Finite volume and asymptotic methods for stochastic neuron models with correlated inputs
Autor: | Fabien Marpeau, Robert Rosenbaum, Aditya Barua, Jianfu Ma, Krešimir Josić |
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Rok vydání: | 2010 |
Předmět: |
Monte Carlo method
Models Neurological Action Potentials Quantitative Biology - Quantitative Methods 01 natural sciences 03 medical and health sciences 0302 clinical medicine 0103 physical sciences Applied mathematics Boundary value problem 010306 general physics Quantitative Methods (q-bio.QM) Mathematics Cerebral Cortex Neurons Stochastic Processes Finite volume method Applied Mathematics Mathematical analysis Process (computing) Numerical Analysis Computer-Assisted Variance (accounting) Agricultural and Biological Sciences (miscellaneous) Orders of magnitude (time) Quantitative Biology - Neurons and Cognition Modeling and Simulation FOS: Biological sciences Fokker–Planck equation Neurons and Cognition (q-bio.NC) Transient (oscillation) 030217 neurology & neurosurgery |
Zdroj: | Journal of mathematical biology. 65(1) |
ISSN: | 1432-1416 |
Popis: | We consider a pair of stochastic integrate and fire neurons receiving correlated stochastic inputs. The evolution of this system can be described by the corresponding Fokker-Planck equation with non-trivial boundary conditions resulting from the refractory period and firing threshold. We propose a finite volume method that is orders of magnitude faster than the Monte Carlo methods traditionally used to model such systems. The resulting numerical approximations are proved to be accurate, nonnegative and integrate to 1. We also approximate the transient evolution of the system using an Ornstein--Uhlenbeck process, and use the result to examine the properties of the joint output of cell pairs. The results suggests that the joint output of a cell pair is most sensitive to changes in input variance, and less sensitive to changes in input mean and correlation. |
Databáze: | OpenAIRE |
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