École normale supérieure de Cachan

About: École normale supérieure de Cachan is a education organization based out in Cachan, Île-de-France, France. It is known for research contribution in the topics: Decidability & Nonlinear system. The organization has 2717 authors who have published 5585 publications receiving 175925 citations.

Weak approximation of stochastic partial differential equations: the nonlinear case

Abstract: We study the error of the Euler scheme applied to a stochastic partial dierential equation We prove that as it is often the case, the weak order of convergence is twice the strong order A key ingredient in our proof is Malliavin calculus which enables us to get rid of the irregular terms of the error We apply our method to the case a semilinear stochastic heat equation driven by a space-time white noise

Stable stationary states of non-local interaction equations

Abstract: In this paper, we are interested in the large-time behaviour of a solution to a non-local interaction equation, where a density of particles/individuals evolves subject to an interaction potential and an external potential. It is known that for regular interaction potentials, stable stationary states of these equations are generically finite sums of Dirac masses. For a finite sum of Dirac masses, we give (i) a condition to be a stationary state, (ii) two necessary conditions of linear stability w.r.t. shifts and reallocations of individual Dirac masses, and (iii) show that these linear stability conditions imply local non-linear stability. Finally, we show that for regular repulsive interaction potential We converging to a singular repulsive interaction potential W, the Dirac-type stationary states approximate weakly a unique stationary state . We illustrate our results with numerical examples.

Spatiotemporal Atlas Estimation for Developmental Delay Detection in Longitudinal Datasets

Abstract: We propose a new methodology to analyze the anatomical variability of a set of longitudinal data (population scanned at several ages). This method accounts not only for the usual 3D anatomical variability (geometry of structures), but also for possible changes in the dynamics of evolution of the structures. It does not require that subjects are scanned the same number of times or at the same ages. First a regression model infers a continuous evolution of shapes from a set of observations of the same subject. Second, spatiotemporal registrations deform jointly (1) the geometry of the evolving structure via 3D deformations and (2) the dynamics of evolution via time change functions. Third, we infer from a population a prototype scenario of evolution and its 4D variability. Our method is used to analyze the morphological evolution of 2D profiles of hominids skulls and to analyze brain growth from amygdala of autistics, developmental delay and control children.

Separation of Photoactive Conformers Based on Hindered Diarylethenes: Efficient Modulation in Photocyclization Quantum Yields

Abstract: Endowing both solvent independency and excellent thermal bistability, the benzobis(thiadiazole)-bridged diarylethene system provides an efficient approach to realize extremely high photocyclization quantum yields (Φo-c, up to 90.6 %) by both separating completely pure anti-parallel conformer and suppressing intramolecular charge transfer (ICT).