Source coding with escort distributions and Renyi entropy bounds

We discuss the interest of escort distributions and R\'enyi entropy in the context of source coding. We first recall a source coding theorem by Campbell relating a generalized measure of length to the R\'enyi-Tsallis entropy. We show that the associated optimal codes can be obtained using considerations on escort-distributions. We propose a new family of measure of length involving escort-distributions and we show that these generalized lengths are also bounded below by the R\'enyi entropy. Furthermore, we obtain that the standard Shannon codes lengths are optimum for the new generalized lengths measures, whatever the entropic index. Finally, we show that there exists in this setting an interplay between standard and escort distributions

A simple probabilistic construction yielding generalized entropies and divergences, escort distributions and q-Gaussians

We give a simple probabilistic description of a transition between two states which leads to a generalized escort distribution. When the parameter of the distribution varies, it defines a parametric curve that we call an escort-path. The R\'enyi divergence appears as a natural by-product of the setting. We study the dynamics of the Fisher information on this path, and show in particular that the thermodynamic divergence is proportional to Jeffreys' divergence. Next, we consider the problem of inferring a distribution on the escort-path, subject to generalized moments constraints. We show that our setting naturally induces a rationale for the minimization of the R\'enyi information divergence. Then, we derive the optimum distribution as a generalized q-Gaussian distribution

An entropic view of Pickands' theorem

It is shown that distributions arising in Renyi-Tsallis maximum entropy setting are related to the Generalized Pareto Distributions (GPD) that are widely used for modeling the tails of distributions. The relevance of such modelization, as well as the ubiquity of GPD in practical situations follows from Balkema-De Haan-Pickands theorem on the distribution of excesses (over a high threshold). We provide an entropic view of this result, by showing that the distribution of a suitably normalized excess variable converges to the solution of a maximum Tsallis entropy, which is the GPD. This highlights the relevance of the so-called Tsallis distributions in many applications as well as some relevance to the use of the corresponding entropy.Comment: 4 pages, accepted to ISIT0

Array processing with model adequation

This paper is an introduction to the array processing problems analysed in this special issue . The objective is twofold . First, to give a simple mathematical model and a formalism ranging the applications presented in the issue . Second, to give some elements on several "classic" methods of array processing, classic in the sense that they do not take into account model errors problems .Cet article constitue une introduction aux problèmes de calibration en traitement d'antenne analysés dans ce numéro spécial. Il a un double objet: d'une part donner un modèle mathématique simple et un formalisme unique couvrant l'ensemble des applications présentées dans ce document; et d'autre part donner quelques éléments sur plusieurs méthodes "classiques" en traitement d'antenne, classiques dans le sens où elles ne tiennent pas compte des problèmes d'erreurs de modèl

On some entropy functionals derived from R\'enyi information divergence

We consider the maximum entropy problems associated with R\'enyi $Q$-entropy, subject to two kinds of constraints on expected values. The constraints considered are a constraint on the standard expectation, and a constraint on the generalized expectation as encountered in nonextensive statistics. The optimum maximum entropy probability distributions, which can exhibit a power-law behaviour, are derived and characterized. The R\'enyi entropy of the optimum distributions can be viewed as a function of the constraint. This defines two families of entropy functionals in the space of possible expected values. General properties of these functionals, including nonnegativity, minimum, convexity, are documented. Their relationships as well as numerical aspects are also discussed. Finally, we work out some specific cases for the reference measure $Q(x)$ and recover in a limit case some well-known entropies

On a (\beta,q)-generalized Fisher information and inequalities involving q-Gaussian distributions

In the present paper, we would like to draw attention to a possible generalized Fisher information that fits well in the formalism of nonextensive thermostatistics. This generalized Fisher information is defined for densities on $\mathbb{R}^{n}.$ Just as the maximum R\'enyi or Tsallis entropy subject to an elliptic moment constraint is a generalized q-Gaussian, we show that the minimization of the generalized Fisher information also leads a generalized q-Gaussian. This yields a generalized Cram\'er-Rao inequality. In addition, we show that the generalized Fisher information naturally pops up in a simple inequality that links the generalized entropies, the generalized Fisher information and an elliptic moment. Finally, we give an extended Stam inequality. In this series of results, the extremal functions are the generalized q-Gaussians. Thus, these results complement the classical characterization of the generalized q-Gaussian and introduce a generalized Fisher information as a new information measure in nonextensive thermostatistics.Comment: v2: corrected equation (A5

