The purpose of this work was to develop methods to estimate the diffusion coefficient and elimination constant for dexamethasone in subcutaneous tissue. Solutions to the diffusion equation were found for different conditions relevant to implantation and injection. These solutions were then used as models for measured autoradiography data where the unknown model parameters were the diffusion coefficient and the elimination constant. The diffusion coefficient and elimination constant were then estimated by curve fitting the measured data to these models. Having these estimates would be of practical importance since inflammation surrounding implantable glucose sensors may be controlled through local release of dexamethasone at the site of implantation. Derivation of the appropriate model, how the model was used to estimate D and k, and various specific profile examples were investigated in detail. Osmotic pumps containing [3H]- dexamethasone were implanted into the subcutaneous tissue of rats. Digital autoradiography was used to measure the distribution of the [3H]-dexamethasone within the subcutaneous tissue at 6, 24, and 60 hours after implantation. Measured concentration profiles, near the catheter tip through which the agent was released, were compared to solutions of the diffusion equation in order to characterize drug diffusion coefficients and elimination constants. There was good agreement between the experimental data and the mathematical model used for estimation. The diffusion coefficient for dexamethasone in subcutaneous tissue was found to be D = 4.11+-1.77x10E-10 m2/s, and the elimination rate constant was found to be k = 3.65+-2.24x10E-5/s. Additionally, [3H]-dexamethasone was injected into the subcutaneous tissue of rats. Digital autoradiography was again used to measure the distribution of the [3H]- dexamethasone within the subcutaneous tissue at 2.5 and 20 minutes after injection. Measured concentration profiles were again compared to a mathematical model of drug diffusion for injection. There was good agreement between the experimental data and the mathematical model. The diffusion coefficient found using this simple injection method was 4.01+-2.01x10E-10 m2/s. The simple method given here for the determination of the diffusion coefficient is general enough to be applied to other substances and tissues as well.

A reconstruction algorithm in computerized tomography is a procedure for reconstructing the attenuation coefficientscient, a real-valued function associated with the object of interest, from the measured projection data. Generally speaking, reconstruction algorithms in CT fall into two categories: direct, e.g., filtered back-projection (FBP), or iterative. In this thesis, we discuss a new fast matrix-free iterative reconstruction method based on a polyenergetic model. While most modern x-ray CT scanners rely on the well-known filtered back-projection algorithm, the corresponding reconstructions can be corrupted by beam hardening artifacts. These artifacts arise from the unrealistic physical assumption of monoenergetic x-ray beams. In this thesis, to compensate, we use an alternative model that accounts for differential absorption of polyenergetic x-ray photons and discretize it directly. We do not assume any prior knowledge about the physical properties of the scanned object. We study and implement different solvers and nonlinear unconstrained optimization methods, such as a Newton-like method and an extension of the Levenberg-Marquardt-Fletcher algorithm. We explain how we can use the structure of the Radon matrix and the properties of FBP to make our method matrix-free and fast. Finally, we discuss how we regularize our problem by applying different regularization methods, such as Tikhonov and regularization in the 1-norm. We present numerical reconstructions based on the associated nonlinear discrete formulation incorporating various iterative optimization methods.

A reconstruction algorithm in computerized tomography is a procedure for reconstructing the attenuation coefficientscient, a real-valued function associated with the object of interest, from the measured projection data. Generally speaking, reconstruction algorithms in CT fall into two categories: direct, e.g., filtered back-projection (FBP), or iterative. In this thesis, we discuss a new fast matrix-free iterative reconstruction method based on a polyenergetic model. While most modern x-ray CT scanners rely on the well-known filtered back-projection algorithm, the corresponding reconstructions can be corrupted by beam hardening artifacts. These artifacts arise from the unrealistic physical assumption of monoenergetic x-ray beams. In this thesis, to compensate, we use an alternative model that accounts for differential absorption of polyenergetic x-ray photons and discretize it directly. We do not assume any prior knowledge about the physical properties of the scanned object. We study and implement different solvers and nonlinear unconstrained optimization methods, such as a Newton-like method and an extension of the Levenberg-Marquardt-Fletcher algorithm. We explain how we can use the structure of the Radon matrix and the properties of FBP to make our method matrix-free and fast. Finally, we discuss how we regularize our problem by applying different regularization methods, such as Tikhonov and regularization in the 1-norm. We present numerical reconstructions based on the associated nonlinear discrete formulation incorporating various iterative optimization methods.

This thesis focuses on detecting, classifying and locating faults on electric power transmission lines. Fault detection, fault classification and fault location have been achieved by using artificial neural networks. Feedforward networks have been employed along with backpropagation algorithm for each of the three phases in the Fault location process. Analysis on neural networks with varying number of hidden layers and neurons per hidden layer has been provided to validate the choice of the neural networks in each step. Simulation results have been provided to demonstrate that artificial neural network based methods are efficient in locating faults on transmission lines and achieve satisfactory performances.

