Output stream of binding neuron with delayed feedback

Vidybida, A. K.; Kravchuk, K. G.

doi:10.1140/epjb/e2009-00309-x

Cited by 9 publications

(31 citation statements)

References 19 publications

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“…The expression right above is in agreement with that found for binding neuron model in [19] and [20].…”

Section: Moments Of Pdfsupporting

confidence: 89%

“…The validity of the obtained formulas (19) has been verified using numerical simulation for the LIF model by means of the Monte Carlo method, see Fig. 2 c.…”

Section: Model-invariant Initial Segment Of P(t)mentioning

confidence: 72%

“…(13), (16), (17) and (18). Furthermore, the initial model-invariant segment of PDF p(t) has been found in the explicit form, see (19). Also, we express the moments of PDF p(t) for a neuron with feedback through the corresponding moments of PDF p 0 (t) for the neuron without feedback.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

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First Passage Time Distribution for Spiking Neuron with Delayed Excitatory Feedback

Shchur

Vidybida

2019

Fluct. Noise Lett.

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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-andfire (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 ∆. 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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“…The expression right above is in agreement with that found for binding neuron model in [19] and [20].…”

Section: Moments Of Pdfsupporting

confidence: 89%

“…The validity of the obtained formulas (19) has been verified using numerical simulation for the LIF model by means of the Monte Carlo method, see Fig. 2 c.…”

Section: Model-invariant Initial Segment Of P(t)mentioning

confidence: 72%

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First Passage Time Distribution for Spiking Neuron with Delayed Excitatory Feedback

Shchur

Vidybida

2019

Fluct. Noise Lett.

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“…In this paper we use the quantal approach, as it is defined in [1] in order to prove that the Markov property is broken in the ISI output stream of a neuronal model belonging to a defined class of models, equipped with delayed fast Cltype inhibitory feedback, which is stimulated with a Poisson stochastic process of input excitatory impulses. Several previous results obtained in the quantal approach are used in this paper, see [8,13,18,29,30].…”

Section: Discussionmentioning

confidence: 99%

“…Namely, in [18] under Poisson stimulation the output ISI pdf and mean ISI are obtained for the BN with threshold (Th) 2, and the mean ISI for Th = 3. In [8,29,30] a BN model with Th = 2 and with delayed feedback, either excitatory or inhibitory, stimulated with Poisson stream is considered. For this case, the ISI pdf is found and also it is proven that the output ISI stream is non-Markov.…”

Section: Discussionmentioning

confidence: 99%

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

Vidybida¹

2018

J. Phys. Stud.

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Delayed feedback makes neuronal firing statistics non-Markovian

Vidybida

Kravchuk

2013

Ukr Math J

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The instantaneous state of a neural network consists of both the degree of excitation of each neuron and the 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. However, future spiking moments depend substantially on the past positions of impulses in the lines. This suggests that the sequence of intervals between firing moments (interspike intervals, ISI) in the network can be non-Markovian. In this paper, we address this question for a simplest possible neural "network", namely, a single neuron with delayed feedback. The neuron receives excitatory input both from the input Poisson process and from its own output through the feedback line. We obtain exact expressions for the conditional probability density P (tn+1 | tn,. .. , t1, t0)dtn+1 and prove that P (tn+1 | tn,. .. , t1, t0) does not reduce to P (tn+1 | tn,. .. , t1) for any n ≥ 0. This means that the output ISI stream cannot be represented as a Markov chain of any finite order. Стан нейронної мережi складається як з величини збудження в кожному з нейронiв, так i зi значень положення iмпульсiв у лiнiях зв'язку. В нейрофiзiологiчних експериментах реєструються моменти пострiлiв окремих нейронiв, а не стани лiнiй зв'язку. Але моменти наступних пострiлiв iстотним чином залежать вiд положення iмпульсiв у лiнiях зв'язку в попереднi моменти. Це наводить на думку, що послiдовнiсть iнтервалiв мiж послiдовними пострiлами окремого нейрона в мережi (мiжспайковi iнтервали, МСI) може складати немарковський точковий стохастичний процес. У цiй роботi дослiджується така можливiсть для найпростiшої з можливих нейронної "мережi", а саме, поодинокого нейрона з затриманим зворотним зв'язком. Нейрон отримує в якостi стимулу збуджувальнi iмпульси вiд пуассонiвського вхiдного процесу i власнi вихiднi збуджувальнi iмпульси через лiнiю зворотного зв'язку. Одержано точнi вирази для щiльностi умовної ймовiрностi P (tn+1 | tn,. .. , t1, t0)dtn+1 i доведено, що P (tn+1 | tn,. .. , t1, t0) не зводиться до P (tn+1 | tn,. .. , t1) для будь-якого n ≥ 0. Це означає, що вихiдний потiк МСI неможливо подати як марковський ланцюг скiнченного порядку.

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Output stream of binding neuron with delayed feedback

Cited by 9 publications

References 19 publications

First Passage Time Distribution for Spiking Neuron with Delayed Excitatory Feedback

First Passage Time Distribution for Spiking Neuron with Delayed Excitatory Feedback

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

Delayed feedback makes neuronal firing statistics non-Markovian

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