Le modèle auto-régressif linéaire (AR) en temps discret et à coefficients aléatoires englobe de nombreuses classes de modèles très utilisés en modélisation statistique. Sous des hypothèses simples, ce modèle a une unique solution stationnaire. Le comportement à l'infini de sa queue a été étudié par H. Kesten, E. LePage puis C. Goldie lorsque les coefficients sont indépendants. Cette thèse étend leurs résultats dans deux directions. Dans une première partie, on étudie le modèle AR scalaire à régime markovien introduit par J. D. Hamilton en économétrie. On obtient un résultat similaire au cas indépendant qui s'étend aussi au temps continu. Dans une deuxième partie, on s'intéresse au modèle multidimensionnel à coefficient indépendants. On étend les résultats existants à une vaste classe de coefficients vérifiant une condition d'irréductibilité et de proximalité. Les techniques utilisées dans les deux parties font appel à la théorie du renouvellement et des opérateurs markoviens.

<p>In this thesis, we explore different algorithms for the inversion of Vandermonde matrices and the corresponding suitable architectures for implement in FPGA. The inversion of Vandermonde matrix is one of the three master projects of the topic, Implementation of a digital error correction algorithm for time-interleaved analog-to-digital converters. The project is divided into two major parts: algorithm comparison and optimization for inversion of Vandermonde matrix; architecture selection for implementation. A CORDIC algorithm for sine and cosine and Newton-Raphson based division are implemented as functional blocks.</p>

<p>Vid analys av vattenprover tagna från t.ex. ett vattendrag betäms halten av olika ämnen. Dessa halter är ofta beroende av vattenföringen. Det är av intresse att ta reda på om observerade förändringar i halterna beror på naturliga variationer eller är orsakade av andra faktorer. För att undersöka detta har föreslagits en statistisk tidsseriemodell som innehåller okända parametrar. Modellen anpassas till uppmätta data vilket leder till ett underbestämt ekvationssystem. I avhandlingen studeras bl.a. olika sätt att säkerställa en unik och rimlig lösning. Grundidén är att införa vissa tilläggsvillkor på de sökta parametrarna. I den studerade modellen kan man t.ex. kräva att vissa parametrar inte varierar kraftigt med tiden men tillåter årstidsvariationer. Det görs genom att dessa parametrar i modellen regulariseras.</p><p>Detta ger upphov till ett minsta kvadratproblem med en eller två regulariseringsparametrar. I och med att inte alla ingående parametrar regulariseras får vi dessutom ett partiellt regulariserat minsta kvadratproblem. I allmänhet känner man inte värden på regulariseringsparametrarna utan problemet kan behöva lösas med flera olika värden på dessa för att få en rimlig lösning. I avhandlingen studeras hur detta problem kan lösas numeriskt med i huvudsak två olika metoder, en iterativ och en direkt metod. Dessutom studeras några sätt att bestämma lämpliga värden på regulariseringsparametrarna.</p><p>I en iterativ lösningsmetod förbättras stegvis en given begynnelseapproximation tills ett lämpligt valt stoppkriterium blir uppfyllt. Vi använder här konjugerade gradientmetoden med speciellt konstruerade prekonditionerare. Antalet iterationer som krävs för att lösa problemet utan prekonditionering och med prekonditionering jämförs både teoretiskt och praktiskt. Metoden undersöks här endast med samma värde på de två regulariseringsparametrarna.</p><p>I den direkta metoden används QR-faktorisering för att lösa minsta kvadratproblemet. Idén är att först utföra de beräkningar som kan göras oberoende av regulariseringsparametrarna samtidigt som hänsyn tas till problemets speciella struktur.</p><p>För att bestämma värden på regulariseringsparametrarna generaliseras Reinsch’s etod till fallet med två parametrar. Även generaliserad korsvalidering och en mindre beräkningstung Monte Carlo-metod undersöks.</p> / <p>Statistical analysis of data from rivers deals with time series which are dependent, e.g., on climatic and seasonal factors. For example, it is a well-known fact that the load of substances in rivers can be strongly dependent on the runoff. It is of interest to find out whether observed changes in riverine loads are due only to natural variation or caused by other factors. Semi-parametric models have been proposed for estimation of time-varying linear relationships between runoff and riverine loads of substances. The aim of this work is to study some numerical methods for solving the linear least squares problem which arises.</p><p>The model gives a linear system of the form <em>A</em><em>1x1</em><em> + A</em><em>2x2</em><em> + n = b</em><em>1</em>. The vector <em>n</em> consists of identically distributed random variables all with mean zero. The unknowns, <em>x,</em> are split into two groups, <em>x</em><em>1</em><em> </em>and <em>x</em><em>2</em><em>.</em> In this model, usually there are more unknowns than observations and the resulting linear system is most often consistent having an infinite number of solutions. Hence some constraint on the parameter vector x is needed. One possibility is to avoid rapid variation in, e.g., the parameters<em> x</em><em>2</em><em>.</em> This can be accomplished by regularizing using a matrix <em>A</em><em>3</em>, which is a discretization of some norm. The problem is formulated</p><p>as a partially regularized least squares problem with one or two regularization parameters. The parameter <em>x</em><em>2</em> has here a two-dimensional structure. By using two different regularization parameters it is possible to regularize separately in each dimension.</p><p>We first study (for the case of one parameter only) the conjugate gradient method for solution of the problem. To improve rate of convergence blockpreconditioners of Schur complement type are suggested, analyzed and tested. Also a direct solution method based on QR decomposition is studied. The idea is to first perform operations independent of the values of the regularization parameters. Here we utilize the special block-structure of the problem. We further discuss the choice of regularization parameters and generalize in particular Reinsch’s method to the case with two parameters. Finally the cross-validation technique is treated. Here also a Monte Carlo method is used by which an approximation to the generalized cross-validation function can be computed efficiently.</p>

