The Experts below are selected from a list of 294 Experts worldwide ranked by ideXlab platform
Tommaso Rizzo - One of the best experts on this subject based on the ideXlab platform.
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Inference algorithm for finite-dimensional spin glasses: belief propagation on the Dual Lattice.
Physical Review E, 2011Co-Authors: Alejandro Lage-castellanos, Federico Ricci-tersenghi, Roberto Mulet, Tommaso RizzoAbstract:Starting from a Cluster Variational Method, and inspired by the correctness of the paramagnetic Ansatz (at high temperatures in general, and at any temperature in the 2D Edwards-Anderson model) we propose a novel message passing algorithm --- the Dual algorithm --- to estimate the marginal probabilities of spin glasses on finite dimensional Lattices. We show that in a wide range of temperatures our algorithm compares very well with Monte Carlo simulations, with the Double Loop algorithm and with exact calculation of the ground state of 2D systems with bimodal and Gaussian interactions. Moreover it is usually 100 times faster than other provably convergent methods, as the Double Loop algorithm.
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inference algorithm for finite dimensional spin glasses belief propagation on the Dual Lattice
Physical Review E, 2011Co-Authors: Alejandro Lagecastellanos, Roberto Mulet, Federico Riccitersenghi, Tommaso RizzoAbstract:Starting from a cluster variational method, and inspired by the correctness of the paramagnetic ansatz [at high temperatures in general, and at any temperature in the two-dimensional (2D) Edwards-Anderson (EA) model] we propose a message-passing algorithm--the Dual algorithm--to estimate the marginal probabilities of spin glasses on finite-dimensional Lattices. We use the EA models in 2D and 3D as benchmarks. The Dual algorithm improves the Bethe approximation, and we show that in a wide range of temperatures (compared to the Bethe critical temperature) our algorithm compares very well with Monte Carlo simulations, with the double-loop algorithm, and with exact calculation of the ground state of 2D systems with bimodal and Gaussian interactions. Moreover, it is usually 100 times faster than other provably convergent methods, as the double-loop algorithm. In 2D and 3D the quality of the inference deteriorates only where the correlation length becomes very large, i.e., at low temperatures in 2D and close to the critical temperature in 3D.
Vyacheslav P Grishukhin - One of the best experts on this subject based on the ideXlab platform.
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the minkowski sum of a zonotope and the voronoi polytope of the root Lattice e_7
Sbornik Mathematics, 2012Co-Authors: Vyacheslav P GrishukhinAbstract:We show that the Minkowski sum of the Voronoi polytope of the root Lattice and the zonotope is a 7-dimensional parallelohedron if and only if the set consists of minimal vectors of the Dual Lattice up to scalar multiplication, and does not contain forbidden sets. The minimal vectors of are the vectors of the classical root system . If the -norm of the roots is set equal to 2, then the scalar products of minimal vectors from the Dual Lattice only take the values . A set of minimal vectors is referred to as forbidden if it consists of six vectors, and the directions of some of these vectors can be changed so as to obtain a set of six vectors with all the pairwise scalar products equal to . Bibliography: 11 titles.
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The Minkowski sum of a zonotope and the Voronoi polytope of the root Lattice $ E_7$
Sbornik Mathematics, 2012Co-Authors: Vyacheslav P GrishukhinAbstract:We show that the Minkowski sum of the Voronoi polytope of the root Lattice and the zonotope is a 7-dimensional parallelohedron if and only if the set consists of minimal vectors of the Dual Lattice up to scalar multiplication, and does not contain forbidden sets. The minimal vectors of are the vectors of the classical root system . If the -norm of the roots is set equal to 2, then the scalar products of minimal vectors from the Dual Lattice only take the values . A set of minimal vectors is referred to as forbidden if it consists of six vectors, and the directions of some of these vectors can be changed so as to obtain a set of six vectors with all the pairwise scalar products equal to . Bibliography: 11 titles.
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delaunay and voronoi polytopes of the root Lattice e7 and of the Dual Lattice e 7
Proceedings of the Steklov Institute of Mathematics, 2011Co-Authors: Vyacheslav P GrishukhinAbstract:We give a detailed geometrically clear description of all faces of the Delaunay and Voronoi polytopes of the root Lattice E7 and the Dual Lattice E*7. Here three uniform polytopes related to the Coxeter-Dynkin diagram of the Lie algebra E7 play a special role. These are the Gosset polytope PGos = 321, which is a Delaunay polytope, the contact polytope 231 (both for the Lattice E7), and the Voronoi polytope PV(E*7) = 132 of the Dual Lattice E*7. This paper can be considered as an illustration of the methods for studying Delaunay and Voronoi polytopes.
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Delaunay and voronoi polytopes of the root Lattice E _7 and of the Dual Lattice E*_7
Proceedings of the Steklov Institute of Mathematics, 2011Co-Authors: Vyacheslav P GrishukhinAbstract:We give a detailed geometrically clear description of all faces of the Delaunay and Voronoi polytopes of the root Lattice E _7 and the Dual Lattice E *_7. Here three uniform polytopes related to the Coxeter-Dynkin diagram of the Lie algebra E _7 play a special role. These are the Gosset polytope P _Gos = 3_21, which is a Delaunay polytope, the contact polytope 2_31 (both for the Lattice E _7), and the Voronoi polytope P _V( E *_7) = 1_32 of the Dual Lattice E *_7. This paper can be considered as an illustration of the methods for studying Delaunay and Voronoi polytopes.
