Cette thèse introduit des nouveaux modèles de signaux musicaux informés par la physique des instruments. Alors que les communautés de l'acoustique instrumentale et du traitement du signal considèrent la modélisation des sons instrumentaux suivant deux approches différentes (respectivement, une modélisation du mécanisme de production du son, opposée à une modélisation des caractéristiques "morphologiques" générales du son), cette thèse propose une approche collaborative en contraignant des modèles de signaux génériques à l'aide d'information basée sur l'acoustique. L'effort est ainsi porté sur la construction de modèles spécifiques à un instrument, avec des applications aussi bien tournées vers l'acoustique (apprentissage de paramètres liés à la facture et à l'accord) que le traitement du signal (transcription de musique). En particulier nous nous concentrons sur l'analyse de musique pour piano, instrument pour lequel les sons produits sont de nature inharmonique. Cependant, l'inclusion d'une telle propriété dans des modèles de signaux est connue pour entraîner des difficultés d'optimisation, allant jusqu'à endommager les performances (en comparaison avec un modèle harmonique plus simple) dans des tâches d'analyse telles que la transcription. Un objectif majeur de cette thèse est d'avoir une meilleure compréhension des difficultés liées à l'inclusion explicite de l'inharmonicité dans des modèles de signaux, et d'étudier l'influence de l'apport de cette information sur les performances d'analyse, en particulier dans une tâche de transcription. / This thesis introduces new models of music signals informed by the physics of the instruments. While instrumental acoustics and audio signal processing target the modeling of musical tones from different perspectives (modeling of the production mechanism of the sound vs modeling of the generic "morphological'' features of the sound), this thesis aims at mixing both approaches by constraining generic signal models with acoustics-based information. Thus, it is here intended to design instrument-specific models for applications both to acoustics (learning of parameters related to the design and the tuning) and signal processing (transcription). In particular, we focus on piano music analysis for which the tones have the well-known property of inharmonicity. The inclusion of such a property in signal models however makes the optimization harder, and may even damage the performance in tasks such as music transcription when compared to a simpler harmonic model. A major goal of this thesis is thus to have a better understanding about the issues arising from the explicit inclusion of the inharmonicity in signal models, and to investigate whether it is really valuable when targeting tasks such as polyphonic music transcription.

The results of a round robin tournament can be represented as a matrix of zeros and ones, by ordering the players and placing a one in the (i,j) position if player i beat player j, and zeros otherwise. These matrices, called tournament matrices, can be represented by graphs, called tournament graphs. They have been the subject of much research and study, yet there have been few attempts to give a wide exposition on the subject. Those that have been done tend to focus on the graph theoretical aspects of tournaments. S. Ree and Y. Koh did write a brief survey from the matrix viewpoint in 1998, but it was not complete and not published. This paper is an attempt to give an exposition on tournament matrices. Recent research will be presented, some new ideas and properties will be proposed, and a few applications of the material will be reviewed.

