A simple algorithm to generate firing times for leaky integrate-and-fire neuronal model

  • Received: 01 December 2012 Accepted: 29 June 2018 Published: 01 September 2013
  • MSC : Primary: 60J60; Secondary: 60H35.

  • A method to generate first passage times for a class of stochastic processes is proposed. It does not require construction of the trajectories as usually needed in simulation studies, but is based on an integral equation whose unknown quantity is the probability density function of the studied first passage times and on the application of the hazard rate method. The proposed procedure is particularly efficient in the case of the Ornstein-Uhlenbeck process, which is important for modeling spiking neuronal activity.

    Citation: Aniello Buonocore, Luigia Caputo, Enrica Pirozzi, Maria Francesca Carfora. A simple algorithm to generate firing times for leaky integrate-and-fire neuronal model[J]. Mathematical Biosciences and Engineering, 2014, 11(1): 1-10. doi: 10.3934/mbe.2014.11.1

    Related Papers:

  • A method to generate first passage times for a class of stochastic processes is proposed. It does not require construction of the trajectories as usually needed in simulation studies, but is based on an integral equation whose unknown quantity is the probability density function of the studied first passage times and on the application of the hazard rate method. The proposed procedure is particularly efficient in the case of the Ornstein-Uhlenbeck process, which is important for modeling spiking neuronal activity.
    加载中
    [1] Advances in Applied Probability, 19 (1987), 784-800.
    [2] Biological Cybernetics, 95 (2006), 1-19.
    [3] Advances in Applied Probability, 33 (2001), 453-482.
    [4] Neural Computation, 23 (2011), 421-434.
    [5] Advances in Applied Probability, 21 (1989), 20-36.
    [6] Biosystems, 48 (1998), 77-83.
    [7] Communications in Statistics-Simulation and Computation, 28 (1999), 1135-1163.
    [8] Methodology and Computing in Applied Probability, 3 (2001), 215-231.
    [9] Journal of Applied Probability, 32 (1995), 635-648.
    [10] Applications of Mathematics (New York), 23, Springer-Verlag, Berlin, 1992.
    [11] Computers in Biology and Medicine, 24 (1994), 91-101.
    [12] Journal of Computational Neuroscience, 21 (2006), 211-223.
    [13] Journal of Applied Probability, 22 (1985), 360-369.
    [14] Journal of Mathematical Analysis and Applications, 54 (1976), 185-199.
    [15] Academic Press, Elsevier, 2007.
    [16] Neural Computation, 11 (1999), 935-951.
    [17] Journal of Statistical Physics, 140 (2010), 1130-1156.
    [18] Journal of Theoretical Biology, 83 (1980), 377-387.
    [19] Cambridge Studies in Mathematical Biology, 8, Cambridge University Press, Cambridge, 1988.

    © 2014 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)
  • Reader Comments
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(34) PDF downloads(408) Cited by(2)

Article outline

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog