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Delayed feedback makes neuronal firing statistics non-Markovian

Delayed feedback makes neuronal firing statistics non-Markovian

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 times of neuronal firing are recorded but not the state of communication lines. Howeve...

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Main Authors: Vidybida, A.K., Kravchuk, K.G.
Format: Article
Language:English
Published: Український математичний журнал 2012
Series:Український математичний журнал
Subjects:
Статті
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/165260
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spelling irk-123456789-1652602020-02-13T01:26:43Z Delayed feedback makes neuronal firing statistics non-Markovian Vidybida, A.K. Kravchuk, K.G. Статті 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 times of neuronal firing are recorded but not the state of communication lines. However, future spiking moments substantially depend 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 the present paper, we analyze this problem for the simplest possible neural “network,” namely, for a single neuron with delayed feedback. 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. 2012 Article Delayed feedback makes neuronal firing statistics non-Markovian / A.K. Vidybida, K.G. Kravchuk // Український математичний журнал. — 2012. — Т. 64, № 12. — С. 1587-1609. — Бібліогр.: 42 назв. — англ. 1027-3190 http://dspace.nbuv.gov.ua/handle/123456789/165260 519.21 en Український математичний журнал Український математичний журнал
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
topic Статті
Статті
spellingShingle Статті
Статті
Vidybida, A.K.
Kravchuk, K.G.
Delayed feedback makes neuronal firing statistics non-Markovian
Український математичний журнал
description 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 times of neuronal firing are recorded but not the state of communication lines. However, future spiking moments substantially depend 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 the present paper, we analyze this problem for the simplest possible neural “network,” namely, for a single neuron with delayed feedback.
format Article
author Vidybida, A.K.
Kravchuk, K.G.
author_facet Vidybida, A.K.
Kravchuk, K.G.
author_sort Vidybida, A.K.
title Delayed feedback makes neuronal firing statistics non-Markovian
title_short Delayed feedback makes neuronal firing statistics non-Markovian
title_full Delayed feedback makes neuronal firing statistics non-Markovian
title_fullStr Delayed feedback makes neuronal firing statistics non-Markovian
title_full_unstemmed Delayed feedback makes neuronal firing statistics non-Markovian
title_sort delayed feedback makes neuronal firing statistics non-markovian
publisher Український математичний журнал
publishDate 2012
topic_facet Статті
url http://dspace.nbuv.gov.ua/handle/123456789/165260
citation_txt Delayed feedback makes neuronal firing statistics non-Markovian / A.K. Vidybida, K.G. Kravchuk // Український математичний журнал. — 2012. — Т. 64, № 12. — С. 1587-1609. — Бібліогр.: 42 назв. — англ.
series Український математичний журнал
work_keys_str_mv AT vidybidaak delayedfeedbackmakesneuronalfiringstatisticsnonmarkovian
AT kravchukkg delayedfeedbackmakesneuronalfiringstatisticsnonmarkovian
first_indexed 2023-10-18T22:15:36Z
last_indexed 2023-10-18T22:15:36Z
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