De nombreux phénomènes physiques peuvent être étudiés au moyen de modélisations et de simulations numériques, courantes dans les applications scientifiques. Pour être calculable sur un ordinateur, des techniques de discrétisation appropriées doivent être considérées, conduisant souvent à un ensemble d’équations linéaires dont les caractéristiques dépendent des techniques de discrétisation. D’un côté, la méthode des éléments finis conduit généralement à des systèmes linéaires creux, tandis que les méthodes des éléments finis de frontière conduisent à des systèmes linéaires denses. La taille des systèmes linéaires en découlant dépend du domaine où le phénomène physique étudié se produit et tend à devenir de plus en plus grand à mesure que les performances des infrastructures informatiques augmentent. Pour des raisons de robustesse numérique, les techniques de solution basées sur la factorisation de la matrice associée au système linéaire sont la méthode de choix utilisée lorsqu’elle est abordable. A cet égard, les méthodes hiérarchiques basées sur de la compression de rang faible ont permis une importante réduction des ressources de calcul nécessaires pour la résolution de systèmes linéaires denses au cours des deux dernières décennies. Pour les systèmes linéaires creux, leur utilisation reste un défi qui a été étudié à la fois par la communauté des matrices hiérarchiques et la communauté des matrices creuses. D’une part, la communauté des matrices hiérarchiques a d’abord exploité la structure creuse du problème via l’utilisation de la dissection emboitée. Bien que cette approche bénéficie de la structure hiérarchique qui en résulte, elle n’est pas aussi efficace que les solveurs creux en ce qui concerne l’exploitation des zéros et la séparation structurelle des zéros et des non-zéros. D’autre part, la factorisation creuse est accomplie de telle sorte qu’elle aboutit à une séquence d’opérations plus petites et denses, ce qui incite les solveurs à utiliser cette propriété et à exploiter les techniques de compression des méthodes hiérarchiques afin de réduire le coût de calcul de ces opérations élémentaires. Néanmoins, la structure hiérarchique globale peut être perdue si la compression des méthodes hiérarchiques n’est utilisée que localement sur des sous-matrices denses. Nous passons en revue ici les principales techniques employées par ces deux communautés, en essayant de mettre en évidence leurs propriétés communes et leurs limites respectives, en mettant l’accent sur les études qui visent à combler l’écart qui les séparent. Partant de ces observations, nous proposons une classe d’algorithmes hiérarchiques basés sur l’analyse symbolique de la structure des facteurs d’une matrice creuse. Ces algorithmes s’appuient sur une information symbolique pour grouper les inconnues entre elles et construire une structure hiérarchique cohérente avec la disposition des non-zéros de la matrice. Nos méthodes s’appuient également sur la compression de rang faible pour réduire la consommation mémoire des sous-matrices les plus grandes ainsi que le temps que met le solveur à trouver une solution. Nous comparons également des techniques de renumérotation se fondant sur des propriétés géométriques ou topologiques. Enfin, nous ouvrons la discussion à un couplage entre la méthode des éléments finis et la méthode des éléments finis de frontière dans un cadre logiciel unique. / Many physical phenomena may be studied through modeling and numerical simulations, commonplace in scientific applications. To be tractable on a computer, appropriated discretization techniques must be considered, which often lead to a set of linear equations whose features depend on the discretization techniques. Among them, the Finite Element Method usually leads to sparse linear systems whereas the Boundary Element Method leads to dense linear systems. The size of the resulting linear systems depends on the domain where the studied physical phenomenon develops and tends to become larger and larger as the performance of the computer facilities increases. For the sake of numerical robustness, the solution techniques based on the factorization of the matrix associated with the linear system are the methods of choice when affordable. In that respect, hierarchical methods based on low-rank compression have allowed a drastic reduction of the computational requirements for the solution of dense linear systems over the last two decades. For sparse linear systems, their application remains a challenge which has been studied by both the community of hierarchical matrices and the community of sparse matrices. On the one hand, the first step taken by the community of hierarchical matrices most often takes advantage of the sparsity of the problem through the use of nested dissection. While this approach benefits from the hierarchical structure, it is not, however, as efficient as sparse solvers regarding the exploitation of zeros and the structural separation of zeros from non-zeros. On the other hand, sparse factorization is organized so as to lead to a sequence of smaller dense operations, enticing sparse solvers to use this property and exploit compression techniques from hierarchical methods in order to reduce the computational cost of these elementary operations. Nonetheless, the globally hierarchical structure may be lost if the compression of hierarchical methods is used only locally on dense submatrices. We here review the main techniques that have been employed by both those communities, trying to highlight their common properties and their respective limits with a special emphasis on studies that have aimed to bridge the gap between them. With these observations in mind, we propose a class of hierarchical algorithms based on the symbolic analysis of the structure of the factors of a sparse matrix. These algorithms rely on a symbolic information to cluster and construct a hierarchical structure coherent with the non-zero pattern of the matrix. Moreover, the resulting hierarchical matrix relies on low-rank compression for the reduction of the memory consumption of large submatrices as well as the time to solution of the solver. We also compare multiple ordering techniques based on geometrical or topological properties. Finally, we open the discussion to a coupling between the Finite Element Method and the Boundary Element Method in a unified computational framework.

Random matrix models have found numerous applications in both Theoretical Physics and Mathematics. In the gauge-gravity duality, for example, the dynamics of the half- BPS sector can be fully described by the holomorphic sector of a single complex matrix model. In this thesis, we study the large-N limit of multi-matrix models at strong-coupling. In particular, we explore the significance of rescaling the matrix fields. In order to investigate this, we consider the matrix quantum mechanics of a single Hermitian system with a quartic interaction. We “compactify” this system on a circle and compute the first-order perturbation theory correction to the ground-state energy. The exact ground-state energy is obtained using the Das-Jevicki-Sakita Collective Field Theory approach. We then discuss the multi-matrix model that results from the compactification of the Higgs sector of N = 4 SYM on S4 (or T S3). For the radial subsector, the saddle-point equations are solved exactly and hence the radial density of eigenvalues for an arbitrary number of even Hermitian matrices is obtained. The single complex matrix model is parametrized in terms of the matrix valued polar coordinates and the first-order perturbation theory density of eigenstates is obtained. We make use of the Harish-Chandra- Itzykson-Zuber (HCIZ) formula to write down the exact saddle-point equations. We then give a complementary approach - based on the Dyson-Schwinger (loop) equations formalism - to the saddle-point method. We reproduce the results obtained for the radial (single matrix) subsector. The two-matrix integral does not close on the original set of variables and thus we map the system onto an auxiliary Penner-type two matrix model. In the absence of a logarithmic potential we derive a radial hemispherical density of eigenvalues. The system is regulated with a logarithm potential, and the Dobroliubov-Makeenko-Semenoff (DMS) loop equations yield an equation of third degree that is satisfied by the generating function. This equation is solved at strong coupling and, accordingly, we obtain the radial density of eigenvalues.

