Representing three-dimensional cross fields using 4th order tensors

This paper presents a new way of describing cross fields based on fourth order tensors. We prove that the new formulation is forming a linear space in $\mathbb{R}^9$. The algebraic structure of the tensors and their projections on \mbox{SO}(3) are presented. The relationship of the new formulation with spherical harmonics is exposed. This paper is quite theoretical. Due to pages limitation, few practical aspects related to the computations of cross fields are exposed. Nevetheless, a global smoothing algorithm is briefly presented and computation of cross fields are finally depicted

The NALCN ion channel is activated by M3 muscarinic receptors in a pancreatic β-cell line

A previously uncharacterized putative ion channel, NALCN (sodium leak channel, non-selective), has been recently shown to be responsible for the tetrodotoxin (TTX)-resistant sodium leak current implicated in the regulation of neuronal excitability. Here, we show that NALCN encodes a current that is activated by M3 muscarinic receptors (M3R) in a pancreatic β-cell line. This current is primarily permeant to sodium ions, independent of intracellular calcium stores and G proteins but dependent on Src activation, and resistant to TTX. The current is recapitulated by co-expression of NALCN and M3R in human embryonic kidney-293 cells and in Xenopus oocytes. We also show that NALCN and M3R belong to the same protein complex, involving the intracellular I–II loop of NALCN and the intracellular i3 loop of M3R. Taken together, our data show the molecular basis of a muscarinic-activated inward sodium current that is independent of G-protein activation, and provide new insights into the properties of NALCN channels

The Inviscid Limit and Boundary Layers for Navier-Stokes Flows

The validity of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations modeling viscous incompressible flows converge to solutions of the Euler equations modeling inviscid incompressible flows as viscosity approaches zero, is one of the most fundamental issues in mathematical fluid mechanics. The problem is classified into two categories: the case when the physical boundary is absent, and the case when the physical boundary is present and the effect of the boundary layer becomes significant. The aim of this article is to review recent progress on the mathematical analysis of this problem in each category.Comment: To appear in "Handbook of Mathematical Analysis in Mechanics of Viscous Fluids", Y. Giga and A. Novotn\'y Ed., Springer. The final publication is available at http://www.springerlink.co

Covichem: A biochemical severity risk score of COVID-19 upon hospital admission

Clinical and laboratory predictors of COVID-19 severity are now well described and combined to propose mortality or severity scores. However, they all necessitate saturable equipment such as scanners, or procedures difficult to implement such as blood gas measures. To provide an easy and fast COVID-19 severity risk score upon hospital admission, and keeping in mind the above limits, we sought for a scoring system needing limited invasive data such as a simple blood test and co-morbidity assessment by anamnesis. A retrospective study of 303 patients (203 from Bordeaux University hospital and an external independent cohort of 100 patients from Paris Pitié-Salpêtrière hospital) collected clinical and biochemical parameters at admission. Using stepwise model selection by Akaike Information Criterion (AIC), we built the severity score Covichem. Among 26 tested variables, 7: obesity, cardiovascular conditions, plasma sodium, albumin, ferritin, LDH and CK were the independent predictors of severity used in Covichem (accuracy 0.87, AUROC 0.91). Accuracy was 0.92 in the external validation cohort (89% sensitivity and 95% specificity). Covichem score could be useful as a rapid, costless and easy to implement severity assessment tool during acute COVID-19 pandemic waves

Hippocampal CA3 Transcriptome Signature Correlates with Initial Precipitating Injury in Refractory Mesial Temporal Lobe Epilepsy

