Les progrès continus dans les techniques du stockage et de la collection des données permettent d'observer et d'enregistrer des processus d’une façon presque continue. Des exemples incluent des données climatiques, des valeurs de transactions financières, des modèles des niveaux de pollution, etc. Pour analyser ces processus, nous avons besoin des outils statistiques appropriés. Une technique très connue est l'analyse de données fonctionnelles (ADF).<p><p>L'objectif principal de ce projet de doctorat est d'analyser la dépendance temporelle de l’ADF. Cette dépendance se produit, par exemple, si les données sont constituées à partir d'un processus en temps continu qui a été découpé en segments, les jours par exemple. Nous sommes alors dans le cadre des séries temporelles fonctionnelles.<p><p>La première partie de la thèse concerne la régression linéaire fonctionnelle, une extension de la régression multivariée. Nous avons découvert une méthode, basé sur les données, pour choisir la dimension de l’estimateur. Contrairement aux résultats existants, cette méthode n’exige pas d'assomptions invérifiables. <p><p>Dans la deuxième partie, on analyse les modèles linéaires fonctionnels dynamiques (MLFD), afin d'étendre les modèles linéaires, déjà reconnu, dans un cadre de la dépendance temporelle. Nous obtenons des estimateurs et des tests statistiques par des méthodes d’analyse harmonique. Nous nous inspirons par des idées de Brillinger qui a étudié ces models dans un contexte d’espaces vectoriels. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Cette thèse étudie une classe des problèmes de Riemann-Hilbert Fuchsiens (à coefficients méromorphes dont tous les pôles sont d'ordre un). Les variétés de Frobenius apparaissent comme une formulation géométrique des structures d'équations de Witten-DijkgraafVerlande-Verlande (WDVV). Nous considérons ces variétés sur les espaces de Hurwitz vus, quant à eux, comme variétés réelles motivés par le fait qu'une variété de Frobenius semisimple peut être construite à partir d'une solution fondamentale du problème de Riemann-Hilbert associé. Une solution au problème Fuchsien de Riemann-Hilbert matriciel (problème de monodromie inverse) correspondant aux structures "réelles doubles" de Frobenius de Dubrovin sur les espaces de Hurwitz, a été construite. La solution est donnée en termes de certaines différentielles méromorphes integrées sur une base appropriée d'homologie relative de la surface de Riemann. La relation avec la solution du problème Fuchsien de Riemann-Hilbert pour les structures de Frobenius Hurwitz de Dubrovin est établie. Une solution du problème de Riemann-Hilbert correspondant aux déformations des "réelles doubles" est aussi donnée.

This dissertation explores the potential of EMD as analyzing tool for audio and speech processing. This signal expansion into IMFs is adaptive and without any prior assumptions (stationarity and linearity) on the signal to be analyzed. Salient properties of EMD such as dyadic filter bank structure, quasi-symmetry of IMF and fully description of IMF by its extrema, are exploited for denoising, coding and watermarking purposes. In speech signals denoising, we initially proposed a technique based on IMFs thresholding. A comparative analysis of performance of this technique compared to the denoising technique based on the wavelet. Then, to remedy the problem of the MMSE filters which requires an estimation of the spectral properties of noise, we introduced the ACWA filter in the denoising procedure. The proposed approach is consisted to filter all IMFs of the noisy signal by ACWA filter. This filtering approach is implemented in the time domain, and also applicable in the context of colored noise. Finally, to handle the case of hybrid speech frames, that is composed of voiced and unvoiced speech, we introduced a stationarity index in the denoising approach to detect the transition between the mixture of voiced and unvoiced sounds. In audio signals coding, we proposed four compression approaches. The first two approaches are based on the EMD, and the other two approaches exploit the EMD in association with Hilbert transform. In particular, we proposed to use a predictive coding of the instantaneous amplitude and frequency of the IMFs Finally, we studied the problem of audio signals watermarking in context of copyright protection. The number of IMFs can be variable depending on the attack type. The proposed approach involves inserting the mark in the extrema of last IMFs. In addition, we introduced a synchronization code in the procedure in order to facility the extraction of the mark. These contributions are illustrated on synthetic and real data and results compared to well established methods such as MMSE filter, wavelets approach, MP3 and AAC coders showing the good performances of EMD based signal processes. These findings demonstrate the real potential of EMD as analyzing tool (in adaptive way) in speech and audio processing.

