Random Measurable Sets and Covariogram Realisability Problems

We provide a characterization of the realisable set covariograms, bringing a rigorous yet abstract solution to the $S\_2$ problem in materials science. Our method is based on the covariogram functional for random mesurable sets (RAMS) and on a result about the representation of positive operators in a locally compact space. RAMS are an alternative to the classical random closed sets in stochastic geometry and geostatistics, they provide a weaker framework allowing to manipulate more irregular functionals, such as the perimeter. We therefore use the illustration provided by the $S\_{2}$ problem to advocate the use of RAMS for solving theoretical problems of geometric nature. Along the way, we extend the theory of random measurable sets, and in particular the local approximation of the perimeter by local covariograms.Comment: 35p

Energy demand prediction for the implementation of an energy tariff emulator to trigger demand response in buildings

Buildings are key actors of the electrical gird. As such they have an important role to play in grid stabilization, especially in a context where renewable energies are mandated to become an increasingly important part of the energy mix. Demand response provides a mechanism to reduce or displace electrical demand to better match electrical production. Buildings can be a pool of flexibility for the grid to operate more efficiently. One of the ways to obtain flexibility from building managers and building users is the introduction of variable energy prices which evolve depending on the expected load and energy generation. In the proposed scenario, the wholesale energy price of electricity, a load prediction, and the elasticity of consumers are used by an energy tariff emulator to predict prices to trigger end user flexibility. In this paper, a cluster analysis to classify users is performed and an aggregated energy prediction is realised using Random Forest machine learning algorithm.This paper is part of a project that has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 768614. This paper reflects only the author´s views and neither the Agency nor the Commission are responsible for any use that may be made of the information contained therein

Effect of transnasal insufflation on sleep disordered breathing in acute stroke: a preliminary study

Background and Purpose: Sleep disordered breathing (SDB) is frequent in acute stroke patients and is associated with early neurologic worsening and poor outcome. Although continuous positive airway pressure (CPAP) effectively treats SDB, compliance is low. The objective of the present study was to assess the tolerance and the efficacy of a continuous high-flow-rate air administered through an open nasal cannula (transnasal insufflation, TNI), a less-intrusive method, to treat SDB in acute stroke patients. Methods: Ten patients (age, 56.8 ± 10.7years), with SDB ranging from moderate to severe (apnea-hypopnea index, AHI, >15/h of sleep) and on a standard sleep study at a mean of 4.8 ± 3.7days after ischemic stroke (range, 1-15days), were selected. The night after, they underwent a second sleep study while receiving TNI (18L/min). Results: TNI was well tolerated by all patients. For the entire group, TNI decreased the AHI from 40.4 ± 25.7 to 30.8 ± 25.7/h (p = 0.001) and the oxygen desaturation index >3% from 40.7 ± 28.4 to 31 ± 22.5/h (p = 0.02). All participants except one showed a decrease in AHI. The percentage of slow-wave sleep significantly increased with TNI from 16.7 ± 8.2% to 22.3 ± 7.4% (p = 0.01). There was also a trend toward a reduction in markers of sleep disruption (number of awakenings, arousal index). Conclusions: TNI improves SDB indices, and possibly sleep parameters, in stroke patients. Although these changes are modest, our findings suggest that TNI is a viable treatment alternative to CPAP in patients with SDB in the acute phase of ischemic strok

Concave majorant of stochastic processes and Burgers turbulence

The asymptotic solution of the inviscid Burgers equations with initial potential $\psi$ is closely related to the convex hull of the graph of $\psi$. In this paper, we study this convex hull, and more precisely its extremal points, if $\psi$ is a stochastic process. The times where those extremal points are reached, called extremal times, form a negligible set for L\'evy processes, their integrated processes, and It\^o processes. We examine more closely the case of a L\'evy process with bounded variation. Its extremal points are almost surely countable, with accumulation only around the extremal values. These results are derived from the general study of the extremal times of $\psi+f$, where $\psi$ is a L\'evy process and $f$ a smooth deterministic drift. These results allow us to show that, for an inviscid Burgers turbulence with a compactly supported initial potential $\psi$, the only point capable of being Lagrangian regular is the time $T$ where $\psi$ reaches its maximum, and that is indeed a regular point iff 0 is regular for both half-lines. As a consequence, if the turbulence occurs on a non-compact interval, there are a.s. no Lagrangian regular points.Comment: 21 page

