O'Grady, Ryan (2011) *Firing Rate Analysis for an Integrate-and-Fire Neuronal Model.* Doctoral Dissertation, University of Pittsburgh.

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## Abstract

We investigate a stochastic linear integrate-and-fire (IF) neuronal model and use the corresponding Fokker-Planck equation (FPE) to study the mean firing rate of a population of IF neurons. The firing rate(or emission rate) function, is given in terms of an eigenfunction expansion solution of the FPE. We consider two parameter regimes of current input and prove the existence of infinitely many branches of eigenvalues and derive their asymptotic properties. We use the eigenfunction expansion solution to prove asymptotic properties of the firing rate function. We also perform a numerical experiment of 10,000 IF neurons and show that our simulation is in agreement with our theoretical results. Finally, we state several open problems for future research.

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## Details | ||||||||||||||||

Item Type: | University of Pittsburgh ETD | |||||||||||||||
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Title: | Firing Rate Analysis for an Integrate-and-Fire Neuronal Model | |||||||||||||||

Status: | Unpublished | |||||||||||||||

Abstract: | We investigate a stochastic linear integrate-and-fire (IF) neuronal model and use the corresponding Fokker-Planck equation (FPE) to study the mean firing rate of a population of IF neurons. The firing rate(or emission rate) function, is given in terms of an eigenfunction expansion solution of the FPE. We consider two parameter regimes of current input and prove the existence of infinitely many branches of eigenvalues and derive their asymptotic properties. We use the eigenfunction expansion solution to prove asymptotic properties of the firing rate function. We also perform a numerical experiment of 10,000 IF neurons and show that our simulation is in agreement with our theoretical results. Finally, we state several open problems for future research. | |||||||||||||||

Date: | 29 September 2011 | |||||||||||||||

Date Type: | Completion | |||||||||||||||

Defense Date: | 22 April 2011 | |||||||||||||||

Approval Date: | 29 September 2011 | |||||||||||||||

Submission Date: | 15 August 2011 | |||||||||||||||

Access Restriction: | 5 year -- Restrict access to University of Pittsburgh for a period of 5 years. | |||||||||||||||

Patent pending: | No | |||||||||||||||

Institution: | University of Pittsburgh | |||||||||||||||

Thesis Type: | Doctoral Dissertation | |||||||||||||||

Refereed: | Yes | |||||||||||||||

Degree: | PhD - Doctor of Philosophy | |||||||||||||||

URN: | etd-08152011-120630 | |||||||||||||||

Uncontrolled Keywords: | eigenfunction expansion; integrate-and-fire; mean firing rate; neuronal model; sde | |||||||||||||||

Schools and Programs: | Dietrich School of Arts and Sciences > Mathematics | |||||||||||||||

Date Deposited: | 10 Nov 2011 14:59 | |||||||||||||||

Last Modified: | 14 Feb 2012 16:17 | |||||||||||||||

Other ID: | http://etd.library.pitt.edu/ETD/available/etd-08152011-120630/, etd-08152011-120630 |

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