D'un point de vue rationnel, la question fondamentale dans l'étude des espaces de configurations dans une variété est la suivante : « Le type d'homotopie rationnel de l'espace des configurations de k points d'une variété simplement connexe dépend-t-il uniquement du type d'homotopie rationnel de cette variété ? » Dans cet ouvrage, nous nous intéressons aux variétés compactes, simplement connexes et sans bord. Dans ce cadre précis, nous étudions le lien entre les invariants d'homotopie rationnelle de l'espace des configurations de 2 points dans une variété, et le modèle minimal de Sullivan de cette variété. Le point clef de ce travail est la construction explicite d'une algèbre de Sullivan minimale qui s'injecte dans le modèle minimal de Sullivan de l'espace des configurations de deux points d'une variété. Nous en déduisons deux résultats essentiels concernant l'algèbre de Lie d'homotopie rationnelle de cet espace. D'une part, nous identifions une relation de cette algèbre de Lie, induite par l'action du groupe des permutations de deux éléments sur l'espace des configurations de deux points. D'autre part, nous prouvons que si la variété est coformelle et de catégorie rationnelle supérieure à 3, alors cette algèbre de Lie est complètement déterminée par le modèle minimal de la variété.

Over the last four decades, relational database systems, with their mathematical basis in first-order logic, have provided a congenial and efficient environment to handle enterprise data during its entire life cycle of generation, storage, maintenance and processing. An organic reason for their pervasive popularity is intrinsic support for declarative user queries, wherein the user only specifies the end objectives, and the system takes on the responsibility of identifying the most efficient means, called “plans”, to achieve these objectives. A crucial input to generating efficient query execution plans are the compile-time estimates of the data volumes that are output by the operators implementing the algebraic predicates present in the query. These volume estimates are typically computed using the “selectivities” of the predicates. Unfortunately, a pervasive problem encountered in practice is that these selectivities often differ significantly from the values actually encountered during query execution, leading to poor plan choices and grossly inflated response times. While the database research community has spent considerable efforts to address the above challenge, the prior techniques all suffer from a systemic limitation - the inability to provide any guarantees on the execution performance. In this thesis, we materially address this long-standing open problem by developing a radically different query processing strategy that lends itself to attractive guarantees on run-time performance. Specifically, in our approach, the compile-time estimation process is completely eschewed for error-prone selectivities. Instead, from the set of optimal plans in the query’s selectivity error space, a limited subset called the “plan bouquet”, is selected such that at least one of the bouquet plans is 2-optimal at each location in the space. Then, at run time, an exploratory sequence of cost-budgeted executions from the plan bouquet is carried out, eventually finding a plan that executes to completion within its assigned budget. The duration and switching of these executions is controlled by a graded progression of isosurfaces projected onto the optimal performance profile. We prove that this construction provides viable guarantees on the worst-case performance relative to an oracular system that magically possesses accurate apriori knowledge of all selectivities. Moreover, it ensures repeatable execution strategies across different invocations of a query, an extremely desirable feature in industrial settings. Our second contribution is a suite of techniques that substantively improve on the performance guarantees offered by the basic bouquet algorithm. First, we present an algorithm that skips carefully chosen executions from the basic plan bouquet sequence, leveraging the observation that an expensive execution may provide better coverage as compared to a series of cheaper siblings, thereby reducing the aggregate exploratory overheads. Next, we explore randomized variants with regard to both the sequence of plan executions and the constitution of the plan bouquet, and show that the resulting guarantees are markedly superior, in expectation, to the corresponding worst case values. From a deployment perspective, the above techniques are appealing since they are completely “black-box”, that is, non-invasive with regard to the database engine, implementable using only API features that are commonly available in modern systems. As a proof of concept, the bouquet approach has been fully prototyped in QUEST, a Java-based tool that provides a visual and interactive demonstration of the bouquet identification and execution phases. In similar spirit, we propose an efficient isosurface identification algorithm that avoids exploration of large portions of the error space and drastically reduces the effort involved in bouquet construction. The plan bouquet approach is ideally suited for “canned” query environments, where the computational investment in bouquet identification is amortized over multiple query invocations. The final contribution of this thesis is extending the advantage of compile-time sub-optimality guarantees to ad hoc query environments where the overheads of the off-line bouquet identification may turn out to be impractical. Specifically, we propose a completely revamped bouquet algorithm that constructs the cost-budgeted execution sequence in an “on-the-fly” manner. This is achieved through a “white-box” interaction style with the engine, whereby the plan output cardinalities exposed by the engine are used to compute lower bounds on the error-prone selectivities during plan executions. For this algorithm, the sub-optimality guarantees are in the form of a low order polynomial of the number of error-prone selectivities in the query. The plan bouquet approach has been empirically evaluated on both PostgreSQL and a commercial engine ComOpt, over the TPC-H and TPC-DS benchmark environments. Our experimental results indicate that it delivers orders of magnitude improvements in the worst-case behavior, without impairing the average-case performance, as compared to the native optimizers of these systems. In absolute terms, the worst case sub-optimality is upper bounded by 20 across the suite of queries, and the average performance is empirically found to be within a factor of 4 wrt the optimal. Even with the on-the-fly bouquet algorithm, the guarantees are found to be within a factor of 3 as compared to those achievable in the corresponding canned query environment. Overall, the plan bouquet approach provides novel performance guarantees that open up exciting possibilities for robust query processing.

