Conservation of geometric structures for non-homogeneous inviscid incompressible fluids

We obtain a result about propagation of geometric properties for solutions of the non-homogeneous incompressible Euler system in any dimension $N\geq2$. In particular, we investigate conservation of striated and conormal regularity, which is a natural way of generalizing the 2-D structure of vortex patches. The results we get are only local in time, even in the dimension N=2; however, we provide an explicit lower bound for the lifespan of the solution. In the case of physical dimension N=2 or 3, we investigate also propagation of H\"older regularity in the interior of a bounded domain

A continuum-tree-valued Markov process

We present a construction of a L\'evy continuum random tree (CRT) associated with a super-critical continuous state branching process using the so-called exploration process and a Girsanov's theorem. We also extend the pruning procedure to this super-critical case. Let $\psi$ be a critical branching mechanism. We set $\psi_\theta(\cdot)=\psi(\cdot+\theta)-\psi(\theta)$. Let $\Theta=(\theta_\infty,+\infty)$ or $\Theta=[\theta_\infty,+\infty)$ be the set of values of $\theta$ for which $\psi_\theta$ is a branching mechanism. The pruning procedure allows to construct a decreasing L\'evy-CRT-valued Markov process (\ct_\theta,\theta\in\Theta), such that $\mathcal{T}_\theta$ has branching mechanism $\psi_\theta$. It is sub-critical if $\theta>0$ and super-critical if $\theta<0$. We then consider the explosion time $A$ of the CRT: the smaller (negative) time $\theta$ for which $\mathcal{T}_\theta$ has finite mass. We describe the law of $A$ as well as the distribution of the CRT just after this explosion time. The CRT just after explosion can be seen as a CRT conditioned not to be extinct which is pruned with an independent intensity related to $A$. We also study the evolution of the CRT-valued process after the explosion time. This extends results from Aldous and Pitman on Galton-Watson trees. For the particular case of the quadratic branching mechanism, we show that after explosion the total mass of the CRT behaves like the inverse of a stable subordinator with index 1/2. This result is related to the size of the tagged fragment for the fragmentation of Aldous' CRT

Fast learning rates in statistical inference through aggregation

We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set $\mathcal{G}$ up to the smallest possible additive term, called the convergence rate. When the reference set is finite and when $n$ denotes the size of the training data, we provide minimax convergence rates of the form $C(\frac{\log|\mathcal{G}|}{n})^v$ with tight evaluation of the positive constant $C$ and with exact $0<v\le1$, the latter value depending on the convexity of the loss function and on the level of noise in the output distribution. The risk upper bounds are based on a sequential randomized algorithm, which at each step concentrates on functions having both low risk and low variance with respect to the previous step prediction function. Our analysis puts forward the links between the probabilistic and worst-case viewpoints, and allows to obtain risk bounds unachievable with the standard statistical learning approach. One of the key ideas of this work is to use probabilistic inequalities with respect to appropriate (Gibbs) distributions on the prediction function space instead of using them with respect to the distribution generating the data. The risk lower bounds are based on refinements of the Assouad lemma taking particularly into account the properties of the loss function. Our key example to illustrate the upper and lower bounds is to consider the $L_q$-regression setting for which an exhaustive analysis of the convergence rates is given while $q$ ranges in $[1;+\infty[$.Comment: Published in at http://dx.doi.org/10.1214/08-AOS623 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Convergence in law in the second Wiener/Wigner chaos

Let L be the class of limiting laws associated with sequences in the second Wiener chaos. We exhibit a large subset L_0 of L satisfying that, for any F_infinity in L_0, the convergence of only a finite number of cumulants suffices to imply the convergence in law of any sequence in the second Wiener chaos to F_infinity. This result is in the spirit of the seminal paper by Nualart and Peccati, in which the authors discovered the surprising fact that convergence in law for sequences of multiple Wiener-It\^o integrals to the Gaussian is equivalent to convergence of just the fourth cumulant. Also, we offer analogues of this result in the case of free Brownian motion and double Wigner integrals, in the context of free probability.Comment: 14 pages. This version corrects an error which, unfortunately, appears in the published version in EC

A new characterization of Talagrand's transport-entropy inequalities and applications

We show that Talagrand's transport inequality is equivalent to a restricted logarithmic Sobolev inequality. This result clarifies the links between these two important functional inequalities. As an application, we give the first proof of the fact that Talagrand's inequality is stable under bounded perturbations.Comment: Published in at http://dx.doi.org/10.1214/10-AOP570 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Résultats de l’enquête sur les pratiques et besoins documentaires auprès des doctorants et chercheurs du PRES Université Paris-Est

Le réseau documentaire UPEdoc, composé des services communs de documentation et services documentaires des établissements membres du PRES Université Paris-Est, a initié en 2010 un projet de portail documentaire pour le développement d\u27 une offre cohérente. Dans cette perspective, une étude a été diligentée en décembre dernier auprès des chercheurs et doctorants pour connaître leurs usages et besoins en matière documentaire. Elle a rencontré un intérêt certain puisque sur les 3 000 chercheurs et doctorants sollicités, près de 800 réponses ont été enregistrées. Ce document présente les résultats complets de l\u27enquête

Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum monotone operators

We propose a primal-dual splitting algorithm for solving monotone inclusions involving a mixture of sums, linear compositions, and parallel sums of set-valued and Lipschitzian operators. An important feature of the algorithm is that the Lipschitzian operators present in the formulation can be processed individually via explicit steps, while the set-valued operators are processed individually via their resolvents. In addition, the algorithm is highly parallel in that most of its steps can be executed simultaneously. This work brings together and notably extends various types of structured monotone inclusion problems and their solution methods. The application to convex minimization problems is given special attention

Cardiovascular effects of dietary salt intake in aged healthy cats: a 2-year prospective randomized, blinded, and controlled study

High salt dry expanded diets are commercially available for cats to increase water intake and urine volume, as part of the prevention or treatment of naturally occurring urinary stone formation (calcium oxalates and struvites). However, chronic high salt intake may have potential cardiovascular adverse effects in both humans, especially in aging individuals, and several animal models. The objective of this prospective, randomized, blinded, and controlled study was to assess the long-term cardiovascular effects of high salt intake in healthy aged cats. Twenty healthy neutered cats (10.1±2.4 years) were randomly allocated into 2 matched groups. One group was fed a high salt diet (3.1 g/Mcal sodium, 5.5 g/Mcal chloride) and the other group a control diet of same composition except for salt content (1.0 g/Mcal sodium, 2.2 g/Mcal chloride). Clinical examination, systolic and diastolic arterial blood pressure measurements, standard transthoracic echocardiography and conventional Doppler examinations were repeatedly performed on non-sedated cats by trained observers before and over 24 months after diet implementation. Radial and longitudinal velocities of the left ventricular free wall and the interventricular septum were also assessed in systole and diastole using 2-dimensional color tissue Doppler imaging. Statistics were performed using a general linear model. No significant effect of dietary salt intake was observed on systolic and diastolic arterial blood pressure values. Out of the 33 tested imaging variables, the only one affected by dietary salt intake was the radial early on late diastolic velocity ratio assessed in the endocardium of the left ventricular free wall, statistically lower in the high salt diet group at 12 months only (P = 0.044). In conclusion, in this study involving healthy aged cats, chronic high dietary salt intake was not associated with an increased risk of systemic arterial hypertension and myocardial dysfunction, as observed in some elderly people, salt-sensitive patients and animal models