Plans dʼexpérience pour lʼestimation de la courbe de concentration et de lʼAUC

The problem of interest is to estimate the concentration curve and the area under the curve (AUC) by estimating the parameters of a linear regression model with autocorrelated error process. We introduce a simple linear nonparametric unbiased estimator of the concentration curve and the AUC. We show that this estimator constructed from an appropriate regular sampling design is asymptotically optimal.     

Construction dʼun champ continu de métriques

Adaptive computation using adaptive meshes is now recognized as essential for solving complex PDE problems. This computation requires, at each step, the definition of a continuous metric field to govern the generation of the adapted meshes. In practice, via an appropriate a posteriori error estimation, metrics are calculated at the vertices of the computational domain mesh. In order to obtain a continuous metric field, the discrete field is interpolated in the whole domain mesh. In this Note, a new method for interpolating discrete metric fields, based on a so-called “natural decomposition” of metrics, is introduced. The proposed method is based on known matrix decompositions and is computationally robust and efficient. Some qualitative comparisons with classical methods are made to show the relevance of this methodology.     

Construction dʼopérades ensemblistes à partir de monoïdes

We study a functorial construction from the category of monoids to the category of set-operads and we give some combinatorial examples of applications.     

Principes de grandes déviations pour l’estimateur à noyau de la densité de probabilité

We establish pointwise and uniform large deviations principles for nonparametric kernel density estimators. The estimates are based on sequences of independent and identically distributed real random variables.     

Paires élémentaires de corps pseudo-finis: dénombrement des complétions

Let II be a complete theory of pseudo-finite fields. In this Note we prove that, in the langage of fields to which we add a unary predicate for a substructure, the theory of non-trivial elementary pairs of models of II has 2^No completions, that is, the maximum that could exist. For a more detailed presentation, see [5].     

Sur une généralisation de la notion de V-variété

We consider a topological space which is locally isomorphic to the quotient of R^k by the action of a discrete group and we call it quasifold of dimension k. Quasifolds generalize manifolds and orbifolds and represent the natural framework for performing symplectic reduction with respect to the induced action of any Lie subgroup, compact or not, of a torus. We define quasitori, Hamiltonian actions of quasitori and the moment mapping for symplectic quasifolds, and we show that every simple convex polytope, rational or not, is the image of the moment mapping for the action of a quasitorus on a quasifold.     

Distances entre exponentielles et puissances d’éléments de certaines algèbres de Banach

Let A be a Banach algebra which does not contain any nonzero idempotent element, let γ > 0, and let . We show that if then . We also show, assuming a suitable spectral condition on x, that if , then Received: 12 July 2006 Revised: 31 January 2007     

Sur une représentation des pseudo-intégrales aléatoires de Stieltjes,déduites de la fonction du mouvement brownien

Sans résumé à M. Enrico Bompiani pour son Jubilé scientifique.     

Réduction de la conjecture de Hodge à une continuité

The obstructions, for a closed differential form on a projective manifold, to be cohomologous to an algebraic cycle with complex coefficients, are computed in terms of the Chow transformation. They can be expressed as an orthogonality condition, on the manifold itself, with families parametrized by the Grassmannian of currents which are completely determined. A parameter does not yield any obstruction if the associated projective subspace meets properly the manifold. The embedding of the manifold is degenerated, in view of applying the characterization of currents associated to algebraic cycles by the Chow transformation. We study the set of periods obtained when the parameter varies, in particular, we prove a continuity result, thanks to the constructibility of the Bernstein polynomial. When the cohomology class is rational, we conjecture that this set is connected.