Nominal Models of Linear Logic

PhD thesisMore than 30 years after the discovery of linear logic, a simple fully-complete model has still not been established. As of today, models of logics with type variables rely on di-natural transformations, with the intuition that a proof should behave uniformly at variable types. Consequently, the interpretations of the proofs are not concrete. The main goal of this thesis was to shift from a 2-categorical setting to a first-order category. We model each literal by a pool of resources of a certain type, that we encode thanks to sorted names. Based on this, we revisit a range of categorical constructions, leading to nominal relational models of linear logic. As these fail to prove fully-complete, we revisit the fully-complete game-model of linear logic established by Melliès. We give a nominal account of concurrent game semantics, with an emphasis on names as resources. Based on them, we present fully complete models of multiplicative additive tensorial, and then linear logics. This model extends the previous result by adding atomic variables, although names do not play a crucial role in this result. On the other hand, it provides a nominal structure that allows for a nominal relationship between the Böhm trees of the linear lambda-terms and the plays of the strategies. However, this full-completeness result for linear logic rests on a quotient. Therefore, in the final chapter, we revisit the concurrent operators model which was first developed by Abramsky and Melliès. In our new model, the axiomatic structure is encoded through nominal techniques and strengthened in such a way that full completeness still holds for MLL. Our model does not depend on any 2-categorical argument or quotient. Furthermore, we show that once enriched with a hypercoherent structure, we get a static fully complete model of MALL

Everolimus (RAD001) sensitizes prostate cancer cells to docetaxel by down-regulation of HIF-1α and sphingosine kinase 1

Resistance to docetaxel is a key problem in current prostate cancer management. Sphingosine kinase 1 (SK1) and phosphoinositide 3-kinase (PI3K)/Akt/mammalian target of rapamycin (mTOR) pathways have been implicated in prostate cancer chemoresistance. Here we investigated whether their combined targeting may re-sensitize prostate cancer cells to docetaxel. In hormone-insensitive PC-3 and DU145 prostate cancer cells the mTOR inhibitor everolimus (RAD001) alone did not lead to significant cell death, however, it strongly sensitized cells to low levels (5 nM) of docetaxel. We show that mTOR inhibition has led to a decrease in hypoxia-inducible factor-1α (HIF-1α) protein levels and SK1 mRNA. HIF-1α accumulation induced by CoCl2 has led to a partial chemoresistance to RAD001/docetaxel combination. SK1 overexpression has completely protected prostate cancer cells from RAD001/docetaxel effects. Using gene knockdown and CoCl2 treatment we showed that SK1 mRNA expression is downstream of HIF-1α. In a human xenograft model in nude mice single RAD001 and docetaxel therapies induced 23% and 15% reduction in prostate tumor volume, respectively, while their combination led to a 58% reduction. RAD001 alone or in combination with docetaxel has suppressed intratumoral mTOR and SK1 signaling, however as evidenced by tumor size, it required docetaxel for clinical efficacy. Combination therapy was well tolerated and had similar levels of toxicity to docetaxel alone. Overall, our data demonstrate a new mechanism of docetaxel sensitization in prostate cancer. This provides a mechanistic basis for further clinical application of RAD001/docetaxel combination in prostate cancer therapy

Well-posedness of the Kolmogorov two-equation model of turbulence in optimal Sobolev spaces

In this paper, we study the well-posedness of the Kolmogorov two-equation model of turbulence in a periodic domain Td, for space dimensions d = 2,3. We admit the average turbulent kinetic energy k to vanish in part of the domain, i.e. we consider the case k ≥ 0; in this situation, the parabolic structure of the equations becomes degenerate. For this system, we prove a local well-posedness result in Sobolev spaces Hs, for any s > 1+d/2. We expect this regularity to be optimal, due to the degeneracy of the system when k ≈ 0. We also prove a continuation criterion and provide a lower bound for the lifespan of the solutions. The proof of the results is based on Littlewood- Paley analysis and paradifferential calculus on the torus, together with a precise commutator decomposition of the non-linear terms involved in the computations

Well-posedness of the Kolmogorov two-equation model of turbulence in optimal Sobolev spaces

In this paper, we study the well-posedness of the Kolmogorov two-equation model of turbulence in a periodic domain $\mathbb{T}^d$, for space dimensions $d=2,3$. We admit the average turbulent kinetic energy $k$ to vanish in part of the domain, \textsl{i.e.} we consider the case $k \geq 0$; in this situation, the parabolic structure of the equations becomes degenerate. For this system, we prove a local well-posedness result in Sobolev spaces $H^s$, for any $s>1+d/2$. We expect this regularity to be optimal, due to the degeneracy of the system when $k \approx 0$. We also prove a continuation criterion and provide a lower bound for the lifespan of the solutions. The proof of the results is based on Littlewood-Paley analysis and paradifferential calculus on the torus, together with a precise commutator decomposition of the non-linear terms involved in the computations.Comment: Submitte

ENFERT (Renaud d’). L’enseignement mathématique à l’école primaire de la Révolution à nos jours. Textes officiels (t. 2 : 1915-2000)

Dans cet imposant ouvrage de 695 pages, réalisé avec la collaboration de Josiane Hélayel, Renaud d’Enfert propose un recueil de cent-un textes officiels concernant l’enseignement mathématique à l’école primaire, de 1915 à la fin du XXe siècle, poursuivant ainsi dans ce deuxième tome le travail entrepris en 2003. Il souligne que cette discipline a connu des évolutions nombreuses et importantes après la Première Guerre mondiale et avant l’introduction des mathématiques modernes dans les années ..

Time-coherency of Bayesian priors on transient semi-Markov chains for audio-to-score alignment

International audienceThis paper proposes a novel insight to the problem of real-time alignment with Bayesian inference. When a prior knowledge about the duration of events is available, Semi-Markov models allow the setting of individual duration distributions but give no clue about their choice. We propose a criterion of temporal coherency for such applications and show it might be obtained with the right choice of estimation method. Theoretical insights are obtained through the study of the prior state probability of transient semi-Markov chains

Dan Jaffé, Jésus sous la plume des historiens juifs du xxe siècle. Approche historique, perspectives historiographiques, analyses méthodologiques

Dans le domaine très fourni des publications consacrées au Jésus de l’histoire, le présent ouvrage propose un angle d’approche original : l’apport des historiens juifs. Il témoigne ainsi d’une évolution significative de la recherche et de l’importance des travaux publiés depuis un siècle par les savants juifs. L’auteur suit un développement chronologique dont rendent compte les neuf chapitres qui composent l’ouvrage : 1. Les historiens juifs et Jésus au xixe siècle (Joseph Salvador et Heinric..