The main result of this thesis is the development of a theory of semidefinite facial reduction for the Euclidean distance matrix completion problem. Our key result shows a close connection between cliques in the graph of the partial Euclidean distance matrix and faces of the semidefinite cone containing the feasible set of the semidefinite relaxation. We show how using semidefinite facial reduction allows us to dramatically reduce the number of variables and constraints required to represent the semidefinite feasible set. We have used this theory to develop a highly efficient algorithm capable of solving many very large Euclidean distance matrix completion problems exactly, without the need for a semidefinite optimization solver. For problems with a low level of noise, our SNLSDPclique algorithm outperforms existing algorithms in terms of both CPU time and accuracy. Using only a laptop, problems of size up to 40,000 nodes can be solved in under a minute and problems with 100,000 nodes require only a few minutes to solve.

The main result of this thesis is the development of a theory of semidefinite facial reduction for the Euclidean distance matrix completion problem. Our key result shows a close connection between cliques in the graph of the partial Euclidean distance matrix and faces of the semidefinite cone containing the feasible set of the semidefinite relaxation. We show how using semidefinite facial reduction allows us to dramatically reduce the number of variables and constraints required to represent the semidefinite feasible set. We have used this theory to develop a highly efficient algorithm capable of solving many very large Euclidean distance matrix completion problems exactly, without the need for a semidefinite optimization solver. For problems with a low level of noise, our SNLSDPclique algorithm outperforms existing algorithms in terms of both CPU time and accuracy. Using only a laptop, problems of size up to 40,000 nodes can be solved in under a minute and problems with 100,000 nodes require only a few minutes to solve.

Recommendation systems are emerging as an important business application as the demand for personalized services in E-commerce increases. Collaborative filtering techniques are widely used for predicting a user's preference or generating a list of items to be recommended. In this thesis, we develop several new approaches for collaborative filtering based on model combination and kernel smoothing. Specifically, we start with an experimental study that compares a wide variety of CF methods under different conditions. Based on this study, we formulate a combination model similar to boosting but where the combination coefficients are functions rather than constant. In another contribution we formulate and analyze a local variation of matrix factorization. This formulation constructs multiple local matrix factorization models and then combines them into a global model. This formulation is based on the local low-rank assumption, a slightly different but more plausible assumption about the rating matrix. We apply this assumption to both rating prediction and ranking problems, with both empirical validations and theoretical analysis. We contribute with this thesis in four aspects. First, the local approaches we present significantly improve the accuracy of recommendations both in rating prediction and ranking problems. Second, with the more realistic local low-rank assumption, we fundamentally change the underlying assumption for matrix factorization-based recommendation systems. Third, we present highly efficient and scalable algorithms which take advantage of parallelism, suited for recent large scale datasets. Lastly, we provide an open source software implementing the local approaches in this thesis as well as many other recent recommendation algorithms, which can be used both in research and production.

The numerical solution of Stein (aka discrete Lyapunov) equations is the primary step in Newton's method for the solution of discrete-time algebraic Riccati equations (DARE). Here we present a low-rank Smith method as well as a low-rank alternating-direction-implicit-iteration to compute low-rank approximations to solutions of Stein equations arising in this context. Numerical results are given to verify the efficiency and accuracy of the proposed algorithms.

