On the many Dirichlet Laplacians on a non-convex polygon and their approximations by point interactions

By Birman and Skvortsov it is known that if \Omegasf is a planar curvilinear polygon with $n$ non-convex corners then the Laplace operator with domain H^2(\Omegasf)\cap H^1_0(\Omegasf) is a closed symmetric operator with deficiency indices $(n,n)$. Here we provide a Kre\u\i n-type resolvent formula for any self-adjoint extensions of such an operator, i.e. for the set of self-adjoint non-Friedrichs Dirichlet Laplacians on \Omegasf, and show that any element in this set is the norm resolvent limit of a suitable sequence of Friedrichs-Dirichlet Laplacians with $n$ point interactions.Comment: Slightly revised version. Accepted for publication in Journal of Functional Analysi

Interior error estimate for periodic homogenization

In a previous article about the homogenization of the classical problem of diff usion in a bounded domain with su ciently smooth boundary we proved that the error is of order $\epsilon^{1/2}$. Now, for an open set with su ciently smooth boundary $C^{1,1}$ and homogeneous Dirichlet or Neuman limits conditions we show that in any open set strongly included in the error is of order $\epsilon$. If the open set $\Omega\subset R^n$ is of polygonal (n=2) or polyhedral (n=3) boundary we also give the global and interrior error estimates

Modèle de caractérisation des visualisations de données complexes en grandes quantités

International audienceVisualizing large and complex datasets is an issue that must be tackled more and more often in the domain of professional systems, given the increasing capacity of data providers. In this paper, we introduce a model supporting the characterization of all the dimensions that have an impact on big and/or complex data representation solutions, which enables us to highlightthe limits of existing visualization solutions.La visualisation de grandes quantités données complexes est un problème de plus en plus courant dans le domaine des systèmes professionnels, en raison des capacités de création et de stockage de données qui augmentent sans cesse. Dans cet article nous présentons un modèle permettant de caractériser l'ensemble des dimensions qui ont un impact sur la représentation de données complexes et/ou en grandes quantités, ce qui nous permet de mettre en avant les limites des solutions de visualisation existantes

Analysis of segregated boundary-domain integral equations for variable-coefficient problems with cracks

This is the pre-print version of the article. The official published version can be obtained from the link below - Copyright @ 2011 Wiley-BlackwellSegregated direct boundary-domain integral equation (BDIE) systems associated with mixed, Dirichlet and Neumann boundary value problems (BVPs) for a scalar “Laplace” PDE with variable coefficient are formulated and analyzed for domains with interior cuts (cracks). The main results established in the paper are the BDIE equivalence to the original BVPs and invertibility of the BDIE operators in the corresponding Sobolev spaces.This work was supported by the International Joint Project Grant - 2005/R4 ”Boundary- Domain Integral Equations: Formulation, Analysis, Localisation” of the Royal Society, UK, and the grant ”Mathematical analysis of localised boundary-domain integral equations for BVPs with variable coefficients” of the EPSRC, UK

Well-posedness and asymptotic behavior of a multidimensional model of morphogen transport

Morphogen transport is a biological process, occurring in the tissue of living organisms, which is a determining step in cell differentiation. We present rigorous analysis of a simple model of this process, which is a system coupling parabolic PDE with ODE. We prove existence and uniqueness of solutions for both stationary and evolution problems. Moreover we show that the solution converges exponentially to the equilibrium in $C^1\times C^0$ topology. We prove all results for arbitrary dimension of the domain. Our results improve significantly previously known results for the same model in the case of one dimensional domain

Analysis of direct segregated boundary-domain integral equations for variable-coefficient mixed bvps in exterior domains

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2013 World Scientific Publishing.Direct segregated systems of boundary-domain integral equations are formulated for the mixed (Dirichlet–Neumann) boundary value problems for a scalar second-order divergent elliptic partial differential equation with a variable coefficient in an exterior three-dimensional domain. The boundary-domain integral equation system equivalence to the original boundary value problems and the Fredholm properties and invertibility of the corresponding boundary-domain integral operators are analyzed in weighted Sobolev spaces suitable for infinite domains. This analysis is based on the corresponding properties of the BVPs in weighted Sobolev spaces that are proved as well.The work was supported by the grant EP/H020497/1 \Mathematical analysis of localised boundary-domain integral equations for BVPs with variable coefficients" of the EPSRC, UK

A Framework for a Priori Evaluation of Multimodal User Interfaces Supporting Cooperation

International audienceIn this short paper we will present our latest research on a new framework being developed for aiding novice designers of highly interactive, cooperative, multimodal systems to make expert decisions in choice of interaction modalities depending on the type of activity and its cooperative nature. Our research is conducted within the field of maritime surveillance the next generation distributed multimodal work support

Expert evaluation of the usability of HeloVis: a 3D Immersive Helical Visualization for SIGINT Analysis

International audienceThis paper presents an evaluation of HeloVis: a 3D interactive visualization that relies on immersive properties to improve user performance during SIGnal INTelligence (SIGINT) analysis. HeloVis draws on perceptive biases, highlighted by Gestalt laws, and on depth perception to enhance the recurrence properties contained in the data. In this paper, we briefly recall what is SIGINT, the challenges that it brings to visual analytics, and the limitations of state of the art SIGINT tools. Then, we present HeloVis, and we evaluate its efficiency through the results of an evaluation that we have made with civil and military operators who are the expert end-users of SIGINT analysis