Ordinal scales are commonly used to measure health status and disease related outcomes in hospital settings as well as in translational medical research. Notable examples include cancer staging, which is a five-category ordinal scale indicating tumor size, node involvement, and likelihood of metastasizing. Glasgow Coma Scale (GCS), which gives a reliable and objective assessment of conscious status of a patient, is an ordinal scaled measure. In addition, repeated measurements are common in clinical practice for tracking and monitoring the progression of complex diseases. Classical ordinal modeling methods based on the likelihood approach have contributed to the analysis of data in which the response categories are ordered and the number of covariates (p) is smaller than the sample size (n). With the emergence of genomic technologies being increasingly applied for obtaining a more accurate diagnosis and prognosis, a novel type of data, known as high-dimensional data where the number of covariates (p) is much larger than the number of samples (n), are generated. However, corresponding statistical methodologies as well as computational software are lacking for analyzing high-dimensional data with an ordinal or a longitudinal ordinal response. In this thesis, we develop a regularization algorithm to build a parsimonious model for predicting an ordinal response. In addition, we utilize the classical ordinal model with longitudinal measurements to incorporate the cutting-edge data mining tool for a comprehensive understanding of the causes of complex disease on both the molecular level and environmental level. Moreover, we develop the corresponding R package for general utilization. The algorithm was applied to several real datasets as well as to simulated data to demonstrate the efficiency in variable selection and precision in prediction and classification. The four real datasets are from: 1) the National Institute of Mental Health Schizophrenia Collaborative Study; 2) the San Diego Health Services Research Example; 3) A gene expression experiment to understand `Decreased Expression of Intelectin 1 in The Human Airway Epithelium of Smokers Compared to Nonsmokers' by Weill Cornell Medical College; and 4) the National Institute of General Medical Sciences Inflammation and the Host Response to Burn Injury Collaborative Study.

A aplicação da análise inversa é objeto de estudo nos mais diversos campos da ciência e da engenharia. A motivação para o tratamento de tais problemas se deve ao fato de que em muitas aplicações dessas áreas do conhecimento, há a necessidade da identificação de parâmetros físicos e geométricos a partir de dados do domínio medidos experimentalmente, já que tais parâmetros de entrada são desconhecidos para uma análise direta do problema. Neste tipo de análise o problema principal está na quantidade e qualidade dos dados experimentais obtidos, que são na maioria das vezes insuficientes para garantir que o sistema gerado apresente solução única, gerando com isto um problema essencialmente mal-posto. Assim, de forma geral o emprego confiável da análise inversa implica na utilização de ferramentas eficientes de aquisição de dados experimentais aliada a técnicas numéricas de regularização que buscam a minimização da função objetiva gerada por algum método numérico, como por exemplo, o método dos elementos de contorno (MEC). Sendo assim, o presente trabalho tem por objetivo apresentar uma formulação para resolução de problemas inversos de valor de contorno e estimativa dos parâmetros do modelo coesivo, através de medidas de campos de deslocamentos, em sólidos bidimensionais com domínio formado por multi-regiões via (MEC), utilizando-se de técnicas tais como: mínimos quadrados, regularização de Tikhonov, decomposição em valor singular (SVD) e filtro de Tikhonov, para regularização do problema. Além disto, são apresentados alguns exemplos de aplicação da formulação desenvolvida. / The application of inverse analysis is nowadays subject of research of many fields in engineering and science. The motivation to consider this problem is due to the fact that in many applications of these knowledge areas, physical and geometric parameters, that are not directly known, can be identified using domain data measured experimentally. In this kind of analysis the main problem is the quantity and the quality of the obtained experimental data, which, many times, are not sufficient to guarantee that the generated system of equations has only one solution, leading therefore to an ill-posed problem. Thus, in general the reliable use of the inverse analysis requires using efficient tools for experimental data acquisition together with the numerical techniques of regularization needed to impose the minimization of the objective function written by using any numerical method, as the boundary element method (BEM) for instance. In this context, the objective of the present work is to derive a formulation for resolution of boundary-value inverse problems and to estimate the material parameters of the cohesive model, by using measured displacements fields, in multi-region two-dimensional solid by BEM, using techniques such as: least squares, Tikhonov regularization, singular value decomposition (SVD) and Tikhonov filtering, for the problem regularization. Some application examples are presented using the developed formulation to illustrate its performance.

