A Simplification of Combinatorial Link Floer Homology

We define a new combinatorial complex computing the hat version of link Floer homology over Z/2Z, which turns out to be significantly smaller than the Manolescu-Ozsvath-Sarkar one.Comment: 20 pages with figures, final version printed in JKTR, v.3 of Oberwolfach Proceeding

Search for universality in one-dimensional ballistic annihilation kinetics

We study the kinetics of ballistic annihilation for a one-dimensional ideal gas with continuous velocity distribution. A dynamical scaling theory for the long time behavior of the system is derived. Its validity is supported by extensive numerical simulations for several velocity distributions. This leads us to the conjecture that all the continuous velocity distributions \phi(v) which are symmetric, regular and such that \phi(0) does not vanish, are attracted in the long time regime towards the same Gaussian distribution and thus belong to the same universality class. Moreover, it is found that the particle density decays as n(t)~t^{-\alpha}, with \alpha=0.785 +/- 0.005.Comment: 8 pages, needs multicol, epsf and revtex. 8 postscript figures included. Submitted to Phys. Rev. E. Also avaiable at http://mykonos.unige.ch/~rey/publi.html#Secon

Kinetics of ballistic annihilation and branching

We consider a one-dimensional model consisting of an assembly of two-velocity particles moving freely between collisions. When two particles meet, they instantaneously annihilate each other and disappear from the system. Moreover each moving particle can spontaneously generate an offspring having the same velocity as its mother with probability 1-q. This model is solved analytically in mean-field approximation and studied by numerical simulations. It is found that for q=1/2 the system exhibits a dynamical phase transition. For q<1/2, the slow dynamics of the system is governed by the coarsening of clusters of particles having the same velocities, while for q>1/2 the system relaxes rapidly towards its stationary state characterized by a distribution of small cluster sizes.Comment: 10 pages, 11 figures, uses multicol, epic, eepic and eepicemu. Also avaiable at http://mykonos.unige.ch/~rey/pubt.htm

Direct Interactions in Relativistic Statistical Mechanics

Directly interacting particles are considered in the multitime formalism of predictive relativistic mechanics. When the equations of motion leave a phase-space volume invariant, it turns out that the phase average of any first integral, covariantly defined as a flux across a $7n$-dimensional surface, is conserved. The Hamiltonian case is discussed, a class of simple models is exhibited, and a tentative definition of equilibrium is proposed.Comment: Plain Tex file, 26 page

Probabilistic ballistic annihilation with continuous velocity distributions

We investigate the problem of ballistically controlled reactions where particles either annihilate upon collision with probability $p$, or undergo an elastic shock with probability $1-p$. Restricting to homogeneous systems, we provide in the scaling regime that emerges in the long time limit, analytical expressions for the exponents describing the time decay of the density and the root-mean-square velocity, as continuous functions of the probability $p$ and of a parameter related to the dissipation of energy. We work at the level of molecular chaos (non-linear Boltzmann equation), and using a systematic Sonine polynomials expansion of the velocity distribution, we obtain in arbitrary dimension the first non-Gaussian correction and the corresponding expressions for the decay exponents. We implement Monte-Carlo simulations in two dimensions, that are in excellent agreement with our analytical predictions. For $p<1$, numerical simulations lead to conjecture that unlike for pure annihilation ($p=1$), the velocity distribution becomes universal, i.e. does not depend on the initial conditions.Comment: 10 pages, 9 eps figures include

Front localization in a ballistic annihilation model

We study the possibility of localization of the front present in a one-dimensional ballistically-controlled annihilation model in which the two annihilating species are initially spatially separated. We construct two different classes of initial conditions, for which the front remains localized.Comment: Using elsart (Elsevier Latex macro) and epsf. 12 Pages, 2 epsf figures. Submitted to Physica

Multimodel Inference and Multimodel Averaging in Empirical Modeling of Occupational Exposure Levels

Empirical modeling of exposure levels has been popular for identifying exposure determinants in occupational hygiene. Traditional data-driven methods used to choose a model on which to base inferences have typically not accounted for the uncertainty linked to the process of selecting the final model. Several new approaches propose making statistical inferences from a set of plausible models rather than from a single model regarded as best. This paper introduces the multimodel averaging approach described in the monograph by Burnham and Anderson. In their approach, a set of plausible models are defined a priori by taking into account the sample size and previous knowledge of variables influent on exposure levels. The Akaike information criterion is then calculated to evaluate the relative support of the data for each model, expressed as Akaike weight, to be interpreted as the probability of the model being the best approximating model given the model set. The model weights can then be used to rank models, quantify the evidence favoring one over another, perform multimodel prediction, estimate the relative influence of the potential predictors and estimate multimodel-averaged effects of determinants. The whole approach is illustrated with the analysis of a data set of 1500 volatile organic compound exposure levels collected by the Institute for work and health (Lausanne, Switzerland) over 20 years, each concentration having been divided by the relevant Swiss occupational exposure limit and log-transformed before analysis. Multimodel inference represents a promising procedure for modeling exposure levels that incorporates the notion that several models can be supported by the data and permits to evaluate to a certain extent model selection uncertainty, which is seldom mentioned in current practic

Liesegang patterns : Studies on the width law

The so-called "width law" for Liesegang patterns, which states that the positions x_n and widths w_n of bands verify the relation x_n \sim w_n^{\alpha} for some \alpha>0, is investigated both experimentally and theoretically. We provide experimental data exhibiting good evidence for values of \alpha close to 1. The value \alpha=1 is supported by theoretical arguments based on a generic model of reaction-diffusion.Comment: 7 pages, RevTeX, two columns, 5 figure

Motion of influential players can support cooperation in Prisoner's Dilemma

We study a spatial Prisoner's dilemma game with two types (A and B) of players located on a square lattice. Players following either cooperator or defector strategies play Prisoner's Dilemma games with their 24 nearest neighbors. The players are allowed to adopt one of their neighbor's strategy with a probability dependent on the payoff difference and type of the given neighbor. Players A and B have different efficiency in the transfer of their own strategies; therefore the strategy adoption probability is reduced by a multiplicative factor (w < 1) from the players of type B. We report that the motion of the influential payers (type A) can improve remarkably the maintenance of cooperation even for their low densitie

Entropy-based characterizations of the observable-dependence of the fluctuation-dissipation temperature

The definition of a nonequilibrium temperature through generalized fluctuation-dissipation relations relies on the independence of the fluctuation-dissipation temperature from the observable considered. We argue that this observable independence is deeply related to the uniformity of the phase-space probability distribution on the hypersurfaces of constant energy. This property is shown explicitly on three different stochastic models, where observable-dependence of the fluctuation-dissipation temperature arises only when the uniformity of the phase-space distribution is broken. The first model is an energy transport model on a ring, with biased local transfer rules. In the second model, defined on a fully connected geometry, energy is exchanged with two heat baths at different temperatures, breaking the uniformity of the phase-space distribution. Finally, in the last model, the system is connected to a zero temperature reservoir, and preserves the uniformity of the phase-space distribution in the relaxation regime, leading to an observable-independent temperature.Comment: 15 pages, 7 figure