Thesis (Ph. D.)--University of Texas at Austin, 1998. / Vita. Includes bibliographical references (leaves 95-96). Available also in a digital version from Dissertation Abstracts.

Inaug.-diss.-Münster i. W.

"The purpose of this paper is to examine the various statements of the Axiom of Choice and the Hausdorff Maximality Principle, and the Tychonoff Product Theorem; and to show that they are logically equivalent"--Preface. / "June, 1957." / Typescript. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Arts." / Advisor: James Watson Ellis, Professor Directing Paper. / Includes bibliographical references (leaf 46).

Since its development, the minimax framework has been one of the corner stones of theoretical statistics, and has contributed to the popularity of many well-known estimators, such as the regularized M-estimators for high-dimensional problems. In this thesis, we will first show through the example of sparse Gaussian sequence model, that the theoretical results under the classical minimax framework are insufficient for explaining empirical observations. In particular, both hard and soft thresholding estimators are (asymptotically) minimax, however, in practice they often exhibit sub-optimal performances at various signal-to-noise ratio (SNR) levels. To alleviate the descrepancy, we first demonstrate that this issue can be resolved if the signal-to-noise ratio is taken into account in the construction of the parameter space. We call the resulting minimax framework the signal-to-noise ratio aware minimaxity. Then, we showcase how one can use higher-order asymptotics to obtain accurate approximations of the SNR-aware minimax risk and discover minimax estimators. Theoretical findings obtained from this refined minimax framework provide new insights and practical guidance for the estimation of sparse signals. In a broader context, we investigated the same problem for sparse linear regression. We assume the random design and allow the feature matrix to be high dimensional as 𝑿 ∈ R^{𝑛 x 𝑝} and 𝑝 ⪢ 𝑛 . This adds an extra layer of challenge to the estimation of coefficients. Previous studies have largely relied on results expressed in rate-minimaxity, where estimators are compared based on minimax risk with order-wise accuracy, without specifying the precise constant in the approximation. This lack of precision contributes to the notable gap between theoretical conclusions of the asymptotic minimax estimators and empirical findings of the sub-optimality. This thesis addresses this gap by initially refining the classical minimax result, providing a characterization of the constant in the first-order approximation. Subsequently, by following the framework of SNR-aware minimaxity we introduced before, we derived improved approximations of minimax risks under different SNR levels. Notably, these refined results demonstrated better alignment with empirical findings compared to classical minimax outcomes. As showcased in the thesis, our enhanced SNR-aware minimax framework not only offers a more accurate depiction of sparse estimation but also unveils the crucial role of SNR in the problem. This insight emerges as a pivotal factor in assessing the optimality of estimators.

