Affine-ruled varieties without the Laurent cancellation property

We describe a method to construct hypersurfaces of the complex affine $n$-space with isomorphic $\mathbb{C}^*$-cylinders. Among these hypersurfaces, we find new explicit counterexamples to the Laurent Cancellation Problem, i.e. hypersurfaces that are non isomorphic, although their $\mathbb{C}^*$-cylinders are isomorphic as abstract algebraic varieties. We also provide examples of non isomorphic varieties $X$ and $Y$ with isomorphic cartesian squares $X\times X$ and $Y\times Y$

Inequivalent embeddings of the Koras-Russell cubic threefold

The Koras-Russell threefold is the hypersurface X of the complex affine four-space defined by the equation x^2y+z^2+t^3+x=0. It is well-known that X is smooth contractible and rational but that it is not algebraically isomorphic to affine three-space. The main result of this article is to show that there exists another hypersurface Y of the affine four-space, which is isomorphic to X as an abstract variety, but such that there exists no algebraic automorphism of the ambient space which restricts to an isomorphism between X and Y. In other words, the two hypersurfaces are inequivalent. The proof of this result is based on the description of the automorphism group of X. We show in particular that all algebraic automorphisms of X extend to automorphisms of the ambient space

Fast community structure local uncovering by independent vertex-centred process

This paper addresses the task of community detection and proposes a local approach based on a distributed list building, where each vertex broadcasts basic information that only depends on its degree and that of its neighbours. A decentralised external process then unveils the community structure. The relevance of the proposed method is experimentally shown on both artificial and real data.Comment: 2015 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, Aug 2015, Paris, France. Proceedings of the 2015 IEEE/ACM International Conference on Advances in Social Networks Analysis and Minin

Study of an Abating Aggregation Operator in Many-Valued Logic

International audienceThis paper considers a parametrised aggregation operator, originally introduced in the formal framework of many-valued logic and in the applicative context of information scoring. It studies this operator, outside this applicative context, looking at specific configurations of interest: highlighting the wide range of its instantiations, from the lower to the upper extreme cases; showing some t-norms it can encode, as specific cases; and also how it allows rich and flexible intermediate behaviours

Conversion Numérique-Analogique sélective d'un signal passe-bande soumis à des interférences

National audienceCet article propose une méthode qui permet une conversion numérique-analogique sélective d’un processus aléatoire passe-bande soumis à des interférences. Cette méthode permet d’effectuer simultanément la conversion numérique-analogique du signal et le rejet de l’interférence à partir des échantillons du processus observé : aucun démodulation préalable du processus passe-bande n’est nécessaire et le filtrage est effectué dans le domaine temporel grâce à l’expression explicite des coefficients du filtre. La méthode se base sur l’utilisation d’un schéma d’échantillonnage périodique non uniforme appelé PNS2 (pour Periodic Nonuniform Sampling d’ordre 2) qui utilise deux séquences d’échantillonnage périodique entrelacées. Des formules appropriées sont établies afin de reconstruire le signal, permettant également de supprimer l’interférence grâce à un filtrage sélectif. L’observation sur une fenêtre de taille infinie (nombre infini d’échantillons) mène à une reconstruction exacte. Cependant, dans les applications, la conversion numérique-analogique est généralement pratiquée en temps réel à l’aide d’une fenêtre d’observation glissante et de taille finie (nombre fini d’échantillons). Ainsi les formules de reconstruction doivent avoir un taux de convergence élevé. Cet article propose donc des formules avec différents taux de convergence grâce à l’utilisation de filtres avec des fonctions de tranfert de régularité croissante. Des simulations se basant sur la variation de différents paramètres expérimentaux nous ont permis de tester la méthode

Matisse : Painting 2D regions for Modeling Free-Form Shapes

International audienceThis paper presents "Matisse", an interactive modeling system aimed at providing the public with a very easy way to design free-form 3D shapes. The user progressively creates a model by painting 2D regions of arbitrary topology while freely changing the view-point and zoom factor. Each region is converted into a 3D shape, using a variant of implicit modeling that fits convolution surfaces to regions with no need of any optimization step. We use intuitive, automatic ways of inferring the thickness and position in depth of each implicit primitive, enabling the user to concentrate only on shape design. When he or she paints partly on top of an existing primitive, the shapes are blended in a local region around the intersection, avoiding some of the well known unwanted blending artifacts of implicit surfaces. The locality of the blend depends on the size of smallest feature, enabling the user to enhance large, smooth primitives with smaller details without blurring the latter away. As the results show, our system enables any unprepared user to create 3D geometry in a very intuitive way

Surfaces Implicites Homothétiques

National audienceNous introduisons un nouveau type de surface implicite à squelette, étendant le modèle des surfaces de convolution. La principale propriété de ces nouvelles surfaces est d'être invariantes par homothétie, ce qui rend leur utilisation bien plus intuitive : les mélanges ont la même allure à toutes les échelles, et nous pouvons contrôler plus précisément l'épaisseur du volume englobé