Science & Mathematics

La simulation numérique par la méthode des éléments finis de tout problème physique s'appuie sur le maillage associé à la géométrie du domaine de calcul. Dans le cadre des problèmes de la mise en forme des matériaux, le maillage qui suit les grandes déformations de la pièce dégénère rapidement. La simulation de tels problèmes nécessite donc la génération de manière automatique de nombreux maillages dont la qualité conditionne la précision des calculs. L'objectif de cette étude est le développement d'une procédure d'adaptation de maillage entièrement automatique permettant le contrôle de l'erreur de discrétisation spatiale et le pilotage de l'étape de remaillage au cours des calculs. Une première partie de ce travail est consacrée à l'étude et l'évaluation numérique des estimateurs d'erreur de type Zienkiewicz-Zhu. Initialement développés pour des problèmes 2D d'élasticité, ces estimateurs sont étendus aux problèmes 3D non linéaires avec des matériaux incompressibles. L'objectif de cette première étude est le développement d'un estimateur fiable et efficace pour le contrôle d'erreur dans le cadre des problèmes de la mise en forme des matériaux. Une fois l'erreur estimée, il est possible de contrôler la qualité de la solution en calculant la taille optimale de chaque élément du maillage. Ceci revient à construire un maillage optimal, soit au sens d'une précision imposée ou au sens de la taille maximale du problème étudié. Il s'agit ainsi, dans cette deuxième partie, de développer une stratégie d'adaptation de maillage, pilotée par l'estimation d'erreur, qui soit efficace et robuste pour la simulation numérique des problèmes industriels de la mise en forme.

A classic family in topological dynamics is that of minimal rotations. One natural extension of this family is the class of nilsystems and their inverse limits. These systems have arisen in recent applications in ergodic theory and in additive combinatorics, renewing interest in studying these classical objects. Minimal rotations can be characterized via the regionally proximal relation. We introduce a new relation, the bi-regionally proximal relation, and show that it characterizes inverse limits of two step nilsystems. Minimal rotations are linked to almost periodic sequences, and more generally nilsystems correspond to nilsequences. Theses sequences were introduced in ergodic theory and have since be used in some questions of Numer Theory. Using our characterization of two step nilsystems we deduce a characterization of two step nilsequences. The proofs rely on in an essential way the study of "parallelepiped structures'' developed by B. Kra and the first author.

Le chikungunya est une maladie transmise par des moustiques du genre Aedes (dont A. albopictus, dit "moustique tigre"). Cette maladie provoque d'intenses fièvres et des douleurs articulaires chroniques fortement invalidantes. Les moustiques potentiellement vecteurs du virus du chikungunya (CHIKV) sont des espèces invasives qui, à la faveur du réchauffement climatique, se sont récemment implantés dans plusieurs régions du monde, dont la région méditerranéenne. Sa présence constitue un terreau favorable à la survenue d'épidémie. A l'heure actuelle, il n'existe ni vaccin, ni traitement médicamenteux efficace. Toutefois, des articles scientifiques ont récemment rapporté que des esters de diterpène isolés du genre Trigonostemon (Euphorbiaceae), avaient une activité inhibitrice de la réplication du CHIKV.Dans le cadre de ces travaux de thèse, des extraits de plantes du genre Euphorbia de Corse ont été étudiés dans le but d'isoler de nouvelles molécules douées d'activité antivirale sur la réplication du CHIKV. En collaboration avec le Dr. P. Leyssen (KU Leuven, Belgique), l'évaluation de l'activité anti-CHIKV de 45 extraits, obtenus à partir de 11 Euphorbiaceae de Corse, a permis de mettre en évidence la forte activité inhibitrice et sélective de des extraits d'espèces du genre Euphorbia in cellulo. L'activité antivirale d'une série de 27 diterpènes de type phorboïde, disponibles commercialement, a également été étudiée. Les résultats ont montré que certains dérivés avaient une forte activité inhibitrice de la réplication du CHIKV, mais aussi sur celle du virus de l'immunodéficience humaine (VIH). Ces études ont permis d'une part, de déduire des relations structure-activité inédites et d'autre part, de soutenir l'hypothèse d'un mécanisme d'action anti-CHIKV impliquant la modulation des protéines kinases C (PKCs) par les phorboïdes. Dans le but de confirmer ou d'infirmer la présence des phorboïdes dans les extraits d'Euphorbia, une première méthode utilisant la chromatographie liquide (LC) haute performance couplée à un spectromètre de masse à trappe d'ions (MSn), a été développée à partir des composés standards. L'application de cette méthodologie a révélé qu'aucun des phorboïdes ciblés n'était présent dans les extraits d'Euphorbia. Ainsi, une seconde procédure LC-MSn a été mise en œuvre afin de détecter - de manière non ciblée - différents types d’esters diterpéniques.

