Sentiment analysis aims to use automated tools to detect subjective information such as opinions, attitudes, and feelings expressed in text, and has received a rapid growth of interest in natural language processing in recent years. Probabilistic topic models, on the other hand, are capable of discovering hidden thematic structure in large archives of documents, and have been an active research area in the field of information retrieval. The work in this thesis focuses on developing topic models for automatic sentiment analysis of web data, by combining the ideas from both research domains. One noticeable issue of most previous work in sentiment analysis is that the trained classifier is domain dependent, and the labelled corpora required for training could be difficult to acquire in real world applications. Another issue is that the dependencies between sentiment/subjectivity and topics are not taken into consideration. The main contribution of this thesis is therefore the introduction of three probabilistic topic models, which address the above concerns by modelling sentiment/subjectivity and topic simultaneously. The first model is called the joint sentiment-topic (JST) model based on latent Dirichlet allocation (LDA), which detects sentiment and topic simultaneously from text. Unlike supervised approaches to sentiment classification which often fail to produce satisfactory performance when applied to new domains, the weakly-supervised nature of JST makes it highly portable to other domains, where the only supervision information required is a domain-independent sentiment lexicon. Apart from document-level sentiment classification results, JST can also extract sentiment-bearing topics automatically, which is a distinct feature compared to the existing sentiment analysis approaches. The second model is a dynamic version of JST called the dynamic joint sentiment-topic (dJST) model. dJST respects the ordering of documents, and allows the analysis of topic and sentiment evolution of document archives that are collected over a long time span. By accounting for the historical dependencies of documents from the past epochs in the generative process, dJST gives a richer posterior topical structure than JST, and can better respond to the permutations of topic prominence. We also derive online inference procedures based on a stochastic EM algorithm for efficiently updating the model parameters. The third model is called the subjectivity detection LDA (subjLDA) model for sentence-level subjectivity detection. Two sets of latent variables were introduced in subjLDA. One is the subjectivity label for each sentence; another is the sentiment label for each word token. By viewing the subjectivity detection problem as weakly-supervised generative model learning, subjLDA significantly outperforms the baseline and is comparable to the supervised approach which relies on much larger amounts of data for training. These models have been evaluated on real world datasets, demonstrating that joint sentiment topic modelling is indeed an important and useful research area with much to offer in the way of good results.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Background: Chronic rhinosinusitis (CRS) is a heterogeneous disease characterized by persistent sinonasal inflammation and sinus microbiome dysbiosis. The basis of this heterogeneity is poorly understood. We sought to address the hypothesis that a limited number of compositionally distinct pathogenic bacterial microbiota exist in CRS patients and invoke discrete immune responses and clinical phenotypes in CRS patients. Results: Sinus brushings from patients with CRS (n = 59) and healthy individuals (n = 10) collected during endoscopic sinus surgery were analyzed using 16S rRNA gene sequencing, predicted metagenomics, and RNA profiling of the mucosal immune response. We show that CRS patients cluster into distinct sub-groups (DSI-III), each defined by specific pattern of bacterial co-colonization (permutational multivariate analysis of variance (PERMANOVA); p = 0.001, r(2) = 0.318). Each sub-group was typically dominated by a pathogenic family: Streptococcaceae (DSI), Pseudomonadaceae (DSII), Corynebacteriaceae [DSIII(a)], or Staphylococcaceae [DSIII(b)]. Each pathogenic microbiota was predicted to be functionally distinct (PERMANOVA; p = 0.005, r(2) = 0.217) and encode uniquely enriched gene pathways including ansamycin biosynthesis (DSI), tryptophan metabolism (DSII), two-component response [DSIII(b)], and the PPAR-gamma signaling pathway [DSIII(a)]. Each is also associated with significantly distinct host immune responses; DSI, II, and III(b) invoked a variety of pro-inflammatory, T(H)1 responses, while DSIII(a), which exhibited significantly increased incidence of nasal polyps (Fisher's exact; p = 0.034, relative risk = 2.16), primarily induced IL-5 expression (Kruskal Wallis; q = 0.045). Conclusions: A large proportion of CRS patient heterogeneity may be explained by the composition of their sinus bacterial microbiota and related host immune response-features which may inform strategies for tailored therapy in this patient population.