Objects such as documents, people, words or utilities, that are related in some way, for instance by citations, friendship, appearance in definitions or physical connections, may be conveniently represented using graphs or networks. An increasing number of such relational databases, as for instance the World Wide Web, digital libraries, social networking web sites or phone calls logs, are available. Relevant information may be hidden in these networks. A user may for instance need to get authority web pages on a particular topic or a list of similar documents from a digital library, or to determine communities of friends from a social networking site or a phone calls log. Unfortunately, extracting this information may not be easy. This thesis is devoted to the study of problems related to information extraction in large graphs with the help of dominant vectors of nonnegative matrices. The graph structure is indeed very useful to retrieve information from a relational database. The correspondence between nonnegative matrices and graphs makes Perron--Frobenius methods a powerful tool for the analysis of networks. In a first part, we analyze the fixed points of a normalized affine iteration used by a database matching algorithm. Then, we consider questions related to PageRank, a ranking method of the web pages based on a random surfer model and used by the well known web search engine Google. In a second part, we study optimal linkage strategies for a web master who wants to maximize the average PageRank score of a web site. Finally, the third part is devoted to the study of a nonlinear variant of PageRank. The simple model that we propose takes into account the mutual influence between web ranking and web surfing.

M.S. / Computer Science / This paper deals with the problem of solving a system of sparse nonsymmetric matrices on a distributed memory multiprocessor computer, the Intel iPSC (hypercube). The processors have substantial local memory but no global shared memory. They communicate among themselves and with a host processor through message passing. The primary interest is to design an algorithm which exploits parallelism, and which performs elimination and solution of large sparse matrices. Elimination is performed by LU- decomposition. The storage scheme is based on linked list data-structure defined for a given generated matrix. The matrix is distributed by columns in a "wrapped" fashion so that elimination in the natural order will be balanced, if the sparsity structure is equally distributed across the columns. Numerical results from experiments running on the hypercube are included along with performance analysis.

Traditional remote sensing image classification has primarily relied on image spectral information and texture information was ignored or not fully utilized. Existing remote sensing software packages have very limited functionalities with respect to texture information extraction and utilization. This research focuses on the use of multi-scale image texture analysis techniques using Gabor filter banks and Wavelet transformations. Gabor filter banks model texture as irradiance patterns in an image over a limited range of spatial frequencies and orientations. Using Gabor filters, each image texture can be differentiated with respect to its dominant spatial frequency and orientation. Wavelet transformations are useful for decomposition of an image into a set of images based on an orthonormal basis. Dyadic transformations are applied to generate a multi-scale image pyramid which can be used for texture analysis. The analysis of texture is carried out using both artificial textures and remotely sensed image corresponding to natural scenes. This research has shown that texture can be extracted and incorporated in conventional classification algorithms to improve the accuracy of classified results. The applicability of Gabor filter banks and Wavelets is explored for classifying and segmenting remote sensing imagery for geographical applications. A qualitative and quantitative comparison between statistical texture indicators and multi-scale texture indicators has been performed. Multi-scale texture indicators derived from Gabor filter banks have been found to be very effective due to the nature of their configurability to target specific textural frequencies and orientations in an image. Wavelet transformations have been found to be effective tools in image texture analysis as they help identify the ideal scale at which texture indicators need to be measured and reduce the computation time taken to derive statistical texture indicators. A robust set of software tools for texture analysis has been developed using the popular .NET and ArcObjects. ArcObjects has been chosen as the API of choice, as these tools can be seamlessly integrated into ArcGIS. This will aid further exploration of image texture analysis by the remote sensing community.

