Anomalous transport: a deterministic approach

We introduce a cycle-expansion (fully deterministic) technique to compute the asymptotic behavior of arbitrary order transport moments. The theory is applied to different kinds of one-dimensional intermittent maps, and Lorentz gas with infinite horizon, confirming the typical appearance of phase transitions in the transport spectrum.Comment: 4 pages, 4 figure

Temporal-varying failures of nodes in networks

We consider networks in which random walkers are removed because of the failure of specific nodes. We interpret the rate of loss as a measure of the importance of nodes, a notion we denote as failure-centrality. We show that the degree of the node is not sufficient to determine this measure and that, in a first approximation, the shortest loops through the node have to be taken into account. We propose approximations of the failure-centrality which are valid for temporal-varying failures and we dwell on the possibility of externally changing the relative importance of nodes in a given network, by exploiting the interference between the loops of a node and the cycles of the temporal pattern of failures. In the limit of long failure cycles we show analytically that the escape in a node is larger than the one estimated from a stochastic failure with the same failure probability. We test our general formalism in two real-world networks (air-transportation and e-mail users) and show how communities lead to deviations from predictions for failures in hubs.Comment: 7 pages, 3 figure

Nontwist non-Hamiltonian systems

We show that the nontwist phenomena previously observed in Hamiltonian systems exist also in time-reversible non-Hamiltonian systems. In particular, we study the two standard collision/reconnection scenarios and we compute the parameter space breakup diagram of the shearless torus. Besides the Hamiltonian routes, the breakup may occur due to the onset of attractors. We study these phenomena in coupled phase oscillators and in non-area-preserving maps.Comment: 7 pages, 5 figure

Dynamical and transport properties in a family of intermittent area-preserving maps

none3We introduce a family of area-preserving maps representing a (non-trivial) two-dimensional extension of the Pomeau-Manneville family in one dimension. We analyze the long-time behavior of recurrence time distributions and correlations, providing analytical and numerical estimates. We study the transport properties of a suitable lift and use a probabilistic argument to derive the full spectrum of transport moments. Finally the dynamical effects of a stochastic perturbation are considered.noneR. Artuso; L. Cavallasca; G. CristadoroR. Artuso; L. Cavallasca; G. Cristador

Linear and fractal diffusion coefficients in a family of one dimensional chaotic maps

We analyse deterministic diffusion in a simple, one-dimensional setting consisting of a family of four parameter dependent, chaotic maps defined over the real line. When iterated under these maps, a probability density function spreads out and one can define a diffusion coefficient. We look at how the diffusion coefficient varies across the family of maps and under parameter variation. Using a technique by which Taylor-Green-Kubo formulae are evaluated in terms of generalised Takagi functions, we derive exact, fully analytical expressions for the diffusion coefficients. Typically, for simple maps these quantities are fractal functions of control parameters. However, our family of four maps exhibits both fractal and linear behavior. We explain these different structures by looking at the topology of the Markov partitions and the ergodic properties of the maps.Comment: 21 pages, 19 figure

Dynamics of transposable elements generates structure and symmetries in genetic sequences

Genetic sequences are known to possess non-trivial composition together with symmetries in the frequencies of their components. Recently, it has been shown that symmetry and structure are hierarchically intertwined in DNA, suggesting a common origin for both features. However, the mechanism leading to this relationship is unknown. Here we investigate a biologically motivated dynamics for the evolution of genetic sequences. We show that a metastable (long-lived) regime emerges in which sequences have symmetry and structure interlaced in a way that matches that of extant genomes.Comment: 6 pagesm 4 figure

Nonequilibrium stationary states with ratchet effect

An ensemble of particles in thermal equilibrium at temperature $T$, modeled by Nos\`e-Hoover dynamics, moves on a triangular lattice of oriented semi-disk elastic scatterers. Despite the scatterer asymmetry a directed transport is clearly ruled out by the second law of thermodynamics. Introduction of a polarized zero mean monochromatic field creates a directed stationary flow with nontrivial dependence on temperature and field parameters. We give a theoretical estimate of directed current induced by a microwave field in an antidot superlattice in semiconductor heterostructures.Comment: 4 pages, 5 figures (small changes added

Do Humans and Deep Convolutional Neural Networks Use Visual Information Similarly for the Categorization of Natural Scenes?

The investigation of visual categorization has recently been aided by the introduction of deep convolutional neural networks (CNNs), which achieve unprecedented accuracy in picture classification after extensive training. Even if the architecture of CNNs is inspired by the organization of the visual brain, the similarity between CNN and human visual processing remains unclear. Here, we investigated this issue by engaging humans and CNNs in a two-class visual categorization task. To this end, pictures containing animals or vehicles were modified to contain only low/high spatial frequency (HSF) information, or were scrambled in the phase of the spatial frequency spectrum. For all types of degradation, accuracy increased as degradation was reduced for both humans and CNNs; however, the thresholds for accurate categorization varied between humans and CNNs. More remarkable differences were observed for HSF information compared to the other two types of degradation, both in terms of overall accuracy and image-level agreement between humans and CNNs. The difficulty with which the CNNs were shown to categorize high-passed natural scenes was reduced by picture whitening, a procedure which is inspired by how visual systems process natural images. The results are discussed concerning the adaptation to regularities in the visual environment (scene statistics); if the visual characteristics of the environment are not learned by CNNs, their visual categorization may depend only on a subset of the visual information on which humans rely, for example, on low spatial frequency information

Relative entropy via non-sequential recursive pair substitutions

The entropy of an ergodic source is the limit of properly rescaled 1-block entropies of sources obtained applying successive non-sequential recursive pairs substitutions (see P. Grassberger 2002 ArXiv:physics/0207023 and D. Benedetto, E. Caglioti and D. Gabrielli 2006 Jour. Stat. Mech. Theo. Exp. 09 doi:10.1088/1742.-5468/2006/09/P09011). In this paper we prove that the cross entropy and the Kullback-Leibler divergence can be obtained in a similar way.Comment: 13 pages , 2 figure