Non-Markovian spiking statistics of a neuron with delayed feedback in presence of refractoriness
Spiking statistics of a self-inhibitory neuron is considered.The neuron receives excitatory input from a Poisson streamand inhibitory impulses through a feedback linewith a delay. After triggering, the neuron is in the refractorystate for a positive period of time. Recently, [...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2013-08-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.81 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590141737140224 |
|---|---|
| author | Kseniia Kravchuk Alexander Vidybida |
| author_facet | Kseniia Kravchuk Alexander Vidybida |
| author_sort | Kseniia Kravchuk |
| collection | DOAJ |
| description | Spiking statistics of a self-inhibitory neuron is considered.The neuron receives excitatory input from a Poisson streamand inhibitory impulses through a feedback linewith a delay. After triggering, the neuron is in the refractorystate for a positive period of time. Recently, [35,6], it was proven for a neuron withdelayed feedback and without the refractory state,that the output stream of interspike intervals (ISI)cannot be represented as a Markov process.The refractory state presence, in a sense limits the memory range in thespiking process, which might restore Markov property to the ISI stream. Here we check such a possibility. For this purpose, we calculatethe conditional probability density $P(t_{n+1}\mid t_{n},\ldots,t_1,t_{0})$,and prove exactly that it does not reduce to $P(t_{n+1}\mid t_{n},\ldots,t_1)$for any $n\ge0$. That means, that activity of the system with refractory stateas well cannot be represented as a Markov process of any order. We conclude that it is namely the delayed feedback presencewhich results in non-Markovian statistics of neuronal firing.As delayed feedback lines are common forany realistic neural network, the non-Markovian statistics of the networkactivity should be taken into account in processing of experimental data. |
| format | Article |
| id | doaj-art-b44e341971c14e3c95b75971f826156d |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-b44e341971c14e3c95b75971f826156d2025-01-24T02:26:48ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-08-011118110410.3934/mbe.2014.11.81Non-Markovian spiking statistics of a neuron with delayed feedback in presence of refractorinessKseniia Kravchuk0Alexander Vidybida1Bogolyubov Institute for Theoretical Physics, Metrologichna str., 14-B, 03680 KyivBogolyubov Institute for Theoretical Physics, Metrologichna str., 14-B, 03680 KyivSpiking statistics of a self-inhibitory neuron is considered.The neuron receives excitatory input from a Poisson streamand inhibitory impulses through a feedback linewith a delay. After triggering, the neuron is in the refractorystate for a positive period of time. Recently, [35,6], it was proven for a neuron withdelayed feedback and without the refractory state,that the output stream of interspike intervals (ISI)cannot be represented as a Markov process.The refractory state presence, in a sense limits the memory range in thespiking process, which might restore Markov property to the ISI stream. Here we check such a possibility. For this purpose, we calculatethe conditional probability density $P(t_{n+1}\mid t_{n},\ldots,t_1,t_{0})$,and prove exactly that it does not reduce to $P(t_{n+1}\mid t_{n},\ldots,t_1)$for any $n\ge0$. That means, that activity of the system with refractory stateas well cannot be represented as a Markov process of any order. We conclude that it is namely the delayed feedback presencewhich results in non-Markovian statistics of neuronal firing.As delayed feedback lines are common forany realistic neural network, the non-Markovian statistics of the networkactivity should be taken into account in processing of experimental data.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.81refractoriness.delayed feedbacknon-markovian statisticsreverberating neural networksisi probability distributionnon-renewal statistics |
| spellingShingle | Kseniia Kravchuk Alexander Vidybida Non-Markovian spiking statistics of a neuron with delayed feedback in presence of refractoriness Mathematical Biosciences and Engineering refractoriness. delayed feedback non-markovian statistics reverberating neural networks isi probability distribution non-renewal statistics |
| title | Non-Markovian spiking statistics of a neuron with delayed feedback in presence of refractoriness |
| title_full | Non-Markovian spiking statistics of a neuron with delayed feedback in presence of refractoriness |
| title_fullStr | Non-Markovian spiking statistics of a neuron with delayed feedback in presence of refractoriness |
| title_full_unstemmed | Non-Markovian spiking statistics of a neuron with delayed feedback in presence of refractoriness |
| title_short | Non-Markovian spiking statistics of a neuron with delayed feedback in presence of refractoriness |
| title_sort | non markovian spiking statistics of a neuron with delayed feedback in presence of refractoriness |
| topic | refractoriness. delayed feedback non-markovian statistics reverberating neural networks isi probability distribution non-renewal statistics |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.81 |
| work_keys_str_mv | AT kseniiakravchuk nonmarkovianspikingstatisticsofaneuronwithdelayedfeedbackinpresenceofrefractoriness AT alexandervidybida nonmarkovianspikingstatisticsofaneuronwithdelayedfeedbackinpresenceofrefractoriness |