Des relations entre les structures musicales et les contextes sociaux dans un répertoire de "sessions" instrumentales irlandaises

La version intégrale de ce mémoire [ou de cette thèse] est disponible uniquement pour consultation individuelle à la Bibliothèque de musique de l’Université de Montréal (www.bib.umontreal.ca/MU)Instants et espaces investis par la musique, les sessions sont actuellement en Irlande un marqueur d’expression culturelle. En surface, celles-ci peuvent être définies en tant que regroupement prévu ou spontané de plusieurs musiciens dans le but de faire de la musique et de passer un agréable moment en communauté. Toutefois, un travail d'enquête réparti sur sept années de recherches dans le nord-ouest irlandais a révélé qu'en profondeur, les sessions représentent un phénomène socioculturel complexe, phénomène social autant que musical, fait musical autant que social, édifice symbolique mixte tissé d'interactions dont la combinatoire à chaque fois renouvelée implique un jeu de relations entre le facteur individuel et les stratégies collectives qui, radicalement, affectent l’ensemble de la structure de l’événement. Comprendre le fonctionnement d'une session revient alors à poser un certain nombre de questions ayant pour finalité de révéler la manière dont les deux pôles du social et du musical se trouvent, en même temps que distincts, inextricablement liés. Les sessions musicales se révèlent ainsi sources d'un certain nombre de problèmes, lesquels, a priori motivés par une connaissance spécifique à notre objet d'étude, conduisent à dépasser le domaine exclusif de l'Irlande pour venir affronter les questionnements plus larges que pose l'ethnomusicologie contemporaine. La présente thèse s'organise en cinq chapitres. Un premier est consacré à une description générale des sessions. L'attention est portée sur les liens dynamiques opérant entre ce qui relève du musical et ce qui procède d'un ordre plus spécifiquement social. Les questions alors soulevées engagent un second chapitre, dont l'organisation est bipartite. Y sont alors exposés, dans un premier temps, les grands axes problématiques sur lesquels cette thèse repose, et dans un second, les réponses méthodologiques impliquées par cette même problématique. Un troisième chapitre consiste à mettre en place l'ensemble des outils nécessaires à la conduite des analyses, à travers une réflexion portant sur les propriétés systématiques de l'ensemble des paramètres sociaux et musicaux caractéristiques de ce que sera notre corpus. L'étape suivante, quatrième chapitre de la thèse, se fonde sur les analyses comparatives d'un corpus de 26 pièces musicales, collectées dans le cadre de 7 situations de sessions distinctes. À travers un cinquième chapitre, le travail se termine enfin par une synthèse fondée sur l'intégralité des résultats analytiques obtenus dans le chapitre précédent.As periods of time and spatial entities invested by music, sessions in Ireland nowadays are a marker of cultural expression. Superficially, those can be defined as a gathering, planned or spontaneous, of several musicians with the prospect to produce music and to share a nice moment together. Yet, a survey pursued over a seven-year research work in north-western Ireland revealed that, in depth, sessions represent complex socio-cultural events, social as much as musical, musical as well as social happening, symbolic entity enriched by interactions whose permanently renewed combination reflects the interplay between individual factors and group strategies, that, radically, affect the whole structure of the event. To understand how a session functions then requires raising a number of questions whose end is to elucidate how the two poles, social and musical, happen to be inextricably linked, though distinct at the same time. Musical sessions thus become a source of problems which, a priori connected to the amount of knowledge specific of our topic, lead to overcome the exclusive domain of Ireland up to facing the broader issues of contemporary ethnomusicology. The present thesis includes five chapters. The first one is a general description of sessions. Attention is paid to the dynamic links operating between what belongs to music and what proceeds from a line more specifically social. Questions then raised trigger a second chapter, whose content is bipartite. First are exposed the major problems on which the thesis rests, and secondly the methodological answers related to the given problematic. A third chapter consists of setting the spectrum of methods required to conduct analyses, through a reflexion bearing on the system properties of the whole range of social and musical parameters that characterize this work. Next step, the fourth chapter is based on the comparative analysis of 26 musical pieces that were collected in the context of seven different situations in distinct sessions. In the fifth chapter, the thesis ends with a synthesis of all analytical results as gathered in the previous chapters

