2,757 research outputs found

    Comparison of Gabay-Toulouse and de Almeida-Thouless instabilities for the spin glass XY model in a field on sparse random graphs

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    Vector spin glasses are known to show two different kinds of phase transitions in presence of an external field: the so-called de Almeida-Thouless and Gabay-Toulouse lines. While the former has been studied to some extent on several topologies (fully connected, random graphs, finite-dimensional lattices, chains with long-range interactions), the latter has been studied only in fully connected models, which however are known to show some unphysical behaviors (e.g. the divergence of these critical lines in the zero-temperature limit). Here we compute analytically both these critical lines for XY spin glasses on random regular graphs. We discuss the different nature of these phase transitions and the dependence of the critical behavior on the field distribution. We also study the crossover between the two different critical behaviors, by suitably tuning the field distribution.Comment: 21 pages, 14 figures; added a long appendix with respect to v

    Multiple phases in modularity-based community detection

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    Detecting communities in a network, based only on the adjacency matrix, is a problem of interest to several scientific disciplines. Recently, Zhang and Moore have introduced an algorithm in [P. Zhang and C. Moore, Proceedings of the National Academy of Sciences 111, 18144 (2014)], called mod-bp, that avoids overfitting the data by optimizing a weighted average of modularity (a popular goodness-of-fit measure in community detection) and entropy (i.e. number of configurations with a given modularity). The adjustment of the relative weight, the "temperature" of the model, is crucial for getting a correct result from mod-bp. In this work we study the many phase transitions that mod-bp may undergo by changing the two parameters of the algorithm: the temperature TT and the maximum number of groups qq. We introduce a new set of order parameters that allow to determine the actual number of groups q^\hat{q}, and we observe on both synthetic and real networks the existence of phases with any q^∈{1,q}\hat{q} \in \{1,q\}, which were unknown before. We discuss how to interpret the results of mod-bp and how to make the optimal choice for the problem of detecting significant communities.Comment: 8 pages, 7 figure

    Solving the inverse Ising problem by mean-field methods in a clustered phase space with many states

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    In this work we explain how to properly use mean-field methods to solve the inverse Ising problem when the phase space is clustered, that is many states are present. The clustering of the phase space can occur for many reasons, e.g. when a system undergoes a phase transition. Mean-field methods for the inverse Ising problem are typically used without taking into account the eventual clustered structure of the input configurations and may led to very bad inference (for instance in the low temperature phase of the Curie-Weiss model). In the present work we explain how to modify mean-field approaches when the phase space is clustered and we illustrate the effectiveness of the new method on different clustered structures (low temperature phases of Curie-Weiss and Hopfield models).Comment: 6 pages, 5 figure

    Velocity shear, turbulent saturation, and steep plasma gradients in the scrape-off layer of inner-wall limited tokamaks

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    The narrow power decay-length (λq\lambda_q), recently found in the scrape-off layer (SOL) of inner-wall limited (IWL) discharges in tokamaks, is studied using 3D, flux-driven, global two-fluid turbulence simulations. The formation of the steep plasma profiles measured is found to arise due to radially sheared E⃗×B⃗\vec{E}\times\vec{B} poloidal flows. A complex interaction between sheared flows and outflowing plasma currents regulates the turbulent saturation, determining the transport levels. We quantify the effects of sheared flows, obtaining theoretical estimates in agreement with our non-linear simulations. Analytical calculations suggest that the IWL λq\lambda_q is roughly equal to the turbulent correlation length.Comment: 5 pages, 5 figure

    A mean field method with correlations determined by linear response

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    We introduce a new mean-field approximation based on the reconciliation of maximum entropy and linear response for correlations in the cluster variation method. Within a general formalism that includes previous mean-field methods, we derive formulas improving upon, e.g., the Bethe approximation and the Sessak-Monasson result at high temperature. Applying the method to direct and inverse Ising problems, we find improvements over standard implementations.Comment: 15 pages, 8 figures, 9 appendices, significant expansion on versions v1 and v

    An improved Belief Propagation algorithm finds many Bethe states in the random field Ising model on random graphs

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    We first present an empirical study of the Belief Propagation (BP) algorithm, when run on the random field Ising model defined on random regular graphs in the zero temperature limit. We introduce the notion of maximal solutions for the BP equations and we use them to fix a fraction of spins in their ground state configuration. At the phase transition point the fraction of unconstrained spins percolates and their number diverges with the system size. This in turn makes the associated optimization problem highly non trivial in the critical region. Using the bounds on the BP messages provided by the maximal solutions we design a new and very easy to implement BP scheme which is able to output a large number of stable fixed points. On one side this new algorithm is able to provide the minimum energy configuration with high probability in a competitive time. On the other side we found that the number of fixed points of the BP algorithm grows with the system size in the critical region. This unexpected feature poses new relevant questions on the physics of this class of models.Comment: 20 pages, 8 figure

    Monte Carlo algorithms are very effective in finding the largest independent set in sparse random graphs

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    The effectiveness of stochastic algorithms based on Monte Carlo dynamics in solving hard optimization problems is mostly unknown. Beyond the basic statement that at a dynamical phase transition the ergodicity breaks and a Monte Carlo dynamics cannot sample correctly the probability distribution in times linear in the system size, there are almost no predictions nor intuitions on the behavior of this class of stochastic dynamics. The situation is particularly intricate because, when using a Monte Carlo based algorithm as an optimization algorithm, one is usually interested in the out of equilibrium behavior which is very hard to analyse. Here we focus on the use of Parallel Tempering in the search for the largest independent set in a sparse random graph, showing that it can find solutions well beyond the dynamical threshold. Comparison with state-of-the-art message passing algorithms reveals that parallel tempering is definitely the algorithm performing best, although a theory explaining its behavior is still lacking.Comment: 14 pages, 12 figure

    Productivity, networks, and export performance: evidence from a cross-country fiÂ…rm dataset

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    This paper uses a newly assembled multi-country multi-industry fiÂ…rm-level dataset to test the effect of productivity and networking on the export probability of Â…firms. Results are in line with the new-new trade theory and with the literature on the information value of networks. Firms are more likely to export if they are more productive, larger, and if they beneÂ…fit from foreign networks (ownership and Â…financial linkages), domestic networks (chamber of commerce, links to regulation), and communication networks (E-mail, internet). Firms bear a lower probability of exporting if they have state or labor networks. Overall, Â…firms with better network connections by one standard deviation enjoy a 15% higher probability of exporting.new-new trade theory; export probability

    The backtracking survey propagation algorithm for solving random K-SAT problems

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    Discrete combinatorial optimization has a central role in many scientific disciplines, however, for hard problems we lack linear time algorithms that would allow us to solve very large instances. Moreover, it is still unclear what are the key features that make a discrete combinatorial optimization problem hard to solve. Here we study random K-satisfiability problems with K=3,4K=3,4, which are known to be very hard close to the SAT-UNSAT threshold, where problems stop having solutions. We show that the backtracking survey propagation algorithm, in a time practically linear in the problem size, is able to find solutions very close to the threshold, in a region unreachable by any other algorithm. All solutions found have no frozen variables, thus supporting the conjecture that only unfrozen solutions can be found in linear time, and that a problem becomes impossible to solve in linear time when all solutions contain frozen variables.Comment: 11 pages, 10 figures. v2: data largely improved and manuscript rewritte
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