Activity of Excitatory Neuron with Delayed Feedback Stimulated with Poisson Stream is Non-Markov

Vidybida, A. K.

doi:10.1007/s10955-015-1301-2

Cited by 7 publications

(21 citation statements)

References 28 publications

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“…For this case, the ISI pdf is found and also it is proven that the output ISI stream is non-Markov. In [13], any neuronal model from a defined class is considered. A delayed feedback is assumed excitatory, and stimulation is Poissonian.…”

Section: Discussionmentioning

confidence: 99%

“…The Cond3, above, limits the set of models as compared to [13]. Namely, it claims that the standard state of [13,Cond3] must be exactly the resting state of neuron. This requirement is imposed due to the specifics of Cl-type fast inhibition.…”

Section: Definitions and Assumptions 21 Neuron Without Feedbackmentioning

confidence: 99%

“…As regards the structure itself, the following representation can be derived similarly as it was done in [13]:…”

Section: The Proofmentioning

confidence: 99%

“…For this configuration it has been proven in the previous paper [8] for the case of Poisson input stream and for a concrete neuronal model -the inhibitory binding neuron 1 with threshold 2 -, that statistics of its interspike intervals (ISIs) is essentially non-Markov 2 . In paper [13], it has been proven for the Poisson input and for a class of excitatory neuronal models that the presence of delayed feedback makes their activity non-Markov. In this paper, we use the approach developed in [13] in order to refine and extend methods of [8] making them applicable to any inhibitory neuron with fast Cl-type inhibition satisfying a number of simple and natural conditions, see Cond0-Cond4, below.…”

Section: Introductionmentioning

confidence: 99%

“…In paper [13], it has been proven for the Poisson input and for a class of excitatory neuronal models that the presence of delayed feedback makes their activity non-Markov. In this paper, we use the approach developed in [13] in order to refine and extend methods of [8] making them applicable to any inhibitory neuron with fast Cl-type inhibition satisfying a number of simple and natural conditions, see Cond0-Cond4, below. The stimulation is assumed to be a Poisson stochastic process.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Fast Cl-type inhibitory neuron with delayed feedback has non-Markov output statistics

Vidybida¹

2018

J. Phys. Stud.

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Section: Discussionmentioning

confidence: 99%

Section: Definitions and Assumptions 21 Neuron Without Feedbackmentioning

confidence: 99%

“…As regards the structure itself, the following representation can be derived similarly as it was done in [13]:…”

Section: The Proofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Fast Cl-type inhibitory neuron with delayed feedback has non-Markov output statistics

Vidybida¹

2018

J. Phys. Stud.

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Relation Between Firing Statistics of Spiking Neuron with Delayed Fast Inhibitory Feedback and Without Feedback

Vidybida

Shchur

2018

Fluct. Noise Lett.

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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 ∆. 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 ∆ 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.a Definition of the binding neuron model can be found in [17]. See also https://en.wikipedia.org/wiki/Binding neuron.

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Distribution of Interspike Intervals of a Neuron with Inhibitory Autapse Stimulated with a Renewal Process

Shchur

Vidybida

2022

Fluct. Noise Lett.

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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) [Formula: see text] 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 [Formula: see text] defined at some initial interval [Formula: see text] of ISI values.

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Activity of Excitatory Neuron with Delayed Feedback Stimulated with Poisson Stream is Non-Markov

Abstract: For a class of excitatory spiking neuron models with delayed feedback fed with a Poisson stochastic process, it is proven that the stream of output interspike intervals cannot be presented as a Markov process of any order.

Cited by 7 publications

References 28 publications

Fast Cl-type inhibitory neuron with delayed feedback has non-Markov output statistics

Fast Cl-type inhibitory neuron with delayed feedback has non-Markov output statistics

Relation Between Firing Statistics of Spiking Neuron with Delayed Fast Inhibitory Feedback and Without Feedback

Distribution of Interspike Intervals of a Neuron with Inhibitory Autapse Stimulated with a Renewal Process

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