Institute Of Mathematiques Of Toulouse

Toulouse, France

Institute Of Mathematiques Of Toulouse

Toulouse, France
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Mestre O.,Institute Of Mathematiques Of Toulouse | Gruber C.,Zentralanstalt fur Meteorologie und Geodynamik | Prieur C.M.,Joseph Fourier University | Caussinus H.,University Paul Sabatier | Jourdain S.,Direction de la Climatologie
Journal of Applied Meteorology and Climatology | Year: 2011

One major concern of climate change is the possible rise of temperature extreme events, in terms of occurrence and intensity. To study this phenomenon, reliable daily series are required, for instance to compute dailybased indices: high-order quantiles, annual extrema, number of days exceeding thresholds, and so on. Because observed series are likely to be affected by changes in the measurement conditions, adapted homogenization procedures are required. Although a very large number of procedures have been proposed for adjustment of observed series at amonthly time scale, fewhave been proposed for adjustment of daily temperature series. This article proposes a newadjustmentmethod for temperature series at a daily time scale. This method, called spline daily homogenization (SPLIDHOM), relies on an indirect nonlinear regression method. Estimation of the regression functions is performed by cubic smoothing splines. This method is able to adjust the mean of the series aswell as high-order quantiles andmoments of the series. When usingwell-correlated series, SPLIDHOM improves the results of two widely usedmethods, as a result of an optimal selection of the smoothing parameter. Applications to the Toulouse, France, temperature series are shown as a real example. © 2011 American Meteorological Society.

Ervedoza S.,Institute Of Mathematiques Of Toulouse | Hillairet M.,University of Paris Dauphine | Lacave C.,University Paris Diderot
Communications in Mathematical Physics | Year: 2014

In this article, we study the long-time behavior of solutions of the two-dimensional fluid-rigid disk problem. The motion of the fluid is modeled by the two-dimensional Navier-Stokes equations, and the disk moves under the influence of the forces exerted by the viscous fluid. We first derive L p-L q decay estimates for the linearized equations and compute the first term in the asymptotic expansion of the solutions of the linearized equations. We then apply these computations to derive time-decay estimates for the solutions to the full Navier-Stokes fluid-rigid disk system. © 2014 Springer-Verlag Berlin Heidelberg.

Egorov Y.V.,Institute Of Mathematiques Of Toulouse
Automation and Remote Control | Year: 2012

One of the unsolved problems of the theory of optimal control, the Butkovskii variational problem which is of importance for applications, was solved.Original Russian Text © F.A. Aliev.

Bouclet J.-M.,Institute Of Mathematiques Of Toulouse | Royer J.,Institute Of Mathematiques Of Toulouse
Communications in Mathematical Physics | Year: 2015

On a class of asymptotically conical manifolds, we prove two types of low frequency estimates for the resolvent of the Laplace-Beltrami operator. The first result is a uniform (Formula Presented) when Re(z) is small, with the optimal weight (Formula Presented). The second one is about powers of the resolvent. For any integer N, we prove uniform (Formula Presented) when Re(Z) belongs to a compact subset of (0, + ∞) and (Formula Presented). These results are obtained by proving similar estimates on a pure cone with a long range perturbation of the metric at infinity. © 2015, Springer-Verlag Berlin Heidelberg.

Fehrenbach J.,Institute Of Mathematiques Of Toulouse | Masmoudi M.,Institute Of Mathematiques Of Toulouse | Melodelima D.,French Institute of Health and Medical Research | Melodelima D.,University of Lyon
Ultrasonics | Year: 2010

This study presents a contribution to the tracking of a moving target during high-intensity focused ultrasound (HIFU) treatment. Indeed, HIFU has proved to be highly efficient in inducing homogeneous and reproducible tumor destruction by thermal coagulation necrosis. However, accurate targeting of human abdominal tumors is difficult to maintain due to the motion induced by breathing. An algorithm is presented to track a region of interest of fixed size in a sequence of images. This algorithm was evaluated on synthetic data and on in vivo sequences of ultrasound liver images acquired using 12 MHz ultrasound imaging probe at a rate of 16 frames/s. The algorithm presented here was derived from the non-linear constant brightness assumption. Since the motion was smooth it was possible to reduce the space of admissible displacements; hence the number of unknown parameters was small compared with the size of the data. The optimal displacement was estimated by a Gauss-Newton method, and the matrix required at each step was assembled by reading the data only once. This algorithm was applied to simulated data, where the true displacement was known and a precise evaluation was possible. The relative error was about 2%. The algorithm was also applied to a video sequence of sonograms acquired during in vivo experiments. These trials were conducted on porcine liver since its size and physiology are similar to humans. Movements were induced by breathing and heart-beating. Two particular frequencies representing breathing (0.26 Hz) and heart beat (1.14 Hz) were identified in the estimated displacement and were correlated with the monitored breathing (0.27 Hz) and electrocardiograms (1.28 Hz). In addition, a region of interest (ROI) modeling the focal zone of a HIFU transducer was tracked along time. Therefore this study provides a mean of determining the location of the targeted region in vivo during HIFU treatments. This can be applied to correct the location of the focal zone accordingly. This method can preferentially be applied to the liver or to any other moving organ. © 2009 Elsevier B.V. All rights reserved.