On the complexity of computing Gr\"obner bases for weighted homogeneous systems

Solving polynomial systems arising from applications is frequently made easier by the structure of the systems. Weighted homogeneity (or quasi-homogeneity) is one example of such a structure: given a system of weights $W=(w\_{1},\dots,w\_{n})$, $W$-homogeneous polynomials are polynomials which are homogeneous w.r.t the weighted degree $\deg\_{W}(X\_{1}^{\alpha\_{1}},\dots,X\_{n}^{\alpha\_{n}}) = \sum w\_{i}\alpha\_{i}$. Gr\"obner bases for weighted homogeneous systems can be computed by adapting existing algorithms for homogeneous systems to the weighted homogeneous case. We show that in this case, the complexity estimate for Algorithm~\F5 \left(\binom{n+\dmax-1}{\dmax}^{\omega}\right) can be divided by a factor $\left(\prod w\_{i} \right)^{\omega}$. For zero-dimensional systems, the complexity of Algorithm~\FGLM $nD^{\omega}$ (where $D$ is the number of solutions of the system) can be divided by the same factor $\left(\prod w\_{i} \right)^{\omega}$. Under genericity assumptions, for zero-dimensional weighted homogeneous systems of $W$-degree $(d\_{1},\dots,d\_{n})$, these complexity estimates are polynomial in the weighted B\'ezout bound $\prod\_{i=1}^{n}d\_{i} / \prod\_{i=1}^{n}w\_{i}$. Furthermore, the maximum degree reached in a run of Algorithm \F5 is bounded by the weighted Macaulay bound $\sum (d\_{i}-w\_{i}) + w\_{n}$, and this bound is sharp if we can order the weights so that $w\_{n}=1$. For overdetermined semi-regular systems, estimates from the homogeneous case can be adapted to the weighted case. We provide some experimental results based on systems arising from a cryptography problem and from polynomial inversion problems. They show that taking advantage of the weighted homogeneous structure yields substantial speed-ups, and allows us to solve systems which were otherwise out of reach

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Efficiency of hyperelastic models for rubber-like materials

International audienceThis paper focuses on the modeling of rubber-like material behaviour under several modes of deformation using hyperelastic constitutive equations. A procedure based on genetic algorithms coupled to classical optimisation methods is proposed to identify the parameters of the models upon experimental data given in the literature. This leads to the classification of nineteen models with respect to criteria related to their capability to predict material behaviour

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Control theory has recently been involved in the field of nuclear magnetic resonance imagery. The goal is to control the magnetic field optimally in order to improve the contrast between two biological matters on the pictures. Geometric optimal control leads us here to analyze mero-morphic vector fields depending upon physical parameters , and having their singularities defined by a deter-minantal variety. The involved matrix has polynomial entries with respect to both the state variables and the parameters. Taking into account the physical constraints of the problem, one needs to classify, with respect to the parameters, the number of real singularities lying in some prescribed semi-algebraic set. We develop a dedicated algorithm for real root classification of the singularities of the rank defects of a polynomial matrix, cut with a given semi-algebraic set. The algorithm works under some genericity assumptions which are easy to check. These assumptions are not so restrictive and are satisfied in the aforementioned application. As more general strategies for real root classification do, our algorithm needs to compute the critical loci of some maps, intersections with the boundary of the semi-algebraic domain, etc. In order to compute these objects, the determinantal structure is exploited through a stratifi-cation by the rank of the polynomial matrix. This speeds up the computations by a factor 100. Furthermore, our implementation is able to solve the application in medical imagery, which was out of reach of more general algorithms for real root classification. For instance, computational results show that the contrast problem where one of the matters is water is partitioned into three distinct classes

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The purpose of this paper is to present an original method for system monitoring with Bayesian networks. Our proposal is to associate a data-driven method to another model-based under a common tool. The two methods are first modeled under a Bayesian network (conditional Gaussian network), and then combined to evaluate the system state. In the proposed framework the residuals and measures coexist under a probabilistic framework. This approach is tested on a simulation of a water heater process under some various circumstances and shows better results than the two methods used alone

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