The combination of the compactness of networks, featuring small diameters, and their
complex architectures results in a variety of critical effects dramatically different from those in …

We review here some recent work in the field of quantum annealing, alias adiabatic
quantum computation. The idea of quantum annealing is to perform optimization by a …

For many random constraint satisfaction problems, by now there exist asymptotically tight
estimates of the largest constraint density for which solutions exist. At the same time, for …

We consider the problem of coloring the vertices of a large sparse random graph with a
given number of colors so that no adjacent vertices have the same color. Using the cavity …

We present a powerful experimental-computational technology for inferring network models
that predict the response of cells to perturbations, and that may be useful in the design of …

Using elementary rigorous methods we prove the existence of a clustered phase in the
random K-SAT problem, for K≥ 8. In this phase the solutions are grouped into clusters …

The cluster variation method (CVM) is a hierarchy of approximate variational techniques for
discrete (Ising-like) models in equilibrium statistical mechanics, improving on the mean-field …

Consider an information source generating a symbol at the root of a tree network whose
links correspond to noisy communication channels, and broadcasting it through the network …

We show that a message-passing process allows us to store in binary “material” synapses a
number of random patterns which almost saturate the information theoretic bounds. We …

Recent experimental studies indicate that synaptic changes induced by neuronal activity are
discrete jumps between a small number of stable states. Learning in systems with discrete …