Mathematical models are an important tool for neuroscientists. During the last thirty years many papers have appeared on single neuron description and specifically on stochastic Integrate and Fire models. Analytical results have been proved and numerical and simulation methods have been developed for their study. Recent reviews collect the main features of these models but do not focus on the methodologies employed to obtain them. The aim of this paper is to fill this gap by upgrading old reviews. The idea is to collect the existing methods and the available analytical results for the most common one dimensional stochastic Integrate and Fire models to make them available for studies on networks. An effort to unify the mathematical notation is also made. The review is divided in two parts: Derivation of the models with the list of the available closed forms expressions for their characterization; Presentation of the existing mathematical and statistical methods for the study of these models.

Stochastic Integrate and Fire Models: a review on mathematical methods and their applications

SACERDOTE, Laura Lea;GIRAUDO, Maria Teresa
2013

Abstract

Mathematical models are an important tool for neuroscientists. During the last thirty years many papers have appeared on single neuron description and specifically on stochastic Integrate and Fire models. Analytical results have been proved and numerical and simulation methods have been developed for their study. Recent reviews collect the main features of these models but do not focus on the methodologies employed to obtain them. The aim of this paper is to fill this gap by upgrading old reviews. The idea is to collect the existing methods and the available analytical results for the most common one dimensional stochastic Integrate and Fire models to make them available for studies on networks. An effort to unify the mathematical notation is also made. The review is divided in two parts: Derivation of the models with the list of the available closed forms expressions for their characterization; Presentation of the existing mathematical and statistical methods for the study of these models.
Stochastic Biomathematical Models with Applications to Neuronal Modeling
Springer
Lecture notes in mathematics
2058
99
148
9783642321566
http://arxiv.org/pdf/1101.5539.pdf
http://link.springer.com/chapter/10.1007/978-3-642-32157-3_5
Neuronal models; diffusion processes; first passage time; parameter estimation
Sacerdote L.; Giraudo MT
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/90846
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