In this paper we extend replica bounds and free energy subadditivity arguments to diluted spin-glass models on graphs with arbitrary, non-Poissonian degree distribution. The new difficulties specific… (More)

The state-of-the-art error correcting codes are based on large random constructions (random graphs, random permutations, . . . ) and are decoded by linear-time iterative algorithms. Because of these… (More)

We introduce and discuss a minimal individual-based model for influenza dynamics. The model takes into account the effects of specific immunization against viral strains, but also infectivity… (More)

In this paper we develop further a metl~od recently introduced by one of us to study metastable states in spm glasses. We consider a 'potential function', defined as the

We consider the quasispecies description of a population evolving in both the “master sequence” landscape (where a single sequence is evolutionarily preferred over all others) and the REM landscape… (More)

We study a finite-range spin-glass model in arbitrary dimension, where the intensity of the coupling between spins decays to zero over some distance γ−1. We prove that, under a positivity condition… (More)

In this note we study the dynamics of a model recently introduced by one of us, that displays glassy phenomena in absence of energy barriers. Using an adiabatic hypothesis we derive an equation for… (More)

We discuss the response of aging systems with short-range interactions to a class of random perturbations. Although these systems are out of equilibrium, the limit value of the free energy at long… (More)

A localized method to distribute paths on random graphs is devised, aimed at finding the shortest paths between given source/destination pairs while avoiding path overlaps at nodes. We propose a… (More)

We introduce a Random Energy Model on a hierarchical lattice where the interaction strength between variables is a decreasing function of their mutual hierarchical distance, making it a nonmean field… (More)