Structural phase transitions in neural networks

  • 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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    [1] Studies of Brain Function, Springer-Verlag, Berlin-Heidelberg-New York, 1982.
    [2] First edition, Cambridge University Press, Cambridge, 1991.
    [3] J. Neurosci., 30 (2010), 11232-11245.
    [4] Network, 6 (1995), 179-224.
    [5] Front. Comput. Neurosci., 4 (2010), 132.
    [6] Neuron., 65 (2010), 563-576.
    [7] Academic Press, New York-San Francisco-London, 1975.
    [8] Die Grundlehren der Mathematischen Wissenschaften, Bd. 119, Springer-Verlag, Berlin; Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963.
    [9] Nature, 419 (2002), 65-70.
    [10] Network, 7 (1996), 357-363.
    [11] Int. J. Neural Syst., 18 (2008), 267-277.
    [12] Biosystems, 89 (2007), 287-293.
    [13] Annals of Applied Probability, 22 (2012), 1989-2047.
    [14] Biol. Cybernet., 92 (2005), 367-379.
    [15] Frontiers in Computational Neuroscience, 4 (2011).
    [16] J. Neurosci., 25 (2005), 1952-1964.
    [17] Science, 319 (2008), 1543-1546.
    [18] Trends in Neurosciences, 27 (2004), 744-750.
    [19] J. Neurophysiol., 79 (1998), 2857-2874.
    [20] Complexity, 10 (2005), 42-50.
    [21] Progress in Neurobiology, 95 (2011), 448-490.
    [22] Oxford University Press, Oxford, 2008.
    [23] J. Comput. Neurosci., 34 (2012), 185-209.
    [24] Brain Research, 1434 (2012), 277-284.
    [25] BioSystems, 89 (2007), 280-286.
    [26] Proc. Natl. Acad. Sci. U.S.A., 96 (1999), 1106-1111.
    [27] Frontiers in computational Neuroscience, 6 (2012).
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