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A message-passing algorithm with damping

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2005年第11期2005卷 P11008-P11008页

作者： Pretti, M Politecn Torino Dipartimento Fis I-10129 Turin Italy

We propose a modified belief propagation algorithm, with overrelaxed dynamics. Such an algorithm turns out to be generally more stable and faster than ordinary belief propagation. We characterize the performance of the algorithm, employed as a tool for combinatorial optimization, on the random satisfiability problem. Moreover, we trace a connection with a recently proposed double-loop algorithm for minimizing Bethe and Kikuchi free energies.

关键词： message-passing algorithms new applications of statistical mechanics

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Fermions and loops on graphs: II. A monomer-dimer model as a series of determinants

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2008年第12期2008卷 P12012-P12012页

作者： Chernyak, Vladimir Y. Chertkov, Michael Wayne State Univ Dept Chem Detroit MI 48202 USA Los Alamos Natl Lab Ctr Nonlinear Studies Los Alamos NM 87545 USA Los Alamos Natl Lab Div Theoret Los Alamos NM 87545 USA

We continue the discussion of the fermion models on graphs that started in the first paper of the series. Here we introduce a graphical gauge model (GGM) and show that: (a) it can be stated as an average/sum of a determinant defined on the graph over a Z(2) (binary) gauge field;(b) it is equivalent to the monomer-dimer (MD) model on the graph;(c) the partition function of the model allows an explicit expression in terms of a series over disjoint directed cycles, where each term is a product of local contributions along the cycle and the determinant of a matrix defined on the remainder of the graph (excluding the cycle). We also establish a relation between the MD model on the graph and the determinant series, discussed in the first paper-however, considered using simple non-belief propagation choice of the gauge. We conclude with a discussion of possible analytic and algorithmic consequences of these results, as well as related questions and challenges.

关键词： rigorous results in statistical mechanics message-passing algorithms gauge theories

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Percolation on the gene regulatory network

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2020年第8期2020卷

作者： Torrisi, Giuseppe Kuhn, Reimer Annibale, Alessia Kings Coll London Dept Math London WC2R 2LS England

We consider a simplified model for gene regulation, where gene expression is regulated by transcription factors (TFs), which are single proteins or protein complexes. Proteins are in turn synthesised from expressed genes, creating a feedback loop of regulation. This leads to a directed bipartite network in which a link from a gene to a TF exists if the gene codes for a protein contributing to the TF, and a link from a TF to a gene exists if the TF regulates the expression of the gene. Both genes and TFs are modelled as binary variables, which indicate, respectively, whether a gene is expressed or not, and a TF is synthesised or not. We consider the scenario where for a TF to be synthesised, all of its contributing genes must be expressed. This results in an 'AND' gate logic for the dynamics of TFs. By adapting percolation theory to directed bipartite graphs, evolving according to the AND logic dynamics, we are able to determine the necessary conditions, in the network parameter space, under which bipartite networks can support a multiplicity of stable gene expression patterns, under noisy conditions, as required in stable cell types. In particular, the analysis reveals the possibility of a bi-stability region, where the extensive percolating cluster is or is not resilient to perturbations. This is remarkably different from the transition observed in standard percolation theory. Finally, we consider perturbations involving single node removal that mimic gene knockout experiments. Results reveal the strong dependence of the gene knockout cascade on the logic implemented in the underlying network dynamics, highlighting in particular that avalanche sizes cannot be easily related to gene-gene interaction networks.

关键词： gene expression and regulation genomic and proteomic networks message-passing algorithms percolation problems

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message passing for quantified Boolean formulas

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2012年第05期2012卷 P05025-P05025页

作者： Zhang, Pan Ramezanpour, Abolfazl Zdeborova, Lenka Zecchina, Riccardo Politecn Torino I-10129 Turin Italy CEA Saclay IPhT F-91191 Gif Sur Yvette France CNRS URA 2306 F-91191 Gif Sur Yvette France

We introduce two types of message passing algorithms for quantified Boolean formulas (QBF). The first type is a message passing based heuristics that can prove unsatisfiability of the QBF by assigning the universal variables in such a way that the remaining formula is unsatisfiable. In the second type, we use message passing to guide branching heuristics of a Davis-Putnam-Logemann-Loveland (DPLL) complete solver. Numerical experiments show that on random QBFs our branching heuristics give robust exponential efficiency gain with respect to state-of-the-art solvers. We also manage to solve some previously unsolved benchmarks from the QBFLIB library. Apart from this, our study sheds light on using message passing in small systems and as subroutines in complete solvers.

