From Aztec diamonds to pyramids: steep tilings

We introduce a family of domino tilings that includes tilings of the Aztec diamond and pyramid partitions as special cases. These tilings live in a strip of $\mathbb{Z}^2$ of the form $1 \leq x-y \leq 2\ell$ for some integer $\ell \geq 1$, and are parametrized by a binary word $w\in\{+,-\}^{2\ell}$ that encodes some periodicity conditions at infinity. Aztec diamond and pyramid partitions correspond respectively to $w=(+-)^\ell$ and to the limit case $w=+^\infty-^\infty$. For each word $w$ and for different types of boundary conditions, we obtain a nice product formula for the generating function of the associated tilings with respect to the number of flips, that admits a natural multivariate generalization. The main tools are a bijective correspondence with sequences of interlaced partitions and the vertex operator formalism (which we slightly extend in order to handle Littlewood-type identities). In probabilistic terms our tilings map to Schur processes of different types (standard, Pfaffian and periodic). We also introduce a more general model that interpolates between domino tilings and plane partitions.Comment: 36 pages, 22 figures (v3: final accepted version with new Figure 6, new improved proof of Proposition 11

Multivariate Juggling Probabilities

We consider refined versions of Markov chains related to juggling introduced by Warrington. We further generalize the construction to juggling with arbitrary heights as well as infinitely many balls, which are expressed more succinctly in terms of Markov chains on integer partitions. In all cases, we give explicit product formulas for the stationary probabilities. The normalization factor in one case can be explicitly written as a homogeneous symmetric polynomial. We also refine and generalize enriched Markov chains on set partitions. Lastly, we prove that in one case, the stationary distribution is attained in bounded time.Comment: 28 pages, 5 figures, final versio

Bumping sequences and multispecies juggling

Building on previous work by four of us (ABCN), we consider further generalizations of Warrington's juggling Markov chains. We first introduce "multispecies" juggling, which consist in having balls of different weights: when a ball is thrown it can possibly bump into a lighter ball that is then sent to a higher position, where it can in turn bump an even lighter ball, etc. We both study the case where the number of balls of each species is conserved and the case where the juggler sends back a ball of the species of its choice. In this latter case, we actually discuss three models: add-drop, annihilation and overwriting. The first two are generalisations of models presented in (ABCN) while the third one is new and its Markov chain has the ultra fast convergence property. We finally consider the case of several jugglers exchanging balls. In all models, we give explicit product formulas for the stationary probability and closed form expressions for the normalisation factor if known.Comment: 25 pages, 9 figures (v3: final version, several typos and figures fixed

Perfect sampling algorithm for Schur processes

We describe random generation algorithms for a large class of random combinatorial objects called Schur processes, which are sequences of random (integer) partitions subject to certain interlacing conditions. This class contains several fundamental combinatorial objects as special cases, such as plane partitions, tilings of Aztec diamonds, pyramid partitions and more generally steep domino tilings of the plane. Our algorithm, which is of polynomial complexity, is both exact (i.e. the output follows exactly the target probability law, which is either Boltzmann or uniform in our case), and entropy optimal (i.e. it reads a minimal number of random bits as an input). The algorithm encompasses previous growth procedures for special Schur processes related to the primal and dual RSK algorithm, as well as the famous domino shuffling algorithm for domino tilings of the Aztec diamond. It can be easily adapted to deal with symmetric Schur processes and general Schur processes involving infinitely many parameters. It is more concrete and easier to implement than Borodin's algorithm, and it is entropy optimal. At a technical level, it relies on unified bijective proofs of the different types of Cauchy and Littlewood identities for Schur functions, and on an adaptation of Fomin's growth diagram description of the RSK algorithm to that setting. Simulations performed with this algorithm suggest interesting limit shape phenomena for the corresponding tiling models, some of which are new.Comment: 26 pages, 19 figures (v3: final version, corrected a few misprints present in v2

Development of a genomic evaluation for milk production for a local bovine breed

DairySN

Sinnamary – Barrage de Petit-Saut

Présentation du programme archéologique de Petit-Saut 1992 L’année 1992 a été sans aucun doute l’année charnière du programme. Sans reprendre l’historique de l’opération, on peut résumer les deux premières années de la façon suivante: L’année 1990 avait marqué le démarrage, les recherches avaient alors porté sur les zones défrichées pour l’accès au barrage, l’inventaire des sites à polissoirs des basses et moyennes vallées du Sinnamary, du Courcibo et de la Crique Tigre, l’inventaire de struc..

