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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
  • Received: 01 January 2013 Accepted: 29 June 2018 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

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  • 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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  • This article has been cited by:

    1. Jérémie Cabessa, Alessandro E. P. Villa, 2015, Chapter 1, 978-3-319-09902-6, 1, 10.1007/978-3-319-09903-3_1
    2. Fioralba Ajazi, George M. Napolitano, Tatyana Turova, Izbassar Zaurbek, Structure of a randomly grown 2-d network, 2015, 136, 03032647, 105, 10.1016/j.biosystems.2015.09.002
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