Constructive influence of noise-flatness in correlation ratchets

The influence of noise-flatness on overdamped motion of Brownian particles in a 1D periodic system with a simple sawtooth potential subjected to both unbiased thermal noise and three-level telegraph noise is considered. The exact formula for the stationary probability flux (current) is presented. The phenomenon of multiple current reversals and some topological properties of the hypersurface of zero current in the parameter space of noises are investigated and illustrated by phase diagrams. The conditions for the existence of four current reversals versus the switching rate of nonequilibrium noise are given. An alternative interpretation of the results in terms of cross-correlation between two dichotomous noises is presented.     

Jamming and crystallization in athermal polymer packings

Dense packings of chains of hard spheres possess characteristic features that do not have a counterpart in corresponding packings of monomeric spheres especially near the maximally random jammed (MRJ) state. From the modelling perspective the additional requirement that spheres keep their connectivity while maximizing the occupied volume fraction imposes severe constraints on generation algorithms of dense chain configurations. The extremely sluggish dynamics imposed by the uncrossability of chains precludes the use of deterministic or stochastic dynamics to generate all but dilute polymer packings. As a viable alternative, especially tailored chain-connectivity-altering Monte Carlo (MC) algorithms have been developed that bypass this kinetic hindrance and have actually been able to produce packings of hard-sphere chains in a volume fraction range spanning from infinite dilution up to the MRJ state. Such very dense athermal polymer packings share a number of structural features with packings of monomeric hard spheres, but also display unique characteristics due to the constraints imposed by connectivity. We give an overview of the most relevant results of our recent modeling work on packings of freely-jointed chains of tangent hard spheres about the MRJ state, local structure, chain dimensions and their scaling with density, topological constraints in the form of entanglements and knots, contact network at jamming, and entropically driven crystallization.     

On the finite size corrections to some random matching problems

We get back to the computation of the leading finite size corrections to some random link matching problems, first adressed by Mézard and Parisi [J. Phys. France 48, 1451 (1987)]. In the so-called bipartite case, their result is in contradiction with subsequent works. We show that they made some mistakes, and correcting them, we get the expected result. In the non bipartite case, we agree with their result but push the analytical treatment further. Received 28 April 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: giorgio.parisi@roma1.infn.it RID="b" ID="b"e-mail: matthieu.ratieville@roma1.infn.it     

Parrondo Games as Lattice Gas Automata

Parrondo games are coin flipping games with the surprising property that alternating plays of two losing games can produce a winning game. We show that this phenomenon can be modelled by probabilistic lattice gas automata. Furthermore, motivated by the recent introduction of quantum coin flipping games, we show that quantum lattice gas automata provide an interesting definition for quantum Parrondo games.     

Unitary Correlations and the Fejér Kernel

Let M be a unitary matrix with eigenvalues t _j , and let f be a function on the unit circle. Define X _f (M)=f(t _j ). We derive exact and asymptotic formulae for the covariance of X _f and X _g with respect to the measures |(M)|²dM where dM is Haar measure and an irreducible character. The asymptotic results include an analysis of the Fejér kernel which may be of independent interest.     

Analyticity of the density of states in the anderson model on the Bethe lattice

Let H=1/2+V on l²(B), whereB is the Bethe lattice andV(x),x B, are i.i.d.r.v.'s with common probability distribution. It is shown that for distributions sufficiently close to the Cauchy distribution, the density of states(E) is analytic in a strip about the real axis.     

Fractal porous media III: Transversal Stokes flow through random and Sierpinski carpets

The transversal Stokes flow of a Newtonian fluid through random and Sierpinski carpets is numerically calculated and the transversal permeability derived. In random carpets derived from site percolation, the average macroscopic permeability varies as (- _c)^3/2, close to the critical porosity _c. This exponent is found to be slightly different from the conductivity exponent. Results for Sierpinski carpets are presented up to the fourth generation. The Carman equation is not verified in these two model porous media.     

Image segmentation using adaptive loopy belief propagation

Loopy belief propagation (LBP) algorithm over pairwise-connected Markov random fields (MRFs) has become widely used for low-level vision problems. However, Pairwise MRF is often insufficient to capture the statistics of natural images well, and LBP is still extremely slow for application on an MRF with large discrete label space. To solve these problems, the present study proposes a new segmentation algorithm based on adaptive LBP. The proposed algorithm utilizes local region information to construct a local region model, as well as a local interaction region MRF model for image segmentation. The adaptive LBP algorithm maximizes the global probability of the proposed MRF model, which employs two very important strategies, namely, “message self-convergence” and “adaptive label pruning”. Message self-convergence can improve the reliability of a pixel in choosing a label in local region, and label pruning can dismiss impossible labels for every pixel. Thus, the most reliable information messages transfer through the LBP algorithm. The experimental results show that the proposed algorithm not only obtains more accurate segmentation results but also greater speed.     

The dynamics of defect ensembles in one-dimensional cellular automata

We investigate the dynamics of ensembles of diffusive defects in one-dimensional deterministic cellular automata. The work builds on earlier results on individual random walks in cellular automata. Here we give a natural condition guaranteeing diffusive behavior also in the presence of other defects. Simple branching and birth mechanisms are introduced and prototype classes of cellular automata exhibiting weakly interacting walks capable of annihilation and coalescence are studied. Their equilibrium behavior is also characterized. The design principles of cellular automata with desired diffusive interaction properties become transparent from this analysis.     

Critical comparison of several order-book models for stock-market fluctuations

Far-from-equilibrium models of interacting particles in one dimension are used as a basis for modelling the stock-market fluctuations. Particle types and their positions are interpreted as buy and sel orders placed on a price axis in the order book. We revisit some modifications of well-known models, starting with the Bak-Paczuski-Shubik model. We look at the four decades old Stigler model and investigate its variants. One of them is the simplified version of the Genoa artificial market. The list of studied models is completed by the models of Maslov and Daniels et al. Generically, in all cases we compare the return distribution, absolute return autocorrelation and the value of the Hurst exponent. It turns out that none of the models reproduces satisfactorily all the empirical data, but the most promising candidates for further development are the Genoa artificial market and the Maslov model with moderate order evaporation.