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Optimal static and dynamic recycling of defective binary devices

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2004年第11期2004卷

作者： Challet, D Castillo, IP Univ Oxford Inst Math Nomura Ctr Quantitat Finance Oxford OX1 3LB England Katholieke Univ Leuven Inst Theoret Fys B-3001 Heverlee Belgium

The binary defect combination problem consists in finding a fully working subset from a given ensemble of imperfect binary components. We determine the typical properties of the model using methods of statistical mechanics, in particular the region in the parameter space where there is almost surely at least one fully working subset. Dynamic recycling of a flux of imperfect binary components leads to zero wastage.

关键词： neuronal networks (theory) message-passing algorithms robust and stochastic optimization stochastic search

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Inference algorithms for gene networks: a statistical mechanics analysis

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

作者： Braunstein, A. Pagnani, A. Weigt, M. Zecchina, R. Inst Sci Interchange I-10133 Turin Italy Politecn Torino I-10129 Turin Italy

The inference of gene regulatory networks from high throughput gene expression data is one of the major challenges in systems biology. This paper aims at analysing and comparing two different algorithmic approaches. The first approach uses pairwise correlations between regulated and regulating genes;the second one uses message-passing techniques for inferring activating and inhibiting regulatory interactions. The performance of these two algorithms can be analysed theoretically on well-defined test sets, using tools from the statistical physics of disordered systems like the replica method. We find that the second algorithm outperforms the first one since it takes into account collective effects of multiple regulators.

关键词： cavity and replica method regulatory networks (theory) message-passing algorithms genomic and proteomic networks

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A novel approach for studying realistic navigations on networks

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2007年第4期2007卷

作者： Sen, Parongama Univ Calcutta Dept Phys Kolkata 700009 W Bengal India

We consider navigation or search schemes on networks which are realistic in the sense that not all search chains can be completed. We show that the quantity mu = rho/s(d), where sd is the average dynamic shortest distance and. the success rate for completion of a search, is a consistent measure for the quality of a search strategy. Taking the example of realistic searches on scale free networks, we. nd that scales with the system size N as N-sigma, where sigma decreases as the searching strategy is improved. This measure is also shown to be sensitive to the distinguishing characteristics of networks. In this new approach, a dynamic small world (DSW) effect is said to exist when delta similar to 0. We show that such a DSW does indeed exist in social networks in which the linking probability is dependent on social distances.

关键词： message-passing algorithms random graphs networks stochastic search communication supply and information networks

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On one-step replica symmetry breaking in the Edwards-Anderson spin glass model

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

作者： Del Ferraro, Gino Wang, Chuang Zhou, Hai-Jun Aurell, Erik KTH Royal Inst Technol AlbaNova Univ Ctr Dept Computat Biol SE-10691 Stockholm Sweden Chinese Acad Sci Inst Theoret Phys State Key Lab Theoret Phys Beijing 100190 Peoples R China Harvard Univ Sch Engn & Appl Sci 33 Oxford St Cambridge MA 02138 USA KTH Royal Inst Technol ACCESS Linnaeus Ctr SE-10044 Stockholm Sweden KTH Royal Inst Technol Ctr Quantum Mat SE-10044 Stockholm Sweden Aalto Univ Dept Appl Phys FIN-00076 Aalto Finland Aalto Univ Dept Comp Sci FIN-00076 Aalto Finland

We consider a one-step replica symmetry breaking description of the Edwards-Anderson spin glass model in 2D. The ingredients of this description are a Kikuchi approximation to the free energy and a second-level statistical model built on the extremal points of the Kikuchi approximation, which are also fixed points of a generalized belief propagation (GBP) scheme. We show that a generalized free energy can be constructed where these extremal points are exponentially weighted by their Kikuchi free energy and a Parisi parameter y, and that the Kikuchi approximation of this generalized free energy leads to second-level, one-step replica symmetry breaking (1RSB), GBP equations. We then proceed analogously to the Bethe approximation case for tree-like graphs, where it has been shown that 1RSB belief propagation equations admit a survey propagation solution. We discuss when and how the one-step-replica symmetry breaking GBP equations that we obtain also allow a simpler class of solutions which can be interpreted as a class of generalized survey propagation equations for the single instance graph case.

关键词： message-passing algorithms optimization over networks spin glasses (theory) cavity and replica method

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Statistical mechanics of budget-constrained auctions

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

作者： Altarelli, F. Braunstein, A. Realpe-Gomez, J. Zecchina, R. ISI Fdn I-10133 Turin Italy Politecn Torino I-10129 Turin Italy

Finding the optimal assignment in budget-constrained auctions is a combinatorial optimization problem with many important applications, a notable example being in the sale of advertisement space by search engines (in this context the problem is often referred to as the off-line AdWords problem). On the basis of the cavity method of statistical mechanics, we introduce a message-passing algorithm that is capable of solving efficiently random instances of the problem extracted from a natural distribution, and we derive from its properties the phase diagram of the problem. As the control parameter (average value of the budgets) is varied, we find two phase transitions delimiting a region in which long-range correlations arise.