Distribution of electrical potentials over the surface of the heart, i.e., the epicardial potentials, is a valuable tool to understand whether there is a defect in the heart. However, it is not easy to detect these potentials non-invasively. Instead, body surface potentials, which occur as a result of the electrical activity of the heart, are measured to diagnose heart defects. However the source electrical signals loose some critical details because of the attenuation and smoothing they encounter due to body tissues such as lungs, fat, etc. Direct measurement of these epicardial potentials requires invasive procedures. Alternatively, one can reconstruct the epicardial potentials non-invasively from the body surface potentials / this method is called the inverse problem of electrocardiography (ECG). The goal of this study is to solve the inverse problem of ECG using several well-known regularization methods and using their combinations with genetic algorihm (GA) and finally compare the performances of these methods. The results show that GA can be combined with the conventional regularization methods and their combination improves the regularization of ill-posed inverse ECG problem. In several studies, the results show that their combination provide a good scheme for solving the ECG inverse problem and the performance of regularization methods can be improved further. We also suggest that GA can be initiated succesfully with a training set of epicardial potentials, and with the optimum, over- and under-regularized Tikhonov regularization solutions.

A aplicação da análise inversa é objeto de estudo nos mais diversos campos da ciência e da engenharia. A motivação para o tratamento de tais problemas se deve ao fato de que em muitas aplicações dessas áreas do conhecimento, há a necessidade da identificação de parâmetros físicos e geométricos a partir de dados do domínio medidos experimentalmente, já que tais parâmetros de entrada são desconhecidos para uma análise direta do problema. Neste tipo de análise o problema principal está na quantidade e qualidade dos dados experimentais obtidos, que são na maioria das vezes insuficientes para garantir que o sistema gerado apresente solução única, gerando com isto um problema essencialmente mal-posto. Assim, de forma geral o emprego confiável da análise inversa implica na utilização de ferramentas eficientes de aquisição de dados experimentais aliada a técnicas numéricas de regularização que buscam a minimização da função objetiva gerada por algum método numérico, como por exemplo, o método dos elementos de contorno (MEC). Sendo assim, o presente trabalho tem por objetivo apresentar uma formulação para resolução de problemas inversos de valor de contorno e estimativa dos parâmetros do modelo coesivo, através de medidas de campos de deslocamentos, em sólidos bidimensionais com domínio formado por multi-regiões via (MEC), utilizando-se de técnicas tais como: mínimos quadrados, regularização de Tikhonov, decomposição em valor singular (SVD) e filtro de Tikhonov, para regularização do problema. Além disto, são apresentados alguns exemplos de aplicação da formulação desenvolvida. / The application of inverse analysis is nowadays subject of research of many fields in engineering and science. The motivation to consider this problem is due to the fact that in many applications of these knowledge areas, physical and geometric parameters, that are not directly known, can be identified using domain data measured experimentally. In this kind of analysis the main problem is the quantity and the quality of the obtained experimental data, which, many times, are not sufficient to guarantee that the generated system of equations has only one solution, leading therefore to an ill-posed problem. Thus, in general the reliable use of the inverse analysis requires using efficient tools for experimental data acquisition together with the numerical techniques of regularization needed to impose the minimization of the objective function written by using any numerical method, as the boundary element method (BEM) for instance. In this context, the objective of the present work is to derive a formulation for resolution of boundary-value inverse problems and to estimate the material parameters of the cohesive model, by using measured displacements fields, in multi-region two-dimensional solid by BEM, using techniques such as: least squares, Tikhonov regularization, singular value decomposition (SVD) and Tikhonov filtering, for the problem regularization. Some application examples are presented using the developed formulation to illustrate its performance.

