents obvious problems when trying to
extend the Frechet mean de nition to the realm of
vineyards. We x this problem by altering the original de
nition of Frechet mean so that it now becomes a probability
measure on the set of persistence diagrams; in a nutshell,
the mean of a set of diagrams will be a weighted sum of
atomic measures, where each atom is itself the (Frechet
mean) persistence diagram of a perturbation of the input
diagrams. We show that this new de nition de nes a (Holder)
continuous map, for each k, from (Dp)k ! P(Dp), and we
present several examples to show how it may become a useful
statistic on vineyards.},
Key = {fds226628}
}
@article{fds227232,
Author = {Christopher J Tralie and Paul Bendich},
Title = {Cover Song Identification with Timbral Shape},
Journal = {Proceedings of the 16th International Society for Music
Information Retrieval},
Pages = {38-44},
Year = {2015},
url = {http://arxiv.org/abs/1507.05143},
Abstract = {We introduce a novel low level feature for identifying cover
songs which quantifies the relative changes in the smoothed
frequency spectrum of a song. Our key insight is that a
sliding window representation of a chunk of audio can be
viewed as a time-ordered point cloud in high dimensions. For
corresponding chunks of audio between different versions of
the same song, these point clouds are approximately rotated,
translated, and scaled copies of each other. If we treat
MFCC embeddings as point clouds and cast the problem as a
relative shape sequence, we are able to correctly identify
42/80 cover songs in the “Covers 80” dataset. By
contrast, all other work to date on cover songs exclusively
relies on matching note sequences from Chroma derived
features.},
Key = {fds227232}
}
@article{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{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},
Month = {August},
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{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{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{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},
Month = {November},
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{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},
Month = {November},
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{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{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 = {H^{1} 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 G_{2}-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},
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, R},
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, R and Griffiths, P and Grossman, D},
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 = {The book also covers the Second Variation, Euler-Lagrange
PDE systems, and higher-order conservation
laws.},
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. },
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, R},
Title = {Pseudo-Reimannian 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, R},
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 = {This article studies some examples of the family of problems
where a Lagrangian is given for maps from one manifold to
another and one is interested in the extremal mappings for
which the Lagrangian density takes a prescribed form. The
first problem is the study of when two minimal graphs can
induce the same area function on the domain without
differing by trivial symmetries. The second problem is
similar but concerns a different `area Lagrangian' first
investigated by Calabi. The third problem classified the
harmonic maps between spheres (more generally, manifolds of
constant sectional curvature) for which the energy density
is a constant multiple of the volume form. In the first and
third cases, the complete solution is described. In the
second case, some information about the solutions is
derived, but the problem is not completely
solved.},
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 Kähler, 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
long-range fading prediction},
Journal = {IEEE Transactions on Wireless Communications},
Volume = {11},
Number = {12},
Pages = {4362-4371},
Year = {2012},
ISSN = {1536-1276},
url = {http://dx.doi.org/10.1109/TWC.2012.101712.111884},
Abstract = {Code diversity integrates space-time coding with beamforming
by using a small number of feedback bits to select from a
family of space-time codes. Different codes lead to
different induced channels at the receiver, where Channel
State Information (CSI) is used to instruct the transmitter
how to choose the code. Feedback can be combined with
sub-optimal low complexity decoding of the component codes
to match Maximum-Likelihood (ML) decoding performance of any
individual code in the family. It can also be combined with
ML decoding of the component codes to improve performance
beyond ML decoding performance of any individual code. Prior
analysis of code diversity did not take into account the
effect of the mobile speed and the delay in the feedback
channel. This paper demonstrates the practicality of code
diversity in space-time coded systems by showing that
performance gains based on instantaneous feedback are
largely preserved when long-range prediction of time-varying
correlated fading channels is employed to compensate for the
effect of the feedback delay. To maintain prediction
accuracy for realistic SNR, noise reduction that employs
oversampled pilots is used prior to fading prediction. We
also propose a robust low pilot rate method that utilizes
interleaving to improve the spectral efficiency. Simulations
are presented for two channel models: the conventional Jakes
model and a realistic physical channel model where the
parameters associated with the reflectors vary in time and
the arrival rays have different strengths and asymmetric
arrival angles. © 2002-2012 IEEE.},
Doi = {10.1109/TWC.2012.101712.111884},
Key = {fds235783}
}
@article{fds235786,
Author = {Carson, WR and Chen, M and Rodrigues, MRD and Calderbank, R and Carin,
L},
Title = {Communications-inspired projection design with application
to compressive sensing},
Journal = {SIAM Journal on Imaging Sciences},
Volume = {5},
Number = {4},
Pages = {1182-1212},
Year = {2012},
ISSN = {1936-4954},
url = {http://hdl.handle.net/10161/8952 Duke open
access},
Abstract = {We consider the recovery of an underlying signal x ∈ ℂm
based on projection measurements of the form y = Mx+w, where
y ∈ ℂℓ and w is measurement noise; we are interested
in the case ℓ ≪ m. It is assumed that the signal model
p(x) is known and that w ~ CN(w; 0,Σw) for known Σ w. The
objective is to design a projection matrix M ∈ ℂℓ×m
to maximize key information-theoretic quantities with
operational significance, including the mutual information
between the signal and the projections I(x; y) or the Rényi
entropy of the projections hα (y) (Shannon entropy is a
special case). By capitalizing on explicit characterizations
of the gradients of the information measures with respect to
the projection matrix, where we also partially extend the
well-known results of Palomar and Verdu ́ from the mutual
information to the Rényi entropy domain, we reveal the key
operations carried out by the optimal projection designs:
mode exposure and mode alignment. Experiments are considered
for the case of compressive sensing (CS) applied to imagery.
