Asymptotics of Bernoulli random walks, bridges, excursions and meanders with a given number of peaks

A Bernoulli random walk is a random trajectory starting from 0 and having i.i.d. increments, each of them being $+1$ or -1, equally likely. The other families cited in the title are Bernoulli random walks under various conditionings. A peak in a trajectory is a local maximum. In this paper, we condition the families of trajectories to have a given number of peaks. We show that, asymptotically, the main effect of setting the number of peaks is to change the order of magnitude of the trajectories. The counting process of the peaks, that encodes the repartition of the peaks in the trajectories, is also studied. It is shown that suitably normalized, it converges to a Brownian bridge which is independent of the limiting trajectory. Applications in terms of plane trees and parallelogram polyominoes are also provided

LINC: A Compact Yet Powerful Coordination Environment

International audienceThis paper presents LINC, a coordination programming environment. It is an evolution of earlier middlewares (the Coordination Language Facility (CLF) and Stitch). The aim is to provide a more flexible and expressive language correcting several of their limitations and an improved run-time environment. LINC provides a compact yet powerful coordination language and an optimised run-time which executes rules. This paper describes the intrinsic properties brought by the LINC environment and how it helps the coordination aspects in a distributed system. This paper also emphasises on the reflexivity of LINC and its usage at system level. Finally, it illustrates through several case studies, how LINC can manage a wide range of application domains

Long range correlations in a 97% excitonic one-dimensional polariton condensate

We report on the realization of an out-of-equilibrium polariton condensate under pulsed excitation in a one-dimensional geometry. We observe macroscopic occupation of a polaritonic mode with only 3% photonic fraction, and a nature strikingly close to that of a bare exciton condensate. With the help of this tiny photonic fraction, the condensate is found to display first-order coherence over distances as large as 10 microns. Based on a driven-dissipative mean field model, we find that the correlations length is limited by the effects of a shallow disorder under non-equilibrium conditions.Comment: 5 pages, 3 figure

VTE : une technique de pointage à distance

National audienceCet article présente la technique d’interaction VTE (Voronoi-based Target Expansion), pour pointer sur une cible numérique affichée sur un écran distant. VTE exploite l’espace libre entre les cibles à l’écran en partageant l’espace de l’écran en zones de grandeur optimale pour chaque cible selon une tesselation de Voronoï. Les zones sont affichées de façon statique sur l’écran et l’utilisateur peut sélectionner une cible en pointant n’importe où dans la zone correspondant à la cible. Ainsi VTE facilite le pointage en augmentant la taille des cibles dans l’espace visuel et moteur. De nombreux environnements nécessitent de pouvoir interagir avec des objets numériques sur un écran distant. Notre domaine d’application est la chirurgie augmentée