Indiana University-Purdue University Indianapolis (IUPUI) / Joint models of longitudinal and survival outcomes have been used with increasing frequency in clinical investigations. Correct specification of fixed and random effects, as well as their functional forms is essential for practical data analysis. However, no existing methods have been developed to meet this need in a joint model setting. In this dissertation, I describe a penalized likelihood-based method with adaptive least absolute shrinkage and selection operator (ALASSO) penalty functions for model selection. By reparameterizing variance components through a Cholesky decomposition, I introduce a penalty function of group shrinkage; the penalized likelihood is approximated by Gaussian quadrature and optimized by an EM algorithm. The functional forms of the independent effects are determined through a procedure for structural discovery. Specifically, I first construct the model by penalized cubic B-spline and then decompose the B-spline to linear and nonlinear elements by spectral decomposition. The decomposition represents the model in a mixed-effects model format, and I then use the mixed-effects variable selection method to perform structural discovery. Simulation studies show excellent performance. A clinical application is described to illustrate the use of the proposed methods, and the analytical results demonstrate the usefulness of the methods.

An experimental investigation of an M level (M = 16, 64 and 256) Quadrature Amplitude Modulation (QAM) transmission system suitable for video transmission is presented. The communication system is based on layered video coding and unequal error protection to make the video bitstream robust to channel errors. An implementation is described in which H.264 video is protected unequally by partitioning the compressed data into two layers of different visual importance. The partition scheme is based on a separation of the group of pictures (GoP) in the intra-coded frame (I-frame) and predictive coded frame (P frame). This partition scheme is then applied to split the H.264-coded video bitstream and is suitable for Constant Bit Rate (CBR) transmission. Unequal error protection is based on uniform and non-uniform M-QAM constellations in conjunction with different scenarios of splitting the transmitted symbol for protection of the more important information of the video data; different constellation arrangements are proposed and evaluated to increase the capacity of the high priority layer. The performance of the transmission system is evaluated under Additive White Gaussian Noise (AWGN) and Rayleigh fading conditions. Simulation results showed that in noisy channels the decoded video can be improved by assigning a larger portion of the video data to the enhancement layer in conjunction with non-uniform constellation arrangements; in better channel conditions the quality of the received video can be improved by assigning more bits in the high priority channel and using uniform constellations. The aforementioned varying conditions can make the video transmission more successful over error-prone channels. Further techniques were developed to combat various channel impairments by considering channel coding methods suitable for layered video coding applications. It is shown that a combination of non-uniform M-QAM and forward error correction (FEC) will yield a better performance. Additionally, antenna diversity techniques are examined and introduced to the transmission system that can offer a significant improvement in the quality of service of mobile video communication systems in environments that can be modelled by a Rayleigh fading channel.

L'idée d'utiliser des bases d'ondelettes dans l'analyse numérique (résolution des équations elliptiques, aux dérivées partielles, intégrales) s'est imposée depuis que ces bases ont fait preuve de leur efficacité dans le traitement du signal. Deux problèmes se posent quant au calcul de la solution dans une base d'ondelettes : - problème 1 : l'étude de la structure de la matrice associée à un noyau K d'un opérateur intégral T dans une base d'ondelettes ; - problème 2 : l'adaptation des techniques de discrétisation de Galerkin aux bases d'ondelettes. Cette thèse contribue à l'étude de ces problèmes par l'introduction d'une nouvelle classe d'opérateurs définis par leur matrice représentative dans une base d'ondelettes et caractérisés par les dérivées fractionnaires de leurs noyaux.

