 Input-output consistency in integrate and fire interconnected neuronsPetr Lansky, Federico Polito and Laura Sacerdote Applied Mathematics and Computation, 2023, vol. 440, issue C 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. Keywords: Target neuron model; Perfect integrate and fire; First passage time; Interspike intervals; Multivariate point process; Time and space structure; Regular variation; Heavy tails; Asymptotic independence (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:440:y:2023:i:c:s0096300322007032 DOI: 10.1016/j.amc.2022.127630 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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