Background: Prolonged febrile seizures constitute an initial precipitating injury (IPI) commonly associated with refractory mesial temporal lobe epilepsy (RMTLE). in order to investigate IPI influence on the transcriptional phenotype underlying RMTLE we comparatively analyzed the transcriptomic signatures of CA3 explants surgically obtained from RMTLE patients with (FS) or without (NFS) febrile seizure history. Texture analyses on MRI images of dentate gyrus were conducted in a subset of surgically removed sclerotic hippocampi for identifying IPI-associated histo-radiological alterations.Methodology/Principal Findings: DNA microarray analysis revealed that CA3 global gene expression differed significantly between FS and NFS subgroups. An integrative functional genomics methodology was used for characterizing the relations between GO biological processes themes and constructing transcriptional interaction networks defining the FS and NFS transcriptomic signatures and its major gene-gene links (hubs). Co-expression network analysis showed that: i) CA3 transcriptomic profiles differ according to the IPI; ii) FS distinctive hubs are mostly linked to glutamatergic signalization while NFS hubs predominantly involve GABAergic pathways and neurotransmission modulation. Both networks have relevant hubs related to nervous system development, what is consistent with cell genesis activity in the hippocampus of RMTLE patients. Moreover, two candidate genes for therapeutic targeting came out from this analysis: SSTR1, a relevant common hub in febrile and afebrile transcriptomes, and CHRM3, due to its putative role in epilepsy susceptibility development. MRI texture analysis allowed an overall accuracy of 90% for pixels correctly classified as belonging to FS or NFS groups. Histological examination revealed that granule cell loss was significantly higher in FS hippocampi.Conclusions/Significance: CA3 transcriptional signatures and dentate gyrus morphology fairly correlate with IPI in RMTLE, indicating that FS-RMTLE represents a distinct phenotype. These findings may shed light on the molecular mechanisms underlying refractory epilepsy phenotypes and contribute to the discovery of novel specific drug targets for therapeutic interventions

Analyse isogéométrique multiéchelle à précision contrôlée en mécanique des structures

Isogeometric analysis applied to structural mechanics problems is a topic of intense concerns for a decade. Indeed, an exact description of geometries studied is allowed by this discretization method suppressing errors due to a bad description of the spatial domain considered. However, a theoretical problem of refinement propagation appears during mesh localization. Local refinement methods for isogeometric analysis has been developed and implied a complexification of the implementation of such a resolution strategy. This PhD thesis expose a space adaptative refinement strategy for linear elastic problems and a space-time one for transient dynamic using isogeometric analysis. For this purpose, a localization method for isogeometric analysis based on a multigrid resolution is developed for 2D linear elastic problems. This method allow to circumvent mesh refinement propagation inherent to isogeometric analysis, and is easier to implement than existing methods. Moreover, the use of isogeometric analysis simplifies refinement procedures occuring during mesh adaptation and which can be really complex using classical finite element analysis. Then, a space-time adaptative refinement based on a multigrid resolution is developed for one dimensional in space problems. A study on operators structure is exposed in order to choose a well suited time integrator. This strategy's performances are highlighted, then an evolution of this method is set up in order to lower computational costs. The space-time adaptaptive refinement is applied to some academical examples to show it good behavior during localization.L’analyse isogéométrique pour la résolution de problèmes de la mécanique du solide suscite de vifs intérêts depuis une dizaine d’année. En effet, cette méthode de discrétisation autorise la description exacte des géométries étudiées permettant ainsi de supprimer les erreurs dues à une mauvaise description du domaine spatial étudié. Cependant elle pose un problème théorique de propagation de raffinement lors de la localisation de maillage. Des méthodes pour contourner ce problème ont été proposée dans la littérature mais complexifient grandement la mise en œuvre de cette stratégie de résolution. Cette thèse propose une stratégie de raffinement localisé adaptatif en espace pour les problèmes de statique et en espace temps pour les problèmes de dynamique transitoire dans le cadre de l’analyse isogéométrique. Pour cela une méthode de localisation pour l’analyse isogéométrique en statique basée sur une résolution multigrille est tout d’abord développée pour des problèmes en deux dimensions. Elle présente l’avantage de contourner la problématique de propagation de raffinement de maillage due à l’analyse isogéométrique tout en étant plus simple à mettre en œuvre que les méthodes déjà existantes. De plus, l’utilisation de l’analyse isogéométrique permet de simplifier les procédures de raffinement lors de l’adaptation de maillage qui peuvent être complexes lors de l’utilisationd’éléments finis classiques. Une méthode de raffinement adaptatif espace temps basée sur une résolution multigrille est ensuite développée pour des problèmes en une dimension. Une étude sur la structure des opérateurs est proposée afin de choisir un intégrateur temporel adapté. Les performances de cette stratégies sont mises en évidence, puis une modification de la méthode de résolution est proposée afin de diminuer significativement les coûts de calculs associées à cette résolution. La méthode de raffinement adaptatif espace temps est appliquée à quelques exemples académiques afin de valider son bon comportement lors de la localisation