Um novo laboratório experimental desenvolvido para investigar a combustão de carvão em atmosferas de oxicombustão é descrito em detalhes na tese. Um reator ciclônico é utilizado para a combustão de carvões de baixo rank em condições de escoamento turbulento e com swirl, e operando em temperaturas similares às encontradas em câmaras de combustão industriais. Um sensor potenciométrico de oxigênio, instalado dentro do reator ciclônico, é utilizado para medir o consumo de oxigênio durante a combustão das amostras de carvão. Amostras de carvão com alto teor de cinzas, das minas do Leão e Bonito localizadas no sul do Brasil, e amostras de carvão linhito pré-seco (LTBK), da região da Lusácia, na Alemanha, foram submetidos à combustão em atmosferas de ar e de oxicombustão (O2/CO2/H2O). Os experimentos foram realizados em três temperaturas médias do gás de combustão: 1073, 1173 e 1273 K. Para as amostras do carvão LTBK, a oxicombustão foi composta com duas atmosferas de O2/CO2 sem vapor d’água (21/79 e 30/70) e três atmosferas de O2/CO2/H2O (30/60/10, 30/50/20 e 30/40/30) em base molar, enquanto para as amostras dos carvões Leão e Bonito, a oxicombustão foi composta com duas atmosferas de O2/CO2 (21/79 e 30/70). As amostras de carvão foram peneiradas para uma faixa de tamanho de partículas de 1250 a 2000 μm e 125 a 500 μm, e com massas de 1g e 3g. Em adição aos testes, amostras de char dos carvões Leão e LTBK foram preparadas para investigar o comportamento da combustão de suas matrizes carbonosas com diferentes níveis de matéria volátil. Primeiramente, a investigação da combustão do carvão é feita diretamente a partir das curvas de concentração de oxigênio medidas para a combustão das amostras de carvão LTBK submetidos às atmosferas de ar e oxicombustão com vapor d’água, conforme explicado no Capítulo 2 desta tese. Entretanto, devido ao grande número de experimentos realizados e a necessidade de entender a influência dos fatores, como temperatura e as composições das atmosferas oxidantes, e as interações entre esses fatores na combustão do carvão, a análise pela metodologia do Projeto de Experimentos (DoE) é aplicada nos experimentos, conforme detalhado no Capítulo 3. A reatividade dos carvões de baixo rank é investigada por meio do cálculo dos parâmetros cinéticos globais e dos coeficientes da taxa de reação de combustão do char, considerando a hipótese de um reator bem misturado, a ser verificada ao longo da investigação, conforme descrito no Capítulo 4. A partir da análise das curvas de concentração de oxigênio (Capítulos 2 e 3), os resultados mostram que a atmosfera de oxicombustão com 79% de CO2 (21/79, O2/CO2) aumenta o consumo de oxigênio para os carvões de alto teor de cinzas, Bonito e Leão, e para o carvão linhito com alto teor de voláteis (LTBK), devido à influência da reação de gaseificação do CO2 a partir de temperaturas acima de 1073 K. A partir da análise dos parâmetros cinéticos globais calculados para avaliar a reatividade dos carvões, os resultados mostram que a hipótese do reator bem misturado não é o suficiente para capturar a cinética da combustão do carvão por batelada no interior do reator ciclônico. A reatividade dos carvões investigados, através das constantes efetivas da taxa de reação, variando-se a composição da atmosfera oxidante, temperatura do gás de combustão, tamanho de partículas, massa da amostra e posição do sensor de oxigênio, têm influência do escoamento com swirl e seus termos advectivos e difusivos. / A novel laboratory facility designed to investigate coal oxy-fuel combustion is described in the present work. A cyclone chamber allows for the combustion of low-rank coal under turbulent conditions and swirling flows, covering a temperature range similar to those found on practical furnaces. A potentiometric oxygen sensor with oxide-ion conducting solid electrolytes, as stabilized zirconia, installed within the cyclone reactor, is used to measure the oxygen consumption during the combustion of coal samples. High ash coals samples, from Leão and Bonito mining sites located in South Brazil, and pre-dried lignite coal samples (LTBK), from the Lusatian region, in Germany, were burned under air and oxy-fuel (O2/CO2/H2O) atmospheres. Experiments were carried out at three average gas combustion temperatures: 1073, 1173 and 1273 K. For LTBK coal, oxy-fuel combustion was composed with two O2/CO2 atmospheres (21/79 and 30/70) and three O2/CO2/H2O atmospheres (30/60/10, 30/50/20 and 30/40/30) in molar basis, whereas for Leão and Bonito coals, the oxy-fuel combustion was composed with two O2/CO2 atmospheres (21/79 and 30/70). Coal samples were sieved to a size range of 1250 to 2000 μm and 125 to 500 μm and with 1g and 3g. In addition, char samples from Leão and lignite coals were prepared in order to investigate the combustion behavior of its carbon matrix for different levels of volatile matter. The investigation of coal combustion behavior is made firstly directly on the oxygen concentration curves measured for LTBK coal samples burned under air and oxy-fuel atmospheres with water vapor, as detailed in Chapter 2 of this thesis. However, due to the great number of experiments performed and the need to understand the influence of the factors, as temperature and atmosphere compositions, and the interactions between them on the coal combustion, the Design of Experiments (DoE) analysis is applied in the laboratory test facility, as developed in Chapter 3. The reactivity of low rank coals is assessed by means of global kinetic parameters and of char combustion reaction coefficients, under assumption of a well stirred reactor to be tested along the investigation, as described in Chapter 4. From the analysis of oxygen concentration curves (Chapter 2 and 3), results show that oxidizer oxy-fuel atmosphere with 79% CO2 (21/79, O2/CO2) increases the oxygen consumption for high ash coals, Bonito and Leão, and for pre-dried lignite coal, LTBK, due to the influence of CO2 gasification reaction on their coal combustion reactions from gas combustion temperatures higher than 1073 K. From the analysis of global kinetic parameters calculated to assess the coal reactivity, the results show that the hypothesis of a well stirred reactor is not enough to capture the kinetic involved in coal combustion burned in batch mode within the cyclone reactor. The coal reactivity investigated with the effective reaction rate constants for different oxidizer atmospheres, gas combustion temperatures, particle diameters, sample masses and oxygen sensor position, is influenced by the swirling flow with its advective and diffusive terms.

