Coupling, Attractiveness and Hydrodynamics for Conservative Particle Systems

Attractiveness is a fundamental tool to study interacting particle systems and the basic coupling construction is a usual route to prove this property, as for instance in simple exclusion. The derived Markovian coupled process $(\xi_t,\zeta_t)_{t\geq 0}$ satisfies: (A) if $\xi_0\leq\zeta_0$ (coordinate-wise), then for all $t\geq 0$, $\xi_t\leq\zeta_t$ a.s. In this paper, we consider generalized misanthrope models which are conservative particle systems on $\Z^d$ such that, in each transition, $k$ particles may jump from a site $x$ to another site $y$, with $k\geq 1$. These models include simple exclusion for which $k=1$, but, beyond that value, the basic coupling construction is not possible and a more refined one is required. We give necessary and sufficient conditions on the rates to insure attractiveness; we construct a Markovian coupled process which both satisfies (A) and makes discrepancies between its two marginals non-increasing. We determine the extremal invariant and translation invariant probability measures under general irreducibility conditions. We apply our results to examples including a two-species asymmetric exclusion process with charge conservation (for which $k\le 2$) which arises from a Solid-on-Solid interface dynamics, and a stick process (for which $k$ is unbounded) in correspondence with a generalized discrete Hammersley-Aldous-Diaconis model. We derive the hydrodynamic limit of these two one-dimensional models

Quadratic Mean Field Games

Mean field games were introduced independently by J-M. Lasry and P-L. Lions, and by M. Huang, R.P. Malham\'e and P. E. Caines, in order to bring a new approach to optimization problems with a large number of interacting agents. The description of such models split in two parts, one describing the evolution of the density of players in some parameter space, the other the value of a cost functional each player tries to minimize for himself, anticipating on the rational behavior of the others. Quadratic Mean Field Games form a particular class among these systems, in which the dynamics of each player is governed by a controlled Langevin equation with an associated cost functional quadratic in the control parameter. In such cases, there exists a deep relationship with the non-linear Schr\"odinger equation in imaginary time, connexion which lead to effective approximation schemes as well as a better understanding of the behavior of Mean Field Games. The aim of this paper is to serve as an introduction to Quadratic Mean Field Games and their connexion with the non-linear Schr\"odinger equation, providing to physicists a good entry point into this new and exciting field.Comment: 62 pages, 4 figure

'Phase diagram' of a mean field game

Mean field games were introduced by J-M.Lasry and P-L. Lions in the mathematical community, and independently by M. Huang and co-workers in the engineering community, to deal with optimization problems when the number of agents becomes very large. In this article we study in detail a particular example called the 'seminar problem' introduced by O.Gu\'eant, J-M Lasry, and P-L. Lions in 2010. This model contains the main ingredients of any mean field game but has the particular feature that all agent are coupled only through a simple random event (the seminar starting time) that they all contribute to form. In the mean field limit, this event becomes deterministic and its value can be fixed through a self consistent procedure. This allows for a rather thorough understanding of the solutions of the problem, through both exact results and a detailed analysis of various limiting regimes. For a sensible class of initial configurations, distinct behaviors can be associated to different domains in the parameter space . For this reason, the 'seminar problem' appears to be an interesting toy model on which both intuition and technical approaches can be tested as a preliminary study toward more complex mean field game models

Envisat's Medium Resolution Imaging Spectrometer (MERIS) Algorithm Theoretical Basis Document: FAPAR and Rectied Channels over Terrestrial Surfaces

This Algorithm Theoretical Basis document (ATBd) describes the Joint Research Center (JRC) procedure used to retrieve information of absorbed photosynthetical radiation by the vegetated terrestrial surfaces from an analysis of the Top Of Atmosphere (TOA) data acquired by MERIS. The code of the proposed algorithm takes the form of a set of several formulae which transform calibrated spectral directional reflectances into a single numerical value. These formulae are designed to extract the green Fraction of Absorbed Photosynthetically Active Radiation (FAPAR) in the plant canopy from the measurements and the rectified channels in the red and near-infrared bands. The methodology described in this document has been optimized to assess the presence on the ground of healthy live green vegetation. The main optimization procedure has been constrained to provide an estimate of FAPAR in the plant canopy, although the outputs are expected to be used in a wide range of applications. This algorithm delivers, in addition to the FAPAR product, the so-called rectified reflectance values in the red and near-infrared spectral bands. These are virtual reflectances largely decontaminated from atmospheric and angular effects. It also provides a categorization of pixel types thanks to a pre-processing identification based on multi-spectral properties. These two virtual reflectances are also computed over bare soils using specific coefficients. This document identifies the sources of input data, outlines the physical principles and mathematical background justifying this approach, describes the proposed algorithm, and lists the assumptions and limitations of this technique.JRC.DDG.H.3-Global environement monitorin

:Gamification & Serious Game : Symposium 2016, July 4 & 5

Reinforcing the bridge between local academic and applied worlds in the domain of Serious Game & Gamification, e.g. applied universities and startups. Focusing on three application domain, Helath, Social, and Education, the figure next page illustrates the variety of short talks of the symposium. The three categories of talks (among 14 corresponding short papers): five concept-oriented in green, nine demo-oriented in black, and three roundtables

Landsat 7 Enhanced Thematic Mapper JRC-FAPAR Algorithm Theoretical Basis Document

This Algorithm Theoretical Basis document (ATBd) describes the Joint Research Center (JRC)- procedure used to retrieve information of absorbed photosynthetical radiation by the vegetated terrestrial surfaces from an analysis of the Top Of Atmosphere (TOA) data acquired by the Landsat 7 Enhanced Thematic Mapper (ETM+) instrument. The corresponding data consist of eight spectral bands, with a spatial resolution of 30 meters for bands 1 to 5 and band 7 whereas the resolution for band 6 (thermal infrared) is 60 meters and resolution for band 8 (panchromatic) is 15 meters. Approximate scene size is 170 km north-south by 183 km east-west. The code of the proposed algorithm takes the form of a set of several formulae which transform calibrated spectral directional reflectances into a single numerical value. These formulae are designed to extract the Fraction of Absorbed Photosynthetically Active Radiation (FAPAR) in the plant canopy from the measurements. The methodology described in this document has been optimized to assess the presence on the ground of healthy live green vegetation. The optimization procedure has been constrained to provide an estimate of FAPAR in the plant canopy, although the outputs are expected to be used in a wide range of applications. This algorithm delivers, in addition to the FAPAR product, the so-called rectied reflectance values in the red and near-infrared spectral bands (Landsat 7 ETM+ Band 3 and Band 4). These are virtual reflectances largely decontaminated from atmospheric and angular effects. It also provides a categorization of pixel types thanks to a pre-processing identication based on multi-spectral properties.JRC.H.3-Global environement monitorin