关键词： cavity and replica method message-passing algorithms applications to game theory and mathematical economics

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A spin glass approach to the directed feedback vertex set problem

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

作者： Zhou, Hai-Jun Chinese Acad Sci Key Lab Theoret Phys Inst Theoret Phys Zhong Guan Cun East Rd 55 Beijing 100190 Peoples R China

A directed graph (digraph) is formed by vertices and arcs (directed edges) from one vertex to another. A feedback vertex set (FVS) is a set of vertices that contains at least one vertex of every directed cycle in this digraph. The directed feedback vertex set problem aims at constructing a FVS of minimum cardinality. This is a fundamental cycle-constrained hard combinatorial optimization problem with wide practical applications. In this paper we construct a spin glass model for the directed FVS problem by converting the global cycle constraints into local arc constraints, and study this model through the replica-symmetric (RS) mean field theory of statistical physics. We then implement a belief propagation-guided decimation (BPD) algorithm for single digraph instances. The BPD algorithm slightly outperforms the simulated annealing algorithm on large random graph instances. The RS mean field results and algorithmic results can be further improved by working on a more restrictive (and more difficult) spin glass model.

关键词： spin glasses (theory) message-passing algorithms

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Stochastic optimization by message passing

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2011年第11期2011卷

作者： Altarelli, F. Braunstein, A. Ramezanpour, A. Zecchina, R. Politecn Torino Dept Phys I-10129 Turin Italy Politecn Torino Ctr Computat Sci I-10129 Turin Italy Coll Carlo Alberto I-10024 Moncalieri Italy Human Genet Fdn I-10126 Turin Italy

Most optimization problems in applied sciences realistically involve uncertainty in the parameters defining the cost function, of which only statistical information is known beforehand. Here we provide an in-depth discussion of how message passing algorithms for stochastic optimization based on the cavity method of statistical physics can be constructed. We focus on two basic problems, namely the independent set problem and the matching problem, for which we display the general method and caveats for the case of the so called two-stage problem with independently distributed stochastic parameters. We compare the results with some greedy algorithms and briefly discuss the extension to more complicated stochastic multi-stage problems.

关键词： message-passing algorithms random graphs networks source and channel coding error correcting codes

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Optimal deployment of resources for maximizing impact in spreading processes

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PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA 2017年第39期114卷 E8138-E8146页

作者： Lokhov, Andrey Y. Saad, David Los Alamos Natl Lab Ctr Nonlinear Studies & Theoret Div T 4 Los Alamos NM 87545 USA Aston Univ Nonlinear & Complex Res Grp Birmingham B4 7ET W Midlands England

The effective use of limited resources for controlling spreading processes on networks is of prime significance in diverse contexts, ranging from the identification of "influential spreaders" for maximizing information dissemination and targeted interventions in regulatory networks, to the development of mitigation policies for infectious diseases and financial contagion in economic systems. Solutions for these optimization tasks that are based purely on topological arguments are not fully satisfactory;in realistic settings, the problem is often characterized by heterogeneous interactions and requires interventions in a dynamic fashion over a finite time window via a restricted set of controllable nodes. The optimal distribution of available resources hence results from an interplay between network topology and spreading dynamics. We show how these problems can be addressed as particular instances of a universal analytical framework based on a scalable dynamic message-passing approach and demonstrate the efficacy of the method on a variety of real-world examples.

关键词： optimal control of spreading processes dynamic resource allocation message-passing algorithms influence maximization mitigation of epidemic outbreak

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Estimator of prediction error based on approximate message passing for penalized linear regression

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2018年第6期2018卷

作者： Sakata, Ayaka Inst Stat Math Midori Cho Tachikawa Tokyo 1908562 Japan Grad Univ Adv Sci SOKENDAI Hayama Kanagawa 2400193 Japan

We propose an estimator of prediction error using an approximate message passing (AMP) algorithm that can be applied to a broad range of sparse penalties. Following Stein's lemma, the estimator of the generalized degrees of freedom, which is a key quantity for the construction of the estimator of the prediction error, is calculated at the AMP fixed point. The resulting form of the AMP-based estimator does not depend on the penalty function, and its value can be further improved by considering the correlation between predictors. The proposed estimator is asymptotically unbiased when the components of the predictors and response variables are independently generated according to a Gaussian distribution. We examine the behavior of the estimator for real data under nonconvex sparse penalties, where Akaike's information criterion does not correspond to an unbiased estimator of the prediction error. The model selected by the proposed estimator is close to that which minimizes the true prediction error.

关键词： statistical inference learning theory message-passing algorithms

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Circular coloring of random graphs: statistical physics investigation

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2016年第8期2016卷

作者： Schmidt, Christian Guenther, Nils-Eric Zdeborova, Lenka CEA Saclay Inst Phys Theor F-91191 Gif Sur Yvette France CNRS F-91191 Gif Sur Yvette France Barcelona Inst Sci & Technol ICFO Inst Ciencies Foton Castelldefels 08860 Spain

Circular coloring is a constraint satisfaction problem where colors are assigned to nodes in a graph in such a way that every pair of connected nodes has two consecutive colors (the first color being consecutive to the last). We study circular coloring of random graphs using the cavity method. We identify two very interesting properties of this problem. For sufficiently many color and sufficiently low temperature there is a spontaneous breaking of the circular symmetry between colors and a phase transition forwards a ferromagnet-like phase. Our second main result concerns 5-circular coloring of random 3-regular graphs. While this case is found colorable, we conclude that the description via one-step replica symmetry breaking is not sufficient. We observe that simulated annealing is very efficient to find proper colorings for this case. The 5-circular coloring of 3-regular random graphs thus provides a first known example of a problem where the ground state energy is known to be exactly zero yet the space of solutions probably requires a full-step replica symmetry breaking treatment.

关键词： random graphs networks cavity and replica method inference of graphical models message-passing algorithms

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