This thesis deals with design of appropriate optimization algorithms for purposes of newly developed tool Mechlab’s parameter estimation, which serves for parameter estimation of simulation models in Matlab/Simulink. Levenberg-Marquardt algorithm had been chosen among other gradient methods. On the other hand, genetic algorithm and simulated annealing had been chosen from category of soft computing techniques to be implemented. Chosen algorithms were tested on artifical problem of mechanical oscilator and also on real datasets from electronic throttle. Proposed simulated annealing worked in both cases whith sufficient results, nevertheless was time-costly. For the oscilator problem, all the algorithms provided accurate solutions, but in the case of real dataset, Levenberg-Marquardt functionality was limited, while genetic algorithm still provided excelent results.

A utilização de Redes Neurais Artificias para fins de identificação e controle de sistemas dinâmicos têm recebido atenção especial de muitos pesquisadores, principalmente no que se refere a sistemas não lineares. Neste trabalho é apresentado um estudo sobre a utilização de um tipo em particular de Rede Neural Artificial, uma Perceptron Multicamadas com Atraso de Tempo, na estimação de estados da etapa fermentativa do processo de Reichstein para produção de vitamina C. A aplicação de Redes Neurais Artificiais a este processo pode ser justificada pela existência de problemas associados à esta etapa, como variáveis de estado não mensuráveis e com incertezas de medida e não linearidade do processo fermentativo, além da dificuldade em se obter um modelo convencional que contemple todas as fases do processo. É estudado também a eficácia do algoritmo de Levenberg-Marquadt, na aceleração do treinamento da Rede Neural Artificial, além de uma comparação do desempenho de estimação de estados das Redes Neurais Artificiais estudadas com o filtro estendido de Kalman, baseado em um modelo não estruturado do processo fermentativo. A análise do desempenho das Redes Neurais Artificiais estudadas é avaliada em termos de uma figura de mérito baseada no erro médio quadrático sendo feitas considerações quanto ao tipo da função de ativação e o número de unidades da camada oculta. Os dados utilizados para treinamento e avaliação da Redes Neurais Artificiais foram obtidos de um conjunto de ensaios interpolados para o intervalo de amostragem desejado. / ldentification and Control of dynamic systems using Artificial Neural Networks has been widely investigated by many researchers in the last few years, with special attention to the application of these in nonlinear systems. ls this works, a study on the utilization of a particular type of Artificial Neural Networks, a Time Delay Multi Layer Perceptron, in the state estimation of the fermentative phase of the Reichstein process of the C vitamin production. The use of Artificial Neural Networks can be justified by the presence of problems, such as uncertain and unmeasurable state variables and process non-linearity, and by the fact that a conventional model that works on all phases of the fermentative processes is very difficult to obtain. The efficiency of the Levenberg Marquadt algorithm on the acceleration of the training process is also studied. Also, a comparison is performed between the studied Artificial Neural Networks and an extended Kalman filter based on a non-structured model for this fermentative process. The analysis of lhe Artificial Neural Networks is carried out using lhe mean square errors taking into consideration lhe activation function and the number of units presents in the hidden layer. A set of batch experimental runs, interpolated to the desired time interval, is used for training and validating the Artificial Neural Networks.

The work done in this thesis is to examine various methods for curve fitting. Linear least squares and non-linear least squares will be described and compared, and the Newton method, Gauss--Newton method and Levenberg--Marquardt method will be applied to example problems. / Syftet med denna uppsats är att beskriva och använda olika metoder för kurvanpassning, det vill säga att passa matematiska funktioner till data. De metoder som undersöks är Newtons metod, Gauss--Newton metoden och Levenberg--Marquardt metoden. Även skillnaden mellan linjär minsta kvadrat anpassning och olinjär minsta kvadrat anpassning. Till sist tillämpas Newton, Gauss Newton och Levenberg--Marquardt metoderna på olika exempel.

