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Input-output consistency in integrate and fire interconnected neurons

Author

Listed:
  • Lansky, Petr
  • Polito, Federico
  • Sacerdote, Laura

Abstract

Interspike intervals describe the output of neurons. Signal transmission in a neuronal network implies that the output of some neurons becomes the input of others. The output should reproduce the main features of the input to avoid a distortion when it becomes the input of other neurons, that is input and output should exhibit some sort of consistency. In this paper, we consider the question: how should we mathematically characterize the input in order to get a consistent output? Here we interpret the consistency by requiring the reproducibility of the input tail behaviour of the interspike intervals distributions in the output. Our answer refers to a system of interconnected neurons with stochastic perfect integrate and fire units. In particular, we show that the class of regularly-varying vectors is a possible choice to obtain such consistency. Some further necessary technical hypotheses are added.

Suggested Citation

  • Lansky, Petr & Polito, Federico & Sacerdote, Laura, 2023. "Input-output consistency in integrate and fire interconnected neurons," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    • Handle: RePEc:eee:apmaco:v:440:y:2023:i:c:s0096300322007032
    DOI: 10.1016/j.amc.2022.127630
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    References listed on IDEAS

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    1. Giacomo Ascione & Bruno Toaldo, 2019. "A Semi-Markov Leaky Integrate-and-Fire Model," Mathematics, MDPI, vol. 7(11), pages 1-24, October.
    2. 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.
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