On a spike train probability model with interacting neural units

  • Received: 01 October 2012 Accepted: 29 June 2018 Published: 01 October 2013
  • MSC : Primary: 60J28, 92B20; Secondary: 60K20.

  • We investigate an extension of the spike train stochastic model based on the conditionalintensity, in which the recovery function includes an interaction between several excitatoryneural units. Such function is proposed as depending both on the time elapsed since thelast spike and on the last spiking unit. Our approach, being somewhat related to thecompeting risks model, allows to obtain the general form of the interspike distribution andof the probability of consecutive spikes from the same unit. Various results are finally presentedin the two cases when the free firing rate function (i) is constant, and (ii) has a sinusoidal form.

    Citation: Antonio Di Crescenzo, Maria Longobardi, Barbara Martinucci. On a spike train probability model with interacting neural units[J]. Mathematical Biosciences and Engineering, 2014, 11(2): 217-231. doi: 10.3934/mbe.2014.11.217

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  • We investigate an extension of the spike train stochastic model based on the conditionalintensity, in which the recovery function includes an interaction between several excitatoryneural units. Such function is proposed as depending both on the time elapsed since thelast spike and on the last spiking unit. Our approach, being somewhat related to thecompeting risks model, allows to obtain the general form of the interspike distribution andof the probability of consecutive spikes from the same unit. Various results are finally presentedin the two cases when the free firing rate function (i) is constant, and (ii) has a sinusoidal form.


    [1] Cerebral Cortex, 7 (1997), 237-252.
    [2] Biosystems, 71 (2003), 23-28.
    [3] Neural Computation, 6 (1994), 622-641.
    [4] Sci. Math. Japon., 70 (2009), 159-174.
    [5] Sci. Math. Japon., 58 (2003), 245-254.
    [6] J. Neurosci., 18 (1998), 2200-2211.
    [7] Biol. Cybern., 95 (2006), 1-19.
    [8] Biol. Cybern., 95 (2006), 97-112.
    [9] Ann. Stat., 35 (2007), 2691-2722.
    [10] Chapman & Hall/CRC, Boca Raton, 2001.
    [11] BMC Neuroscience, 10 (2009), P110.
    [12] BioSystems, 58 (2000), 19-26.
    [13] J. Math. Biol., 42 (2001), 1-25.
    [14] Stat. Prob. Lett., 78 (2008), 2248-2257.
    [15] in Cybernetics and Systems 2010 (ed. R. Trappl), Austrian Society for Cybernetic Studies, Vienna, 2010, 169-174.
    [16] J. Stat. Plann. Infer., 136 (2006), 1638-1654.
    [17] Sci. Math. Japon., 67 (2008), 125-135.
    [18] in Cybernetics and Systems 2004 (ed. R. Trappl), Austrian Society for Cybernetic Studies, Vienna, 2004, 205-210.
    [19] Biophy. J., 4 (1964), 41-68.
    [20] J. Neurosci. Meth., 171 (2008), 288-295.
    [21] J. Comput. Neurosci., 3 (1996), 275-299.
    [22] J. Acoust. Soc. Am., 74 (1983), 493-501.
    [23] Neural Comput., 13 (2001), 1713-1720.
    [24] PLoS ONE, 2 (2007), e439.
    [25] J. Acoust. Soc. Am., 77 (1985), 1452-1464.
    [26] Neural Comput., 20 (2008), 2696-2714.
    [27] Notes taken by Charles E. Smith, Lecture Notes in Biomathematics, Vol. 14, Springer-Verlag, Berlin-New York, 1977.
    [28] in Imagination and Rigor. Essays on Eduardo R. Caianiello's Scientific Heritage (ed. S. Termini), Springer-Verlag Italia, 2006, 133-145.
    [29] in Structure: from Physics to General Systems - Festschrift Volume in Honour of E.R. Caianiello on his Seventieth Birthday (eds. M. Marinaro and G. Scarpetta), World Scientific, Singapore, 1992, 78-94.
    [30] Math. Japon., 50 (1999), 247-322.
    [31] The Journal of Neuroscience, 13 (1993), 334-350.
    [32] Biophys. J., 5 (1965), 173-194.
    [33] J. Stat. Phys., 78 (1995), 917-935.
    [34] Phys. Rev. E (3), 59 (1999), 956-969.
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