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169,854
Diffraction of Random Tilings: Some Rigorous Results
 J. STAT. PHYS
, 1999
"... The diffraction of stochastic point sets, both Bernoulli and Markov, and of random tilings with crystallographic symmetries is investigated in rigorous terms. In particular, we derive the diffraction spectrum of 1D random tilings, of stochastic product tilings built from cuboids, and of planar rando ..."
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Cited by 29 (17 self)
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The diffraction of stochastic point sets, both Bernoulli and Markov, and of random tilings with crystallographic symmetries is investigated in rigorous terms. In particular, we derive the diffraction spectrum of 1D random tilings, of stochastic product tilings built from cuboids, and of planar
The number “6 ” in Planar Tilings
"... Abstract: This paper obtains some important properties of planar normal tiling and proves purely combinatorially Grünbaum’s Theorem. Moreover, we give the sixneighbortheorem and definite “relative density ” to describe the increase of tiles with some special properties. Finally, Γpm−tilings are ..."
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Abstract: This paper obtains some important properties of planar normal tiling and proves purely combinatorially Grünbaum’s Theorem. Moreover, we give the sixneighbortheorem and definite “relative density ” to describe the increase of tiles with some special properties. Finally, Γpm−tilings
Approximation Algorithms for Projective Clustering
 Proceedings of the ACM SIGMOD International Conference on Management of data, Philadelphia
, 2000
"... We consider the following two instances of the projective clustering problem: Given a set S of n points in R d and an integer k ? 0; cover S by k hyperstrips (resp. hypercylinders) so that the maximum width of a hyperstrip (resp., the maximum diameter of a hypercylinder) is minimized. Let w ..."
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Cited by 299 (22 self)
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be the smallest value so that S can be covered by k hyperstrips (resp. hypercylinders), each of width (resp. diameter) at most w : In the plane, the two problems are equivalent. It is NPHard to compute k planar strips of width even at most Cw ; for any constant C ? 0 [50]. This paper contains four main
Grammatical self assembly for planar tiles
 in The 2004 International Conference on MEMs, NANO and Smart Systems
, 2004
"... We introduce a formal grammatical process for planar selfassembling systems with conformal switching which instantiates the geometry of the tiles. This extends prior work which gave a grammatical structure that models only the topology of the assembly. The addition of geometric data leads to the pr ..."
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Cited by 2 (0 self)
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We introduce a formal grammatical process for planar selfassembling systems with conformal switching which instantiates the geometry of the tiles. This extends prior work which gave a grammatical structure that models only the topology of the assembly. The addition of geometric data leads
Random Walks And Harmonic Functions On Infinite Planar Graphs, Using Square Tilings
"... . We study a wide class of transient planar graphs, through a geometric model given by a square tiling of a cylinder. For many graphs, the geometric boundary of the tiling is a circle, and is easy to describe in general. The simple random walk on the graph converges (with probability 1 ) to a poi ..."
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Cited by 25 (5 self)
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. We study a wide class of transient planar graphs, through a geometric model given by a square tiling of a cylinder. For many graphs, the geometric boundary of the tiling is a circle, and is easy to describe in general. The simple random walk on the graph converges (with probability 1 ) to a
Nonintersecting paths, random tilings and random matrices
 Probab. Theory Related Fields
, 2002
"... Abstract. We investigate certain measures induced by families of nonintersecting paths in domino tilings of the Aztec diamond, rhombus tilings of an abchexagon, a dimer model on a cylindrical brick lattice and a growth model. The measures obtained, e.g. the Krawtchouk and Hahn ensembles, have the s ..."
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Cited by 124 (11 self)
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Abstract. We investigate certain measures induced by families of nonintersecting paths in domino tilings of the Aztec diamond, rhombus tilings of an abchexagon, a dimer model on a cylindrical brick lattice and a growth model. The measures obtained, e.g. the Krawtchouk and Hahn ensembles, have
Random Tilings  NSF Proposal
"... this document shows a random dominotiling of the Aztec diamond of order 64, generated by dominoshuffling software written in 1993 by my undergraduate assistant Sameera Iyengar. This picture, and others like it, suggested that there is a qualitative difference between the behavior of a random tili ..."
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this document shows a random dominotiling of the Aztec diamond of order 64, generated by dominoshuffling software written in 1993 by my undergraduate assistant Sameera Iyengar. This picture, and others like it, suggested that there is a qualitative difference between the behavior of a random
Markov Chain Algorithms for Planar Lattice Structures
, 1995
"... Consider the following Markov chain, whose states are all domino tilings of a 2n x 2n chessboard: starting from some arbitrary tiling, pick a 2 x 2 window uniformly at random. If the four squares appearing in this window are covered by two parallel dominoes, rotate the dominoes 90° in place. Repeat ..."
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Cited by 106 (11 self)
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Consider the following Markov chain, whose states are all domino tilings of a 2n x 2n chessboard: starting from some arbitrary tiling, pick a 2 x 2 window uniformly at random. If the four squares appearing in this window are covered by two parallel dominoes, rotate the dominoes 90° in place. Repeat
Keypoint recognition using randomized trees
 IEEE Trans. Pattern Anal. Mach. Intell
"... In many 3–D objectdetection and poseestimation problems, runtime performance is of critical importance. However, there usually is time to train the system, which we will show to be very useful. Assuming that several registered images of the target object are available, we developed a keypointbas ..."
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Cited by 211 (17 self)
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the training phase. We have incorporated these ideas into a realtime system that detects planar, nonplanar, and deformable objects. It then estimates the pose of the rigid ones and the deformations of the others.
Results 1  10
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169,854