Dynamic criticality in driven disordered systems: Role of depinning and driving rate in Barkhausen noise

We study Barkhausen noise in a diluted two-dimensional Ising model with the extended domain wall and weak random fields occurring due to coarse graining. We report two types of scaling behavior corresponding to (a) low disorder regime where a single domain wall slips through a series of positions when the external field is increased, and (b) large disorder regime, which is characterized with nucleation of many domains. The effects of finite concentration of nonmagnetic ions and variable driving rate on the scaling exponents is discussed in both regimes. The universal scaling behavior at low disorder is shown to belong to a class of critical dynamic systems, which are described by a fixed point of the stochastic transport equation with self-consistent disorder correlations.Comment: Revtex, 4 PostScript figure

Traffic on complex networks: Towards understanding global statistical properties from microscopic density fluctuations

We study the microscopic time fluctuations of traffic load and the global statistical properties of a dense traffic of particles on scale-free cyclic graphs. For a wide range of driving rates R the traffic is stationary and the load time series exhibits antipersistence due to the regulatory role of the superstructure associated with two hub nodes in the network. We discuss how the superstructure affects the functioning of the network at high traffic density and at the jamming threshold. The degree of correlations systematically decreases with increasing traffic density and eventually disappears when approaching a jamming density Rc. Already before jamming we observe qualitative changes in the global network-load distributions and the particle queuing times. These changes are related to the occurrence of temporary crises in which the network-load increases dramatically, and then slowly falls back to a value characterizing free flow

Transport Processes on Homogeneous Planar Graphs with Scale-Free Loops

We consider the role of network geometry in two types of diffusion processes: transport of constant-density information packets with queuing on nodes, and constant voltage-driven tunneling of electrons. The underlying network is a homogeneous graph with scale-free distribution of loops, which is constrained to a planar geometry and fixed node connectivity $k=3$. We determine properties of noise, flow and return-times statistics for both processes on this graph and relate the observed differences to the microscopic process details. Our main findings are: (i) Through the local interaction between packets queuing at the same node, long-range correlations build up in traffic streams, which are practically absent in the case of electron transport; (ii) Noise fluctuations in the number of packets and in the number of tunnelings recorded at each node appear to obey the scaling laws in two distinct universality classes; (iii) The topological inhomogeneity of betweenness plays the key role in the occurrence of broad distributions of return times and in the dynamic flow. The maximum-flow spanning trees are characteristic for each process type.Comment: 14 pages, 5 figure

Correlations of triggering noise in driven magnetic clusters

We show that the temporal fluctuations $\Delta H(t)$ of the threshold driving field $H(t)$, which triggers an avalanche in slowly driven disordered ferromagnets with many domains, exhibit long-range correlations in space and time. The probability distribution of the distance between {\it successive} avalanches as well as the distribution of trapping times of domain wall at a given point in space have fractal properties with the universal scaling exponents. We show how these correlations are related to the scaling behavior of Barkhausen avalanches occurring by magnetization reversal. We also suggest a transport equation which takes into account the observed noise correlations.Comment: 7 pages, Revtex, 4 figure

Criticality in driven cellular automata with defects

We study three models of driven sandpile-type automata in the presence of quenched random defects. When the dynamics is conservative, all these models, termed the random sites (A), random bonds (B), and random slopes (C), self-organize into a critical state. For Model C the concentration-dependent exponents are nonuniversal. In the case of nonconservative defects, the asymptotic state is subcritical. Possible defect-mediated nonequilibrium phase transitions are also discussed.Comment: 13 pages, Latex, 6 PostScript figures included, all uuencoded Z-compressed ta

Convergence Rate of Stochastic Gradient Search in the Case of Multiple and Non-Isolated Minima

The convergence rate of stochastic gradient search is analyzed in this paper. Using arguments based on differential geometry and Lojasiewicz inequalities, tight bounds on the convergence rate of general stochastic gradient algorithms are derived. As opposed to the existing results, the results presented in this paper allow the objective function to have multiple, non-isolated minima, impose no restriction on the values of the Hessian (of the objective function) and do not require the algorithm estimates to have a single limit point. Applying these new results, the convergence rate of recursive prediction error identification algorithms is studied. The convergence rate of supervised and temporal-difference learning algorithms is also analyzed using the results derived in the paper

The Globalization Debate: The Sceptics

A devastating criticism of a hard core argumentation, stemming from skeptical authors, has strongly challenged an enthusiasm noticeable in most theoretical analyses of globalization, bringing to light many darker sides of the globalization phenomena. A detailed critical re-examination of their often unrealistic assumptions has presented a very serious challenge to globalists and has made room for the arising of the so called great globalization debate, which has started over time to shape the mainstream of the contemporary social philosophy. In this paper we are closely looking into the way in which sceptics realize their devastating criticism of globalists? argumentation.Globalization, The great globalization debate, Sceptics