Giorgio Parisi

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Numerical models indicate that collective animal behavior may emerge from simple local rules of interaction among the individuals. However, very little is known about the nature of such interaction, so that models and theories mostly rely on aprioristic assumptions. By reconstructing the three-dimensional positions of individual birds in airborne flocks of(More)
We study the satisfiability of random Boolean expressions built from many clauses with K variables per clause (K-satisfiability). Expressions with a ratio alpha of clauses to variables less than a threshold alphac are almost always satisfiable, whereas those with a ratio above this threshold are almost always unsatisfiable. We show the existence of an(More)
We propose a new global optimization method (Simulated Tempering) for simulating effectively a system with a rough free energy landscape (i.e. many coexisting states) at finite non-zero temperature. This method is related to simulated annealing, but here the temperature becomes a dynamic variable, and the system is always kept at equilibrium. We analyze the(More)
From bird flocks to fish schools, animal groups often seem to react to environmental perturbations as if of one mind. Most studies in collective animal behavior have aimed to understand how a globally ordered state may emerge from simple behavioral rules. Less effort has been devoted to understanding the origin of collective response, namely the way the(More)
In this note we put forward a conjecture on the average optimal length for bipartite matching with a finite number of elements where the different lengths are independent one from the others and have an exponential distribution. The problem of random bipartite matching (or assignment) is interesting both from the point of view of optimisation theory and of(More)
This is the second paper of a series of two about the structural properties that influence the asymptotic dynamics of Random Boolean Networks. Here we study the functionally independent clusters in which the relevant elements, introduced and studied in our first paper [3], are subdivided. We show that the phase transition in Random Boolean Networks can also(More)
In this note I present a simple model for the idiotypic network among antibodies and study its relevance for the maintenance of immunological memory; in particular, the memory capacity of such a model is studied. Some of the similarities with the spin glass model and with neural networks are discussed.