La modélisation inverse de la dispersion atmosphérique consiste à reconstruire les caractéristiques d’une source (quantité de polluants rejetée, position) à partir de mesures de concentration dans l’air, en utilisant un modèle direct de dispersion et un algorithme d’inversion. Nous avons utilisé dans cette étude deux modèles directs de dispersion atmosphérique SIRANE (Soulhac, 2000; Soulhac et al., 2011) et SIRANERISK (Cierco et Soulhac, 2009a; Lamaison et al., 2011a, 2011b). Il s’agit de deux modèles opérationnels de « réseau des rues », basés sur le calcul du bilan de masse à différents niveaux du réseau. Leur concept permet de décrire correctement les différents phénomènes physiques de dispersion et de transport de la pollution atmosphérique dans des réseaux urbains complexes. L’étude de validation de ces deux modèles directs de dispersion a été effectuée après avoir évalué la fiabilité des paramétrages adoptés pour simuler les échanges verticaux entre la canopée et l'atmosphère, les transferts aux intersections de rues et la canalisation de l’écoulement à l’intérieur du réseau de rues. Pour cela, nous avons utilisé des mesures en soufflerie effectuées dans plusieurs configurations académiques. Nous avons développé au cours de cette thèse un système de modélisation inverse de dispersion atmosphérique (nommé ReWind) qui consiste à déterminer les caractéristiques d’une source de polluant (débit, position) à partir des concentrations mesurées, en résolvant numériquement le système matriciel linéaire qui relie le vecteur des débits au vecteur des concentrations. La fiabilité des résultats et l’optimisation des temps de calcul d’inversion sont assurées par le couplage de plusieurs méthodes mathématiques de résolution et d’optimisation, bien adaptées pour traiter le cas des problèmes mal posés. L’étude de sensibilité de cet algorithme d’inversion à certains paramètres d’entrée (comme les conditions météorologiques, les positions des récepteurs,…) a été effectuée en utilisant des observations synthétiques (fictives) fournies par le modèle direct de dispersion atmosphérique. La spécificité des travaux entrepris dans le cadre de ce travail a consisté à appliquer ReWind dans des configurations complexes de quartier urbain, et à utiliser toute la variabilité turbulente des mesures expérimentales obtenues en soufflerie pour qualifier ses performances à reconstruire les paramètres sources dans des conditions représentatives de situations de crise en milieu urbain ou industriel. L’application de l’approche inverse en utilisant des signaux instantanés de concentration mesurés en soufflerie plutôt que des valeurs moyennes, a montré que le modèle ReWind fournit des résultats d’inversion qui sont globalement satisfaisants et particulièrement encourageants en termes de reproduction de la quantité de masse totale de polluant rejetée dans l’atmosphère. Cependant, l’algorithme présente quelques difficultés pour estimer à la fois le débit et la position de la source dans certains cas. En effet, les résultats de l’inversion sont assez influencés par le critère de recherche (d’optimisation), le nombre de récepteurs impactés par le panache, la qualité des observations et la fiabilité du modèle direct de dispersion atmosphérique. / The aim of this study is to develop an inverse atmospheric dispersion model for crisis management in urban areas and industrial sites. The inverse modes allows for the reconstruction of the characteristics of a pollutant source (emission rate, position) from concentration measurements, by combining a direct dispersion model and an inversion algorithm, and assuming as known both site topography and meteorological conditions. The direct models used in these study, named SIRANE and SIRANERISK, are both operational "street network" models. These are based on the decomposition of the urban atmosphere into two sub-domains: the urban boundary layer and the urban canopy, represented as a series of interconnected boxes. Parametric laws govern the mass exchanges between the boxes under the assumption that the pollutant dispersion within the canopy can be fully simulated by modelling three main bulk transfer phenomena: channelling along street axes, transfers at street intersections and vertical exchange between a street canyon and the overlying atmosphere. The first part of this study is devoted to a detailed validation of these direct models in order to test the parameterisations implemented in them. This is achieved by comparing their outputs with wind tunnel experiments of the dispersion of steady and unsteady pollutant releases in idealised urban geometries. In the second part we use these models and experiments to test the performances of an inversion algorithm, named REWind. The specificity of this work is twofold. The first concerns the application of the inversion algorithm - using as input data instantaneous concentration signals registered at fixed receptors and not only time-averaged or ensemble averaged concentrations. - in urban like geometries, using an operational urban dispersion model as direct model. The application of the inverse approach by using instantaneous concentration signals rather than the averaged concentrations showed that the ReWind model generally provides reliable estimates of the total pollutant mass discharged at the source. However, the algorithm has some difficulties in estimating both emission rate and position of the source. We also show that the performances of the inversion algorithm are significantly influenced by the cost function used to the optimization, the number of receptors and the parameterizations adopted in the direct atmospheric dispersion model.