Cerebral autoregulation describes the clinically observed phenomenon that cerebral blood flow remains relatively constant in healthy human subjects despite large systemic changes in blood pressure, dissolved blood gas concentrations, heart rate and other systemic variables. Cerebral autoregulation is known to be impaired post ischaemic stroke, after severe head injury, in patients suffering from autonomic dysfunction and under the action of various drugs. Cerebral auto-regulation is a dynamic, multivariate phenomenon. Sensitive techniques are required to monitor cerebral auto-regulation in a clinical setting. This thesis presents 4 related signal processing studies of cerebral autoregulation. The first study shows how consideration of changes in blood gas concentrations simultaneously with changes in blood pressure can improve the accuracy of an existing frequency domain technique for monitoring cerebral autoregulation from spontaneous fluctuations in blood pressure and a transcranial doppler measure of cerebral blood flow velocity. The second study shows how the continuous wavelet transform can be used to investigate coupling between blood pressure and near infrared spectroscopy measures of cerebral haemodynamics in patients with autonomic failure. This introduces time information into the frequency based assessment, however neglects the contribution of blood gas concentrations. The third study shows how this limitation can be resolved by introducing a new time-varying multivariate system identification algorithm based around the dual tree undecimated wavelet transform. All frequency and time-frequency domain methods of monitoring cerebral autoregulation assume linear coupling between the variables under consideration. The fourth study therefore considers nonlinear techniques of monitoring cerebral autoregulation, and illustrates some of the difficulties inherent in this form of analysis. The general approach taken in this thesis is to formulate a simple system model; usually in the form of an ODE or a stochastic process. The form of the model is adapted to encapsulate a hypothesis about features of cerebral autoregulation, particularly those features that may be difficult to recover using existing methods of analysis. The performance of the proposed method of analysis is then evaluated under these conditions. After this testing, the techniques are then applied to data provided by the Laboratory of Human Cerebrovascular Physiology in Alberta, Canada, and the National Hospital for Neurology and Neurosurgery in London, UK.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

- ABSTRACT - Noncommutative Choquet theory Let S be a linear subspace of a commutative C∗ -algebra C(X) that se- parates points of C(X) and contains identity. Then the closure of the Choquet boundary of the function system S is the Šilov boundary relati- ve to S. In the case of a noncommutative unital C∗ -algebra A, consider S a self-adjoint linear subspace of A that contains identity and generates A. Let us call S operator system. Then the noncommutative formulation of the stated assertion is that the intersection of all boundary representa- tions for S is the Šilov ideal for S. To that end it is sufficient to show that S has sufficiently many boundary representations. In the present work we make for the proof of that this holds for separable operator system.

Une partie symétrique X d'un groupe G est un sous-groupe K-approximatif s'il existe une partie finie E ⊂ G de taille K telle que X2 ⊂ E.X. L'étude combinatoire des groupes approximatifs a grandement bénéficié des apports de la Théorie des Modèles : en 2009, Hrushovski montre qu'une ultralimite de groupes approximatifs finis possède une composante connexe modèle-théorique, donc un quotient localement compact X/H. En appliquant les résultats de Gleason et Yamabe sur le cinquième problème de Hilbert, cela permet de trouver un morphisme vers un groupe de Lie, et d'en déduire des résultats de nilpotence. Cela a permis à Breuillard, Green et Tao de classifier tous les groupes approximatifs finis, en retrouvant un quotient X/H de manière combinatoire. Dans cette thèse, on s'intéresse à la construction d'un sous-groupe H type-définissable et d'indice borné, qui garantit l'existence d'un quotient localement compact. On montre que l'approche combinatoire de Breuillard, Green et Tao peut être vue de cette manière, et on la généralise à tous les groupes approximatifs définissablement moyennables. On montre aussi que si H est type-définissable dans un langage L∗, alors on peut construire un sous-groupe H qui est type-définissable sur un langage réduit L, et toujours d'indice borné. L'existence de H ne dépend donc pas du choix du langage / A symmetric subset X in a group G is a K-approximate subgroup if there exists a finite set E ⊂ G of cardinality K such that X2 ⊂ E.X. The study of approximate subgroups in multiplicative combinatorics experienced a significate advance through the use of model theory. In 2009, Hrushovski showed that an ultralimit of finite approximate subgroups has a model-theoretic connected component, thus a locally compact quotient X/H. Using the results of Gleason and Yamabe about Hilbert’s fifth problem, this allows the construction of a morphism to a Lie group, and deduce some results about nilpotency. This lead to the theorem of Breuillard, Green and Tao classifying all finite approximate subgroups, using a combinatorial construction of the quotient X/H. In this thesis, we are intersested in the conditions needed to construct a type definable subgroup H of bounded index in X. This implies the existence of a locally compact quotient.We show that the combinatorial construction of Breuillard, Green and Tao can be seen in a definable way, and give a generalisation to all definably amenable approximate subgroups. Also, we show that if H is type-definable in a language L∗, then it is possible to construct a subgroup H which is type-definable in a reduct L, still with bounded index. Thus the existence of a subgroup H does not depend on the choice of a base language.

