In this paper we give an overview of a recently developed theory 1, 22 which allows for calculating nite size corrections to the dynamical equations describing the dynamics of separable Neural Networks , away from saturation. According to this theory, nite size eeects are described by a linear-noise Fokker Planck equation for the uctua-tions corresponding… (More)
A simple model of coupled dynamics of fast neurons and slow interactions , modelling self-organization in recurrent neural networks, leads naturally to an effective statistical mechanics characterized by a partition function which is an average over a replicated system. This is reminiscent of the replica trick used to study spin-glasses, but with the… (More)
We apply our recently developed information-theoretic measures for the characterisation and comparison of protein-protein interaction networks. These measures are used to quantify topological network features via macroscopic statistical properties. Network differences are assessed based on these macroscopic properties as opposed to microscopic overlap,… (More)
There is currently great interest in determining physical parameters, e.g. fluorescence lifetime, of individual molecules that inform on environmental conditions, whilst avoiding the artefacts of ensemble averaging. Protein interactions, molecular dynamics and sub-species can all be studied. In a burst integrated fluorescence lifetime (BIFL) experiment,… (More)
We study the dynamics of supervised learning in layered neural networks , in the regime where the size p of the training set is proportional to the number N of inputs. Here the local fields are no longer described by Gaussian distributions. We use dynamical replica theory to predict the evolution of macroscopic observables, including the relevant error… (More)
We describe the application of tools from statistical mechanics to analyse the dynamics of various classes of supervised learning rules in perceptrons. The character of this paper is mostly that of a cross between a biased non-encyclopedic review and lecture notes: we try to present a coherent and self-contained picture of the basics of this field, to… (More)
We generate new mathematical tools with which to quantify the macroscopic topological structure of large directed networks. This is achieved via a statistical mechanical analysis of constrained maximum entropy ensembles of directed random graphs with prescribed joint distributions for in-and out-degrees and prescribed degree-degree correlation functions. We… (More)
We describe the use of modern analytical techniques in solving the dynamics of symmetric and nonsymmetric recurrent neural networks near saturation. These explicitly take into account the correlations between the post-synaptic potentials, and thereby allow for a reliable prediction of transients.