Since the inverse problem in Diffusive Optical Tomography (DOT) is nonlinear and severely ill-posed, only low resolution reconstructions are feasible when noise is added to the data nowadays. The purpose of this thesis is to improve image reconstruction in DOT of the main optical properties of tissues with some novel mathematical methods. We have used the Landweber (L) method, the Landweber-Kaczmarz (LK) method and its improved Loping-Landweber-Kaczmarz (L-LK) method combined with sparsity or with total variation regularizations for single and simultaneous image reconstructions of the absorption and scattering coefficients. The sparsity method assumes the existence of a sparse solution which has a simple description and is superposed onto a known background. The sparsity method is solved using a smooth gradient and a soft thresholding operator. Moreover, we have proposed an improved sparsity method. For the total variation reconstruction imaging, we have used the split Bregman method and the lagged diffusivity method. For the total variation method, we also have implemented a memory-efficient method to minimise the storage of large Hessian matrices. In addition, an individual and simultaneous contrast value reconstructions are presented using the level set (LS) method. Besides, the shape derivative of DOT based on the RTE is derived using shape sensitivity analysis, and some reconstructions for the absorption coefficient are presented using this shape derivative via the LS method.\\Whereas most of the approaches for solving the nonlinear problem of DOT make use of the diffusion approximation (DA) to the radiative transfer equation (RTE) to model the propagation of the light in tissue, the accuracy of the DA is not satisfactory in situations where the medium is not scattering dominant, in particular close to the light sources and to the boundary, as well as inside low-scattering or non-scattering regions. Therefore, we have solved the inverse problem in DOT by the more accurate time-dependant RTE in two dimensions.

Develop new strategies to design and operate the multilateration systems, used for air traffic control operations, in a more efficient way. The design strategies are based on the utilization of metaheuristic optimization techniques and they are intended to found the optimal spatial distribution of the system ground stations, taking into account the most relevant system operation parameters. The strategies to operate the systems are based on the development of new positioning methods which allow solving the problems of uncertainty position and poor accuracy that the current systems can present. The new strategies can be applied to design, deploy and operate the multilateration systems for airport surface surveillance as well as takeoff-landing, approach and enroute control. An important advance in the current knowledge of air traffic control is expected from the development of these strategies, because they solve several deficiencies that have been made clear, by the international scientific community, in the last years. / Mantilla Gaviria, IA. (2013). New Strategies to Improve Multilateration Systems in the Air Traffic Control [Tesis doctoral]. Editorial Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/29688

A identificação de parâmetros físicos e geométricos utilizando medições experimentais é um procedimento comum no tratamento de muitos problemas da ciência e engenharia. Neste contexto, a análise inversa apresenta-se como uma importante ferramenta no tratamento desses problemas. Este trabalho apresenta formulações que acoplam o uso do método dos elementos de contorno (MEC) e a técnica de correlação de imagens digitais (CID) (para obtenção dos campos de deslocamentos) na resolução de alguns problemas inversos de interesse para engenharia de estruturas. Implementou-se um código computacional baseado no MEC, em técnicas de regularização e em algoritmo genético, para análise inversa em problemas de identificação das propriedades dos materiais, recuperação das condições de contorno e identificação de parâmetros do modelo coesivo de fraturamento. Exemplos com dados oriundos de uma prévia análise direta (simulando dados experimentais) são apresentados para demonstrar a eficiência das formulações propostas. Ensaios de vigas em flexão em três pontos com entalhe foram realizados com aquisição de imagens para obtenção dos campos de deslocamentos da região de propagação da fissura, via CID. Estes campos foram utilizados para alimentar o modelo inverso proposto. A técnica de