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Evoked Patterns of Oscillatory Activity in Mean-Field Neuronal Networks

Pina, Jason (2019) Evoked Patterns of Oscillatory Activity in Mean-Field Neuronal Networks. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Oscillatory behaviors in populations of neurons are oberved in diverse contexts. In tasks involving working memory, a form of short-term memory, oscillations in different frequency bands have been shown to increase across varying spatial scales using recording methods such as EEG (electroencephalogram) and MEG (magnetoencephalogram). Such oscillatory activity has also been observed in the context of neural binding, where different features of objects that are perceived or recalled are associated with one another. These sets of data suggest that oscillatory dynamics may also play a key role in the maintenance and manipulation of items in working memory.

Using similar recording techniques, including EEG and MEG, oscillatory neuronal activity has also been seen to occur when certain images that cause aversion and headaches in healthy human subjects or seizures in those with pattern-sensitive epilepsy are presented. The images most likely to cause such responses are those with dominant spatial frequencies near 3--5 cycles per degree, the same band of wavenumbers to which normal human vision exhibits the greatest contrast sensitivity.

We model these oscillatory behaviors using mean-field, Wilson-Cowan-type neuronal networks. In the case of working memory and binding, we find that including the activity of certain long-lasting excitatory synapses in addition to the usual inhibitory and shorter-term excitatory synaptic activity allows for bistability between a low steady state and a high oscillatory state. By coupling several such populations together, both in-phase and out-of-phase oscillations arise, corresponding to distinct and bound items in working memory, respectively. We analyze the network's dynamics and dependence on biophysically relevant parameters using a combination of techniques, including numerical bifurcation analysis and weak coupling theory. In the case of spatially resonant responses to static simtuli, we employ Wilson-Cowan networks extended in one and two spatial dimensions. By placing the networks near Turing-Hopf bifurcations, we find they exhibit spatial resonances that compare well with empirical results. Using simulations, numerical bifurcation analysis, and perturbation theory, we characterize the observed dynamics and gain mathematical insight into the mechanisms that lead to these dynamics.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Pina, Jasonjay.pina@pitt.edujep1130000-0003-1385-8762
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairErmentrout, G.
Committee MemberDoiron,
Committee MemberOswald,
Committee MemberRubin,
Date: 31 January 2019
Date Type: Publication
Defense Date: 30 November 2018
Approval Date: 31 January 2019
Submission Date: 7 December 2018
Access Restriction: 1 year -- Restrict access to University of Pittsburgh for a period of 1 year.
Number of Pages: 186
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: neuronal networks, working memory, pattern formation, neural binding, mean field
Date Deposited: 31 Jan 2019 17:57
Last Modified: 31 Jan 2020 06:15


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