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This thesis aims at developing efficient algorithms for solving some fundamental engineering problems in data science and machine learning. We investigate a variety of acceleration techniques for improving the convergence times of optimization algorithms.  First, we investigate how problem structure can be exploited to accelerate the solution of highly structured problems such as generalized eigenvalue and elastic net regression. We then consider Anderson acceleration, a generic and parameter-free extrapolation scheme, and show how it can be adapted to accelerate practical convergence of proximal gradient methods for a broad class of non-smooth problems. For all the methods developed in this thesis, we design novel algorithms, perform mathematical analysis of convergence rates, and conduct practical experiments on real-world data sets. / <p>QC 20191105</p>

An investigation of the temperature response and corresponding lesion growth resulting from in vivo interstitial laser photocoagulation was performed in order to test the applicability of Arrhenius theory. The irradiations were performed in vivo in rabbit muscle for various exposures at 1.0W using an 805 nm diode laser source coupled to an optical fibre with a pre-charred tip, thereby forcing it to function as a point heat source. Temperature responses were measured using a five-microthermocouple array along a range of radial distances from the point heat source. Each temperature profile was fitted with a curve predicted by the Weinbaum-Jiji bioheat transfer equation. The lesions were resected 48 hours after irradiation and the boundary of thermal damage resulting in necrosis was determined histologically. Numerical integration of the Arrhenius integral using temperature-time data at the lesion boundary produced corresponding activation energy and pre-exponential factor pairs (Ea , a) consistent with reported values for various other endpoints and tissue types. As well, theoretical predictions of the lesion growth from Arrhenius theory agreed well with experimental results. However, the thermal parameters, which are generally assumed to be constant when solving the bioheat transfer equation, were found to vary with radial distance from the source, presumably due to a dependence on temperature. / Thesis / Master of Science (MS)

Despite significant vector control advancements in the past years, the current malaria trends suggest that new control strategies are urgently required. These new approaches should address the current frontline intervention challenges like increasing insecticide resistance in mosquitoes and residual transmission issues. Insecticide-treated livestock (ITL) is one of the novel potential strategies to overcome the above challenges. ITL involves treating livestock near humans with an insecticide like ivermectin (IVM) to kill zoophagic malaria vectors. However, ivermectin pharmacokinetics data suggests that most IVM-administered drugs remain intact, and more than 90 % of this drug is eliminated in feces. Biological metabolites: 3′′-O-demethylivermectin (3DI) and 24-hydroxymethyl ivermectin (24OHI) are also excreted in feces. Therefore, using manure from treated cattle as fertilizers contaminates the soil, ground, and surface water with IVM or its metabolites through leaching and hydraulic water flow affecting the soil and aquatic ecosystems. Contemplating the contamination impacts, these drugs' environmental fate and effects could be regarded before massive IVM applications. Many researchers have tried to address this subject in temperate regions compared to the tropics, where IVM is urgently needed. Regional discrepancies such as soil types and climate can independently and dependently determine the fate and impact of ivermectin. Our research investigates the environmental fate of IVM and its primary biological metabolites. Laboratory and field studies in Tanzania and Virginia were conducted to simulate the difference between tropical and temperate climates. Soil and soil-manure mixture spiked with IVM were layered into two 5 mm layers in columns exposed to natural sunlight. The remaining IVM and its primary metabolite were quantified using Liquid Chromatography with a tandem mass spectrometry detector (LC-MS/MS. These compounds degraded up to 1.5 times faster in Tanzania than in Virginia, depending on temperature, soil depths and type, organic matter, and soil moisture. When IVM is subcutaneously injected into cattle, drug residues and metabolites: 3DI and 24OHI are excreted in feces following a positive skewed Poisson distribution profile. IVM, 3DI, and 24OH were found to degrade rapidly when cattle pats when exposed to the field. Since we conducted our study in the Summer, no IVM or its metabolites leached into the soil beneath. The obtained half-lives suggest that ivermectin's massive drug administration has little to worry about, primarily when the dung from treated cattle is spread into the field in thin layers in the Summer before farm application. / Doctor of Philosophy / Despite significant vector control advancements in the past years, the current malaria trends suggest that new control strategies are urgently required. These new approaches should address the current frontline intervention challenges like increasing drug resistance in mosquitoes and residual transmission issues. Treating cattle with ivermectin is one of the novel potential strategies to overcome the above challenges. This strategy is effective because the amount of ivermectin (IVM) found in the blood of treated cattle is enough to kill malaria vectors feeding on them. However, the literature suggests that most IVM-administered drugs remain intact, and more than 90 % of this drug is eliminated in feces. Metabolite bioproducts: 3″-O-demethylivermectin (3DI) and 24-hydroxymethyl ivermectin (24OHI) are also excreted in feces. Therefore, using manure from treated cattle as fertilizers contaminates the soil, ground, and surface water with IVM or its metabolites through leaching and hydraulic water flow affecting the soil and aqua ecosystems. Contemplating the contamination impacts, these drugs' environmental fate and effects could be regarded before massive IVM applications. Many researchers have tried to address this subject in temperate regions compared to the tropics, where IVM is more needed. Regional discrepancies such as soil types and climate can independently and dependently determine the fate and impact of ivermectin. Our research investigates the environmental fate of IVM and its primary bioproducts. Laboratory and field studies in Tanzania and Virginia were conducted to simulate the difference between tropical and temperate climates. Soil and soil-manure mixture spiked with IVM were layered into two 5 mm layers in columns exposed to natural sunlight. The remaining IVM and its primary metabolite were quantified on the appropriate instrument. These compounds degraded up to 1.5 times faster in Tanzania than in Virginia, depending on temperature, soil depths and type, organic matter, and soil moisture. When IVM drug is injected into cattle, the intact drug and its bioproducts: 3DI and 24OHI, are eliminated in feces following a favorable skewed normal distribution profile. IVM, 3DI, and 24OH were found to degrade rapidly when cattle pats when exposed to the field. Since we conducted our study in the Summer, no IVM or its bioproducts leached into the soil beneath. The obtained data suggest that ivermectin's massive drug administration has little to worry about, primarily when the dung from treated cattle is spread into the field in thin layers in the Summer before farm application.

