Philosophiae Doctor - PhD (Mathematics) / The main theme of this thesis is the construction of linear codes from adjacency matrices or sub-matrices of adjacency matrices of regular graphs. We first examine the binary codes from the row span of biadjacency matrices and their transposes for some classes of bipartite graphs. In this case we consider a sub-matrix of an adjacency matrix of a graph as the generator of the code. We then shift our attention to uniform subset graphs by exploring the automorphism groups of graph covers and some classes of uniform subset graphs. In the sequel, we explore equal codes from adjacency matrices of non-isomorphic uniform subset graphs and finally consider codes generated by an adjacency matrix formed by adding adjacency matrices of two classes of uniform subset graphs.

Seja $B_mM$ o grupo de tranças com $m$ cordas sobre uma superfície $M$ e seja $N$ uma subsuperfície de $M$. Estudaremos inicialmente condições necessárias e suficientes para as quais $B_nN$ é um subgrupo de $B_mM$ ($m$ podendo ser diferente de $n$), isto é, se considerarmos a inclusão $i\\colon N \\to M$, queremos estabelecer condições sobre $M$ e $N$ para que a aplicação induzida $i_\\ast \\colon B_nN \\to B_mM$ seja injetora. Em seguida, sob certas hipóteses para $N$ e $M$ calcularemos o comensurador, normalizador e centralizador de $B_nN$ em $B_mM$, sendo esse o objetivo principal desta dissertação. / Let $B_m(M)$ be the braid group with $m$ strings on a surface $M$ and let $N$ be a subsurface of $M$. We will study the necessary and sufficient conditions out of which $B_n(N)$ is a subgroup of $B_m(M)$ ($m$ can be different of $n$), it means, if we consider the inclusion $i \\colon N \\to M$, we would like to establish conditions for $M$ and $N$ for the induced application $i_\\ast \\colon B_nN \\to B_mM$ should be injective. After that, under some certain conditions for $M$ and $N$ we will calculate the commensurator, normalizer and centralizer of $Bn(N)$ in $Bm(M)$, being this one the principal objective of this work.

Coeliac disease (CD) is a clinically heterogeneous autoimmune disease with variable presentation and progression triggered by gluten intake. Molecular or genetic factors contribute to disease heterogeneity, but the reasons for different outcomes are poorly understood. Transcriptome studies of tissue biopsies from CD patients are scarce. Here, we present a high-resolution analysis of the transcriptomes extracted from duodenal biopsies of 24 children and adolescents with active CD and 21 individuals without CD but with intestinal afflictions as controls. The transcriptomes of CD patients divide into three groups—a mixed group presenting the control cases, and CD-low and CD-high groups referring to lower and higher levels of CD severity. Persistence of symptoms was weakly associated with subgroup, but the highest marsh stages were present in subgroup CD-high, together with the highest cell cycle rates as an indicator of virtually complete villous atrophy. Considerable variation in inflammation-level between subgroups was further deciphered into immune cell types using cell type de-convolution. Self-organizing maps portrayal was applied to provide high-resolution landscapes of the CD-transcriptome. We find asymmetric patterns of miRNA and long non-coding RNA and discuss the effect of epigenetic regulation. Expression of genes involved in interferon gamma signaling represent suitable markers to distinguish CD from non-CD cases. Multiple pathways overlay in CD biopsies in different ways, giving rise to heterogeneous transcriptional patterns, which potentially provide information about etiology and the course of the disease.

