Results 11  20
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71
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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random tilings based on solvable dimer models, augmented by a brief outline of the diraction from the classical 2D Ising lattice gas. We also give a summary of the measure theoretic approach to mathematical diraction theory which underlies the unique decomposition of the diffraction spectrum into its
Random triangle in square: geometrical approach
, 2000
"... The classical problem of mean area of random triangle within the square is solved by a simple and explicit method. Some other related problems are also solved using Mathematica. I. INTRO space we consider random triangle (RT) inside the plane rectangle when all possible cases are explicitly apparent ..."
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The classical problem of mean area of random triangle within the square is solved by a simple and explicit method. Some other related problems are also solved using Mathematica. I. INTRO space we consider random triangle (RT) inside the plane rectangle when all possible cases are explicitly
Random Obtuse Triangles and Convex Quadrilaterals
, 2009
"... We intend to discuss in detail two well known geometrical probability problems. The first one deals with finding the probability that a random triangle is obtuse in nature. We initially discuss the various ways of choosing a random triangle. The problem is at first analyzed based on random angles (a ..."
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We intend to discuss in detail two well known geometrical probability problems. The first one deals with finding the probability that a random triangle is obtuse in nature. We initially discuss the various ways of choosing a random triangle. The problem is at first analyzed based on random angles
A random tiling model for two dimensional electrostatics
 Mem. Amer. Math. Soc
"... Abstract. We consider triangular holes on the hexagonal lattice and we study their interaction when the rest of the lattice is covered by dimers. More precisely, we analyze the joint correlation of these triangular plurimers in a “sea ” of dimers. We determine the asymptotics of the joint correlatio ..."
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Cited by 13 (11 self)
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the plurimers as electrical charges, with charge equal to the difference between the number of downpointing and uppointing unit triangles in a plurimer, the logarithm of the joint correlation behaves exactly like the electrostatic potential energy of this twodimensional electrostatic system: it is obtained
Phase Transitions in Random Dyadic Tilings and Rectangular
"... We study rectangular dissections of an n × n lattice region into rectangles of area n, where n = 2k for an even integer k. We show that there is a natural edgeflipping Markov chain that connects the state space. A similar edgeflipping chain is also known to connect the state space when restricted ..."
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to dyadic tilings, where each rectangle is required to have the form R = [s2u, (s + 1)2u]×[t2v, (t+1)2v], where s, t, u and v are nonnegative integers. The mixing time of these chains is open. We consider a weighted version of these Markov chains where, given a parameter λ> 0, we would like to generate
Geometric and Combinatorial Tiles in 01 Data
 In: Proceedings PKDD’04. Volume 3202 of LNAI
, 2004
"... In this paper we introduce a simple probabilistic model, hierarchical tiles, for 01 data. A basic tile (X,Y,p) specifies a subset X of the rows and a subset Y of the columns of the data, i.e., a rectangle, and gives a probability p for the occurrence of 1s in the cells of X x Y. A hierarchical tile ..."
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Cited by 22 (0 self)
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In this paper we introduce a simple probabilistic model, hierarchical tiles, for 01 data. A basic tile (X,Y,p) specifies a subset X of the rows and a subset Y of the columns of the data, i.e., a rectangle, and gives a probability p for the occurrence of 1s in the cells of X x Y. A hierarchical
THE EMERGENCE OF THE ELECTROSTATIC FIELD AS A FEYNMAN SUM IN RANDOM TILINGS WITH HOLES
, 2009
"... We consider random lozenge tilings on the triangular lattice with holes Q1,..., Qn in some fixed position. For each unit triangle not in a hole, consider the average orientation of the lozenge covering it. We show that the scaling limit of this discrete field is the electrostatic field obtained wh ..."
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Cited by 12 (10 self)
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We consider random lozenge tilings on the triangular lattice with holes Q1,..., Qn in some fixed position. For each unit triangle not in a hole, consider the average orientation of the lozenge covering it. We show that the scaling limit of this discrete field is the electrostatic field obtained
A Note on Tiling under Tomographic Constraints
, 2003
"... Given a tiling of a 2D grid with several types of tiles, we can count for every row and column how many tiles of each type it intersects. These numbers are called the projections. We are interested in the problem of reconstructing a tiling which has given projections. Some simple variants of this ..."
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Cited by 2 (1 self)
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of this problem, involving tiles that are 1 x 1 or 1 x 2 rectangles, have been studied in the past, and were proved to be either solvable in polynomial time or NPcomplete. In this note we make progress toward a comprehensive classification of various tiling reconstruction problems, by proving NP
3SUM, 3XOR, Triangles
, 2013
"... We show that if one can solve 3SUM on a set of size n in time n1+ɛ then one can list t triangles in a graph with m edges in time Õ(m1+ɛt1/3+ɛ ′ ) for any ɛ ′> 0. This is a reversal of Pǎtra¸scu’s reduction from 3SUM to listing triangles (STOC ’10). We then reexecute both Pǎtra¸scu’s reduction an ..."
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Cited by 3 (0 self)
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and our reversal for the variant 3XOR of 3SUM where integer summation is replaced by bitwise xor. As a corollary we obtain that if 3XOR is solvable in linear time but 3SUM requires quadratic randomized time, or vice versa, then the randomized time complexity of listing m triangles in a graph with m edges
Sunflowers and Testing TriangleFreeness of Functions
"... A function f: Fn2 → {0, 1} is trianglefree if there are no x1, x2, x3 ∈ Fn2 satisfying x1 + x2 + x3 = 0 and f (x1) = f (x2) = f (x3) = 1. In testing trianglefreeness, the goal is to distinguish with high probability trianglefree functions from those that are εfar from being trianglefree. It ..."
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.239 (Fu and Kleinberg, RANDOM, 2014). In this work we introduce a new approach to proving lower bounds on the query complexity of trianglefreeness. We relate the problem to combinatorial questions on collections of vectors in ZnD and to sunflower conjectures studied by Alon, Shpilka, and Umans (Comput
Results 11  20
of
71