Sampling local properties of attractors via Extreme Value Theory

We provide formulas to compute the coefficients entering the affine scaling needed to get a non-degenerate function for the asymptotic distribution of the maxima of some kind of observable computed along the orbit of a randomly perturbed dynamical system. This will give information on the local geometrical properties of the stationary measure. We will consider systems perturbed with additive noise and with observational noise. Moreover we will apply our techniques to chaotic systems and to contractive systems, showing that both share the same qualitative behavior when perturbed

Dynamical properties of chimera states for globally coupled map lattices

We study the stability properties and long-term dynamical behavior of chimera states in globally coupled map lattices. In particular, we give a formula for the transverse Lyapunov exponent associated with blocks of synchronized sites. We use these results to study clustered dynamics from a numerical perspective, and give numerical evidence of attracting chimeras having chaotic dynamics, as well as periodic behaviors. Finally, we obtain some results ruling out the existence of absolutely continuous invariant measures supported on chimera states in strong coupling regimes

Coherent presentations of a class of monoids admitting a Garside family

This paper shows how to construct coherent presentations of a class of monoids, including left-cancellative noetherian monoids containing no nontrivial invertible element and admitting a Garside family. Thereby, it resolves the question of finding a unifying generalisation of the following two distinct extensions of Deligne's original construction of coherent presentations for spherical Artin-Tits monoids: to general Artin-Tits monoids, and to Garside monoids. The result is applied to a dual braid monoid, and to some monoids which are neither Artin-Tits nor Garside. For the Artin-Tits monoid of type $\widetilde{A}_{2}$, a finite coherent presentation is given, having a finite Garside family as a generating set

Statistical Properties of Random Dynamical Systems with Contracting Direction

International audienceWe present a mostly numerical investigation on randomly perturbed piecewise contracting maps (PCM) with the goal to study the extreme value limit distribution of observables related to local recurrence. Our analysis will focus on PCM under additive noise, but we will also consider the hyperbolic attractor of the Baker's map when perturbed with another kind of noise, namely, the randomly applied stochastic perturbation. A comparison of the two kind of noises will be considered with respect to the computation of the extremal index

Stability of synchronization under stochastic perturbations in leaky integrate and fire neural networks of finite size.

International audienceIn the present paper, we study the synchronization in a model of neural network which can be considered as a noisy version of the model of \citet{mirollo1990synchronization}, namely, fully-connected and totally excitatory integrate and fire neural network with Gaussian white noises. Using a large deviation principle, we prove the stability of the synchronized state under stochastic perturbations. Then, we give a lower bound on the probability of synchronization for networks which are not initially synchronized. This bound shows the robustness of the emergence of synchronization in presence of small stochastic perturbations

Influence du procédé de dépulpage de la drupe de Coffea arabica L. sur la fermentation

Au cours du traitement de postrécolte du café Arabica, l'eau utilisée a une influence directe sur les paramètres physico-chimiques, microbiologiques et biochimiques de la fermentation. Elle intervient lors du dépulpage et du transport des drupes dépulpées jusqu'à la cuve de fermentation, solubilise alors les sucres simples du mucilage, ralentit la croissance microbienne et en conséquence l'acidification du milieu fermentaire. Le dépulpage et le transport du café avec ou sans eau ne modifient pas la composition biochimique du café vert. Par ailleurs, les propriétés organoleptiques à la tasse ont été jugées identiques. Les technologies moins polluantes, dépulpage et transport sans eau des drupes dépulpées, permettent aux producteurs de contrôler la durée et l'acidité produite. En revanche, il est nécessaire de réduire le temps de fermentation car le pH devient plus rapidement acide. Des durées prolongées pourraient provoquer des surfermentations et développer des mauvais goûts. (Résumé d'auteur

Super-resolution wavefront reconstruction

Super-Resolution (SR) is a technique that seeks to upscale the resolution of a set of measured signals. SR retrieves higher-frequency signal content by combining multiple lower resolution sampled data sets. SR is well known both in the temporal and spatial domains. It is widely used in imaging to reduce aliasing and enhance the resolution of coarsely sampled images.This paper applies the SR technique to the bi-dimensional wavefront reconstruction. In particular, we show how SR is intrinsically suited for tomographic multi WaveFront Sensor (WFS) AO systems revealing many of its advantages with minimal design effort. This paper provides a direct space and Fourier-optics description of the wavefront sensing operation and demonstrate how SR can be exploited through signal reconstruction, especially in the framework of Periodic Nonuniform Sampling. Both meta uniform and nonuniform sampling schemes are investigated. Then, the SR bi-dimensional model for a Shack Hartmann (SH) WFS is provided and the characteristics of the sensitivity function are analyzed. The SR concept is finally validated with numerical simulations of representative multi WFS SH AO systems. Our results show that combining several WFS samples in a SR framework grants access to a larger number of modes than the native one offered by a single WFS and that despite the fixed sub-aperture size across samples. Furthermore, we show that the associated noise propagation is not degraded under SR. Finally, the concept is extended to the signal produced by single Pyramid WFS. In conclusion, SR applied to wavefront reconstruction offers a new parameter space to explore as it decouples the size of the subaperture from the desired wavefront sampling resolution. By cutting short with old assumptions, new, more flexible and better performing AO designs become now possible.Comment: Astronomy & Astrophysics Section: 13. Astronomical instrumentation AA/2022/4395

Multilayer modeling of thermoacoustic sound generation for thermophone analysis and design

International audienc