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To date, the structural significance of the skin of fish larvae in osmoregulation has received little attention and the evidence for salt secretion by cutaneous chloride cells is based largely on morphological observations. Thus, in the present study, a combination of microscopical and electrophysiological techniques were utilised to determine the role of the skin of early post-hatch turbot larvae in osmoregulation. A number of specialised structural features were revealed in the skin of the turbot larva with electron microscopy which would appear to provide some protection against the high osmotic and ionic gradients tending to dehydrate and salt load the body tissue and fluids. In the heterogenous epidermis, consisting of both transporting and non-transporting cells, only the shallow junctions between chloride cells and accessory cells were believed to permit ion influx and/or water loss via the paracellular pathway; the extensive junctions between adjacent pavement cells and pavement cells and neighbouring chloride cells effectively occluding the passage of ions and water through the extracellular space. Chloride cells were revealed in the skin and prebranchial epithelium of the turbot larva from hatching, but accessory cells, and thus "leaky" junctions, were only observed in association with the closely juxtaposed chloride cells in the prebranchial epithelium which, although densely packed, represented just a small area of the otherwise "tight" skin. Water and ion permeation through the external plasma membrane of the superficial pavement cells might further be impeded by the extracellular glycocalyx coat observed in TEM. In addition, the large numbers of mucous cells, which were a characteristic feature of the skin of the turbot larva, may produce a protective mucus coating of low permeability. The apparent "tightness" of the skin was reflected by the measurements of diffusional water permeability (Pdiff) from early stage larvae which suggested that the larvae of turbot were relative impermeable to water compared with the gills of adults. Nevertheless, the rates of water turnover were still sufficiently high that a net osmotic loss of water must be replaced by water uptake through drinking. The observation that the Pdiff of early stage turbot larvae increased with development substantiates earlier supposition that the drinking rates of larvae are a direct function of the permeability of the larva to water. A study of the chronology of chloride cell development utilising specific fluorochromes and electron microscopy revealed that the prebranchial chloride cells, which closely resembled the chloride cells described in the branchial epithelium of juveniles, were both numerous and well equipped to participate in active salt extrusion in turbot larvae even at hatching. In view of the early hypertrophy and proliferation of the prebranchial cells, their rapid increase in Na+,K+-ATPase binding sites, and the subsequent degeneration of the cutaneous chloride cells observed with larval development, it was concluded that the prebranchial chloride cells are the primary site for active ion excretion shortly after yolksac absorption. The potential importance of the cutaneous chloride cells in salt extrusion was also considered, but in view of the apparent lack of accessory cell associations and the small number of apical pits observed in SEM and TEM sections, questions were raised as to the significance of these cells in ion excretion. Measurements of the trans epithelial electrical potential (TEP) from early stage turbot using intracellular micro electrode techniques confirmed that the larvae of turbot maintain ionic gradients by the active extrusion of ions that enter into the body cavity down electrical or chemical gradients. The TEP was found to be largely the result of a Na+ diffusion potential with an additive electrogenic potential due to CI- transport, which was somehow functionally connected to Na+,K+ -ATPase. Furthermore, the concentration of Na+ in the external bathing medium was found to have a direct regulatory influence on the rate of CI- secretion, suggesting that the active secretion of Cl across the skin must be coupled to Na+. These conclusions are consistent with the current theories proposed for salt extrusion by the chloride cells in the adult teleost.

Orientador: Nilva Kazue Sakomura / Resumo: Doenças entéricas se apresentam como um dos maiores problemas da produção avícola. Historicamente, antibióticos promotores de crescimento (APC’s) têm sido usados para controlar essa situação. No entanto, as preocupações a respeito de resistência bacteriana a antibióticos têm levado a proibições regionais para reduzir o uso de APC’s. Alternativamente, microrganismos administrados diretamente na dieta como por exemplo os probióticos, podem impactar positivamente sobre a microbiota intestinal, prevenindo problemas entéricos que, inevitavelmente culminam em perdas no desempenho das aves. Outro ponto importante a ser considerado quando se fala em desafio sanitário é o consumo de ração dos animais. A utilização de modelos matemáticos que consideram o fator desafio para modelagem do consumo ainda é escasso. Nesse sentido, essa dissertação foi conduzida com dois principais propósitos: 1) investigar os efeitos de Bacillus amyloliquefaciens CECT 5940 como probiótico (DFM) sozinho ou em associação com bacitracina metileno disalicilato (BMD) em frangos de corte sobre desafio de patógeno entérico. 2) modelar o consumo relativo de animais sobre condição de desafio sanitário e integrar esse modelo dentro de um modelo mecanicista de simulação, o Broiler Growth Model (BGM). Assim, permitindo a modelagem do desempenho de animais sob condição de desafio sanitário. Para isso, um total de 1.530 frangos de corte machos Cobb500 com um dia de idade foram casualizados em cinco tratamentos, com nove r... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Enteric diseases appear one of the biggest problems of poultry production. Historically, antibiotics growth promoter (AGPs) have been used to control this framework. However, concerns about antibiotic resistance bacteria have led regional bans for reducing the use of AGPs. Alternatively, microorganisms directly supplemented in diets such as probiotics, may exhibit a positive impact on intestinal microbiota avoiding enteric problems that inevitably causes loss on broilers performance. Another important point to be considered when talking about sanitary challenge is the feed intake. The use of mathematical models that consider the challenge factor for modelling in this feed intake is still scarce. In this sense, this project was conducted with two main purposes: 1) to investigate the effects of Bacillus amyloliquefaciens CECT 5940 as a probiotic (DFM) alone or in combination with bacitracin methylene disalicylate (BMD) in broilers on enteric pathogen challenge. 2) Model the relative feed intake of animals under sanitary challenge condition and to integrate this model into the mechanistic simulation model, the Broiler Growth Model (BGM). Thus, allowing the modelling of performance of animals under sanitary challenge condition. For such, a total of 1,530-day-old male Cobb500 chicks, were randomly assigned to five treatments, with nine replicate pens with 34 birds each. Treatments included positive control (PC, basal diet without additives or challenge); negative control (NC, basa... (Complete abstract click electronic access below) / Mestre

