On the cubic NLS on 3D compact domains

We prove bilinear estimates for the Schr\"odinger equation on 3D domains, with Dirichlet boundary conditions. On non-trapping domains, they match the $\mathbb{R}^3$ case, while on bounded domains they match the generic boundary less manifold case. As an application, we obtain global well-posedness for the defocusing cubic NLS for data in $H^s_0(\Omega)$, $1<s\leq 3$, with $\Omega$ any bounded domain with smooth boundary.Comment: 15 pages, updated references and corrected typos. To appear in Journal of the Institute of Mathematics of Jussie

Conditioning and initial enlargement of filtration on a Riemannian manifold

We extend to Riemannian manifolds the theory of conditioned stochastic differential equations. We also provide some enlargement formulas for the Brownian filtration in this nonflat setting.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000012

Issues in cross-cultural studies of advertising audiovisual material

This article presents an approach to cross-cultural studies of advertising audiovisual material that departs from the typical rigid marketing models. It favours a more qualitative inductive approach to corpuses, in which audiovisual texts are not approached or compared through the use of standardised American tools. After reviewing the usual marketing tools, the article focuses on the steps researchers can usefully take, from the gathering of audiovisual texts from two different environments to their classification, two important steps that are critical in such studies

How Many Dissimilarity/Kernel Self Organizing Map Variants Do We Need?

In numerous applicative contexts, data are too rich and too complex to be represented by numerical vectors. A general approach to extend machine learning and data mining techniques to such data is to really on a dissimilarity or on a kernel that measures how different or similar two objects are. This approach has been used to define several variants of the Self Organizing Map (SOM). This paper reviews those variants in using a common set of notations in order to outline differences and similarities between them. It discusses the advantages and drawbacks of the variants, as well as the actual relevance of the dissimilarity/kernel SOM for practical applications