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Stochastic Neural Oscillators

Abouzeid, Aushra (2011) Stochastic Neural Oscillators. Doctoral Dissertation, University of Pittsburgh.

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    Abstract

    We seek to understand collective neural phenomena such as synchronization, correlation transfer and information propagation in the presence of additive broadband noise. Our findings contribute to a growing scientific literature that has shown that uncoupled type II neural oscillators synchronize more readily under the influence of noisy input currents than do type I oscillators. We use stochastic phase reduction and regular perturbations to show that the type II phase response curve (PRC) minimizes the Lyapunov exponent. We also derived expressions for the correlation between output spike trains using the steady state probability distribution of the phase difference between oscillators. Over short time scales we find that, for a given level of input correlation, spike trains from type II membranes show greater output correlation than from type I. However, we find the reverse is true for oscillators observed over long time scales, in agreement with recent results. Previous investigations of specific ion channels have generated insights into mechanisms by which neuromodulators can switch the bifurcation structure of an oscillator. In a similar vein, we undertake an exploratory and qualitative study of the influence of the A-type potassium current on spike train synchrony, correlation transfer and information content in a reduced 3-dimensional neuron model that exhibits both type I and type II oscillations, as well as a bifurcation to bursting dynamics. Using the local Lyapunov exponent in place of the PRC as a measure of sensitivity to perturbation, we find that the region of bursting dynamics shows prolonged elevated sensitivity during the inter-burst interval. In the oscillatory regime, a similar phenomenon occurs near the bifurcation to bursting, and we see that the magnitude of the PRC grows markedly as this border is approached. Furthermore, we find that the highly sensitive dynamics result in a combination of spike time reliability and increased ISI variability that produces greater mutual information between a spike train and a broadband input signal. These findings suggest that there may be an optimal balance of dynamical sensitivity and stability that maximizes the computationally relevant statistical dependence between input signals and output spike trains.


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    Item Type: University of Pittsburgh ETD
    ETD Committee:
    ETD Committee TypeCommittee MemberEmailORCID
    Committee ChairErmentrout, Bardbard@pitt.edu
    Committee MemberDoiron, Brentbrent.doiron@gmail.com
    Committee MemberUrban, Nathannurban@cmu.edu
    Committee MemberTroy, William C.troy@math.pitt.edu
    Title: Stochastic Neural Oscillators
    Status: Unpublished
    Abstract: We seek to understand collective neural phenomena such as synchronization, correlation transfer and information propagation in the presence of additive broadband noise. Our findings contribute to a growing scientific literature that has shown that uncoupled type II neural oscillators synchronize more readily under the influence of noisy input currents than do type I oscillators. We use stochastic phase reduction and regular perturbations to show that the type II phase response curve (PRC) minimizes the Lyapunov exponent. We also derived expressions for the correlation between output spike trains using the steady state probability distribution of the phase difference between oscillators. Over short time scales we find that, for a given level of input correlation, spike trains from type II membranes show greater output correlation than from type I. However, we find the reverse is true for oscillators observed over long time scales, in agreement with recent results. Previous investigations of specific ion channels have generated insights into mechanisms by which neuromodulators can switch the bifurcation structure of an oscillator. In a similar vein, we undertake an exploratory and qualitative study of the influence of the A-type potassium current on spike train synchrony, correlation transfer and information content in a reduced 3-dimensional neuron model that exhibits both type I and type II oscillations, as well as a bifurcation to bursting dynamics. Using the local Lyapunov exponent in place of the PRC as a measure of sensitivity to perturbation, we find that the region of bursting dynamics shows prolonged elevated sensitivity during the inter-burst interval. In the oscillatory regime, a similar phenomenon occurs near the bifurcation to bursting, and we see that the magnitude of the PRC grows markedly as this border is approached. Furthermore, we find that the highly sensitive dynamics result in a combination of spike time reliability and increased ISI variability that produces greater mutual information between a spike train and a broadband input signal. These findings suggest that there may be an optimal balance of dynamical sensitivity and stability that maximizes the computationally relevant statistical dependence between input signals and output spike trains.
    Date: 15 September 2011
    Date Type: Completion
    Defense Date: 05 April 2011
    Approval Date: 15 September 2011
    Submission Date: 16 August 2011
    Access Restriction: No restriction; The work is available for access worldwide immediately.
    Patent pending: No
    Institution: University of Pittsburgh
    Thesis Type: Doctoral Dissertation
    Refereed: Yes
    Degree: PhD - Doctor of Philosophy
    URN: etd-08162011-211818
    Uncontrolled Keywords: Euler-Lagrange; Lyapunov exponent; slow-fast analysis; entropy; information
    Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
    Date Deposited: 10 Nov 2011 14:59
    Last Modified: 17 Feb 2012 16:08
    Other ID: http://etd.library.pitt.edu/ETD/available/etd-08162011-211818/, etd-08162011-211818

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