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complexity measures and information planes of x-ray astrophysical sources

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2011年第3期2011卷 P03029-P03029页

作者： Lovallo, Michele Telesca, Luciano Azienda Reg Protez Ambiente Basilicata I-85100 Potenza Italy CNR Ist Metodol Anal Ambientale I-85050 Tito PZ Italy

The complex dynamics of x-ray astrophysical sources is investigated by analyzing their daily light curves in four different energy bands by using three information-theoretic measures: Fisher information measure, the Shannon entropy and the disequilibrium. The obtained results suggest a universal complex behavior in the x-ray light, independent of the source and of the energy band.

关键词： disordered systems (experiment) typical-case computational complexity nonlinear dynamics

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Statistical mechanics of learning orthogonal signals for general covariance models

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2010年第04期2010卷 P04009-P04009页

作者： Hoyle, David C. Univ Manchester Fac Life Sci Manchester M13 9PT Lancs England

Statistical mechanics techniques have proved to be useful tools in quantifying the accuracy with which signal vectors are extracted from experimental data. However, analysis has previously been limited to specific model forms for the population covariance C, which may be inappropriate for real world data sets. In this paper we obtain new statistical mechanical results for a general population covariance matrix C. For data sets consisting of p sample points in R(N) we use the replica method to study the accuracy of orthogonal signal vectors estimated from the sample data. In the asymptotic limit of N, p -> infinity at fixed alpha = p/N, we derive analytical results for the signal direction learning curves. In the asymptotic limit the learning curves follow a single universal form, each displaying a retarded learning transition. An explicit formula for the location of the retarded learning transition is obtained and we find marked variation in the location of the retarded learning transition dependent on the distribution of population covariance eigenvalues. The results of the replica analysis are confirmed against simulation.

关键词： data mining (theory) analysis of algorithms typical-case computational complexity

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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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Biased measures for random constraint satisfaction problems: larger interaction range and asymptotic expansion

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2020年第10期2020卷

作者： Budzynski, Louise Semerjian, Guilhem Univ Paris Sorbonne Univ CNRS Lab PhysEcole Normale SuperENSUniv PSL F-75005 Paris France

We investigate the clustering transition undergone by an exemplary random constraint satisfaction problem, the bicoloring of k-uniform random hypergraphs, when its solutions are weighted non-uniformly, with a soft interaction between variables belonging to distinct hyperedges. We show that the threshold alpha(d)(k) for the transition can be further increased with respect to a restricted interaction within the hyperedges, and perform an asymptotic expansion of alpha(d)(k) in the large k limit. We find that alpha(d)(k) = 2(k-1/k) (ln k + ln ln k + gamma(d) + o(1)), where the constant gamma(d) is strictly larger than for the uniform measure over solutions.

关键词： cavity and replica method random graphs networks typical-case computational complexity

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Focused local search for random 3-satisfiability

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2005年第06期2005卷 P06006-P06006页

作者： Seitz, S Alava, M Orponen, P Aalto Univ Lab Theoret Comp Sci FI-02015 Helsinki Finland Aalto Univ Phys Lab FI-02015 Helsinki Finland

A local search algorithm solving an NP-complete optimization problem can be viewed as a stochastic process moving in an 'energy landscape' towards eventually finding an optimal solution. For the random 3-satisfiability problem, the heuristic of focusing the local moves on the currently unsatisfied clauses is known to be very effective: the time to solution has been observed to grow only linearly in the number of variables, for a given clauses-to-variables ratio a sufficiently far below the critical satisfiability threshold alpha(c) approximate to 4.27. We present numerical results on the behaviour of three focused local search algorithms for this problem, considering in particular the characteristics of a focused variant of simple Metropolis dynamics. We estimate the optimal value for the 'temperature' parameter. for this algorithm, such that its linear time regime extends as close to alpha(c) as possible. Similar parameter optimization is performed also for the well-known WalkSAT algorithm and for the less studied, but very well performing focused record-to-record travel method. We observe that with an appropriate choice of parameters, the linear time regime for each of these algorithms seems to extend well into ratios alpha > 4.2-much further than has so far been generally assumed. We discuss the statistics of solution times for the algorithms, relate their performance to the process of 'whitening', and present some conjectures on the shape of their computational phase diagrams.

关键词： energy landscapes (experiment) analysis of algorithms stochastic search typical-case computational complexity

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Biased landscapes for random constraint satisfaction problems

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2019年第2期2019卷 023302-023302页

作者： Budzynski, Louise Ricci-Tersenghi, Federico Semerjian, Guilhem Univ Paris Diderot Sorbonne Univ Univ PSL Lab Phys TheorENSCNRSSorbonne Paris Cite Paris France Sapienza Univ Roma Diparimento Fis Ple Aldo Moro 5 I-00185 Rome Italy UOS Roma CNR Nanotec Ple Aldo Moro 5 I-00185 Rome Italy INFN Sez Roma 1 Ple Aldo Moro 5 I-00185 Rome Italy

The typical complexity of constraint satisfaction problems (CSPs) can be investigated by means of random ensembles of instances. The latter exhibit many threshold phenomena besides their satisfiability phase transition, in particular a clustering or dynamic phase transition (related to the tree reconstruction problem) at which their typical solutions shatter into disconnected components. In this paper we study the evolution of this phenomenon under a bias that breaks the uniformity among solutions of one CSP instance, concentrating on the bicoloring of k-uniform random hypergraphs. We show that for small k the clustering transition can be delayed in this way to higher density of constraints, and that this strategy has a positive impact on the performances of simulated annealing algorithms. We characterize the modest gain that can be expected in the large k limit from the simple implementation of the biasing idea studied here. This paper contains also a contribution of a more methodological nature, made of a review and extension of the methods to determine numerically the discontinuous dynamic transition threshold.