Um novo laboratório experimental desenvolvido para investigar a combustão de carvão em atmosferas de oxicombustão é descrito em detalhes na tese. Um reator ciclônico é utilizado para a combustão de carvões de baixo rank em condições de escoamento turbulento e com swirl, e operando em temperaturas similares às encontradas em câmaras de combustão industriais. Um sensor potenciométrico de oxigênio, instalado dentro do reator ciclônico, é utilizado para medir o consumo de oxigênio durante a combustão das amostras de carvão. Amostras de carvão com alto teor de cinzas, das minas do Leão e Bonito localizadas no sul do Brasil, e amostras de carvão linhito pré-seco (LTBK), da região da Lusácia, na Alemanha, foram submetidos à combustão em atmosferas de ar e de oxicombustão (O2/CO2/H2O). Os experimentos foram realizados em três temperaturas médias do gás de combustão: 1073, 1173 e 1273 K. Para as amostras do carvão LTBK, a oxicombustão foi composta com duas atmosferas de O2/CO2 sem vapor d’água (21/79 e 30/70) e três atmosferas de O2/CO2/H2O (30/60/10, 30/50/20 e 30/40/30) em base molar, enquanto para as amostras dos carvões Leão e Bonito, a oxicombustão foi composta com duas atmosferas de O2/CO2 (21/79 e 30/70). As amostras de carvão foram peneiradas para uma faixa de tamanho de partículas de 1250 a 2000 μm e 125 a 500 μm, e com massas de 1g e 3g. Em adição aos testes, amostras de char dos carvões Leão e LTBK foram preparadas para investigar o comportamento da combustão de suas matrizes carbonosas com diferentes níveis de matéria volátil. Primeiramente, a investigação da combustão do carvão é feita diretamente a partir das curvas de concentração de oxigênio medidas para a combustão das amostras de carvão LTBK submetidos às atmosferas de ar e oxicombustão com vapor d’água, conforme explicado no Capítulo 2 desta tese. Entretanto, devido ao grande número de experimentos realizados e a necessidade de entender a influência dos fatores, como temperatura e as composições das atmosferas oxidantes, e as interações entre esses fatores na combustão do carvão, a análise pela metodologia do Projeto de Experimentos (DoE) é aplicada nos experimentos, conforme detalhado no Capítulo 3. A reatividade dos carvões de baixo rank é investigada por meio do cálculo dos parâmetros cinéticos globais e dos coeficientes da taxa de reação de combustão do char, considerando a hipótese de um reator bem misturado, a ser verificada ao longo da investigação, conforme descrito no Capítulo 4. A partir da análise das curvas de concentração de oxigênio (Capítulos 2 e 3), os resultados mostram que a atmosfera de oxicombustão com 79% de CO2 (21/79, O2/CO2) aumenta o consumo de oxigênio para os carvões de alto teor de cinzas, Bonito e Leão, e para o carvão linhito com alto teor de voláteis (LTBK), devido à influência da reação de gaseificação do CO2 a partir de temperaturas acima de 1073 K. A partir da análise dos parâmetros cinéticos globais calculados para avaliar a reatividade dos carvões, os resultados mostram que a hipótese do reator bem misturado não é o suficiente para capturar a cinética da combustão do carvão por batelada no interior do reator ciclônico. A reatividade dos carvões investigados, através das constantes efetivas da taxa de reação, variando-se a composição da atmosfera oxidante, temperatura do gás de combustão, tamanho de partículas, massa da amostra e posição do sensor de oxigênio, têm influência do escoamento com swirl e seus termos advectivos e difusivos. / A novel laboratory facility designed to investigate coal oxy-fuel combustion is described in the present work. A cyclone chamber allows for the combustion of low-rank coal under turbulent conditions and swirling flows, covering a temperature range similar to those found on practical furnaces. A potentiometric oxygen sensor with oxide-ion conducting solid electrolytes, as stabilized zirconia, installed within the cyclone reactor, is used to measure the oxygen consumption during the combustion of coal samples. High ash coals samples, from Leão and Bonito mining sites located in South Brazil, and pre-dried lignite coal samples (LTBK), from the Lusatian region, in Germany, were burned under air and oxy-fuel (O2/CO2/H2O) atmospheres. Experiments were carried out at three average gas combustion temperatures: 1073, 1173 and 1273 K. For LTBK coal, oxy-fuel combustion was composed with two O2/CO2 atmospheres (21/79 and 30/70) and three O2/CO2/H2O atmospheres (30/60/10, 30/50/20 and 30/40/30) in molar basis, whereas for Leão and Bonito coals, the oxy-fuel combustion was composed with two O2/CO2 atmospheres (21/79 and 30/70). Coal samples were sieved to a size range of 1250 to 2000 μm and 125 to 500 μm and with 1g and 3g. In addition, char samples from Leão and lignite coals were prepared in order to investigate the combustion behavior of its carbon matrix for different levels of volatile matter. The investigation of coal combustion behavior is made firstly directly on the oxygen concentration curves measured for LTBK coal samples burned under air and oxy-fuel atmospheres with water vapor, as detailed in Chapter 2 of this thesis. However, due to the great number of experiments performed and the need to understand the influence of the factors, as temperature and atmosphere compositions, and the interactions between them on the coal combustion, the Design of Experiments (DoE) analysis is applied in the laboratory test facility, as developed in Chapter 3. The reactivity of low rank coals is assessed by means of global kinetic parameters and of char combustion reaction coefficients, under assumption of a well stirred reactor to be tested along the investigation, as described in Chapter 4. From the analysis of oxygen concentration curves (Chapter 2 and 3), results show that oxidizer oxy-fuel atmosphere with 79% CO2 (21/79, O2/CO2) increases the oxygen consumption for high ash coals, Bonito and Leão, and for pre-dried lignite coal, LTBK, due to the influence of CO2 gasification reaction on their coal combustion reactions from gas combustion temperatures higher than 1073 K. From the analysis of global kinetic parameters calculated to assess the coal reactivity, the results show that the hypothesis of a well stirred reactor is not enough to capture the kinetic involved in coal combustion burned in batch mode within the cyclone reactor. The coal reactivity investigated with the effective reaction rate constants for different oxidizer atmospheres, gas combustion temperatures, particle diameters, sample masses and oxygen sensor position, is influenced by the swirling flow with its advective and diffusive terms.

