Recovering measures from approximate values on balls

In a metric space $(X,d)$ we reconstruct an approximation of a Borel measure $\mu$ starting from a premeasure $q$ defined on the collection of closed balls, and such that $q$ approximates the values of $\mu$ on these balls. More precisely, under a geometric assumption on the distance ensuring a Besicovitch covering property, and provided that there exists a Borel measure on $X$ satisfying an asymptotic doubling-type condition, we show that a suitable packing construction produces a measure ${\hat\mu}^{q}$ which is equivalent to $\mu$. Moreover we show the stability of this process with respect to the accuracy of the initial approximation. We also investigate the case of signed measures.Comment: 29 pages, 5 figure

Quantitative conditions of rectifiability for varifolds

46 pagesOur purpose is to state quantitative conditions ensuring the rectifiability of a $d$--varifold $V$ obtained as the limit of a sequence of $d$--varifolds $(V_i)_i$ which need not to be rectifiable. More specifically, we introduce a sequence $\left\lbrace \mathcal{E}_i \right\rbrace_i$ of functionals defined on $d$--varifolds, such that if $\displaystyle \sup_i \mathcal{E}_i (V_i) < +\infty$ and $V_i$ satisfies a uniform density estimate at some scale $\beta_i$, then $V = \lim_i V_i$ is $d$--rectifiable. \noindent The main motivation of this work is to set up a theoretical framework where curves, surfaces, or even more general $d$--rectifiable sets minimizing geometrical functionals (like the length for curves or the area for surfaces), can be approximated by ''discrete'' objects (volumetric approximations, pixelizations, point clouds etc.) minimizing some suitable ''discrete'' functionals

Gender research from multiple disciplines : profiles, commitments and interrelations in an interdisciplinary group

One of the greatest difficulties in interdisciplinary work is being able to focus on a common project when efforts and hierarchies do not advance in the same direction. In this paper, we describe a particular group, Genre Egalité et Mixité, and its operation. This interdisciplinary research group on gender in education, created at the University of Lyon, explores the issue along three axes: professor training, scientific research and the creation of a specialised library. Coming from several disciplines, researchers have different profiles and, consequently, different conceptions of feminism, which makes the team unique

A gas dynamics scheme for a two moments model of radiative transfer

We address the discretization of the Levermore's two moments and entropy model of the radiative transfer equation. We present a new approach for the discretization of this model: first we rewrite the moment equations as a Compressible Gas Dynamics equation by introducing an additionnal quantity that plays the role of a density. After that we discretize using a Lagrange-projection scheme. The Lagrange-projection scheme permits us to incorporate the source terms in the fluxes of an acoustic solver in the Lagrange step, using the well-known "piecewise steady approximation" and thus to capture correctly the diffusion regime. Moreover we show that the discretization is entropic and preserve the flux-limited property of the moment model. Numerical examples illustrate the feasability of our approach

An asymptotic preserving scheme for Hydrodynamics Radiative Transfert Models

In this paper, we shall propose a numerical scheme consisting of two steps: the first based relaxation method and the second on the so called well balanced scheme. The derivation of the scheme relies on the resolution of the stationnary Riemann problem with source terms. The obtained scheme is compatible with the diffusive regime of hydrodynamics radiative transfert models. Some numericalresults are shown

Tracking fast changing non-stationary distributions with a topologically adaptive neural network: Application to video tracking

International audienceIn this paper, an original method named GNG-T, extended from GNG-U algorithm by Fritzke is presented. The method performs continuously vector quantization over a distribution that changes over time. It deals with both sudden changes and continuous ones, and is thus suited for video tracking framework, where continuous tracking is required as well as fast adaptation to incoming and outgoing people. The central mechanism relies on the management of quantization resolution, that cope with stopping condition problems of usual Growing Neural Gas inspired methods. Application to video tracking is briefly presented

Discovering the phase of a dynamical system from a stream of partial observations with a multi-map self-organizing architecture

International audienceThis paper presents a self-organizing architecture made of several maps, implementing a recurrent neural network to cope with partial observations of the phase of some dynamical system. The purpose of self-organization is to set up a distributed representation of the actual phase, although the observations received from the system are ambiguous (i.e. the same observation may correspond to distinct phases). The setting up of such a representation is illustrated by experiments, and then the paper concludes on extensions toward adaptive state representations for partially observable Markovian decision processes

Tracking non-stationary dynamical system phase using multi-map and temporal self-organizing architecture

International audienceThis paper presents a multi-map recurrent neural architecture, exhibiting self-organization to deal with the partial observations of the phase of some dynamical system. The architecture captures the dynamics of the system by building up a representation of its phases, coping with ambiguity when distinct phases provide identical observations. The architecture updates the resulted representation to adapt to changes in its dynamics due to self-organization property. Experiments illustrate the dynamics of the architecture when fulfilling this goal