Let H be the Hawaiian Earring, and let H denote its fundamental group. Assume (Bi) is an inverse system of bouquets of circles whose inverse limit is H. We give an explicit bijection between finite normal covering spaces of H and finite normal covering spaces of Bi. This bijection induces a correspondence between a certain family of inverse sequences of these covering spaces. The correspondence preserves the inverse limit of these sequences, thus offering two methods of constructing the same limit. Finally, we characterize all spaces that can be obtained in this fashion as a particular type of fibrations of H.

Un grand vin de garde se distingue par sa capacité à se bonifier avec le temps, exprimant alors une complexité aromatique particulièrement attendue par les dégustateurs. L’apparition du bouquet de vieillissement, signature de la qualité organoleptique des grands vins vieillis en bouteille, est un des phénomènes les plus impressionnants de l’œnologie mais également l’un des plus mal connus. En effet, ses déterminants sensoriels et moléculaires ont jusqu’à présent été peu étudiés. Grâce à une approche holistique séquencée en trois étapes, nous avons pu décrypter sensoriellement le concept du bouquet de vieillissement des vins rouges de Bordeaux. Une définition sensorielle partagée par des professionnels du vin a pu émerger, s’articulant autour de huit notes aromatiques principales : « sous-bois », « truffe », « fruits frais rouges et noirs », « épicé », « réglisse », « menthe », « grillé » et « empyreumatique ». D’autre part, nous avons pu souligner l’importance de l’expertise dans la définition d’un tel concept olfactif, nécessitant à la fois des connaissances œnologiques, des compétences sensorielles et des ressources lexicales. Par une étude moléculaire ciblée sur certaines classes de molécules aromatiques se formant et/ou conservées au cours du vieillissement en bouteille, nous avons pu identifier que plusieurs composés soufrés volatils tels le sulfure de diméthyle, le 2-furaneméthanethiol et le 3-sulfanylhexanol contribuaient activement à la typicité du bouquet de vieillissement. Présents à des teneurs significativement plus élevées dans les vins rouges exprimant un bouquet de vieillissement, nous avons montré que ces composés volatils participaient plus particulièrement aux notes aromatiques caractéristiques de sous-bois, truffe et empyreumatique. La mise en œuvre de fractionnements d’extraits de vins et de reconstitutions aromatiques, puis l’application de la GC-O et de la GC-MS sur les fractions d’intérêt ont permis par la suite d’identifier la D,L-pipéritone, un monoterpène associé pour la première fois aux nuances de menthe typiques du bouquet de vieillissement des vins rouges de Bordeaux. Enfin, nous avons montré que certains paramètres du terroir pouvaient influencer l’expression aromatique du bouquet de vieillissement. La mesure du rapport isotopique (δC13) de l’éthanol a permis de retracer l’état hydrique des vignes ayant produit les vins étudiés et a montré qu’une contrainte hydrique modérée ou forte de la vigne était favorable à cette typicité. De plus, la différence sensorielle de la note menthe observée entre les vins rouges de Bordeaux semble trouver son origine dans la nature du cépage, avec des teneurs en D,L-pipéritone significativement plus importantes dans les vins pour lesquels le Cabernet Sauvignon est le cépage prédominant. / A wine with ageing potential is noticeable by its ability to improve over time, expressing the aromatic complexity particularly expected by wine tasters. The development of wine ageing bouquet, the "signature" of the organoleptic quality of fine wines aged in bottle, is one of the most fascinating but least known phenomena in oenology. Indeed, both its sensory and molecular markers are poorly documented.A three-step holistic approach made it possible to decipher the sensory characteristics of the ageing bouquet of red Bordeaux wines. More precisely, a shared sensory definition emerged among wine professionals, structured around eight main aromatic notes: "undergrowth", "truffle", "fresh red- and black berry fruits", "spicy», "liquorice", "mint», "toasted" and "empyreumatic". Furthermore, the importance of expertise based on oenological knowledge, sensory skills, and lexical capabilities in defining olfactory concepts was highlighted. A molecular study, targeting specific classes of aromatic compounds formed and/or preserved during bottle ageing, identified dimethyl sulphide, 2-furanmethanethiol and 3-sulfanylhexanol as key contributors to the typicality of wine ageing bouquet. These volatile compounds were present in the highest concentrations in all wines with an ageing bouquet and participated more specifically in their undergrowth, truffle, and empyreumatic aromas. Subsequently, wine fractionations and aromatic reconstitutions, analyzed by both GC-O and GC-MS, were used to identify D,L-piperitone, a monoterpene which was shown for the first time to be involved in the typical mint nuances in the ageing bouquet of red Bordeaux wines. Finally, influence of some parameters of “terroir” was highlighted. Isotope ratio measurement (δC13) in ethanol of studied wines was used as an indicator of vine water status and revealed that a moderate to severe water deficit was in favor to the genesis of a wine ageing bouquet. Interestingly, the sensory difference in minty character observed in red Bordeaux wines apparently originated from grapes, as D,L-piperitone levels were significantly higher in wines where Cabernet Sauvignon was dominant

