Thesis (Ph. D.)--Lehigh University, 2006. / Includes vita. Includes bibliographical references (leaves 72-76).

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 Ho Wing Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 85). / Introduction --- p.1 / Chapter 1 --- Preliminaries --- p.3 / Chapter 1.1 --- Gateaux and Frechet Differentiability --- p.4 / Chapter 1.2 --- β-Differentiability --- p.9 / Chapter 1.3 --- Monotone Operators and Usco Maps --- p.14 / Chapter 2 --- Variational Principle --- p.25 / Chapter 2.1 --- A Generalized Variational Principle --- p.27 / Chapter 2.2 --- A Smooth Variational Principle --- p.37 / Chapter 3 --- Differentiability of Convex Functions --- p.47 / Chapter 3.1 --- On Banach Spaces with β-Smooth Bump Functions --- p.48 / Chapter 3.2 --- A Characterization of Asplund Spaces --- p.64 / Chapter 4 --- More on Differentiability --- p.70 / Chapter 4.1 --- Introduction --- p.70 / Chapter 4.2 --- Differentiability Theorems --- p.75

Dynamical systems theory represents a prominent theoretical framework for the investigation of movement coordination and control in complex neurobiological systems. Central to this theory is the investigation of pattern formation in biological movement through application of tools from nonlinear dynamics. Movement patterns are regarded as attractors and changes in movement coordination can be described as phase transitions. Phase transitions typically exhibit certain key indicators like critical fluctuations, critical slowing down and hysteresis, which enable the formulation of hypotheses and experimental testing. An extensive body of literature exists which tested these characteristics and robustly supports the tenets of dynamical systems theory in the movement sciences. However, the majority of studies have tended to use a limited range of movement models for experimentation, mainly bimanual rhythmical movements, and at present it is not clear to what extent the results can be transferred to other domains such as discrete movements and/or multi-articular actions. The present work investigated coordination and control of discrete, multi-articular actions as exemplified by a movement model from the sports domain: the basketball hook shot. Accordingly, the aims of the research programme were three-fold. First, identification of an appropriate movement model. Second, development of an analytical apparatus to enable the application of dynamical systems theory to new movement models. Third, to relate key principles of dynamical systems theory to investigations of this new movement model. A summary of four related studies that were undertaken is as follows: 1. Based on a biomechanical analysis, the kinematics of the basketball hook shot in four participants of different skill levels were investigated. Participants were asked to throw from different shooting distances, which were varied in a systematic manner between 2m and 9m in two different conditions (with and without a defender present). There was a common significant trend for increasing throwing velocity paired with increasing wrist trajectory radii as shooting distance increased. Continuous angle kinematics showed high levels of inter- and intra-individual variability particularly related to throwing distance. Comparison of the kinematics when throwing with and without a defender present indicated differences for a novice performer, but not for more skilled individuals. In summary, the basketball hook shot is a suitable movement model for investigating the application of dynamical systems theory to a discrete, multi-articular movement model where throwing distance resembles a candidate control parameter. 2. Experimentation under the dynamical systems theoretical paradigm usually entails the systematic variation of a candidate control parameter in a scaling procedure. However there is no consensus regarding a suitable analysis procedure for discrete, multiarticular actions. Extending upon previous approaches, a cluster analysis method was developed which made the systematic identification of different movement patterns possible. The validity of the analysis method was demonstrated using distinct movement models: 1) bimanual, wrist movement, 2) three different basketball shots, 3) a basketball hook shot scaling experiment. In study 1, the results obtained from the cluster analysis approach matched results obtained by a traditional analysis using discrete relative phase. In study 2, the results from the method matched the a-priori known distinction into three different basketball techniques. Study 3 was designed specifically to facilitate a bimodal throwing pattern due to laboratory restrictions in throwing height. The cluster analysis again was able to identify the a-priori known distribution. Additionally, a hysteresis effect for throwing distance was identified further strengthening the validity of the chosen movement model. 3. Using eight participants, hook shot throwing distance was varied between 2m and 9m in both directions. Some distinct inter-individual differences were found in regards to movement patterning. For two subjects clear transitions between qualitatively distinct different patterns could be established. However, no qualitative differences were apparent for the remaining participants where it was suggested that a single movement pattern was continually scaled according to the throwing distance. The data supported the concept of degeneracy in that once additional movement degrees of freedom are made available these can be exploited by actors. The underlying attractor dynamics for the basketball hook shot were quite distinct from the bistable regime typically observed in rhythmical bimanual movement models. 4. To provide further evidence in support of the view that observed changes in movement patterning during a hook shot represented a phase transition, a perturbation experiment with five participants was performed. Throwing distance was once again varied in a scaling manner between 2m and 9m. The participants wore a wristband which could be attached to a weight which served as a mechanical perturbation to the throwing movement. Investigation of relaxation time-scales did not provide any evidence for critical slowing down. The movements showed high variation between all subsequent trials and no systematic variation in relation to either the mechanical perturbation or the successive jumps in throwing distance was indicated by the data. In summary, the results of the research programme highlighted some important differences between discrete multi-articular and bimanual rhythmical movement models. Based on these differences many of the findings ubiquitous in the domain of rhythmical movements may be specific to these and accordingly may not be readily generalized to movement models from other domains. This highlights the need for more research focussing on various movement models in order to broaden the scope of the dynamical systems framework and enhance further insight into movement coordination and control in complex neurobiological systems.

Thesis (Ph. D.)--Harvard University, 1968. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 1-5 (last group)).

Thesis (M.A..)--Marshall University, 2009. / Title from document title page. Includes abstract. Document formatted into pages: contains 95 pages. Includes bibliographical references p. 94-95.

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