Some Results about the Quality of Planar Mesh Elements

In this report are presented some new results about both triangle and planar quadrangle quality measures. First, in the context of triangular mesh optimization based on control over edge lenghts, the relations between the edge ratio and the usual shape quality measure are fully examined. Second, a modification of the norm is proposed, in order to comply with the case where the reference element is no longer equilateral, but a right isosceles triangle. Third, generalizations of and to planar quadrangle quality measure are proposed and justified, and their limitations, depending on the user expectations, are exhibited, justifying the use of a more complex quality measure. Finally, a natural use of the norm for quadrangular elements is proposed

Construction d'une contrainte Delaunay-admissible en dimension 2.

Ce rapport propose une méthode de redéfinition {\em a priori}, c'est-à-dire avant toute construction d'une triangulation, d'un champ de contraintes bidimensionnel constitué d'arêtes, afin d'assurer qu'il apparaisse dans toute triangulation de Delaunay de l'enveloppe convexe du nuage de points auquel ce champ se rapporte. Une classification géométrique des arêtes constitutives de la contrainte est présentée, préalablement à la démonstration d'une condition nécessaire et suffisante d'existence d'une arête dans toute triangulation de Delaunay de l'enveloppe convexe d'un ensemble donné de points. L'hypothÉse restrictive de la position générale n'est pas faite. Ensuite, deux algorithmes de subdivision des arêtes sont proposés, et leur convergence est établie. Un jeu représentatif d'exemples illustre l'approche choisie

Genetic variation affects morphological retinal phenotypes extracted from UK Biobank optical coherence tomography images

Optical Coherence Tomography (OCT) enables non-invasive imaging of the retina and is used to diagnose and manage ophthalmic diseases including glaucoma. We present the first large-scale genome-wide association study of inner retinal morphology using phenotypes derived from OCT images of 31,434 UK Biobank participants. We identify 46 loci associated with thickness of the retinal nerve fibre layer or ganglion cell inner plexiform layer. Only one of these loci has been associated with glaucoma, and despite its clear role as a biomarker for the disease, Mendelian randomisation does not support inner retinal thickness being on the same genetic causal pathway as glaucoma. We extracted overall retinal thickness at the fovea, representative of foveal hypoplasia, with which three of the 46 SNPs were associated. We additionally associate these three loci with visual acuity. In contrast to the Mendelian causes of severe foveal hypoplasia, our results suggest a spectrum of foveal hypoplasia, in part genetically determined, with consequences on visual function

PSEN1ΔE9, APPswe, and APOE4 Confer Disparate Phenotypes in Human iPSC-Derived Microglia

Summary Here we elucidate the effect of Alzheimer disease (AD)-predisposing genetic backgrounds, APOE4, PSEN1ΔE9, and APPswe, on functionality of human microglia-like cells (iMGLs). We present a physiologically relevant high-yield protocol for producing iMGLs from induced pluripotent stem cells. Differentiation is directed with small molecules through primitive erythromyeloid progenitors to re-create microglial ontogeny from yolk sac. The iMGLs express microglial signature genes and respond to ADP with intracellular Ca2+ release distinguishing them from macrophages. Using 16 iPSC lines from healthy donors, AD patients and isogenic controls, we reveal that the APOE4 genotype has a profound impact on several aspects of microglial functionality, whereas PSEN1ΔE9 and APPswe mutations trigger minor alterations. The APOE4 genotype impairs phagocytosis, migration, and metabolic activity of iMGLs but exacerbates their cytokine secretion. This indicates that APOE4 iMGLs are fundamentally unable to mount normal microglial functionality in AD.Peer reviewe

A priori Delaunay-conformity

. This communication presents a method for redening a priori a eld of constraints represented in two dimensions by a set of edges, in three dimensions by a surface triangulation. The aim is to provide a resulting constraint, strongly Delaunay-conforming, (i.e., that will be built by any Delaunay triangulation of the convex hull of the associated set of vertices). We show that the two-dimensional problem can be easily solved, and hence, we give a classication of edges leading to a convergent algorithm. Although the classication extends to faces, an essential property vanishes in three dimensions, excluding a simple extrapolation of the method. Nevertheless, a heuristic algorithm, based on face subdivisions, governed by a geometric estimate and by means of edge swapping is given in three dimensions. Several examples emphasize the proposed method in two and three dimensions. Keywords. Triangulation, Delaunay triangulation, constrained triangulation, surface triangulation. Introduction..