CID originou dados em quantidade e precisão suficientes para os fins almejados neste trabalho. A utilização do MEC mostrou-se simples e de grande eficiência para a solução dos problemas inversos tratados. / The identification of physical and geometrical parameters utilizing experimental measurements is a common procedure in treating many problems of science and engineering. In this context, the inverse analysis is an important tool in treating these problems. This work presents formulations that associate the use of boundary element method (BEM) and the technique of digital image correlation (DIC) (for obtaining the displacement fields) in solving some inverse problems of interest to Structure Engineering. A computer code based on the BEM, on regularization techniques and genetic algorithm has been implemented for the treatment of problems such as Identification of material properties, recovery of boundary conditions and identification of cohesive model parameters. Examples with data from a previous direct analysis (simulating experimental data) are presented to demonstrate the effectiveness of the proposed formulations. Three point flexural tests with notch were performed and images were acquired to obtain the displacement fields on one lateral surface of the samples, via DIC. These displacement fields were used to feed the inverse model proposed. The DIC technique resulted in quantitative and accurate data for the purposes of this study. The use of the BEM proved to be simple and efficient in solving the inverse problems treated.

L’échographie dynamique de contraste (DCE-US) est actuellement proposée comme technique d’imagerie fonctionnelle permettant d’évaluer les nouvelles thérapies anti-angiogéniques. Dans ce contexte, L'UPRES EA 4040, Université Paris-Sud 11, et le service d'Echographie de l'Institut Gustave Roussy ont développé une méthodologie permettant de calculer automatiquement, à partir de la courbe de prise de contraste moyenne obtenue dans la tumeur après injection en bolus d’un agent de contraste, un ensemble de paramètres semi-quantitatifs. Actuellement, l’état hémodynamique du patient ou encore les conditions d’injection du produit de contraste ne sont pas pris en compte dans le calcul de ces paramètres à l’inverse d’autres modalités (imagerie par résonance magnétique dynamique de contraste ou scanner de perfusion). L’objectif de cette thèse était donc d’étendre la méthode de déconvolution utilisée en routine dans les autres modalités d’imagerie à l’échographie de contraste. Celle-ci permet de s’affranchir des conditions citées précédemment en déconvoluant la courbe de prise de contraste issue de la tumeur par la fonction d’entrée artérielle, donnant ainsi accès aux paramètres quantitatifs flux sanguin, volume sanguin et temps de transit moyen. Mon travail de recherche s’est alors articulé autour de trois axes. Le premier visait à développer la méthode de quantification par déconvolution dédiée à l’échographie de contraste, avec l’élaboration d’un outil méthodologique suivie de l’évaluation de son apport sur la variabilité des paramètres de la microvascularisation. Des évaluations comparatives de variabilité intra-opérateur ont alors mis en évidence une diminution drastique des coefficients de variation des paramètres de la microvascularisation de 30% à 13% avec la méthode de déconvolution. Le deuxième axe était centré sur l’étude des sources de variabilité influençant les paramètres de la microvascularisation portant à la fois sur les conditions expérimentales et sur les conditions physiologiques de la tumeur. Enfin, le dernier axe a reposé sur une étude rétrospective menée sur 12 patients pour lesquels nous avons évalué l’intérêt de la déconvolution en comparant l’évolution des paramètres quantitatifs et semi-quantitatifs de la microvascularisation en fonction des réponses des tumeurs obtenues par les critères RECIST à partir d’un scan effectué à 2 mois. Cette méthodologie est prometteuse et peut permettre à terme une évaluation plus robuste et précoce des thérapies anti-angiogéniques que les méthodologies actuellement utilisées en routine dans le cadre des examens DCE-US. / Dynamic contrast-enhanced ultrasonography (DCE-US) is currently used as a functional imaging technique for evaluating anti-angiogenic therapies. A mathematical model has been developed by the UPRES EA 4040, Paris-Sud university and the Gustave Roussy Institute to evaluate semi-quantitative microvascularization parameters directly from time-intensity curves. But DCE-US evaluation of such parameters