Um novo laboratório experimental desenvolvido para investigar a combustão de carvão em atmosferas de oxicombustão é descrito em detalhes na tese. Um reator ciclônico é utilizado para a combustão de carvões de baixo rank em condições de escoamento turbulento e com swirl, e operando em temperaturas similares às encontradas em câmaras de combustão industriais. Um sensor potenciométrico de oxigênio, instalado dentro do reator ciclônico, é utilizado para medir o consumo de oxigênio durante a combustão das amostras de carvão. Amostras de carvão com alto teor de cinzas, das minas do Leão e Bonito localizadas no sul do Brasil, e amostras de carvão linhito pré-seco (LTBK), da região da Lusácia, na Alemanha, foram submetidos à combustão em atmosferas de ar e de oxicombustão (O2/CO2/H2O). Os experimentos foram realizados em três temperaturas médias do gás de combustão: 1073, 1173 e 1273 K. Para as amostras do carvão LTBK, a oxicombustão foi composta com duas atmosferas de O2/CO2 sem vapor d’água (21/79 e 30/70) e três atmosferas de O2/CO2/H2O (30/60/10, 30/50/20 e 30/40/30) em base molar, enquanto para as amostras dos carvões Leão e Bonito, a oxicombustão foi composta com duas atmosferas de O2/CO2 (21/79 e 30/70). As amostras de carvão foram peneiradas para uma faixa de tamanho de partículas de 1250 a 2000 μm e 125 a 500 μm, e com massas de 1g e 3g. Em adição aos testes, amostras de char dos carvões Leão e LTBK foram preparadas para investigar o comportamento da combustão de suas matrizes carbonosas com diferentes níveis de matéria volátil. Primeiramente, a investigação da combustão do carvão é feita diretamente a partir das curvas de concentração de oxigênio medidas para a combustão das amostras de carvão LTBK submetidos às atmosferas de ar e oxicombustão com vapor d’água, conforme explicado no Capítulo 2 desta tese. Entretanto, devido ao grande número de experimentos realizados e a necessidade de entender a influência dos fatores, como temperatura e as composições das atmosferas oxidantes, e as interações entre esses fatores na combustão do carvão, a análise pela metodologia do Projeto de Experimentos (DoE) é aplicada nos experimentos, conforme detalhado no Capítulo 3. A reatividade dos carvões de baixo rank é investigada por meio do cálculo dos parâmetros cinéticos globais e dos coeficientes da taxa de reação de combustão do char, considerando a hipótese de um reator bem misturado, a ser verificada ao longo da investigação, conforme descrito no Capítulo 4. A partir da análise das curvas de concentração de oxigênio (Capítulos 2 e 3), os resultados mostram que a atmosfera de oxicombustão com 79% de CO2 (21/79, O2/CO2) aumenta o consumo de oxigênio para os carvões de alto teor de cinzas, Bonito e Leão, e para o carvão linhito com alto teor de voláteis (LTBK), devido à influência da reação de gaseificação do CO2 a partir de temperaturas acima de 1073 K. A partir da análise dos parâmetros cinéticos globais calculados para avaliar a reatividade dos carvões, os resultados mostram que a hipótese do reator bem misturado não é o suficiente para capturar a cinética da combustão do carvão por batelada no interior do reator ciclônico. A reatividade dos carvões investigados, através das constantes efetivas da taxa de reação, variando-se a composição da atmosfera oxidante, temperatura