Over the last several decades, the field of education has the seen the introduction and normalization of high-stakes standardized testing as part of the educational routine. With this introduction, questions concerning how these standardized tests have altered the educational landscape for teachers remain. 'Teaching to the test' has become a household phrase, one that can have both positive and negative undertones. To better understand how teachers negotiate the influences over their curricular and instructional decisions requires the studying of both their planning and implementation processes as well as how they interact with the official curriculum. Guiding this investigation are two comprehensive questions. How does a veteran teacher's understanding of historical significance impact how they ascribe value to the purpose, nature and utility of history as a school discipline over time and space? How tightly aligned are a veteran teacher's conceptions and perceptions of the purpose, nature and utility of history as a school subject with their observed pedagogical practices? This study sought to investigate the various influences over a teachers' curricular and instructional decision-making by building on previous research. Through interviews, surveys, classroom observations, and collecting documents, I was able to capture the planning and implementation routines of a veteran teacher. Through these methods, it was discovered that the multitude of influences were much more fluid and intertwined than first thought. This study sheds light on the web of influences teachers have to operate in on a daily basis. / Ph. D. / Over the last several decades, the field of education has the seen the introduction and normalization of high-stakes standardized testing as part of the educational routine. With this introduction, questions concerning how these standardized tests have altered the educational landscape for teachers remain. “Teaching to the test” has become a household phrase, one that can have both positive and negative undertones. In an attempt to better understand how teachers determine what is important enough to teach, this study investigates the planning and implementation processes of a veteran teacher. More specifically, this study sought to investigate the various influences over a teachers’ curricular and instructional decision-making by building on previous research. Within a high-stakes testing environment, is it as simple as “teaching to the test?” Through interviews, surveys, classroom observations, and collecting documents, I was able to capture the planning and implementation routines of a veteran teacher. Through these methods, it was discovered that the multitude of influences were much more fluid and intertwined than first thought. This study sheds light on the web of influences teachers have to operate in on a daily basis.

Liquefaction of granular soil deposits can have extremely detrimental effects on the stability of embankment dams, natural soil slopes, and mine tailings. The residual or liquefied shear strength of the liquefiable soils is a very important parameter when evaluating stability and deformation of level and sloping ground. Current procedures for estimating the liquefied shear strength are based on extensive laboratory testing programs or from the back-analysis of failures where liquefaction was involved and in-situ testing data was available. All available procedures utilize deterministic methods for estimation and selection of the liquefied shear strength. Over the past decade, there has been an increasing trend towards analyzing geotechnical problems using probability and reliability. This study presents procedures for assessing the liquefied shear strength of cohesionless soil deposits within a risk-based framework. Probabilistic slope stability procedures using reliability methods and Monte Carlo Simulations are developed to incorporate uncertainties associated with geometrical and material parameters. The probabilistic methods are applied to flow liquefaction case histories from the 1999 Kocaeli/Duzce, Turkey Earthquake, where extensive liquefaction was observed. The methods presented in this paper should aid in making better decisions about the design and rehabilitation of structures constructed of or atop liquefiable soil deposits. / Master of Science

Es wird die Axiomatisierbarkeit einer Klasse von temporalen Prädikatenlogiken über verzweigenden Strukturen gezeigt. Entscheidbarkeitsresultate folgen für diverse Fragmente dieser Logiken. Anwendungen werden diskutiert.

Es wird die Axiomatisierbarkeit einer Klasse von temporalen Prädikatenlogiken über verzweigenden Strukturen gezeigt. Entscheidbarkeitsresultate folgen für diverse Fragmente dieser Logiken. Anwendungen werden diskutiert.

