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Linear-Threshold Network Dynamics: P...

McCreesh, Michael Patrick Durrell,

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Linear-Threshold Network Dynamics: Properties and Applications to Dynamical Brain Behaviors /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Linear-Threshold Network Dynamics: Properties and Applications to Dynamical Brain Behaviors // Michael Patrick Durrell McCreesh.
Author:	McCreesh, Michael Patrick Durrell,
Description:	1 electronic resource (160 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-03, Section: B.
Contained By:	Dissertations Abstracts International86-03B.
Subject:	Systems science. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31300642
ISBN:	9798384239017

Linear-Threshold Network Dynamics: Properties and Applications to Dynamical Brain Behaviors /
McCreesh, Michael Patrick Durrell,

Linear-Threshold Network Dynamics: Properties and Applications to Dynamical Brain Behaviors /Michael Patrick Durrell McCreesh. - 1 electronic resource (160 pages)

Source: Dissertations Abstracts International, Volume: 86-03, Section: B.

The brain, composed of billions of interconnected neurons, forms a complex network that exhibits an incredibly wide array of behaviors. Treating this structure as a dynamical system provides a multitude of tools to use to model and understand the relationship between structure and function in the brain. As subnetworks exist at all levels in the brain, ranging from networks of individual neurons to networks of entire regions, a diverse set of models, each with different properties have been considered to study different dynamic brain behaviors. One such class of models are firing rate models, which monitor the average spike rate of populations of neurons. A particular firing rate model is the linear-threshold network model, which exhibits a wide range of rich behaviors based on the underlying network structure and inputs. This ability to exhibit a variety of behaviors motivates the use of this model to study a variety of dynamical behaviors observed in the brain.This dissertation considers three problems within the realm of modeling dynamical brain behaviors with the linear-threshold model. First, motivated by the appearance of oscillatory behavior when observing brain activity, we study the existence of oscillations in the linear-threshold dynamics. In order to provide sufficient conditions for oscillations in specific network topologies we also provide conditions for the stability of equilibrium points that maintain a specific support. Second, we discuss the dynamical brain behavior of selective inhibition and recruitment. We consider thalamocortical networks with both hierarchical and star-connected topologies, and focus on how the inclusion of the thalamus can improve the stabilizability properties of the linear-threshold dynamics relevant to the application. We finish by investigating the problem of reference tracking for the linear-threshold dynamics, which can be used to frame many brain behaviors. We approach this both analytically and with a data-driven approach to better match observations on how the brain processes information.

English

ISBN: 9798384239017Subjects--Topical Terms:

3168411
Systems science.
Subjects--Index Terms:

Linear-threshold model

Linear-Threshold Network Dynamics: Properties and Applications to Dynamical Brain Behaviors /
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245 1 0 $a Linear-Threshold Network Dynamics: Properties and Applications to Dynamical Brain Behaviors / $c Michael Patrick Durrell McCreesh.
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500 $a Source: Dissertations Abstracts International, Volume: 86-03, Section: B.
500 $a Advisors: Cortes, Jorge Committee members: Atanasov, Nikolay; Kramer, Boris; Krstic, Miroslav; Nozari, Erfan.
502 $b Ph.D. $c University of California, San Diego $d 2024.
520 $a The brain, composed of billions of interconnected neurons, forms a complex network that exhibits an incredibly wide array of behaviors. Treating this structure as a dynamical system provides a multitude of tools to use to model and understand the relationship between structure and function in the brain. As subnetworks exist at all levels in the brain, ranging from networks of individual neurons to networks of entire regions, a diverse set of models, each with different properties have been considered to study different dynamic brain behaviors. One such class of models are firing rate models, which monitor the average spike rate of populations of neurons. A particular firing rate model is the linear-threshold network model, which exhibits a wide range of rich behaviors based on the underlying network structure and inputs. This ability to exhibit a variety of behaviors motivates the use of this model to study a variety of dynamical behaviors observed in the brain.This dissertation considers three problems within the realm of modeling dynamical brain behaviors with the linear-threshold model. First, motivated by the appearance of oscillatory behavior when observing brain activity, we study the existence of oscillations in the linear-threshold dynamics. In order to provide sufficient conditions for oscillations in specific network topologies we also provide conditions for the stability of equilibrium points that maintain a specific support. Second, we discuss the dynamical brain behavior of selective inhibition and recruitment. We consider thalamocortical networks with both hierarchical and star-connected topologies, and focus on how the inclusion of the thalamus can improve the stabilizability properties of the linear-threshold dynamics relevant to the application. We finish by investigating the problem of reference tracking for the linear-threshold dynamics, which can be used to frame many brain behaviors. We approach this both analytically and with a data-driven approach to better match observations on how the brain processes information.
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650 4 $a Systems science. $3 3168411
650 4 $a Applied mathematics. $3 2122814
650 4 $a Mathematics. $3 515831
653 $a Linear-threshold model
653 $a Network dynamics
653 $a Dynamical brain behaviors
653 $a Data-driven approach
690 $a 0790
690 $a 0364
690 $a 0405
710 2 $a University of California, San Diego. $b Mechanical and Aerospace Engineering. $e degree granting institution. $3 3816116
720 1 $a Cortes, Jorge $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-03B.
790 $a 0033
791 $a Ph.D.
792 $a 2024
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31300642