A top tree data structure solves one of the most general variants of a well- studied dynamic trees problem consisting in maintenance of a tree along with some aggregated information on paths or in individual trees, possibly in a mutable way, under operations of inserting and removing edges. It provides a simple interface separated from both an internal top tree structure representing a hierarchical partitioning of the graph, and a driver ensuring its depth to be logarithmic, which has a crucial role for the efficiency of the data structure. The driver proposed in this thesis is based on biased trees, combining techniques used in the worst-case version of link/cut trees and in the amortized driver for top trees: An input forest is decomposed into heavy paths and interleaving vertices, all of them being represented by biased trees connected together to form exactly the top tree structure. The driver is meant to be a more efficient alternative to the originally proposed one, and a comparably efficient alternative to the driver proposed by Werneck; there is a room for their experimental comparison.

In June 2013, the American Medical Association (AMA) made the highly controversial decision to designate obesity a disease. Proponents predicted the decision would lead to reduced weight-related stigma, whereas opponents predicted designating a third of the population as “diseased” would exacerbate stigma. To determine the effects of defining obesity as a disease on explicit and implicit weight-biased attitudes and explicit weight-biased beliefs, female undergraduate students (N = 146) were randomly assigned to one of two groups: disease or lifestyle. Participants in the disease group (n = 71) were asked to read an article describing obesity as a disease caused by biology and genes; participants in the lifestyle group (n = 75) read an article describing obesity as the result of personal choices, including over-consumption of food and inactivity. Explicit weight-biased attitudes and beliefs were measured pre- and post-exposure to the article. Change in beliefs about the controllability of weight was examined as a potential meditator of the relationship between group and explicit weight-biased attitudes; and body mass index (BMI), health orientation, and fitness orientation were examined as potential moderators. Results revealed a significant interaction between group and time on weight-biased beliefs. Participants in the disease group exhibited stronger beliefs that obesity is outside a person’s control from pre- to post-exposure, whereas participants in the lifestyle group exhibited a weakening in these beliefs over the same time period. Contrary to hypotheses, this change in beliefs about the controllability of weight did not extend to weight-biased attitudes.

Magnetic bearings are increasingly being used in a wide variety of applications in the industry such as compressors, turbines, motors, generators etc. Also, there are different types available depending upon their construction. The research presented here investigates a high temperature permanent magnet biased magnetic bearing system which is jointly being researched by National Aeronautics and Space Administration (NASA) and Electron Energy Corporation (EEC). The purpose of this research was to develop a permanent magnet biased magnetic bearing system using high temperature (HT) permanent magnets (PM) developed by EEC. This system was designed for high performance, high temperature (1000F) and high speed applications. The entire system consisted of two radial bearings, two catcher bearings, one axial thrust bearing and a motor. The central rotor shaft is powered by a high temperature permanent magnet motor to be able to run at the designed conditions of 20,000 rpm. This thesis documents the design of a feedback control law that stabilizes this HTPM biased AMB levitated system and summarizes efforts to build a test rig for the HT tests of the machine. A decentralized PD control law is used to achieve successful levitation. An existing PD analog controller with single input single output (SISO) control law for each axis (previously used for a flywheel test rig) is used as a feedback controller for this HTPM magnetic bearing system. Modeling and simulation of the resulting closed loop system is done in Matlab to test for stability and an iterative approach leads to optimum values of proportional and derivative gain pairs. The notch filter locations are also determined through this closed loop iterative simulation.

Modern data analysis often involves a large number of variables, which gives rise to the problem of multicollinearity in regression models. It is well-known that in a linear model, when the design matrix X is nearly singular, then the ordinary least squares (OLS) estimator may perform poorly because of its numerical instability and large variance. To overcome this problem, many linear or nonlinear biased estimators are studied. In this work we consider a class of generalized shrunken least squares (GSLS) estimators that include many well-known linear biased estimators proposed in the literature. We compare these estimators under the mean square error and matrix mean square error criteria. Moreover, a simulation study and two numerical examples are used to illustrate some of the theoretical results.

Modern data analysis often involves a large number of variables, which gives rise to the problem of multicollinearity in regression models. It is well-known that in a linear model, when the design matrix X is nearly singular, then the ordinary least squares (OLS) estimator may perform poorly because of its numerical instability and large variance. To overcome this problem, many linear or nonlinear biased estimators are studied. In this work we consider a class of generalized shrunken least squares (GSLS) estimators that include many well-known linear biased estimators proposed in the literature. We compare these estimators under the mean square error and matrix mean square error criteria. Moreover, a simulation study and two numerical examples are used to illustrate some of the theoretical results.

