Weyl quantization of degree 2 symplectic graded manifolds

Let $S$ be a spinor bundle of a pseudo-Euclidean vector bundle $(E,\mathrm{g})$ of even rank. We introduce a new filtration on the algebra $\mathcal{D}(M,S)$ of differential operators on $S$. As main property, the associated graded algebra $\mathrm{gr}\mathcal{D}(M,S)$ is isomorphic to the algebra $\mathcal{O}(\mathcal{M})$ of functions on $\mathcal{M}$, where $\mathcal{M}$ is the symplectic graded manifold of degree $2$ canonically associated to $(E,\mathrm{g})$. Accordingly, we define the Weyl quantization on $\mathcal{M}$ as a map $\mathcal{WQ}_\hbar:\mathcal{O}(\mathcal{M})\to\mathcal{D}(M,S)$, and prove that $\mathcal{WQ}_\hbar$ satisfies all desired usual properties. As an application, we obtain a bijection between Courant algebroid structures $(E,\mathrm{g},\rho,[\cdot,\cdot])$, that are encoded by Hamiltonian generating functions on $\mathcal{M}$, and skew-symmetric Dirac generating operators $D\in\mathcal{D}(M,S)$. The operator $D^2$ gives a new invariant of $(E,\mathrm{g},\rho,[\cdot,\cdot])$, which generalizes the square norm of the Cartan $3$-form of a quadratic Lie algebra. We study in detail the particular case of $E$ being the double of a Lie bialgebroid $(A,A^*)$.Comment: 41 page

Recherche, offres de formation et nouveaux métiers en matière environnementale

International audienceDans le contexte de mutation technologique imposée par les nouvelles contraintes environnementales, le système de formation et de recherche se trouve confronté à un paradoxe : d'un côté, au niveau de l'enseignement supérieur et de la recherche, il est le principal acteur dans la construction de nouveaux savoirs et de l'autre, au niveau des offres de formations professionnelles et des diplômes qui s'y rattachent, il traverse une période d'adaptation pour répondre en la matière à la demande économique et sociale qui connaît une progression rapide et importante

« Interprétation d’un conflit : retour sur les spécificités de la mobilisation en France contre la loi Travail (2016) »

International audienceInterprétation d'un conflit : retour sur les spécificités de la mobilisation en France contre la loi Travail (2016) Jean-Philippe MELCHIOR Les mobilisations sociales d'envergure nationale modifient souvent, à plus ou moins brève échéance, le rapport des forces politiques. En France, le mouvement de grève de novembre-décembre 1995 a fragilisé le gouvernement d'Alain Juppé et a fait perdre à la droite les élections législatives anticipées du printemps 1997. Plus proche de nous, la longue mobilisation des salariés contre la réforme des retraites, imposée par Nicolas Sarkozy en 2010, a renforcé le discrédit de ce dernier et favorisé la victoire de François Hollande à l'élection présidentielle de 2012. De même, il est possible de relier la sévérité des défaites subies par le candidat socialiste Benoît Hamon à la présidentielle et par les candidats socialistes aux élections législatives du printemps 2017 à l'importante mobilisation sociale du printemps 2016 contre la loi El Khomri. Certes, avant même que l'opposition au projet de la loi Travail 1 ne conduise à la première journée d'action organisée par les syndicats du 9 mars 2016, la cote de popularité du président de la République François Hollande, était déjà très basse 2. Cependant, en oeuvrant avec son Premier ministre à la remise en cause de plusieurs éléments essentiels du code du travail, un an avant la fin de son mandat, le chef de l'État prit le risque de se couper définitivement de pans entiers de son électorat. Quant à ses liens avec sa majorité, ils s'étaient tellement dégradés du fait de l'orientation néolibérale de ses choix économiques qu'il fallut utiliser à plusieurs reprises la procédure du 49.3 pour faire adopter le texte, procédure pourtant dénoncée avec vigueur par François Hollande quelques années plus tôt quand il était dans l'opposition 3. Un tel constat oblige à comprendre ce qui s'est fondamentalement joué lors de ce conflit social. Dans un premier temps, il s'agira de caractériser le conflit et de le mettre en perspective avec d'autres mobilisations sociales plus anciennes. Les premiers éléments de diagnostic étant posés, il sera possible, dans un deuxième temps, d'analyser les raisons de la défaite et d'interroger les effets 1 L'intitulé exact de ce texte est le suivant : « Loi relative au travail, à la modernisation du dialogue social et à la sécurisation des parcours professionnels ». Par commodité, elle sera appelée « loi Travail » ou « loi El Khomri » dans ce chapitre. 2 En février 2016, 80% des Français estimaient que François Hollande n'était pas un bon président. L'impopularité a atteint 83% en mai et 86% en octobre. Sondages Odoxa-France Inter. 3 Lors du vote du Contrat Première Embauche (CPE) en 2006, François Hollande avait déclaré : « Le 49.3 est une brutalité, le 49.3 est un déni de démocratie, le 49.3 est une manière de freiner ou d'empêcher le débat parlementaire. » Ouest France, 10 mai 2016

Prevalence of Human African Trypanosomiasis in the Democratic Republic of the Congo

Human African Trypanosomiasis (HAT) is a major public health problem in the Democratic Republic of the Congo (DRC). Active and passive surveillance for HAT is conducted but may underestimate the true prevalence of the disease. We used ELISA to screen 7,769 leftover dried blood spots from a nationally representative population-based survey, the 2007 Demographic and Health Survey. 26 samples were positive by ELISA. Three of these were also positive by trypanolysis and/or PCR. From these data, we estimate that there were 18,592 people with HAT (95% confidence interval, 4,883–32,302) in the DRC in 2007, slightly more than twice as many as were reported

Variability and reproducibility of multi-echo T2 relaxometry: Insights from multi-site, multi-session and multi-subject MRI acquisitions

Quantitative magnetic resonance imaging (qMRI) can increase the specificity and sensitivity of conventional weighted MRI to underlying pathology by comparing meaningful physical or chemical parameters, measured in physical units, with normative values acquired in a healthy population. This study focuses on multi-echo T2 relaxometry, a qMRI technique that probes the complex tissue microstructure by differentiating compartment-specific T2 relaxation times. However, estimation methods are still limited by their sensitivity to the underlying noise. Moreover, estimating the model's parameters is challenging because the resulting inverse problem is ill-posed, requiring advanced numerical regularization techniques. As a result, the estimates from distinct regularization strategies are different. In this work, we aimed to investigate the variability and reproducibility of different techniques for estimating the transverse relaxation time of the intra- and extra-cellular space (T2IE) in gray (GM) and white matter (WM) tissue in a clinical setting, using a multi-site, multi-session, and multi-run T2 relaxometry dataset. To this end, we evaluated three different techniques for estimating the T2 spectra (two regularized non-negative least squares methods and a machine learning approach). Two independent analyses were performed to study the effect of using raw and denoised data. For both the GM and WM regions, and the raw and denoised data, our results suggest that the principal source of variance is the inter-subject variability, showing a higher coefficient of variation (CoV) than those estimated for the inter-site, inter-session, and inter-run, respectively. For all reconstruction methods studied, the CoV ranged between 0.32 and 1.64%. Interestingly, the inter-session variability was close to the inter-scanner variability with no statistical differences, suggesting that T2IE is a robust parameter that could be employed in multi-site neuroimaging studies. Furthermore, the three tested methods showed consistent results and similar intra-class correlation (ICC), with values superior to 0.7 for most regions. Results from raw data were slightly more reproducible than those from denoised data. The regularized non-negative least squares method based on the L-curve technique produced the best results, with ICC values ranging from 0.72 to 0.92

Modelling human choices: MADeM and decision‑making

Research supported by FAPESP 2015/50122-0 and DFG-GRTK 1740/2. RP and AR are also part of the Research, Innovation and Dissemination Center for Neuromathematics FAPESP grant (2013/07699-0). RP is supported by a FAPESP scholarship (2013/25667-8). ACR is partially supported by a CNPq fellowship (grant 306251/2014-0)

The evolving SARS-CoV-2 epidemic in Africa: Insights from rapidly expanding genomic surveillance

INTRODUCTION Investment in Africa over the past year with regard to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) sequencing has led to a massive increase in the number of sequences, which, to date, exceeds 100,000 sequences generated to track the pandemic on the continent. These sequences have profoundly affected how public health officials in Africa have navigated the COVID-19 pandemic. RATIONALE We demonstrate how the first 100,000 SARS-CoV-2 sequences from Africa have helped monitor the epidemic on the continent, how genomic surveillance expanded over the course of the pandemic, and how we adapted our sequencing methods to deal with an evolving virus. Finally, we also examine how viral lineages have spread across the continent in a phylogeographic framework to gain insights into the underlying temporal and spatial transmission dynamics for several variants of concern (VOCs). RESULTS Our results indicate that the number of countries in Africa that can sequence the virus within their own borders is growing and that this is coupled with a shorter turnaround time from the time of sampling to sequence submission. Ongoing evolution necessitated the continual updating of primer sets, and, as a result, eight primer sets were designed in tandem with viral evolution and used to ensure effective sequencing of the virus. The pandemic unfolded through multiple waves of infection that were each driven by distinct genetic lineages, with B.1-like ancestral strains associated with the first pandemic wave of infections in 2020. Successive waves on the continent were fueled by different VOCs, with Alpha and Beta cocirculating in distinct spatial patterns during the second wave and Delta and Omicron affecting the whole continent during the third and fourth waves, respectively. Phylogeographic reconstruction points toward distinct differences in viral importation and exportation patterns associated with the Alpha, Beta, Delta, and Omicron variants and subvariants, when considering both Africa versus the rest of the world and viral dissemination within the continent. Our epidemiological and phylogenetic inferences therefore underscore the heterogeneous nature of the pandemic on the continent and highlight key insights and challenges, for instance, recognizing the limitations of low testing proportions. We also highlight the early warning capacity that genomic surveillance in Africa has had for the rest of the world with the detection of new lineages and variants, the most recent being the characterization of various Omicron subvariants. CONCLUSION Sustained investment for diagnostics and genomic surveillance in Africa is needed as the virus continues to evolve. This is important not only to help combat SARS-CoV-2 on the continent but also because it can be used as a platform to help address the many emerging and reemerging infectious disease threats in Africa. In particular, capacity building for local sequencing within countries or within the continent should be prioritized because this is generally associated with shorter turnaround times, providing the most benefit to local public health authorities tasked with pandemic response and mitigation and allowing for the fastest reaction to localized outbreaks. These investments are crucial for pandemic preparedness and response and will serve the health of the continent well into the 21st century