In this context, we provide a demonstration of the
performance improvement possible through the application of
the novel projection designs in relation to conventional
ones, as well as justification for a fast online projection
design method with which state-of-the-art adaptive CS signal
recovery is achieved. © 2012 Society for Industrial and
Applied Mathematics.},
Doi = {10.1137/120878380},
Key = {fds235786}
}
@article{fds236001,
Author = {Jafarpour, S and Duarte, MF and Calderbank, R},
Title = {Beyond worst-case reconstruction in deterministic compressed
sensing},
Journal = {IEEE International Symposium on Information Theory -
Proceedings},
Pages = {1852-1856},
Year = {2012},
url = {http://dx.doi.org/10.1109/ISIT.2012.6283601},
Abstract = {The role of random measurement in compressive sensing is
analogous to the role of random codes in coding theory. In
coding theory, decoders that can correct beyond the minimum
distance of a code allow random codes to achieve the Shannon
limit. In compressed sensing, the counterpart of minimum
distance is the spark of the measurement matrix, i.e., the
size of the smallest set of linearly dependent columns. This
paper constructs a family of measurement matrices where the
columns are formed by exponentiating codewords from a
classical binary error-correcting code of block length M.
The columns can be partitioned into mutually unbiased bases,
and the spark of the corresponding measurement matrix is
shown to be O(√M) by identifying a configuration of
columns that plays a role similar to that of the Dirac comb
in classical Fourier analysis. Further, an explicit basis
for the null space of these measurement matrices is given in
terms of indicator functions of binary self-dual codes.
Reliable reconstruction of k-sparse inputs is shown for k of
order M/log(M) which is best possible and far beyond the
worst case lower bound provided by the spark. © 2012
IEEE.},
Doi = {10.1109/ISIT.2012.6283601},
Key = {fds236001}
}
@article{fds236002,
Author = {Zeng, M and Calderbank, R and Cui, S},
Title = {On design of rateless codes over dying binary erasure
channel},
Journal = {IEEE Transactions on Communications},
Volume = {60},
Number = {4},
Pages = {889-894},
Year = {2012},
ISSN = {0090-6778},
url = {http://dx.doi.org/10.1109/TCOMM.2012.022712.110038},
Abstract = {In this paper, we study a practical coding scheme for the
dying binary erasure channel (DBEC), which is a binary
erasure channel (BEC) subject to a random fatal failure. We
consider the rateless codes and optimize the degree
distribution to maximize the average recovery probability.
In particular, we first study the upper bound of the average
recovery probability, based on which we define the objective
function as the gap between the upper bound and the average
recovery probability achieved by a particular degree
distribution. We then seek the optimal degree distribution
by minimizing the objective function. A simple and heuristic
approach is also proposed to provide a suboptimal but good
degree distribution. Simulation results are presented to
show the significant performance gain over the conventional
LT codes. © 2012 IEEE.},
Doi = {10.1109/TCOMM.2012.022712.110038},
Key = {fds236002}
}
@article{fds236003,
Author = {Applebaum, L and Bajwa, WU and Duarte, MF and Calderbank,
R},
Title = {Asynchronous code-division random access using convex
optimization},
Journal = {Physical Communication},
Volume = {5},
Number = {2},
Pages = {129-147},
Year = {2012},
ISSN = {1874-4907},
url = {http://dx.doi.org/10.1016/j.phycom.2011.09.006},
Abstract = {Many applications in cellular systems and sensor networks
involve a random subset of a large number of users
asynchronously reporting activity to a base station. This
paper examines the problem of multiuser detection (MUD) in
random access channels for such applications. Traditional
orthogonal signaling ignores the random nature of user
activity in this problem and limits the total number of
users to be on the order of the number of signal space
dimensions. Contention-based schemes, on the other hand,
suffer from delays caused by colliding transmissions and the
hidden node problem. In contrast, this paper presents a
novel pairing of an asynchronous non-orthogonal
code-division random access scheme with a convex
optimization-based MUD algorithm that overcomes the issues
associated with orthogonal signaling and contention-based
methods. Two key distinguishing features of the proposed MUD
algorithm are that it does not require knowledge of the
delay or channel state information of every user and it has
polynomial-time computational complexity. The main
analytical contribution of this paper is the relationship
between the performance of the proposed MUD algorithm in the
presence of arbitrary or random delays and two simple
metrics of the set of user codewords. The study of these
metrics is then focused on two specific sets of codewords,
random binary codewords and specially constructed algebraic
codewords, for asynchronous random access. The ensuing
analysis confirms that the proposed scheme together with
either of these two codeword sets significantly outperforms
the orthogonal signaling-based random access in terms of the
total number of users in the system. © 2011 Elsevier
B.V.},
Doi = {10.1016/j.phycom.2011.09.006},
Key = {fds236003}
}
@article{fds236004,
Author = {Bajwa, WU and Calderbank, R and Mixon, DG},
Title = {Two are better than one: Fundamental parameters of frame
coherence},
Journal = {Applied and Computational Harmonic Analysis},
Volume = {33},
Number = {1},
Pages = {58-78},
Year = {2012},
ISSN = {1063-5203},
url = {http://dx.doi.org/10.1016/j.acha.2011.09.005},
Abstract = {This paper investigates two parameters that measure the
coherence of a frame: worst-case and average coherence. We
first use worst-case and average coherence to derive
near-optimal probabilistic guarantees on both sparse signal
detection and reconstruction in the presence of noise. Next,
we provide a catalog of nearly tight frames with small
worst-case and average coherence. Later, we find a new lower
bound on worst-case coherence; we compare it to the Welch
bound and use it to interpret recently reported signal
reconstruction results. Finally, we give an algorithm that
transforms frames in a way that decreases average coherence
without changing the spectral norm or worst-case coherence.
