arXiv subjects

Alexander Vidybida

Publications and source records attributed to Alexander Vidybida.

12 recordsLinked to original sources

arXiv2023

Maximization of the olfactory receptor neuron selectivity in the sub-threshold regime

It is known that if odors are presented to an olfactory receptor neuron (ORN) in a sub-threshold concentration -- i.e., when the average value of the number of the ORN bound receptor proteins (RPs) is insufficient for the generation of spikes, but such a generation is still possible due to fluctuations around the average value -- the ORN selectivity can be higher than the selectivity at higher concentrations and, in particular, higher than the selectivity of the ORN's RPs. In this work, the optimal odorant concentration providing the highest ORN selectivity is found in the framework of a simplified ORN model, and the dependence of the highest selectivity on the total number of RPs in the ORN, $N$, and its threshold value $N_{0}$ is derived. The effect of enhanced selectivity in the sub-threshold regime is best manifested, if $N_{0}$ is close to either unity or $N$. It is also more pronounced at large $N$-values.

physics.bio-ph↗

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.

q-bio.NC↗

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.

q-bio.NC↗

arXiv2020

Calculating permutation entropy without permutations

A method for analyzing sequential data sets, similar to the permutation entropy one, is discussed. The characteristic features of this method are as follows: it preserves information about equal values, if any, in the embedding vectors; it is exempt of combinatorics; it delivers the same entropy value as does the permutation method, provided the embedding vectors do not have equal components. In the latter case this method can be used instead of the permutation one. If embedding vectors have equal components this method could be more precise in discriminating between similar data sets.

physics.data-an↗

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.

q-bio.NC↗

arXiv2019

Stochastic mechanism for improving selectivity of olfactory projection neurons

A mechanism is proposed for increasing selectivity of olfactory bulb projection neurons as compared to the olfactory receptor neurons, which could operate under low odor concentration, when the lateral inhibition mechanism becomes inefficient. The mechanism proposed is based on the threshold-type reaction to stimuli a projection neuron receives from the receptor neurons, the stochastic nature of those stimuli and electrical leakage in the projection neurons. The mechanism operates at the level of individual projection neuron and does not require involvement of other bulbar neurons. Keywords: olfactory receptor neuron; projection neuron; selectivity; stochastic process; theory

q-bio.NC↗

arXiv2019

Trade-off between sensitivity and selectivity in olfactory receptor neuron

It was observed before that due to convergence in the olfactory system a possible amplification can be as large as the degree of convergence. This is in the case when a single impulse from the converging inputs is enough to trigger the secondary neuron. On the other hand, if a number of impulses are required for triggering, a gain in discriminating ability may be obtained along with decrease in sensitivity gained due to the convergence. We discuss this trade-off in terms of concrete estimates using olfactory sensory neuron and the set of its receptor proteins as an example of system with convergence.

q-bio.NC↗

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↗

arXiv2014

Output stream of binding neuron with delayed feedback

A binding neuron (BN) whith delayed feedback is considered. The neuron is fed externally with a Poisson stream of intensity $λ$. The neuron's output spikes are fed into its input with time delay $Δ$. The resulting output stream of the BN is not Poissonian, and we look for its interspike intervals (ISI) distribution. For BN with threshold 2 an exact mathematical expression as function of $λ$, $Δ$ and BN's internal memory, $τ$ is derived for the ISI distribution, and for higher thresholds it is found numerically. The distributions found are characterized with discontinuities of jump type, and include singularity of Dirac's $δ$-function type. It is concluded that delayed feedback presence can radically alter neuronal output firing statistics.

q-bio.NC↗

arXiv2013

Firing statistics of inhibitory neuron with delayed feedback. II. Non-Markovian behavior

The instantaneous state of a neural network consists of both the degree of excitation of each neuron the network is composed of and positions of impulses in communication lines between the neurons. In neurophysiological experiments, the neuronal firing moments are registered, but not the state of communication lines. But future spiking moments depend essentially on the past positions of impulses in the lines. This suggests, that the sequence of intervals between firing moments (inter-spike intervals, ISIs) in the network could be non-Markovian. In this paper, we address this question for a simplest possible neural "net", namely, a single inhibitory neuron with delayed feedback. The neuron receives excitatory input from the driving Poisson stream and inhibitory impulses from its own output through the feedback line. We obtain analytic expressions for conditional probability density P(t_{n+1}| t_n,...,t_1,t_0), which gives the probability to get an output ISI of duration t_{n+1} provided the previous (n+1) output ISIs had durations t_n,...,t_1,t_0. It is proven exactly, that P(t_{n+1}| t_n,...,t_1,t_0) does not reduce to P(t_{n+1}| t_n,...,t_1) for any n>=0. This means that the output ISIs stream cannot be represented as a Markov chain of any finite order.

q-bio.NC↗

arXiv2013

Computer simulation of inhibition-dependent binding in a neural network

Reverberating dynamics of neural network is modelled on PC in order to illustrate possible role of inhibition as binding controller in the network. The network is composed of binding neurons. In the binding neuron model the degree of temporal coherence between synaptic inputs is decisive for triggering, and slow inhibition is expressed in terms of the degree, which is necessary for triggering. Two learning mechanisms are implemented in the network, namely, adjusting synaptic strength and/or propagation delays. By means of forced playing of external pattern the network is taught to support dynamics with disconnected and bound patterns of activity. By choosing either high, or low inhibition one can switch between the disconnected and bound patterns, respectively. This is interpreted as inhibition-controlled binding in the network.

q-bio.NC↗

arXiv2010

Delayed feedback causes non-Markovian behavior of neuronal firing statistics

The instantaneous state of a neural network consists of both the degree of excitation of each neuron, the network is composed of, and positions of impulses in communication lines between neurons. In neurophysiological experiments, the neuronal firing moments are registered, but not the state of communication lines. But future spiking moments depend essentially on the past positions of impulses in the lines. This suggests, that the sequence of intervals between firing moments (interspike intervals, ISIs) in the network could be non-Markovian. In this paper, we address this question for a simplest possible neural "net", namely, a single neuron with delayed feedback. The neuron receives excitatory input both from the driving Poisson stream and from its own output through the feedback line. We obtain analytical expressions for conditional probability density $P(t_{n+1} | t_n,...,t_1,t_0)$, which gives the probability to get an output ISI of duration $t_{n+1}$ provided the previous $(n+1)$ output ISIs had durations $t_n,...,t_1,t_0$. It is proven exactly, that $P(t_{n+1} | t_n,...,t_1,t_0)$ does not reduce to $P(t_{n+1} | t_n,...,t_1)$ for any $n \geq 0$. This means that the output ISIs stream cannot be represented as Markov chain of any finite order.

q-bio.NC↗