Polymorphic evolution sequence and evolutionary branching

We are interested in the study of models describing the evolution of a polymorphic population with mutation and selection in the specific scales of the biological framework of adaptive dynamics. The population size is assumed to be large and the mutation rate small. We prove that under a good combination of these two scales, the population process is approximated in the long time scale of mutations by a Markov pure jump process describing the successive trait equilibria of the population. This process, which generalizes the so-called trait substitution sequence, is called polymorphic evolution sequence. Then we introduce a scaling of the size of mutations and we study the polymorphic evolution sequence in the limit of small mutations. From this study in the neighborhood of evolutionary singularities, we obtain a full mathematical justification of a heuristic criterion for the phenomenon of evolutionary branching. To this end we finely analyze the asymptotic behavior of 3-dimensional competitive Lotka-Volterra systems

Laser Doppler flowmetry signals: pointwise Hölder exponents of experimental signals from young healthy subjects and numerically simulated data

We analyze the complexity of laser Doppler flowmetry (LDF) signals which give a peripheral view of the cardiovascular system. For this purpose, experimental and numerically simulated LDF signals are processed. The experimental signals are recorded in young healthy subjects. The numerically simulated LDF data are computed from a model containing six nonlinear coupled oscillators reflecting six almost periodic rhythmic activities present in experimental LDF signals. In the model, the oscillators are coupled with both linear and parametric couplings in order to represent cardiovascular system behaviors. To our knowledge this modeling has never been proposed yet. The complexity of all the experimental and simulated signals is studied by the computation of pointwise Hölder exponents. The latter identify the possible multifractal characteristics of data. The pointwise Hölder exponents are determined with a parametric generalized quadratic variation based estimation method first calibrated from white noise measures. The results of our signal processing analysis show that experimental LDF signals are weakly multifractal for young healthy subjects at rest. Furthermore, our findings together with another recent work of our group show that pointwise Hölder exponents of the simulated data do not describe the ones of the young healthy subjects but are closer to the ones of elderly healthy people. This paper provides useful information to go deeper into the modeling of LDF data, that could bring enlightenment for a better understanding of the peripheral cardiovascular system

Estimation of the covariance function of a Gaussian stationary process with scaling methods

Rapport technique du departement de biometrie * INRA, centre de Jouy Diffusion du document : INRA, centre de JouyInternational audienc

Quelques méthodes nouvelles en analyse d'image

National audienc

Estimating the singularity function of a gaussian process with applications

International audienceA non-parametric estimator of the singularity function of a discretely observed Gaussian process on [0, 1 is built, using projection kernels on [0, 1. This estimator is based on a generalized quadratic variation procedure. A first asymptotic study is done with respect to the integrated mean square error, for which we find the classical non-parametric rate of convergence. In a second asymptotic study, we prove weak convergence in distribution of our estimator, suitably normalized. These results are applied to two related topics: estimation of the mean square error in estimating linear functionals of a random process; and estimation of the diffusion coefficient in a diffusion model

Wavelet coefficients of a Gaussian process and applications

National audienc

Estimation of the singularity of the covariance function of a Gaussian process

Rapport technique du departement de biometrie * INRA, centre de Jouy Diffusion du document : INRA, centre de JouyInternational audienc