© 2011 Elsevier Inc. All rights reserved.},
Doi = {10.1016/j.acha.2011.09.005},
Key = {fds236004}
}
@article{fds236005,
Author = {Wu, Y and Jia, T and Calderbank, R and Duel-Hallen, A and Hallen,
H},
Title = {Enabling Code Diversity for Mobile Radio Channels using
Long-Range Fading Prediction},
Journal = {IEEE Transactions on Wireless Communications},
Year = {2012},
ISSN = {1536-1276},
url = {http://dx.doi.org/10.1109/TWC.2012.101712.111884},
Abstract = {Code diversity integrates space-time coding with beamforming
by using a small number of feedback bits to select from a
family of space-time codes. Different codes lead to
different induced channels at the receiver, where Channel
State Information (CSI) is used to instruct the transmitter
how to choose the code. Feedback can be combined with
sub-optimal low complexity decoding of the component codes
to match Maximum-Likelihood (ML) decoding performance of any
individual code in the family. It can also be combined with
ML decoding of the component codes to improve performance
beyond ML decoding performance of any individual code. Prior
analysis of code diversity did not take into account the
effect of the mobile speed and the delay in the feedback
channel. This paper demonstrates the practicality of code
diversity in space-time coded systems by showing that
performance gains based on instantaneous feedback are
largely preserved when long-range prediction of time-varying
correlated fading channels is employed to compensate for the
effect of the feedback delay. To maintain prediction
accuracy for realistic SNR, noise reduction that employs
oversampled pilots is used prior to fading prediction. We
also propose a robust low pilot rate method that utilizes
interleaving to improve the spectral efficiency. Simulations
are presented for two channel models: the conventional Jakes
model and a realistic physical channel model where the
parameters associated with the reflectors vary in time and
the arrival rays have different strengths and asymmetric
arrival angles.},
Doi = {10.1109/TWC.2012.101712.111884},
Key = {fds236005}
}
@article{fds236077,
Author = {Chen, M and Carson, W and Rodrigues, M and Calderbank, R and Carin,
L},
Title = {Communications inspired linear discriminant
analysis},
Journal = {Proceedings of the 29th International Conference on Machine
Learning, ICML 2012},
Volume = {1},
Pages = {919-926},
Year = {2012},
url = {http://hdl.handle.net/10161/8956 Duke open
access},
Abstract = {We study the problem of supervised linear dimensionality
reduction, taking an information-theoretic viewpoint. The
linear projection matrix is designed by maximizing the
mutual information between the projected signal and the
class label. By harnessing a recent theoretical result on
the gradient of mutual information, the above optimization
problem can be solved directly using gradient descent,
without requiring simplification of the objective function.
Theoretical analysis and empirical comparison are made
between the proposed method and two closely related methods,
and comparisons are also made with a method in which Rényi
entropy is used to define the mutual information (in this
case the gradient may be computed simply, under a special
parameter setting). Relative to these alternative
approaches, the proposed method achieves promising results
on real datasets. Copyright 2012 by the author(s)/owner(s).},
Key = {fds236077}
}
@article{fds236078,
Author = {Chi, Y and Eldar, YC and Calderbank, R},
Title = {PETRELS: Subspace estimation and tracking from partial
observations},
Journal = {IEEE International Conference on Acoustics Speech and Signal
Processing},
Pages = {3301-3304},
Year = {2012},
ISSN = {1520-6149},
url = {http://dx.doi.org/10.1109/ICASSP.2012.6288621},
Abstract = {We consider the problem of reconstructing a data stream from
a small subset of its entries, where the data stream is
assumed to lie in a low-dimensional linear subspace,
possibly corrupted by noise. It is also important to track
the change of underlying subspace for many applications.
This problem can be viewed as a sequential low-rank matrix
completion problem in which the subspace is learned in an
online fashion. The proposed algorithm, called Parallel
Estimation and Tracking by REcursive Least Squares
(PETRELS), identifies the underlying low-dimensional
subspace via a recursive procedure for each row of the
subspace matrix in parallel, and then reconstructs the
missing entries via least-squares estimation if required.
PETRELS outperforms previous approaches by discounting
observations in order to capture long-term behavior of the
data stream and be able to adapt to it. Numerical examples
are provided for direction-of-arrival estimation and matrix
completion, comparing PETRELS with state of the art batch
algorithms. © 2012 IEEE.},
Doi = {10.1109/ICASSP.2012.6288621},
Key = {fds236078}
}
@article{fds236079,
Author = {Qureshi, TR and Zoltowski, MD and Calderbank, R},
Title = {A novel approach to Doppler compensation and estimation for
multiple targets in MIMO radar with unitary waveform matrix
scheduling},
Journal = {IEEE International Conference on Acoustics Speech and Signal
Processing},
Pages = {2473-2476},
Year = {2012},
ISSN = {1520-6149},
url = {http://dx.doi.org/10.1109/ICASSP.2012.6288417},
Abstract = {In this paper, we present a method of detecting the range
and Doppler phase of a point target using multiple antennas.