Experimental Study of electron acceleration by plasma beat-waves with Nd lasers

International audienceWe have observed the acceleration of electrons by a beat-wave generated in a deuterium plasma by two Nd-YAG and Nd-YLF laser wavelengths. Electrons injected at an energy of 3.3 MeV are observed to be accelerated up to 4.7 MeV after the plasma. The energy gain is compatible with a peak electric field of the order of 1.2 GV/m. The experiment has been performed with different injection energies, from 2.5 to 3.3 MeV, with different plasma dimensions, and with different laser intensitie

RNA interference therapeutics targeting angiotensinogen ameliorate preeclamptic phenotype in rodent models

Preeclampsia, with the hallmark features of new-onset hypertension and proteinuria after 20 weeks of gestation, is a major cause of fetal and maternal morbidity and mortality. Studies have demonstrated a role for the renin-angiotensin system (RAS) in its pathogenesis; however, small-molecule RAS blockers are contraindicated because of fetal toxicity. We evaluated whether siRNA targeting maternal hepatic angiotensinogen (Agt) could ameliorate symptoms of preeclampsia without adverse placental or fetal effects in 2 rodent models. The first model used a cross of females expressing human Agt with males expressing human renin, resulting in upregulation of the circulating and uteroplacental RAS. The second model induced ischemia/reperfusion injury and subsequent local and systemic inflammation by surgically reducing placental blood flow midgestation (reduced uterine perfusion pressure [RUPP]). These models featured hypertension, proteinuria, and fetal growth restriction, with altered biomarkers. siRNA treatment ameliorated the preeclamptic phenotype in both models, reduced blood pressure, and improved intrauterine growth restriction, with no observed deleterious effects on the fetus. Treatment also improved the angiogenic balance and proteinuria in the transgenic model, and it reduced angiotensin receptor activating antibodies in both. Thus, an RNAi therapeutic targeting Agt ameliorated the clinical sequelae and improved fetal outcomes in 2 rodent models of preeclampsia

Intercalibration of the barrel electromagnetic calorimeter of the CMS experiment at start-up

Calibration of the relative response of the individual channels of the barrel electromagnetic calorimeter of the CMS detector was accomplished, before installation, with cosmic ray muons and test beams. One fourth of the calorimeter was exposed to a beam of high energy electrons and the relative calibration of the channels, the intercalibration, was found to be reproducible to a precision of about 0.3%. Additionally, data were collected with cosmic rays for the entire ECAL barrel during the commissioning phase. By comparing the intercalibration constants obtained with the electron beam data with those from the cosmic ray data, it is demonstrated that the latter provide an intercalibration precision of 1.5% over most of the barrel ECAL. The best intercalibration precision is expected to come from the analysis of events collected in situ during the LHC operation. Using data collected with both electrons and pion beams, several aspects of the intercalibration procedures based on electrons or neutral pions were investigated

Rapid Acoustic Survey for Biodiversity Appraisal

Biodiversity assessment remains one of the most difficult challenges encountered by ecologists and conservation biologists. This task is becoming even more urgent with the current increase of habitat loss. Many methods–from rapid biodiversity assessments (RBA) to all-taxa biodiversity inventories (ATBI)–have been developed for decades to estimate local species richness. However, these methods are costly and invasive. Several animals–birds, mammals, amphibians, fishes and arthropods–produce sounds when moving, communicating or sensing their environment. Here we propose a new concept and method to describe biodiversity. We suggest to forego species or morphospecies identification used by ATBI and RBA respectively but rather to tackle the problem at another evolutionary unit, the community level. We also propose that a part of diversity can be estimated and compared through a rapid acoustic analysis of the sound produced by animal communities. We produced α and β diversity indexes that we first tested with 540 simulated acoustic communities. The α index, which measures acoustic entropy, shows a logarithmic correlation with the number of species within the acoustic community. The β index, which estimates both temporal and spectral dissimilarities, is linearly linked to the number of unshared species between acoustic communities. We then applied both indexes to two closely spaced Tanzanian dry lowland coastal forests. Indexes reveal for this small sample a lower acoustic diversity for the most disturbed forest and acoustic dissimilarities between the two forests suggest that degradation could have significantly decreased and modified community composition. Our results demonstrate for the first time that an indicator of biological diversity can be reliably obtained in a non-invasive way and with a limited sampling effort. This new approach may facilitate the appraisal of animal diversity at large spatial and temporal scales