Flux reconstruction method for time-harmonic linear propagation problems: 1D a priori error analysis

International audienceThe Flux Reconstruction (FR) method is well established for hyperbolic equations in the Computational Fluid Dynamics field, but has barely been studied for electromagnetism. In this article, we propose to describe the FR formulation for time-harmonic linear hyperbolic problems. In particular, this formalism includes the Maxwell's equations and the unidimensional wave equations, for which the method is detailed. We then focus on the wave equations for incoming boundary conditions, and prove the well-posedness of the associated FR method and quasi-optimal a priori error estimates, which are explicit in terms of the flux correction polynomials and discretisation parameters. Numerical experiments finally validate the main behaviours of the estimates, and confirm the good properties of the method for the Maxwell problem.La méthode Flux Reconstruction (FR) est largement établie pour les équations hyperboliques de la mécanique des fluides, mais n'a été encore que peu étudiée dans le cadre de l'électromagnétisme. Dans cet article, nous nous proposons donc de décrire la formulation FR pour des problèmes hyperboliques linéaires harmoniques. Ce formalisme général contient en particulier le problème de Maxwell et l'équation des ondes unidimensionnelle, pour lesquelles la méthode est détaillée. Nous nous concentrons ensuite sur l'équation des ondes pour des conditions de bord entrantes, et prouvons le caractère bien posé de la méthode FR associée, ainsi que des estimations d'erreur a priori quasi-optimales et explicites en les polynômes de correction de flux et les paramètres de discrétisation. Finalement, des expériences numériques permettent de valider les principaux comportements de ces estimations, et confirment les bonnes propriétés de la méthode pour les équations de Maxwell

North and South in the ancient Central Andes: contextualizing the archaeological record with evidence from linguistics and molecular anthropology

The Central Andes are characterized by the early emergence of complex societies and a chequered yet continuous cultural tradition. However, at least for certain points of time in the cultural development, the overall cohesiveness of this ‘culture area’ has been called into question, favoring an alternative perspective that emphasizes the existence of several relatively independent nuclei of development on the North Coast, the southern Peruvian Highlands and the Titicaca basin, with distinct cultural expressions and political organization. Here, we engage archaeological evidence and its interpretation with newly emerging perspectives from linguistics and genetics (modern and ancient DNA), including new targeted genetic analysis, to add fresh evidence to the question of the internal structure and cohesiveness of the ancient Central Andes as a culture area. The double cultural/biological approach points at a North vs. South structure bisecting the Central Andes that becomes appreciable ~2,000 years ago; however, as the evidence from all three disciplines indicates, too, the spheres have remained connected and hence maintained an overall cohesiveness. Our analysis suggests that demographic population structure precedes the constitution of distinct cultural domains, a pattern which is to be verified in other chronological transects in South America and at a global scale.1. Introduction 2. Central Andean archaeology: North and South. 3. From archaeology to a broad anthropological perspective: Conceptualization and limitations 4. The view from language 4.1. Perspectives on North-South structure in the Central Andes from 16th century language geography 4.2. Perspectives on North-South structure in the Central Andes from language contact patterns and areal convergence in language structure 5. The view from genetics 5.1. Perspectives on North-South structure in the Central Andes from studies of uniparental markers 5.2. Perspectives on North-South structure in the Central Andes from full genome analyses 5.3. Timing the emergence of population structure in genetics 5.3.1. Introduction 5.3.2. Methods 5.3.3. Results 6. Discussio

Rare predicted loss-of-function variants of type I IFN immunity genes are associated with life-threatening COVID-19

BackgroundWe previously reported that impaired type I IFN activity, due to inborn errors of TLR3- and TLR7-dependent type I interferon (IFN) immunity or to autoantibodies against type I IFN, account for 15-20% of cases of life-threatening COVID-19 in unvaccinated patients. Therefore, the determinants of life-threatening COVID-19 remain to be identified in similar to 80% of cases.MethodsWe report here a genome-wide rare variant burden association analysis in 3269 unvaccinated patients with life-threatening COVID-19, and 1373 unvaccinated SARS-CoV-2-infected individuals without pneumonia. Among the 928 patients tested for autoantibodies against type I IFN, a quarter (234) were positive and were excluded.ResultsNo gene reached genome-wide significance. Under a recessive model, the most significant gene with at-risk variants was TLR7, with an OR of 27.68 (95%CI 1.5-528.7, P=1.1x10(-4)) for biochemically loss-of-function (bLOF) variants. We replicated the enrichment in rare predicted LOF (pLOF) variants at 13 influenza susceptibility loci involved in TLR3-dependent type I IFN immunity (OR=3.70[95%CI 1.3-8.2], P=2.1x10(-4)). This enrichment was further strengthened by (1) adding the recently reported TYK2 and TLR7 COVID-19 loci, particularly under a recessive model (OR=19.65[95%CI 2.1-2635.4], P=3.4x10(-3)), and (2) considering as pLOF branchpoint variants with potentially strong impacts on splicing among the 15 loci (OR=4.40[9%CI 2.3-8.4], P=7.7x10(-8)). Finally, the patients with pLOF/bLOF variants at these 15 loci were significantly younger (mean age [SD]=43.3 [20.3] years) than the other patients (56.0 [17.3] years; P=1.68x10(-5)).ConclusionsRare variants of TLR3- and TLR7-dependent type I IFN immunity genes can underlie life-threatening COVID-19, particularly with recessive inheritance, in patients under 60 years old

Correction: Rare predicted loss-of-function variants of type I IFN immunity genes are associated with life-threatening COVID-19

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