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Dynamic critical behavior of the swendsen-wang algorithm: The two-dimensional three-state Potts model revisited

JOURNAL OF STATISTICAL PHYSICS 1997年第1-2期87卷 1-36页

作者： Salas, J Sokal, AD NYU DEPT PHYS NEW YORK NY 10003 USA

We have performed a high-precision Monte Carlo study of the dynamic critical behavior of the swendsen-wang algorithm for the two-dimensional three-state Ports model. We find that the Li-Sokal bound (tau(int,E) greater than or equal to const x C-H) is almost but not quite sharp. The ratio tau(int,E)/C-H Seems to diverge either as a small power (approximate to 0.08) or as a logarithm.

关键词： Potts model swendsen-wang algorithm cluster algorithm Monte Carlo Li-Sokal bound dynamic critical phenomena

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A version of the swendsen-wang algorithm for restoration of images degraded by Poisson noise

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PATTERN RECOGNITION 2003年第4期36卷 931-941页

作者： Lasota, S Niemiro, W Univ Warsaw Inst Appl Math & Mech PL-02097 Warsaw Poland Univ Warsaw Inst Informat PL-02097 Warsaw Poland

An algorithm for restoration of images degraded by Poisson noise is proposed. The algorithm belongs to the family of Markov chain Monte Carlo methods with auxiliary variables. We explicitly use the fact that medical images consist of finitely many, often relatively few, grey-levels. The continuous scale of grey-levels is discretized in an adaptive way, so that a straightforward application of the swendsen-wang (Phys. Rev. Lett. 58 (1987) 86) algorithm becomes possible. Partial decoupling method due to Higdon (J. Am. Statist. Assoc. 93 (1998) 442, 585) is also incorporated into the algorithm. Simulation results suggest that the algorithm is reliable and efficient. (C) 2002 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.

关键词： Bayesian image restoration Gibbs distributions Gibbs sampler swendsen-wang algorithm Markov chain Monte Carlo intensity estimation

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Dynamic critical behavior of the swendsen-wang algorithm for the three-dimensional Ising model

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NUCLEAR PHYSICS B 2004年第3期691卷 259-291页

作者： Ossola, G Sokal, AD NYU Dept Phys New York NY 10003 USA

We have performed a high-precision Monte Carlo study of the dynamic critical behavior of the swendsen-wang algorithm for the three-dimensional Ising model at the critical point. For the dynamic critical exponents associated to the integrated autocorrelation times of the "energy-like" observables, we find z(int,N) = z(int,epsilon) = z(int,epsilon')= 0.459 +/- 0.005 +/- 0.025, where the first error bar represents statistical error (68% confidence interval) and the second error bar represents possible systematic error due to corrections to scaling (68% subjective confidence interval). For the "susceptibility-like" observables, we find z(int,M2) = z(int,S2) = 0.443 +/- 0.005 +/- 0.030. For the dynamic critical exponent associated to the exponential autocorrelation time, we find z(exp) approximate to 0.481. Our data are consistent with the Coddington-Baillie conjecture z(SW) = beta/v approximate to 0.5183, especially if it is interpreted as referring to z(exp). (C) 2004 Elsevier B.V. All rights reserved.

关键词： Ising model Potts model swendsen-wang algorithm cluster algorithm Monte Carlo autocorrelation time dynamic critical exponent

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A GENERALIZED swendsen-wang algorithm FOR BAYESIAN NONPARAMETRIC JOINT SEGMENTATION OF MULTIPLE IMAGES

A GENERALIZED SWENDSEN-WANG ALGORITHM FOR BAYESIAN NONPARAME...

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IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Sodjo, Jessica Giremus, Audrey Dobigeon, Nicolas Giovannelli, Jean-Francois Univ Bordeaux CNRS BINP IMS F-33400 Talence France ENSEEIHT IRIT INP F-31071 Talence France

ISBN: (纸本)9781509041176

A generalized swendsen-wang (GSW) algorithm is proposed for the joint segmentation of a set of multiple images sharing, in part, an unknown number of common classes. The class labels are a priori modeled by a combination of the hierarchical Dirichlet process (HDP) and the Potts model. The HDP allows the number of regions in each image and classes to be automatically inferred while the Potts model ensures spatially consistent segmentations. Compared to a classical Gibbs sampler, the GSW ensures a better exploration of the posterior distribution of the labels. To avoid label switching issues, the best partition is estimated using the Dahl's criterion.

关键词： Image segmentation Bayesian nonparametrics Dirichlet Process swendsen-wang algorithm Potts model

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swendsen-wang algorithm on the mean-field Potts model

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RANDOM STRUCTURES & algorithmS 2019年第1期54卷 82-147页

作者： Galanis, Andreas Stefankovic, Daniel Vigoda, Eric Univ Oxford Wolfson BldgParks Rd Oxford OX1 3QD England Univ Rochester Dept Comp Sci Rochester NY 14627 USA Georgia Inst Technol Sch Comp Sci Atlanta GA 30332 USA

We study the q-state ferromagnetic Potts model on the n-vertex complete graph known as the mean-field (CurieWeiss) model. We analyze the swendsen-wang algorithm which is a Markov chain that utilizes the random cluster representation for the ferromagnetic Potts model to recolor large sets of vertices in one step and potentially overcomes obstacles that inhibit single-site Glauber dynamics. Long et al. studied the case q = 2, the swendsen-wang algorithm for the mean-field ferromagnetic Ising model, and showed that the mixing time satisfies: (i) circle minus(1) for beta < beta(c), (ii) circle minus(n(1/4)) for beta = beta(c), (iii) circle minus(log n) for beta > beta(c), where beta(c) is the critical temperature for the ordered/disordered phase transition. In contrast, for q = 3 there are two critical temperatures 0 < beta(u) < beta(rc) that are relevant. We prove that the mixing time of the swendsen-wang algorithm for the ferromagnetic Potts model on the n-vertex complete graph satisfies: (i) circle minus(1) for beta < beta(u), (ii) circle minus(n(1/3)) for beta = beta(u), (iii) exp(n(Omega(1))) for beta(u) < beta < beta(rc), and (iv) circle minus(log n) for beta = beta(rc). These results complement refined results of Cuff et al. on the mixing time of the Glauber dynamics for the ferromagnetic Potts model.

