Damage spreading transition in glasses: A probe for the ruggedness of the configurational landscape

We consider damage spreading transitions in the framework of mode-coupling theory. This theory describes relaxation processes in glasses in the mean-field approximation which are known to be characterized by the presence of an exponentially large number of metastable states. For systems evolving under identical but arbitrarily correlated noises, we demonstrate that there exists a critical temperature T0 which separates two different dynamical regimes depending on whether damage spreads or not in the asymptotic long-time limit. This transition exists for generic noise correlations such that the zero damage solution is stable at high temperatures, being minimal for maximal noise correlations. Although this dynamical transition depends on the type of noise correlations, we show that the asymptotic damage has the good properties of a dynamical order parameter, such as (i) independence of the initial damage; (ii) independence of the class of initial condition; and (iii) stability of the transition in the presence of asymmetric interactions which violate detailed balance. For maximally correlated noises we suggest that damage spreading occurs due to the presence of a divergent number of saddle points (as well as metastable states) in the thermodynamic limit consequence of the ruggedness of the free-energy landscape which characterizes the glassy state. These results are then compared to extensive numerical simulations of a mean-field glass model (the Bernasconi model) with Monte Carlo heat-bath dynamics. The freedom of choosing arbitrary noise correlations for Langevin dynamics makes damage spreading an interesting tool to probe the ruggedness of the configurational landscape.

Topology of the world trade web

Economy, and consequently trade, is a fundamental part of human social organization which, until now, has not been studied within the network modeling framework. Here we present the first, to the best of our knowledge, empirical characterization of the world trade web, that is, the network built upon the trade relationships between different countries in the world. This network displays the typical properties of complex networks, namely, scale-free degree distribution, the small-world property, a high clustering coefficient, and, in addition, degree-degree correlation between different vertices. All these properties make the world trade web a complex network, which is far from being well described through a classical random network description.

Dynamical properties of the Zhang model of self-organized criticality

Critical exponents of the infinitely slowly driven Zhang model of self-organized criticality are computed for d=2 and 3, with particular emphasis devoted to the various roughening exponents. Besides confirming recent estimates of some exponents, new quantities are monitored, and their critical exponents computed. Among other results, it is shown that the three-dimensional exponents do not coincide with the Bak-Tang-Wiesenfeld [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] (Abelian) model, and that the dynamical exponent as computed from the correlation length and from the roughness of the energy profile do not necessarily coincide, as is usually implicitly assumed. An explanation for this is provided. The possibility of comparing these results with those obtained from renormalization group arguments is also briefly addressed.

Statistics of depth probed by cw measurement of photons in a turbid medium

Photon migration in a turbid medium has been modeled in many different ways. The motivation for such modeling is based on technology that can be used to probe potentially diagnostic optical properties of biological tissue. Surprisingly, one of the more effective models is also one of the simplest. It is based on statistical properties of a nearest-neighbor lattice random walk. Here we develop a theory allowing one to calculate the number of visits by a photon to a given depth, if it is eventually detected at an absorbing surface. This mimics cw measurements made on biological tissue and is directed towards characterizing the depth reached by photons injected at the surface. Our development of the theory uses formalism based on the theory of a continuous-time random walk (CTRW). Formally exact results are given in the Fourier-Laplace domain, which, in turn, are used to generate approximations for parameters of physical interest.

Mean first-passage time for system driven by the coin-toss square wave

We study the mean-first-passage-time problem for systems driven by the coin-toss square-wave signal. Exact analytic solutions are obtained for the driftless case. We also obtain approximate solutions for the potential case. The mean-first-passage time exhibits discontinuities and a remarkable nonsmooth oscillatory behavior which, to our knowledge, has not been observed for other kinds of driving noise.

Effect of the output of the system in signal detection

We analyze the consequences that the choice of the output of the system has in the efficiency of signal detection. It is shown that the output signal and the signal-to-noise ratio (SNR), used to characterize the phenomenon of stochastic resonance, strongly depend on the form of the output. In particular, the SNR may be enhanced for an adequate output.

Generalized Langevin equations: Anomalous diffusion and probability distributions

We study the motion of a particle governed by a generalized Langevin equation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to superdiffusive, along with subdiffusive and diffusive. When the random force is Gaussian, we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions.

When telegrapher's equation furnishes a better approximation to transport equation than the difussion approximation

It has been suggested that a solution to the transport equation which includes anisotropic scattering can be approximated by the solution to a telegrapher's equation [A.J. Ishimaru, Appl. Opt. 28, 2210 (1989)]. We show that in one dimension the telegrapher's equation furnishes an exact solution to the transport equation. In two dimensions, we show that, since the solution can become negative, the telegrapher's equation will not furnish a usable approximation. A comparison between simulated data in three dimensions indicates that the solution to the telegrapher's equation is a good approximation to that of the full transport equation at the times at which the diffusion equation furnishes an equally good approximation.

Stochastic resonance in nonpotential systems

We propose a method to analytically show the possibility for the appearance of a maximum in the signal-to-noise ratio in nonpotential systems. We apply our results to the FitzHugh-Nagumo model under a periodic external forcing, showing that the model exhibits stochastic resonance. The procedure that we follow is based on the reduction to a one-dimensional dynamics in the adiabatic limit and in the topology of the phase space of the systems under study. Its application to other nonpotential systems is also discussed.

Generalization of the persistent random walk to dimensions greater than 1

We propose a generalization of the persistent random walk for dimensions greater than 1. Based on a cubic lattice, the model is suitable for an arbitrary dimension d. We study the continuum limit and obtain the equation satisfied by the probability density function for the position of the random walker. An exact solution is obtained for the projected motion along an axis. This solution, which is written in terms of the free-space solution of the one-dimensional telegraphers equation, may open a new way to address the problem of light propagation through thin slabs.

The Nonequilibrium thermodynamics of small systems

The interactions of tiny objects with their environments are dominated by thermal fluctuations. Guided by theory and assisted by new micromanipulation tools, scientists have begun to study such interactions in detail.

Asymmetric Little spin-Glass model

We study the static properties of the Little model with asymmetric couplings. We show that the thermodynamics of this model coincides with that of the Sherrington-Kirkpatrick model, and we compute the main finite-size corrections to the difference of the free energy between these two models and to some clarifying order parameters. Our results agree with numerical simulations. Numerical results are presented for the symmetric Little model, which show that the same conclusions are also valid in this case.

Statistical properties of new neutrality tests against population growth.

A number of statistical tests for detecting population growth are described. We compared the statistical power of these tests with that of others available in the literature. The tests evaluated fall into three categories: those tests based on the distribution of the mutation frequencies, on the haplotype distribution, and on the mismatch distribution. We found that, for an extensive variety of cases, the most powerful tests for detecting population growth are Fu"s FS test and the newly developed R2 test. The behavior of the R2 test is superior for small sample sizes, whereas FS is better for large sample sizes. We also show that some popular statistics based on the mismatch distribution are very conservative. Key words: population growth, population expansion, coalescent simulations, neutrality tests