Park, Youngmin
(2018)
Dimension Reduction of Neural Models Across Multiple Spatio-temporal Scales.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
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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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
|
| 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 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/34106 |
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