As a key illustrative example, we consider a 4 x 4 system
employing a unitary matrix waveform set, e.g., formed from
Golay complementary sequences. When a non-negligible Doppler
shift is induced by the target motion, the waveform matrix
formed from the complementary sequences is no longer
unitary, resulting in significantly degraded target range
estimates. To solve this problem, we adopt a subspace based
approach exploiting the observation that the receive matrix
formed from matched filtering of the reflected waveforms has
a (non-trivial) null-space. Through processing of the
waveforms with the appropriate vector from the null-space,
we can significantly improve the range detection
performance. Also, another very important target aspect is
the velocity with which the target is moving, and to
determine that, the exact Doppler phase shift induced by the
target motion needs to be estimated with reasonable
accuracy. To accomplish this task, we develop a strategy
that uses the MUSIC algorithm to estimate the Doppler phase,
and we use simulations to show that the phase estimates
obtained are reasonably accurate even at low SNRs. © 2012
IEEE.},
Doi = {10.1109/ICASSP.2012.6288417},
Key = {fds236079}
}
@article{fds236080,
Author = {Carson, WR and Rodrigues, MRD and Chen, M and Carin, L and Calderbank,
R},
Title = {How to focus the discriminative power of a
dictionary},
Journal = {IEEE International Conference on Acoustics Speech and Signal
Processing},
Pages = {1365-1368},
Year = {2012},
ISSN = {1520-6149},
url = {http://dx.doi.org/10.1109/ICASSP.2012.6288144},
Abstract = {This paper is motivated by the challenge of high fidelity
processing of images using a relatively small set of
projection measurements. This is a problem of great interest
in many sensing applications, for example where high
photodetector counts are precluded by a combination of
available power, form factor and expense. The emerging
methods of dictionary learning and compressive sensing offer
great potential for addressing this challenge. Combining
these methods requires that the signals of interest be
representable as a sparse combination of elements of some
dictionary. This paper develops a method that aligns the
discriminative power of such a dictionary with the physical
limitations of the imaging system. Alignment is accomplished
by designing a projection matrix that exposes and then
aligns the modes of the noise with those of the dictionary.
The design algorithm is obtained by modifying an algorithm
for designing the pre-filter to maximize the rate and
reliability of a Multiple Input Multiple Output (MIMO)
communications channel. The difference is that in the
communications problem a source is being matched to a
channel, whereas in the imaging problem a channel, or
equivalently the noise covariance, is being matched to a
source. Our results shown that using the proposed
communications design framework we can reduce reconstruction
error between 20%, after only 20 projections of a 28 x 28
image, and 10% after 100 projections. Furthermore, we
noticeably see the superior quality of the reconstructed
images. © 2012 IEEE.},
Doi = {10.1109/ICASSP.2012.6288144},
Key = {fds236080}
}
@article{fds236081,
Author = {Nokleby, M and Bajwa, WU and Calderbank, R and Aazhang,
B},
Title = {Hierarchical averaging over wireless sensor
networks},
Journal = {IEEE International Conference on Acoustics Speech and Signal
Processing},
Pages = {3121-3124},
Year = {2012},
ISSN = {1520-6149},
url = {http://dx.doi.org/10.1109/ICASSP.2012.6288576},
Abstract = {We introduce an approach to gossip algorithms that exploits
three aspects of the wireless medium: superposition,
broadcast, and power control. Instead of sending pairwise
messages between neighbors on a fixed network topology, we
construct gossip algorithms in which nodes can
simultaneously recover multiple neighbors' messages and in
which nodes can adjust the set of their neighbors by
adjusting transmit power. We present two averaging
algorithms, each based on a hierarchical clustering of the
network. In the first algorithm, clusters of nodes transmit
their estimates locally and randomly select a representative
node for communications at the next level. In the second,
each cluster mutually averages and then cooperatively
transmits at the next level. For path-loss environments,
these schemes achieve order-optimal or near order-optimal
performance. © 2012 IEEE.},
Doi = {10.1109/ICASSP.2012.6288576},
Key = {fds236081}
}
@article{fds236082,
Author = {Xie, Y and Chi, Y and Applebaum, L and Calderbank,
R},
Title = {Compressive demodulation of mutually interfering
signals},
Journal = {2012 IEEE Statistical Signal Processing Workshop, SSP
2012},
Pages = {592-595},
Year = {2012},
url = {http://dx.doi.org/10.1109/SSP.2012.6319768},
Abstract = {The challenge of Multiuser Detection (MUD) is that of
demodulating mutually interfering signals given that at any
time instant the number of active users is typically small.
The promise of compressed sensing is the demodulation of
sparse superpositions of signature waveforms from very few
measurements. This paper considers signature waveforms that
are are drawn from a Gabor frame. It describes a MUD
architecture that uses subsampling to convert analog input
to a digital signal, and then uses iterative matching
pursuit to recover the active users. Compressive
demodulation requires K logN samples to recover K active
users whereas standard MUD requires N samples. The paper
provides theoretical performance guarantees and consistent
numerical simulations. © 2012 IEEE.},
Doi = {10.1109/SSP.2012.6319768},
Key = {fds236082}
}
@article{fds236083,
Author = {Calderbank, R and Jafarpour, S},
Title = {Finding needles in compressed haystacks},
Journal = {IEEE International Conference on Acoustics Speech and Signal
Processing},
Pages = {3441-3444},
Year = {2012},
ISSN = {1520-6149},
url = {http://dx.doi.org/10.1109/ICASSP.2012.6288656},
Abstract = {In this paper, we investigate the problem of compressed
learning, i.e. learning directly in the compressed domain.
In particular, we provide tight bounds demonstrating that
the linear kernel SVMs classifier in the measurement domain,
with high probability, has true accuracy close to the
accuracy of the best linear threshold classifier in the data
domain. Furthermore, we indicate that for a family of
well-known deterministic compressed sensing matrices,
compressed learning is provided on the fly. Finally, we
support our claims with experimental results in the texture
analysis application. © 2012 IEEE.},
Doi = {10.1109/ICASSP.2012.6288656},
Key = {fds236083}
}
@article{fds236084,
Author = {Duarte, MF and Matthews, TE and Warren, WS and Calderbank,
R},
Title = {Melanoma classification from hidden Markov tree
features},
Journal = {IEEE International Conference on Acoustics Speech and Signal
Processing},
Pages = {685-688},
Year = {2012},
ISSN = {1520-6149},
url = {http://dx.doi.org/10.1109/ICASSP.2012.6287976},
Abstract = {Melanoma detection relies on visual inspection of skin
samples under the microscope via a qualitative set of
indicators, causing large discordance among pathologists.
