arXiv subjects

Olha Shchur

Publications and source records attributed to Olha Shchur.

4 recordsLinked to original sources

arXiv2022

Distribution of interspike intervals of a neuron with inhibitory autapse stimulated with a renewal process

In this paper, we study analytically the impact of an inhibitory autapse on neuronal activity. In order to do this, we formulate conditions on a set of non-adaptive spiking neuron models with delayed feedback inhibition, instead of considering a particular neuronal model. The neuron is stimulated with a stochastic point renewal process of excitatory impulses. Probability density function (PDF) $p(t)$ of output interspike intervals (ISIs) of such a neuron is found exactly without any approximations made. It is expressed in terms of ISIs PDF for the input renewal stream and ISIs PDF for that same neuron without any feedback. Obtained results are applied to a subset of neuronal models with threshold 2 when the time intervals between input impulses are distributed according to the Erlang-2 distribution. In that case we have found explicitly the model-independent initial part of ISIs PDF $p(t)$ defined at some initial interval $[0;T_2]$ of ISI values.

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arXiv2020

Moment-generating function of output stream of leaky integrate-and-fire neuron

The statistics of the output activity of a neuron during its stimulation by the stream of input impulses that forms the stochastic Poisson process is studied. The leaky integrate-and-fire neuron is considered as a neuron model. A new representation of the probability distribution function of the output interspike interval durations is found. Based on it, the moment-generating function of the probability distribution is calculated explicitly. The latter, according to Curtiss theorem, completely determines the distribution itself. In particular, explicit expressions are derived from the moment-generating function for the moments of all orders. The first moment coincides with the one found earlier. Formulas for the second and third moments have been checked numerically by direct modeling of the stochastic dynamics of a neuron with specific physical parameters.

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arXiv2019

First passage time distribution for spiking neuron with delayed excitatory feedback

A class of spiking neuronal models with threshold 2 is considered. It is defined by a set of conditions typical for basic threshold-type models, such as the leaky integrate-and-fire (LIF) or the binding neuron model and also for some artificial neurons. A neuron is stimulated with a Poisson stream of excitatory impulses. Each output impulse is conveyed through the feedback line to the neuron input after finite delay $Δ$. This impulse is identical to those delivered from the input stream. We have obtained a general relation allowing calculating exactly the probability density function (PDF) $p(t)$ for distribution of the first passage time of crossing the threshold, which is the distribution of output interspike intervals (ISI) values for this neuron. The calculation is based on known PDF $p^0(t)$ for that same neuron without feedback, intensity of the input stream $λ$ and properties of the feedback line. Also, we derive exact relation for calculating the moments of $p(t)$ based on known moments of $p^0(t)$. The obtained general expression for $p(t)$ is checked numerically using Monte Carlo simulation for the case of LIF model. The course of $p(t)$ has a $δ$-function type peculiarity. This fact contributes to the discussion about the possibility to model neuronal activity with Poisson process, supporting the "no" answer.

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arXiv2018

Relation between firing statistics of spiking neuron with delayed fast inhibitory feedback and without feedback

We consider a class of spiking neuronal models, defined by a set of conditions typical for basic threshold-type models, such as the leaky integrate-and-fire or the binding neuron model and also for some artificial neurons. A neuron is fed with a Poisson process. Each output impulse is applied to the neuron itself after a finite delay $Δ$. This impulse acts as being delivered through a fast Cl-type inhibitory synapse. We derive a general relation which allows calculating exactly the probability density function (pdf) $p(t)$ of output interspike intervals of a neuron with feedback based on known pdf $p^0(t)$ for the same neuron without feedback and on the properties of the feedback line (the $Δ$ value). Similar relations between corresponding moments are derived. Furthermore, we prove that initial segment of pdf $p^0(t)$ for a neuron with a fixed threshold level is the same for any neuron satisfying the imposed conditions and is completely determined by the input stream. For the Poisson input stream, we calculate that initial segment exactly and, based on it, obtain exactly the initial segment of pdf $p(t)$ for a neuron with feedback. That is the initial segment of $p(t)$ is model-independent as well. The obtained expressions are checked by means of Monte Carlo simulation. The course of $p(t)$ has a pronounced peculiarity, which makes it impossible to approximate $p(t)$ by Poisson or another simple stochastic process.

q-bio.NC↗