Loading [Contrib]/a11y/accessibility-menu.js
Search Advanced

Mathematical Biosciences and Engineering

2016, Volume 13, Issue 3: 597-611. doi: 10.3934/mbe.2016010
Previous Article Next Article

A new firing paradigm for integrate and fire stochastic neuronal models

  • 1.
    Department of Mathematics "G. Peano", University of Torino, Via Carlo Alberto 10, 10123 Torino
  • 2.
    Department of Mathematics G. Peano, University of Torino, Via Carlo Alberto 10, 10123 - Torino
  • Received: 01 May 2015 Accepted: 29 June 2018 Published: 01 January 2016

  • MSC : 60J99, 92Bxx.

  • A new definition of firing time is given in the framework of Integrate and Fire neuronal models. The classical absorption condition at the threshold is relaxed and the firing time is defined as the first time the membrane potential process lies above a fixed depolarisation level for a sufficiently long time. The mathematical properties of the new firing time are investigated both for the Perfect Integrator and the Leaky Integrator. In the latter case, a simulation study is presented to complete the analysis where analytical results are not yet achieved.

    Citation: Roberta Sirovich, Luisa Testa. A new firing paradigm for integrate and fire stochastic neuronal models[J]. Mathematical Biosciences and Engineering, 2016, 13(3): 597-611. doi: 10.3934/mbe.2016010

    Related Papers:

    [1] 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
    [2] Aniello Buonocore, Luigia Caputo, Enrica Pirozzi, Maria Francesca Carfora . A simple algorithm to generate firing times for leaky integrate-and-fire neuronal model. Mathematical Biosciences and Engineering, 2014, 11(1): 1-10. doi: 10.3934/mbe.2014.11.1
    [3] Jakub Cupera . Diffusion approximation of neuronal models revisited. Mathematical Biosciences and Engineering, 2014, 11(1): 11-25. doi: 10.3934/mbe.2014.11.11
    [4] 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
    [5] 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
    [6] 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
    [7] Massimiliano Tamborrino . Approximation of the first passage time density of a Wiener process to an exponentially decaying boundary by two-piecewise linear threshold. Application to neuronal spiking activity. Mathematical Biosciences and Engineering, 2016, 13(3): 613-629. doi: 10.3934/mbe.2016011
    [8] Michele Barbi, Angelo Di Garbo, Rita Balocchi . Improved integrate-and-fire model for RSA. Mathematical Biosciences and Engineering, 2007, 4(4): 609-615. doi: 10.3934/mbe.2007.4.609
    [9] 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
    [10] Xiaodong Qian . Evaluation on sustainable development of fire safety management policies in smart cities based on big data. Mathematical Biosciences and Engineering, 2023, 20(9): 17003-17017. doi: 10.3934/mbe.2023758
  • A new definition of firing time is given in the framework of Integrate and Fire neuronal models. The classical absorption condition at the threshold is relaxed and the firing time is defined as the first time the membrane potential process lies above a fixed depolarisation level for a sufficiently long time. The mathematical properties of the new firing time are investigated both for the Perfect Integrator and the Leaky Integrator. In the latter case, a simulation study is presented to complete the analysis where analytical results are not yet achieved.


    [1] Queueing Systems, 10 (1992), 5-87.
    [2] ORSA Journal on Computing, 7 (1995), 36-43.
    [3] Stochastic Models, 21 (2005), 967-980.
    [4] Ann. Appl. Probab., 12 (2002), 1071-1095.
    [5] Scandinavian Journal of Statistics, 40 (2013), 274-293.
    [6] Physical Review E, 78 (2008), 011918.
    [7] Physical Review E, 81 (2010), 031916.
    [8] Mathematical Biosciences and Engineering, 11 (2014), 189-201.
    [9] Advances in Applied Probability, 19 (1987), 784-800.
    [10] Biological Cybernetics, 95 (2006), 1-19.
    [11] Biological Cybernetics, 95 (2006), 97-112.
    [12] Journal of Theoretical Biology, 350 (2014), 81-89.
    [13] Frontiers in Neural Circuits, 8 (2014), p11.
    [14] Advances in Applied Probabability, 29 (1997), 165-184.
    [15] Probabilistic Engineering Mechanics, 23 (2008), 170-179.
    [16] Physical Review. E (3), 71 (2005), 011907, 9pp.
    [17] Physical Review E, 73 (2006), 061910, 9pp.
    [18] Journal of Mathematical Biology, 67 (2013), 453-481.
    [19] Bulletin of Mathematical Biology, 75 (2013), 629-648.
    [20] Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 129 (1999), 57-75.
    [21] Biophysical Journal, 4 (1964), 41-68.
    [22] Cambridge University Press, 2002.
    [23] Annals of Probability, 7 (1979), 244-266.
    [24] Advances in Applied Probability, 21 (1989), 20-36.
    [25] Neural Computation, 23 (2011), 1743-1767.
    [26] Comm. Statist. Simulation Comput., 28 (1999), 1135-1163.
    [27] Frontiers in Computational Neuroscience, 7 (2013), p131.
    [28] Biological Cybernetics, 73 (1995), 209-221.
    [29] in Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. III: Probability theory, Univ. California Press, Berkeley, Calif., 1972, 225-239.
    [30] in Advances in Neural Information Processing Systems 18 (eds. Y. Weiss, B. Sch\"olkopf and J. Platt), MIT Press, 2006, 595-602.
    [31] Springer-Verlag, 1991.
    [32] Frontiers in Computational Neuroscience, 3 (2009), p9.
    [33] Brain Research, 1536 (2013), 97-106.
    [34] Mathematical Bioscience, 67 (1983), 247-260.
    [35] Biological Cybernetics, 99 (2008), 253-262.
    [36] Neural Computation, 16 (2004), 477-489.
    [37] Journal of Computational Neuroscence, 21 (2006), 211-223.
    [38] Courier Corporation, 1972.
    [39] Physical Review E, 72 (2005), 021911, 21pp.
    [40] Springer-Verlag, 2003.
    [41] Bernoulli, 9 (2003), 1-24.
    [42] Springer-Verlag, Berlin-New York, 1977.
    [43] Biological Cybernetics, 35 (1979), 1-9.
    [44] Physical Review E, 76 (2007), 021919.
    [45] Cambridge University Press, Cambridge, 2000.
    [46] in Stochastic Biomathematical Models, Lecture Notes in Math., 2058, Springer, Heidelberg, 2013, 99-148.
    [47] Mathematical Bioscience, 39 (1978), 53-70.
    [48] Lifetime Data Analysis, 21 (2015), 331-352.
    [49] Physica D: Nonlinear Phenomena, 288 (2014), 45-52.
    [50] Cambridge Studies in Mathematical Biology, 8, Cambridge University Press, Cambridge, 1988.
    [51] Cambridge Studies in Mathematical Biology, 8, Cambridge University Press, Cambridge, 1988.
    [52] The Journal of Neuroscience, 24 (2004), 3060-3069.

  • This article has been cited by:

    1. Roberta Sirovich, Luisa Testa, On the first positive and negative excursion exceeding a given length, 2019, 150, 01677152, 137, 10.1016/j.spl.2019.03.008
  • Reader Comments
  • © 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)
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
3.9

Metrics

Article views(2656) PDF downloads(456) Cited by(1)

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