We use the cavity method to study the parallel dynamics of disordered Ising models on a
graph. In particular, we derive a set of recursive equations in single-site probabilities of …

The entropy of a hierarchical network topology in an ensemble of sparse random networks,
with “hidden variables” associated with its nodes, is the log-likelihood that a given network …

Schelling's models of segregation, first described in 1969 (Am Econ Rev 59: 488–493, 1969)
are among the best known models of self-organising behaviour. Their original purpose was …

We analyse the equilibrium behaviour and non-equilibrium dynamics of sparse Boolean
networks with self-interactions that evolve according to synchronous Glauber dynamics …

Many real-world networks are directed, sparse, and hierarchical, with a mixture of
feedforward and feedback connections with respect to the hierarchy. Moreover, a small …

A fundamental question about brain function is why the connectivity in the cortex is diluted,
in that neurons in a local region of the neocortex and in the CA3 part of the hippocampal …

We study the stochastic parallel dynamics of Ising spin systems defined on finitely connected
directed random graphs with arbitrary degree distributions, using generating functional …

In this paper we investigate the equilibrium properties of bidirectional associative memories
(BAMs). Introduced by Kosko in 1988 as a generalization of the Hopfield model to a bipartite …

We use finite connectivity equilibrium replica theory to solve models of finitely connected unit-
length vectorial spins, with random pair-interactions which are of the orthogonal matrix type …

The connectivity of the cerebral cortex is diluted, with the probability of excitatory
connections between even nearby pyramidal cells rarely more than 0.1, and in the …