Dans cette thèse, le mouvement brownien branchant (MBB) est un système aléatoire de particules, où celles-ci diffusent sur la droite réelle selon des mouvements browniens et branchent à taux constant en un nombre aléatoire de particules d'espérance supérieure à 1. Nous étudions deux modèles de MBB avec sélection : le MBB avec absorption à une droite espace-temps et le N -MBB, où, dès que le nombre de particules dépasse un nombre donné N , seules les N particules les plus à droite sont gardées tandis que les autres sont enlevées du système. Pour le premier modèle, nous étudions la loi du nombre de particules absorbées dans le cas où le processus s'éteint presque sûrement, en utilisant un lien entre les équations de Fisher-Kolmogorov-Petrovskii-Piskounov (FKPP) et de Briot-Bouquet. Pour le deuxième modèle, dont l'étude représente la plus grande partie de cette thèse, nous donnons des asymptotiques précises sur la position du nuage de particules quand N est grand. Plus précisément, nous montrons qu'elle converge à l'échelle de temps log³ N vers un processus de Lévy plus une dérive linéaire, tous les deux explicites, confirmant des prévisions de Brunet, Derrida, Mueller et Munier. Cette étude contribue à la compréhension de fronts du type FKPP sous l'influence de bruit. Enfin, une troisième partie montre le lien qui existe entre le MBB et des processus ponctuels stables.

Neste trabalho,apresentamos um breve compêndio sobre o estudo topológico das fibras de Milnor. Abordamoso caso clássico, estudado por J. Milnor, e a generalização apresentada por Lê D. T. para o caso de germes de funções analíticas definidas em variedades singulares. Nestas duas situações, os resultados principais tratam de germes de funções com singularidades isoladas / In this work, we present a brief compendium about the topological study of J. Milnor fibers. We address the classic case, studied by Milnor, and the generalization presented by Lê D. T. for the case of germs of analytic functions defined on singular varieties. In both situations, the main results deal with germs of functions with isolated singularities

