First-passage-time statistics of a Brownian particle driven by an arbitrary unidimensional potential with a superimposed exponential time-dependent drift

In one-dimensional systems, the dynamics of a Brownian particle are governed by the force derived from a potential as well as by diffusion properties. In this work, we obtain the first-passage-time statistics of a Brownian particle driven by an arbitrary potential with an exponential temporally deca...

ver descrição completa

Detalhes bibliográficos
Autor: Urdapilleta, Eugenio
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2015
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositório:CONICET Digital (CONICET)
Idioma:inglês
OAI Identifier:oai:ri.conicet.gov.ar:11336/60074
Acesso em linha:http://hdl.handle.net/11336/60074
Access Level:Acceso aberto
Palavra-chave:Diffusion
First-Passage-Time
Neuron Models
Time-Dependent Drift
https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
id AR_03df80de44c28575900b1e08b43dfd3b
oai_identifier_str oai:ri.conicet.gov.ar:11336/60074
network_acronym_str AR
network_name_str Argentina
repository_id_str
spelling First-passage-time statistics of a Brownian particle driven by an arbitrary unidimensional potential with a superimposed exponential time-dependent driftUrdapilleta, EugenioDiffusionFirst-Passage-TimeNeuron ModelsTime-Dependent Drifthttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1In one-dimensional systems, the dynamics of a Brownian particle are governed by the force derived from a potential as well as by diffusion properties. In this work, we obtain the first-passage-time statistics of a Brownian particle driven by an arbitrary potential with an exponential temporally decaying superimposed field up to a prescribed threshold. The general system analyzed here describes the sub-threshold signal integration of integrate-and-fire neuron models, of any kind, supplemented by an adaptation-like current, whereas the first-passage-time corresponds to the declaration of a spike. Following our previous studies, we base our analysis on the backward Fokker-Planck equation and study the survival probability and the first-passage-time density function in the space of the initial condition. By proposing a series solution we obtain a system of recurrence equations, which given the specific structure of the exponential time-dependent drift, easily admit a simpler Laplace representation. Naturally, the present general derivation agrees with the explicit solution we found previously for the Wiener process in (2012 J. Phys. A: Math. Theor. 45 185001). However, to demonstrate the generality of the approach, we further explicitly evaluate the first-passage-time statistics of the underlying Ornstein-Uhlenbeck process. To test the validity of the series solution, we extensively compare theoretical expressions with the data obtained from numerical simulations in different regimes. As shown, agreement is precise whenever the series is truncated at an appropriate order. Beyond the fact that both the Wiener and Ornstein-Uhlenbeck processes have a direct interpretation in the context of neuronal models, given their ubiquity in different fields, our present results will be of interest in other settings where an additive state-independent temporal relaxation process is being developed as the particle diffuses.Fil: Urdapilleta, Eugenio. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaIOP Publishing2015-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/60074Urdapilleta, Eugenio; First-passage-time statistics of a Brownian particle driven by an arbitrary unidimensional potential with a superimposed exponential time-dependent drift; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 48; 50; 11-20151751-8113CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8113/48/50/505001info:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/article/10.1088/1751-8113/48/50/505001/metainfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T13:38:23Zoai:ri.conicet.gov.ar:11336/60074instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982024-05-08 13:38:24.014CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv First-passage-time statistics of a Brownian particle driven by an arbitrary unidimensional potential with a superimposed exponential time-dependent drift
title First-passage-time statistics of a Brownian particle driven by an arbitrary unidimensional potential with a superimposed exponential time-dependent drift
spellingShingle First-passage-time statistics of a Brownian particle driven by an arbitrary unidimensional potential with a superimposed exponential time-dependent drift
Urdapilleta, Eugenio
Diffusion
First-Passage-Time
Neuron Models
Time-Dependent Drift
https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
title_short First-passage-time statistics of a Brownian particle driven by an arbitrary unidimensional potential with a superimposed exponential time-dependent drift
title_full First-passage-time statistics of a Brownian particle driven by an arbitrary unidimensional potential with a superimposed exponential time-dependent drift
title_fullStr First-passage-time statistics of a Brownian particle driven by an arbitrary unidimensional potential with a superimposed exponential time-dependent drift
title_full_unstemmed First-passage-time statistics of a Brownian particle driven by an arbitrary unidimensional potential with a superimposed exponential time-dependent drift
title_sort First-passage-time statistics of a Brownian particle driven by an arbitrary unidimensional potential with a superimposed exponential time-dependent drift
dc.creator.none.fl_str_mv Urdapilleta, Eugenio
author Urdapilleta, Eugenio
author_facet Urdapilleta, Eugenio
author_role author
dc.subject.none.fl_str_mv Diffusion
First-Passage-Time
Neuron Models
Time-Dependent Drift
https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
topic Diffusion
First-Passage-Time
Neuron Models
Time-Dependent Drift
https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
description In one-dimensional systems, the dynamics of a Brownian particle are governed by the force derived from a potential as well as by diffusion properties. In this work, we obtain the first-passage-time statistics of a Brownian particle driven by an arbitrary potential with an exponential temporally decaying superimposed field up to a prescribed threshold. The general system analyzed here describes the sub-threshold signal integration of integrate-and-fire neuron models, of any kind, supplemented by an adaptation-like current, whereas the first-passage-time corresponds to the declaration of a spike. Following our previous studies, we base our analysis on the backward Fokker-Planck equation and study the survival probability and the first-passage-time density function in the space of the initial condition. By proposing a series solution we obtain a system of recurrence equations, which given the specific structure of the exponential time-dependent drift, easily admit a simpler Laplace representation. Naturally, the present general derivation agrees with the explicit solution we found previously for the Wiener process in (2012 J. Phys. A: Math. Theor. 45 185001). However, to demonstrate the generality of the approach, we further explicitly evaluate the first-passage-time statistics of the underlying Ornstein-Uhlenbeck process. To test the validity of the series solution, we extensively compare theoretical expressions with the data obtained from numerical simulations in different regimes. As shown, agreement is precise whenever the series is truncated at an appropriate order. Beyond the fact that both the Wiener and Ornstein-Uhlenbeck processes have a direct interpretation in the context of neuronal models, given their ubiquity in different fields, our present results will be of interest in other settings where an additive state-independent temporal relaxation process is being developed as the particle diffuses.
publishDate 2015
dc.date.none.fl_str_mv 2015-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/60074
Urdapilleta, Eugenio; First-passage-time statistics of a Brownian particle driven by an arbitrary unidimensional potential with a superimposed exponential time-dependent drift; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 48; 50; 11-2015
1751-8113
CONICET Digital
CONICET
url http://hdl.handle.net/11336/60074
identifier_str_mv Urdapilleta, Eugenio; First-passage-time statistics of a Brownian particle driven by an arbitrary unidimensional potential with a superimposed exponential time-dependent drift; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 48; 50; 11-2015
1751-8113
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8113/48/50/505001
info:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/article/10.1088/1751-8113/48/50/505001/meta
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv IOP Publishing
publisher.none.fl_str_mv IOP Publishing
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1799194873944866816
score 15.811543

Registros relacionados