The effect of nursing method and ingestion of maternal faeces on the development of the bacteroides, lactobacillus and coliform flora of the caecum in the first 10 days of life were examined in freely nursed pups having access to maternal faeces (Group FF), pups nursed once a day and having access (Group CF), or having no access (Group CN) to maternal faeces. Colonisation of the caecum by Bacteroides commenced already on day 3 after birth. On day 2 the bacteroides counts were below 100, while on day 4 they were already between 100 and 10 000. In Group CN, the Bacteroides counts were lower (by 14 to 40%) throughout the 10-day period studied than in the groups having access to maternal faeces. Differences between groups were significant only on days 4 and 6. The average number of maternal faecal pellets left behind the doe in Group CN was 3-4 (between 0.5 and 6.4 per doe). In Groups FF and CF the pellets became smaller, crumbled and finally disappeared from the nest box, they were consumed by the pups and could be found in their gastric content. The lactobacillus counts decreased in all three groups with age, from 6.0 to 3.5 log10 CFU*g-1 (FF), 4.6 to 2.8 log10 CFU*g-1 (CF) and 5.1 to 3.1 log10 CFU*g-1 (CN), respectively. The coliform counts were higher in the first 4 days in FF (5.6 log10 CFU*g-1) than in CF (< 2 log10 CFU*g-1) and CN (2-3.6 log10 CFU*g-1) animals. Bacteroides could be cultured from the surface of the vulvar labia (max. 1000 colony count) and the vagina (max. 190 colony count), so young rabbits could become "infected" by them already in the doe's vagina. Thus prevention of ingestion of maternal faeces only slightly influenced the development of the bacteroides flora, the faeces left behind by the doe did not play an exclusive role in their colonisation.

Let $M$ be a closed and connected manifold, $H: T^*M\times{\mathbb R}/{\mathbb Z} \rightarrow {\mathbb R}$ a Tonelli 1-periodic Hamiltonian, and ${\mathcal L} \subset T^*M$ a Lagrangian submanifold Hamiltonianly isotopic to the zero section. We prove that if ${\mathcal L}$ is invariant by the time-one map of $H$, then ${\mathcal L}$ is a graph over $M$. An interesting consequence in the autonomous case is that in this case, ${\mathcal L}$ is invariant by all the time t maps of the Hamiltonian flow of $H$.

We consider two covering variants of the network design problem. We are given a set of origin/destination (O/D) pairs and each such O/D pair is covered if there exists a path in the network from the origin to the destination whose length is not larger than a given threshold. In the first problem, called the maximal covering network design problem, one must determine a network that maximizes the total demand of the covered O/D pairs subject to a budget constraint on the design costs of the network. In the second problem, called the partial covering network design problem, the design cost is minimized while a lower bound is set on the total demand covered. After presenting formulations, we develop a Benders decomposition approach to solve the problems. Further, we consider two different stabilization methods to determine the Benders cuts as well as the addition of cut-set inequalities to the master problem. Computational experiments show the efficiency of these different aspects.

The twistor space of representations on an open variety maps to a weight two space of local monodromy transformations around a divisor component at infinty. The space of $\sigma$-invariant sections of this slope-two bundle over the twistor line is a real $3$ dimensional space whose parameters correspond to the complex residue of the Higgs field, and the real parabolic weight of a harmonic bundle.

