Heteroclinic intersections between Invariant Circles of Volume-Preserving Maps

We develop a Melnikov method for volume-preserving maps with codimension one invariant manifolds. The Melnikov function is shown to be related to the flux of the perturbation through the unperturbed invariant surface. As an example, we compute the Melnikov function for a perturbation of a three-dimensional map that has a heteroclinic connection between a pair of invariant circles. The intersection curves of the manifolds are shown to undergo bifurcations in homologyComment: LaTex with 10 eps figure

Learning by message-passing in networks of discrete synapses

We show that a message-passing process allows to store in binary "material" synapses a number of random patterns which almost saturates the information theoretic bounds. We apply the learning algorithm to networks characterized by a wide range of different connection topologies and of size comparable with that of biological systems (e.g. $n\simeq10^{5}-10^{6}$). The algorithm can be turned into an on-line --fault tolerant-- learning protocol of potential interest in modeling aspects of synaptic plasticity and in building neuromorphic devices.Comment: 4 pages, 3 figures; references updated and minor corrections; accepted in PR

Entropy landscape and non-Gibbs solutions in constraint satisfaction problems

We study the entropy landscape of solutions for the bicoloring problem in random graphs, a representative difficult constraint satisfaction problem. Our goal is to classify which type of clusters of solutions are addressed by different algorithms. In the first part of the study we use the cavity method to obtain the number of clusters with a given internal entropy and determine the phase diagram of the problem, e.g. dynamical, rigidity and SAT-UNSAT transitions. In the second part of the paper we analyze different algorithms and locate their behavior in the entropy landscape of the problem. For instance we show that a smoothed version of a decimation strategy based on Belief Propagation is able to find solutions belonging to sub-dominant clusters even beyond the so called rigidity transition where the thermodynamically relevant clusters become frozen. These non-equilibrium solutions belong to the most probable unfrozen clusters.Comment: 38 pages, 10 figure

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

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.Comment: 43 pages, 41 figure

Distillation of GHZ states by selective information manipulation

Methods for distilling maximally entangled tripartite (GHZ) states from arbitrary entangled tripartite pure states are described. These techniques work for virtually any input state. Each technique has two stages which we call primary and secondary distillation. Primary distillation produces a GHZ state with some probability, so that when applied to an ensemble of systems, a certain percentage is discarded. Secondary distillation produces further GHZs from the discarded systems. These protocols are developed with the help of an approach to quantum information theory based on absolutely selective information, which has other potential applications.Comment: minor corrections, especially of some numerical values; conclusions unaffecte

The theoretical capacity of the Parity Source Coder

The Parity Source Coder is a protocol for data compression which is based on a set of parity checks organized in a sparse random network. We consider here the case of memoryless unbiased binary sources. We show that the theoretical capacity saturate the Shannon limit at large K. We also find that the first corrections to the leading behavior are exponentially small, so that the behavior at finite K is very close to the optimal one.Comment: Added references, minor change

Fractal Spin Glass Properties of Low Energy Configurations in the Frenkel-Kontorova chain

We study numerically and analytically the classical one-dimensional Frenkel-Kontorova chain in the regime of pinned phase characterized by phonon gap. Our results show the existence of exponentially many static equilibrium configurations which are exponentially close to the energy of the ground state. The energies of these configurations form a fractal quasi-degenerate band structure which is described on the basis of elementary excitations. Contrary to the ground state, the configurations inside these bands are disordered.Comment: revtex, 9 pages, 9 figure

Local information transfer as a spatiotemporal filter for complex systems

We present a measure of local information transfer, derived from an existing averaged information-theoretical measure, namely transfer entropy. Local transfer entropy is used to produce profiles of the information transfer into each spatiotemporal point in a complex system. These spatiotemporal profiles are useful not only as an analytical tool, but also allow explicit investigation of different parameter settings and forms of the transfer entropy metric itself. As an example, local transfer entropy is applied to cellular automata, where it is demonstrated to be a novel method of filtering for coherent structure. More importantly, local transfer entropy provides the first quantitative evidence for the long-held conjecture that the emergent traveling coherent structures known as particles (both gliders and domain walls, which have analogues in many physical processes) are the dominant information transfer agents in cellular automata.Comment: 12 page

Gender, economics and culture: diversity and the international evolution of smoking prevalence

Aims: To examine whether the observed diversity between national patterns of smoking prevalence could require modification of the World Health Organization (WHO) linear model for an international `smoking pandemic' (a worldwide epidemic) to address data from non-western countries. Method: We conducted secondary research using current measures in three publicly available databases: Globalink, the International Labour Organization and the World Bank (all internetaccessible). The measures we used are the separate percentage data for men and women on: smoking and employment and national income per capita (US$) and percentage growth per annum. Results: Regression analysis showed that women smokers were more frequent in countries with higher national income, but women were less likely to smoke in countries of rapid growth. Men were less likely to smoke in countries with higher national income, but more likely to smoke in countries of rapid growth. Two principle components together explained 62% of all the variance in the international data. The largest factor was positively correlated with the percentage of employed females, the percentage of female smokers and national income per capita, but negatively correlated with the percentage of male smokers and percentage annual growth. The effect of female employment was not continuous, but above a threshold of 51%, was associated with a higher prevalence of female smoking. The smaller, second factor was only weakly correlated with any smoking variables. Conclusions: In his 1994 model (subsequently adopted by the WHO) Lopez looked at historical trends in `stages' of smoking prevalence. These have been associated with `stages' of economic development. We extended this analysis to look at a dynamic change (% annual growth) and a social indicator (employment). Male and female smoking is affected differentially by economic change and by level of income. These are also strongly related to the percentage of women in employment. This has implications for workplace policies on smoking