Topological aggregation, the twin paradox and the No Show paradox

International audienceConsider the framework of topological aggregation introduced by Chichilnisky (1980). We prove that in this framework the Twin Paradox and the No Show Paradox cannot be avoided. Anonymity and unanimity are not needed to obtain these results

Asymptotic Properties of Random Polytopes

International audienceRandom polytopes have constituted some of the central objects of stochastic geometry for more than 150 years. They are in general generated as convex hulls of a random set of points in the Euclidean space. The study of such models requires the use of ingredients coming from both convex geometry and probability theory. In the last decades, the study has been focused on their asymptotic properties and in particular expectation and variance estimates. In several joint works with Tomasz Schreiber and J. E. Yukich, we have investigated the scaling limit of several models (uniform model in the unit-ball, uniform model in a smooth convex body, Gaussian model) and have deduced from it limiting variances for several geometric characteristics including the number of k-dimensional faces and the volume. In this paper, we survey the most recent advances on these questions and we emphasize the particular cases of random polytopes in the unit-ball and Gaussian polytopes

Cross Talk Between Plasma Membrane Na+/Ca2+ Exchanger-1 and TRPC/Orai-Containing Channels: Key Players in Arterial Hypertension

Arterial smooth muscle (ASM) Na(+)/Ca(2+) exchanger type 1 (NCX1) and TRPC/Orai-containing receptor/store-operated cation channels (ROC/SOC) are clustered with α2 Na(+) pumps in plasma membrane microdomains adjacent to the underlying junctional sarcoplasmic reticulum. This arrangement enables these transport proteins to function as integrated units to help regulate local Na(+) metabolism, Ca(2+) signaling and arterial tone. They thus influence vascular resistance and blood pressure (BP). For instance, up-regulation of NCX1 and TRPC6 has been implicated in the pathogenesis of high BP in several models of essential hypertension: ouabain-induced hypertensive rats, Milan hypertensive strain rats, and Dahl salt-sensitive hypertensive rats, which all have elevated plasma ouabain levels. Enhanced expression and function of arterial smooth muscle NCX1 and TRPC/Orai1-containing channels in experimental and clinical hypertension implies that these proteins are potential targets for pharmacological intervention