关键词： cavity and replica method random graphs networks typical-case computational complexity

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Stable roommates problem with random preferences

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2015年第1期000卷 P01020-P01020页

作者： Mertens, Stephan Univ Magdeburg Inst Theoret Phys D-39016 Magdeburg Germany Santa Fe Inst Santa Fe NM 87501 USA

The stable roommates problem with n agents has worst case complexity O(n(2)) in time and space. Random instances can be solved faster and with less memory, however. We introduce an algorithm that has average time and space complexity O(n 32) for random instances. We use this algorithm to simulate large instances of the stable roommates problem and to measure the probabilty p(n) that a random instance of size n admits a stable matching. Our data support the conjecture that p(n) = Theta(n(-1/4)).

关键词： disordered systems (theory) analysis of algorithms typical-case computational complexity interacting agent models

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Finding network communities using modularity density

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2016年第12期2016卷 123402-123402页

作者： Botta, Federico del Genio, Charo I. Univ Warwick Ctr Complex Sci Coventry CV4 7AL W Midlands England Univ Warwick Sch Life Sci Coventry CV4 7AL W Midlands England

Many real-world complex networks exhibit a community structure, in which the modules correspond to actual functional units. Identifying these communities is a key challenge for scientists. A common approach is to search for the network partition that maximizes a quality function. Here, we present a detailed analysis of a recently proposed function, namely modularity density. We show that it does not incur in the drawbacks su. ered by traditional modularity, and that it can identify networks without ground-truth community structure, deriving its analytical dependence on link density in generic random graphs. In addition, we show that modularity density allows an easy comparison between networks of di. erent sizes, and we also present some limitations that methods based on modularity density may su. er from. Finally, we introduce an e. cient, quadratic community detection algorithm based on modularity density maximization, validating its accuracy against theoretical predictions and on a set of benchmark networks.

关键词： Random graphs networks Analysis of algorithms Heuristics algorithms typical-case computational complexity

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On the behaviour of random K-SAT on trees

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2012年第05期2012卷 P05009-P05009页

作者： Krishnamurthy, Supriya Sumedha Stockholm Univ Dept Phys SE-10691 Stockholm Sweden KTH Sch Comp Sci & Commun SE-10044 Stockholm Sweden Natl Inst Sci Educ & Res Inst Phys Campus Bhubaneswar 751005 Orissa India

We consider the K-satisfiability problem on a regular d-ary rooted tree. For this model, we demonstrate how we can calculate in closed form the moments of the total number of solutions as a function of d and K, where the average is over all realizations for a fixed assignment of the surface variables. We find that different moments pick out different 'critical' values of d, below which they diverge as the total number of variables on the tree -> infinity and above which they decay. We show that K-SAT on the random graph also behaves similarly. We also calculate exactly the fraction of instances that have solutions for all K. On the tree, this quantity decays to 0 (as the number of variables increases) for any d > 1. However, the recursion relations for this quantity have a non-trivial fixed point solution which indicates the existence of a different transition in the interior of an infinite rooted tree.

关键词： solvable lattice models exact results random graphs networks typical-case computational complexity

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The large deviations of the whitening process in random constraint satisfaction problems

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2016年第5期2016卷 053401-053401页

作者： Braunstein, Alfredo Dall'Asta, Luca Semerjian, Guilhem Zdeborova, Lenka Politecn Torino Corso Duca Abruzzi 24 I-10129 Turin Italy Human Genet Fdn Via Nizza 52 I-10126 Turin Italy Collegio Carlo Alberto Via Real Collegio 30 I-10024 Moncalieri Italy Univ Paris 06 Sorbonne Univ PSL Res Univ LPTENSEcole Normale SuperCNRSUMR 8549 24 Rue Lhomond F-75005 Paris France Univ Paris Saclay CEA CNRS Inst Phys Theor F-91191 Gif Sur Yvette France

Random constraint satisfaction problems undergo several phase transitions as the ratio between the number of constraints and the number of variables is varied. When this ratio exceeds the satisfiability threshold no more solutions exist;the satisfiable phase, for less constrained problems, is itself divided in an unclustered regime and a clustered one. In the latter solutions are grouped in clusters of nearby solutions separated in configuration space from solutions of other clusters. In addition the rigidity transition signals the appearance of so-called frozen variables in typical solutions: beyond this threshold most solutions belong to clusters with an extensive number of variables taking the same values in all solutions of the cluster. In this paper we refine the description of this phenomenon by estimating the location of the freezing transition, corresponding to the disappearance of all unfrozen solutions (not only typical ones). We also unveil phase transitions for the existence and uniqueness of locked solutions, in which all variables are frozen. From a technical point of view we characterize atypical solutions with a number of frozen variables different from the typical value via a large deviation study of the dynamics of a stripping process (whitening) that unveils the frozen variables of a solution, building upon recent works on atypical trajectories of the bootstrap percolation dynamics. Our results also bear some relevance from an algorithmic perspective, previous numerical studies having shown that heuristic algorithms of various kinds usually output unfrozen solutions.

关键词： cavity and replica method message-passing algorithms spin glasses (theory) typical-case computational complexity

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