New developments in pump-probe imaging enable the extraction
of melanin intensity levels from skin samples and provide
baseline qualitative figures for melanoma detection and
classification. However, such basic figures do not capture
the diverse types of cellular structure that distinguish
different stages of melanoma. In this paper, we propose an
initial approach for feature extraction for classification
purposes via Hidden Markov Tree models trained on skin
sample melanin intensity images. Our experimental results
show that the proposed features provide a mathematical
microscope that is able to better discriminate cellular
structure, enabling successful classification of skin
samples that are mislabeled when the baseline melanin
intensity qualitative figures are used. © 2012
IEEE.},
Doi = {10.1109/ICASSP.2012.6287976},
Key = {fds236084}
}
@article{fds235768,
Author = {Simpson, MJ and Wilson, JW and Matthews, TE and Duarte, M and Calderbank, R and Warren, WS},
Title = {Imaging the distribution of melanin in human skin lesions
with pump-probe microscopy},
Journal = {Optics InfoBase Conference Papers},
Year = {2011},
Month = {December},
Key = {fds235768}
}
@article{fds235977,
Author = {Wolff, J and Martens, M and Jafarpour, S and Daubechies, I and Calderbank, R},
Title = {Uncovering elements of style},
Journal = {IEEE International Conference on Acoustics Speech and Signal
Processing},
Pages = {1017-1020},
Year = {2011},
ISSN = {1520-6149},
url = {http://dx.doi.org/10.1109/ICASSP.2011.5946579},
Abstract = {This paper relates the style of 16th century Flemish
paintings by Goossen van der Weyden (GvdW) to the style of
preliminary sketches or underpaintings made prior to
executing the painting. Van der Weyden made underpaintings
in markedly different styles for reasons as yet not
understood by art historians. The analysis presented here
starts from a classification of the underpaintings into four
distinct styles by experts in art history. Analysis of the
painted surfaces by a combination of wavelet analysis,
hidden Markov trees and boosting algorithms can distinguish
the four underpainting styles with greater than 90%
cross-validation accuracy. On a subsequent blind test this
classifier provided insight into the hypothesis by art
historians that different patches of the finished painting
were executed by different hands. © 2011
IEEE.},
Doi = {10.1109/ICASSP.2011.5946579},
Key = {fds235977}
}
@article{fds235978,
Author = {Goparaju, S and Calderbank, AR and Carson, WR and Rodrigues, MRD and Perez-Cruz, F},
Title = {When to add another dimension when communicating over MIMO
channels},
Journal = {IEEE International Conference on Acoustics Speech and Signal
Processing},
Pages = {3100-3103},
Year = {2011},
ISSN = {1520-6149},
url = {http://dx.doi.org/10.1109/ICASSP.2011.5946351},
Abstract = {This paper introduces a divide and conquer approach to the
design of transmit and receive filters for communication
over a Multiple Input Multiple Output (MIMO) Gaussian
channel subject to an average power constraint. It involves
conversion to a set of parallel scalar channels, possibly
with very different gains, followed by coding per
sub-channel (i.e. over time) rather than coding across
sub-channels (i.e. over time and space). The loss in
performance is negligible at high signal-to-noise ratio
(SNR) and not significant at medium SNR. The advantages are
reduction in signal processing complexity and greater
insight into the SNR thresholds at which a channel is first
allocated power. This insight is a consequence of
formulating the optimal power allocation in terms of an
upper bound on error rate that is determined by parameters
of the input lattice such as the minimum distance and
kissing number. The resulting thresholds are given
explicitly in terms of these lattice parameters. By
contrast, when the optimization problem is phrased in terms
of maximizing mutual information, the solution is mercury
waterfilling, and the thresholds are implicit. © 2011
IEEE.},
Doi = {10.1109/ICASSP.2011.5946351},
Key = {fds235978}
}
@article{fds235979,
Author = {Wu, Y and Zheng, H and Calderbank, R and Kulkarni, S and Poor,
HV},
Title = {On optimal precoding in wireless multicast
systems},
Journal = {IEEE International Conference on Acoustics Speech and Signal
Processing},
Pages = {3068-3071},
Year = {2011},
ISSN = {1520-6149},
url = {http://dx.doi.org/10.1109/ICASSP.2011.5946306},
Abstract = {Precoding has been extensively studied for point-to-point
communications, including the problems of constructing the
precoding codebook and selecting the best precoder. This
paper investigates precoding for a multicast channel in
which a base station is sending the same information to all
users and each user sends back the index of its best
precoding matrix. It is assumed that users do not
collaborate and that no channel state information is known
at the base station. Optimization problems are formulated to
reduce the packet drop rate. A set of probabilistic
algorithms that effectively reduce the average package drop
rate are presented. It is shown numerically that these new
schemes lead to significant improvements. © 2011
IEEE.},
Doi = {10.1109/ICASSP.2011.5946306},
Key = {fds235979}
}
@article{fds235980,
Author = {Kostina, V and Duarte, MF and Jafarpour, S and Calderbank,
R},
Title = {The value of redundant measurement in compressed
sensing},
Journal = {IEEE International Conference on Acoustics Speech and Signal
Processing},
Pages = {3656-3659},
Year = {2011},
ISSN = {1520-6149},
url = {http://dx.doi.org/10.1109/ICASSP.2011.5947143},
Abstract = {The aim of compressed sensing is to recover attributes of
sparse signals using very few measurements. Given an overall
bit budget for quantization, this paper demonstrates that
there is value to redundant measurement. The measurement
matrices considered here are required to have the property
that signal recovery is still possible even after dropping
certain subsets of D measurements. It introduces the concept
of a measurement matrix that is weakly democratic in the
sense that the amount of information about the signal
carried by each of the designated D-subsets is the same.