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La découverte de motifs qui caractérisent fortement une classe vis à vis d'une autre reste encore un problème difficile en fouille de données. La découverte de sous-groupes (Subgroup Discovery, SD) est une approche formelle de fouille de motifs qui permet la construction de classifieurs intelligibles mais surtout d'émettre des hypothèses sur les données. Cependant, cette approche fait encore face à deux problèmes majeurs : (i) comment définir des mesures de qualité appropriées pour caractériser l'intérêt d'un motif et (ii) comment sélectionner une méthode heuristique adaptée lorsqu’une énumération exhaustive de l'espace de recherche n'est pas réalisable. Le premier problème a été résolu par la fouille de modèles exceptionnels (Exceptional Model Mining, EMM) qui permet l'extraction de motifs couvrant des objets de la base de données pour lesquels le modèle induit sur les attributs de classe est significativement différent du modèle induit par l'ensemble des objets du jeu de données. Le second problème a été étudié en SD et EMM principalement avec la mise en place de méthodes heuristiques de type recherche en faisceau (beam-search) ou avec des algorithmes génétiques qui permettent la découverte de motifs non redondants, diversifiés et de bonne qualité. Dans cette thèse, nous soutenons que la nature gloutonne des méthodes d'énumération précédentes génère cependant des ensembles de motifs manquant de diversité. Nous définissons formellement la fouille de données comme un jeu que nous résolvons par l'utilisation de la recherche arborescente de Monte Carlo (Monte Carlo Tree Search, MCTS), une technique récente principalement utilisée pour la résolution de jeux et de problèmes de planning en intelligence artificielle. Contrairement aux méthodes traditionnelles d'échantillonnage, MCTS donne la possibilité d'obtenir une solution à tout instant sans qu'aucune hypothèse ne soit faite que ce soit sur la mesure de qualité ou sur les données. Cette méthode d'énumération converge vers une approche exhaustive si les budgets temps et mémoire disponibles sont suffisants. Le compromis entre l'exploration et l'exploitation que propose cette approche permet une augmentation significative de la diversité dans l'ensemble des motifs calculés. Nous montrons que la recherche arborescente de Monte Carlo appliquée à la fouille de motifs permet de trouver rapidement un ensemble de motifs diversifiés et de bonne qualité à l'aide d'expérimentations sur des jeux de données de référence et sur un jeu de données réel traitant de l'olfaction. Nous proposons et validons également une nouvelle mesure de qualité spécialement conçue pour des jeux de donnée multi labels présentant une grande variance de fréquences des labels. / The discovery of patterns that strongly distinguish one class label from another is still a challenging data-mining task. Subgroup Discovery (SD) is a formal pattern mining framework that enables the construction of intelligible classifiers, and, most importantly, to elicit interesting hypotheses from the data. However, SD still faces two major issues: (i) how to define appropriate quality measures to characterize the interestingness of a pattern; (ii) how to select an accurate heuristic search technique when exhaustive enumeration of the pattern space is unfeasible. The first issue has been tackled by Exceptional Model Mining (EMM) for discovering patterns that cover tuples that locally induce a model substantially different from the model of the whole dataset. The second issue has been studied in SD and EMM mainly with the use of beam-search strategies and genetic algorithms for discovering a pattern set that is non-redundant, diverse and of high quality. In this thesis, we argue that the greedy nature of most such previous approaches produces pattern sets that lack diversity. Consequently, we formally define pattern mining as a game and solve it with Monte Carlo Tree Search (MCTS), a recent technique mainly used for games and planning problems in artificial intelligence. Contrary to traditional sampling methods, MCTS leads to an any-time pattern mining approach without assumptions on either the quality measure or the data. It converges to an exhaustive search if given enough time and memory. The exploration/exploitation trade-off allows the diversity of the result set to be improved considerably compared to existing heuristics. We show that MCTS quickly finds a diverse pattern set of high quality in our application in neurosciences. We also propose and validate a new quality measure especially tuned for imbalanced multi-label data.