does not yet take into account physiological variations of the patient or even the way the contrast agent is injected as opposed to other functional modalities (dynamic magnetic resonance imaging or perfusion scintigraphy). The aim of my PhD was to develop a deconvolution process dedicated to the DCE-US imaging, which is currently used as a routine method in other imaging modalities. Such a process would allow access to quantitatively-defined microvascularization parameters since it would provide absolute evaluation of the tumor blood flow, the tumor blood volume and the mean transit time. This PhD has been led according to three main goals. First, we developed a deconvolution method involving the creation of a quantification tool and validation through studies of the microvascularization parameter variability. Evaluation and comparison of intra-operator variabilities demonstrated a decrease in the coefficients of variation from 30% to 13% when microvascularization parameters were extracted using the deconvolution process. Secondly, we evaluated sources of variation that influence microvascularization parameters concerning both the experimental conditions and the physiological conditions of the tumor. Finally, we performed a retrospective study involving 12 patients for whom we evaluated the benefit of the deconvolution process: we compared the evolution of the quantitative and semi-quantitative microvascularization parameters based on tumor responses evaluated by the RECIST criteria obtained through a scan performed after 2 months. Deconvolution is a promising process that may allow an earlier, more robust evaluation of anti-angiogenic treatments than the DCE-US method in current clinical use.

A identificação de parâmetros físicos e geométricos utilizando medições experimentais é um procedimento comum no tratamento de muitos problemas da ciência e engenharia. Neste contexto, a análise inversa apresenta-se como uma importante ferramenta no tratamento desses problemas. Este trabalho apresenta formulações que acoplam o uso do método dos elementos de contorno (MEC) e a técnica de correlação de imagens digitais (CID) (para obtenção dos campos de deslocamentos) na resolução de alguns problemas inversos de interesse para engenharia de estruturas. Implementou-se um código computacional baseado no MEC, em técnicas de regularização e em algoritmo genético, para análise inversa em problemas de identificação das propriedades dos materiais, recuperação das condições de contorno e identificação de parâmetros do modelo coesivo de fraturamento. Exemplos com dados oriundos de uma prévia análise direta (simulando dados experimentais) são apresentados para demonstrar a eficiência das formulações propostas. Ensaios de vigas em flexão em três pontos com entalhe foram realizados com aquisição de imagens para obtenção dos campos de deslocamentos da região de propagação da fissura, via CID. Estes campos foram utilizados para alimentar o modelo inverso proposto. A técnica de CID originou dados em quantidade e precisão suficientes para os fins almejados neste trabalho. A utilização do MEC mostrou-se simples e de grande eficiência para a solução dos problemas inversos tratados. / The identification of physical and geometrical parameters utilizing experimental measurements is a common procedure in treating many problems of science and engineering. In this context, the inverse analysis is an important tool in treating these problems. This work presents formulations that associate the use of boundary element method (BEM) and the technique of digital image correlation (DIC) (for obtaining the displacement fields) in solving some inverse problems of interest to Structure Engineering. A computer code based on the BEM, on regularization techniques and genetic algorithm has been implemented for the treatment of problems such as Identification of material properties, recovery of boundary conditions and identification of cohesive model parameters. Examples with data from a previous direct analysis (simulating experimental data) are presented to demonstrate the effectiveness of the proposed formulations. Three point flexural tests with notch were performed and images were acquired to obtain the displacement fields on one lateral surface of the samples, via DIC. These displacement fields were used to feed the inverse model proposed. The DIC technique resulted in quantitative and accurate data for the purposes of this study. The use of the BEM proved to be simple and efficient in solving the inverse problems treated.