Examples of deterministic measurement matrices that are
weakly democratic are constructed by exponentiating
codewords from the binary second order Reed Muller code. The
value in rejecting D measurements that are on average
larger, is to be able to provide a finer grid for vector
quantization of the remaining measurements, even after
discounting the original budget by the bits used to identify
the reject set. Simulation results demonstrate that
redundancy improves recovery SNR, sometimes by a wide
margin. Optimum performance occurs when a significant
fraction of measurements are rejected. © 2011
IEEE.},
Doi = {10.1109/ICASSP.2011.5947143},
Key = {fds235980}
}
@article{fds235981,
Author = {Krishnamurthy, K and Bajwa, WU and Willett, R and Calderbank,
R},
Title = {Fast level set estimation from projection
measurements},
Journal = {IEEE Workshop on Statistical Signal Processing
Proceedings},
Pages = {585-588},
Year = {2011},
url = {http://dx.doi.org/10.1109/SSP.2011.5967766},
Abstract = {Estimation of the level set of a function (i.e., regions
where the function exceeds some value) is an important
problem with applications in digital elevation maps, medical
imaging, and astronomy. In many applications, however, the
function of interest is acquired through indirect
measurements, such as tomographic projections,
coded-aperture measurements, or pseudo-random projections
associated with compressed sensing. This paper describes a
new methodology and associated theoretical analysis for
rapid and accurate estimation of the level set from such
projection measurements. The proposed method estimates the
level set from projection measurements without an
intermediate function reconstruction step, thereby leading
to significantly faster computation. In addition, the
coherence of the projection operator and McDiarmid's
inequality are used to characterize the estimator's
performance. © 2011 IEEE.},
Doi = {10.1109/SSP.2011.5967766},
Key = {fds235981}
}
@article{fds235982,
Author = {Harms, A and Bajwa, WU and Calderbank, R},
Title = {Beating Nyquist through correlations: A constrained random
demodulator for sampling of sparse bandlimited
signals},
Journal = {IEEE International Conference on Acoustics Speech and Signal
Processing},
Pages = {5968-5971},
Year = {2011},
ISSN = {1520-6149},
url = {http://dx.doi.org/10.1109/ICASSP.2011.5947721},
Abstract = {Technological constraints severely limit the rate at which
analog-to-digital converters can reliably sample signals.
Recently, Tropp et al. proposed an architecture, termed the
random demodulator (RD), that attempts to overcome this
obstacle for sparse bandlimited signals. One integral
component of the RD architecture is a white noise-like,
bipolar modulating waveform that changes polarity at a rate
equal to the signal bandwidth. Since there is a hardware
limitation to how fast analog waveforms can change polarity
without undergoing shape distortion, this leads to the RD
also having a constraint on the maximum allowable bandwidth.
In this paper, an extension of the RD, termed the
constrained random demodulator (CRD), is proposed that
bypasses this bottleneck by replacing the original
modulating waveform with a run-length limited (RLL)
modulating waveform that changes polarity at a slower rate
than the signal bandwidth. One of the main contributions of
the paper is establishing that the CRD, despite employing a
modulating waveform with correlations, enjoys some
theoretical guarantees for certain RLL waveforms. In
addition, for a given sampling rate and rate of change in
the modulating waveform polarity, numerical simulations
confirm that the CRD, using an appropriate RLL waveform, can
sample a signal with an even wider bandwidth without a
significant loss in performance. © 2011
IEEE.},
Doi = {10.1109/ICASSP.2011.5947721},
Key = {fds235982}
}
@article{fds235983,
Author = {Applebaum, L and Bajwa, WU and Calderbank, AR and Haupt, J and Nowak,
R},
Title = {Deterministic pilot sequences for sparse channel estimation
in OFDM systems},
Journal = {17th DSP 2011 International Conference on Digital Signal
Processing, Proceedings},
Year = {2011},
url = {http://dx.doi.org/10.1109/ICDSP.2011.6005024},
Abstract = {This paper examines the problem of multipath channel
estimation in single-antenna orthogonal frequency division
multiplexing (OFDM) systems. In particular, we study the
problem of pilot assisted channel estimation in wideband
OFDM systems, where the time-domain (discrete) channel is
approximately sparse. Existing works on this topic
established that techniques from the compressed sensing
literature can yield accurate channel estimates using a
relatively small number of pilot tones, provided the pilots
are selected randomly. Here, we describe a general purpose
procedure for deterministic selection of pilot tones to be
used for channel estimation, and establish guarantees for
channel estimation accuracy using these sequences along with
recovery techniques from the compressed sensing literature.
Simulation results are presented to demonstrate the
effectiveness of the proposed procedure in practice. © 2011
IEEE.},
Doi = {10.1109/ICDSP.2011.6005024},
Key = {fds235983}
}
@article{fds235984,
Author = {Mixon, DG and Bajwa, WU and Calderbank, R},
Title = {Frame coherence and sparse signal processing},
Journal = {IEEE International Symposium on Information Theory -
Proceedings},
Pages = {663-667},
Year = {2011},
url = {http://dx.doi.org/10.1109/ISIT.2011.6034214},
Abstract = {The sparse signal processing literature often uses random
sensing matrices to obtain performance guarantees.
Unfortunately, in the real world, sensing matrices do not
always come from random processes. It is therefore desirable
to evaluate whether an arbitrary matrix, or frame, is
suitable for sensing sparse signals. To this end, the
present paper investigates two parameters that measure the
coherence of a frame: worst-case and average coherence. We
first provide several examples of frames that have small
spectral norm, worst-case coherence, and average coherence.
Next, we present a new lower bound on worst-case coherence
and compare it to the Welch bound. Later, we propose an
algorithm that decreases the average coherence of a frame
without changing its spectral norm or worst-case coherence.