Ce mémoire décrit mes travaux de thèse de doctorat menés au sein de l’équipe ComSee (Computers that See) rattachée à l’axe ISPR (Image, Systèmes de Perception et Robotique) de l’Institut Pascal. Celle-ci a été financée par la Région Auvergne et le Fonds Européen de Développement Régional. Les travaux présentés s’inscrivent dans le cadre d’applications de localisation pour la robotique mobile et la Réalité Augmentée. Le framework réalisé au cours de cette thèse est une approche générique pour l’implémentation d’applications de SLAM : Simultaneous Localization And Mapping (algorithme de localisation par rapport à un modèle simultanément reconstruit). L’approche intègre une multitude de contraintes dans les processus de localisation et de reconstruction. Ces contraintes proviennent de données capteurs mais également d’a priori liés au contexte applicatif. Chaque contrainte est utilisée au sein d’un même algorithme d’optimisation afin d’améliorer l’estimation du mouvement ainsi que la précision du modèle reconstruit. Trois problèmes ont été abordés au cours de ce travail. Le premier concerne l’utilisation de contraintes sur le modèle reconstruit pour l’estimation précise d’objets 3D partiellement connus et présents dans l’environnement. La seconde problématique traite de la fusion de données multi-capteurs, donc hétérogènes et asynchrones, en utilisant un unique algorithme d’optimisation. La dernière problématique concerne la génération automatique et efficace d’algorithmes d’optimisation à contraintes multiples. L’objectif est de proposer une solution temps réel 1 aux problèmes de SLAM à contraintes multiples. Une approche générique est utilisée pour concevoir le framework afin de gérer une multitude de configurations liées aux différentes contraintes des problèmes de SLAM. Un intérêt tout particulier a été porté à la faible consommation de ressources (mémoire et CPU) tout en conservant une grande portabilité. De plus, la méta-programmation est utilisée pour générer automatiquement et spécifiquement les parties les plus complexes du code en fonction du problème à résoudre. La bibliothèque d’optimisation LMA qui a été développée au cours de cette thèse est mise à disposition de la communauté en open-source. Des expérimentations sont présentées à la fois sur des données de synthèse et des données réelles. Un comparatif exhaustif met en évidence les performances de la bibliothèque LMA face aux alternatives les plus utilisées de l’état de l’art. De plus, le framework de SLAM est utilisé sur des problèmes impliquant une difficulté et une quantité de contraintes croissantes. Les applications de robotique mobile et de Réalité Augmentée mettent en évidence des performances temps réel et un niveau de précision qui croît avec le nombre de contraintes utilisées. / This report describes my thesis work conducted within the ComSee (Computers That See) team related to the ISPR axis (ImageS, Perception Systems and Robotics) of Institut Pascal. It was financed by the Auvergne Région and the European Fund of Regional Development. The thesis was motivated by localization issues related to Augmented Reality and autonomous navigation. The framework developed during this thesis is a generic approach to implement SLAM algorithms : Simultaneous Localization And Mapping. The proposed approach use multiple constraints in the localization and mapping processes. Those constraints come from sensors data and also from knowledge given by the application context. Each constraint is used into one optimization algorithm in order to improve the estimation of the motion and the accuracy of the map. Three problems have been tackled. The first deals with constraints on the map to accurately estimate the pose of 3D objects partially known in the environment. The second problem is about merging multiple heterogeneous and asynchronous data coming from different sensors using an optimization algorithm. The last problem is to write an efficient and real-time implementation of the SLAM problem using multiple constraints. A generic approach is used to design the framework and to generate different configurations, according to the constraints, of each SLAM problem. A particular interest has been put in the low computational requirement (in term of memory and CPU) while offering a high portability. Moreover, meta-programming techniques have been used to automatically and specifically generate the more complex parts of the code according to the given problem. The optimization library LMA, developed during this thesis, is made available of the community in open-source. Several experiments were done on synthesis and real data. An exhaustive benchmark shows the performances of the LMA library compared to the most used alternatives of the state of the art. Moreover, the SLAM framework is used on different problems with an increasing difficulty and amount of constraints. Augmented Reality and autonomous navigation applications show the good performances and accuracies in multiple constraints context.