The maximum entropy principle, pioneered by Jaynes, provides a method for finding the least biased probability distribution for the description of a system or process, given as prior information the expectation values of a set (in general, a small number) of relevant quantities associated with the system. The maximum entropy method was originally advanced by Jaynes as the basis of an information theory inspired foundation for equilibrium statistical mechanics. It was soon realised that the method is very useful to tackle several problems in physics and other fields. In particular it constitutes a powerful tool for obtaining approximate and sometimes exact solutions to several important partial differential equations of theoretical physics. In Chapter 1 a brief review of Shannon’s information measure and Jaynes’ maximum entropy formalism is provided. As an illustration of the maximum entropy principle a brief explanation of how it can be used to derive the standard grand canonical formalism in statistical mechanics is given. The work leading up to this thesis has resulted in the following publications in peer-review research journals: • J.-H. Schönfeldt and A.R. Plastino, Maximum entropy approach to the collisional Vlasov equation: Exact solutions, Physica A, 369 (2006) 408-416, • J.-H. Schönfeldt, N. Jimenez, A.R. Plastino, A. Plastino and M. Casas, Maximum entropy principle and classical evolution equations with source terms, Physica A, 374 (2007) 573-584, • J.-H. Schönfeldt, G.B. Roston, A.R. Plastino and A. Plastino, Maximum entropy principle, evolution equations, and physics education, Rev. Mex. Fis. E, 52 (2)(2006) 151-159. Chapter 2 is based on Schönfeldt and Plastino (2006). Two different ways for obtaining exact maximum entropy solutions for a reduced collisional Vlasov equation endowed with a Fokker-Planck like collision term are investigated. Chapter 3 is based on Schönfeldt et al. (2007). Most applications of the maximum entropy principle to time dependent scenarios involved evolution equations exhibiting the form of a continuity equations and, consequently, preserving normalization in time. In Chapter 3 the maximum entropy principle is applied to evolution equations with source terms and, consequently, not preserving normalization. We explore in detail the structure and main properties of the dynamical equations connecting the time dependent relevant mean values , the associated Lagrange multipliers, the partition function, and the entropy of the maximum entropy scheme. In particular, we compare the H-theorems verified by the maximum entropy approximate solutions with the Htheorems verified by the exact solutions. Chapter 4 is based on Schönfeldt et al. (2006). In chapter 4 it is discussed how the maximum entropy principle can be incorporated into the teaching of aspects of theoretical physics related to, but not restricted to, statistical mechanics. We focus our attention on the study of maximum entropy solutions to evolution equations that exhibit the form of continuity equations (eg. Liouville equation, the diffusion equation the Fokker-Planck equation, etc.). / Dissertation (MSc (Physics))--University of Pretoria, 2008. / Physics / MSc / unrestricted

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By increasing genomic size, whole-genome duplication (WGD) is considered a major source of evolutionary innovation and speciation. We examined sequence evolution and expression divergence following WGD in a tetraploid African clawed frog (\textit{Silurana}). We hypothesized that the redundancy generated by WGD might allow for sex-specific and/or tissue-specific divergence, contributing to sexual dimorphism in this frog, and that such changes could be detected at both the expression and sequence levels. We investigated this hypothesis with a transcriptome-based approach, comparing both sexes across brain, heart and liver. We compared molecular evolution and expression divergence of duplicate gene homeologs to singleton genes and to an extant diploid relative, and identified genes with evidence for sex-biased expression. In doing so, we provide evidence for an allopolyploid mechanism of WGD and speciation in \textit{Silurana}. Additionally, we find that female-biased gene expression is more prevalent among duplicate genes than male-biased expression, particularly in brain where expression levels are highest. We similarly identified antagonistically sex-biased homeologs with indication of positive selection. Our results indicate that divergent evolution at both the sequence and expression levels following WGD favors the co-option of female-biased gene expression and may help resolve sexually antagonistic selection in this frog, thereby facilitating the evolution of sexual dimorphism. / Thesis / Master of Science (MSc) / Whole-genome duplication (WGD) is considered a major source of evolutionary innovation and a driver of speciation. By increasing genetic content and introducing redundancy, selective pressures are reduced and paralogous pairs diverge. We investigate how sex and tissue type contribute to duplicate gene divergence following WGD in a tetraploid African clawed frog. We find evidence for sex-dependent variation in sex-biased expression patterns of duplicate genes in brain, heart and liver, and evaluate how molecular evolution of duplicate genes accounts for expression divergence between sexes. This thesis provides a general framework for investigating sex-biased duplicate gene evolution in an amphibious tetrapod.

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