Τα σύγχρονα τηλεπικοινωνιακά συστήματα, καθώς επίσης και οι επόμενες γενιές τους, πρέπει να προσαρμόζονται για να υποστηρίζουν ένα μεγάλο αριθμό από υπηρεσίες με διαφορετικές απαιτήσεις ποιότητας. Για παράδειγμα, στα κυψελικά συστήματα, οι κυψέλες μικραίνουν σε μέγεθος και αυξάνονται σε πλήθος για να υποστηρίζουν ένα συνεχώς αυξανόμενο πλήθος χρηστών. Επίσης, σε μια άλλη κατεύθυνση, τα δίκτυα αισθητήρων αποτελούνται από μικρές συσκευές που εισάγουν περιορισμούς μεγέϑους, ενέργειας και επεξεργαστικής ισχύος. Αυτά τα δυο παραδείγματα επιδεικνύου τόσο την αυξανόμενη πολυπλοκότητα των τηλεπικοινωνιακών συστημάτων όσο και τις ιδιαίτερες απαιτήσεις που υπάρχουν στους μεμονωμένους κόμβους τους. Τα τηλεπικοινωνιακά συστήματα πολλαπλών εισόδων και εξόδων έχουν την δυνατότητα να προσφέρουν αυξημένη χωρητικότητα και αξιοπιστία στην μετάδοση δεδομένων μέσω της έννοιας της χωρικής ποικιλομορφίας (space diversity). Συγκεκριμένα, αυτό επιτυγχάνεται με την μετάδοση της ζητούμενης πληροφορίας μέσω ενός αριθμού από διαφορετικά χωρικά μονοπάτια τα οποία δημιουργούνται από την ύπαρξη πολλαπλών κεραιών στον πομπό ή/και στον δέκτη. Ωστόσο, η προαναφερόμενη πολυπλοκότητα στα τηλεπικοινωνιακά συστήματα και οι ιδιαίτερες απαιτήσεις των κόμβων έχουν ως αποτέλεσμα να μην επαρκούν οι τεχνικές που έχουν αναπτυχθεί. Μια πιθανή διέξοδο έρχεται να δώσει η ιδέα της συνεργασίας. Η έννοια της συνεργασίας έχει διάφορες οπτικές γωνίες σε ένα τηλεπικοινωνιακό σύστημα. Πρώτον, αν οι συσκευές δεν μπορούν να υποστηρίξουν πολλαπλές κεραίες (π.χ. λόγω μεγέϑους όπως στα δίκτυα αισθητήρων και στα κινητά τηλέφωνα), σίγουρα μπορούν να συνεργαστούν ώστε με έναν κατανεμημένο τρόπο να προσφέρουν σε επίπεδο συστήματος τα απαραίτητα διαφορετικά χωρικά μονοπάτια. Δεύτερον, ακόμη και αν είναι δυνατή η χρήση πολλαπλών κεραιών σε κάποιον κόμβο ενός δικτύου, π.χ. σε σταθμούς ϐάσης κυψελικών συστημάτων, ο αριθμός τους μπορεί απλώς να μην αρκεί λόγω της αυξημένης πολυπλοκότητας και του μεγέθους του δικτύου. Η κατάλληλη χρήση συνεργατικών κόμβων μπορεί να δώσει επίσης λύση στον εν λόγω περιορισμό.Η παρούσα διδακτορική διατριβή ϑα ϐασιστεί πάνω σε συνεργατικά συστήματα υπό την πρώτη οπτική γωνία που παρουσιάστηκε παραπάνω. Συγκεκριμένα, ϑα ϑεωϱηθεί ένα συνεργατικό δίκτυο με τρεις κόμβους, δηλαδή μια πηγή, έναν αναμεταδότη και έναν προορισμό. ϑα μελετηθούν τεχνικές εκτίμησης των καναλιών που συμμετέχουν στην μετάδοση της πληροφορίας αναδεικνύοντας τα ϐασικά χαρακτηριστικά που εισάγει η έννοια της συνεργασίας στις εν λόγω τεχνικές. Επίσης, ϑα παρουσιαστούν υλοποιήσεις διαφόρων συνεργατικών πρωτοκόλλων μετάδοσης σε ένα πραγματικό τηλεπικοινωνιακό σύστημα προσφέροντας έτσι την απαραίτητη πρακτική διαίσθηση πίσω από αυτά τα συστήματα. Συγκεκριμένα, αφού παρουσιαστούν κάποιες ϐασικές έννοιες για τις συνεργατικές επικοινωνίες και την λειτουργία της εκτίμησης καναλιών, ϑα μελετηθεί το πρόβλημα εκτίμησης με μερική επίβλεψη σε σχέση με το μοντέλο του συνεργατικού συστήματος που ϑεωρήθηκε. Προτείνονται εναλλακτικά σχήματα για την υλοποίηση του εκτιμητή καθώς επίσης και ένας απλός σχεδιασμός της ακολουθίας συμβόλων που υποβοηθάει το εφαρμοζόμενο κριτήριο ετεροσυσχέτισης. ΄Ολες οι έννοιες που παρουσιάζονται σε αυτό το κεφάλαιο υποστηρίζονται με πειραματικά και ημιαναλυτικά επιχειρήματα. Στην συνέχεια, παρουσιάζεται το πρόβλημα σχεδιασμού της κατανομής ενέργειας σε σύμβολα εκμάθησης για την εκτίμηση συσχετισμένων καναλιών. Αφού περιγραφεί το προς μελέτη πρόβλημα, ϑα επικεντρωθούμε στο κριτήριο ελαχίστων τετραγώνων για το οποίο παρουσιάζονται η ϐέλτιστη και τρεις υποβέλτιστες λύσεις που συνοδεύονται από χρήσιμα συμπεράσματα και παρατηρήσεις. ΄Επειτα, μελετάται το κριτήριο ελάχιστου μέσου τετραγωνικού σφάλματος για δυο περιπτώσεις. Στην πρώτη, παρουσιάζεται μια ανάλυση χειρότερης περίπτωσης και γίνεται η σύνδεση των λύσεων του προβλήματος με τις λύσεις του προηγούμενου κριτηρίου. Επίσης, υπό την υπόθεση των καναλιών χωρίς συσχέτιση, παρουσιάζεται η ϐέλτιστη λύση για τον σχεδιασμό της ακολουθίας των συμβόλων εκμάθησης. Στην τρίτη κατεύθυνση, ϑα παρουσιαστεί αρχικά το σύστημα στο οποίο ϑα υλοποιηθούν και εκτελεστούν τα πρωτόκολλα συνεργατικής επικοινωνίας. Στην συνέχεια, παρουσιάζονται τα εν λόγω σχήματα και το κεφάλαιο καταλήγει με την πειραματική διαδικασία, την παρουσίαση