A counter-example to the theorem of Hiemer and Snurnikov

A planar polygonal billiard $\P$ is said to have the finite blocking property if for every pair $(O,A)$ of points in $\P$ there exists a finite number of ``blocking'' points $B_1, ..., B_n$ such that every billiard trajectory from $O$ to $A$ meets one of the $B_i$'s. As a counter-example to a theorem of Hiemer and Snurnikov, we construct a family of rational billiards that lack the finite blocking property.Comment: 5 pages, 3 figure

On the finite blocking property

A planar polygonal billiard $\P$ is said to have the finite blocking property if for every pair $(O,A)$ of points in $\P$ there exists a finite number of ``blocking'' points $B_1, ..., B_n$ such that every billiard trajectory from $O$ to $A$ meets one of the $B_i$'s. Generalizing our construction of a counter-example to a theorem of Hiemer and Snurnikov (see \cite{Mo}), we show that the only regular polygons that have the finite blocking property are the square, the equilateral triangle and the hexagon. Then we extend this result to translation surfaces. We prove that the only Veech surfaces with the finite blocking property are the torus branched coverings. We also provide a local sufficient condition for a translation surface to fail the finite blocking property. This enables us to give a complete classification for the L-shaped surfaces as well as to obtain a density result in the space of translation surfaces in every genus $g\geq 2$.Comment: 24 page

Spreading huge free software without internet connection, via self-replicating USB keys

We describe and discuss an affordable way to spread huge software without relying on internet connection, via the use of self-replicating live USB keys.Comment: 5 pages, accepted to Extremecom 201

Finite blocking property versus pure periodicity

A translation surface S is said to have the finite blocking property if for every pair (O,A) of points in S there exists a finite number of "blocking" points B_1,...,B_n such that every geodesic from O to A meets one of the B_i's. S is said to be purely periodic if the directional flow is periodic in each direction whose directional flow contains a periodic trajectory (this implies that S admits a cylinder decomposition in such directions). We will prove that finite blocking property implies pure periodicity. We will also classify the surfaces that have the finite blocking property in genus 2: such surfaces are exactly the torus branched coverings. Moreover, we prove that in every stratum, such surfaces form a set of null measure. In the Appendix, we prove that completely periodic translation surfaces form a set of null measure in every stratum.Comment: 16 pages, 6 figures. v4 : minor changes to take referee's suggestions into account. In particular, an appendix is added with a proof of the following result: "In genus $g\geq 2$, the set of completely periodic translation surfaces has measure zero in every stratum

Modelling Constrained Dynamic Software Architecture with Attributed Graph Rewriting Systems

Dynamic software architectures are studied for handling adap- tation in distributed systems, coping with new requirements, new envi- ronments, and failures. Graph rewriting systems have shown their ap- propriateness to model such architectures, particularly while considering the consistency of theirs reconfigurations. They provide generic formal means to specify structural properties, but imply a poor description of specific issues like behavioural properties. This paper lifts this limita- tion by proposing a formal approach for integrating the consideration of constraints, non-trivial attributes, and their propagation within the framework of graph rewriting systems

Illumination dans les billards polygonaux et dynamique symbolique

The first part of this thesis deals with illumination on polygonal billiards and translation surfaces.We study the relationships between the finite blocking property (illumination property), pure periodicity (dynamical property) and being a torus branched covering (geometrical property).We show that those three properties are equivalent for the Veech surfaces, for the translation surfaces of genus 2, for the surfaces whose homology is generated by the periodic orbits of the geodesic flow and therefore on a dense open subset of full measure in every stratum of the moduli space of translation surfaces.The second part deals with symbolic dynamics.We give some bounds of the number of invariant ergodic probability measures of a subshift that depend on the geometry of combinatorial objects associated to its language: the Rauzy graphs and the tree of left special factors. Then, we then introduce and study a particular class of subshifts: the multi-scale quasiperiodic subshifts.We prove that they are uniquely ergodic and that their Kolmogorov complexity and their topologocal entropy vanish.La premièere partie de cette thèse traite d'illumination dans les billards polygonaux et les surfaces de translation. Nous étudions les relations entre la propriété de blocage fini (propriété d'illumination), la pure périodicité (propriété dynamique) et le fait d'être un un revêtement ramifié d'un tore plat (propriété géométrique). Nous montrons que ces trois notions sont équivalentes pour les surfaces de Veech, pour les surfaces de translation de genre 2, pour les surfaces dont l'homologie est engendrée par les orbites périodiques du flot géodésique et en particulier sur un ouvert dense de mesure pleine dans chaque strate de l'espace des modules des surfaces de translation.La deuxième partie traite de dynamique symbolique topologique.Nous majorons le nombre de mesures de probabilité ergodiques invariantes d'un sous-shift en fonction de la géométrie d'objets combinatoires associés à son langage : les graphes de Rauzy et l'arbre des spéciaux à gauche.Puis nous introduisons et étudions une classe particulière de sous-shifts : les sous-shifts quasipériodiques multiéchelle. Nous montrons entre autres qu'ils sont uniquement ergodiques, de complexité de Kolmogorov et d'entropie topologique nulles

Rôle d'une base de connaissance dans SemIoTics, un système autonome contrôlant un appartement connecté

National audienceL'Internet des Objets représente une réalité de plus en plus concrète au fur et à mesure que se déploient de larges réseaux d'objets connectés. Ceux-ci ouvrent de larges perspectives d'applications, mais rencontrent des difficultés en terme d'interopérabilité, de configuration ou de passage à l'échelle. Ces probléma-tiques peuvent être traitées par le recours aux principes du web de données liées, d'où l'émergence d'ontologies dédiées aux applications de l'IoT, comme IoT-O, une ontologie pour l'IoT.Par ailleurs, une description en-richie des systèmes permet d'envisager leur configuration autonome : on parle alors d'autonomic computing. Ce papier présente SemIoTics, un système autonome reposant sur des bases de connaissance pour la gestion d'un appartement connecté. Nous présentons tout d'abord une vision générique d'une architecture de réseaux d'objets connectés qui permet de guider une analyse des travaux à l'interface du web sémantique et de l'IoT. Nous décrivons ensuite les deux bases de connaissances spécialisant IoT-O sur lesquelles s'appuie SemIoTics, et leur relation avec le dispositif expérimental. Enfin, la structure de ce système autonome de domotique est présenté en détails, et mis en relation avec l'architecture identifiée dans l'état de l'art

Correctness by Construction and Style Preserving Reconfigurations of Distributed Systems.

In distributed systems and dynamic environments, software architectures may evolve. A crucial issue when conducting system evolutions is to maintain the system in a consistent and functional state. Based on formal proofs in design-time, correctness by construction has recently emerged to efficiently guarantee system coherency. This article proposes a new method for the construction and specification of correct by construction system reconfigurations. Such transformations are characterized by graph rewriting rules that necessarily preserve the coherency of a system. We firstly propose operators on graph transformations and show that they conserve their correctness. Given a system specified by a graph grammar, these operators then serve to construct and characterize a set of correct transformations. We show in particular that any correct configuration can be reached starting from any other one without inconsistent intermediate step, using these transformations only