A new proof of the Herman-Avila-Bochi formula for Lyapunov exponents of SL(2,R)-cocycles

We study the geometry of the action of SL(2,R) on the projective line in order to present a new and simpler proof of the Herman-Avila-Bochi formula. This formula gives the average Lyapunov exponent of a class of 1-families of SL(2,R)-cocycles.Comment: 13 pages, 2 figure

Punctual Hilbert Schemes and Certified Approximate Singularities

In this paper we provide a new method to certify that a nearby polynomial system has a singular isolated root with a prescribed multiplicity structure. More precisely, given a polynomial system f $=(f\_1, \ldots, f\_N)\in C[x\_1, \ldots, x\_n]^N$, we present a Newton iteration on an extended deflated system that locally converges, under regularity conditions, to a small deformation of $f$ such that this deformed system has an exact singular root. The iteration simultaneously converges to the coordinates of the singular root and the coefficients of the so called inverse system that describes the multiplicity structure at the root. We use $$\alpha$$-theory test to certify the quadratic convergence, and togive bounds on the size of the deformation and on the approximation error. The approach relies on an analysis of the punctual Hilbert scheme, for which we provide a new description. We show in particular that some of its strata can be rationally parametrized and exploit these parametrizations in the certification. We show in numerical experimentation how the approximate inverse system can be computed as a starting point of the Newton iterations and the fast numerical convergence to the singular root with its multiplicity structure, certified by our criteria.Comment: International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata, Franc

Ethanol application at veraison decreases acidity in Cabernet Sauvignon grapes

Research NoteSpraying ethanol (5 % v/v in water) onto grape clusters at mid-veraison led to a 30 % drop in the malic acid concentration at harvest. As a consequence, titratable acidity also dropped by 10 %. The concentration of tartaric acid did not change significantly. The mode of action of ethanol on malic acid metabolism is discussed.

From error bounds to the complexity of first-order descent methods for convex functions

This paper shows that error bounds can be used as effective tools for deriving complexity results for first-order descent methods in convex minimization. In a first stage, this objective led us to revisit the interplay between error bounds and the Kurdyka-\L ojasiewicz (KL) inequality. One can show the equivalence between the two concepts for convex functions having a moderately flat profile near the set of minimizers (as those of functions with H\"olderian growth). A counterexample shows that the equivalence is no longer true for extremely flat functions. This fact reveals the relevance of an approach based on KL inequality. In a second stage, we show how KL inequalities can in turn be employed to compute new complexity bounds for a wealth of descent methods for convex problems. Our approach is completely original and makes use of a one-dimensional worst-case proximal sequence in the spirit of the famous majorant method of Kantorovich. Our result applies to a very simple abstract scheme that covers a wide class of descent methods. As a byproduct of our study, we also provide new results for the globalization of KL inequalities in the convex framework. Our main results inaugurate a simple methodology: derive an error bound, compute the desingularizing function whenever possible, identify essential constants in the descent method and finally compute the complexity using the one-dimensional worst case proximal sequence. Our method is illustrated through projection methods for feasibility problems, and through the famous iterative shrinkage thresholding algorithm (ISTA), for which we show that the complexity bound is of the form $O(q^{k})$ where the constituents of the bound only depend on error bound constants obtained for an arbitrary least squares objective with $\ell^1$ regularization

Defining and cataloging exoplanets: The exoplanet.eu database

We describe an online database for extra-solar planetary-mass candidates, updated regularly as new data are available. We first discuss criteria for the inclusion of objects in the catalog: "definition" of a planet and several aspects of the confidence level of planet candidates. {\bf We are led to point out the conflict between sharpness of belonging or not to a catalogue and fuzziness of the confidence level.} We then describe the different tables of extra-solar planetary systems, including unconfirmed candidates (which will ultimately be confirmed, or not, by direct imaging). It also provides online tools: histogrammes of planet and host star data, cross-correlations between these parameters and some VO services. Future evolutions of the database are presented.Comment: Accepted in Astronomy and Astrophysics (revised version