Dans cette thèse, nous nous intéressons à la construction d'éléments finis d'ordre élevé adaptés aux maillages hybrides, pour la résolution de systèmes hyperboliques linéaires en régimes harmonique et temporel. L'accent est plus particulièrement porté sur la construction d'éléments pyramidaux. On étudie trois formulations pour lesquelles on cherche des éléments finis "optimaux" au sens de la convergence dans la norme de l'espace considéré pour la formulation. Pour les formulations H^1 et H(rot), on construit des éléments finis "optimaux" nodaux et hp. Les matrices élémentaires sont évaluées grâce à des formules de quadrature adaptées et des estimations d'erreur sont effectuées pour vérifier la convergence des éléments optimaux construits. Pour la formulation discontinue LDG (Local Discontinuous Galerkin), on présente des éléments utilisant des fonctions de base orthogonales permettant de mettre au point une construction de la matrice de masse et un produit matrice-vecteur rapides. Dans le cas des trois formulations, on étudie les propriétés numériques des éléments construits, on vérifie que l'on retrouve bien numériquement la convergence théorique et on compare nos éléments avec d'autres éléments trouvés dans la littérature. Finalement, on présente des expériences numériques en 3D avec l'équation des ondes ou de Helmholtz, et les équations de Maxwell dans le cas des régimes temporels et harmoniques. On montre ainsi l'efficacité des maillages hybrides par rapport aux maillages purement tétraédriques ou aux maillages hexaédriques obtenus en découpant chaque tétraèdre d'un maillage purement tétraédrique en quatre hexaèdres.

Coherent detection together with multilevel modulation formats has the potential to significantly increase the capacity of existing optical communication systems at no extra cost in signal bandwidth. However, these modulation formats are more susceptible to the impact of different noise sources and distortions as the distance between its constellation points in the complex plane reduces with the modulation index. In this context, digital signal processing (DSP) plays a key role as it allows compensating for the impairments occurring during signal generation, transmission and/or detection relaxing the complexity of the overall system. The transition towards pluggable optical transceivers, offers flexibility for network design/upgrade but sets strict requirements on the power consumption of the DSP thus limiting its complexity. The DSP module complexity however, scales with the modulation order and, in this scenario, low complex yet high performance DSP algorithms are highly desired. In this thesis, we mainly focus on the impact of laser phase noise arising from the transmitter and local oscillator (LO) lasers in coherent optical communication systems employing high order modulation formats. In these systems, the phase noise of the transmitting and LO lasers translate into phase noise in the received constellation impeding the proper recovery of the transmitted data. In order to increase the system phase noise tolerance, we firstly explore the possibility of re-arranging the constellation points in a circularly shaped mQAM (C-mQAM) constellation shape to exploit its inherent phase noise tolerance. Different low-complex carrier phase recovery (CPR) schemes applicable to these constellations are proposed along with a discussion on its performance and implementation complexity. Secondly, the design guidelines of high performance and low complex CPR schemes for conventional square mQAM constellations are presented. We identify the inherent limitation of the state-of-the-art blind phase search (BPS) carrier phase recovery algorithm which hinders its achievable performance and implementation complexity and present a low complex solution to overcome it. The design guidelines of multi-stage CPR schemes for high order modulation formats, where the BPS algorithm is employed at any of the stages, are also provided and discussed. Finally, the interplay between the received dispersed signal and the LO phase noise is analytically investigated to characterize the origin of the equalization enhanced phase noise phenomena. / <p>QC 20170516</p> / EU project ICONE, gr. #608099

