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Mathematical Biosciences and Engineering

2014, Volume 11, Issue 1: 139-148. doi: 10.3934/mbe.2014.11.139
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Structural phase transitions in neural networks

  • 1.
    Mathematical Center, University of Lund, Box 118, Lund S-221 00
  • Published: 01 September 2013

  • MSC : Primary: 60K35, 82C32, 05C80; Secondary: 82B43.

  • A model is considered for a neural network that is a stochasticprocess on a random graph. The neurons are represented by``integrate-and-fire" processes. The structure of the graph isdetermined by the probabilities of the connections, and it depends on theactivity in the network. The dependence between theinitial level ofsparseness of the connections and thedynamics of activation in the network was investigated. A balanced regime was foundbetween activity, i.e., the level of excitation in the network, andinhibition, that allows formation of synfire chains.

    Citation: Tatyana S. Turova. Structural phase transitions in neural networks[J]. Mathematical Biosciences and Engineering, 2014, 11(1): 139-148. doi: 10.3934/mbe.2014.11.139

    Related Papers:

  • A model is considered for a neural network that is a stochasticprocess on a random graph. The neurons are represented by``integrate-and-fire" processes. The structure of the graph isdetermined by the probabilities of the connections, and it depends on theactivity in the network. The dependence between theinitial level ofsparseness of the connections and thedynamics of activation in the network was investigated. A balanced regime was foundbetween activity, i.e., the level of excitation in the network, andinhibition, that allows formation of synfire chains.


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  • © 2014 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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