No description available.

Malware is the source or a catalyst for many of the attacks on our cyberspace. Malware analysts and other cybersecurity professionals are responsible for responding to and understanding attacks to mount a defense against the attacks in our cyberspace. The sheer amount of malware alone makes this a difficult task, but malware is also increasing in complexity. This research provides empirical evidence that a hybrid approach using token-based and semantic-based code clones can identify similarities between malware. In addition, the use of different normalization techniques and the use of undirected matrices versus directed matrices were studied. Lastly, the impact of the use of inexact code clones was evaluated. Our results showed that our approach to determining the similarity between malware outperforms two methods currently used in malware analyses. In addition, we showed that overly generalized normalization of code sections would hinder the performance of the proposed method. At the same time, there is no significant difference between the use of directed and undirected matrices. This research also confirmed the positive impact of using inexact code clones when determining similarity.

No description available.

During conditions of osmotic stress, some plants accumulate compatible osmolytes such as glycine betaine or choline-0-sulphate. Choline is required as a precursor for synthesis of both osmolytes and choline is also required by all plants as a component of phospholipids. In the betaine accumulator spinach, choline synthesis requires three sequential N-methylations of phosphoethanolamine (PEA) to generate phosphocholine (PCho), with the first N-methylation being catalyzed by S-adenosyi-L-methionine: PEA Nmethyltransferase (PEAMeT). Choline synthesis and, more particularly the activity of PEAMeT, are up-regulated by salinity (Summers and Weretilnyk, 1993). This thesis reports on the partial purification and preliminary characterization of PEAMeT from spinach. A variety of column chromatography matrices including DEAE Sepharose, phenyl Sepharose, w-aminohexyl agarose, hydroxylapatite, phenyl Superose, Mono Q and adenosine agarose, have been used to purify PEAMeT. A 5403- fold purified preparation yielded a specific activity of 189 nmol· min-1 • mg-1 protein. SDS-PAGE analysis of this preparation revealed a number of polypeptide bands but only one which photoaffinity cross-linked to [3H]SAM. The estimated native molecular weight (MW) of PEAMeT was found to be 77 kDa by gel filtration chromatography and an estimated MW of 54 kDa was determined by SDS-PAGE. SDS-PAGE analysis of samples photoaffinity crosslinked to [3H]SAM gave a slightly higher estimated MW of 57 kDa. Effects of various factors on PEAMeT assay conditions were evaluated using partially purified PEAMeT preparations. PEAMeT activity as a function of pH gave a unimodal curve with an apparent pH optimum at 7.8 with 1 00 mM HEPES-KOH buffer. In vitro PEAMeT activity was inhibited by phosphate, PCho, S-adenosyi-L-homocysteine, ca+ 2, Mn+2 and co+2 but not by choline, betaine, ethanolamine, mono- and dimethylethanolamine or Mg+2 • Phosphobase N-methyltransferase activities present in preparations enriched for PEAMeT activity can catalyse the reaction sequence PEA- PMEA - PDEA - PCho. Under optimized assay conditions using PEA as the sole substrate, PMEA, PDEA and PCho were quantified and were detected in the order: PMEA (77%) > PDEA (17%) > PCho (6%). Thus a single enzyme, PEAMeT, is capable of converting PEA to PCho in leaves of spinach. The existence of a second enzyme which converts PMEA to PCho has also been reported for leaves and roots of spinach (Weretilnyk and Summers, 1992). The presence of two enzymes with overlapping activities raises questions regarding the roles of these two enzymes in choline metabolism. For example, do these enzymes also have overlapping functions in choline synthesis, particularly under conditions of osmotic stress? / Thesis / Master of Science (MSc)

No description available.

yes / Highlights: Non-additive probabilities and Choquet integrals in a classical context. The use of Choquet integrals in a quantum context. Approximation of partially known density matrices with Choquet integrals.