Metric shape of hypersurfaces with small extrinsic radius or large λ1 \lambda_1

We determine the Hausdorff limit-set of the Euclidean hypersurfaces with large $\lambda_1$ or small extrinsic radius. The result depends on the $L^p$ norm of the curvature that is assumed to be bounded a priori, with a critical behaviour for $p$ equal to the dimension minus 1

Hypersurfaces with small extrinsic radius or large λ1\lambda_1 in Euclidean spaces

We prove that hypersurfaces of $\R^{n+1}$ which are almost extremal for the Reilly inequality on $\lambda_1$ and have $L^p$-bounded mean curvature ($p>n$) are Hausdorff close to a sphere, have almost constant mean curvature and have a spectrum which asymptotically contains the spectrum of the sphere. We prove the same result for the Hasanis-Koutroufiotis inequality on extrinsic radius. We also prove that when a supplementary $L^q$ bound on the second fundamental is assumed, the almost extremal manifolds are Lipschitz close to a sphere when $q>n$, but not necessarily diffeomorphic to a sphere when $q\leqslant n$.Comment: 24 page

Canakinumab in patients with COVID-19 and type 2 diabetes - A multicentre, randomised, double-blind, placebo-controlled trial

BACKGROUND: Patients with type 2 diabetes and obesity have chronic activation of the innate immune system possibly contributing to the higher risk of hyperinflammatory response to SARS-CoV2 and severe COVID-19 observed in this population. We tested whether interleukin-1β (IL-1β) blockade using canakinumab improves clinical outcome. METHODS: CanCovDia was a multicenter, randomised, double-blind, placebo-controlled trial to assess the efficacy of canakinumab plus standard-of-care compared with placebo plus standard-of-care in patients with type 2 diabetes and a BMI > 25 kg/m$^{2}$ hospitalised with SARS-CoV2 infection in seven tertiary-hospitals in Switzerland. Patients were randomly assigned 1:1 to a single intravenous dose of canakinumab (body weight adapted dose of 450-750 mg) or placebo. Canakinumab and placebo were compared based on an unmatched win-ratio approach based on length of survival, ventilation, ICU stay and hospitalization at day 29. This study is registered with ClinicalTrials.gov, NCT04510493. FINDINGS: Between October 17, 2020, and May 12, 2021, 116 patients were randomly assigned with 58 in each group. One participant dropped out in each group for the primary analysis. At the time of randomization, 85 patients (74·6 %) were treated with dexamethasone. The win-ratio of canakinumab vs placebo was 1·08 (95 % CI 0·69-1·69; p = 0·72). During four weeks, in the canakinumab vs placebo group 4 (7·0%) vs 7 (12·3%) participants died, 11 (20·0 %) vs 16 (28·1%) patients were on ICU, 12 (23·5 %) vs 11 (21·6%) were hospitalised for more than 3 weeks, respectively. Median ventilation time at four weeks in the canakinumab vs placebo group was 10 [IQR 6.0, 16.5] and 16 days [IQR 14.0, 23.0], respectively. There was no statistically significant difference in HbA1c after four weeks despite a lower number of anti-diabetes drug administered in patients treated with canakinumab. Finally, high-sensitive CRP and IL-6 was lowered by canakinumab. Serious adverse events were reported in 13 patients (11·4%) in each group. INTERPRETATION: In patients with type 2 diabetes who were hospitalised with COVID-19, treatment with canakinumab in addition to standard-of-care did not result in a statistically significant improvement of the primary composite outcome. Patients treated with canakinumab required significantly less anti-diabetes drugs to achieve similar glycaemic control. Canakinumab was associated with a prolonged reduction of systemic inflammation. FUNDING: Swiss National Science Foundation grant #198415 and University of Basel. Novartis supplied study medication

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

L’inégalité économique des territoires. Les écarts continuent de se creuser.

International audienceL’évolution récente de la pyramide des âges et un solde migratoire positif conduisent à une hausse du nombre d’actifs en France métropolitaine. Les deux tiers de cette augmentation s’expliquent par celle des cadres. Mais elle est très inégalement distribuée dans l’Hexagone, d’où un accroissement des disparités territoriales. On voit mal comment le regroupement des régions et les lois créant une nouvelle strate intercommunale, les « métropoles », pourraient renverser cette tendance

Les villes moyennes françaises : une catégorisation à l'épreuve des dynamiques sociodémographiques

International audienceL’étude des villes moyennes se heurte dès le départ à la difficulté d’en donner une définition qui fasse l’unanimité. Il existe en effet plusieurs critères de délimitation de la ville (politique, morphologique, fonctionnel) qui présentent tous une certaine instabilité dans le temps. En outre, il est possible d’adopter différents seuils démographiques pour distinguer les villes moyennes des plus grandes et des plus petites ; de plus, si les bornes de l’intervalle défini sont fixes dans le temps, les effectifs des populations ne le sont pas et peuvent donc s’en affranchir.Devant ces limites, on peut considérer que les villes moyennes sont bien « un objet réel non identifié » et qu’à ce titre il est impossible à appréhender de manière scientifique. Mais on peut aussi soumettre les imperfections d’une catégorisation a priori à un examen des caractéristiques de cet ensemble saisies d’un point de vue transversal et longitudinal et ainsi se donner l’opportunité d’évaluer la légitimité de cette catégorie « villes moyennes ». C’est ce que nous proposons dans cet article. L’analyse des caractéristiques et de la dynamique sociodémographiques sur plus de 40 ans (1968-2010) de l’ensemble des aires urbaines françaises comptant de 20 000 à 200 000 habitants en 2010 met en évidence une homogénéité interne et une hétérogénéité externe suffisamment importantes pour légitimer a posteriori cette catégorisation initiale. Certes, toutes les villes moyennes n’ont pas connu la même trajectoire sociodémographique depuis la fin des années 60 et elles n’ont pas toutes les mêmes caractéristiques en 2010. Mais au-delà des inévitables différences, elles semblent suivre, tant au niveau national que régional, un modèle d’évolution commun qui les distingue nettement des autres catégories d’aires urbaines françaises