On a spike train probability model with interacting neural units
We investigate an extension of the spike train stochastic model based on the conditionalintensity, in which the recovery function includes an interaction between several excitatoryneural units. Such function is proposed as depending both on the time elapsed since thelast spike and on the last spikin...
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| Format: | Article |
| Language: | English |
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AIMS Press
2013-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.217 |
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| author | Antonio Di Crescenzo Maria Longobardi Barbara Martinucci |
| author_facet | Antonio Di Crescenzo Maria Longobardi Barbara Martinucci |
| author_sort | Antonio Di Crescenzo |
| collection | DOAJ |
| description | We investigate an extension of the spike train stochastic model based on the conditionalintensity, in which the recovery function includes an interaction between several excitatoryneural units. Such function is proposed as depending both on the time elapsed since thelast spike and on the last spiking unit. Our approach, being somewhat related to thecompeting risks model, allows to obtain the general form of the interspike distribution andof the probability of consecutive spikes from the same unit. Various results are finally presentedin the two cases when the free firing rate function (i) is constant, and (ii) has a sinusoidal form. |
| format | Article |
| id | doaj-art-b7295d9dde5f45ffb304bcf04c7341d3 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-b7295d9dde5f45ffb304bcf04c7341d32025-01-24T02:28:02ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-09-0111221723110.3934/mbe.2014.11.217On a spike train probability model with interacting neural unitsAntonio Di Crescenzo0Maria Longobardi1Barbara Martinucci2Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II, 132, I-84084 Fisciano (SA)Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, I-80126 NapoliDipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II, 132, I-84084 Fisciano (SA)We investigate an extension of the spike train stochastic model based on the conditionalintensity, in which the recovery function includes an interaction between several excitatoryneural units. Such function is proposed as depending both on the time elapsed since thelast spike and on the last spiking unit. Our approach, being somewhat related to thecompeting risks model, allows to obtain the general form of the interspike distribution andof the probability of consecutive spikes from the same unit. Various results are finally presentedin the two cases when the free firing rate function (i) is constant, and (ii) has a sinusoidal form.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.217recovery function.firing ratecumulative firing raterefractory periodconditional intensitypoisson processneural model |
| spellingShingle | Antonio Di Crescenzo Maria Longobardi Barbara Martinucci On a spike train probability model with interacting neural units Mathematical Biosciences and Engineering recovery function. firing rate cumulative firing rate refractory period conditional intensity poisson process neural model |
| title | On a spike train probability model with interacting neural units |
| title_full | On a spike train probability model with interacting neural units |
| title_fullStr | On a spike train probability model with interacting neural units |
| title_full_unstemmed | On a spike train probability model with interacting neural units |
| title_short | On a spike train probability model with interacting neural units |
| title_sort | on a spike train probability model with interacting neural units |
| topic | recovery function. firing rate cumulative firing rate refractory period conditional intensity poisson process neural model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.217 |
| work_keys_str_mv | AT antoniodicrescenzo onaspiketrainprobabilitymodelwithinteractingneuralunits AT marialongobardi onaspiketrainprobabilitymodelwithinteractingneuralunits AT barbaramartinucci onaspiketrainprobabilitymodelwithinteractingneuralunits |