Finally, we use worst-case and average coherence, as opposed
to the Restricted Isometry Property, to garner near-optimal
probabilistic guarantees on both sparse signal detection and
reconstruction in the presence of noise. This contrasts with
recent results that only guarantee noiseless signal recovery
from arbitrary frames, and which further assume independence
across the nonzero entries of the signalin a sense,
requiring small average coherence replaces the need for such
an assumption. © 2011 IEEE.},
Doi = {10.1109/ISIT.2011.6034214},
Key = {fds235984}
}
@article{fds235985,
Author = {Calderbank, R and Jafarpour, S and Nastasescu,
M},
Title = {Covering radius and the Restricted Isometry
Property},
Journal = {2011 IEEE Information Theory Workshop, ITW
2011},
Pages = {558-562},
Year = {2011},
url = {http://dx.doi.org/10.1109/ITW.2011.6089564},
Abstract = {The Restricted Isometry Property or RIP introduced by Candes
and Tao requires an n × p dictionary to act as a near
isometry on all k-sparse signals. This paper provides a very
simple condition under which a dictionary Φ (C) obtained by
exponentiating codewords from a binary linear code C
satisfies the RIP with high probability. The method is to
bound the difference between the dictionary Φ(C) and a
second dictionary A generated by a random Bernoulli process
which is known to satisfy the RIP with high probability. The
difference Δ-Φ (C) is controlled by the covering radius of
C, a fundamental parameter that is bounded above by the
number of weights in the dual code C ⊥ (the external
distance of C). The main result complements a more
sophisticated asymptotic analysis by Babadi and Tarokh of
the distribution of eigenvalues of random submatrices of
Φ(C). In this analysis, divergence from the distribution
corresponding to the full Bernoulli matrix depends on a
different fundamental parameter of C, namely the minimum
distance of the dual code C ⊥. © 2011
IEEE.},
Doi = {10.1109/ITW.2011.6089564},
Key = {fds235985}
}
@article{fds235986,
Author = {Gomaa, A and Chi, Y and Al-Dhahir, N and Calderbank,
R},
Title = {On training signal design for multi-user MIMO-OFDM:
Performance analysis and tradeoffs},
Journal = {IEEE VTS ... Vehicular Technology Conference : VTC :
[proceedings]},
Year = {2011},
ISSN = {1550-2252},
url = {http://dx.doi.org/10.1109/VETECF.2011.6092844},
Abstract = {This paper addresses spectrally-efficient multiantenna
multi-carrier uplink transmission scenarios where the users
overlap in time and frequency and are separated using
spatial processing at the base station. The robustness of
the proposed training sequences to residual carrier
frequency offset and phase noise is evaluated analytically.
This analysis reveals an interesting design tradeoff between
the Peak-to-Average Power Ratio of a training sequence and
the increase in channel estimation mean squared error over
the ideal case when these two impairments are not present.
© 2011 IEEE.},
Doi = {10.1109/VETECF.2011.6092844},
Key = {fds235986}
}
@article{fds235987,
Author = {Applebaum, L and Bajwa, WU and Calderbank, R and Howard,
S},
Title = {Choir codes: Coding for full duplex interference
management},
Journal = {2011 49th Annual Allerton Conference on Communication,
Control, and Computing, Allerton 2011},
Pages = {1-8},
Year = {2011},
url = {http://dx.doi.org/10.1109/Allerton.2011.6120141},
Abstract = {Communication networks conventionally operate with
half-duplex methods and interference avoiding schemes to
manage multiple transceivers. Here we consider a method in
which nodes transmit and receive in concert to achieve full
duplex communication without transmitter coordination. We
build on a recent framework for full-duplex communication in
ad-hoc wireless networks recently proposed by Zhang, Luo and
Guo. An individual node in the wireless network either
transmits or it listens to transmissions from other nodes
but it cannot do both at the same time. There might be as
many nodes as there are MAC addresses but we assume that
only a small subset of nodes contribute to the superposition
received at any given node in the network. We develop
deterministic algebraic coding methods that allow
simultaneous communication across the entire network. We
call such codes choir codes. Users are assigned subspaces of
F 2m to define their transmit and listen times. Codewords on
these subspaces are designed and proven to adhere to bounds
on worst-case coherence and the associated matrix spectral
norm. This in turn provides guarantees for multi-user
detection using convex optimization. Further, we show that
matrices for each receiver's listening times can be related
by permutations, thus guaranteeing fairness between
receivers. Compared with earlier work using random codes,
our methods have significant improvements including reduced
decoding/detection error and non-asymptotic results.
Simulation results verify that, as a method to manage
interference, our scheme has significant advantages over
seeking to eliminate or align interference through extensive
exchange of fine-grained channel state information. © 2011
IEEE.},
Doi = {10.1109/Allerton.2011.6120141},
Key = {fds235987}
}
@article{fds235988,
Author = {Nokleby, M and Bajwa, WU and Calderbank, R and Aazhang,
B},
Title = {Gossiping in groups: Distributed averaging over the wireless
medium},
Journal = {2011 49th Annual Allerton Conference on Communication,
Control, and Computing, Allerton 2011},
Pages = {1242-1249},
Year = {2011},
url = {http://dx.doi.org/10.1109/Allerton.2011.6120310},
Abstract = {We present an approach to gossip algorithms tailored to the
practical considerations of wireless communications.
