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Coincidences of Hypercubic Lattices in 4 dimensions
, 2008
"... We consider the CSLs of 4–dimensional hypercubic lattices. In particular, we derive the coincidence index Σ and calculate the number of different CSLs as well as the number of inequivalent CSLs for a given Σ. The hypercubic face centered case is dealt with in detail and it is sketched how to derive ..."
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Cited by 7 (6 self)
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We consider the CSLs of 4–dimensional hypercubic lattices. In particular, we derive the coincidence index Σ and calculate the number of different CSLs as well as the number of inequivalent CSLs for a given Σ. The hypercubic face centered case is dealt with in detail and it is sketched how to derive
Hypercubic lattice reduction and analysis of GGH and NTRU signatures
 In Proc. of Eurocrypt ’03, volume 2656 of LNCS
, 2003
"... Abstract. In this paper, we introduce a new lattice reduction technique applicable to the narrow, but important class of Hypercubic lattices, (L ∼ = Z N). Hypercubic lattices arise during transcript analysis of certain GGH, and NTRUSign signature schemes. After a few thousand signatures, key recove ..."
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Cited by 8 (0 self)
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Abstract. In this paper, we introduce a new lattice reduction technique applicable to the narrow, but important class of Hypercubic lattices, (L ∼ = Z N). Hypercubic lattices arise during transcript analysis of certain GGH, and NTRUSign signature schemes. After a few thousand signatures, key
Spanning trees on hypercubic lattices and nonorientable surfaces
, 2000
"... We consider the problem of enumerating spanning trees on lattices. Closedform expressions are obtained for the spanning tree generating function for a hypercubic lattice of size N1×N2× · · ·×Nd in d dimensions under free, periodic, and a combination of free and periodic boundary conditions. Result ..."
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Cited by 8 (4 self)
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We consider the problem of enumerating spanning trees on lattices. Closedform expressions are obtained for the spanning tree generating function for a hypercubic lattice of size N1×N2× · · ·×Nd in d dimensions under free, periodic, and a combination of free and periodic boundary conditions
On the sampling problem for Hcolorings on the hypercubic lattice
 IN THE PROCEEDINGS OF THE DIMACSDIMATIA WORKSHOP ON GRAPHS, HOMOMORPHISMS AND STATISTICAL PHYSICS
, 2000
"... We consider the problem of random Hcolorings of rectangular subsets of the hypercubic lattice Z d, with weight λi ∈ (0, ∞) for the color i. First, we assume that H is nontrivial in the sense that it is neither the completely looped complete graph nor the complete bipartite graph. We consider quasi ..."
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Cited by 4 (0 self)
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We consider the problem of random Hcolorings of rectangular subsets of the hypercubic lattice Z d, with weight λi ∈ (0, ∞) for the color i. First, we assume that H is nontrivial in the sense that it is neither the completely looped complete graph nor the complete bipartite graph. We consider
A Novel Autoassociative Memory on the Complex Hypercubic Lattice
"... Abstract. In this paper we have defined a novel activation function called the multilevel signum for the real and complex valued associative memories. The major motivation of such a function is to increase the number of patterns that can be stored in a memory without increasing the number of neuron ..."
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of neurons. The state of such a network can be described as one of the points that lie on a complex bounded lattice. The convergence behavior of such a network is observed which is supported with the simulation results performed on a sample dataset of 1000 instances 1
Discretization Errors and Rotational Symmetry: The Laplacian Operator on NonHypercubical Lattices
, 2008
"... Discretizations of the Laplacian operator on nonhypercubical lattices are discussed in a systematic approach. It is shown that order a2 errors always exist for discretizations involving only nearest neighbors. Among all lattices with the same density of lattice sites, the hypercubical lattices alwa ..."
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Discretizations of the Laplacian operator on nonhypercubical lattices are discussed in a systematic approach. It is shown that order a2 errors always exist for discretizations involving only nearest neighbors. Among all lattices with the same density of lattice sites, the hypercubical lattices
Numerical study of selfavoiding loops on &dimensional hypercubic lattices
, 1983
"... Abstract. The loop gas in d = 2, 3,4 and 5 dimensions and with multiplicities m = 0, 1, 1.5, 2, 3 and 4 is investigated by the Monte Carlo method. The critical temperatures and approximate values for the critical exponent v corresponding to secondorder phase transitions are obtained for d = 2 and 3 ..."
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Abstract. The loop gas in d = 2, 3,4 and 5 dimensions and with multiplicities m = 0, 1, 1.5, 2, 3 and 4 is investigated by the Monte Carlo method. The critical temperatures and approximate values for the critical exponent v corresponding to secondorder phase transitions are obtained for d = 2 and 3. 1.
Stretched exponential behavior and random walks on diluted hypercubic lattices
"... Diffusion on a diluted hypercube has been proposed as a model for glassy relaxation and is an example of the more general class of stochastic processes on graphs. In this article we determine numerically through large scale simulations the eigenvalue spectra for this stochastic process and calcula ..."
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Diffusion on a diluted hypercube has been proposed as a model for glassy relaxation and is an example of the more general class of stochastic processes on graphs. In this article we determine numerically through large scale simulations the eigenvalue spectra for this stochastic process
Results 1  10
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8,947