La résolution de systèmes linéaires creux est critique dans de nombreux domaines de la simulation numérique. Beaucoup d'applications, notamment industrielles, utilisent des méthodes directes en raison de leur précision et de leur robustesse. La qualité du résultat, les fonctionnalités numériques, ainsi que le temps de calcul sont critiques pour les applications. Par ailleurs, les ressources matérielles (nombre de processeurs, mémoire) doivent être utilisées de manière optimale. Dans cette habilitation, nous décrivons des travaux poursuivant ces objectifs dans le cadre de la plate-forme logicielle MUMPS, développée à Toulouse, Lyon-Grenoble et Bordeaux depuis une quinzaine d'années. Le cœur de l'approche repose sur une parallélisation originale de la méthode multifrontale : une gestion asynchrone du parallélisme, associée à des ordonnanceurs distribués, permet de traiter des structures de données dynamiques et autorise ainsi le pivotage numérique. Nous nous intéressons à l'ordonnancement des tâches, à l'optimisation de la mémoire et à différentes fonctionnalités numériques. Les travaux en cours et les objectifs futurs visent à résoudre efficacement des problèmes de plus en plus gros, sans perte sur les aspects numériques, et tout en adaptant nos approches aux évolutions rapides des calculateurs. Dans ce contexte, les aspects génie logiciel et transfert deviennent critiques afin de maintenir sur le long terme une plate-forme logicielle comme MUMPS. Cette plate-forme est à la fois nécessaire à nos travaux de recherche et utilisée en production ; elle maximise ainsi les retours applicatifs qui valident nos travaux et permettent d'orienter nos recherches futures.

This thesis describes the development of liquid chromatography tandem mass spectrometry (LC-MS/MS) methods for the trace analysis of active pharmaceutical ingredients (APIs) and their metabolites in aqueous environmental matrices. The research was focused on the development of chiral LC-MS/MS methods for the analysis of fluoxetine and metoprolol, as well as their chiral metabolites in environmental water samples. A method was also developed for the achiral compounds, diazepam and nordiazepam. The LC-MS/MS methods were validated by the use of the isotope-labeled compounds. As these isotope-labeled compounds were not found in the wastewater samples, the validation could be assessed at trace level concentrations in the actual matrices in which the analytes were detected. The analytes were extracted from the water samples using solid phase extraction methods. Different types of solid phase extraction sorbents were evaluated. Fluoxetine and norfluoxetine were extracted through the use of a mixed mode polymeric based extraction sorbent. A hydrophilic and lipophilic balanced sorbent was employed for the simultaneous extraction of metoprolol and its metabolites, the base α-hydroxymetoprolol and the acidic metabolite deaminated metoprolol. Moreover, silica based C18 extraction discs were applied for the sample preparation of diazepam and nordiazepam. The chromatographic separations were conducted in reversed phase LC with MS compatible mobile phases. The enantiomers of fluoxetine and norfluoxetine were simultaneously separated using the chiral stationary phase (CSP), α1-acid glycoprotein (AGP). The Chiral AGP column was also applied for the separation of the enantiomers of deaminated metoprolol. For the simultaneous separation of the metoprolol enantiomers and the four stereoisomers of α-hydroxymetoprolol, the cellobiohydrolase (CBH) protein based CSP was used. An octadecyl silica based LC column was applied for the separation of diazepam and nordiazepam. The analytes were detected by the use of tandem quadrupole mass spectrometry operating in selective reactive monitoring mode. High resolution MS, employing a quadrupole time-of-flight (QqTOF) mass analyzer, was utilized for the identification of an unknown compound in wastewater samples. The APIs and their metabolites, as well as their respective enantiomers, were quantified in raw and treated wastewater from Uppsala, Sweden along with surface water from the River Fyris in Uppsala.

