Barycenter in Wasserstein space existence and consistency

International audienceWe study barycenters in the Wasserstein space Pp(E) of a locally compact geodesic space (E, d). In this framework, we define the barycenter of a measure P on Pp(E) as its Fréchet mean. The paper establishes its existence and states consistency with respect to P. We thus extends previous results on R^d , with conditions on P or on the sequence converging to P for consistency

24h rue Khao San (Bangkok). Enclave touristique et observation photographique

Références de la thèseLe Bigot B. (2017). Penser les rapports aux lieux dans les mobilités privilégiées : étude croisée des backpackers en Thaïlande et des hivernants au Maroc. Thèse de doctorat en Géographie, Paris 1. Cette image est extraite d’une thèse qui analyse les mobilités privilégiées internationales à partir d’une lecture spatiale croisant deux groupes : les backpackers, parfois appelés routards, et les hivernants, seniors passant une partie de l’année à l’étranger (Le Bigot, 2017)..

Weighted Frechet Means as Convex Combinations in Metric Spaces: Properties and Generalized Median Inequalities

In this short note, we study the properties of the weighted Frechet mean as a convex combination operator on an arbitrary metric space, (Y,d). We show that this binary operator is commutative, non-associative, idempotent, invariant to multiplication by a constant weight and possesses an identity element. We also treat the properties of the weighted cumulative Frechet mean. These tools allow us to derive several types of median inequalities for abstract metric spaces that hold for both negative and positive Alexandrov spaces. In particular, we show through an example that these bounds cannot be improved upon in general metric spaces. For weighted Frechet means, however, such inequalities can solely be derived for weights equal or greater than one. This latter limitation highlights the inherent difficulties associated with working with abstract-valued random variables.Comment: 7 pages, 1 figure. Submitted to Probability and Statistics Letter

The influence of reference acceptance and reuse on conversational memory traces.

International audienceNot all pieces of information mentioned during an interaction are equally accessible in speakers’ conversational memory. The current study sought to test whether 2 basic features of dialogue management (reference acceptance and reuse) affect reference recognition. Dyads of speakers were asked to discuss a route for an imaginary person, thus referring to the landmarks to be encountered. The results revealed that the participants’ conversational memory for the references produced during the interaction depended on whether these had been reused during the interaction and by whom, along with landmark visibility during the interaction. These findings have implications for partner adaptation in dialogue, which depends in part on what speakers remember of past interactions. (PsycINFO Database Record (c) 2016 APA, all rights reserved

Peaks detection and alignment for mass spectrometry data

The goal of this paper is to review existing methods for protein mass spectrometry data analysis, and to present a new methodology for automatic extraction of significant peaks (biomarkers). For the pre-processing step required for data from MALDI-TOF or SELDI- TOF spectra, we use a purely nonparametric approach that combines stationary invariant wavelet transform for noise removal and penalized spline quantile regression for baseline correction. We further present a multi-scale spectra alignment technique that is based on identification of statistically significant peaks from a set of spectra. This method allows one to find common peaks in a set of spectra that can subsequently be mapped to individual proteins. This may serve as useful biomarkers in medical applications, or as individual features for further multidimensional statistical analysis. MALDI-TOF spectra obtained from serum samples are used throughout the paper to illustrate the methodology

Beneficial effects of spatial sharing of visual attention on player's performance in a video game

International audienceIn user interface design, spatial proximity between areas of interest is considered beneficial for user's performance. This study aimed at investigating the impact of split visual attention on players' performance in a video game. The first experiment showed that closer proximity of an important element of a video game user interface, namely the score, with the most watched area of the game screen did not lead to significantly better performance. The second experiment showed that the players' performance was actually better when the score was displayed below the game screen, though the scattering of eye fixations was larger than in the other conditions. For video games user interface, spatial sharing of visual attention may lead to better players' performance

On the consistency of Fr\'echet means in deformable models for curve and image analysis

A new class of statistical deformable models is introduced to study high-dimensional curves or images. In addition to the standard measurement error term, these deformable models include an extra error term modeling the individual variations in intensity around a mean pattern. It is shown that an appropriate tool for statistical inference in such models is the notion of sample Fr\'echet means, which leads to estimators of the deformation parameters and the mean pattern. The main contribution of this paper is to study how the behavior of these estimators depends on the number n of design points and the number J of observed curves (or images). Numerical experiments are given to illustrate the finite sample performances of the procedure

Influence d'arrière-plans en mouvement sur la performance de recherche visuelle

National audienceLes interfaces visuelles de certains environnements virtuels, comme les jeux vidéo, présentent des scènes dynamiques complexes composées d'éléments d'information présentés sur des fonds structurés en mouvement. Le but de cette étude était d'observer l'impact de deux types de mouvement du fond sur la performance et les mouvements du regard d'observateurs lors d'une tâche typique de recherche visuelle. Les résultats ont montré que des fonds en mouvement simulant soit un déplacement " latéral ", soit un déplacement " en profondeur " de l'observateur modifiaient les mouvements du regard par rapport à un fond " statique ". Cependant, seul le mouvement " en profondeur " diminuait la performance de recherche visuelle par rapport au fond " statique ". Ces résultats peuvent s'expliquer par les différents mouvements compensatoires du regard, tels que le nystagmus optocinétique, déclenchés par les différents mouvements du fond

Nonlinear diffusion equations for anisotropic MHD turbulence with cross-helicity

Nonlinear diffusion equations of spectral transfer are systematically derived for anisotropic magnetohydrodynamics in the regime of wave turbulence. The background of the analysis is the asymptotic Alfv\'en wave turbulence equations from which a differential limit is taken. The result is a universal diffusion-type equation in ${\bf k}$-space which describes in a simple way and without free parameter the energy transport perpendicular to the external magnetic field ${\bf B_0}$ for transverse and parallel fluctuations. These equations are compatible with both the thermodynamic equilibrium and the finite flux spectra derived by Galtier et al. (2000); it improves therefore the model built heuristically by Litwick \& Goldreich (2003) for which only the second solution was recovered. This new system offers a powerful description of a wide class of astrophysical plasmas with non-zero cross-helicity.Comment: 20 pages, 3 figure