Em modelos de regressão em que uma covariável é medida com erro, é comum o uso de estruturas que relacionam a covariável observada com a verdadeira covariável não observada. Essas estruturas são usualmente aditivas ou multiplicativas. Na literatura existem diversos trabalhos interessantes que tratam de modelos de regressão com erro de medida aditivo, muitos dos quais são modelos lineares com covariáveis e erro de medida normalmente distribuídos. Para modelos em que o erro de medida é multipicativo, não se encontra na literatura o mesmo desenvolvimento teórico encontrado para modelos em que o erro de medida é aditivo. O mesmo vale para situações em que as suposições de normalidade para as covariáveis e erro de medida não se aplicam. Este trabalho propõe a construção, definição, métodos de estimação e análise de diagnóstico para modelos de regressão com erro de medida multiplicativo em uma das covariáveis. Para esses modelos, consideramos que a variável resposta possa pertencer ou à classe de modelos de regressão série de potências modificadas ou à família exponencial. O rol de distribuições pertencentes à família série de potências modificada é bem abrangente, portanto, neste trabalho, desenvolvemos a teoria de estimação e validação do modelo primeiramente de forma geral e, para exemplificar, apresentamos o modelo de regressão binomial negativa com erro de medida. para o caso em que a variável resposta pertença à família exponencial. apresentamos o modelo de regressão beta com erro de medida multiplicativo. Todos os modelos propostos foram analisados através de estados de simulação e aplicados a conjuntos de dados reais. / In regression models in which a covariate is measured with erros, it is common to use structures that correlate the observed covariate with the true non-observed covariate. Such structures are usually additive or multiplicative. In the literatue there are several interesting works that deal with regression models having an additive measuremsnt error, many of which are linear models with covariate and measurement error normally distributed. For models having a multiplicative measurement error, one does not find in the literature the same theoretical amount of works as one finds for models in which the measurement error is additive. The same happens in situations where the supositions of normality for the covariates and the measurement errors do not apply. The presente work proposes the construction,definition, estimation methods, and diagnostic analysis for the regression models with a multiplicative measurement error in one of the covariates. For these models it is considered that the response variable may belong either to the class of modified power series regression models or to the exponential family. The list of distributions belonging to the family modified power series is rather comprehensive; for this reason this work develops, firstly and in a general way, the models estimation and validation theory, and, as an example, presents the model of negative binomial regression with measurement error. In the case where response variable belongs to the exponential family, the model of beta regression with multiplicative measurement error is presented. All proposed models were analysed through simulationb studies and applied to real data sets.

Neste trabalho são apresentadas algumas extensões dos modelos potência-alfa assumindo o contexto em que as observações estão censuradas ou limitadas. Inicialmente propomos um novo modelo assimétrico que estende os modelos t-assimétrico (Azzalini e Capitanio, 2003) e t-potência (Zhao e Kim, 2016) e inclui a distribuição t de Student como caso particular. Este novo modelo é capaz de ajustar dados com alto grau de assimetria e curtose, ainda maior do que os modelos t-assimétrico e t-potência. Em seguida estendemos o modelo t-potência às situações em que os dados apresentam censura, com alto grau de assimetria e caudas pesadas. Este modelo generaliza o modelo de regressão linear t de Student para dados censurados por Arellano-Valle et al. (2012). O trabalho também introduz o modelo linear misto normal-potência para dados assimétricos. Aqui a inferência estatística é realizada desde uma perspectiva clássica usando o método de máxima verossimilhança junto com o método de integração numérica de Gauss-Hermite para aproximar as integrais envolvidas na função de verossimilhança. Mais tarde, o modelo linear com interceptos aleatórios para dados duplamente censurados é estudado. Este modelo é desenvolvido sob a suposição de que os erros e os efeitos aleatórios seguem distribuições normal-potência e normal- assimétrica. Para todos os modelos estudados foram realizados estudos de simulação a fim de estudar as suas bondades de ajuste e limitações. Finalmente, ilustram-se todos os métodos propostos com dados reais. / In this work some extensions of the alpha-power models are presented, assuming the context in which the observations are censored or limited. Initially we propose a new asymmetric model that extends the skew-t (Azzalini e Capitanio, 2003) and power-t (Zhao e Kim, 2016) models and includes the Students t-distribution as a particular case. This new model is able to adjust data with a high degree of asymmetry and cursose, even higher than the skew-t and power-t models. Then we extend the power-t model to situations in which the data present censorship, with a high degree of asymmetry and heavy tails. This model generalizes the Students t linear censored regression model t by Arellano-Valle et al. (2012) The work also introduces the power-normal linear mixed model for asymmetric data. Here statistical inference is performed from a classical perspective using the maximum likelihood method together with the Gauss-Hermite numerical integration method to approximate the integrals involved in the likelihood function. Later, the linear model with random intercepts for doubly censored data is studied. This model is developed under the assumption that errors and random effects follow power-normal and skew-normal distributions. For all the models studied, simulation studies were carried out to study their benefits and limitations. Finally, all proposed methods with real data are illustrated.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Desenvolvemos nesta dissertação um método híbrido direto para o cálculo do fator de desvantagem e descrição da distribuição do fluxo de nêutrons em sistemas combustível-moderador. Na modelagem matemática, utilizamos a equação de transporte de Boltzmann independente do tempo, considerando espalhamento linearmente anisotrópico no modelo monoenergético e espalhamento isotrópico no modelo multigrupo, na formulação de ordenadas discretas (SN), em geometria unidimensional. Desenvolvemos nesta dissertação um método híbrido direto para o cálculo do fator de desvantagem e descrição da distribuição do fluxo de nêutrons em sistemas combustível-moderador. Na modelagem matemática, utilizamos a equação de transporte de Boltzmann independente do tempo, considerando espalhamento linearmente anisotrópico no modelo monoenergético e espalhamento isotrópico no modelo multigrupo, na formulação de ordenadas discretas (SN), em geometria unidimensional. Descrevemos uma análise espectral das equações de ordenadas discretas (SN)a um grupo e a dois grupos de energia, onde seguimos uma analogia com o método de Case. Utilizamos, neste método, quadraturas angulares diferentes no combustível (NC) e no moderador (NM), onde em geral assumimos que NC > NM . Condições de continuidade especiais que acoplam os fluxos angulares que emergem do combustível (moderador) e incidem no moderador (combustível), foram utilizadas com base na equivalência entre as equações SN e PN-1, o que caracteriza a propriedade híbrida do modelo proposto. Sendo um método híbrido direto, utilizamos as NC + NM equações lineares e algébricas constituídas pelas (NC + NM)/2 condições de contorno reflexivas e (NC + NM)/2 condições de continuidade para determinarmos as NC + NM constantes. Com essas constantes podemos calcular os valores dos fluxos angulares e dos fluxos escalares em qualquer ponto do domínio. Apresentamos resultados numéricos para ilustrar a eficiência e a precisão do método proposto. / In this masters dissertation we describe a hybrid direct method for calculating the disadvantage factor and the neutron flux distribution in fuel-moderator lattices. For the mathematical model, we used the discrete ordinates (SN) transport equation, considering linearly anisotropic scattering in the monoenergetic model and isotropic scattering in the energy multigroup model in slab geometry. We describe a spectral analysis of the monoenergetic and two-group SN equations, in a way which is very similar to the Case method. The basic idea is to use higher order angular quadrature set in the highly absorbing fuel region (SNF)and lower order angular quadrature set in the diffusive moderator region (SNM) i.e., NF > NM. Therefore, we apply special continuity conditions for the fuel existing fluxes that constitute the incoming fluxes for the moderator region, and conversely for the moderator existing fluxes that constitute the incoming fluxes for the fuel region, based on the equivalence of the SN and PN-1 equations, which characterize the hybrid model. As a direct hybrid method, we use NF + NM linear algebraic equations composed of (NF + NM)/2 reflexive boundary conditions and (NF + NM)/2 continuity conditions to solve for the NF + NM expansion coefficients. With these coefficients we can calculate the numerical values for the angular fluxes and for the scalar fluxes at any location of domain. We present numerical results to illustrate the efficiency and the accuracy of the offered method.

