Thesis (Dr. rer. nat.)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2001. / "11 Februar 2001." Includes bibliographical references (p. 123-124).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1973. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

No description available.

published_or_final_version / abstract / Mathematics / Master / Master of Philosophy

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

published_or_final_version / Mathematics / Master / Master of Philosophy

Despite the high-dimensional nature of the nervous system, humans produce low-dimensional cognitive and behavioral dynamics. How high-dimensional 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 non-linear dynamical systems and Synergetics and can be used to understand how high-dimensional systems that exhibit multiple time-scale behavior can produce low-dimensional dynamics. Low-dimensional functional dynamics arises as a result of the timescale separation of the systems component's dynamics. The low-dimensional 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 / (removal of nodes) on network dynamics. It is also shown how low-dimensional functional dynamics can be obtained from firing-rate 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. / 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.

by Li Cheung Shing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1991. / Bibliography: leaves 111-115. / Introduction --- p.1 / Chapter Chapter 1 --- "Real hypersurfaces,CR manifolds and the imbedding problem" --- p.5 / Chapter § 1.1 --- Non-equivalence of real analytic hypersurfaces in C2 --- p.5 / Chapter § 1.2 --- The Lewy operator --- p.8 / Chapter § 1.3 --- CR manifolds --- p.19 / Chapter § 1.4 --- Imbedding of CR manifolds --- p.24 / Chapter Chapter 2 --- Geometry of the real hyperquadric --- p.30 / Chapter § 2.1 --- The real hyperquadric --- p.30 / Chapter § 2.2 --- Q-frames --- p.31 / Chapter § 2.3 --- Maurer Cartan forms --- p.33 / Chapter § 2.4 --- Structural equations and chains --- p.36 / Chapter Chapter 3 --- Moser normal form --- p.40 / Chapter § 3.1 --- Formal theory of the normal form --- p.40 / Chapter § 3.2 --- Geometric theory of the normal form --- p.48 / Chapter Chapter 4 --- Cartan-Chern invariants and pseudohermitian geometry --- p.67 / Chapter §4.1 --- Cartan's solution of the equivalence problem --- p.67 / Chapter § 4.2 --- Chern's construction in higher dimensions --- p.69 / Chapter §4.3 --- Webster's invariants for pseudohermitian manifolds --- p.72 / Chapter § 4.4 --- Geometric interpretation of Webster's invariants --- p.76 / Chapter § 4.5 --- Applications --- p.80 / Chapter Chapter 5 --- Fefferman metric --- p.86 / Chapter § 5.1 --- Differential geometry on the boundary --- p.86 / Chapter § 5.2 --- Computations --- p.93 / Chapter §5.3 --- An example of spiral chains --- p.103 / References --- p.111

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1979. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Vita. / Bibliography: leaves 131-133. / Ph.D.