Structural phase transitions in  neural networks

Tatyana S. Turova

doi:10.3934/mbe.2014.11.139

Article Contents

2014, Volume 11, Issue 1: 139-148. Doi: 10.3934/mbe.2014.11.139

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Structural phase transitions in neural networks

Tatyana S. Turova^1,

1.
Mathematical Center, University of Lund, Box 118, Lund S-221 00

Received: December 31, 2012

Revised: May 31, 2013

Published: August 2013

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Abstract

A model is considered for a neural network that is a stochastic process on a random graph. The neurons are represented by ``integrate-and-fire" processes. The structure of the graph is determined by the probabilities of the connections, and it depends on the activity in the network. The dependence between the initial level of sparseness of the connections and the dynamics of activation in the network was investigated. A balanced regime was found between activity, i.e., the level of excitation in the network, and inhibition, that allows formation of synfire chains.

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Mathematics Subject Classification: Primary: 60K35, 82C32, 05C80; Secondary: 82B43.

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