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Mathematical properties of time windowing in neural systems.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Mathematical properties of time windowing in neural systems.
Author:	Mitchell, Colleen Catharine.
Description:	58 p.
Notes:	Source: Dissertation Abstracts International, Volume: 64-08, Section: B, page: 3853.
Notes:	Supervisor: Michael Reed.
Contained By:	Dissertation Abstracts International64-08B.
Subject:	Mathematics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3102249
ISBN:	0496498193

Mathematical properties of time windowing in neural systems.
Mitchell, Colleen Catharine.

Mathematical properties of time windowing in neural systems. [electronic resource] - 58 p.

Source: Dissertation Abstracts International, Volume: 64-08, Section: B, page: 3853.

Thesis (Ph.D.)--Duke University, 2003.

Coincidence detection, in which a neuron fires when it receives many, nearly simultaneous inputs, has recently been proposed as a mechanism by which neurons in the auditory brainstem that receive many imprecise inputs can generate a precise output. We study coincidence detection and the precision of neural timing in a model neural system with n identical input neurons whose firing times in response to stimulation are chosen independently from a density f. These input neurons stimulate a target cell, which fires when it receives m hits within epsilon msec. The mathematical question is to understand the behavior of the output of this target cell, specifically how the probability density of its time of firing gm,n,epsilon,f depends on m, n, epsilon and the analytic characteristics of the input density f. Specifically to show the effects of these parameters on the standard deviation of the output. We prove, using mainly analytic and functional analytic techniques, that the density gm,n,epsilon,f converges as epsilon → 0 to the input density f raised to the mth power and normalized and to the density of the mth order statistic as epsilon → infinity. We also give conditions for convergence of the density in L1, pointwise, and uniformly as well as conditions for the convergence of the standard deviations. We also describe Monte Carlo results which show that dependence on the parameters is complex and often counterintuitive.

ISBN: 0496498193Subjects--Topical Terms:

184409
Mathematics.

Mathematical properties of time windowing in neural systems.
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500 $a Source: Dissertation Abstracts International, Volume: 64-08, Section: B, page: 3853.
500 $a Supervisor: Michael Reed.
502 $a Thesis (Ph.D.)--Duke University, 2003.
520 # $a Coincidence detection, in which a neuron fires when it receives many, nearly simultaneous inputs, has recently been proposed as a mechanism by which neurons in the auditory brainstem that receive many imprecise inputs can generate a precise output. We study coincidence detection and the precision of neural timing in a model neural system with n identical input neurons whose firing times in response to stimulation are chosen independently from a density f. These input neurons stimulate a target cell, which fires when it receives m hits within epsilon msec. The mathematical question is to understand the behavior of the output of this target cell, specifically how the probability density of its time of firing gm,n,epsilon,f depends on m, n, epsilon and the analytic characteristics of the input density f. Specifically to show the effects of these parameters on the standard deviation of the output. We prove, using mainly analytic and functional analytic techniques, that the density gm,n,epsilon,f converges as epsilon → 0 to the input density f raised to the mth power and normalized and to the density of the mth order statistic as epsilon → infinity. We also give conditions for convergence of the density in L1, pointwise, and uniformly as well as conditions for the convergence of the standard deviations. We also describe Monte Carlo results which show that dependence on the parameters is complex and often counterintuitive.
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