και αξιολόγηση των αποτελεσμάτων καθώς και την εξαγωγή χρήσιμων συμπερασμάτων. Στο τέλος της διατριβής περιγράφονται συνοπτικά τα ϐασικά συμπεράσματα που έχουν προκύψει και παρουσιάζονται κάποιες ενδιαφέρουσες νέες κατευθύνσεις. / Contemporary communication systems, as well as their next generations, are expected to adapt to a rapidly increasing number of desired applications and quality of service levels. For example, in cellular systems, the cells are getting smaller in size and larger in numbers in order to support the increasing number of users. Also, towards another direction, wireless sensor network consist of small devices that comply with stringent constraints such as size, consumed energy and computational power. These examples demonstrate both the high complexity of communication networks and the specific requirements that exist in individual communication nodes. Multiple input multiple output systems are capable of offering high capacity and reliable data communications utilizing the notion of spatial diversity. This is achieved by transmitting the desired information through different spatial paths that are created because of multiple antennas at the transmitter and/or the receiver side. However, the aforementioned complexity of communication networks and the specific requirements of the nodes have as a result that currently proposed techniques, for such systems, are inadequate. A possible solution to this dead end is the idea of cooperation. Cooperation has several aspects in a communication system. Firstly, if the nodes cannot support multiple antennas (e.g. due to size restriction as in sensor networks and mobile phones), they can cooperate in order to provide, in a distributed manner, the desired spatial paths. Secondly, even if multiple antennas can be used, as in base stations, their number might not be good enough because of the increased complexity and size of the network. The appropriate use of cooperative nodes can provide a solution to this problem, too. This dissertation has been focused on cooperative systems that are viewed according to the first aspect. Specifically, it has been assumed that the cooperative network consists of three nodes, a source, a relay and a destination. On this network, channel estimation techniques have been studied pointing out the main characteristics that are inherent to cooperation. Moreover, test-bed implementations have been provided for several well known cooperative schemes and protocols pointing out the practical aspects of such systems. In more detail, after the presentation of some introductory notions on cooperation and channel estimation, a semi-blind technique has been studied that is based on the so called cross-relation criterion. Two alternative schemes for constructing the channel estimator have been proposed as well as a simple training design procedure for improving the estimation performance has been devised. The results that have been produced are supported by semi analytic arguments and computer simulations. Then, a training design problem has been studied for a training based channel estimator. The design has been focused on the energy allocation of training symbols under the assumption that channel taps are correlated. After the description of the problem, the least squares criterion has been utilized and the optimal solution, along with three suboptimal ones, has been presented and useful conclusions have been drawn. Also, the problem has been studied under the minimum mean square error criterion for two cases. In the first one, a worst case analysis has been presented. There, a connection to the least squares solution was provided. In the second case, relaxing the assumption of correlated channel taps, the optimal solution has been presented. In the third direction, a number of well known protocols have been implemented in a test-bed system. A measurement campaign has been conducted to acquire the bit error performance and the computational complexity of the protocols. The protocols have been compared according to three different metrics and useful insights have been identified. The dissertation is concluded with a brief presentation of the main points that have been raised in the aforementioned directions. Moreover, new interesting research directions have been provided.

