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Structured flows on manifolds
 Date Issued:
 2008
 Summary:
 Despite the highdimensional nature of the nervous system, humans produce lowdimensional cognitive and behavioral dynamics. How highdimensional networks with complex connectivity give rise to functionally meaningful dynamics is not well understood. How does a neural network encode function? How can functional dynamics be systematically obtained from networks? There exist few frameworks in the current literature that answer these questions satisfactorily. In this dissertation I propose a general theoretical framework entitled 'Structured Flows on Manifolds' and its underlying mathematical basis. The framework is based on the principles of nonlinear dynamical systems and Synergetics and can be used to understand how highdimensional systems that exhibit multiple timescale behavior can produce lowdimensional dynamics. Lowdimensional functional dynamics arises as a result of the timescale separation of the systems component's dynamics. The lowdimensional space in which the functi onal dynamics occurs is regarded as a manifold onto which the entire systems dynamics collapses. For the duration of the function the system will stay on the manifold and evolve along the manifold. From a network perspective the manifold is viewed as the product of the interactions of the network nodes. The subsequent flows on the manifold are a result of the asymmetries of network's interactions. A distributed functional architecture based on this perspective is presented. Within this distributed functional architecture, issues related to networks such as flexibility, redundancy and robustness of the network's dynamics are addressed. Flexibility in networks is demonstrated by showing how the same network can produce different types of dynamics as a function of the asymmetrical coupling between nodes. Redundancy can be achieved by systematically creating different networks that exhibit the same dynamics. The framework is also used to systematically probe the effects of lesion
Title:  Structured flows on manifolds: distributed functional architectures. 
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Name(s): 
Pillai, Ajay S. Florida Atlantic University Charles E. Schmidt College of Science Center for Complex Systems and Brain Sciences 

Type of Resource:  text  
Genre:  Electronic Thesis Or Dissertation  
Date Issued:  2008  
Publisher:  Florida Atlantic University  
Physical Form:  electronic  
Extent:  xxii, 124 p. : ill. (some col.).  
Language(s):  English  
Summary:  Despite the highdimensional nature of the nervous system, humans produce lowdimensional cognitive and behavioral dynamics. How highdimensional networks with complex connectivity give rise to functionally meaningful dynamics is not well understood. How does a neural network encode function? How can functional dynamics be systematically obtained from networks? There exist few frameworks in the current literature that answer these questions satisfactorily. In this dissertation I propose a general theoretical framework entitled 'Structured Flows on Manifolds' and its underlying mathematical basis. The framework is based on the principles of nonlinear dynamical systems and Synergetics and can be used to understand how highdimensional systems that exhibit multiple timescale behavior can produce lowdimensional dynamics. Lowdimensional functional dynamics arises as a result of the timescale separation of the systems component's dynamics. The lowdimensional space in which the functi onal dynamics occurs is regarded as a manifold onto which the entire systems dynamics collapses. For the duration of the function the system will stay on the manifold and evolve along the manifold. From a network perspective the manifold is viewed as the product of the interactions of the network nodes. The subsequent flows on the manifold are a result of the asymmetries of network's interactions. A distributed functional architecture based on this perspective is presented. Within this distributed functional architecture, issues related to networks such as flexibility, redundancy and robustness of the network's dynamics are addressed. Flexibility in networks is demonstrated by showing how the same network can produce different types of dynamics as a function of the asymmetrical coupling between nodes. Redundancy can be achieved by systematically creating different networks that exhibit the same dynamics. The framework is also used to systematically probe the effects of lesion  
Summary:  (removal of nodes) on network dynamics. It is also shown how lowdimensional functional dynamics can be obtained from firingrate neuron models by placing biologically realistic constraints on the coupling. Finally the theoretical framework is applied to real data. Using the structured flows on manifolds approach we quantify team performance and team coordination and develop objective measures of team performance based on skill level.  
Identifier:  243800679 (oclc), 77649 (digitool), FADT77649 (IID), fau:4309 (fedora)  
Note(s): 
by Ajay S. Pillai. Thesis (Ph.D.)Florida Atlantic University, 2008. Includes bibliography. Electronic reproduction. Boca Raton, FL : 2008 Mode of access: World Wide Web. 

Subject(s): 
Manifolds (Mathematics) Differentiable dynamical systems Mathematical physics 

Persistent Link to This Record:  http://purl.flvc.org/FAU/77649  
Use and Reproduction:  http://rightsstatements.org/vocab/InC/1.0/  
Host Institution:  FAU 