Why Global Integration May Lead to Terrorism: An Evolutionary Theory of Mimetic Rivalry

We study the emergence of the recent form of terrorism using evolutionary game theory. The model is an economic interpretation of René Girard's theory of mimetic rivalry. This theory presents terrorism as the result of competition between countries, when the desire to imitate the leading country is frustrated by the impossibility of doing so. We define a multi-country setup where interaction takes place in an international trade game, which is a coordination game. Countries follow a simple behavioral rule trying to reduce the gap between the maximal payoff obtained and their own payoff. In a coordination game, this may lead to mimetic rivalry behavior, that is the deliberate choice of a strategy degrading the situation of the leading country. Paradoxically, we find that the desire of convergence may lead to a more partitioned world economy.Terrorism Evolutionary game theory Mimetic Rivalry Risk-dominance

Deviation results for Mandelbrot's multiplicative cascades with exponential tails

Let $W$ be a nonnegative random variable with expectation $1$. For all $r \geqslant 2$, we consider the total mass $Z_r^\infty$ of the associated Mandelbrot multiplicative cascade in the $r$-ary tree. For all $n \geqslant 1$, we also consider the total mass $Z_r^n$ of the measure at height $n$ in the $r$-ary tree. Liu, Rio, Rouault \cite{lrr,liu2000limit,Rouault04} established large deviation results for $(Z_r^n)_{r \geqslant 2}$ for all $n \in [[1,\infty[[$ (resp., for $n = \infty$) in case $W$ has an everywhere finite cumulant generating function $\Lambda_W$ (resp., $W$ is bounded). Here, we extend these results to the case where $\Lambda_W$ is only finite on a neighborhood of zero. And we establish all deviation results (moderate, large, and very large deviations). It is noticeable that we obtain nonconvex rate functions. Moreover, our proof of upper bounds of deviations for $(Z_r^\infty)_{r \geqslant 2}$ rely on the moment bound instead of the standard Chernoff bound

Fusarium head blight: epidemiological origin of the effects of cultural practices on head blight attacks and the production of mycotoxins by Fusarium in wheat grains

International audienceFusarium head blight is an ancient disease and is very common throughout the world. In this article, we review current knowledge concerning the effects of cultural practices on the development of head blight and the production of toxins in the field. The qualitative effects of these practices on the severity of the disease and/or the production of toxins are in the process of being elucidated but, in many cases, detailed studies have not yet been carried out or conflicting results have been obtained. However, it should be noted that these effects have not yet been quantified. Three different cultural practices are today considered to be of prime importance for combating this disease and the production of mycotoxins: deep tillage, the choice of the preceding crop in the rotation and the choice of appropriate cultivar, as varietal effects exist

Sensitivity indices for multivariate outputs

International audienceWe define and study a generalization of Sobol sensitivity indices for the case of a vector output.Nous définissons et étudions une généralisation des indices de Sobol pour des sorties vectorielles

Sensitivity analysis for multidimensional and functional outputs

International audienceLet $X:=(X_1, \ldots, X_p)$ be random objects (the inputs), defined on some probability space $(\Omega,{\mathcal{F}}, \mathbb P)$ and valued in some measurable space $E=E_1\times\ldots \times E_p$. Further, let $Y:=Y = f(X_1, \ldots, X_p)$ be the output. Here, $f$ is a measurable function from $E$ to some Hilbert space $\mathbb{H}$ ($\mathbb{H}$ could be either of finite or infinite dimension). In this work, we give a natural generalization of the Sobol indices (that are classically defined when $Y\in\R$ ), when the output belongs to $\mathbb{H}$. These indices have very nice properties. First, they are invariant. under isometry and scaling. Further they can be, as in dimension $1$, easily estimated by using the so-called Pick and Freeze method. We investigate the asymptotic behaviour of such estimation scheme

Estimation of the Sobol indices in a linear functional multidimensional model

International audienceWe consider a functional linear model where the explicative variables are stochastic processes taking values in a Hilbert space, the main example is given by Gaussian processes in L2([0; 1]). We propose estimators of the Sobol indices in this functional linear model. Our estimators are based on Ustatistics. We prove the asymptotic normality and the efficiency of our estimators and we compare them from a theoretical and practical point of view with classical estimators of Sobol indices

Atome Hôtel : un web-documentaire pour revisiter le tableau périodique des éléments

Rendre attractif et ludique, le tableau périodique des éléments, cet icône de la chimie : tel est l’objectif que s’est fixé le service de culture scientifique de l’université de Montpellier. Les initiateurs de l'opération présentent les différentes étapes de ce projet qui a finalement pris la forme d’un web-documentaire, fruit d’une collaboration étroite entre des scientifiques et une équipe créative spécialisée dans le multimédia

New estimation of Sobol' indices using kernels

In this work, we develop an approach mentioned by da Veiga and Gamboa in 2013. It consists in extending the very interestingpoint of view introduced in \cite{gine2008simple} to estimate general nonlinear integral functionals of a density on the real line, by using empirically a kernel estimator erasing the diagonal terms. Relaxing the positiveness assumption on the kernel and choosing a kernel of order large enough, we are able to prove a central limit theorem for estimating Sobol' indices of any order (the bias is killed thanks to this signed kernel)