5 research outputs found
Gibbs Measures on Attractors in Biological Neural Networks
Projet MEVALWe consider a class of nonreversible processes with a local interaction as a model of biological neural networks. We study the structure of equilibrium measures on attractors. There exist first and second order phase transitions with respect to the grey level parameter
A General Formalism for Inhomogeneous Random Graphs
We present and investigate an extension of the classical random graph to a
general class of inhomogeneous random graph models, where vertices come in
different types, and the probability of realizing an edge depends on the types
of its terminal vertices. This approach provides a general framework for the
analysis of a large class of models. The generic phase structure is derived
using generating function techniques, and relations to other classes of models
are pointed out.Comment: 7 pages, no figures. To appear in Phys. Rev.
Properties of Random Graphs with Hidden Color
We investigate in some detail a recently suggested general class of ensembles
of sparse undirected random graphs based on a hidden stub-coloring, with or
without the restriction to nondegenerate graphs. The calculability of local and
global structural properties of graphs from the resulting ensembles is
demonstrated. Cluster size statistics are derived with generating function
techniques, yielding a well-defined percolation threshold. Explicit rules are
derived for the enumeration of small subgraphs. Duality and redundancy is
discussed, and subclasses corresponding to commonly studied models are
identified.Comment: 14 pages, LaTeX, no figure
Gibbs Measures on Attractors in Biological Neural Networks
: We consider a class of nonreversible processes with a local interaction as a model of biological neural networks. We study the structure of equilibrium measures on attractors. There exist first and second order phase transitions with respect to the grey level parameter. Key-words: neural networks, attractor, phase transitions, grey level, cerebellar cortex. (R'esum'e : tsvp) Postal address: University of Lund, Department of Mathematical Statistics, Box 118, S-221 00 Lund, Sweden Unite de recherche INRIA Rocquencourt Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France) Telephone : (33) 01 39 63 55 11 -- Telecopie : (33) 01 39 63 53 Mesures de Gibbs sur les Attracteurs dans les R'eseaux de Neurones Biologiques. R'esum'e : On consid`ere des processus stochastiques non reversibles `a interaction locale comme un mod`ele de reseaux de neurones biologiques. Mots-cl'e : r'eseaux de neurones, transition de phase, attracteur. Gibbs Measures on Attractors in Biolo..
Gibbs measures on attractors in biological neural networks
Theme 1 - Reseaux et systemes. Projet MevalAvailable from INIST (FR), Document Supply Service, under shelf-number : 14802 E, issue : a.1997 n.3189 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueSIGLEFRFranc