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Clarke F.,Camille Jordan Institute
Annual Reviews in Control | Year: 2011

We study the controllability and stability of control systems that are nonlinear, and for which, for whatever reason, linearization fails. We begin by motivating the need for two seemingly exotic tools: nonsmooth control-Lyapunov functions, and discontinuous feedbacks. With the aid of nonsmooth analysis, we build a theory around these tools. We proceed to apply it in various contexts, focusing principally on the design of discontinuous stabilizing feedbacks. © 2010 Elsevier Ltd. All rights reserved.

Ernst A.,Karolinska Institutet | Alkass K.,Karolinska Institutet | Bernard S.,Camille Jordan Institute | Salehpour M.,Uppsala University | And 5 more authors.
Cell | Year: 2014

In most mammals, neurons are added throughout life in the hippocampus and olfactory bulb. One area where neuroblasts that give rise to adult-born neurons are generated is the lateral ventricle wall of the brain. We show, using histological and carbon-14 dating approaches, that in adult humans new neurons integrate in the striatum, which is adjacent to this neurogenic niche. The neuronal turnover in the striatum appears restricted to interneurons, and postnatally generated striatal neurons are preferentially depleted in patients with Huntington's disease. Our findings demonstrate a unique pattern of neurogenesis in the adult human brain. © 2014 Elsevier Inc.

Le Roux D.Y.,Camille Jordan Institute
Journal of Computational Physics | Year: 2012

For most of the discretization schemes, the numerical approximation of shallow-water models is a delicate problem. Indeed, the coupling between the momentum and the continuity equations usually leads to the appearance of spurious solutions and to anomalous dissipation/dispersion in the representation of the fast (Poincaré) and slow (Rossby) waves. In order to understand these difficulties and to select appropriate spatial discretization schemes, Fourier/dispersion analyses and the study of the null space of the associated discretized problems have proven beneficial. However, the cause of spurious oscillations and reduced convergence rates, that have been detected for most of mixed-order finite element shallow-water formulations, in simulating classical problems of geophysical fluid dynamics, is still an open question. The aim of the present study is to show that when spurious inertial solutions are present, they are mainly responsible for the aforementioned problems. Further, a criterion is found which determines the existence and the number of spurious inertial solutions. As it is delicate to cure spurious inertial modes, a class of possible discretization schemes is proposed, that is not affected by such spurious solutions. © 2012 Elsevier Inc.

Filbet F.,Camille Jordan Institute
Multiscale Modeling and Simulation | Year: 2012

In this paper we present several numerical results performed with a fully deterministic scheme to discretize the Boltzmann equation of rarefied gas dynamics in a bounded domain for multiscale problems. Periodic, specular reflection and diffusive boundary conditions are discussed and investigated numerically. The collision operator is treated by a Fourier approximation of the collision integral, which guarantees spectral accuracy in velocity with a computational cost of MN log(N), where N is the number of degrees of freedom in velocity space andM represents the number of discrete angles of the collision kernel. This algorithm is coupled with a second order finite volume scheme in space and a time discretization allowing us to deal for rarefied regimes as well as their hydrodynamic limit. Our numerical results show that the proposed approach significantly improves the near-wall nonstationary flow accuracy of standard numerical methods over a wide range of Knudsen numbers, in particular when the solution to the Boltzmann equation is close to the local equilibrium and for slow motion flows. © 2012 Society for Industrial and Applied Mathematics.

Kasraoui A.,Camille Jordan Institute
European Journal of Combinatorics | Year: 2010

We put recent results on the symmetry of the joint distribution of the numbers of crossings and nestings of two edges over matchings, set partitions and linked partitions in the larger context of enumeration of increasing and decreasing sequences of length 2 in fillings of moon polyominoes. © 2009 Elsevier Ltd. All rights reserved.

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