Sur certaines figures minima

Moyennes de certaines fonctions arithmétiques sur les entiers friables, 2

Moyennes de certaines fonctions multiplicatives sur les entiers friables, 2

We derive new, very precise estimates for averages of arithmetic functions over friable integers from analytic information on their associated Dirichlet series. These yield significant improvements upon available results in classical cases, in particular concerning the effective expansion of “abstract” main terms of de Bruijn type. These results also permit new applications, linked to the solub...

Préquantification De Certaines Variétés De Poisson

A surjective submersion π : M → B carrying a field of simplectic structures on the fibres is symplectic if this Poisson structure is minimal. A symplectic submersion may be interpreted as a family of mechanical systems depending on a parameter in B. We give some conditions to find a closed form which represent the foliated form σ gluing the symplectic forms on the fibres. This is the first step...

Plongement de certaines théories homotopiques de Quillen dans les dérivateurs

L’objectif de ce papier est de comparer la 2-catégorie des théories homotopiques de Quillen combinatoires propres à gauche avec une 2-catégorie de dérivateurs de Grothendieck. La 2-catégorie THQcpg des théories homotopiques de Quillen combinatoires propres à gauche est la bi-localisation de la 2-catégorieModQcpg des catégories modèles de Quillen combinatoires propres à gauche relativement aux é...

Flat Minima

We present a new algorithm for finding low-complexity neural networks with high generalization capability. The algorithm searches for a "flat" minimum of the error function. A flat minimum is a large connected region in weight space where the error remains approximately constant. An MDL-based, Bayesian argument suggests that flat minima correspond to "simple" networks and low expected overfitti...