Traditional gossip algorithms operate via the pairwise
exchange of estimates, which fails to capture the broadcast
and superposition nature of the wireless medium. Adapting
the virtual full-duplex framework of Guo and Zhang, we
construct a communications scheme in which each node can
broadcast its estimate to its neighbors while simultaneously
receiving its neighbors' estimates. This full-duplex scheme
gives rise to group gossip, a more flexible family of gossip
algorithms built on multilateral, rather than pairwise,
exchanges. Our approach obviates the need for
orthogonalization or medium access; only local information
and synchronization are necessary. Additionally, group
gossip has better convergence properties than does
randomized gossip. Group gossip permits a tighter bound on
the convergence speed than randomized gossip, and in general
the upper bound on the convergence time is at most one-third
that of randomized gossip. © 2011 IEEE.},
Doi = {10.1109/Allerton.2011.6120310},
Key = {fds235988}
}
@article{fds235989,
Author = {Dang, W and Pezeshki, A and Howard, S and Moran, W and Calderbank,
R},
Title = {Coordinating complementary waveforms for sidelobe
suppression},
Journal = {Conference Record of the Asilomar Conference on Signals,
Systems and Computers},
Pages = {2096-2100},
Year = {2011},
ISSN = {1058-6393},
url = {http://dx.doi.org/10.1109/ACSSC.2011.6190398},
Abstract = {We present a general method for constructing radar transmit
pulse trains and receive filters for which the radar
point-spread function in delay and Doppler, given by the
cross-ambiguity function of the transmit pulse train and the
pulse train used in the receive filter, is essentially free
of range sidelobes inside a Doppler interval around the
zero-Doppler axis. The transmit pulse train is constructed
by coordinating the transmission of a pair of Golay
complementary waveforms across time according to zeros and
ones in a binary sequence P. The pulse train used to filter
the received signal is constructed in a similar way, in
terms of sequencing the Golay waveforms, but each waveform
in the pulse train is weighted by an element from another
sequence Q. We show that a spectrum jointly determined by P
and Q sequences controls the size of the range sidelobes of
the cross-ambiguity function and by properly choosing P and
Q we can clear out the range sidelobes inside a Doppler
interval around the zero-Doppler axis. The joint design of P
and Q enables a tradeoff between the order of the spectral
null for range sidelobe suppression and the signal-to-noise
ratio at the receiver output. We establish this trade-off
and derive a necessary and sufficient condition for the
construction of P and Q sequences that produce a null of a
desired order. © 2011 IEEE.},
Doi = {10.1109/ACSSC.2011.6190398},
Key = {fds235989}
}
@article{fds235990,
Author = {Wu, Y and Viswanathan, H and Klein, T and Haner, M and Calderbank,
R},
Title = {Capacity optimization in networks with heterogeneous radio
access technologies},
Journal = {GLOBECOM - IEEE Global Telecommunications
Conference},
Year = {2011},
url = {http://dx.doi.org/10.1109/GLOCOM.2011.6134226},
Abstract = {As it becomes common for wireless service providers (WSP) to
employ multiple heterogeneous radio access technologies
(RAT), the management of the combined resources across
multiple RATs arises as an important issue. The WSP's
objective is to assign different users to the different RATs
so as to maximize network capacity (or total utility) while
ensuring that individual users' quality of service (QoS)
requirements are met. In this paper, we consider this
resource allocation problem for two scenarios: voice
communication and video communication. For voice
communication, we propose a stable and optimal assignment
scheme based on the deferred acceptance algorithm for both
static and online cases. For video communication,
identifying the NP-hardness of the problem, we propose and
compare a set of heuristic algorithms including a
low-complexity, high-performance scheme. © 2011
IEEE.},
Doi = {10.1109/GLOCOM.2011.6134226},
Key = {fds235990}
}
@article{fds235991,
Author = {Li, Y and Papachristodoulou, A and Chiang, M and Calderbank,
AR},
Title = {Congestion control and its stability in networks with delay
sensitive traffic},
Journal = {Computer Networks},
Volume = {55},
Number = {1},
Pages = {20-32},
Year = {2011},
ISSN = {1389-1286},
url = {http://dx.doi.org/10.1016/j.comnet.2010.07.001},
Abstract = {We consider congestion control in a network with delay
sensitive/ insensitive traffic, modelled by adding explicit
delay terms to the utility function measuring user's
happiness on the Quality of Service (QoS). A new Network
Utility Maximization (NUM) problem is formulated and solved
in a decentralized way via appropriate algorithms
implemented at the users (primal) and/or links (dual). For
the dual algorithm, delay-independent and delay-dependent
stability conditions are derived when propagation delays are
taken into account. A system with voice and data traffic is
considered as example and the properties of the congestion
control algorithm are assessed. © 2010 Elsevier B.V. All
rights reserved.},
Doi = {10.1016/j.comnet.2010.07.001},
Key = {fds235991}
}
@article{fds235992,
Author = {Chi, Y and Gomaa, A and Al-Dhahir, N and Calderbank,
R},
Title = {MMSE-optimal training sequences for spectrally-efficient
Multi-User MIMO-OFDM systems},
Journal = {European Signal Processing Conference},
Pages = {634-638},
Year = {2011},
ISSN = {2219-5491},
Abstract = {This paper proposes a new family of optimal training
sequences in terms of minimizing the mean-square channel
estimation error for spectrally-efficient Multi-User
MIMO-OFDM systems with an arbitrary number of transmit
antennas and an arbitrary number of training symbols. It
addresses uplink transmission scenarios where the users
overlap in time and frequency and are separated using
spatial processing at the base station. In particular,
optimal training sequences can be obtained easily from
standard signal constellations such as QPSK with desired low
PAPR, making it appealing for practical use. © 2011
EURASIP.},
Key = {fds235992}
}
@article{fds235993,
Author = {Sirinaunpiboon, S and Calderbank, AR and Howard,
SD},
Title = {Fast essentially maximum likelihood decoding of the Golden
code},
Journal = {IEEE Transactions on Information Theory},
Volume = {57},
Number = {6},
Pages = {3537-3541},
Year = {2011},
ISSN = {0018-9448},
url = {http://dx.doi.org/10.1109/TIT.2011.2136870},
Abstract = {The Golden code is a full-rate full-diversity space-time
code which has been incorporated in the IEEE 802.16 (WiMAX)
standard. The worst case complexity of a tree-based sphere
decoder for a square QAM constellation is O(N 3), where n is
the size of the underlying QAM constellation; the worst case
will dominate average decoding complexity on any channel
with a significant line of sight component. In this paper,
we presen |