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

Estimating river discharge from earth Observation measurement of river surface hydraulic variables

River discharge is a key variable for quantifying the water cycle, its fluxes and stocks at different scales. These scales range from a local scale for the efficient management of water resources to a global scale for the monitoring of climate change. Therefore, developing Earth observation (EO) techniques for the measurement or estimation of river discharge poses a major challenge. A key question deals with the possibility of deriving river discharge values from EO surface variables (width, level, slope, and velocity are the only such variables accessible through EO) without any in situ measurement. Based on a literature study and original investigations, this study explores the possibilities of estimating river discharge from water surface variables. The proposed method relies on limiting assumptions to simplify river flow equations to obtain the values of the hydraulic parameters at a given river station without using ground measurements. Once the hydraulic parameters are identified, the method allows the estimation of the river discharge corresponding to a set of surface measurements of hydraulic variables

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

Beam tests of the trigger and digital processing electronics for the electromagnetic calorimeter of the CMS experiment

A prototype of the trigger and digital processing electronics for the electromagnetic calorimeter of the CMS experiment, coupled to a prototype of the PbWO4 crystal calorimeter, was tested during summer 96 in the H4 beamline at the CERN SPS. A very successful operation was achieved for this system, which runs in synchronous and pipelined mode at the LHC clock frequency, and performs the basic trigger and data acquisition functions needed in the CMS electromagnetic calorimeter. The performance of the trigger front-end electronics is well within the established requirements: a highly efficient bunch crossing identification ( > 99.9%), a good trigger energy resolution ( s/E ~9%/sq( E)+2%) and a highly efficient electron cluster shape identification ( ~99%) have been achieved. The FERMI digitizing system based on a dynamic analog compressor and a sampling ADC showed a very good perform ance, in particular the energy resolution for 150 GeV electrons was 0.54%, equal to the resolution obtained with a conventional charge integration ADC system

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