Dans cette thèse, nous nous intéressons à des compactifications géométriques variées. Nous décrivons l'espace des sous-groupes fermés du groupe RxZ. Nous étudions la compactification de Chabauty des espaces symétriques de type non compact. Nous définissons et étudions la compactification de Chabauty de l'espace des plats maximaux des espaces symétriques de SL3(R) et de SL4(R). Nous étudions les limites géométriques de plats maximaux de l'espace symétrique ou de l'immeuble de Bruhat-Tits associé à SL3 sur un corps local. Nous définissons et étudions une compactification à la Thurston des espaces de classes d'isométrie de réseaux marqués. Nous définissons une compactification à la Thurston de l'espace de Torelli d'une surface et nous décrivons la stratification naturelle d'une partie de son bord. / In our thesis, we focus on various geometric compactifications. We describe the space of closed subgroups of RxZ. We study the Chabauty compactification of symmetric spaces of non-compact type. We define and study the Chabauty compactification of the space of maximal flats of the symmetric spaces of SL3(R) and SL4(R). We study the geometric limits of maximal flats in the symmetric space or in the Bruhat-Tits building associated to SL3 over a local field. We define and study a Thurston-like compactification of spaces of isometry classes of marked lattices. We define a Thurston-like compactification of the Torelli space of a surface and we describe the natural stratification of a subset of the boundary.

Cette thèse est une contribution au domaine des cubulations de groupes hyperboliques au sens de Gromov. Nous nous intéressons au cas particulier des groupes fondamentaux de variétés hyperboliques réelles compactes. La philosophie inspirée dans ce domaine par les travaux de M. Sageev est que si un groupe hyperbolique possède suffisamment de sous-groupes de codimension 1 quasi-convexes, alors il agit géométriquement sur un complexe cubique CAT(0) de dimension finie. Nous démontrons un critère précis de cubulation pour les groupes fondamentaux de variétés hyperboliques compactes, à l'aide de constructions d'espaces à murs quasi-isométriques à l'espace hyperbolique réel. Nous nous restreignons par la suite au cas particulier de la dimension 3 et plus particulièrement aux 3-variétés hyperboliques compactes virtuellement fibrées sur le cercle. Nous exploitons alors une construction de surfaces immergées incompressibles dites coupées-croisées due à D. Cooper, D. Long et A. Reid dans une telle 3-variété M pour fabriquer des sous-groupes de surface de son groupe fondamental~G. En raffinant des arguments de J. Masters et en exploitant la structure de l'application de Cannon-Thurston, nous parvenons à construire des sous-groupes de surfaces quasi-convexes de G en quantité suffisante pour que leurs ensembles limites permettent de séparer toutes les paires de points distincts du bord du revêtement universel de M. En conséquence de cette construction, G agit géométriquement sur un complexe cubique CAT(0) de dimension finie. D. Wise soulève alors la question de savoir si ce groupe G peut agir géométriquement et également virtuellement co-spécialement (au sens de F. Haglund et D. Wise) sur un complexe cubique CAT(0). Une réponse positive résoudrait les conjectures selon lesquelles G est large et le premier nombre de Betti virtuel de M est infini. Nous faisons remarquer que pour obtenir une réponse positive à cette question, il suffit de trouver une surface coupée-croisée virtuellement plongée dans un revêtement fini fibré sur le cercle de M. Nous concluons en présentant des conditions algébriques, puis géométriques et cohomologiques suffisantes pour qu'une surface coupée-croisée donnée soit virtuellement plongée. / This thesis contributes to the study of geometric actions of word-hyperbolic groups on finite dimensional CAT(0) cube complexes. We are mainly interested in the case of fundamental groups of closed hyperbolic manifolds. The philosophy coming from pioneer work of M. Sageev is that a hyperbolic group with sufficiently many quasi-convex codimension one subgroups acts geometrically on a finite dimensional CAT(0) cube complex. We prove a precise criterion for cubulation in the case of closed hyperbolic manifolds, by constructing spaces with walls quasi-isometric to real hyperbolic space. We next focus on the case of three dimensional closed hyperbolic manifolds which are virtually fibered over the circle. In this setting, we use a construction of incompressibly immersed cut-and-cross-join surfaces due to D. Cooper, D. Long and A. Reid that yields surface subgroups of the fundamental group G of the 3-manifold M. By expanding on work of J. Masters and using the structure of the Cannon-Thurston map, we are able to build many quasi-convex surface subgroups of G whose limits sets may be used to separate any pair of distinct points in the boundary of the universal cover of M. As a consequence, G acts geometrically on a finite dimensional CAT(0) cube complex. D. Wise then asks if it is possible that G acts both geometrically and virtually co-specially (in the sense of F. Haglund and D. Wise) on a CAT(0) cube complex. A positive answer would solve the long-standing conjectures that G is large and M has infinite virtual first Betti number. We then explain why finding a virtually embedded cut-and-cross-join surface in a finite cover of M would be enough to solve this problem. Finally, we give some algebraic and then geometric and cohomological sufficient conditions for a given cut-and-cross-join surface to virtually embed.

