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Firing Rate Analysis for an Integrate-and-Fire Neuronal Model

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 (Unpublished)

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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
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
O'Grady, Ryanrmo3@pitt.eduRMO3
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairTroy, Williamtroy@math.pitt.eduTROY
Committee MemberDoiron, Brentbdoiron@pitt.eduBDOIRON
Committee MemberCaginalp, Gunduzcaginalp@pitt.eduCAGINALP
Committee MemberIyengar, Satishssi@pitt.eduSSI
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.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: eigenfunction expansion; integrate-and-fire; mean firing rate; neuronal model; sde
Other ID: http://etd.library.pitt.edu/ETD/available/etd-08152011-120630/, etd-08152011-120630
Date Deposited: 10 Nov 2011 19:59
Last Modified: 15 Nov 2016 13:49
URI: http://d-scholarship.pitt.edu/id/eprint/9112

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