Ce travail consiste en une étude des phénomènes de coalescence dans un nuage de gouttes, par la simulation numérique directe d'un écoulement turbulent gazeux, couplée avec une approche de suivi Lagrangien pour la phase dispersée. La première étape consiste à développer et valider une méthode de détection des collisions pour une phase polydispersée. Elle est ensuite implémentée dans un code couplé de simulation directe et de suivi Lagrangien existant. Des simulations sont menées pour une turbulence homogène isotrope de la phase continue et pour des phases dispersées en équilibre avec le fluide. L'influence de l'inertie des gouttes et de la turbulence sur le taux de coalescence des gouttes est discutée dans un régime de coalescence permanente. Un aperçu est donné de la prise en compte d'autres régimes de collision et de coalescence entre gouttes. Ces simulations sont la base de développement et de validation des approches utilisées dans les calculs à l'échelle industrielle. En particulier, les résultats des simulations sont comparés avec les prédictions d'une approche Lagrangienne de type Monte-Carlo et de l'approche Eulerienne 'Direct Quadrature Method of Moments' (DQMOM). Différents types de fermeture des termes de coalescence sont validés. Les uns sont basés sur l'hypothèse de chaos-moléculaire, les autres sont capables de prendre en compte des corrélations de vitesses des gouttes avant la collision. Il est montré que cette derniere approche prédit beaucoup mieux le taux de coalescence par comparaison avec les résultats des simulations déterministes. / Coalescence in a droplet cloud is studied in this work by means of direct numerical simulation of the turbulent gas flow, which is coupled with a Lagrangian tracking of the disperse phase. In a first step, a collision detection algorithm is developed and validated, which can account for a polydisperse phase. This algorithm is then implemented into an existing code for direct numerical simulations coupled with a Lagrangian tracking scheme. Second, simulations are performed for the configuration of homogeneous isotropic turbulence of the fluid phase and a disperse phase in local equilibrium with the fluid. The influence of both droplet inertia and turbulence intensity on the coalescence rate of droplets is discussed in a pure permanent coalescence regime. First results are given, if other droplet collision outcomes than permanent coalescence (i.e. stretching and reflexive separation) are considered. These results show a strong dependence on the droplet inertia via the relative velocity of the colliding droplets at the moment of collision. The performed simulations serve also as reference data base for the development and validation of statistical modeling approaches, which can be used for simulations of industrial problems. In particular, the simulation results are compared to predictions from a Lagrangian Monte-Carlo type approach and the Eulerian 'Direct Quadrature Method of Moments' (DQMOM) approach. Different closures are validated for the coalescence terms in these approaches, which are based either on the assumption of molecular-chaos, or based on a formulation, which allows to account for the correlation of droplet velocities before collision by the fluid turbulence. It is shown that the latter predicts much better the coalescence rates in comparison with results obtained by the performed deterministic simulations.

Neste trabalho são apresentadas algumas extensões dos modelos potência-alfa assumindo o contexto em que as observações estão censuradas ou limitadas. Inicialmente propomos um novo modelo assimétrico que estende os modelos t-assimétrico (Azzalini e Capitanio, 2003) e t-potência (Zhao e Kim, 2016) e inclui a distribuição t de Student como caso particular. Este novo modelo é capaz de ajustar dados com alto grau de assimetria e curtose, ainda maior do que os modelos t-assimétrico e t-potência. Em seguida estendemos o modelo t-potência às situações em que os dados apresentam censura, com alto grau de assimetria e caudas pesadas. Este modelo generaliza o modelo de regressão linear t de Student para dados censurados por Arellano-Valle et al. (2012). O trabalho também introduz o modelo linear misto normal-potência para dados assimétricos. Aqui a inferência estatística é realizada desde uma perspectiva clássica usando o método de máxima verossimilhança junto com o método de integração numérica de Gauss-Hermite para aproximar as integrais envolvidas na função de verossimilhança. Mais tarde, o modelo linear com interceptos aleatórios para dados duplamente censurados é estudado. Este modelo é desenvolvido sob a suposição de que os erros e os efeitos aleatórios seguem distribuições normal-potência e normal- assimétrica. Para todos os modelos estudados foram realizados estudos de simulação a fim de estudar as suas bondades de ajuste e limitações. Finalmente, ilustram-se todos os métodos propostos com dados reais. / In this work some extensions of the alpha-power models are presented, assuming the context in which the observations are censored or limited. Initially we propose a new asymmetric model that extends the skew-t (Azzalini e Capitanio, 2003) and power-t (Zhao e Kim, 2016) models and includes the Students t-distribution as a particular case. This new model is able to adjust data with a high degree of asymmetry and cursose, even higher than the skew-t and power-t models. Then we extend the power-t model to situations in which the data present censorship, with a high degree of asymmetry and heavy tails. This model generalizes the Students t linear censored regression model t by Arellano-Valle et al. (2012) The work also introduces the power-normal linear mixed model for asymmetric data. Here statistical inference is performed from a classical perspective using the maximum likelihood method together with the Gauss-Hermite numerical integration method to approximate the integrals involved in the likelihood function. Later, the linear model with random intercepts for doubly censored data is studied. This model is developed under the assumption that errors and random effects follow power-normal and skew-normal distributions. For all the models studied, simulation studies were carried out to study their benefits and limitations. Finally, all proposed methods with real data are illustrated.