This book contains a detailed and self-contained presentation of the replica theory of infinite range spin glasses. The authors also explain recent theoretical developments, paying particular… Expand

Abstract:So far the problem of a spin glass on a Bethe lattice has been solved only at the replica symmetric level, which is wrong in the spin glass phase. Because of some technical difficulties,… Expand

A class of optimization algorithms that can deal with the proliferation of metastable states are introduced; one such algorithm has been tested successfully on the largest existing benchmark of K-satisfiability.Expand

Abstract We investigate several statistical properties of the order book of three liquid stocks of the Paris Bourse. The results are to a large degree independent of the stock studied. The most… Expand

A new type of message passing algorithm which allows to find efficiently a satisfiable assignment of the variables in the difficult region and is iterative and composed of two main parts.Expand

This paper presents the probabilistic approach to reconstruction and discusses its optimality and robustness, and develops the asymptotic analysis of the corresponding phase diagrams with and without measurement noise.Expand

We introduce a simple model of economy, where the time evolution is described by an equation capturing both exchange between individuals and random speculative trading, in such a way that the… Expand

This book presents a unified approach to a rich and rapidly evolving research domain at the interface between statistical physics, theoretical computer science/discrete mathematics, and… Expand