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Dimension Reduction of Neural Models Across Multiple Spatio-temporal Scales

Park, Youngmin (2018) Dimension Reduction of Neural Models Across Multiple Spatio-temporal Scales. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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In general, reducing the dimensionality of a complex model is a natural first step to gaining insight into the system. In this dissertation, we reduce the dimensions of models at three different scales: first at the scale of microscopic single-neurons, second at the scale of macroscopic infinite neurons, and third at an in-between spatial scale of finite neural populations. Each model also exhibits a separation of timescales, making them amenable to the method of multiple timescales, which is the primary dimension-reduction tool of this dissertation. In the first case, the method of multiple timescales reduces the dynamics of two coupled n-dimensional neurons into one scalar differential equation representing the slow timescale phase-locking properties of the oscillators as a function of an exogenous slowly varying parameter. This result extends the classic theory of weakly coupled oscillators. In the second case, the method reduces the many spatio-temporal \yp{dynamics of} ``bump'' solutions of a neural field model into its scalar coordinates, which are much easier to analyze analytically. This result generalizes existing studies on neural field spatio-temporal dynamics to the case of a smooth firing rate function and general even kernel. In the third case, we reduce the dimension of the oscillators at the spiking level -- similar to the first case -- but with additional slowly varying synaptic variables. This result generalizes existing studies that use scalar oscillators and the Ott-Antonsen ansatz to reduce the dimensionality and determine the synchronization properties of large neural populations.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Park, Youngminyop6@pitt.eduyop60000-0003-1778-2160
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairErmentrout,
Committee MemberCoalson,
Committee MemberDoiron,
Committee MemberRubin,
Date: 28 June 2018
Date Type: Publication
Defense Date: 30 March 2018
Approval Date: 28 June 2018
Submission Date: 5 April 2018
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 193
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: Oscillators, synchrony, mean field, neural models
Additional Information: ETD Draft
Date Deposited: 28 Jun 2018 19:21
Last Modified: 28 Jun 2018 19:21


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