Apocynaceae presents the flowers with the highest degree of synorganization among the eudicots and highly elaborated pollination mechanisms associated with the high diversity of glands. The osmophore stands out as responsible to produce a floral scent which attracts pollinators and, despite its fundamental relevance for pollination, its structure and mechanism of production and release of the perfume is essentially unknown in Apocynaceae. This present work aims to characterize morphologically and ultrastructurally the osmophores of Apocynaceae, besides chemically identifying the compounds that constitute the floral scent. Species from two subfamilies were selected to describe the diversity of osmophores and types of scent in the family. The osmophores were firstly located histochemically and, later, this region was processed for transmission electron microscopy. Micromorphological analysis was performed by scanning electron microscopy, and the identification of volatile oils made by GC-MS. Osmophores are located on the adaxial surface of the free portion of the petals. They varied in the shape of epidermal cells, striation of the cuticle and presence of trichomes. This gland is mostly formed by secretory epidermis and parenchyma, except in Plumeria, where the osmophores are exclusively epidermal. The secretory cells presented thick walls in the Asclepiadoideae and secretion produced by plastids and SER in all species. Several vesicles perform the intercellular transport of secretion, as well as its release to the environment. However, Plumeria and Ditassa transfer the secretion produced to the vacuole before releasing it, and Tabernaemontana has a mixed release process. The composition of the scent varied among species, with great production of hydrocarbons, alcohols, ketones or monoterpenes depending on the species. Apocynaceae presents a high morphological and metabolic diversity in the osmophores which cannot be correlated with their morphology, subcellular organization, period of secretion release or pollination syndrome. This is the first comprehensive structural study of osmophores in this family that points out to very distinct evolutionary processes that may be related to multiple emergences in the phylogeny and speciesspecific associations with pollinators / Apocynaceae apresenta as flores com o maior grau de sinorganização das eudicotiledôneas e mecanismos de polinização altamente elaborados associados à mais alta diversidade de glândulas. O osmóforo destaca-se como responsável pela produção do perfume floral para atração dos polinizadores e, a despeito de sua importância fundamental para a polinização, a sua estrutura e mecanismo de produção e liberação do perfume é praticamente desconhecido nas Apocynaceae. O presente trabalho tem o propósito de caracterizar morfológica e ultraestruturalmente os osmóforos de Apocynaceae, além de identificar quimicamente os compostos que constituem o perfume floral. Espécies de duas subfamílias foram selecionadas, visando descrever a diversidade de osmóforos e tipos de perfume na família. Primeiramente, os osmóforos foram localizados histoquimicamente e, posteriormente, essa região foi processada para microscopia eletrônica de transmissão. Análise micromorfológica foi realizada através de microscopia eletrônica de transmissão. Análise micromorfológica foi realizada através de microscopia eletrônica de varredura e a identificação dos óleos voláteis, através de GC/MS. Os osmóforos estão localizados na superfície adaxial da porção livre das pétalas. Eles variaram quanto ao formato das células epidérmicas, ornamentação da cutícula e presença de tricomas. Esta glândula é, em sua maioria, formada por epiderme e parênquima secretores, exceto em Plumeria, onde os osmóforos são exclusivamente epidérmicos. As células secretoras apresentaram paredes espessas nas Asclepiadoideae e secreção produzida pelos plastídeos e REL em todas as espécies. Diversas vesículas realizam o transporte intercelular da secreção, assim como a sua liberação para o meio externo. Contudo, Plumeria e Ditassa transferem a secreção produzida para o vacúolo antes de liberá-la e Tabernaemontana possui processo de liberação misto. A composição do perfume variou entre as espécies, havendo grande produção de hidrocarbonetos, alcoóis, cetonas ou monoterpenos dependendo da espécie. Apocynaceae apresenta uma alta diversidade morfológica e metabólica em seus osmóforos que não pode ser correlacionada à morfologia, organização subcelular, período de liberação da secreção ou síndrome de polinização. Esse é o primeiro estudo estrutural abrangente sobre osmóforos na família e aponta para processos evolutivos muito distintos que podem estar relacionados a múltiplos surgimentos na filogenia e associações espécie-específicas com os polinizadores

Neste trabalho,apresentamos um breve compêndio sobre o estudo topológico das fibras de Milnor. Abordamoso caso clássico, estudado por J. Milnor, e a generalização apresentada por Lê D. T. para o caso de germes de funções analíticas definidas em variedades singulares. Nestas duas situações, os resultados principais tratam de germes de funções com singularidades isoladas / In this work, we present a brief compendium about the topological study of J. Milnor fibers. We address the classic case, studied by Milnor, and the generalization presented by Lê D. T. for the case of germs of analytic functions defined on singular varieties. In both situations, the main results deal with germs of functions with isolated singularities

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