Inhibition enhances the coherence in the Jacobi neuronal model

D’Onofrio, Giuseppe; Lánský, Petr; Tamborrino, Massimiliano

doi:10.1016/j.chaos.2019.07.040

Cited by 10 publications

(4 citation statements)

References 44 publications

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“…To measure the accuracy, we again use rRMSE (31), but since there are no reasonably simple formulas for MSE for all the estimators, we will calculate the values using numerical simulations for spike trains with the GM, IG and LN probability distributions of the ISIs. For the parameters, we use the following values, λ = 1, r ∈{0, 0.1}, n ∈{2, 10, 50} and FF ∈ [0.1, 10]. For each combination of parameters, the values of error were calculated based on 20000 estimates for each estimator.…”

Section: Comparison Of and With The Standard Estimatorsmentioning

confidence: 99%

Estimation of the instantaneous spike train variability

Rajdl,

Kostal

2023

Preprint

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The variability of neuronal spike trains is usually measured by the Fano factor or the co-efficient of variation of interspike intervals, but their estimation is problematic, especially with limited amount of data. In this paper we show that it is in fact possible to estimate a quantity equivalent to the Fano factor and the squared coefficient of variation based on the intervals from only one specific (random) time. This leads to two very simple but precise Fano factor estimators, that can be interpreted as estimators of instantaneous variability. We derive their properties, evaluate their accuracy in various situations and show that they are often more accurate than the standard estimators. The presented estimators are particularly suitable for the case where variability changes rapidly.

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Section: Comparison Of and With The Standard Estimatorsmentioning

confidence: 99%

Estimation of the instantaneous spike train variability

Rajdl,

Kostal

2023

Preprint

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“…On the one hand, the inhibition is well known to be regulatory of neuronal excitability and has a role in information transmission. The study, for state-dependent inputs, of the effect of inhibition on output indicators like signal to noise ratio, effective diffusion coefficient of the spike count and degree of coherence demonstrates that inhibitory input acts to decrease membrane potential fluctuations increasing spike regularity (see for example [3,4,18,46]). Moreover the state dependence of the jumps preserves the fundamental improvement with respect to the Ornstein-Uhlenbeck model that the changes in the depolarization depends on the actual value of the voltage.…”

Section: A Jacobi Process With Jumps As a Neuronal Modelmentioning

confidence: 99%

Jacobi processes with jumps as neuronal models: a first passage time analysis

D’Onofrio¹,

Patie²,

Sacerdote³

2022

Preprint

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To overcome some limits of classical neuronal models, we propose a Markovian generalization of the classical model based on Jacobi processes by introducing downwards jumps to describe the activity of a single neuron. The statistical analysis of inter-spike intervals is performed by studying the first-passage times of the proposed Markovian Jacobi process with jumps through a constant boundary. In particular, we characterize its Laplace transform which is expressed in terms of some generalization of hypergeometric functions that we introduce, and, deduce a closed-form expression for its expectation. Our approach, which is original in the context of first passage time problems, relies on intertwining relations between the semigroups of the classical Jacobi process and its generalization which have been recently established in [10]. A numerical investigation of the firing rate of the considered neuron is performed for some choices of the involved parameters and of the jumps distributions.

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“…The two most commonly used characteristics for measuring spike train variability are the coefficient of variation (CV), based on the variance of the lengths of the ISIs, and the Fano factor (FF), based on the variance of the number of spikes in a time window (Ditlevsen & Lansky, 2011;Stevenson, 2016;Rajdl et al, 2020;D'Onofrio et al, 2019). They are used, e. g., to measure the variability of real neuronal data (Festa et al, 2021;de Ruyter van Steveninck et al, 1997) or to study the neuronal variability using theoretical neuronal models (Protachevicz et al, 2022;Christodoulou & Bugmann, 2001).…”

Section: Introductionmentioning

confidence: 99%