Biomedical subjects

A C C Coolen

Publications and source records attributed to A C C Coolen.

3 recordsLinked to original sources

PubMed2005

Dynamical replica analysis of disordered Ising spin systems on finitely connected random graphs.

We study the dynamics of macroscopic observables such as the magnetization and the energy per degree of freedom in Ising spin models on random graphs of finite connectivity, with random bonds and/or heterogeneous degree distributions. To do so, we generalize existing versions of dynamical replica theory and cavity field techniques to systems with strongly disordered and locally treelike interactions. We illustrate our results via application to, e.g., +/-J spin glasses on random graphs and of the overlap in finite connectivity Sourlas codes. All results are tested against Monte Carlo simulations.

Journal Article↗

PubMed2003

Statistical mechanics beyond the Hopfield model: solvable problems in neural network theory.

We present four 'case study' examples of solvable problems in the theory of recurrent neural networks, which are relevant to our understanding of information processing in the brain, but which are also interesting from a purely statistical mechanical point of view, even at the level of simple models (which helps in stimulating interdisciplinary work). The examples concern issues in network dynamics, network connectivity, spike timing and synaptic plasticity.

Action Potentials↗

PubMed2001

Dynamics of the batch minority game with inhomogeneous decision noise.

We study the dynamics of a version of the batch minority game, with random external information and with different types of inhomogeneous decision noise (additive and multiplicative), using generating functional techniques à la De Dominicis. The control parameters in this model are the ratio alpha=p/N of the number p of possible values for the external information over the number N of trading agents, and the statistical properties of the agents' decision noise parameters. The presence of decision noise is found to have the general effect of damping macroscopic oscillations, which explains why in certain parameter regions it can effectively reduce the market volatility, as observed in earlier studies. In the limit N-->infinity we (i) solve the first few time steps of the dynamics (for any alpha), (ii) calculate the location alpha(c) of the phase transition (signaling the onset of anomalous response), and (iii) solve the statics for alpha>alpha(c). We find that alpha(c) is not sensitive to additive decision noise, but we arrive at nontrivial phase diagrams in the case of multiplicative noise. Our theoretical results find excellent confirmation in numerical simulations.

Journal Article↗