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

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

Strategic Niche Management (SNM) beyond sustainability. An exploration of key findings of SNM through the lens of ICT and privacy

Recently the governance of socio-technical transitions to sustainability is gaining attention in the field of innovation studies. One particular approach is that of Strategic Niche Management (SNM), which advocates the creation of protected space to experiment with radically new sustainable socio-technical practices. This paper contributes by asking whether this approach is also useful for analysis and governance of other types of socially desirable change. This question is addressed through a review of six key-findings of Strategic Niche Management and an original case study in the field of Near Field Communication (NFC) technologies for mobile payment. The social value at stake in this case is not sustainability but privacy. We draw three main conclusions. First, we find that the key-findings and concepts in SNM for sustainability are helpful to understand and interpret much of the data collected for the NFC case and privacy. However, there are notable differences in each of the key-findings, i.e findings related to a) the local-global distinction in SNM, b) expectations, c) social networks, d) learning, e) protection, and f) niche-regime interactions. Second, in relation to governance, the role of sustainability values (being a promising value to pursue) and privacy values (being a bottom-line value to defend) are notably different. Third, these differences result in different roles of public bodies in niche development. The paper ends with discussing the consequences for SNM for sustainability research and future research topics.Strategic Niche Management, sustainability, NFC, mobile payment, privacy

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

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

S'era d'Escorca (Escorca, Mallorca) i algunes cavitats veïnes

&#091;spa&#093; Esta nota tiene como principal objetivo la descripción morfogénica de tres fenómenos kársticos situados en las cercanías del predio de Escorca (Mallorca), aportándose al mismo tiempo informaciones adicionales sobre aspectos específicos de cada uno de ellos. Una de las formas kársticas que nos interesan es S'Era d'Escorca; se trata de una dolina de subsidencia desarrollada, sobre una formación superficial coluvial, a causa de procesos de disolución afectando a materiales infra-yacentes . Es de destacar la leyenda que gravita desde hace siglos sobre este accidente geográfico. Son descritas también dos simas cercanas a S'Era d'Escorca, las cuales albergan una interesante flora. Por sus dimensiones, sobresale el Avenc d'Escorca o de Sa Vessa que alcanza los -139 metros de profundidad, poseyendo un pozo inicial de 11 7 metros de vertical absoluta. Se presta especial atención a clarificar la toponimia de las formas kársticas que nos ocupan

Avenc de s'Aigo

&#091;spa&#093; Se describe el Avenc de S'Aigo, localizado en la Coma de Mortitx (Escorca, Mallorca). Fue explorado y topografiado por primera vez en 1970 descendiéndose un amplio pozo de 110 m. de profundidad. Exploraciones posteriores, realizadas en 1981 y 1982, han dado como resultado el hallazgo de una gran sala situada en un lateral del pozo inicial. Asimismo se encontró una nueva continuación por la que se alcanza una cota de -133 metros. Se adjunta topografía y ficha técnica de la sima.&#091;eng&#093; It is described the Avenc de S'Aigo, located in the Coma de Mortitx (Escorca, Mallorca). It was explored and topographied for the first time in 1970, going down through a'wide pit, 110 meters deep. Further explorations performed in 1981 and 1982 have given as results the discovery of a great room placed in one lateral of the initial pit. Likewise it was found a new continuation by which is reached the -133 meters depth. It is enclosed the topography and equipment card of this pothole