Nonstationary shot noise modeling of neuron membrane potentials by closed-form moments and Gram-Charlier expansions
We present exact analytical expressions of moments of all orders for neuronal membrane potentials in the multiplicative nonstationary Poisson shot noise model. As an application, we derive closed-form Gram-Charlier density expansions that show how the probability density functions of potentials in s...
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| Format: | Journal Article |
| Language: | English |
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2022
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| Online Access: | https://hdl.handle.net/10356/161517 |
| _version_ | 1826114943050579968 |
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| author | Privault, Nicolas |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Privault, Nicolas |
| author_sort | Privault, Nicolas |
| collection | NTU |
| description | We present exact analytical expressions of moments of all orders for neuronal membrane potentials in the multiplicative nonstationary Poisson shot noise model. As an application, we derive closed-form Gram-Charlier density expansions that show how the probability density functions of potentials in such models differ from their Gaussian diffusion approximations. This approach extends the results of Brigham and Destexhe (Preprint, 2015a; Phys Rev E 91:062102, 2015b) by the use of exact combinatorial expressions for the moments of multiplicative nonstationary filtered shot noise processes. Our results are confirmed by stochastic simulations and apply to single- and multiple-noise-source models. |
| first_indexed | 2024-10-01T03:47:26Z |
| format | Journal Article |
| id | ntu-10356/161517 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T03:47:26Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1615172022-09-06T06:03:41Z Nonstationary shot noise modeling of neuron membrane potentials by closed-form moments and Gram-Charlier expansions Privault, Nicolas School of Physical and Mathematical Sciences Science::Mathematics Poisson Point Processes Moments We present exact analytical expressions of moments of all orders for neuronal membrane potentials in the multiplicative nonstationary Poisson shot noise model. As an application, we derive closed-form Gram-Charlier density expansions that show how the probability density functions of potentials in such models differ from their Gaussian diffusion approximations. This approach extends the results of Brigham and Destexhe (Preprint, 2015a; Phys Rev E 91:062102, 2015b) by the use of exact combinatorial expressions for the moments of multiplicative nonstationary filtered shot noise processes. Our results are confirmed by stochastic simulations and apply to single- and multiple-noise-source models. Ministry of Education (MOE) This research is supported by the Ministry of Education, Singapore, under its Tier 1 Grant MOE2018-T1-001-201. 2022-09-06T06:03:41Z 2022-09-06T06:03:41Z 2020 Journal Article Privault, N. (2020). Nonstationary shot noise modeling of neuron membrane potentials by closed-form moments and Gram-Charlier expansions. Biological Cybernetics, 114(4-5), 499-518. https://dx.doi.org/10.1007/s00422-020-00844-8 0340-1200 https://hdl.handle.net/10356/161517 10.1007/s00422-020-00844-8 32955621 2-s2.0-85091134477 4-5 114 499 518 en MOE2018-T1-001-201 Biological Cybernetics © 2020 Springer Nature. All rights reserved. |
| spellingShingle | Science::Mathematics Poisson Point Processes Moments Privault, Nicolas Nonstationary shot noise modeling of neuron membrane potentials by closed-form moments and Gram-Charlier expansions |
| title | Nonstationary shot noise modeling of neuron membrane potentials by closed-form moments and Gram-Charlier expansions |
| title_full | Nonstationary shot noise modeling of neuron membrane potentials by closed-form moments and Gram-Charlier expansions |
| title_fullStr | Nonstationary shot noise modeling of neuron membrane potentials by closed-form moments and Gram-Charlier expansions |
| title_full_unstemmed | Nonstationary shot noise modeling of neuron membrane potentials by closed-form moments and Gram-Charlier expansions |
| title_short | Nonstationary shot noise modeling of neuron membrane potentials by closed-form moments and Gram-Charlier expansions |
| title_sort | nonstationary shot noise modeling of neuron membrane potentials by closed form moments and gram charlier expansions |
| topic | Science::Mathematics Poisson Point Processes Moments |
| url | https://hdl.handle.net/10356/161517 |
| work_keys_str_mv | AT privaultnicolas nonstationaryshotnoisemodelingofneuronmembranepotentialsbyclosedformmomentsandgramcharlierexpansions |