High Performance Computing (HPC) clouds need to be efficiently shared between selfish tenants having applications with different resource requirements and Service Level Objectives (SLOs). The main difficulty relies on providing concurrent resource access to such tenants while maximizing the resource utilization. To overcome this challenge, we propose Merkat, a market-based SLO-driven cloud platform. Merkat relies on a market-based model specifically designed for on-demand fine-grain resource allocation to maximize resource utilization and it uses a combination of currency distribution and dynamic resource pricing to ensure proper resource distribution among tenants. To meet the tenant’s SLO, Merkat uses autonomous controllers, which apply adaptation policies that: (i) dynamically tune the application’s provisioned CPU and memory per virtual machine in contention periods, or (ii) dynamically change the number of virtual machines. Our evaluation with simulation and on the Grid’5000 testbed shows that Merkat provides flexible support for different application types and SLOs and good tenant satisfaction compared to existing centralized systems, while the infrastructure resource utilization is improved.

My thesis entitled « Corporate governance and product market competition : three essays » is a theoretical research in industrial organization. The primary objective is to investigate how product market (competition or collusion) interacts with the top-level design of corporate governance, which concerns specifically the stakeholders' relationships and managerial incentives (static and dynamic) under imperfect information. It is mainly based on three chapters dealing with different subtopics of this theme.The first chapter examines how social concern and product market competition (Cournot vs. Bertrand) may influence the relationships (conflicting or conciliating) between main stakeholders (shareholders, consumers and employees). We consider two identical firms, both taking care of the interests of consumers in their objective functions and allowing their employees' wages be negotiated with labor unions. We show that social concern may reverse the traditional ranking between Cournot and Bertrand equilibria. Our model also shows that price competition (compared to quantity competition) can to some extent attenuate the shareholders' conflicts with both consumers and employees.The second chapter investigates how managerial incentive payment under both adverse selection and moral hazard might interact with product market competition. We consider a Cournot oligopoly market consisting of n identical managerial firms, of which the initial marginal cost is the manager's private information and his unobservable effort indirectly reduces the initial level of marginal cost. We show with this setting that the optimal incentive payment solving informational problems is not necessarily influenced by product market competition.The third chapter studies how the optimal contract between shareholder and manager (solving repeated moral hazard) may influence the stability of a cartel. We consider a cartel consisting of two identical firms, within each a risk neutral shareholder offers a menu of contracts to a risk-averse manager who may shirk in each period. The manager's unobservable effort influences the firm's marginal cost (as in chapter 2). We show in contrary with the benchmark case (under perfect information) that the degree of risk-aversion plays no longer a role upon the stability of collusion: when the managerial compensation is independent of gross profit, the implementation of the optimal long-term contract solves repeated moral hazard but also constrains the manager's discretion over the decision of market conduct (collusion, deviation, or competition).

In this article we draw on lessons for collaborative lesson research (CLR) from its effective functioning as part of the design of a large-scale intervention, which aimed to improve student attainment in mathematics. The context of the research is that of post-16 students in England retaking the national examination for 16 year-olds because they failed to attain what is considered a good grade at first sitting. Improvement rates for these students is notoriously low. However, our large scale randomised controlled trial that allowed us to investigate the efficacy of CLR found that this leads to improvements in student outcomes, above and beyond teaching with access to the same accompanying professional development programme and resources. Here we reflect on what we might learn for CLR more generally.

Based on certain intuitions of Marx and Engels, a degree of long-standing acknowledgement of ecological problems has existed within Marxist thought. This acknowledgement led to decisive advances in the 1980s, and the trend is currently going through a significant transformation. As currently formulated, the approach foregrounds three crucial questions : matter as the basis for social life and as a stake in economic exchange ; work as the transformation of the world and as a social relation ; the long-term history of capitalism, as apprehended as the development of variable relations with regard to the appropriation and exploitation of nature. The importance of these three issues demonstrates that the Marxist tradition still constitutes an important resource for contemporary social theory.