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A Semi-Markov Leaky Integrate-and-Fire Model

Author

Listed:
  • Giacomo Ascione

    (Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Università degli Studi di Napoli Federico II, I-80126 Naples, Italy
    These authors contributed equally to this work.)

  • Bruno Toaldo

    (Dipartimento di Matematica “Giuseppe Peano”, Università degli Studi di Torino, 10123 Torino, Italy
    These authors contributed equally to this work.)

Abstract

In this paper, a Leaky Integrate-and-Fire (LIF) model for the membrane potential of a neuron is considered, in case the potential process is a semi-Markov process. Semi-Markov property is obtained here by means of the time-change of a Gauss-Markov process. This model has some merits, including heavy-tailed distribution of the waiting times between spikes. This and other properties of the process, such as the mean, variance and autocovariance, are discussed.

Suggested Citation

  • Giacomo Ascione & Bruno Toaldo, 2019. "A Semi-Markov Leaky Integrate-and-Fire Model," Mathematics, MDPI, vol. 7(11), pages 1-24, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1022-:d:281238
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    References listed on IDEAS

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    1. Dexter O. Cahoy & Federico Polito & Vir Phoha, 2015. "Transient Behavior of Fractional Queues and Related Processes," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 739-759, September.
    2. Erhan Cinlar, 1974. "Markov Additive Processes and Semi-Regeneration," Discussion Papers 118, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Meerschaert, Mark M. & Toaldo, Bruno, 2019. "Relaxation patterns and semi-Markov dynamics," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2850-2879.
    4. Yasuhiro Tsubo & Yoshikazu Isomura & Tomoki Fukai, 2012. "Power-Law Inter-Spike Interval Distributions Infer a Conditional Maximization of Entropy in Cortical Neurons," PLOS Computational Biology, Public Library of Science, vol. 8(4), pages 1-11, April.
    5. Aniello Buonocore & Luigia Caputo & Enrica Pirozzi & Luigi M. Ricciardi, 2011. "The First Passage Time Problem for Gauss-Diffusion Processes: Algorithmic Approaches and Applications to LIF Neuronal Model," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 29-57, March.
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    Cited by:

    1. Lansky, Petr & Polito, Federico & Sacerdote, Laura, 2023. "Input-output consistency in integrate and fire interconnected neurons," Applied Mathematics and Computation, Elsevier, vol. 440(C).

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