关键词： analysis of algorithms heuristics message-passing algorithms typical-case computational complexity

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Recovering the state sequence of hidden Markov models using mean-field approximations

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2009年第7期2009卷 P07026-P07026页

作者： Sinton, Antoine Ecole Normale Super Phys Theor Lab F-75231 Paris 05 France

Inferring the sequence of states from observations is one of the most fundamental problems in hidden Markov models. In statistical physics language, this problem is equivalent to computing the marginals of a one-dimensional model with a random external field. While this task can be accomplished through transfer matrix methods, it becomes quickly intractable when the underlying state space is large. This paper develops several low complexity approximate algorithms to address this inference problem when the state space becomes large. The new algorithms are based on various mean-field approximations of the transfer matrix. Their performances are studied in detail on a simple realistic model for DNA pyrosequencing.

关键词： disordered systems (theory) analysis of algorithms message-passing algorithms

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Practical optimization of Steiner trees via the cavity method

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2016年第7期2016卷

作者： Braunstein, Alfredo Muntoni, Anna Politecn Torino DISAT Corso Duca Abruzzi 24 Turin Italy Human Genet Fdn Via Nizza 52 Turin Italy Coll Carlo Alberto Via Real Collegio 30 Moncalieri Italy

The optimization version of the cavity method for single instances, called Max-Sum, has been applied in the past to the minimum Steiner tree problem on graphs and variants. Max-Sum has been shown experimentally to give asymptotically optimal results on certain types of weighted random graphs, and to give good solutions in short computation times for some types of real networks. However, the hypotheses behind the formulation and the cavity method itself limit substantially the class of instances on which the approach gives good results (or even converges). Moreover, in the standard model formulation, the diameter of the tree solution is limited by a predefined bound, that a. ects both computation time and convergence properties. In this work we describe two main enhancements to the Max-Sum equations to be able to cope with optimization of real-world instances. First, we develop an alternative 'flat' model formulation that allows the relevant configuration space to be reduced substantially, making the approach feasible on instances with large solution diameter, in particular when the number of terminal nodes is small. Second, we propose an integration between Max-Sum and three greedy heuristics. This integration allows Max-Sum to be transformed into a highly competitive self-contained algorithm, in which a feasible solution is given at each step of the iterative procedure. Part of this development participated in the 2014 DIMACS Challenge on Steiner problems, and we report the results here. The performance on the challenge of the proposed approach was highly satisfactory: it maintained a small gap to the best bound in most cases, and obtained the best results on several instances in two different categories. We also present several improvements with respect to the version of the algorithm that participated in the competition, including new best solutions for some of the instances of the challenge.

关键词： message-passing algorithms optimization over networks random graphs networks

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Boolean constraint satisfaction problems for reaction networks

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2013年第9期2013卷

作者： Seganti, A. De Martino, A. Ricci-Tersenghi, F. Univ Roma La Sapienza Dept Fis I-00185 Rome Italy Univ Roma La Sapienza Dept Fis UOS Roma IPCF CNR I-00185 Rome Italy Ist Italiano Tecnol Ctr Life Nano Sci Sapienza I-00161 Rome Italy Univ Roma La Sapienza Dept Fis Ist Nazl Fis Nucl Sez Roma 1 I-00185 Rome Italy

We define and study a class of (random) Boolean constraint satisfaction problems representing minimal feasibility constraints for networks of chemical reactions. The constraints we consider encode, respectively, for hard mass-balance conditions (where the consumption and production fluxes of each chemical species are matched) and for soft mass-balance conditions (where a net production of compounds is in principle allowed). We solve these constraint satisfaction problems under the Bethe approximation and derive the corresponding belief propagation equations, which involve eight different messages. The statistical properties of ensembles of random problems are studied via the population dynamics methods. By varying a chemical potential attached to the activity of reactions, we find first-order transitions and strong hysteresis, suggesting a non-trivial structure in the space of feasible solutions.

