Gaussian Belief with dynamic data and in dynamic network

In this paper we analyse Belief Propagation over a Gaussian model in a dynamic environment. Recently, this has been proposed as a method to average local measurement values by a distributed protocol ("Consensus Propagation", Moallemi & Van Roy, 2006), where the average is available for read-out at every single node. In the case that the underlying network is constant but the values to be averaged fluctuate ("dynamic data"), convergence and accuracy are determined by the spectral properties of an associated Ruelle-Perron-Frobenius operator. For Gaussian models on Erdos-Renyi graphs, numerical computation points to a spectral gap remaining in the large-size limit, implying exceptionally good scalability. In a model where the underlying network also fluctuates ("dynamic network"), averaging is more effective than in the dynamic data case. Altogether, this implies very good performance of these methods in very large systems, and opens a new field of statistical physics of large (and dynamic) information systems.Comment: 5 pages, 7 figure

On Cavity Approximations for Graphical Models

We reformulate the Cavity Approximation (CA), a class of algorithms recently introduced for improving the Bethe approximation estimates of marginals in graphical models. In our new formulation, which allows for the treatment of multivalued variables, a further generalization to factor graphs with arbitrary order of interaction factors is explicitly carried out, and a message passing algorithm that implements the first order correction to the Bethe approximation is described. Furthermore we investigate an implementation of the CA for pairwise interactions. In all cases considered we could confirm that CA[k] with increasing $k$ provides a sequence of approximations of markedly increasing precision. Furthermore in some cases we could also confirm the general expectation that the approximation of order $k$, whose computational complexity is $O(N^{k+1})$ has an error that scales as $1/N^{k+1}$ with the size of the system. We discuss the relation between this approach and some recent developments in the field.Comment: Extension to factor graphs and comments on related work adde

Structural change of vortex patterns in anisotropic Bose-Einstein condensates

We study the changes in the spatial distribution of vortices in a rotating Bose-Einstein condensate due to an increasing anisotropy of the trapping potential. Once the rotational symmetry is broken, we find that the vortex system undergoes a rich variety of structural changes, including the formation of zig-zag and linear configurations. These spatial re-arrangements are well signaled by the change in the behavior of the vortex-pattern eigenmodes against the anisotropy parameter. The existence of such structural changes opens up possibilities for the coherent exploitation of effective many-body systems based on vortex patterns.Comment: 5 pages, 4 figure

Causality re-established

Causality never gained the status of a "law" or "principle" in physics. Some recent literature even popularized the false idea that causality is a notion that should be banned from theory. Such misconception relies on an alleged universality of reversibility of laws of physics, based either on determinism of classical theory, or on the multiverse interpretation of quantum theory, in both cases motivated by mere interpretational requirements for realism of the theory. Here, I will show that a properly defined unambiguous notion of causality is a theorem of quantum theory, which is also a falsifiable proposition of the theory. Such causality notion appeared in the literature within the framework of operational probabilistic theories. It is a genuinely theoretical notion, corresponding to establish a definite partial order among events, in the same way as we do by using the future causal cone on Minkowski space. The causality notion is logically completely independent of the misidentified concept of "determinism", and, being a consequence of quantum theory, is ubiquitous in physics. In addition, as classical theory can be regarded as a restriction of quantum theory, causality holds also in the classical case, although the determinism of the theory trivializes it. I then conclude arguing that causality naturally establishes an arrow of time. This implies that the scenario of the "Block Universe" and the connected "Past Hypothesis" are incompatible with causality, and thus with quantum theory: they both are doomed to remain mere interpretations and, as such, not falsifiable, similar to the hypothesis of "super-determinism". This article is part of a discussion meeting issue "Foundations of quantum mechanics and their impact on contemporary society".Comment: Presented at the Royal Society of London, on 11/12/ 2017, at the conference "Foundations of quantum mechanics and their impact on contemporary society". To appear on Philosophical Transactions of the Royal Society

A very fast inference algorithm for finite-dimensional spin glasses: Belief Propagation on the dual lattice

Starting from a Cluster Variational Method, and inspired by the correctness of the paramagnetic Ansatz (at high temperatures in general, and at any temperature in the 2D Edwards-Anderson model) we propose a novel message passing algorithm --- the Dual algorithm --- to estimate the marginal probabilities of spin glasses on finite dimensional lattices. We show that in a wide range of temperatures our algorithm compares very well with Monte Carlo simulations, with the Double Loop algorithm and with exact calculation of the ground state of 2D systems with bimodal and Gaussian interactions. Moreover it is usually 100 times faster than other provably convergent methods, as the Double Loop algorithm.Comment: 23 pages, 12 figures. v2: improved introductio

The Bethe approximation for solving the inverse Ising problem: a comparison with other inference methods

The inverse Ising problem consists in inferring the coupling constants of an Ising model given the correlation matrix. The fastest methods for solving this problem are based on mean-field approximations, but which one performs better in the general case is still not completely clear. In the first part of this work, I summarize the formulas for several mean- field approximations and I derive new analytical expressions for the Bethe approximation, which allow to solve the inverse Ising problem without running the Susceptibility Propagation algorithm (thus avoiding the lack of convergence). In the second part, I compare the accuracy of different mean field approximations on several models (diluted ferromagnets and spin glasses) defined on random graphs and regular lattices, showing which one is in general more effective. A simple improvement over these approximations is proposed. Also a fundamental limitation is found in using methods based on TAP and Bethe approximations in presence of an external field.Comment: v3: strongly revised version with new methods and results, 25 pages, 21 figure

Bayesian Network Structure Learning with Permutation Tests

In literature there are several studies on the performance of Bayesian network structure learning algorithms. The focus of these studies is almost always the heuristics the learning algorithms are based on, i.e. the maximisation algorithms (in score-based algorithms) or the techniques for learning the dependencies of each variable (in constraint-based algorithms). In this paper we investigate how the use of permutation tests instead of parametric ones affects the performance of Bayesian network structure learning from discrete data. Shrinkage tests are also covered to provide a broad overview of the techniques developed in current literature.Comment: 13 pages, 4 figures. Presented at the Conference 'Statistics for Complex Problems', Padova, June 15, 201

Vortices with fractional flux in two-gap superconductors and in extended Faddeev model

We discuss vortices allowed in two-gap superconductors, bilayer systems and in equivalent extended Faddeev model. We show that in these systems there exist vortices which carry an arbitrary fraction of magnetic flux quantum. Besides that we discuss topological defects which do not carry magnetic flux and describe features of ordinary one-magnetic-flux-quantum vortices in the two-gap system. The results should be relevant for the newly discovered two-band superconductor $Mg B_2$.Comment: v2 references added, v3 journal version, presentation improved. Links to related papers are available at the home page of the author http://www.teorfys.uu.se/PEOPLE/ego