The Double Star Plasma Electron and Current Experiment

The Double Star Project is a collaboration between Chinese and European space agencies, in which two Chinese magnetospheric research spacecraft, carrying Chinese and European instruments, have been launched into equatorial (on 29 December 2003) and polar (on 25 July 2004) orbits designed to enable complementary studies with the Cluster spacecraft. The two Double Star spacecraft TC-1 and TC-2 each carry a Double Star Plasma Electron and Current Experiment (PEACE) instrument. These two instruments were based on Cluster Flight Spare equipment, but differ from Cluster instruments in two important respects. Firstly, a Double Star PEACE instrument has only a single sensor, which must be operated in a manner not originally envisaged in the Cluster context in order to sample the full range of energies. Secondly, the DPU hardware was modified and major changes of onboard software were implemented, most notably a completely different approach to data compression has been adopted for Double Star, which allows high resolution 3-dimensional distributions to be transmitted almost every spin, a significant improvement over Cluster. This paper describes these instruments, and includes examples of data collected in various magnetospheric regions encountered by the spacecraft which have been chosen to illustrate the power of combined Double Star and Cluster measurements

An update on the Hirsch conjecture

The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most fundamental, basic and old problems in polytope theory, what we know is quite scarce. Most notably, no polynomial upper bound is known for the diameters that are conjectured to be linear. In contrast, very few polytopes are known where the bound $n-d$ is attained. This paper collects known results and remarks both on the positive and on the negative side of the conjecture. Some proofs are included, but only those that we hope are accessible to a general mathematical audience without introducing too many technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2 and put into the appendix arXiv:0912.423

Artificial reefs: from ecological processes to fishing enhancement tools

info:eu-repo/semantics/publishedVersio

Free exopolysaccharide from Mycoplasma mycoides subsp. mycoides possesses anti-inflammatory properties

In this study we explored the immunomodulatory properties of highly purified free galactan, the soluble exopolysaccharide secreted by Mycoplasma mycoides subsp. mycoides (Mmm). Galactan was shown to bind to TLR2 but not TLR4 using HEK293 reporter cells and to induce the production of the anti-inflammatory cytokine IL-10 in bovine macrophages, whereas low IL-12p40 and no TNF-α, both pro-inflammatory cytokines, were induced in these cells. In addition, pre-treatment of macrophages with galactan substantially reduced lipopolysaccharide (LPS)-induced production of pro-inflammatory cytokines TNF- and IL-12p40 while increasing LPS-induced secretion of immunosuppressive IL-10. Also, galactan did not activate naïve lymphocytes and induced only low production of the Th1 cytokine IFN-γ in Mmm-experienced lymphocytes. Finally, galactan triggered weak recall proliferation of CD4+ T lymphocytes from contagious bovine pleuropneumonia-infected animals despite having a positive effect on the expression of co-stimulatory molecules on macrophages. All together, these results suggest that galactan possesses anti-inflammatory properties and potentially provides Mmm with a mechanism to evade host innate and adaptive cell-mediated immune responses. (Résumé d'auteur

Statistical Computing on Non-Linear Spaces for Computational Anatomy

International audienceComputational anatomy is an emerging discipline that aims at analyzing and modeling the individual anatomy of organs and their biological variability across a population. However, understanding and modeling the shape of organs is made difficult by the absence of physical models for comparing different subjects, the complexity of shapes, and the high number of degrees of freedom implied. Moreover, the geometric nature of the anatomical features usually extracted raises the need for statistics on objects like curves, surfaces and deformations that do not belong to standard Euclidean spaces. We explain in this chapter how the Riemannian structure can provide a powerful framework to build generic statistical computing tools. We show that few computational tools derive for each Riemannian metric can be used in practice as the basic atoms to build more complex generic algorithms such as interpolation, filtering and anisotropic diffusion on fields of geometric features. This computational framework is illustrated with the analysis of the shape of the scoliotic spine and the modeling of the brain variability from sulcal lines where the results suggest new anatomical findings