Pour une démocratie socio-environnementale : cadre pour une plate-forme participative « transition écologique »

Contribution publiée in Penser une démocratie alimentaire Volume II – Proposition Lascaux entre ressources naturelles et besoins fondamentaux, F. Collart Dutilleul et T. Bréger (dir), Inida, San José, 2014, pp. 87-111.International audienceL’anthropocène triomphant actuel, avec ses forçages environnementaux et sociaux, est à l’origine de l’accélération des dégradations des milieux de vie sur Terre et de l’accentuation des tensions sociales et géopolitiques. Passer à un anthropocène de gestion équitable, informé et sobre vis-à-vis de toutes les ressources et dans tous les secteurs d’activité (slow anthropocene), impose une analyse préalable sur l’ensemble des activités et des rapports humains. Cette transition dite « écologique », mais en réalité à la fois sociétale et écologique, est tout sauf un ajustement technique de secteurs dits prioritaires et technocratiques. Elle est avant tout culturelle, politique et philosophique au sens propre du terme. Elle est un horizon pour des trajectoires de développement humain, pour des constructions sociales et économiques, censées redéfinir socialement richesse, bien-être, travail etc. La dénomination « transition écologique » est largement véhiculée, mais ses bases conceptuelles ne sont pas entièrement acquises ni même élaborées. Dans ce contexte, les étudiants en première année de Master BioSciences à l’Ecole Normale Supérieure (ENS) de Lyon ont préparé une première étude analytique de ce changement radical et global de société pour mieux comprendre dans quelle société ils souhaitent vivre, en donnant du sens aux activités humaines présentes et à venir. Une trentaine de dossiers sur divers secteurs d’activités et acteurs de la société ont été produits et ont servis de support à cette synthèse. Plus largement, le but est de construire un socle conceptuel et une plate-forme de travail sur lesquels les questions de fond, mais aussi opérationnelles, peuvent être posées et étudiées en permanence. Cette démarche participative est ouverte à la collectivité sur le site http://institutmichelserres.ens-lyon.fr/

Invading Basement Membrane Matrix Is Sufficient for MDA-MB-231 Breast Cancer Cells to Develop a Stable In Vivo Metastatic Phenotype

1 - ArticleIntroduction: The poor efficacy of various anti-cancer treatments against metastatic cells has focused attention on the role of tumor microenvironment in cancer progression. To understand the contribution of the extracellular matrix (ECM) environment to this phenomenon, we isolated ECM surrogate invading cell populations from MDA-MB-231 breast cancer cells and studied their genotype and malignant phenotype. Methods: We isolated invasive subpopulations (INV) from non invasive populations (REF) using a 2D-Matrigel assay, a surrogate of basal membrane passage. INV and REF populations were investigated by microarray assay and for their capacities to adhere, invade and transmigrate in vitro, and to form metastases in nude mice. Results: REF and INV subpopulations were stable in culture and present different transcriptome profiles. INV cells were characterized by reduced expression of cell adhesion and cell-cell junction genes (44% of down regulated genes) and by a gain in expression of anti-apoptotic and pro-angiogenic gene sets. In line with this observation, in vitro INV cells showed reduced adhesion and increased motility through endothelial monolayers and fibronectin. When injected into the circulation, INV cells induced metastases formation, and reduced injected mice survival by up to 80% as compared to REF cells. In nude mice, INV xenografts grew rapidly inducing vessel formation and displaying resistance to apoptosis. Conclusion: Our findings reveal that the in vitro ECM microenvironment per se was sufficient to select for tumor cells with a stable metastatic phenotype in vivo characterized by loss of adhesion molecules expression and induction of proangiogenic and survival factors

Vaccine breakthrough hypoxemic COVID-19 pneumonia in patients with auto-Abs neutralizing type I IFNs

Life-threatening `breakthrough' cases of critical COVID-19 are attributed to poor or waning antibody response to the SARS- CoV-2 vaccine in individuals already at risk. Pre-existing autoantibodies (auto-Abs) neutralizing type I IFNs underlie at least 15% of critical COVID-19 pneumonia cases in unvaccinated individuals; however, their contribution to hypoxemic breakthrough cases in vaccinated people remains unknown. Here, we studied a cohort of 48 individuals ( age 20-86 years) who received 2 doses of an mRNA vaccine and developed a breakthrough infection with hypoxemic COVID-19 pneumonia 2 weeks to 4 months later. Antibody levels to the vaccine, neutralization of the virus, and auto- Abs to type I IFNs were measured in the plasma. Forty-two individuals had no known deficiency of B cell immunity and a normal antibody response to the vaccine. Among them, ten (24%) had auto-Abs neutralizing type I IFNs (aged 43-86 years). Eight of these ten patients had auto-Abs neutralizing both IFN-a2 and IFN-., while two neutralized IFN-omega only. No patient neutralized IFN-ss. Seven neutralized 10 ng/mL of type I IFNs, and three 100 pg/mL only. Seven patients neutralized SARS-CoV-2 D614G and the Delta variant (B.1.617.2) efficiently, while one patient neutralized Delta slightly less efficiently. Two of the three patients neutralizing only 100 pg/mL of type I IFNs neutralized both D61G and Delta less efficiently. Despite two mRNA vaccine inoculations and the presence of circulating antibodies capable of neutralizing SARS-CoV-2, auto-Abs neutralizing type I IFNs may underlie a significant proportion of hypoxemic COVID-19 pneumonia cases, highlighting the importance of this particularly vulnerable population