Martin R Albrecht - One of the best experts on this subject based on the ideXlab platform.
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EUROCRYPT (2) - On Dual Lattice Attacks Against Small-Secret LWE and Parameter Choices in HElib and SEAL
Lecture Notes in Computer Science, 2017Co-Authors: Martin R AlbrechtAbstract:We present novel variants of the Dual-Lattice attack against LWE in the presence of an unusually short secret. These variants are informed by recent progress in BKW-style algorithms for solving LWE. Applying them to parameter sets suggested by the homomorphic encryption libraries HElib and SEAL yields revised security estimates. Our techniques scale the exponent of the Dual-Lattice attack by a factor of \((2\,L)/(2\,L+1)\) when \(\log q = \varTheta {\left( L \log n\right) }\), when the secret has constant hamming weight \(h\) and where \(L\) is the maximum depth of supported circuits. They also allow to half the dimension of the Lattice under consideration at a multiplicative cost of \(2^{h}\) operations. Moreover, our techniques yield revised concrete security estimates. For example, both libraries promise 80 bits of security for LWE instances with \(n=1024\) and \(\log _2 q \approx {47}\), while the techniques described in this work lead to estimated costs of 68 bits (SEAL) and 62 bits (HElib).
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On Dual Lattice Attacks Against Small-Secret LWE and Parameter Choices in HElib and SEAL
Advances in Cryptology – EUROCRYPT 2017, 2017Co-Authors: Martin R AlbrechtAbstract:We present novel variants of the Dual-Lattice attack against LWE in the presence of an unusually short secret. These variants are informed by recent progress in BKW-style algorithms for solving LWE. Applying them to parameter sets suggested by the homomorphic encryption libraries HElib and SEAL yields revised security estimates. Our techniques scale the exponent of the Dual-Lattice attack by a factor of $$(2\,L)/(2\,L+1)$$ when $$\log q = \varTheta {\left( L \log n\right) }$$ , when the secret has constant hamming weight $$h$$ and where $$L$$ is the maximum depth of supported circuits. They also allow to half the dimension of the Lattice under consideration at a multiplicative cost of $$2^{h}$$ operations. Moreover, our techniques yield revised concrete security estimates. For example, both libraries promise 80 bits of security for LWE instances with $$n=1024$$ and $$\log _2 q \approx {47}$$ , while the techniques described in this work lead to estimated costs of 68 bits (SEAL) and 62 bits (HElib).
Roberto Mulet - One of the best experts on this subject based on the ideXlab platform.
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Inference algorithm for finite-dimensional spin glasses: belief propagation on the Dual Lattice.
Physical Review E, 2011Co-Authors: Alejandro Lage-castellanos, Federico Ricci-tersenghi, Roberto Mulet, Tommaso RizzoAbstract:Starting from a Cluster Variational Method, and inspired by the correctness of the paramagnetic Ansatz (at high temperatures in general, and at any temperature in the 2D Edwards-Anderson model) we propose a novel message passing algorithm --- the Dual algorithm --- to estimate the marginal probabilities of spin glasses on finite dimensional Lattices. We show that in a wide range of temperatures our algorithm compares very well with Monte Carlo simulations, with the Double Loop algorithm and with exact calculation of the ground state of 2D systems with bimodal and Gaussian interactions. Moreover it is usually 100 times faster than other provably convergent methods, as the Double Loop algorithm.
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inference algorithm for finite dimensional spin glasses belief propagation on the Dual Lattice
Physical Review E, 2011Co-Authors: Alejandro Lagecastellanos, Roberto Mulet, Federico Riccitersenghi, Tommaso RizzoAbstract:Starting from a cluster variational method, and inspired by the correctness of the paramagnetic ansatz [at high temperatures in general, and at any temperature in the two-dimensional (2D) Edwards-Anderson (EA) model] we propose a message-passing algorithm--the Dual algorithm--to estimate the marginal probabilities of spin glasses on finite-dimensional Lattices. We use the EA models in 2D and 3D as benchmarks. The Dual algorithm improves the Bethe approximation, and we show that in a wide range of temperatures (compared to the Bethe critical temperature) our algorithm compares very well with Monte Carlo simulations, with the double-loop algorithm, and with exact calculation of the ground state of 2D systems with bimodal and Gaussian interactions. Moreover, it is usually 100 times faster than other provably convergent methods, as the double-loop algorithm. In 2D and 3D the quality of the inference deteriorates only where the correlation length becomes very large, i.e., at low temperatures in 2D and close to the critical temperature in 3D.
Lars Kastner - One of the best experts on this subject based on the ideXlab platform.
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Negative Deformations of Toric Singularities that are Smooth in Codimension Two
Bolyai Society Mathematical Studies, 2013Co-Authors: Klaus Altmann, Lars KastnerAbstract:Given a cone σ ⊆ N ℝ with smooth two-dimensional faces and, moreover, an element R ∈ σ∨ ∩ M of the Dual Lattice, we describe the part of the versal deformation of the associated toric variety TV(σ) that is built from the deformation parameters of multidegree R.