The polytopic model (PM) structure is often used in the areas of automatic control and fault detection and isolation (FDI). It is an alternative to the multiple model approach which explicitly allows for interpolation among local models. This thesis proposes a novel approach to PM estimation by modeling the set of PM weights as a random vector with Dirichlet Distribution (DD). A new approximate (adaptive) PM estimator, referred to as a Quasi-Bayesian Adaptive Kalman Filter (QBAKF) is derived and implemented. The model weights and state estimation in the QBAKF is performed adaptively by a simple QB weights' estimator and a single KF on the PM with the estimated weights. Since PM estimation problem is nonlinear and non-Gaussian, a DD marginalized particle filter (DDMPF) is also developed and implemented similar to MPF. The simulation results show that the newly proposed algorithms have better estimation accuracy, design simplicity, and computational requirements for PM estimation.

O princípio das gavetas de Dirichlet é um resultado matemático baseado numa proposição relativamente simples: se desejamos distribuir N +1 objetos em N gavetas, necessariamente alguma das gavetas conterá pelo menos 2 objetos. Apesar de parecer pouco relevante, devido a sua obviedade, esse teorema constitui uma ferramenta bastante importante na prova de outros resultados matemáticos. O presente trabalho, demonstra o Princípio das Gavetas em duas versões, uma mais simples e a outra mais geral, exibe algumas aplicações que evidenciam a sua importância como ferramenta de prova, e ao mesmo tempo, utiliza da sua simplicidade para motivar o estudo do próprio resultado assim como o de outros conceitos matemáticos. O banco de questões separado por níveis de dificuldade e o plano de aula têm o propósito de subsidiar o trabalho do professor no desenvolvimento desse interessante resultado matemático. / The Dirichlets drawers principle is a mathematical result based on a relatively simple proposition: if we wish to distribute N+1 objects in N drawers, necessarily some of the drawers will contain at least 2 objects. Although it seems insignificant due to its obviousness, this result is a very important tool in proving other mathematical results. The present work proves the Dirichlets principle, also know as pigeonhole principle in two versions, one simpler and the other more general, exibits some applications that show its importance as a tool of proof, and at the same time uses its simplicity to motivate the study of the own result as well as other mathematical concepts. The set of problems separated by difficulty levels and the lesson plan are intended to subsidize the teachers work in the development of this interesting mathematical result.

Das Hauptgebiet der Arbeit stellt die Approximation der Lösungen partieller Differentialgleichungen mit Dirichlet-Randbedingungen durch Splinefunktionen dar. Partielle Differentialgleichungen finden ihre Anwendung beispielsweise in Bereichen der Elektrostatik, der Elastizitätstheorie, der Strömungslehre sowie bei der Untersuchung der Ausbreitung von Wärme und Schall. Manche Approximationsaufgaben besitzen keine eindeutige Lösung. Durch Anwendung der Penalized Least Squares Methode wurde gezeigt, dass die Eindeutigkeit der gesuchten Lösung von gewissen Minimierungsaufgaben sichergestellt werden kann. Unter Umständen lässt sich sogar eine höhere Stabilität des numerischen Verfahrens gewinnen. Für die numerischen Betrachtungen wurde ein umfangreiches, effizientes C-Programm erstellt, welches die Grundlage zur Bestätigung der theoretischen Voraussagen mit den praktischen Anwendungen bildete. / This work focuses on approximating solutions of partial differential equations with Dirichlet boundary conditions by means of spline functions. The application of partial differential equations concerns the fields of electrostatics, elasticity, fluid flow as well as the analysis of the propagation of heat and sound. Some approximation problems do not have a unique solution. By applying the penalized least squares method it has been shown that uniqueness of the solution of a certain class of minimizing problems can be guaranteed. In some cases it is even possible to reach higher stability of the numerical method. For the numerical analysis we have developed an extensive and efficient C code. It serves as the basis to confirm theoretical predictions with practical applications.

It is a standard practice in small area estimation (SAE) to use a model-based approach to borrow information from neighboring areas or from areas with similar characteristics. However, survey data tend to have gaps, ties and outliers, and parametric models may be problematic because statistical inference is sensitive to parametric assumptions. We propose nonparametric hierarchical Bayesian models for multi-stage finite population sampling to robustify the inference and allow for heterogeneity, outliers, skewness, etc. Bayesian predictive inference for SAE is studied by embedding a parametric model in a nonparametric model. The Dirichlet process (DP) has attractive properties such as clustering that permits borrowing information. We exemplify by considering in detail two-stage and three-stage hierarchical Bayesian models with DPs at various stages. The computational difficulties of the predictive inference when the population size is much larger than the sample size can be overcome by the stick-breaking algorithm and approximate methods. Moreover, the model comparison is conducted by computing log pseudo marginal likelihood and Bayes factors. We illustrate the methodology using body mass index (BMI) data from the National Health and Nutrition Examination Survey and simulated data. We conclude that a nonparametric model should be used unless there is a strong belief in the specific parametric form of a model.