[pt] O presente trabalho propõe um método estatístico computacionalmente eficiente (chamado Green-FOSM) para consideração de incertezas em problemas geomecânicos, com o objetivo de melhorar o processo de tomada de decisão ao analisar problemas associados com o processo de injeção ou depleção de fluídos. A novidade do método proposto está associada com a utilização do método das funções de Green (GFA), que, com o auxílio do método estatístico first-order second-moment (FOSM), é utilizado para propagar as inerentes incertezas associadas às propriedades mecânicas do material para o campo de deslocamento da formação geológica. Além disso, através dos conceitos de grid estocástico e função de autocorrelação, o método proposto permite a consideração da variabilidade espacial de variáveis aleatórias de entrada que representam essas propriedades mecânicas. O GFA utiliza as soluções fundamentais da mecânica clássica (solução fundamental de Kelvin, solução fundamental de Melan, entre outras) e o teorema da reciprocidade para determinar o campo de deslocamento de uma formação geológica com geometria irregular e diferentes tipos de materiais. A grande vantagem deste método em relação ao clássico método dos elementos finitos (MEF) é que ele não requer a imposição de condições de contorno e a análise do problema pode ser realizada considerando apenas o domínio do reservatório ou outras regiões de interesse. Esta estratégia de modelagem diminui os graus de liberdade do modelo e o tempo de processamento da análise. Desta forma, como o GFA requer menos esforço computacional, este método torna-se ideal para ser utilizado na propagação de incertezas em problemas geomecânicos. Inicialmente, baseado no método das funções de Green original proposto por Peres et al. (2021), foi proposto uma versão iterativa do método Green-FOSM, que apresenta resultados estatísticos semelhantes aos encontrados através da clássica simulação de Monte Carlo (SMC). Nesta versão original, o campo de deslocamento é PUC-Rio - Certificação Digital Nº 1912634/CA calculado usando um esquema numérico iterativo que diminui o desempenho computacional do método e pode gerar problemas de convergência. Tais limitações tem dificultado a aplicação do GFA original e do método Green-FOSM iterativo em problemas reais. Assim, o presente trabalho desenvolveu uma nova versão do GFA que utiliza um esquema numérico não-iterativo. Para os problemas de validação analisados, o método não-iterativo demonstra ser até 17.5 vezes mais rápido do que a versão original. Além disso, esta versão demonstra ser capaz de expandir a aplicabilidade do GFA, pois os problemas de convergência foram eliminados e os resultados obtidos por este método, ao analisar um perfil geológico representativo do pré-sal brasileiro, são semelhantes aos encontrados via MEF. Por fim, a partir do GFA não-iterativo foi proposta uma versão não-iterativa do método Green-FOSM. Esta versão não-iterativa é capaz de analisar probabilisticamente formações geológicas complexas, como é o caso das formações geológicas do présal brasileiro. Utilizando os mesmos recursos computacionais, o método GreenFOSM não-iterativo é no mínimo 200 vezes mais rápido que o método iterativo. De forma geral, os resultados encontrados nas análises realizadas (determinísticas e probabilísticas) são próximos dos resultados obtidos pelo método de referência (MEF e SMC, respectivamente). / [en] The present work proposes a computationally efficient stochastic statistical method (called Green-FOSM) that considers uncertainties in geomechanical problems, with the objective of improving the decision-making process related to problems associated with the process of fluid injection or depletion. The novelty of the method lies in the use of the Green s function approach (GFA), which, together, with the first-order second-moment statistical method (FOSM), is used to propagate uncertainties associated with the mechanical properties of material to the displacement field of the geological formation. Furthermore, using the concepts of stochastic grid and autocorrelation function, the proposed method allows the consideration of the spatial variability of random variables that represent these mechanical properties. The GFA uses the fundamental solutions of classical mechanics (Kelvin fundamental solution, Melan fundamental solution, among others) and the reciprocity theorem to calculate the displacement field of a geological formation with irregular geometry, and different types of materials. The great advantage of this method compared to the classical finite element method (FEM) is that it does not require the imposition of boundary conditions and the analysis of the problem can be performed considering only the reservoir or other regions of interest. This modeling strategy decreases the degrees of freedom of the model and the CPU time of the deterministic analysis. In this way, as the GFA requires less computational effort, this approach becomes ideal for propagating the uncertainties in geomechanical problems. Initially, an iterative version of the Green-FOSM method was proposed, which presents statistical results similar to those found through the classic Monte Carlo simulation (MCS). In this initial version, the displacement field is calculated using an iterative numerical scheme, which decreases the computational performance of the method and can generate convergence problems. Such limitations would restrict the application of the PUC-Rio - Certificação Digital number 1912634/CA original GFA and the iterative Green-FOSM method in real problems. Thus, the present work also developed a new version of the GFA, which uses a non-iterative numerical scheme. For the proposed validation problems, the non-iterative method proved to be up to 17.5 times faster than the original version. This version is able to expand the applicability of the GFA, since the convergence problems were eliminated and the results obtained by this method, when analyzing a representative geological profile of the Brazilian pre-salt, are similar to those found via FEM. Finally, based on the non-iterative GFA, a non-iterative version of the Green-FOSM method was proposed. This non-iterative version is capable of probabilistically analyzing complex geological formations, such as the Brazilian pre-salt geological formations. Using the same computational resources, the non-iterative GreenFOSM method is at least 200 times faster than the iterative Green-FOSM method. In general, the results found in the investigated analyzes (deterministic and probabilistic) are close to the results obtained by the reference method (FEM and MCS, respectively).

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