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Camera Placement in Integer Lattices
 Centrum voor Wiskunde en Informatica, Department of Algorithmics and Architecture
, 1992
"... The camera placement problem concerns the placement of a fixed number of pointcameras on the integer lattice of dtuples of integers in order to maximize their visibility. We give a caracterization of optimal configurations of size s less than 5 d and use it to compute in time O(s log s) an optim ..."
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Cited by 3 (1 self)
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The camera placement problem concerns the placement of a fixed number of pointcameras on the integer lattice of dtuples of integers in order to maximize their visibility. We give a caracterization of optimal configurations of size s less than 5 d and use it to compute in time O(s log s
Embedding Linkages on an Integer Lattice
"... This paper answers the following question: Given an "erector set" linkage, a connected set of fixedlength links, what is the minimal ffl needed to adjust the edge lengths so that the vertices of the linkage can be placed on integer lattice points? Each edge length is allowed to change ..."
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This paper answers the following question: Given an "erector set" linkage, a connected set of fixedlength links, what is the minimal ffl needed to adjust the edge lengths so that the vertices of the linkage can be placed on integer lattice points? Each edge length is allowed
1.1 Integer lattices
"... Lattices have been studied by cryptographers for quite some time, in both the field of cryptanalysis (see for example [16–18]) and as a source of hard problems on which to build encryption schemes (see [1, 8, 9]). In this lecture, we describe the NTRU encryption algorithm, and the lattice problems o ..."
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on which this is based. We begin with some definitions and a brief overview of lattices. If a1, a2,..., an are n independent vectors in Rm, n ≤ m, then the integer lattice with these vectors as basis is the set L = { �n 1 xiai: xi ∈ Z}. A lattice is often represented as matrix A whose rows are the basis
Monochromatic Corners on the Integer Lattice
, 2010
"... Theorem (Graham and Solymosi) Given any integer r> 0, if the lattice points in the N × N grid are arbitrarily rcolored, and N> 223r, then there exist at least δ(r)N 3 monochromatic “corners”, i.e. triples of points (x, y), (x + d, y), (x, y + d) for some d> 0, where δ(r) = (3r) −2r+2. Pro ..."
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Theorem (Graham and Solymosi) Given any integer r> 0, if the lattice points in the N × N grid are arbitrarily rcolored, and N> 223r, then there exist at least δ(r)N 3 monochromatic “corners”, i.e. triples of points (x, y), (x + d, y), (x, y + d) for some d> 0, where δ(r) = (3r) −2r+2
Integer Lattice Gases
, 1997
"... We generalize the hydrodynamic lattice gas model to include arbitrary numbers of particles moving in each lattice direction. For this generalization we derive the equilibrium distribution function and the hydrodynamic equations, including the equation of state and the prefactor of the inertial term ..."
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Cited by 10 (5 self)
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We generalize the hydrodynamic lattice gas model to include arbitrary numbers of particles moving in each lattice direction. For this generalization we derive the equilibrium distribution function and the hydrodynamic equations, including the equation of state and the prefactor of the inertial term
On some questions related to integer lattice points on the plane.
"... Several questions related to integer lattice points on the plane occupy central position ..."
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Several questions related to integer lattice points on the plane occupy central position
Choosing a spanning tree for the integer lattice uniformly
, 1991
"... Consider the nearest neighbor graph for the integer lattice Z d in d dimensions. For a large finite piece of it, consider choosing a spanning tree for that piece uniformly among all possible subgraphs that are spanning trees. As the piece gets larger, this approaches a limiting measure on the set of ..."
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Cited by 106 (6 self)
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Consider the nearest neighbor graph for the integer lattice Z d in d dimensions. For a large finite piece of it, consider choosing a spanning tree for that piece uniformly among all possible subgraphs that are spanning trees. As the piece gets larger, this approaches a limiting measure on the set
A BrunnMinkowski inequality for the integer lattice
 TRANS. AMER. MATH. SOC
, 2001
"... A close discrete analog of the classical BrunnMinkowksi inequality that holds for finite subsets of the integer lattice is obtained. This is applied to obtain strong new lower bounds for the cardinality of the sum of two finite sets, one of which has full dimension, and, in fact, a method for com ..."
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Cited by 24 (3 self)
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A close discrete analog of the classical BrunnMinkowksi inequality that holds for finite subsets of the integer lattice is obtained. This is applied to obtain strong new lower bounds for the cardinality of the sum of two finite sets, one of which has full dimension, and, in fact, a method
Substitution Tilings and Separated Nets with Similarities to the Integer Lattice
, 810
"... We show that any primitive substitution tiling of R 2 creates a separated net which is biLipschitz to Z 2. Then we show that if H is a primitive Pisot substitution in R d, for every separated net Y, that corresponds to some tiling τ ∈ XH, there exists a bijection Φ between Y and the integer lattice ..."
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Cited by 9 (2 self)
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We show that any primitive substitution tiling of R 2 creates a separated net which is biLipschitz to Z 2. Then we show that if H is a primitive Pisot substitution in R d, for every separated net Y, that corresponds to some tiling τ ∈ XH, there exists a bijection Φ between Y and the integer lattice
STABILITY IN RANDOM BOOLEAN CELLULAR AUTOMATA ON THE INTEGER LATTICE
, 2007
"... We consider random boolean cellular automata on the integer lattice, i.e., the cells are identified with the integers from 1 to N. The behaviour of the automaton is mainly determined by the support of the random variable that selects one of the sixteen possible Boolean rules, independently for each ..."
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We consider random boolean cellular automata on the integer lattice, i.e., the cells are identified with the integers from 1 to N. The behaviour of the automaton is mainly determined by the support of the random variable that selects one of the sixteen possible Boolean rules, independently
Results 1  10
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