We review critically the concepts and the applications of Cayley Trees and Bethe Lattices in
statistical mechanics in a tentative effort to remove widespread misuse of these simple, but …

We present a fascinating model that has lately caught attention among physicists working in
complexity related fields. Though it originated from mathematics and later from economics …

We study the satisfiability of random Boolean expressions built from many clauses with K
variables per clause (K-satisfiability). Expressions with a ratio α of clauses to variables less …

In this note we explain the use of the cavity method directly at zero temperature, in the case
of the spin glass on a lattice with a local tree like structure, which is the proper generalization …

We show that discrete synaptic weights can be efficiently used for learning in large scale
neural systems, and lead to unanticipated computational performance. We focus on the …

We derive analytical solutions for p-spin models with finite connectivity at zero temperature.
These models are the statistical mechanics equivalent of p-XORSAT problems in theoretical …

Much of human knowledge sits in large databases of unstructured text. Leveraging this
knowledge requires algorithms that extract and record metadata on unstructured text …

The problem of controllability of the dynamical state of a network is central in network theory
and has wide applications ranging from network medicine to financial markets. The driver …

In this paper we generalize to the case of diluted spin models and random combinatorial
optimization problems a technique recently introduced by Guerra (cond-mat/0205123) to …

These lecture notes can be read in two ways. The first two sections contain a review of the
phenomenology of several physical systems with slow nonequilibrium dynamics. In the …