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Mathematical Biosciences and Engineering

2016, Volume 13, Issue 3: 537-550. doi: 10.3934/mbe.2016006
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Fluctuation scaling in neural spike trains

  • 1.
    Department of Statistical Modeling, The Institute of Statistical Mathematics, 10-3 Midoricho, Tachikawa, Tokyo
  • 2.
    Principles of Informatics Research Division, National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo
  • Received: 01 March 2015 Accepted: 29 June 2018 Published: 01 January 2016

  • MSC : Primary: 92B20, 92C20; Secondary: 60K15.

  • Fluctuation scaling has been observed universally in a wide variety of phenomena. In time series that describe sequences of events, fluctuation scaling is expressed as power function relationships between the mean and variance of either inter-event intervals or counting statistics, depending on measurement variables. In this article, fluctuation scaling has been formulated for a series of events in which scaling laws in the inter-event intervals and counting statistics were related. We have considered the first-passage time of an Ornstein-Uhlenbeck process and used a conductance-based neuron model with excitatory and inhibitory synaptic inputs to demonstrate the emergence of fluctuation scaling with various exponents, depending on the input regimes and the ratio between excitation and inhibition. Furthermore, we have discussed the possible implication of these results in the context of neural coding.

    Citation: Shinsuke Koyama, Ryota Kobayashi. Fluctuation scaling in neural spike trains[J]. Mathematical Biosciences and Engineering, 2016, 13(3): 537-550. doi: 10.3934/mbe.2016006

    Related Papers:

  • Fluctuation scaling has been observed universally in a wide variety of phenomena. In time series that describe sequences of events, fluctuation scaling is expressed as power function relationships between the mean and variance of either inter-event intervals or counting statistics, depending on measurement variables. In this article, fluctuation scaling has been formulated for a series of events in which scaling laws in the inter-event intervals and counting statistics were related. We have considered the first-passage time of an Ornstein-Uhlenbeck process and used a conductance-based neuron model with excitatory and inhibitory synaptic inputs to demonstrate the emergence of fluctuation scaling with various exponents, depending on the input regimes and the ratio between excitation and inhibition. Furthermore, we have discussed the possible implication of these results in the context of neural coding.


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    [1] Dover, New York, 1965.
    [2] Nature, 333 (1988), 514-519.
    [3] Neuron, 62 (2009), 310-311.
    [4] Springer, New York, 1981.
    [5] Biol. Cybern., 85 (2001), 247-255.
    [6] Biol. Cybern., 95 (2006), 1-19.
    [7] Nat. Neurosci., 13 (2010), 369-378.
    [8] Neuron, 69 (2011), 818-831.
    [9] Nat. Neurosci., 15 (2012), 1472-1474.
    [10] Chapman and Hall, London, 1962.
    [11] Chapman and Hall, London, 1966.
    [12] Springer Series in Statistics, Springer-Verlag, New York, 1988.
    [13] Phys. Rev. Lett., 92 (2004), 028701.
    [14] in Methods in Neuronal Modeling (eds. C. Koch and I. Segev), MIT Press, Cambridge, MA, 1998, 1-26.
    [15] Phys. Rev. E., 71 (2005), 011907, 9pp.
    [16] Adv. Phys., 57 (2008), 89-142.
    [17] Phys. Rev. E, 81 (2010), 066112.
    [18] Biol. Cybern., 73 (1995), 209-221.
    [19] J. Comput. Neurosci., 3 (1996), 275-299.
    [20] in Selected Tables in Mathematical Statistics, 3, American Mathematical Society, 1975, 233-327.
    [21] J. Natl. Cancer Inst., 79 (1987), 1113-1115.
    [22] BMC Evol. Biol., 4 (2004), p3.
    [23] Biol. Cybern., 56 (1987), 19-26.
    [24] Neural Comput., 18 (2006), 634-659.
    [25] Neural Comput., 18 (2006), 1896-1931.
    [26] J. Appl. Probab., 22 (1985), 360-369.
    [27] J. Amer. Statist. Assoc., 83 (1988), 9-27.
    [28] J. Appl. Probab., 25 (1988), 43-57.
    [29] Neural Comput., 17 (2005), 923-947.
    [30] Bull. Math. Biophys., 31 (1969), 341-357.
    [31] J. Neurosci., 18 (1998), 3870-3896.
    [32] Phys. Rev., 81 (1951), 617-623.
    [33] John Wiley & Sons, Inc., New York, 1975.
    [34] Nature, 189 (1961), 732-735.
    [35] Exp. Brain Res., 41 (1981), 414-419.
    [36] Vis. Neurosci., 9 (1992), 535-553.
    [37] Cambridge University Press, New York, 1988.
    [38] 2nd edition, North-Holland, Amsterdam, 1992.
    [39] J. Theor. Biol., 257 (2009), 90-99.
    [40] J. Theoret. Neurobiol., 1 (1982), 197-218.
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  • © 2016 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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