A Wright-Fisher model with indirect selection

We study a generalization of the Wright--Fisher model in which some individuals adopt a behavior that is harmful to others without any direct advantage for themselves. This model is motivated by studies of spiteful behavior in nature, including several species of parasitoid hymenoptera in which sperm-depleted males continue to mate de- spite not being fertile. We first study a single reproductive season, then use it as a building block for a generalized Wright--Fisher model. In the large population limit, for male-skewed sex ratios, we rigorously derive the convergence of the renormalized process to a diffusion with a frequency-dependent selection and genetic drift. This allows a quantitative comparison of the indirect selective advantage with the direct one classically considered in the Wright--Fisher model. From the mathematical point of view, each season is modeled by a mix between samplings with and without replacement, and analyzed by a sort of "reverse numerical analysis", viewing a key recurrence relation as a discretization scheme for a PDE. The diffusion approximation is then obtained by classical methods

Ergodicity of the zigzag process

The zigzag process is a Piecewise Deterministic Markov Process which can be used in a MCMC framework to sample from a given target distribution. We prove the convergence of this process to its target under very weak assumptions, and establish a central limit theorem for empirical averages under stronger assumptions on the decay of the target measure. We use the classical "Meyn-Tweedie" approach. The main difficulty turns out to be the proof that the process can indeed reach all the points in the space, even if we consider the minimal switching rates

Functional inequalities and uniqueness of the Gibbs measure -- from log-Sobolev to Poincar\'e

In a statistical mechanics model with unbounded spins, we prove uniqueness of the Gibbs measure under various assumptions on finite volume functional inequalities. We follow the approach of G. Royer (1999) and obtain uniqueness by showing convergence properties of a Glauber-Langevin dynamics. The result was known when the measures on the box $[-n,n]^d$ (with free boundary conditions) satisfied the same logarithmic Sobolev inequality. We generalize this in two directions: either the constants may be allowed to grow sub-linearly in the diameter, or we may suppose a weaker inequality than log-Sobolev, but stronger than Poincar\'e. We conclude by giving a heuristic argument showing that this could be the right inequalities to look at

Quantitative ergodicity for some switched dynamical systems

We provide quantitative bounds for the long time behavior of a class of Piecewise Deterministic Markov Processes with state space Rd \times E where E is a finite set. The continuous component evolves according to a smooth vector field that switches at the jump times of the discrete coordinate. The jump rates may depend on the whole position of the process. Under regularity assumptions on the jump rates and stability conditions for the vector fields we provide explicit exponential upper bounds for the convergence to equilibrium in terms of Wasserstein distances. As an example, we obtain convergence results for a stochastic version of the Morris-Lecar model of neurobiology

Gérer le risque dans une métropole : le système français face à l'inondation dans l’agglomération parisienne

Le propos de cet article est de montrer qu’une des principales difficultés de gestion des inondations en ville réside dans la faible prise en compte des interactions entre le risque et la spécificité de l'espace urbain. La situation est encore plus complexe dans le cas de l'agglomération parisienne, où les dynamiques métropolitaines viennent s’ajouter aux dynamiques urbaines classiques. Il s’agit donc d'étudier les outils de gestion existants ainsi que les systèmes d’acteurs auxquels ils renvoient, afin de souligner les limites du dispositif français et de proposer des pistes de réflexion pour l’élaboration d’une gouvernance des inondations qui intègre le risque dans les dynamiques territoriales de la métropole.The focus of this paper is to discuss the difficulties with flood hazard management in urban areas. The main problem is that interactions between flood risk and spatial characteristics of cities are barely taken into consideration. The case of the Parisian metropolitan area is even more complicated as metropolitan and local urban dynamics combine. We examine the management tools currently being used and the system of actors involved to show the limits of the French operations. We then explore ways to develop a governance framework that takes flood hazard into account when considering metropolitan land development

Robustesse des partitions de textes : une exploration autour de l'apport des motifs de mots.

International audienceLes partitions d'ensembles de textes peuvent être d'origine endogène - provenir d'une classification non supervisée - ou exogène, par catégorisation a priori des textes par des experts. Dans les deux cas se pose la question du caractère généralisable des catégories qu'elles expriment. Dans le cadre de la recherche d'une meilleure catégorisation des domaines scientifiques, et à partir d'un extrait significatif de la base de référence Web of Science, nous avons appliqué la méthodologie classique de l'apprentissage automatique (sous-corpus distincts: apprentissage, ajustement, test) à une partition non supervisée du domaine de la génomique. Les résultats sur cet ensemble de 120 000 résumés d'articles font la preuve d'une qualité et d'une robustesse accrues quand on caractérise chaque partition, plutôt que par de simples termes, par des motifs de termes. Ces motifs spécifiques de chaque catégorie sont extraits par notre méthode Midova de sélection et détermination de liaisons complexes entre variables booléennes par "pulvérisation" des effectifs impliqués dans chaque relation n-aire

Robustesse des classements bibliométriques, à travers la convergence des thèmes obtenus par citations et lexiques : une méthode hybride pour une représentation mixte

17 pagesNational audienceAlors que les méthodes d'analyse multidimensionnelles habituelles considèrent les objets étudiés sous un seul point de vue, nous présentons ici une exploration méthodologique autour de la prise en compte de points de vue multiples, dans le prolongement d'une étude précédente de 4 années de nanosciences sur le WoS. Nous avons utilisé une méthode hybride entre clustering et décomposition matricielle pour comparer deux partitions des articles, l'une, lexicale, à partir de l'extraction de termes simples et composés, l'autre à partir des citations émises. Méthode qui nous a permis de placer les clusters des deux types dans un espace commun, et de conclure en présentant son apport par rapport à nos résultats antérieurs

The Extraction of Community Structures from Publication Networks to Support Ethnographic Observations of Field Differences in Scientific Communication

The scientific community of researchers in a research specialty is an important unit of analysis for understanding the field specific shaping of scientific communication practices. These scientific communities are, however, a challenging unit of analysis to capture and compare because they overlap, have fuzzy boundaries, and evolve over time. We describe a network analytic approach that reveals the complexities of these communities through examination of their publication networks in combination with insights from ethnographic field studies. We suggest that the structures revealed indicate overlapping sub- communities within a research specialty and we provide evidence that they differ in disciplinary orientation and research practices. By mapping the community structures of scientific fields we aim to increase confidence about the domain of validity of ethnographic observations as well as of collaborative patterns extracted from publication networks thereby enabling the systematic study of field differences. The network analytic methods presented include methods to optimize the delineation of a bibliographic data set in order to adequately represent a research specialty, and methods to extract community structures from this data. We demonstrate the application of these methods in a case study of two research specialties in the physical and chemical sciences.Comment: Accepted for publication in JASIS