Over the last five decades, a rich literature on the welfare state has developed. Multiple theories and models seek to explain the contemporary welfare state, including structural functionalist, structural-Marxist and Marxist perspectives, culturalist approaches, pluralist analyses, neo-institutionalist theories, power resources theory, Harold Wilensky and Lebeaux’s dual model, Richard Titmuss’s tri-polar model, and Gøsta Esping-Andersen’s tri-polar model, all designed to account for the emergence of and variations among welfare states. However, these theories and models originated within the developed world, and empirical examinations of these theories are largely restricted within this part of the world. The welfare state literature is too confined to the West today. This study examines key welfare state theories and models in the contexts of developing and least developed nations employing a combination of quantitative, qualitative, and comparative methodologies. It suggests that social policies and programs in the developing nations can be systematically understood in the light of mainstream Western theories and models of the welfare state. Therefore, in addition to challenging current practices that limit the study of the welfare state within particular geographical areas, the research presented here provides rationale for increased efforts to understand welfare policies and programs in developing nations. This will increase our knowledge about the applicability of theories in the developing world and will enrich the understanding of the developed world, and thus contribute to the advancement of welfare state scholarship. / February 2016

Este trabalho aborda o problema de controle ótimo por modos deslizantes via função penalidade para sistemas de tempo discreto. Para resolver este problema será desenvolvido uma estrutura matricial alternativa baseada no problema de mínimos quadrados ponderados e funções penalidade. A partir desta nova formulação é possível obter a lei de controle ótimo por modos deslizantes, as equações de Riccati e a matriz do ganho de realimentação através desta estrutura matricial alternativa. A motivação para propormos essa nova abordagem é mostrar que é possível obter uma solução alternativa para o problema clássico de controle ótimo por modos deslizantes. / This work introduces a penalty function approach to deal with the optimal sliding mode control problem for discrete-time systems. To solve this problem an alternative array structure based on the problem of weighted least squares penalty function will be developed. Using this alternative matrix structure, the optimal sliding mode control law of, the matrix Riccati equations and feedback gain were obtained. The motivation of this new approach is to show that it is possible to obtain an alternative solution to the classic problem of optimal sliding mode control.

A linear regression model, where covariates and a response are subject to errors, is considered in this thesis. For so-called errors-in-variables (EIV) model, suitable error structures are proposed, various unknown parameter estimation techniques are performed, and recent algebraic and statistical results are summarized. An extension of the total least squares (TLS) estimate in the EIV model-the EIV estimate-is invented. Its invariant (with respect to scale) and equivariant (with respect to the covariates' rotation, to the change of covariates direction, and to the interchange of covariates) properties are derived. Moreover, it is shown that the EIV estimate coincides with any unitarily invariant penalizing solution to the EIV problem. It is demonstrated that the asymptotic normality of the EIV estimate is computationally useless for a construction of confidence intervals or hypothesis testing. A proper bootstrap procedure is constructed to overcome such an issue. The validity of the bootstrap technique is proved. A simulation study and a real data example assure of its appropriateness. Strong and uniformly strong mixing errors are taken into account instead of the independent ones. For such a case, the strong consistency and the asymptotic normality of the EIV estimate are shown. Despite of that, their...