Vid analys av vattenprover tagna från t.ex. ett vattendrag betäms halten av olika ämnen. Dessa halter är ofta beroende av vattenföringen. Det är av intresse att ta reda på om observerade förändringar i halterna beror på naturliga variationer eller är orsakade av andra faktorer. För att undersöka detta har föreslagits en statistisk tidsseriemodell som innehåller okända parametrar. Modellen anpassas till uppmätta data vilket leder till ett underbestämt ekvationssystem. I avhandlingen studeras bl.a. olika sätt att säkerställa en unik och rimlig lösning. Grundidén är att införa vissa tilläggsvillkor på de sökta parametrarna. I den studerade modellen kan man t.ex. kräva att vissa parametrar inte varierar kraftigt med tiden men tillåter årstidsvariationer. Det görs genom att dessa parametrar i modellen regulariseras. Detta ger upphov till ett minsta kvadratproblem med en eller två regulariseringsparametrar. I och med att inte alla ingående parametrar regulariseras får vi dessutom ett partiellt regulariserat minsta kvadratproblem. I allmänhet känner man inte värden på regulariseringsparametrarna utan problemet kan behöva lösas med flera olika värden på dessa för att få en rimlig lösning. I avhandlingen studeras hur detta problem kan lösas numeriskt med i huvudsak två olika metoder, en iterativ och en direkt metod. Dessutom studeras några sätt att bestämma lämpliga värden på regulariseringsparametrarna. I en iterativ lösningsmetod förbättras stegvis en given begynnelseapproximation tills ett lämpligt valt stoppkriterium blir uppfyllt. Vi använder här konjugerade gradientmetoden med speciellt konstruerade prekonditionerare. Antalet iterationer som krävs för att lösa problemet utan prekonditionering och med prekonditionering jämförs både teoretiskt och praktiskt. Metoden undersöks här endast med samma värde på de två regulariseringsparametrarna. I den direkta metoden används QR-faktorisering för att lösa minsta kvadratproblemet. Idén är att först utföra de beräkningar som kan göras oberoende av regulariseringsparametrarna samtidigt som hänsyn tas till problemets speciella struktur. För att bestämma värden på regulariseringsparametrarna generaliseras Reinsch’s etod till fallet med två parametrar. Även generaliserad korsvalidering och en mindre beräkningstung Monte Carlo-metod undersöks. / Statistical analysis of data from rivers deals with time series which are dependent, e.g., on climatic and seasonal factors. For example, it is a well-known fact that the load of substances in rivers can be strongly dependent on the runoff. It is of interest to find out whether observed changes in riverine loads are due only to natural variation or caused by other factors. Semi-parametric models have been proposed for estimation of time-varying linear relationships between runoff and riverine loads of substances. The aim of this work is to study some numerical methods for solving the linear least squares problem which arises. The model gives a linear system of the form A1x1 + A2x2 + n = b1. The vector n consists of identically distributed random variables all with mean zero. The unknowns, x, are split into two groups, x1 and x2. In this model, usually there are more unknowns than observations and the resulting linear system is most often consistent having an infinite number of solutions. Hence some constraint on the parameter vector x is needed. One possibility is to avoid rapid variation in, e.g., the parameters x2. This can be accomplished by regularizing using a matrix A3, which is a discretization of some norm. The problem is formulated as a partially regularized least squares problem with one or two regularization parameters. The parameter x2 has here a two-dimensional structure. By using two different regularization parameters it is possible to regularize separately in each dimension. We first study (for the case of one parameter only) the conjugate gradient method for solution of the problem. To improve rate of convergence blockpreconditioners of Schur complement type are suggested, analyzed and tested. Also a direct solution method based on QR decomposition is studied. The idea is to first perform operations independent of the values of the regularization parameters. Here we utilize the special block-structure of the problem. We further discuss the choice of regularization parameters and generalize in particular Reinsch’s method to the case with two parameters. Finally the cross-validation technique is treated. Here also a Monte Carlo method is used by which an approximation to the generalized cross-validation function can be computed efficiently.

This thesis deals with quantum chemistry methods for large systems. In particular, the thesis focuses on the efficient construction of the Coulomb and exchange matrices which are important parts of the Fock matrix in Hartree-Fock calculations. Density matrix purification, which is a method used to construct the density matrix for a given Fock matrix, is also discussed. The methods described are not only applicable in the Hartree-Fock case, but also in Kohn-Sham Density Functional Theory calculations, where the Coulomb and exchange matrices are parts of the Kohn-Sham matrix. Screening techniques for reducing the computational complexity of both Coulomb and exchange computations are discussed, including the fast multipole method, used for efficient computation of the Coulomb matrix. The thesis also discusses how sparsity in the matrices occurring in Hartree-Fock and Kohn-Sham Density Functional Theory calculations can be used to achieve more efficient storage of matrices as well as more efficient operations on them. / QC 20100817