do gás de combustão, tamanho de partículas, massa da amostra e posição do sensor de oxigênio, têm influência do escoamento com swirl e seus termos advectivos e difusivos. / A novel laboratory facility designed to investigate coal oxy-fuel combustion is described in the present work. A cyclone chamber allows for the combustion of low-rank coal under turbulent conditions and swirling flows, covering a temperature range similar to those found on practical furnaces. A potentiometric oxygen sensor with oxide-ion conducting solid electrolytes, as stabilized zirconia, installed within the cyclone reactor, is used to measure the oxygen consumption during the combustion of coal samples. High ash coals samples, from Leão and Bonito mining sites located in South Brazil, and pre-dried lignite coal samples (LTBK), from the Lusatian region, in Germany, were burned under air and oxy-fuel (O2/CO2/H2O) atmospheres. Experiments were carried out at three average gas combustion temperatures: 1073, 1173 and 1273 K. For LTBK coal, oxy-fuel combustion was composed with two O2/CO2 atmospheres (21/79 and 30/70) and three O2/CO2/H2O atmospheres (30/60/10, 30/50/20 and 30/40/30) in molar basis, whereas for Leão and Bonito coals, the oxy-fuel combustion was composed with two O2/CO2 atmospheres (21/79 and 30/70). Coal samples were sieved to a size range of 1250 to 2000 μm and 125 to 500 μm and with 1g and 3g. In addition, char samples from Leão and lignite coals were prepared in order to investigate the combustion behavior of its carbon matrix for different levels of volatile matter. The investigation of coal combustion behavior is made firstly directly on the oxygen concentration curves measured for LTBK coal samples burned under air and oxy-fuel atmospheres with water vapor, as detailed in Chapter 2 of this thesis. However, due to the great number of experiments performed and the need to understand the influence of the factors, as temperature and atmosphere compositions, and the interactions between them on the coal combustion, the Design of Experiments (DoE) analysis is applied in the laboratory test facility, as developed in Chapter 3. The reactivity of low rank coals is assessed by means of global kinetic parameters and of char combustion reaction coefficients, under assumption of a well stirred reactor to be tested along the investigation, as described in Chapter 4. From the analysis of oxygen concentration curves (Chapter 2 and 3), results show that oxidizer oxy-fuel atmosphere with 79% CO2 (21/79, O2/CO2) increases the oxygen consumption for high ash coals, Bonito and Leão, and for pre-dried lignite coal, LTBK, due to the influence of CO2 gasification reaction on their coal combustion reactions from gas combustion temperatures higher than 1073 K. From the analysis of global kinetic parameters calculated to assess the coal reactivity, the results show that the hypothesis of a well stirred reactor is not enough to capture the kinetic involved in coal combustion burned in batch mode within the cyclone reactor. The coal reactivity investigated with the effective reaction rate constants for different oxidizer atmospheres, gas combustion temperatures, particle diameters, sample masses and oxygen sensor position, is influenced by the swirling flow with its advective and diffusive terms.