Cette thèse est consacrée à la recherche des zéros d'un opérateur maximal monotone structuré, à l'aide de systèmes dynamiques dissipatifs continus et discrets. Les solutions sont obtenues comme limites des trajectoires lorsque le temps t tend vers l'infini. On s'intéressera principalement aux dynamiques obtenues par régularisation de type Levenberg-Marquardt de la méthode de Newton. On décrira aussi les approches basées sur des dynamiques voisines.Dans un cadre Hilbertien, on s'intéresse à la recherche des zéros de l'opérateur maximal monotone structuré M = A + B, où A est un opérateur maximal monotone général et B est un opérateur monotone Lipschitzien. Nous introduisons des dynamiques continues et discrètes de type Newton régularisé faisant intervenir d'une façon séparée les résolvantes de l'opérateur A (implicites), et des évaluations de B (explicites). A l'aide de la représentation de Minty de l'opérateur A comme une variété Lipschitzienne, nous reformulons ces dynamiques sous une forme relevant du théorème de Cauchy-Lipschitz. Nous nous intéressons au cas particulier où A est le sous différentiel d'une fonction convexe, semi-continue inférieurement, et propre, et B est le gradient d'une fonction convexe, différentiable. Nous étudions le comportement asymptotique des trajectoires. Lorsque le terme de régularisation ne tend pas trop vite vers zéro, et en s'appuyant sur une analyse asymptotique de type Lyapunov, nous montrons la convergence des trajectoires. Par ailleurs, nous montrons la dépendance Lipschitzienne des trajectoires par rapport au terme de régularisation.Puis nous élargissons notre étude en considérant différentes classes de systèmes dynamiques visant à résoudre les inclusions monotones gouvernées par un opérateur maximal monotone structuré M = $partialPhi$+ B, où $partialPhi$ désigne le sous différentiel d'une fonction convexe, semicontinue inférieurement, et propre, et B est un opérateur monotone cocoercif. En s'appuyant sur une analyse asymptotique de type Lyapunov, nous étudions le comportement asymptotique des trajectoires de ces systèmes. La discrétisation temporelle de ces dynamiques fournit desalgorithmes forward-backward (certains nouveaux ).Finalement, nous nous intéressons à l'étude du comportement asymptotique des trajectoires de systèmes dynamiques de type Newton régularisé, dans lesquels on introduit un terme supplémentaire de viscosité évanescente de type Tikhonov. On obtient ainsi la sélection asymptotique d'une solution de norme minimale. / This thesis is devoted to finding zeroes of structured maximal monotone operators, by using discrete and continuous dissipative dynamical systems. The solutions are obtained as the limits of trajectories when the time t tends towards infinity.We pay special attention to the dynamics that are obtained by Levenberg-Marquardt regularization of Newton's method. We also revisit the approaches based on some related dynamical systems.In a Hilbert framework, we are interested in finding zeroes of a structured maximal monotone operator M = A + B, where A is a general maximal monotone operator, and B is monotone and locally Lipschitz continuous. We introduce discrete and continuous dynamical systems which are linked to Newton's method. They involve separately B and the resolvents of A, and are designed to splitting methods. Based on the Minty representation of A as a Lipschitz manifold, we show that these dynamics can be formulated as differential systems, which are relevant to the Cauchy-Lipschitz theorem. We focus on the particular case where A is the subdifferential of a convex lower semicontinuous proper function, and B is the gradient of a convex, continuously differentiable function. We study the asymptotic behavior of trajectories. When the regularization parameter does not tend to zero too rapidly, and by using Lyapunov asymptotic analysis, we show the convergence of trajectories. Besides, we show the Lipschitz continuous dependence of the solution with respect to the regularization term.Then we extend our study by considering various classes of dynamical systems which aim at solving inclusions governed by structured monotone operators M = $partialPhi$+ B, where $partialPhi$ is the subdifferential of a convex lower semicontinuous function, and B is a monotone cocoercive operator. By a Lyapunov analysis, we show the convergence properties of the orbits of these systems. The time discretization of these dynamics gives various forward-backward splittingmethods (some new).Finally, we focus on the study of the asymptotic behavior of trajectories of the regularized Newton dynamics, in which we introduce an additional vanishing Tikhonov-like viscosity term.We thus obtain the asymptotic selection of the solution of minimal norm.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Um Estudo para a solução numérica do modelo de difusão com retenção, proposta por Bevilacqua et al. (2011), é apresentado, bem como uma formulação implícita para o problema inverso para a estimativa dos parâmetros envolvidos na formulação matemática do modelo. Através de um estudo minucioso da análise de sensibilidade e do cálculo do coeficiente de correlação de Pearson, são identificadas as chances de se obter sucesso na solução do problema inverso através do método determinístico de Levenberg-Marquardt e dos métodos estocásticos Algoritmo de Colisão de Partículas (Particle Collision Algorithm - PCA) e Evolução Diferencial (Differential Evolution - DE). São apresentados os resultados obtidos através destes três métodos de otimização para três casos de conjunto de parâmetros. Foi observada uma forte correlação entre dois destes três parâmetros, o que dificultou a estimativa simultânea dos mesmos. Porém, foi obtido sucesso nas estimativas individuais de cada parâmetro. Foram obtidos bons resultados para os fatores que multiplicam os termos diferenciais da equação que modela o fenômeno de difusão com retenção. / A Study for the numerical solution of the diffusion model with retention, proposed by Bevilacqua et al.(2011), using the finite difference method is presented, as well as an implicit formulation for the inverse problem to estimate the parameters involved in the formulation of the mathematical model. Through of a thorougth study of sensitivity analysis and calculating the Pearson correlation coefficient, are identified the chances of success in solving the inverse problem using the deterministic method of Levenberg-Marquardt and stochastic methods Particle Collision Algorithm - PCA and Differential Evolution - DE. Presents the results obtained from these three methods of optimization for three cases of parameter set. We observed a strong correlation between two of these three parameters, making it difficult to estimate simultaneously the same. However, success was obtained in the individual estimates for each parameter. Good results were obtained for the factors that increase the terms of the differential equation that models the phenomenon of diffusion with retention.