Diese Dissertation behandelt nicht-holomorphe Diese Dissertation behandelt nicht-holomorphe Eisensteinreihen und Dessins d''Enfants. Nicht-holomorphe Eisensteinreihen entstehen aus Untergruppen der Modulgruppe, indem man über alle Elemente der Gruppe modulo dem Stabilisator einer Spitze aufsummiert. Die zweite Struktur, Dessins d''Enfants, sind bipartite Graphen die in topologische Flächen eingebettet sind. Dessins d''Enfants stehen in Korrespondenz zu Belyi-Paaren und Untergruppen der Modulgruppe von endlichem Index. Deshalb bestehen zwischen Eisensteinreihen und Dessins d''Enfants Verbindungen und ein Schwerpunkt dieser Arbeit ist es, Informationen und Wissen über das eine Objekt in das andere zu übertragen. Bezüglich Dessins d''Enfants beschäftigen wir uns mit Symmetrien. Wir waren in der Lage, Automorphismen von algebraischen Kurven im assoziierten Dessin, in der zugehörigen Untergruppe sowie insbesondere auf den Spitzen zu interpretieren. Außerdem beschreiben wir die Zusammenhänge zwischen Dessins für Untergruppen, dadurch können wir für zwei Untergruppen anhand ihres Dessins entscheiden, ob sie in einander enthalten sind. In Kombination mit hier erbrachten Resultaten zu den Hauptkongruenzuntergruppen führt dies zu einem implementierten Algorithmus, der prüft, ob eine Gruppe eine Kongruenzuntergruppe ist oder nicht. Auf der Seite der Eisensteinreihen untersucht dieser Text Streukonstanten, Greensche Funktionen und Kroneckergrenzformeln. In der Streumatrix fanden wir Symmetrien (für bestimmte Gruppen). Für Greensche Funktionen wurde eine Spurformel bewiesen. Wir zeigten, dass Eisensteinreihen eine Identität erfüllen, die wir Kroneckergrenzformel nennen; sie vergleicht den konstanten Term der Eisensteinreihe mit Funktionen, die von ausgezeichneten Modulformen kommen. Die Dissertation gipfelt in der Berechnung der Streukonstanten für die Untergruppen assoziiert zu den Fermatkurven, die fast alle Nichtkongruenzuntergruppen sind. / In this dissertation non-holomorphic Eisenstein series and Dessins d''Enfants are considered. Non-holomorphic Eisenstein series are created out of subgroups of the modular group by summing up over all elements modulo the stabilizer of a cusp. The second main object, Dessins d''Enfants, are bipartite graphs that are embedded into topological surfaces. There is a correspondence between Dessins D''Enfants, Belyi pairs and subgroups of the modular group of finite index. Therefore Eisenstein series and Dessins d''Enfants are related and a focus of this work is how to use the one to find information about the other. The main results concerning Dessins d''Enfants in this thesis are investigations of symmetries of Dessins. We have been able to interpret automorphisms of algebraic curves on the associated Dessin, the subgroups and in particular the set of cusps. Furthermore, we describe the relation of Dessins for subgroups. Therefore, with help of the Dessins we can decide if two subgroups are contained in each other. Together with our results on the Dessins for principal congruence subgroups this leads to an implemented algorithm that checks if a subgroup is a congruence subgroup or not. On the side of Eisenstein series we consider scattering constants, Green''s functions and Kronecker limit formulas. We found symmetries in the scattering matrix for certain groups. For Green''s functions we established a trace formula. We showed that Eisenstein series fulfill an identity we call Kronecker limit formula in which they are compared with functions coming from certain modular forms. Most of the work done in this thesis culminates in the calculation of the scattering constants for the subgroups associated to Fermat curves; most of these groups are non-congruence.