In this thesis we analyse the high-order in time discontinuous Galerkin nite element method (DGFEM) for second-order in time linear abstract wave equations. Our abstract approximation analysis is a generalisation of the approach introduced by Claes Johnson (in Comput. Methods Appl. Mech. Engrg., 107:117-129, 1993), writing the second order problem as a system of fi rst order problems. We consider abstract spatial (time independent) operators, highorder in time basis functions when discretising in time; we also prove approximation results in case of linear constraints, e.g. non-homogeneous boundary data. We take the two steps approximation approach i.e. using high-order in time DGFEM; the discretisation approach in time introduced by D Schötzau (PhD thesis, Swiss Federal institute of technology, Zürich, 1999) to fi rst obtain the semidiscrete scheme and then conformal spatial discretisation to obtain the fully-discrete formulation. We have shown solvability, unconditional stability and conditional a priori error estimates within our abstract framework for the fully discretized problem. The skew-symmetric spatial forms arising in our abstract framework for the semi- and fully-discrete schemes do not full ll the underlying assumptions in D. Schötzau's work. But the semi-discrete and fully discrete forms satisfy an Inf-sup condition, essential for our proofs; in this sense our approach is also a generalisation of D. Schötzau's work. All estimates are given in a norm in space and time which is weaker than the Hilbert norm belonging to our abstract function spaces, a typical complication in evolution problems. To the best of the author's knowledge, with the approximation approach we used, these stability and a priori error estimates with their abstract structure have not been shown before for the abstract variational formulation used in this thesis. Finally we apply our abstract framework to the acoustic and an elasto-dynamic linear equations with non-homogeneous Dirichlet boundary data.

The thesis deals with subsemigroups of (Nm 0 , +), a special discussion is later devoted to the cases m = 1, m = 2 and m = 3. We prove that a subsemigroup of Nm 0 is finitely generated if and only if its generated cone is finitely generated (equivalently polyhedral) and we describe basic topological properties of such cones. We give a few examples illustrating that conditions sufficient for finite generation in N2 0 can not be easily trans- ferred to higher dimensions. We define the Hilbert basis and the related notion of Carathéodory's rank. Besides their basic properties we prove that Carathédory's rank of a subsemigroup of Nm 0 , m = 1, 2, 3, is less than or equal to m. A particular attention is devoted to the subsemigroups containing non-trivial subsemigroups of "subtractive" elements.

Made available in DSpace on 2015-04-22T22:16:06Z (GMT). No. of bitstreams: 1 daiana santos.pdf: 1011976 bytes, checksum: 0d1f23d4c01774fbad224c1c0fbe0359 (MD5) Previous issue date: 2013-09-23 / FAPEAM - Fundação de Amparo à Pesquisa do Estado do Amazonas / In this dissertation, we present a proximal point method for solving problems balance in Hilbert spaces proposed by Alfredo Iusem and Wilfredo Sosa in [1]. We analyzed the convergence of this mehtod for troubleshooting balance. We verified the sequence generated by the method of classical proximal point and generated sequence the proximal point method to balance problems are the same. These results were obtained using variations of monotonicity of the function that defines the balance problem. In the final analysis is made on the weakening of the hypothesis assumed by function. / Nesta dissertação, apresentamos um método de ponto proximal para resolução de problemas de equilíbrio em espaços de Hilbert proposto por Alfredo Iusem e Wilfredo Sosa em [1]. Analisamos a convergência deste método para soluções de problemas de equilíbrio. Verificamos que a sequência gerada pelo método de ponto proximal clássico e a sequência gerada pelo método de ponto proximal para problemas de equilíbrio coincidem. Esses resultados foram obtidos usando variações de monotonicidade sobre a função que define o problema de equilíbrio. Uma análise final é feita sobre o enfraquecimento das hipóteses assumidas pela função.