This dissertation consists of three chapters on semi-parametric Bayesian Econometric methods. Chapter 1 applies a semi-parametric method to demand systems, and compares the abilities to recover the true elasticities of different approaches to linearly estimating the widely used Almost Ideal demand model, by either iteration or approximation. Chapter 2 co-authored with Dr. Melvyn Weeks introduces a new semi-parametric Bayesian Generalized Least Square estimator, which employs the Dirichlet Process prior to cope with potential heterogeneity in the error distributions. Two methods are discussed as special cases of the GLS estimator, the Seemingly Unrelated Regression for equation systems, and the Random Effects Model for panel data, which can be applied to many fields such as the demand analysis in Chapter 1. Chapter 3 focuses on the subset selection for the efficiencies of firms, which addresses the influence of heterogeneity in the distributions of efficiencies on subset selections by applying the semi-parametric Bayesian Random Effects Model introduced in Chapter 2.

This work offers new computational methods for the optimal control of the conjugate heat transfer (CHT) problem in thermal science. Conjugate heat transfer has many important industrial applications, such as heat exchange processes in power plants and cooling in electronic packaging industry, and has been a staple of computational methods in thermal science for many years. This work considers the Dirichlet boundary control of fluid-solid CHT problems. The CHT system falls into the category of multi-physics problems. Its domain typically consists of two parts, namely, a solid region subject to thermal heating or cooling and a conjugate fluid region responsible for thermal convection transport. These two different physical systems are strongly coupled through the thermal boundary condition at the fluid-solid interface. The objective in the CHT boundary control problem is to select optimally the fluid inflow profile that minimizes an objective function that involves the sum of the mismatch between the temperature distribution in the system and a prescribed temperature profile and the cost of the control. This objective is realized by minimizing a nonlinear objective function of the boundary control and the fluid temperature variables, subject to partial differential equations (PDE) constraints governed by the coupled heat diffusion equation in the solid region and mass, momentum and energy conservation equations in the fluid region. Although CHT has received extensive attention as a forward problem, the optimal Dirichlet velocity boundary control for the coupled CHT process to our knowledge is only very sparsely studied analytically or computationally in the literature [131]. Therefore, in Part I, we describe the formulation of the optimal control problem and introduce the building blocks for the finite element modeling of the CHT problem, namely, the diffusion equation for the solid temperature, the convection-diffusion equation for the fluid temperature, the incompressible viscous Navier-Stokes equations for the fluid velocity and pressure, and the model verification of CHT simulations. In Part II, we provide theoretical analysis to explain the nonsmoothness issue which has been observed in this study and in Dirichlet boundary control of Navier-Stokes flows by other scientists. Based on these findings, we use either explicit or implicit numerical smoothing to resolve the nonsmoothness issue. Moreover, we use the numerical continuation on regularization parameters to alleviate the difficulty of locating the global minimum in one shot for highly nonlinear optimization problems even when the initial guess is far from optimal. Two suites of numerical experiments have been provided to demonstrate the feasibility, effectiveness and robustness of the optimization scheme. In Part III, we demonstrate the strategy of achieving parallel scalable algorithms for CHT models in Simulations of Reactor Thermal Hydraulics. Our motivation originates from the observation that parallel processing is necessary for optimal control problems of very large scale, when the simulation of the underlying physics (or PDE constraints) involves millions or billions of degrees of freedom. To achieve the overall scalability of optimal control problems governed by PDE constraints, scalable components that resolve the PDE constraints and their adjoints are the key. In this Part, first we provide the strategy of designing parallel scalable solvers for each building blocks of the CHT modeling, namely, for the discrete diffusive operator, the discrete convection-diffusion operator, and the discrete Navier-Stokes operator. Second, we demonstrate a pair of effective, robust, parallel, and scalable solvers built with collaborators for simulations of reactor thermal hydraulics. Finally, in the the section of future work, we outline the roadmap of parallel and scalable solutions for Dirichlet boundary control of fluid-solid conjugate heat transfer processes.

Neste trabalho estudamos a existência e unicidade de soluções para o problema de Dirichlet para a equação das hipersuperfícies de curvatura média constante em domínios limitados do espaço euclidiano. / In this work we study the existence and uniqueness of solutions to the Dirichlet problem for the constant mean curvature equation in bounded domains of the Euclidean space.