In this work, we study and extend algorithms for Sparse Regression and Causal Inference problems. Both the problems are fundamental in the area of Data Science. The goal of regression problem is to nd out the \best" relationship between an output variable and input variables, given samples of the input and output values. We consider sparse regression under a high-dimensional linear model with strongly correlated variables, situations which cannot be handled well using many existing model selection algorithms. We study the performance of the popular feature selection algorithms such as LASSO, Elastic Net, BoLasso, Clustered Lasso as well as Projected Gradient Descent algorithms under this setting in terms of their running time, stability and consistency in recovering the true support. We also propose a new feature selection algorithm, BoPGD, which cluster the features rst based on their sample correlation and do subsequent sparse estimation using a bootstrapped variant of the projected gradient descent method with projection on the non-convex L0 ball. We attempt to characterize the efficiency and consistency of our algorithm by performing a host of experiments on both synthetic and real world datasets. Discovering causal relationships, beyond mere correlation, is widely recognized as a fundamental problem. The Causal Inference problems use observations to infer the underlying causal structure of the data generating process. The input to these problems is either a multivariate time series or i.i.d sequences and the output is a Feature Causal Graph where the nodes correspond to the variables and edges capture the direction of causality. For high dimensional datasets, determining the causal relationships becomes a challenging task because of the curse of dimensionality. Graphical modeling of temporal data based on the concept of \Granger Causality" has gained much attention in this context. The blend of Granger methods along with model selection techniques, such as LASSO, enables efficient discovery of a \sparse" sub-set of causal variables in high dimensional settings. However, these temporal causal methods use an input parameter, L, the maximum time lag. This parameter is the maximum gap in time between the occurrence of the output phenomenon and the causal input stimulus. How-ever, in many situations of interest, the maximum time lag is not known, and indeed, finding the range of causal e ects is an important problem. In this work, we propose and evaluate a data-driven and computationally efficient method for Granger causality inference in the Vector Auto Regressive (VAR) model without foreknowledge of the maximum time lag. We present two algorithms Lasso Granger++ and Group Lasso Granger++ which not only constructs the hypothesis feature causal graph, but also simultaneously estimates a value of maxlag (L) for each variable by balancing the trade-o between \goodness of t" and \model complexity".

The FT-Raman techniques were developed to quantify reactions that follow on mixing aqueous solutions of bis-(1,3-diaminopropane)diaquacobalt( III) ion ([Co(tn)2(0H)(H20)]2+) and p-nitrophenylphosphate (PNPP). For the development and validation of the kinetic modelling technique, the well-studied inversion of sucrose was utilized. Rate constants and concentrations could be estimated using calibration solutions and modelling methods. It was found that the results obtained are comparable to literature values. Hence this technique could be further used for the [Co(tn)2(0H)(H20)]2+ assisted hydrolysis of PNPP. It was found that rate constants where the pH is maintained at 7.30 give results which differ from those where the pH is started at 7.30 and allowed to change during the reaction. The average rate constant for 2:1 ([Co(tn)2(0H)(H20)]2+:PNPP reactions was found to be approximately 3 x 104 times the unassisted PNPP hydrolysis rate. / Chemistry / M. Sc. (Chemistry)

ARRUDA, Alexandre Matos. Um sistema infinitário para a lógica de menor ponto fixo. 2007. 91 f. : Dissertação (mestrado) - Universidade Federal do Ceará, Departamento de Computação, Fortaleza-CE, 2007. / Submitted by guaracy araujo (guaraa3355@gmail.com) on 2016-05-20T15:28:27Z No. of bitstreams: 1 2007_dis_amarruda.pdf: 427889 bytes, checksum: b0a54f14f17ff89b515a4101e02f5b58 (MD5) / Approved for entry into archive by guaracy araujo (guaraa3355@gmail.com) on 2016-05-20T15:29:23Z (GMT) No. of bitstreams: 1 2007_dis_amarruda.pdf: 427889 bytes, checksum: b0a54f14f17ff89b515a4101e02f5b58 (MD5) / Made available in DSpace on 2016-05-20T15:29:23Z (GMT). No. of bitstreams: 1 2007_dis_amarruda.pdf: 427889 bytes, checksum: b0a54f14f17ff89b515a4101e02f5b58 (MD5) Previous issue date: 2007 / The notion of the least fixed-point of an operator is widely applied in computer science as, for instance, in the context of query languages for relational databases. Some extensions of FOL with _xed-point operators on finite structures, as the least fixed-point logic (LFP), were proposed to deal with problem problems related to the expressivity of FOL. LFP captures the complexity class PTIME over the class of _nite ordered structures. The descriptive characterization of computational classes is a central issue within _nite model theory (FMT). Trakhtenbrot's theorem, considered the starting point of FMT, states that validity over finite models is not recursively enumerable, that is, completeness fails over finite models. This result is based on an underlying assumption that any deductive system is of finite nature. However, we can relax such assumption as done in the scope of proof theory for arithmetic. Proof theory has roots in the Hilbert's programme. Proof theoretical consequences are, for instance, related to normalization theorems, consistency, decidability, and complexity results. The proof theory for arithmetic is also motivated by Godel incompleteness theorems. It aims to o_er an example of a true mathematically meaningful principle not derivable in first-order arithmetic. One way of presenting this proof is based on a definition of a proof system with an infinitary rule, the w-rule, that establishes the consistency of first-order arithmetic through a proof-theoretical perspective. Motivated by this proof, here we will propose an in_nitary proof system for LFP that will allow us to investigate proof theoretical properties. With such in_nitary deductive system, we aim to present a proof theory for a logic traditionally defined within the scope of FMT. It opens up an alternative way of proving results already obtained within FMT and also new results through a proof theoretical perspective. Moreover, we will propose a normalization procedure with some restrictions on the rules, such this deductive system can be used in a theorem prover to compute queries on relational databases. / A noção de menor ponto-fixo de um operador é amplamente aplicada na ciência da computação como, por exemplo, no contexto das linguagens de consulta para bancos de dados relacionais. Algumas extensões da Lógica de Primeira-Ordem (FOL)1 com operadores de ponto-fixo em estruturas finitas, como a lógica de menor ponto-fixo (LFP)2, foram propostas para lidar com problemas relacionados á expressividade de FOL. A LFP captura as classes de complexidade PTIME sobre a classe das estruturas finitas ordenadas. A caracterização descritiva de classes computacionais é uma abordagem central em Teoria do Modelos Finitos (FMT)3. O teorema de Trakhtenbrot, considerado o ponto de partida para FMT, estabelece que a validade sobre modelos finitos não é recursivamente enumerável, isto é, a completude falha sobre modelos finitos. Este resultado é baseado na hipótese de que qualquer sistema dedutivo é de natureza finita. Entretanto, nos podemos relaxar tal hipótese como foi feito no escopo da teoria da prova para aritmética. A teoria da prova tem raízes no programa de Hilbert. Conseqüências teóricas da noção de prova são, por exemplo, relacionadas a teoremas de normalização, consistência, decidibilidade, e resultados de complexidade. A teoria da prova para aritmética também é motivada pelos teoremas de incompletude de Gödel, cujo alvo foi fornecer um exemplo de um princípio matemático verdadeiro e significativo que não é derivável na aritmética de primeira-ordem. Um meio de apresentar esta prova é baseado na definição de um sistema de prova com uma regra infinitária, a w-rule, que estabiliza a consistência da aritmética de primeira-ordem através de uma perspectiva de teoria da prova. Motivados por esta prova, iremos propor aqui um sistema infinitário de prova para LFP que nos permitirá investigar propriedades em teoria da prova. Com tal sistema dedutivo infinito, pretendemos apresentar uma teoria da prova para uma lógica tradicionalmente definida no escopo de FMT. Permanece aberto um caminho alternativo de provar resultados já obtidos com FMT e também novos resultados do ponto de vista da teoria da prova. Além disso, iremos propor um procedimento de normalização com restrições para este sistema dedutivo, que pode ser usado em um provador de teoremas para computar consultas em banco de dados relacionais

L'algorithme de Levenberg-Marquardt (LM) est parmi les algorithmes les plus populaires pour la résolution des problèmes des moindres carrés non linéaire. Motivés par la structure des problèmes de l'assimilation de données, nous considérons dans cette thèse l'extension de l'algorithme LM aux situations dans lesquelles le sous problème linéarisé, qui a la forme min||Ax - b ||^2, est résolu de façon approximative, et/ou les données sont bruitées et ne sont précises qu'avec une certaine probabilité. Sous des hypothèses appropriées, on montre que le nouvel algorithme converge presque sûrement vers un point stationnaire du premier ordre. Notre approche est appliquée à une instance dans l'assimilation de données variationnelles où les modèles stochastiques du gradient sont calculés par le lisseur de Kalman d'ensemble (EnKS). On montre la convergence dans L^p de l'EnKS vers le lisseur de Kalman, quand la taille de l'ensemble tend vers l'infini. On montre aussi la convergence de l'approche LM-EnKS, qui est une variante de l'algorithme de LM avec l'EnKS utilisé comme solveur linéaire, vers l'algorithme classique de LM ou le sous problème est résolu de façon exacte. La sensibilité de la méthode de décomposition en valeurs singulières tronquée est étudiée. Nous formulons une expression explicite pour le conditionnement de la solution des moindres carrés tronqués. Cette expression est donnée en termes de valeurs singulières de A et les coefficients de Fourier de b. / The Levenberg-Marquardt algorithm (LM) is one of the most popular algorithms for the solution of nonlinear least squares problems. Motivated by the problem structure in data assimilation, we consider in this thesis the extension of the LM algorithm to the scenarios where the linearized least squares subproblems, of the form min||Ax - b ||^2, are solved inexactly and/or the gradient model is noisy and accurate only within a certain probability. Under appropriate assumptions, we show that the modified algorithm converges globally and almost surely to a first order stationary point. Our approach is applied to an instance in variational data assimilation where stochastic models of the gradient are computed by the so-called ensemble Kalman smoother (EnKS). A convergence proof in L^p of EnKS in the limit for large ensembles to the Kalman smoother is given. We also show the convergence of LM-EnKS approach, which is a variant of the LM algorithm with EnKS as a linear solver, to the classical LM algorithm where the linearized subproblem is solved exactly. The sensitivity of the trucated sigular value decomposition method to solve the linearized subprobems is studied. We formulate an explicit expression for the condition number of the truncated least squares solution. This expression is given in terms of the singular values of A and the Fourier coefficients of b.

Cette thèse s'inscrit dans le cadre de l'analyse statistique de données en grande dimension. Nous avons en effet aujourd'hui accès à un nombre toujours plus important d'information. L'enjeu majeur repose alors sur notre capacité à explorer de vastes quantités de données et à en inférer notamment les structures de dépendance. L'objet de cette thèse est d'étudier et d'apporter des garanties théoriques à certaines méthodes d'estimation de structures de dépendance de données en grande dimension.La première partie de la thèse est consacrée à l'étude de modèles parcimonieux et aux méthodes de type Lasso. Après avoir présenté les résultats importants sur ce sujet dans le chapitre 1, nous généralisons le cas gaussien à des modèles exponentiels généraux. La contribution majeure à cette partie est présentée dans le chapitre 2 et consiste en l'établissement d'inégalités oracles pour une procédure Group Lasso appliquée aux modèles linéaires généralisés. Ces résultats montrent les bonnes performances de cet estimateur sous certaines conditions sur le modèle et sont illustrés dans le cas du modèle Poissonien. Dans la deuxième partie de la thèse, nous revenons au modèle de régression linéaire, toujours en grande dimension mais l'hypothèse de parcimonie est cette fois remplacée par l'existence d'une structure de faible dimension sous-jacente aux données. Nous nous penchons dans cette partie plus particulièrement sur la méthode PLS qui cherche à trouver une décomposition optimale des prédicteurs étant donné un vecteur réponse. Nous rappelons les fondements de la méthode dans le chapitre 3. La contribution majeure à cette partie consiste en l'établissement pour la PLS d'une expression analytique explicite de la structure de dépendance liant les prédicteurs à la réponse. Les deux chapitres suivants illustrent la puissance de cette formule aux travers de nouveaux résultats théoriques sur la PLS . Dans une troisième et dernière partie, nous nous intéressons à la modélisation de structures au travers de graphes et plus particulièrement à la détection de communautés. Après avoir dressé un état de l'art du sujet, nous portons notre attention sur une méthode en particulier connue sous le nom de spectral clustering et qui permet de partitionner les noeuds d'un graphe en se basant sur une matrice de similarité. Nous proposons dans cette thèse une adaptation de cette méthode basée sur l'utilisation d'une pénalité de type l1. Nous illustrons notre méthode sur des simulations. / This thesis falls within the context of high-dimensional data analysis. Nowadays we have access to an increasing amount of information. The major challenge relies on our ability to explore a huge amount of data and to infer their dependency structures.The purpose of this thesis is to study and provide theoretical guarantees to some specific methods that aim at estimating dependency structures for high-dimensional data. The first part of the thesis is devoted to the study of sparse models through Lasso-type methods. In Chapter 1, we present the main results on this topic and then we generalize the Gaussian case to any distribution from the exponential family. The major contribution to this field is presented in Chapter 2 and consists in oracle inequalities for a Group Lasso procedure applied to generalized linear models. These results show that this estimator achieves good performances under some specific conditions on the model. We illustrate this part by considering the case of the Poisson model. The second part concerns linear regression in high dimension but the sparsity assumptions is replaced by a low dimensional structure underlying the data. We focus in particular on the PLS method that attempts to find an optimal decomposition of the predictors given a response. We recall the main idea in Chapter 3. The major contribution to this part consists in a new explicit analytical expression of the dependency structure that links the predictors to the response. The next two chapters illustrate the power of this formula by emphasising new theoretical results for PLS. The third and last part is dedicated to graphs modelling and especially to community detection. After presenting the main trends on this topic, we draw our attention to Spectral Clustering that allows to cluster nodes of a graph with respect to a similarity matrix. In this thesis, we suggest an alternative to this method by considering a $l_1$ penalty. We illustrate this method through simulations.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Uma das ferramentas básicas no controle estatístico de processos são os gráficos de controle de Shewhart, úteis no monitoramento das características-chave da qualidade nos processos de produção. Este monitoramento pode ser feito através de gráficos de controle univariados ou multivariados, quando a característica de qualidade é representada, respectivamente, por uma variável aleatória univariada ou multivariada. Em alguns casos, a qualidade pode ser representada por algum tipo de perfil, uma relação linear ou não-linear entre suas características. Este trabalho é dedicado ao estudo da fase II de gráficos de controle, ao monitoramento de uma variável, em um processo de produção, que é representada por um perfil linear, e os coeficientes de regressão são estimados pelo método de mínimos quadrados ordinários e pelo filtro de Kalman. Utiliza-se o gráfico de controle 2 c para o monitoramento dos parâmetros, intercepto e coeficiente de inclinação, do modelo de regressão linear simples. É proposto a aplicação das estimativas do filtro de Kalman ao gráfico de controle 2 c e também o estudo da eficiência deste gráfico com tais estimativas, bem como, a comparação com as estimativas obtidas pelo método de mínimos quadrados ordinários. Através de uma métrica construída com as estimativas do filtro de Kalman e com as estimativas do método de mínimos quadrados ordinários, compara-se o desempenho do gráfico de controle 2 c e verifica-se que este é mais rápido na detecção de mudanças nos parâmetros do modelo do processo quando suas estimativas são geradas pelo filtro de Kalman do que pelo método de mínimos quadrados ordinários. / Shewhart chart is a fundamental tool in statistical process control, and is useful in the monitoring of key quality characteristics in production processes. That monitoring can be done by univariate or by multivariate control charts, when the quality characteristic can be represented by a random variable or random vector. There are however certain cases where the quality can be represented by a profile, linear or nonlinear, between its characteristics. This work is dedicated to the control strategy for Phase II, to the monitoring of variables in a production process following a linear profile and the regression coefficients estimated by least squares and by Kalman filter. Our aim is to compare the performance of the 2 c control chart when the parameters of the model are estimated by those alternative techniques. Control chart 2 c has been used to monitor parameters of simple linear regression model. It has been proposed to apply the Kalman Filter estimates in the control chart 2 c and to analyse the efficiency of this chart considering such estimates, as well as, the comparison with the least squares estimates. The performance of this chart has been compared by those two techniques of estimation and has been confirmed that the control chart 2 c is more efficient when combined with the Filter Kalman estimates than with the least squares estimates.