Amalgam has been used as a dental restorative material for centuries, but its potential health effects and biopersistance has lead to a decreased use especially in the Nordic countries. New materials have been introduced, partly to replace the mercury containing amalgam and partly because of esthetical reasons. The possible health effects of amalgam have been studied extensively and the material has been replaced with other less well-examined materials during the last few decades. The prevalence of side effects of dental materials is considered to be low in relation to the vast number of dental treatments undertaken. With the introduction of new and more complex materials, side effects related to dental treatment may increase. Epidemiological data suggest that the side effects of dental resins that have almost completely replaced amalgam fillings in Scandinavia, possess a risk for adverse reactions; however, the causal relation has not been fully established. Therefore, the type and extent of side effects caused by resin-based materials are of great interest. The aims of the study were: - to describe the change in health over time for patients with problems related to their dental materials. The hypothesis was that the patients could be divided into subgroups based on their symptoms and that the ability to recover differs between these groups [Paper I]. Furthermore, to determine whether factors such as the replacement of dental restorative materials and follow-up time had any impact on the perceived health. - to assess the long-term development of symptoms and their social consequences among patients referred for diagnosis and treatment of symptoms related to dental materials [Paper II] - to investigate the possible risks with dental restorative materials other than amalgam [Paper III]. - to describe side effects assessed to be caused by resin-based materials that occurred in a group of patients as well as treatment and long-term consequences of the reactions [Paper IV]. A questionnaire was sent to 614 patients [Paper I and II] that had been referred to the School of Dentistry, Umeå, Sweden, with symptoms allegedly caused by dental materials. The questionnaire contained questions on, among others; civil status, present health, medical and dental treatment and other measures and precautions taken because of psychosocial problems related to current employment situation, feelings, self-image and coping behavior. Moreover, information was collected [Paper III] from the Swedish Dental Materials Register 2003 (DentMr), a compilation of MSDS for 487 materials, and information from the user guide of the materials. The Material Safety Data Sheets (MSDS) included in the DentMR were examined regarding the given composition of the products, the occurrence of CAS-numbers and the risk- and safety phrases of the substances. Information was collected [Paper IV] on 36 patients with reactions to resin-based restorative materials from the Swedish National Register of Side-Effects of Dental Materials. Patients with complex symptoms had a more unfavorable long-term prognosis concerning persistent complaints than those with local symptoms only. Furthermore, the results indicate that the patients might experience health improvements after removal of their dental restorative materials. However, the reason for this improvement was unclear. Replacement of dental restorative materials had no significant impact on the ability to recover completely. Our results also indicate a relationship between patients’ self-related health and social consequences in daily life. Those with remaining complex symptoms had more often stopped working or had decreased their work hours because of their symptoms The information about hazards with dental materials seems insufficiently described in MSDS and there might be materials with side effects unknown to both patients and dental professionals. A literature search indicated that some of the listed substances had possible hazards, e.g. substances with embryotoxic and neurotoxic potential. The patients were very heterogeneous; a few with only local symptom free reactions while other had more complex symptoms. The latter group would gain from a multidisciplinary approach, i.e. dental, medical, as well as social and psychological factors have to be considered when developing care management programs for this group of patients. Furthermore, there is a need for stronger regulations of dental materials, such as those applied to pharmaceutical drugs. Finally, it was found that the majority of symptoms suspected to be caused by resin-based materials were local or a combination of local and extra-oral symptoms that appeared within the first 24 hours after treatment. The most frequent adverse effect reported was skin problems/dermatitis. It appears as though immediate reactions to resin based materials are not uncommon and more prevalent than allergic reactions. Still, we have had, difficulties in verifying associations between the dental restorative materials and adverse reactions and also to identify the offending component.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal