In this thesis, the properties of the Bose-Einstein condensation (BEC) in low dimensions are reviewed. Three dimensional weakly interacting Bose systems are examined by the variational method. The effects of both the attractive and the repulsive interatomic forces are studied. Thomas-Fermi approximation is applied to find the ground state energy and the chemical potential. The occurrence of the BEC in low dimensional systems, is studied for ideal gases confined by both harmonic and power-law potentials. The properties of BEC in highly anisotropic trap are investigated and the conditions for reduced dimensionality are derived.

In dieser Arbeit werden Zufallsfeld-Ising-Modelle mit einem eingefrorenen dichotomen symmetrischen Zufallsfeld für den eindimensionalen Fall und das Bethe-Gitter untersucht. Dabei wird die kanonische Zustandssumme zu der eines einzelnen Spins in einem effektiven Feld umformuliert. Im ersten Teil der Arbeit werden das mulktifraktale Spektrum dieses effektiven Feldes untersucht, Übergänge im Spektrum erklärt und Ungleichungen zwischen lokalen und globalen Dimensionsbegriffen bewiesen, die eine weitgehend vollständige Charakterisierung des multifraktalen Spektrums durch eine Reihe von Schranken erlauben. Ein weiterer Teil der Arbeit beschäftigt sich mit einer ähnlichen Charakterisierung des Maßes der lokalen Magnetisierung, das aus dem Maß des effektiven Feldes durch Faltung hervorgeht. In diesem Zusammenhang wird die Faltung von Multifraktalen in einem allgemeineren Rahmen behandelt und Zusammenhänge zwischen den multifraktalen Eigenschaften der Faltung und denen der gefalteten Maße bewiesen. Im dritten Teil der Dissertation wird der Phasenübergang von Ferro- zu Paramagnetismus im Modell auf dem Bethe Gitter untersucht. Neben verbesserten exakten Schranken für die Eindeutigkeit des paramagnetischen Zustands werden im wesentlichen drei Kriterien für die tatsächliche Lage des Übergangs angegeben und numerisch ausgewertet. Die multifraktalen Eigenschaften des effektiven Felds im Modell auf dem Bethe-Gitter schließlich erweisen sich als trivial, da die interessanten Dimensionen nicht existieren. / In this work random field Ising models with quenched dichotomous symmetric random field are considered for the one-dimensional case and on the Bethe lattice. To this end the canonical partition function is reformulated to the partition function of one spin in an effective field. In the first part of the work the multifractal spectrum of this effective field is investigated, transitions in the spectrum are explained and inequalities between local and global generalized fractal dimensions are proven which allow to characterize the multifractal spectrum bei various bounds. A further part of the work is dedicated to the characterization of the measure of the local magnetization which is obtained by convolution of the measure of the effective field with itself. In this context the convolution of multifractals is investigated in a more general setup and relations between the multifractal properties of the convolution and the multifractal properties of the convoluted measures are proven. The phase transition from ferro- to paramagnetismus for the model on the Bethe lattice is investigated in the third part of the thesis. Apart from improved exact bounds for the uniqueness of the paramagnetic state essentially three criteria for the transition are developped and numerically evaluated to determine the transition line. The multifractal properties of the effective field for the model on the Bethe lattice finally turn out to be trivial because the interesting dimensions do not exist.

Pattern discovery is an important area of data mining referring to a class of techniques designed for the extraction of interesting patterns from the data. A pattern is some kind of a local structure that captures correlations and dependencies present in the elements of the data. In general, pattern discovery is about finding all patterns of `interest' in the data and a popular measure of interestingness for a pattern is its frequency of occurrence in the data. Thus the problem of frequent pattern discovery is to find all patterns in the data whose frequency of occurrence exceeds some user defined threshold. However, frequency of a pattern is not the only measure for finding patterns of interest and there also exist other measures and techniques for finding interesting patterns. This thesis is concerned with efficient discovery of inherent patterns from long sequence (or temporally ordered) data. Mining of such sequentially ordered data is called temporal data mining and the temporal patterns that are discovered from large sequential data are called episodes. More specifically, this thesis explores efficient methods for finding small and relevant subsets of episodes from sequence data that best characterize the data. The thesis also discusses methods for comparing datasets, based on comparing the sets of patterns representing the datasets. The data in a frequent episode discovery framework is abstractly viewed as a single long sequence of events. Here, the event is a tuple, (Ei; ti), where Ei is referred to as an event-type (taking values from a finite alphabet set) and ti is the time of occurrence. The events are ordered in the non-decreasing order of the time of occurrence. The pattern of interest in such a sequence is called an episode, which is a collection of event-types with a partial order defined over it. In this thesis, the focus is on a special type of episode called serial episode, where there is a total order defined among the collection of event-types representing the episode. The occurrence of an episode is essentially a subset of events from the data whose event-types match the set of eventtypes associated with the episode and the order in which they occur conforms to the underlying partial order of the episode. The frequency of an episode is some measure of how often it occurs in the event stream. Many different notions of frequency have been defined in literature. Given a frequency definition, the goal of frequent episode discovery is to unearth all episodes which have a frequency greater than a user-defined threshold. The size of an episode is the number of event-types in the episode. An episode β is called a subepisode of another episode β, if the collection of event-types of β is a subset of the corresponding collection of α and the event-types of β satisfy the same partial order relationships present among the corresponding event-types of α. The set of all episodes can be arranged in a partial order lattice, where each level i contains episodes of size i and the partial order is the subepisode relationship. In general, there are two approaches for mining frequent episodes, based on the way one traverses this lattice. The first approach is to traverse this lattice in a breadth-first manner, and is called the Apriori approach. The other approach is the Pattern growth approach, where the lattice is traversed in a depth-first manner. There exist different frequency notions for episodes, and many Apriori based algorithms have been proposed for mining frequent episodes under the different frequencies. However there do not exist Pattern-growth based methods for many of the frequency notions. The first part of the thesis proposes new Pattern-growth methods for discovering frequent serial episodes under two frequency notions called the non-overlapped frequency and the total frequency. Special cases, where certain additional conditions, called the span and gap constraints, are imposed on the occurrences of the episodes are also considered. The proposed methods, in general, consist of two steps: the candidate generation step and the counting step. The candidate generation step involves finding potential frequent episodes. This is done by following the general Pattern growth approach for finding the candidates, which is the depth-first traversal of the lattice of all episodes. The second step, which is the counting step, involves counting the frequencies of the episodes. The thesis presents efficient methods for counting the occurrences of serial episodes using occurrence windows of subepisodes for both the non-overlapped and total frequency. The relative advantages of Pattern-growth approaches over Apriori approaches are also discussed. Through detailed simulation results, the effectiveness of this approach on a host of synthetic and real data sets is shown. It is shown that the proposed methods are highly scalable and efficient in runtime as compared to the existing Apriori approaches. One of the main issues in frequent pattern mining is the huge number of frequent patterns, returned by the discovery methods, irrespective of the approach taken to solve the problems. The second part of this thesis, addresses this issue and discusses methods of selecting a small subset of relevant episodes from event sequences. There have been a few approaches, discussed in the literature, for finding a small subset of patterns. One set of methods are information theory based methods, where patterns that provide maximum information are searched for. Another approach is the Minimum Description Length (MDL) principle based summarization schemes. Here the data is encoded using a subset of patterns (which forms the model for the data) and its occurrences. The subset of patterns that has the maximum efficiency in encoding the data is the best representative model for the data. The MDL principle takes into account both the encoding efficiency of the model as well as model complexity. A method, called Constrained Serial episode Coding(CSC), is proposed based on the MDL principle, which returns a highly relevant, non-redundant and small subset of serial episodes. This also includes an encoding scheme, where the model representation and the encoding of the data are efficient. An interesting feature of this algorithm for isolating a small set of relevant episodes is that it does not need a user-specified threshold on frequency. The effectiveness of this method is shown on two types of data. The first is data obtained from a detailed simulator for a reconfigurable coupled conveyor system. The conveyor system consists of different intersecting paths and packages flow through such a network. Mining of such data can allow one to unearth the main paths of package ows which can be useful in remote monitoring and visualization of the system. On this data, it is shown that the proposed method is able to return highly consistent sub paths, in the form of serial episodes, with great encoding efficiency as compared to other known related sequence summarization schemes, like SQS and GoKrimp. The second type of data consists of a collection of multi-class sequence datasets. It is shown that the selected episodes from the proposed method form good features in classi cation. The proposed method is compared with SQS and GoKrimp, and it is shown that the episodes selected by this method help in achieving better classification results as compared to other methods. The third and nal part of the thesis discusses methods for comparing sets of patterns representing different datasets. There are many instances when one is interested in comparing datasets. For example, in streaming data, one is interested in knowing whether the characteristics of the data are the same or have changed significantly. In other cases, one may simply like to compare two datasets and quantify the degree of similarity between them. Often, data are characterized by a set of patterns as described above. Comparing sets of patterns representing datasets gives information about the similarity/dissimilarity between the datasets. However not many measures exist for comparing sets of patterns. This thesis proposes a similarity measure for comparing sets of patterns which in turn aids in comparison of di erent datasets. First, a kernel for comparing two patterns, called the Pattern Kernel, is proposed. This kernel is proposed for three types of patterns: serial episodes, sequential patterns and itemsets. Using this kernel, a Pattern Set Kernel is proposed for comparing different sets of patterns. The effectiveness of this kernel is shown in classification and change detection. The thesis concludes with a summary of the main contributions and some suggestions for extending the work presented here.

[pt] O trabalho identifica as bases necessárias para apontar o método adequado de interpretação das normas do Direito Regulatório. Para atingir esse ponto, no entanto, perpassa pela discussão a respeito de qual o método adequado de interpretação da Constituição e da lei em geral. O resultado (prático) das teorias constitucionais ou das teorias de interpretação jurídica depende de fatores que muitas vezes são negligenciados, o que repercute, obviamente, na correção dessas teorias, fazendo com que a discussão a respeito do formalismo jurídico seja retomada, com argumentos mais robustos a seu favor. A hipótese levantada é a de que os teóricos constitucionais e os da interpretação jurídica brasileiros geralmente desenvolvem suas teorias como se fossem ser aplicadas por eles próprios ou por grandes especialistas e/ou a partir de critérios abstratos, negligenciando o fato de a regra interpretativa defendida poder acabar resultando num Direito inadequado, no nível operacional, tendo em vista as limitações dos agentes responsáveis por sua aplicação e as contingências do mundo real. No caso do Direito Regulatório, obtém-se um melhor direito caso adotado pelos juízes o formalismo deferencial (ou formalismo maximilianista) como postura interpretativa, ao invés de uma postura interpretativa não formalista, como a póspositivista e a neoconstitucionalista. Existem fatores externos ao Direito que repercutem decisivamente na capacidade de aplicação da Constituição e da lei que não são perceptíveis à análise moral e/ou conceitual-teórica. Portanto, se não identificados e adequadamente trabalhados, levam à construção de uma teoria constitucional ou da interpretação jurídica sem maior valor prático, gerando disfunções no sistema constitucional e legal, além de um Direito ruim, caso empregada. Propõe-se identificar a interpretação jurídica e o direito adequados sob outra perspectiva que não a moral ou teórico-conceitual-abstrata, demonstrando que existem teorias sólidas contrárias a uma leitura moral da Constituição pelo Poder Judiciário, bem como que a defesa da aplicação prática da leitura moral da Constituição depende de análises prévias geralmente negligenciadas pelos seus defensores, de maneira que pode gerar resultados (negativos) bastante diversos do pretendido. Essa outra perspectiva, importante principalmente para a escolha do método interpretativo, seria a institucional. De modo que incitar o jurista e o servidor público em geral ao perfeccionismo na aplicação do Direito pode levar, e leva muitas vezes, a um mal Direito. Pode repercutir negativamente, inclusive, no funcionamento do sistema republicano (o papel e responsabilidade das instituições) e da democracia (legitimidade das instituições que decidem) do Estado. Conclui que a maioria das questões legais e constitucionais é decidida, no Estado, pelo Legislativo e pela Administração Pública. Não chegam ao Judiciário. Foi constatada a maior capacidade decisória do Legislativo e da Administração Pública, quando comparados aos tribunais, no que toca à escolha das regras e doutrinas interpretativas, bem como na interpretação de textos normativos vagos, ambíguos e principiológicos, notadamente em matérias de extrema complexidade e especificidade técnica, como as normas regulatórias e as normas constitucionais incidentes sobre estas últimas. Por outro lado, identificou-se uma maior capacidade decisória dos tribunais no âmbito dos textos normativos claros e específicos (regras jurídicas). Verificou-se que o STF e o STJ têm, em geral, essa visão, adotando uma postura formalista deferencial quanto às normas regulatórias, mesmo estando a doutrina nacional em peso no sentido inverso. Desse modo e, ao constatar o deslocamento do paradoxo da onipotência para o Judiciário, reforçado após a década de 1990 no Brasil, acredita-se no acolhimento do formalismo deferencial como postura interpretativa estratégica pelos juízes. Já a / [en] This research identifies the necessary foundations to point out the proper method of interpreting the norms of Regulatory Law. To reach this point, however, this thesis goes through the discussion of which is the proper method of interpreting the Constitution and the statutes in general. The (practical) results of the constitutional theories or of the theories of legal interpretation depend on factors that are often overlooked, which affects obviously in the correctness of these theories, resuming the discussion of legal formalism, with more robust arguments in its favor. The proposed hypothesis is that the Brazilian theorists of constitutional and legal interpretation generally develop their theories as if they would be applied by themselves or by prominent experts and / or with abstract criteria, neglecting the fact that the proposed interpretive rule may result in an inappropriate Law, at the operational level, given the limitations of the agents responsible for its implementation and real-world contingencies. In Regulatory Law, specifically, a better law is obtained if a deferential formalism (or maximilianist formalism) is adopted by the judges as interpretive standard, rather than a non-formalist interpretive standard, such as the post-positivist and the neoconstitucionalist one. There are external factors that affect decisively the ability to enforce the Constitution and the statutes, which are not perceptible to the moral and / or conceptual-theoretical analysis. So, if not identified and adequately addressed, these factors lead to the elaboration of a constitutional or legal interpretation theory that lacks substantial practical value, and which enforcement will generate dysfunctions in the constitutional and legal system, and also a bad law. It is proposed that the appropriate law and legal interpretation is identified from a perspective other than the moral or theoretical-conceptual-abstract perspective, to show that there are solid theories opposing a moral reading of the Constitution by the judiciary branch, and that the defense of the practical application the moral reading of the Constitution depends on previous analyzes generally neglected by their defenders. This moral reading can yield unexpected (negative) results. This other perspective, especially important for the choice of interpretive method, would be institutional. To call the scholars and public servants in general to use perfectionism in the application of law may lead, and often leads to a bad law. It may even negatively impact the functioning of the republican system (the role and responsibility of institutions) and democracy (legitimacy of the deciding institutions) of the State. The conclusion of this research is that the majority of the legal and constitutional issues are decided by the Legislature and the Public Administration. They do not even reach the courts. It was noted that of the Legislature and the Public Administration have greater decision-making capacity, when compared to the courts, in regard to the choice of interpretive rules and theories, as well as in the interpretation of vague, ambiguous and principle-oriented legal provisions, especially in matters of extreme complexity and technicality, such as the regulatory standards and related constitutional provisions. On the other hand, we identified a greater decisionmaking ability of the courts within legal provisions that are clear and specific (legal rules). It was noticed that the Federal Supreme Court (STF) and the Superior Court of Justice (STJ) generally share this view, adopting a deferential formalist approach regarding regulatory standards, even though the majority of Brazilian legal scholars tend to follow the opposite direction. Thus, observing the shift of the paradox of omnipotence towards the Judiciary, intensified in Brazil after the 1990s, we believe that the adoption of deferential formalism interpretive standard by the judges is strategic. On the other hand the Public Administration and the Legislature should

Dans ce mémoire, nous étudions les propriétés génériques satisfaites par des mesures invariantes par l’action du flot géodésique {∅t}t∈R sur des variétés M non compactes de courbure sectionnelle négative pincée. Nous nous intéressons dans un premier temps au cas des variétés hyperboliques. L’existence d’une représentation symbolique du flot géodésique pour les variétés hyperboliques convexes cocompactes ainsi que la propriété de mélange topologique du flot géodésique nous permet de démontrer que l’ensemble des mesures de probabilité ∅t−invariantes, faiblement mélangeantes est résiduel dans l’ensemble M1 des mesures de probabilité invariantes par l’action du flot géodésique. Si nous supposons que la courbure de M est variable, nous ignorons si le flot géodésique est topologiquement mélangeant. Ainsi les méthodes utilisées précédemment ne peuvent plus s’adapter à notre situation. Afin de généraliser le résultat précédent, nous faisons appel à des outils issus du formalisme thermodynamique développés récemment par F.Paulin, M.Pollicott et B.Schapira. Plus précisément, la démonstration de notre résultat repose sur la possibilité de construire, pour toute orbite périodique Op une suite de mesures de Gibbs mélangeantes, finies, convergeant faiblement vers la mesure de Dirac supportée sur Op. Nous montrons que ce fait est possible lorsque M est géométriquement finie. Dans le cas contraire, il n’existe pas d’exemple de variétés géométriquement infinies possédant une mesure de Gibbs finie. Cependant, nous conjecturons que ce fait est possible pour toute variété M. Afin de supporter cette affirmation, nous démontrons dans la dernière partie de ce manuscrit un critère de finitude pour les mesures de Gibbs. / In this work, we study the properties satisfied by the probability measures invariant by the geodesic flow {∅t}t∈R on non compact manifolds M with pinched negative sectional curvature. First, we restrict our study to hyperbolic manifolds. In this case, ∅t is topologically mixing in restriction to its non-wandering set. Moreover, if M is convex cocompact, there exists a symbolic representation of the geodesic flow which allows us to prove that the set of ∅t-invariant, weakly-mixing probability measures is a dense Gδ−set in the set M1 of probability measures invariant by the geodesic flow. The question of the topological mixing of the geodesic flow is still open when the curvature of M is non constant. So the methods used on hyperbolic manifolds do not apply on manifolds with variable curvature. To generalize the previous result, we use thermodynamics tools developed recently by F.Paulin, M.Pollicott et B.Schapira. More precisely, the proof of our result relies on our capacity of constructing, for all periodic orbits Op a sequence of mixing and finite Gibbs measures converging to the Dirac measure supported on Op. We will show that such a construction is possible when M is geometrically finite. If it is not, there are no examples of geometrically infinite manifolds with a finite Gibbs measure. We conjecture that it is always possible to construct a finite Gibbs measure on a pinched negatively curved manifold. To support this conjecture, we prove a finiteness criterion for Gibbs measures.

[pt] A presente tese é primordialmente um trabalho de filosofia do direito. Não obstante, também pode ser encarada como uma contribuição para o estudo filosófico sobre a natureza das regras prescritivas (e do uso diretivo ou prescritivo da linguagem), englobando: uma investigação sobre as regras e suas notas características e contingentes e um estudo sobre as diferentes maneiras por meio das quais elas podem integrar o raciocínio prático dos seus destinatários. Para não usar a linguagem de férias, as regras serão discutidas dentro do cenário do positivismo conceitual. O objetivo é mostrar alguns dos principais problemas que devem ser enfrentados quando se pretende levar as regras a sério. Trata-se de uma incursão nas fontes filosóficas dos casos difíceis do direito, quando encarado como um sistema de regras. / [en] The present thesis is primarily an exercise in philosophy of law. However, it can also be viewed as a contribution to the recurring philosophical investigations about the nature of prescriptive rules (and the directive or prescritive use of language in general), encompassing: an inquiry about rules and their characteristic and contigent marks, and a research of several ways by means of which they can play a part in the practical reasoning of its addressees. In order not to use language on holiday, the discussion about rules will be held on the stage set up by conceptual positivism. The aim is to point out some of the main problems that must be faced when rules are taken seriously. In a nutshell, the thesis is an incursion into the philosophical sources of hard cases, when law is conceived as a system of rules.

O presente trabalho analisa os fundamentos da responsabilidade civil pelo fato do produto e do serviço no direito brasileiro. O estudo está centrado na controvérsia entre a teoria formalista e a teoria funcionalista, que apresentam concepções distintas de direito privado. Para avaliar essa controvérsia e fornecer os fundamentos da responsabilidade civil pelo fato do produto e do serviço, são desenvolvidos os sentidos de justiça aristotélica e de direito kantiano. O estudo decide, com base nos referidos conhecimentos, entre a aplicação da teoria clássica da culpa, da teoria do risco ou de uma teoria específica. / The present study analyzes the basis of product and service related torts in Brazilian law. It is centered in the controversy between the formalist and the funcionalist theories, which have distinct conceptions of private law. The meanings of Aristotelian justice and Kantian law are developed in order to acess this controversy as well as to provide the basis of the legal discipline of product and service related torts. The research decides, based on such knowledge, between the application of the classical theory of fault, of the risk theory or, for the elaboration of a specific theory.

Três são os objetivos centrais deste trabalho: (a) especificar, por meio de uma reconstrução histórico-evolutiva do pensamento teórico, os elementos constitutivos (objeto, método, princípios primeiros, teoria da verdade e comunidade científica) e as exigências normativas (objetividade, coerência, clareza e transparência, justificação e consensualização) de um empreendimento que pretenda se qualificar como ciência, de modo propor uma concepção analógica de ciência que possa ser aplicável ao campo do direito; (b) identificar e detalhar os três diferentes paradigmas científicos que se desenvolveram no direito tributário brasileiro (Empírico-econômico, Normativo-comportamental e Formalista-linguístico), de modo a analisar, criticamente, os seus pressupostos teóricos, buscando, com isso, demonstrar a insuficiência dos modelos teóricos que foram até hoje utilizados no campo da ciência tributária brasileira, principalmente em razão do seu reducionismo explicativo; e (c) propor uma concepção mais abrangente e complexa de ciência jurídica – pautada na concepção de ciência prática (scientia practica) desenvolvida pela tradição filosófica aristotélico-tomista – a qual teria pretensões de, não apenas descrever o direito positivo, mas também de explicar, esclarecer e tornar mais inteligível as diferentes dimensões do fenômeno tributário, não apenas no que se refere ao momento da positivação das normas jurídicas, mas também no que se refere aos momentos anteriores e posteriores a esse processo, ou seja, que também se dedique a analisar os motivos, causas, efeitos, consequências e fins das normas de tributação. Portanto, a concepção de ciência prática aplicável ao direito tributário pressupõe o desenvolvimento de uma dimensão formal, material, eficiente/instrumental e final do seu respectivo objeto de estudo, o que culmina na elaboração de uma deontologia tributária, de uma ontologia tributária, de uma metodologia tributária e de uma teleologia tributária. / Three are the central goals of this thesis: (a) first to specify, by means of a historical and evolutionary reconstruction of the scientific thought, which are the constitutive elements (object, method, first principles, theory of truth and scientific community) and the normative requirements (objectivity, consistency, clarity and transparency, justification and consensualization) of a theoretical enterprise that intends to affirm itself as scientific, as to propose an analogical conception of science that could be applied to the field of Law; (b) to identify and detail the three different scientific paradigms that have been developed in Brazilian Tax Law (Empirical-economical, Normative-behavioral and Formalistic-linguistic), in order to, critically, analyze its theoretical assumptions, seeking to demonstrate the inadequacy of these theoretical models applied in Brazilian Tax Law, especially because of their explanatory reductionism; and (c) to propose a more comprehensive and complex notion of legal science, based on the conception of practical science (scientia practica) – based on the philosophical tradition of Aristotle and Aquinas – which would have claims, not only describe the positive law, but also to explain, clarify and make more intelligible the different dimensions of the taxation phenomenon, not only regarding the procedure that creates legal norms, but also that pays attention to the moments that come before and after this process, namely, that also focuses on analyzing the motives, causes, effects, consequences and ends of taxation. Therefore, a concept of practical science applicable to Tax Law demands the development of a formal, a material, an efficient/instrumental and a finalistic dimension of its object of study. This will require a Theory of Taxation that has a Deontological aspect, an Ontological aspect, a Methodological aspect and a Teleological aspect.

Bien qu’ayant vu le jour dans un cadre dit relativiste avec l’avènement de la théorie de la relativité générale, le lien intime existant entre géométrie de l’espace-temps d’une part, et gravitation d’autre part, peut se voir étendu aux théories dites nonrelativistes, l’exemple paradigmatique en étant la reformulation géométrique de la gravitation Newtonienne initiée par E. Cartan. De tels espace-temps nonrelativistes diffèrent structurellement de leurs homologues relativistes, ces disparités étant le plus naturellement expliquées en réinterprétant ces premiers comme réduction dimensionnelle d’espace-temps relativistes privilégiés. L’ambition de cette thèse est double : Dans une première partie, nous nous intéressons à une généralisation de la classe d’espace-temps relativistes permettant le formalisme ambiant, étudions leur interprétation géométrique ainsi que la classe élargie de structures nonrelativistes pouvant y être plongées. La seconde partie de ce manuscrit concerne le point de vue, informé par la théorie des groupes, que porte E. Cartan sur la géométrie différentielle et plus précisément l’éclairage que projettent les géométries de Cartan sur les structures nonrelativistes, à la fois dans leur définition intrinsèque et dans leur relation avec des structures relativistes au travers du formalisme ambiant. / With the advent of general relativity, the profound interaction between the geometry of spacetime and gravitational phenomena became a truism of modern physics. However, the intimate relationship between spacetime geometry and gravitation is by no means restricted to relativistic physics but can in fact be successfully applied to nonrelativistic physics, the paradigmatic example being E. Cartan geometrisation of Newtonian gravity. This geometrisation of nonrelativistic gravitation involves some nonrelativistic structures whose discrepancies in comparison with their relativistic peers are better understood when embedded inside specific classes of relativistic gravitational waves. The ambition of this Doctoral Thesis is twofold: In a first part, we discuss a generalisation of the class of gravitational waves allowing the embedding of nonrelativistic features, explore their geometric properties and the new nonrelativistic structures emerging from this study. In a second part, we advocate how the group-theoretically oriented approach of Cartan to differential geometry can shed new light on nonrelativistic structures, both in an intrinsic and ambient fashion.

The dissertation explores how quality-judgments on works of art are created within the contemporary art world. The research starts with the examination of modernist art theories supported by the museum, and continues with the exploration of the impact of the art market on quality-judgments. Although the art market had already distorted the idea of quality, further contradictions and difficulties have risen within judgment-making after the 1960s due to the dematerialisation of the work of art. Art criticism should have been able to deal with this complexity, but it is demonstrated that art criticism is a subjective field and even if there is a universal theory on quality, it often fails when applied to the particular work of art. Throughout the dissertation it is demonstrated that although ‘good art’ is a subjective, power- and discourse-dependent concept, all art professionals seek something that is an inherent quality of the artwork. However, regardless of the existence of such inherent value, judgments on quality are constructed by and subjected to power-struggle. / Art History, Visual Arts and Musicology / M.A. (Art History)