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Thesis (Ph. M.)--University of Wisconsin--Madison, 1937. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. M.)--University of Wisconsin--Madison, 1945. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (M.S.)--University of Wisconsin--Madison, 1944. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Master of Science / Department of Statistics / Paul Nelson / A first step in model building in regression analysis often consists of selecting a parsimonious set of independent variables from a pool of candidate independent variables. This report uses simulation to study and compare the performance of two widely used sequential, variable selection algorithms, stepwise and backward elimination. A score is developed to assess the ability of any variable selection method to terminate with the correct model. It is found that backward elimination performs slightly better than stepwise, increasing sample size leads to a relatively small improvement in both methods and that the magnitude of the variance of the error term is the major factor determining the performance of both.

We study behavior for negative times t of the 2D periodic Navier-Stokes equations and Burgers' original model for turbulence. Both systems are proved to have rich sets of solutions that exist for all t - R and increase exponentially as t -> -(Infinity) However, our study shows that the behavior of these solutions as well as the geometrical structure of the sets of their initial data are very different. As a consequence, Burgers original model for turbulence becomes the first known dissipative system that despite possessing a rich set of backward-time exponentially growing solutions, does not display any similarities, as t -> -(Infinity), to the linear case.

The thesis is based on the use of mathematical theories and techniques to gain qualitative and quantitative insight into the transmission dynamics of hepatitis C virus (HCV) in an IDU (injecting drug user) population. A deterministic model, which stratifies the IDU population into eight mutually-exclusive compartments (based on epidemiological status), is considered. Rigorous qualitative analysis of the model establishes, for the first time, the presence of the phenomenon of backward bifurcation in HCV transmission dynamics. Three routes (or causes) to such a dynamic phenomenon have been established. Furthermore, five main parameters that play a dominant role on the transmission dynamics of the disease have been identified. Numerical simulations of the model show that the re-infection of recovered individuals has marginal effect on the HCV burden (as measured in terms of the cumulative incidence and prevalence of the disease) in the IDU community.

Particle smoothing is useful for offline state inference and parameter learning in nonlinear/non-Gaussian state-space models. However, many particle smoothers, such as the popular forward filter/backward simulator (FFBS), are plagued by a quadratic computational complexity in the number of particles. One approach to tackle this issue is to use rejection-sampling-based FFBS (RS-FFBS), which asymptotically reaches linear complexity. In practice, however, the constants can be quite large and the actual gain in computational time limited. In this contribution, we develop a hybrid method, governed by an adaptive stopping rule, in order to exploit the benefits, but avoid the drawbacks, of RS-FFBS. The resulting particle smoother is shown in a simulation study to be considerably more computationally efficient than both FFBS and RS-FFBS. / CNDM / CADICS

An extensive review was made to study the wake characteristics of a backward-facing step. Experimental and numerical studies of the backward-facing step suggest that the wake of a separated shear layer to be dependent on parameters such as: expansion ratio, aspect ratio, free stream turbulence intensity, boundary layer state and thickness at separation. The individual and combined effects of these parameters on the reattachment length are investigated and discussed in detail in this thesis. A new scaling parameter, sum of step height and boundary layer thickness at separation is proposed, which yields significant collapse of the available data. Based on the literature review, an axisymmetric model is designed for further investigating the dynamics of the flow independent of aforementioned parameters. Additionally, porous suction strips are incorporated to study the step wake characteristics independent of Reynolds number. This model has been built and will be tested extensively at UTIAS.