关键词： Curie-Weiss model mean-field Ferromagnetic Potts model phase transitions swendsen-wang algorithm

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Dynamic critical behavior of a swendsen-wang-type algorithm for the Ashkin-Teller model

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JOURNAL OF STATISTICAL PHYSICS 1996年第3-4期85卷 297-361页

作者： Salas, J Sokal, AD Department of Physics New York University New York

We study the dynamic critical behavior of a swendsen-wang-type algorithm for the Ashkin-Teller model. We find that the Li-Sokal bound on the autocorrelation time (tau(int), g greater than or equal to constxC(H)) holds along the self-dual curve of the symmetric Ashkin-Teller model, and is almost, but not quite sharp. The ratio tau(int)epsilon/C-H appears to tend to infinity either as a logarithm or as a small power (0.05 less than or similar to P less than or similar to 0.12). In an appendix we discuss the problem of extracting estimates of the exponential autocorrelation time.

关键词： Ashkin-Teller model Ising model Potts model Monte Carlo dynamical critical behavior cluster algorithm swendsen-wang algorithm Li-Sokal bound critical slowing down autocorrelation time, fitting correlated data

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A generalized swendsen-wang algorithm for Bayesian nonparametric joint segmentation of multiple images

A generalized Swendsen-Wang algorithm for Bayesian nonparame...

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IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Jessica Sodjo Audrey Giremus Nicolas Dobigeon Jean-FranCois Giovannelli IMS (Univ. Bordeaux CNRS BINP) F-33400 Talence France IRIT/INP-ENSEEIHT Toulouse F-31071 France

ISBN: (纸本)9781509041183

关键词： Image segmentation Bayesian nonparametrics Dirichlet Process swendsen-wang algorithm Potts model Potts model multiple image image segmentation GSW HIGH DELTA PRESSURE Posterior distribution

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Positron emission tomography by Markov chain Monte Carlo with auxiliary variables

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PATTERN RECOGNITION 2005年第2期38卷 241-250页

作者： Koronacki, J Lasota, S Niemiro, W Univ Warsaw Inst Appl Math PL-02097 Warsaw Poland Univ Warsaw Inst Informat PL-02097 Warsaw Poland Polish Acad Sci Inst Comp Sci PL-01237 Warsaw Poland

We propose a new algorithm for positron emission tomography (PET) image reconstruction. The algorithm belongs to the family of Markov chain Monte Carlo methods with auxiliary variables. The idea is to iteratively generate hidden variables at one step and use them for image restoration at another step. The well-known model of Vardi et al. Q. Amer. Statist. Assoc. 80 (1985) 8) for PET is combined with the Bayesian model of Lasota and Niemiro (Pattern Recognition 36 (2003) 931) for the underlying images. This latter model takes advantage of the fact that medical images often consist of relatively few grey-levels of unknown intensity. The algorithm of Lasota and Niemiro (Pattern Recognition 36 (2003) 931) is used in the image restoration part of the PET algorithm, essentially as a noise-filtering and smoothing device. It is now equipped with an additional data reconstruction step. We include simulation results which suggest that the method is truly reliable. We also describe a version of the basic algorithm, in which a random simulation step is replaced by computation of expected value, similarly as in the EM algorithm. (C) 2004 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.

关键词： positron emission tomography Markov chain Monte Carlo ill-posed inverse problems intensity estimation Poisson noise Bayesian image restoration Gibbs distribution Gibbs sampler swendsen-wang algorithm

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Logarithmic corrections and finite-size scaling in the two-dimensional 4-state Potts model

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JOURNAL OF STATISTICAL PHYSICS 1997年第3-4期88卷 567-615页

作者： Salas, J Sokal, AD NYU DEPT PHYS NEW YORK NY 10003 USA

We analyze the scaling and finite-size-scaling behavior of the two-dimensional 4-state Potts model. We find new multiplicative logarithmic corrections for the susceptibility, in addition to the already known ones for the specific heat. We also find additive logarithmic corrections to scaling, some of which are universal. We have checked the theoretical predictions at criticality and off criticality by means of high-precision Monte Carlo data.

关键词： scaling finite-size scaling critical phenomena renormalization group logarithmic corrections corrections to scaling Potts model Ashkin-Teller model swendsen-wang algorithm cluster algorithm Monte Carlo

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ANNEALED IMPORTANCE SAMPLING FOR ISING MODELS WITH MIXED BOUNDARY CONDITIONS

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Journal of Computational Mathematics 2023年第3期41卷 542-550页

作者： Lexing Ying Department of Mathematics Stanford UniversityStanfordCA 94305USA

This note introduces a method for sampling Ising models with mixed boundary *** an application of annealed importance sampling and the swendsen-wang algorithm,the method adopts a sequence of intermediate distributions that keeps the temperature fixed but turns on the boundary condition *** numerical results show that the variance of the sample weights is relatively small.

关键词： Ising model Annealed importance sampling swendsen-wang algorithm

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