Rates of convergence for robust geometric inference

Distances to compact sets are widely used in the field of Topological Data Analysis for inferring geometric and topological features from point clouds. In this context, the distance to a probability measure (DTM) has been introduced by Chazal et al. (2011) as a robust alternative to the distance a compact set. In practice, the DTM can be estimated by its empirical counterpart, that is the distance to the empirical measure (DTEM). In this paper we give a tight control of the deviation of the DTEM. Our analysis relies on a local analysis of empirical processes. In particular, we show that the rates of convergence of the DTEM directly depends on the regularity at zero of a particular quantile fonction which contains some local information about the geometry of the support. This quantile function is the relevant quantity to describe precisely how difficult is a geometric inference problem. Several numerical experiments illustrate the convergence of the DTEM and also confirm that our bounds are tight

Maximal regularity and Hardy spaces

In this work, we consider the Cauchy problem for $u' - Au = f$ with $A$ the Laplacian operator on some Riemannian manifolds or a sublapacian on some Lie groups or some second order elliptic operators on a domain. We show the boundedness of the operator of maximal regularity $f\mapsto Au$ and its adjoint on appropriate Hardy spaces which we define and study for this purpose. As a consequence we reobtain the maximal $L^q$ regularity on $L^p$ spaces for $p,q$ between 1 and $\infty$.Comment: 27 page

Addendum to "Maximal regularity and Hardy spaces"

We correct an inaccuracy in a previous article [Auscher, Pascal; Bernicot, Fr\'ed\'eric; Zhao, Jiman. Maximal regularity and Hardy spaces. Collect. Math. 59 (2008), no. 1, 103-127.

Anticipatory Semantic Processes

Why anticipatory processes correspond to cognitive abilities of living systems? To be adapted to an environment, behaviors need at least i) internal representations of events occurring in the external environment; and ii) internal anticipations of possible events to occur in the external environment. Interactions of these two opposite but complementary cognitive properties lead to various patterns of experimental data on semantic processing. How to investigate dynamic semantic processes? Experimental studies in cognitive psychology offer several interests such as: i) the control of the semantic environment such as words embedded in sentences; ii) the methodological tools allowing the observation of anticipations and adapted oculomotor behavior during reading; and iii) the analyze of different anticipatory processes within the theoretical framework of semantic processing. What are the different types of semantic anticipations? Experimental data show that semantic anticipatory processes involve i) the coding in memory of sequences of words occurring in textual environments; ii) the anticipation of possible future words from currently perceived words; and iii) the selection of anticipated words as a function of the sequences of perceived words, achieved by anticipatory activations and inhibitory selection processes. How to modelize anticipatory semantic processes? Localist or distributed neural networks models can account for some types of semantic processes, anticipatory or not. Attractor neural networks coding temporal sequences are presented as good candidate for modeling anticipatory semantic processes, according to specific properties of the human brain such as i) auto-associative memory; ii) learning and memorization of sequences of patterns; and iii) anticipation of memorized patterns from previously perceived patterns

La pratique du football en Franche-Comté: un football des champs et un football des villes

Avec un peu plus de 45 000 licenciés, le football est en Franche- Comté le sport qui compte le plus de pratiquants. Peu onéreux dans sa pratique, il est accessible à tous et s'adresse en théorie à toutes les catégories socioéconomiques : le football est un sport de masse par excellence qui peut jouer le rôle de ciment social. Au cours de ces dernières années, le football a été confronté à la concurrence d'autres sports, le tennis notamment, qui bénéficient d'une organisation plus souple. Après une période de dynamisme, le football a ralenti sa progression durant les années soixante et soixante-dix. Les années quatre vingt verront se succéder en alternance les années de recul et les années de croissance du nombre de ses licenciés

Noncircular Waveforms Exploitation for Radar Signal Processing : Survey and Study for Agile Radar Waveform

International audienceWith new generation of Active Digital Radar Antenna, there is a renewal of waveform generation and processing approaches, and new strategies can be explored to optimize waveform design and waveform analysis and to benefit of all potential waveform diversity. Among these strategies, building and exploitation of the Noncircularity of waveforms is a promising issue. Up to the middle of the nineties, most of the signals encountered in practice are assumed to be second order (SO) circular (or proper), with a zero second correlation function. However, in numerous operational contexts such as in radio communications, the observed signals are either SO noncircular (or improper) or jointly SO noncircular with a particular signal to estimate, to detect or to demodulate, with some information contained in the second correlation function of the signals. Exploitation of this information in the processing of SO noncircular signals may generate dramatic gain in performance with respect to conventional processing and opens new perspective in signal processing. The purpose of this paper is to present a short overview of the interest of taking into account the potential SO noncircularity of the signals in signal processing and to describe the potential interest of SO noncircular waveforms for radar applications