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Use of an hourglass model in neuronal coding

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

M. Cottrell  and
T. S. Turova
M. Cottrell*
Affiliation:
Université Paris 1
T. S. Turova*
Affiliation:
University of Lund
*
∗Postal address: SAMOS, Université Paris 1, 90 rue de Tolbiac, F-75634 Paris Cedex 13, France
∗∗Postal address: Department of Mathematical Statistics, University of Lund, Box 118, S-221 00 Lund, Sweden. Email address: [email protected]
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Abstract

We study a system of interacting renewal processes which is a model for neuronal activity. We show that the system possesses an exponentially large number (with respect to the number of neurons in the network) of limiting configurations of the ‘firing neurons’. These we call patterns. Furthermore, under certain conditions of symmetry we find an algorithm to control limiting patterns by means of the connection parameters.

Keywords

Ergodicityhourglass modelstochastic neural network

MSC classification

Primary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 1 , March 2000 , pp. 168 - 186
Copyright
Copyright © 2000 by The Applied Probability Trust 

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