by Ki-sing Ng. / Thesis (M.Phil.)--Chinese University of Hong Kong. / Bibliography: leaves 30.

by Lo Yiu Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 89-90). / Abstract also in Chinese. / Abstract --- p.iii / Acknowledgements --- p.iv / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1. --- Main Idea --- p.5 / Chapter 1.2. --- Organization --- p.8 / Chapter Chapter 2. --- Geometric and Analytic Preliminaries --- p.9 / Chapter 2.1. --- A Review on Measure Theory --- p.9 / Chapter 2.2. --- Submanifolds in Rn --- p.11 / Chapter 2.3. --- Several Results from PDEs --- p.17 / Chapter 2.4. --- Biharmonic Comparison Lemma --- p.20 / Chapter Chapter 3. --- Approximate Graphical Decomposition --- p.24 / Chapter 3.1. --- Some Preliminaries --- p.24 / Chapter 3.2. --- Approximate Graphical Decomposition --- p.30 / Chapter Chapter 4. --- Existence & Regularity of Measure-theoretic Limits of Minimizing Sequence --- p.41 / Chapter 4.1. --- Willmore Functional and Area --- p.41 / Chapter 4.2. --- Existence of Measure-theoretic Limit of Minimizing Sequence --- p.45 / Chapter 4.3. --- Higher Regularity at Good Points --- p.54 / Chapter 4.4. --- Convergence in Hausdorff Distance Sense --- p.62 / Chapter 4.5. --- Regularity near Bad Points --- p.64 / Chapter Chapter 5. --- Existence of Genus 1 Minimizers in Rn --- p.83 / References --- p.89

The provision and pricing of parking are recognized as important tools for achieving transportation demand management (TDM) objectives. Much of the existing literature on the topic concentrates on downtown cores and calls for the application of maximum parking allowances to limit supplies. This thesis presents an analysis of existing suburban parking supplies in order to quantify parking maxima. The total number of spaces provided, footprint required to accommodate the spaces and the employment to which parking is providing are quantified. The totals are separated by different land use categories and quantities of employment are normalized to account for high trip-generating jobs such as retail. Parking supplies are examined as a function of traditional land use market theory and across primary land use categories. The results indicate that employment is a fairly weak indicator of parking supply, while weighted employment that considers the effects of retail is a much stronger indicator. On average, very high and very low land use densities have the lowest parking requirements per employee (0.39 spaces per employee) while moderate land use densities have the least diversity of land use, yet the highest supply of employee parking (4.01 spaces per employee). The methodology applied may be used to produce quantitative maxima to be incorporated into local parking bylaws that are recognized as potentially strong TDM tools. Further research that compares the observed parking supply patterns across a series of mid-sized cities is recommended to make stronger conclusions regarding the range of maximum values.