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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| Date: | 2012 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Український математичний журнал
2012
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| Series: | Український математичний журнал |
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/165260 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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. |
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