关键词： cavity and replica method message-passing algorithms random graphs networks metabolic networks

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Scaling of average receiving time and average weighted shortest path on weighted-crystal network

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2021年第8期2021卷

作者： Li, Jun Li, Xiaoyan Sun, Yu Zhenjiang 1 High Sch Zhenjiang 212013 Jiangsu Peoples R China Jiangsu Univ Sch Math Sci Zhenjiang 212013 Jiangsu Peoples R China

In this paper, we focus on a network with even nodes named the weighted-crystal network, which is different from the regular iterative rules. By employing the self-similarity of the crystal network, we study and calculate the average receiving time (ART) and average weighted shortest path (AWSP) after dividing the network into n + 1 blocks. In particular, we pay attention to the hexagon crystal network in order to obtain exact results. The obtained scaled results show that ART grows linearly or sublinearly with the iterative and increases with the weight factor r. Meanwhile, the results of AWSP indicate that AWSP exhibits a sublinear dependence on the network order when r = 1. Otherwise, AWSP tends towards constants when 0 < r < 1.

关键词： message-passing algorithms network dynamics first passage traffic models

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Belief propagation guided decimation algorithms for random constraint satisfaction problems with growing domains

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2021年第3期2021卷

作者： Zhao, Chun-Yan Fu, Yan-Rong Univ Shanghai Sci & Technol Coll Sci Shanghai 200093 Peoples R China

We propose three kinds of belief propagation (BP) guided decimation algorithms using asynchronous updating strategy to solve a prototype of random constraint satisfaction problem with growing domains referred to as model RB. For model RB, the exact satisfiability phase transitions have been established rigorously, and almost all instances are intrinsic hard in the transition region. Finding solutions of a random instance of model RB is very challenging, and the problem size is limited to 10(2). The BP guided decimation algorithms we proposed are called asynchronous updating belief propagation (ABP) algorithm, asynchronous updating belief propagation* (ABP*) algorithm, and asynchronous updating belief propagation with variable order (VABP) algorithm, respectively. In the BP part of the algorithms, we adopt asynchronous updating strategy to obtain the latest passing messages between constraints and variables, which can improve the convergence of BP equations. We also use a damping factor that adds the old messages with a certain weight into the new messages sent from variables to constraints, to reduce the occurrence of oscillation during the convergence of BP equations. In the ABP algorithm, we compute the marginal probability distribution of all variables according to the messages obtained after the BP equations converge, then select the most biased variable and fix its value on the component with the maximum probability. While the ABP* algorithm considers how to continue the decimation process if the BP equations do not converge. Different from the previous two algorithms, in the VABP algorithm, we first choose a random order of the variables, and then assign values to the variables according to the given order after BP converges. Experimental results suggest that the three kinds of BP guided decimation algorithms appear to be very effective in solving random instances of model RB even when the constraint tightness is close to the theoretical satisfiability thresho

关键词： analysis of algorithms heuristics algorithms message-passing algorithms belief propagation

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Spectral bounds for the Ising ferromagnet on an arbitrary given graph

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2017年第5期2017卷

作者： Saade, Alaa Krzakala, Florent Zdeborova, Lenka PSL Univ CNRS UMR 8550 Lab Phys Stat F-75005 Paris France Ecole Normale Super F-75005 Paris France UPMC Univ Paris 06 Sorbonne Univ Paris France Univ Calif Berkeley Simons Inst Theory Comp Berkeley CA 94720 USA Univ Paris Saclay CEA CNRS Inst Phys Theor F-91191 Gif Sur Yvette France

We revisit classical bounds of Fisher on the ferromagnetic Ising model (Fisher 1967 Phys. Rev. 162 480), and show how to efficiently use them on an arbitrary given graph to rigorously upper-bound the partition function, magnetizations, and correlations. The results are valid on any finite graph, with arbitrary topology and arbitrary positive couplings and fields. Our results are based on high temperature expansions of the aforementioned quantities, and are expressed in terms of two related linear operators: the non-backtracking operator and the Bethe Hessian. As a by-product, we show that in a well-defined high-temperature region, the susceptibility propagation algorithm (Mezard 2009 J. Physiol. 103 107-13) converges and provides an upper bound on the true spin-spin correlations.

关键词： inference of graphical models random graphs networks message-passing algorithms statistical inference

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