Asymptotics for the critical level and a strong invariance principle for high intensity shot noise fields

We study fine properties of the convergence of a high intensity shot noise field towards the Gaussian field with the same covariance structure. In particular we (i) establish a strong invariance principle, i.e. a quantitative coupling between a high intensity shot noise field and the Gaussian limit such that they are uniformly close on large domains with high probability, and (ii) use this to derive an asymptotic expansion for the critical level above which the excursion sets of the shot noise field percolate.Comment: 24 pages, 2 figures. Version accepted for publication in AIH

Regularity conditions in the realisability problem with applications to point processes and random closed sets

We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the extension needed for interpreting it as a probability measure. It is shown in which case the extension can be chosen to possess some invariance properties. The results are applied to the existence of point processes with given correlation measure and random closed sets with given two-point covering function or contact distribution function. It is shown that the regularity condition can be efficiently checked in many cases in order to ensure that the obtained point processes are indeed locally finite and random sets have closed realisations.Comment: Published in at http://dx.doi.org/10.1214/13-AAP990 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Geometry of open strings ending on backreacting D3-branes

We investigate open string theory on backreacting D3-branes using a spacetime approach. We study in detail the half-BPS supergravity solutions describing open strings ending on D3-branes, in the near horizon of the D3-branes. We recover quantitatively several non-trivial features of open string physics including the appearance of D3-brane spikes, the polarization of fundamental strings into D5-branes, and the Hanany-Witten effect. Finally we detail the computation of the gravitational potential between two open strings, and contrast it with the holographic computation of Wilson lines. We argue that the D-brane backreaction has a large influence on the low-energy gravity, which may lead to experimental tests for string theory brane-world scenarios.Comment: 64 pages, 20 figure

Pour une démocratie socio-environnementale : cadre pour une plate-forme participative « transition écologique »

Contribution publiée in Penser une démocratie alimentaire Volume II – Proposition Lascaux entre ressources naturelles et besoins fondamentaux, F. Collart Dutilleul et T. Bréger (dir), Inida, San José, 2014, pp. 87-111.International audienceL’anthropocène triomphant actuel, avec ses forçages environnementaux et sociaux, est à l’origine de l’accélération des dégradations des milieux de vie sur Terre et de l’accentuation des tensions sociales et géopolitiques. Passer à un anthropocène de gestion équitable, informé et sobre vis-à-vis de toutes les ressources et dans tous les secteurs d’activité (slow anthropocene), impose une analyse préalable sur l’ensemble des activités et des rapports humains. Cette transition dite « écologique », mais en réalité à la fois sociétale et écologique, est tout sauf un ajustement technique de secteurs dits prioritaires et technocratiques. Elle est avant tout culturelle, politique et philosophique au sens propre du terme. Elle est un horizon pour des trajectoires de développement humain, pour des constructions sociales et économiques, censées redéfinir socialement richesse, bien-être, travail etc. La dénomination « transition écologique » est largement véhiculée, mais ses bases conceptuelles ne sont pas entièrement acquises ni même élaborées. Dans ce contexte, les étudiants en première année de Master BioSciences à l’Ecole Normale Supérieure (ENS) de Lyon ont préparé une première étude analytique de ce changement radical et global de société pour mieux comprendre dans quelle société ils souhaitent vivre, en donnant du sens aux activités humaines présentes et à venir. Une trentaine de dossiers sur divers secteurs d’activités et acteurs de la société ont été produits et ont servis de support à cette synthèse. Plus largement, le but est de construire un socle conceptuel et une plate-forme de travail sur lesquels les questions de fond, mais aussi opérationnelles, peuvent être posées et étudiées en permanence. Cette démarche participative est ouverte à la collectivité sur le site http://institutmichelserres.ens-lyon.fr/