No description available.

Ground penetrating radar (GPR) has been extensively utilized as a highly efficient and non-destructive testing method for infrastructure evaluation, such as highway rebar detection, bridge decks inspection, asphalt pavement monitoring, underground pipe leakage detection, railroad ballast assessment, etc. The focus of this dissertation is to investigate the key techniques to tackle with GPR signal processing from three perspectives: (1) Removing or suppressing the radar clutter signal; (2) Detecting the underground target or the region of interest (RoI) in the GPR image; (3) Imaging the underground target to eliminate or alleviate the feature distortion and reconstructing the shape of the target with good fidelity. In the first part of this dissertation, a low-rank and sparse representation based approach is designed to remove the clutter produced by rough ground surface reflection for impulse radar. In the second part, Hilbert Transform and 2-D Renyi entropy based statistical analysis is explored to improve RoI detection efficiency and to reduce the computational cost for more sophisticated data post-processing. In the third part, a back-projection imaging algorithm is designed for both ground-coupled and air-coupled multistatic GPR configurations. Since the refraction phenomenon at the air-ground interface is considered and the spatial offsets between the transceiver antennas are compensated in this algorithm, the data points collected by receiver antennas in time domain can be accurately mapped back to the spatial domain and the targets can be imaged in the scene space under testing. Experimental results validate that the proposed three-stage cascade signal processing methodologies can improve the performance of GPR system.

This thesis focuses on two topics, computational methods for large spatial datasets and functional data ranking. Both are tackling the challenges of big and high-dimensional data. The first topic is motivated by the prohibitive computational burden in fitting Gaussian process models to large and irregularly spaced spatial datasets. Various approximation methods have been introduced to reduce the computational cost, but many rely on unrealistic assumptions about the process and retaining statistical efficiency remains an issue. We propose a new scheme to approximate the maximum likelihood estimator and the kriging predictor when the exact computation is infeasible. The proposed method provides different types of hierarchical low-rank approximations that are both computationally and statistically efficient. We explore the improvement of the approximation theoretically and investigate the performance by simulations. For real applications, we analyze a soil moisture dataset with 2 million measurements with the hierarchical low-rank approximation and apply the proposed fast kriging to fill gaps for satellite images. The second topic is motivated by rank-based outlier detection methods for functional data. Compared to magnitude outliers, it is more challenging to detect shape outliers as they are often masked among samples. We develop a new notion of functional data depth by taking the integration of a univariate depth function. Having a form of the integrated depth, it shares many desirable features. Furthermore, the novel formation leads to a useful decomposition for detecting both shape and magnitude outliers. Our simulation studies show the proposed outlier detection procedure outperforms competitors in various outlier models. We also illustrate our methodology using real datasets of curves, images, and video frames. Finally, we introduce the functional data ranking technique to spatio-temporal statistics for visualizing and assessing covariance properties, such as separability and full symmetry. We formulate test functions as functions of temporal lags for each pair of spatial locations and develop a rank-based testing procedure induced by functional data depth for assessing these properties. The method is illustrated using simulated data from widely used spatio-temporal covariance models, as well as real datasets from weather stations and climate model outputs.