Viability, Optimality and Stability of Dynamical Systems and Estimation of Convergence of Numerical Schemes

AMS subject classification: 49N35,49N55,65Lxx.We present in this paper some recent developments dealing with dynamical controlled systems with state constraints. After recalling the basic frame of Viability Theory and it numerical aspects, we estimate the convergence of numerical schemes for computing the optimal time for target problem. We give also a relaxation result for decomposable problems. These properties are enhanced through the study of the Norvegian Fishermen problem arising in Dynamic of Population. Another interesting application of this approach is shortly presented when considering the approximation of the so-called the minimal time of crisis. This appears for problems where some constraints are “soft” (reversibility) and others are “hard” (irreversibility)

An Algorithm for Viability Kernels in Hoelderian Case: Approximation by Discrete Dynamical Systems

In this paper, we study two new methods for approximating the viability kernel of a given set for a Holderian differential inclusion. We approximate this kernel by viability kernels for discrete dynamical systems. We prove a convergence result when the differential inclusion is replaced by a sequence of recursive inclusions. Furthermore, when the given set is approached by a sequence of suitable finite sets, we prove our second main convergence result. This paper is the first step to obtain numerical methods

Constructing and exploring wells of energy landscapes

Landscape paradigm is ubiquitous in physics and other natural sciences, but it has to be supplemented with both quantitative and qualitatively meaningful tools for analyzing the topography of a given landscape. We here consider dynamic explorations of the relief and introduce as basic topographic features ``wells of duration $T$ and altitude $y$''. We determine an intrinsic exploration mechanism governing the evolutions from an initial state in the well up to its rim in a prescribed time, whose finite-difference approximations on finite grids yield a constructive algorithm for determining the wells. Our main results are thus (i) a quantitative characterization of landscape topography rooted in a dynamic exploration of the landscape, (ii) an alternative to stochastic gradient dynamics for performing such an exploration, (iii) a constructive access to the wells and (iv) the determination of some bare dynamic features inherent to the landscape. The mathematical tools used here are not familiar in physics: They come from set-valued analysis (differential calculus of set-valued maps and differential inclusions) and viability theory (capture basins of targets under evolutionary systems) which have been developed during the last two decades; we therefore propose a minimal appendix exposing them at the end of this paper to bridge the possible gap.Comment: 28 pages, submitted to J. Math. Phys -

Prospective evaluation of a new Aspergillus IgG EIA kit for the diagnosis of chronic and allergic pulmonary aspergillosis

International audienc

Inherent thermometry in a hybrid superconducting tunnel junction

We discuss inherent thermometry in a Superconductor - Normal metal - Superconductor tunnel junction. In this configuration, the energy selectivity of single-particle tunneling can provide a significant electron cooling, depending on the bias voltage. The usual approach for measuring the electron temperature consists in using an additional pair of superconducting tunnel junctions as probes. In this paper, we discuss our experiment performed on a different design with no such thermometer. The quasi-equilibrium in the central metallic island is discussed in terms of a kinetic equation including injection and relaxation terms. We determine the electron temperature by comparing the micro-cooler experimental current-voltage characteristic with isothermal theoretical predictions. The limits of validity of this approach, due to the junctions asymmetry, the Andreev reflection or the presence of sub-gap states are discussed

Genomic prediction models for grain yield of spring bread wheat in diverse agro-ecological zones

Genomic and pedigree predictions for grain yield and agronomic traits were carried out using high density molecular data on a set of 803 spring wheat lines that were evaluated in 5 sites characterized by several environmental co-variables. Seven statistical models were tested using two random cross-validations schemes. Two other prediction problems were studied, namely predicting the lines’ performance at one site with another (pairwise-site) and at untested sites (leave-one-site-out). Grain yield ranged from 3.7 to 9.0 t ha−1 across sites. The best predictability was observed when genotypic and pedigree data were included in the models and their interaction with sites and the environmental co-variables. The leave-one-site-out increased average prediction accuracy over pairwise-site for all the traits, specifically from 0.27 to 0.36 for grain yield. Days to anthesis, maturity, and plant height predictions had high heritability and gave the highest accuracy for prediction models. Genomic and pedigree models coupled with environmental co-variables gave high prediction accuracy due to high genetic correlation between sites. This study provides an example of model prediction considering climate data along-with genomic and pedigree information. Such comprehensive models can be used to achieve rapid enhancement of wheat yield enhancement in current and future climate change scenario

Rapid cognitive decline, one-year institutional admission and one-year mortality: Analysis of the ability to predict and inter-tool agreement of four validated clinical frailty indexes in the safes cohort

Objectives: To evaluate the predictive ability of four clinical frailty indexes as regards one-year rapid cognitive decline (RCD — defined as the loss of at least 3 points on the MMSE score), and one-year institutional admission (IA) and mortality respectively; and to measure their agreement for identifying groups at risk of these severe outcomes. Design: One-year follow-up and multicentre study of old patients participating in the SAFEs cohort study. Setting: Nine university hospitals in France. Participants: 1,306 patients aged 75 or older (mean age 85±6 years; 65% female) hospitalized in medical divisions through an Emergency department. Measurements: Four frailty indexes (Winograd; Rockwood; Donini; and Schoevaerdts) reflecting the multidimensionality of the frailty concept, using an ordinal scoring system able to discriminate different grades of frailty, and constructed based on the accumulation of identified deficits after comprehensive geriatric assessment conducted during the first week of hospital stay, were used to categorize participants into three different grades of frailty: Gl — not frail; G2 — moderately frail; and G3 — severely frail. Comparisons between groups were performed using Fisher's exact test. Agreement between indexes was evaluated using Cohen's Kappa coefficient. Results: All patients were classified as frail by at least one of the four indexes. The Winograd and Rockwood indexes mainly classified subjects as G2 (85% and 96%), and the Donini and Schoevaerdts indexes mainly as G3 (71% and 67%). Among the SAFEs cohort population, 250, 1047 and 1,306 subjects were eligible for analyses of predictability for RCD, 1-year IA and 1-year mortality respectively. At 1 year, 84 subjects (34%) experienced RCD, 377 (36%) were admitted into an institutional setting, and 445 (34%) had died With the Rockwood index, all subjects who expenenced RCD were classified in G2; and in G2 and G3 when the Donini and Schoevaerdts indexes were used No significant difference was found between frailty grade and RCD, whereas frailty grade was significantly associated with an increased risk of IA and death, whatever the frailty index considered. Agreement between the different indexes of frailty was poor with Kappa coefficients ranging from −0.02 to 0.15. Conclusion: These findings confirm the poor clinimetric properties of these current indexes to measure frailty, underlining the fact that further work is needed to develop a better and more widely-accepted definition of frailty and therefore a better understanding of its pathophysiolog