Search Advanced

Mathematical Biosciences and Engineering

2014, Volume 11, Issue 2: 217-231. doi: 10.3934/mbe.2014.11.217
Previous Article Next Article

On a spike train probability model with interacting neural units

  • 1.
    Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II, 132, I-84084 Fisciano (SA)
  • 2.
    Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, I-80126 Napoli
  • 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

    Related Papers:

    [1] Hideaki Kim, Shigeru Shinomoto . Estimating nonstationary inputs from a single spike train based on a neuron model with adaptation. Mathematical Biosciences and Engineering, 2014, 11(1): 49-62. doi: 10.3934/mbe.2014.11.49
    [2] Aniello Buonocore, Luigia Caputo, Enrica Pirozzi, Maria Francesca Carfora . Gauss-diffusion processes for modeling the dynamics of a couple of interacting neurons. Mathematical Biosciences and Engineering, 2014, 11(2): 189-201. doi: 10.3934/mbe.2014.11.189
    [3] Nikita Ratanov . A two-state neuronal model with alternating exponential excitation. Mathematical Biosciences and Engineering, 2019, 16(5): 3411-3434. doi: 10.3934/mbe.2019171
    [4] Achilleas Koutsou, Jacob Kanev, Maria Economidou, Chris Christodoulou . Integrator or coincidence detector --- what shapes the relation of stimulus synchrony and the operational mode of a neuron?. Mathematical Biosciences and Engineering, 2016, 13(3): 521-535. doi: 10.3934/mbe.2016005
    [5] Aldana M. González Montoro, Ricardo Cao, Christel Faes, Geert Molenberghs, Nelson Espinosa, Javier Cudeiro, Jorge Mariño . Cross nearest-spike interval based method to measure synchrony dynamics. Mathematical Biosciences and Engineering, 2014, 11(1): 27-48. doi: 10.3934/mbe.2014.11.27
    [6] Aniello Buonocore, Luigia Caputo, Enrica Pirozzi, Maria Francesca Carfora . A leaky integrate-and-fire model with adaptation for the generation of a spike train. Mathematical Biosciences and Engineering, 2016, 13(3): 483-493. doi: 10.3934/mbe.2016002
    [7] Kyle Wendling, Cheng Ly . Firing rate distributions in a feedforward network of neural oscillators with intrinsic and network heterogeneity. Mathematical Biosciences and Engineering, 2019, 16(4): 2023-2048. doi: 10.3934/mbe.2019099
    [8] Virginia Giorno, Serena Spina . On the return process with refractoriness for a non-homogeneous Ornstein-Uhlenbeck neuronal model. Mathematical Biosciences and Engineering, 2014, 11(2): 285-302. doi: 10.3934/mbe.2014.11.285
    [9] Shinsuke Koyama, Lubomir Kostal . The effect of interspike interval statistics on the information gainunder the rate coding hypothesis. Mathematical Biosciences and Engineering, 2014, 11(1): 63-80. doi: 10.3934/mbe.2014.11.63
    [10] Kseniia Kravchuk, Alexander Vidybida . Non-Markovian spiking statistics of a neuron with delayed feedback in presence of refractoriness. Mathematical Biosciences and Engineering, 2014, 11(1): 81-104. doi: 10.3934/mbe.2014.11.81
  • 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.
  • Reader Comments
  • © 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)
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
Mathematical Biosciences and Engineering
4.4

Metrics

Article views(2262) PDF downloads(471) Cited by(0)

Preview PDF
Download XML
Export Citation
Article outline
Abstract
References

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog