Mathematical Biosciences and Engineering, 2014, 11(1): 139-148. doi: 10.3934/mbe.2014.11.139.

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

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Structural phase transitions in neural networks

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

   

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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Keywords bootstrap percolation; neural networks.; Integrate-and-fire neurons; random graphs

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

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This article has been cited by

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

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Copyright Info: 2014, Tatyana S. Turova, licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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