High Order Scheme for a Non Linear Maxwell System Modelling Kerr Effect

The paper is devoted to the derivation of an efficient numerical scheme for the Kerr-Maxwell system. We begin by studying the 1-D Riemann problem. We obtain a result of existence and uniqueness for large data. Then we develop a high order Roe solver and exhibit solutions in 1-d and 2-d simulatio- ns

Réduction du conditionnement pour les problèmes de discrétisation microlocale

Dans cet article, nous analysons les propriétés de conditionnement des systèmes linéaires venant de la discrétisation microlocale. Ces systèmes utilisent des fonctions de base localement oscillantes pour modéliser des problèmes de propagation d'onde en régime harmonique. Ces problèmes étant très mal conditionnés, nous proposons d'abord une analyse de la difficulté en terme de \emph{sur-discrétisation} ; celle-ci créant des ondes évanescentes. La première solution que nous regardons est de projeter le problème sur l'espace orthogonal à ces modes. Nous faisons cela sur un problème modèle mais ça n'est pas une solution satisfaisante pour des systèmes de taille importante. Nous proposons alors de transformer le système à l'aide d'une base d'ondelettes. Il apparaît que cette transformation différencie fortement les gros coefficients des petits. Ceci nous permet de réaliser un filtrage de la matrice transformée pour obtenir un système réduit qui est bien conditionné. Il s'agit ici d'un usage non classique des ondelettes puisqu'elles agissent dans le domaine spectral. Nous obtenons finalement une méthode qui n'utilise qu'un degré de liberté par longueur d'onde environ pour simuler des problèmes de diffraction

Imagerie microonde : reconstruction quantitative du profil de permittivité complexe d'hétérogénéités enterrées.

Ce rapport propose plusieurs algorithmes d'inversion quantitative permettant la reconstruction des profils de permittivité et de conductivité d'objets enterrés à partir de la mesure d'un champ électromagnétique diffracté. Toutes les méthodes itératives développées dans le rapport utilisent les propriétés des approches multifréquence et multiincidence. Une technique de régularisation avec préservation des discontinuités de l'objet est enfin introduite dans le processus de reconstruction. Chaque partie est illustrée à l'aide d'images reconstruites à partir de données simulées

Gaze trajectory prediction in the context of social robotics

Social robotics is an emerging field of robotics that focuses on the interactions between robots and humans. It has attracted much interest due to concerns about an aging society and the need for assistive environments. Within this context, this paper focuses on gaze control and eye tracking as a means for robot control. It aims to improve the usability of human–machine interfaces based on gaze control by developing advanced algorithms for predicting the trajectory of the human gaze. The paper proposes two approaches to gaze-trajectory prediction: probabilistic and symbolic. Both approaches use machine learning. The probabilistic method mixes two state models representing gaze locations and directions. The symbolic method treats the gaze-trajectory prediction problem similar to how word-prediction problems are handled in web browsers. Comparative experiments prove the feasibility of both approaches and show that the probabilistic approach achieves better prediction results

A high-wavenumber boundary-element method for an acoustic scattering problem

In this paper we show stability and convergence for a novel Galerkin boundary element method approach to the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data. This problem models, for example, outdoor sound propagation over inhomogeneous flat terrain. To achieve a good approximation with a relatively low number of degrees of freedom we employ a graded mesh with smaller elements adjacent to discontinuities in impedance, and a special set of basis functions for the Galerkin method so that, on each element, the approximation space consists of polynomials (of degree $\nu$) multiplied by traces of plane waves on the boundary. In the case where the impedance is constant outside an interval $[a,b]$, which only requires the discretization of $[a,b]$, we show theoretically and experimentally that the $L_2$ error in computing the acoustic field on $[a,b]$ is ${\cal O}(\log^{\nu+3/2}|k(b-a)| M^{-(\nu+1)})$, where $M$ is the number of degrees of freedom and $k$ is the wavenumber. This indicates that the proposed method is especially commendable for large intervals or a high wavenumber. In a final section we sketch how the same methodology extends to more general scattering problems

A non Overlapping Domain Decomposition Method for the Exterior Helmholtz Problem

In this paper, we first show that the domain decomposition methods that are usually efficient for solving elliptic problems typically fail when applied to acoustics problems.Next, we present an alternative domain decomposition algorithm that is better suited for the exterior Helmholtz problem. We describe it in a formalism that can use either one or two Lagrange multiplier fields for solving the corresponding interface problem by a Krylov method. In order to improve convergence and ensure scalability with respect the number of subdomains, we propose two complementary preconditioning techniques. The first preconditioner is based on a spectral analysis of the resulting interface operator and targets the high frequency components of the error. The second preconditioner is based on a coarsening technique, employs plane waves, and addresses the low frequency components of the error. Finally, we show numerically that, using both preconditioners, the convergence rate of the proposed domain decomposition method is quasi independent of the number of elements in the mesh, the number of subdomains, and depends only weakly on the wavenumber, which makes this method uniquely suitable for solving large-scale high frequency exterior acoustics problems

Stage-Wise Learning of Reaching Using Little Prior Knowledge

In some manipulation robotics environments, because of the difficulty of precisely modeling dynamics and computing features which describe well the variety of scene appearances, hand-programming a robot behavior is often intractable. Deep reinforcement learning methods partially alleviate this problem in that they can dispense with hand-crafted features for the state representation and do not need pre-computed dynamics. However, they often use prior information in the task definition in the form of shaping rewards which guide the robot toward goal state areas but require engineering or human supervision and can lead to sub-optimal behavior. In this work we consider a complex robot reaching task with a large range of initial object positions and initial arm positions and propose a new learning approach with minimal supervision. Inspired by developmental robotics, our method consists of a weakly-supervised stage-wise procedure of three tasks. First, the robot learns to fixate the object with a 2-camera system. Second, it learns hand-eye coordination by learning to fixate its end-effector. Third, using the knowledge acquired in the previous steps, it learns to reach the object at different positions and from a large set of initial robot joint angles. Experiments in a simulated environment show that our stage-wise framework yields similar reaching performances, compared with a supervised setting without using kinematic models, hand-crafted features, calibration parameters or supervised visual modules

On the initial estimate of interface forces in FETI methods

The Balanced Domain Decomposition (BDD) method and the Finite Element Tearing and Interconnecting (FETI) method are two commonly used non-overlapping domain decomposition methods. Due to strong theoretical and numerical similarities, these two methods are generally considered as being equivalently efficient. However, for some particular cases, such as for structures with strong heterogeneities, FETI requires a large number of iterations to compute the solution compared to BDD. In this paper, the origin of the bad efficiency of FETI in these particular cases is traced back to poor initial estimates of the interface stresses. To improve the estimation of interface forces a novel strategy for splitting interface forces between neighboring substructures is proposed. The additional computational cost incurred is not significant. This yields a new initialization for the FETI method and restores numerical efficiency which makes FETI comparable to BDD even for problems where FETI was performing poorly. Various simple test problems are presented to discuss the efficiency of the proposed strategy and to illustrate the so-obtained numerical equivalence between the BDD and FETI solvers

Conventional Anti-glioblastoma Chemotherapy Affects Proteoglycan Composition of Brain Extracellular Matrix in Rat Experimental Model in vivo

Temozolomide (TMZ) is a conventional chemotherapy drug for adjuvant treatment of glioblastoma multiforme (GBM), often accompanied by dexamethasone (DXM) to prevent brain oedema and alleviate clinical side effects. Here, we aimed to investigate an ability of the drugs to affect normal brain tissue in terms of proteoglycan (PG) composition/content in experimental rat model in vivo. Age- and brain zone-specific transcriptional patterns of PGs were demonstrated for 8, 60, and 120 days old rats, and syndecan-1, glypican-1, decorin, biglycan, and lumican were identified as the most expressed PGs. DXM treatment affected both PG core proteins expression (mainly syndecan-1, glypican-1, decorin, biglycan, lumican, versican, brevican, and NG2) and heparan sulphate (HS)/chondroitin sulphate (CS) content in organotypic brain slice culture ex vivo and experimental animals in vivo in a dose-dependent manner. TMZ treatment did not result in the significant changes in PG core proteins expression both in normal rat brain hippocampus and cortex in vivo (although generics did), but demonstrated significant effects onto polysaccharide HS/CS content in the brain tissue. The effects were age- and brain zone-specific and similar with the age-related PGs expression changes in rat brain. Combination of TMZ with DXM resulted in the most profound deterioration in PGs composition and content in the brain tissue both at core protein and glycosaminoglycan levels. Taken together, the obtained results demonstrate that conventional anti-glioblastoma therapy affects proteoglycan structure and composition in normal brain tissue, potentially resulting in deterioration of brain extracellular matrix and formation of the favourable tumorigenic niche for the expansion of the residual glioma cells. During the TMZ chemotherapy, dose and regimen of DXM treatment matter, and repetitive low DXM doses seem to be more sparing treatment compared with high DXM dose(s), which should be avoided where possible, especially in combination with TMZ

Renal macro- and microcirculation autoregulatory capacity during early sepsis and norepinephrine infusion in rats

INTRODUCTION: The relationships between systemic hemodynamics and renal blood flow and renal microcirculation are poorly known in sepsis. Norepinephrine (NE) infusion may add another level of complexity. METHODS: Ventilated and anesthetized rats were submitted to various mean arterial pressure (MAP) steps by blood removal, in presence and absence of sepsis and/or NE. Renal blood flow (RBF) and blood velocity (Vm) in renal cortical capillaries (using Sidestream Dark Field Imaging) were measured. Data were analyzed using linear mixed models enabling us to display the effects of both the considered explanatory variables and their interactions. RESULTS: Positive correlations were found between MAP and RBF. Sepsis had no independent impact on RBF whereas norepinephrine decreased RBF, regardless of the presence of sepsis. The relationship between MAP and RBF was weaker above a MAP of 100 mmHg as opposed to below 100 mmHg, with RBF displaying a relative "plateau" above this threshold. Sepsis and NE impacted carotid blood flow (CBF) differently compared to RBF, demonstrating organ specificity. A positive relationship was observed between MAP and Vm. Sepsis increased Vm while nNE decreased Vm irrespective of MAP. Sepsis was associated with an increase in serum creatinine determined at the end of the experiments, which was prevented by NE infusion. CONCLUSION: In our model, sepsis at an early phase did not impact RBF over a large range of MAP. NE elicited a renal vasoconstrictive effect. Autoregulation of RBF appeared conserved in sepsis. Conversely, sepsis was associated with "hypervelocity" of blood flow in cortical peritubular capillaries reversed by NE infusion