<p>Pages 8, 38, 70, 116 and 120 have no body of text in the hardcopy. All are end pages of sections with a title at the top.</p> / <p>Many symbols could not be replicated using the Special Characters list. Please download thesis to read abstract.</p> / Doctor of Philosophy (PhD)

No description available.

Neural systems are often stochastic, non-linear, and non-autonomous. The complex manifestation of these aspects hinders the interpretation of neuroscientific data. Neuroscience thus benefits from the inclusion of theoretical models in its methodology. Detailed biophysical models of neural systems, however, are often plagued by high-dimensional and poorly constrained parameter spaces. As an alternative, data-driven effective models can often explain the core dynamical features of a dataset with few underlying assumptions. By lumping high-dimensional fluctuations into low-dimensional stochastic terms, observed time-series can be well-represented by stochastic dynamical systems. Here, I apply this approach to two datasets from weakly electric fish. The rate of electrosensory sampling of freely behaving fish displays spontaneous transitions between two preferred values: an active exploratory state and a resting state. I show that, over a long timescale, this rate can be modelled with a stochastic double-well system where a slow external agent modulates the relative depth of the wells. On a shorter timescale, however, fish exhibit abrupt and transient increases in sampling rate not consistent with a diffusion process. I develop and apply a novel inference method to construct a jump-diffusion process that fits the observed fluctuations. This same technique is successfully applied to intrinsic membrane voltage noise in pyramidal neurons of the primary electrosensory processing area, which display abrupt depolarization events along with diffusive fluctuations. I then characterize a novel sensory acquisition strategy whereby fish adopt a rhythmic movement pattern coupled with stochastic oscillations of their sampling rate. Lastly, in the context of differentiating between self-generated and external electrosensory signals, I model the sensory signature of communication signals between fish. This analysis provides supporting evidence for the presence of a sensory ambiguity associated with these signals.

No description available.

Li, Yong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (p. 58-60). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- "Entropy, Pressure and Variational Principle" --- p.4 / Chapter 2.1 --- Entropy --- p.5 / Chapter 2.1.1 --- Entropy of a Partition --- p.5 / Chapter 2.1.2 --- Conditional Entropy --- p.6 / Chapter 2.1.3 --- Entropy of a Measure-Preserving Transformation --- p.7 / Chapter 2.2 --- Topological Pressure --- p.9 / Chapter 3 --- Ruelle Operator Theorem --- p.11 / Chapter 3.1 --- Ruelle Operator Theorem --- p.11 / Chapter 3.2 --- Subshifts of Finite Type --- p.26 / Chapter 4 --- Applications in Dimension Theory --- p.35 / Chapter 4.1 --- Hausdorff Dimension of Cookie-Cutter Sets --- p.35 / Chapter 4.2 --- General Case --- p.44 / Bibliography --- p.58

Avian influenza strains have been proven to be highly virulent in human populations, killing approximately 70 percent of infected individuals. Although the virus is able to spread across species from birds-to-humans, some strains, such as H5N1, have not been observed to spread from human-to-human. Pigs are capable of infection by both avian and human strains and seem to be likely candidates as intermediate hosts for co-infection of the inter-species strains. A co-infected pig potentially acts as a mixing vessel and could produce a new strain as a result of a recombination process. Humans could be immunologically naive to these new strains, hence making them super-strains. We propose an interacting host system (IHS) for such a process that considers three host species that interact by sharing strains; that is, a primary and secondary host species can both infect an intermediate host. When an intermediate host is co-infected with the strains from both the other hosts, co-infected individuals may become carriers of a super-strain back into the primary host population. The model is formulated as a classical susceptible-infectious-susceptible (SIS) model, where the primary and intermediate host species have a super-infection and co-infection with recombination structure, respectively. The intermediate host is coupled to the other host species at compartments of given infectious subclasses of the primary and secondary hosts. We use the model to give a new perspective for the trade-off hypothesis for disease virulence, by analyzing the behavior of a highly virulent super-strain. We give permanence conditions for a number of the subsystems of the IHS in terms of basic reproductive numbers of independent strains. We also simulate several relevant scenarios showing complicated dynamics and connections with epidemic forecasting.

No description available.

The present work is divided in two parts. The first is concerned with the dynamics on the Grassmann manifold of k-dimensional subvector spaces of an n dimensional real or complex vector space induced by a linear invertible transformation A of the vector space into itself. The Grassmann map GA sends p to Ap, and one asks, what are the dynamics of GA? In the second part, I consider dynamics induced by a linear cocycle covering a diffeomorphism of a compact manifold, acting on the Grassmann bundle of k-dimensional linear subspaces of TN. I prove a Kupka-Smale theorem for the space of cocycles covering diffeomorphisms of a compact manifold. The proof of this theorem implies the same type of results for derived cocycles parametrized in the space of diffeomorphisms. The results of the second part can be generalized without effort to cocycles covering endomorphisms of N.

No description available.

No description available.