Royer J.,Institute Of Mathematiques Of Toulouse
Annales Henri Poincare | Year: 2015

We prove exponential decay for the solution of the Schrödinger equation on a dissipative waveguide. The absorption is effective everywhere on the boundary, but the geometric control condition is not satisfied. The proof relies on separation of variables and the Riesz basis property for the eigenfunctions of the transverse operator. The case where the absorption index takes negative values is also discussed. © 2014, Springer Basel.

Ferraty F.,Institute Of Mathematiques Of Toulouse | Hall P.,University of Melbourne | Vieu P.,Institute Of Mathematiques Of Toulouse
Biometrika | Year: 2010

We suggest a way of reducing the very high dimension of a functional predictor, X, to a low number of dimensions chosen so as to give the best predictive performance. Specifically, if X is observed on a fine grid of design points t1,..., tr, we propose a method for choosing a small subset of these, say ti1,..., ti k, to optimize the prediction of a response variable, Y. The values tij are referred to as the most predictive design points, or covariates, for a given value of k, and are computed using information contained in a set of independent observations (Xi, Yi) of (X, Y). The algorithm is based on local linear regression, and calculations can be accelerated using linear regression to preselect the design points. Boosting can be employed to further improve the predictive performance. We illustrate the usefulness of our ideas through simulations and examples drawn from chemometrics, and we develop theoretical arguments showing that the methodology can be applied successfully in a range of settings. © 2010 Biometrica Trust.

Bachoc F.,Institute Of Mathematiques Of Toulouse | Ammar K.,CEA Saclay Nuclear Research Center | Martinez J.-M.,CEA Saclay Nuclear Research Center
Nuclear Science and Engineering | Year: 2016

It is now common practice in nuclear engineering to base extensive studies on numerical computer models. These studies require running computer codes in potentially thousands of numerical configurations and without expert individual controls on the computational and physical aspects of each simulation. In this paper, we compare different statistical metamodeling techniques and show how metamodels can help improve the global behavior of codes in these extensive studies. We consider the metamodeling of the Germinal thermomechanical code by Kriging, kernel regression, and neural networks. Kriging provides the most accurate predictions, while neural networks yield the fastest metamodel functions. All three metamodels can conveniently detect strong computation failures. However, it is more challenging to detect code instabilities, that is, groups of computations that are all valid but numerically inconsistent with one another. For code instability detection, we find that Kriging provides an interesting tool.

Apkarian P.,ONERA | Dao M.N.,Hanoi National University of Education | Noll D.,Institute Of Mathematiques Of Toulouse
IEEE Transactions on Automatic Control | Year: 2015

We present a new approach to parametric robust controller design, where we compute controllers of arbitrary order and structure which minimize the worst-case H∞ norm over a pre-specified set of uncertain parameters. At the core of our method is a nonsmooth minimization method tailored to functions which are semi-infinite minima of smooth functions. A rich test bench and a more detailed example illustrate the potential of the technique, which can deal with complex problems involving multiple possibly repeated uncertain parameters. © 2015 IEEE.

Dimarco G.,University of Ferrara | Mieussens L.,Institute Of Mathematiques Of Bordeaux | Rispoli V.,Institute Of Mathematiques Of Toulouse
Journal of Computational Physics | Year: 2014

In this work we present an efficient strategy to deal with plasma physics simulations in which localized departures from thermodynamical equilibrium are present. The method is based on the introduction of intermediate regions which allows smooth transitions between kinetic and fluid zones. In this paper we extend Domain Decomposition techniques, obtained through dynamic coupling and buffer zones, to the study of plasmas and, moreover, we combine them with Asymptotic Preserving and Asymptotically Accurate strategies for the time integration. We use a hybrid scheme in which both kinetic and fluid descriptions are considered and coupled together while the kinetic model is solved by asymptotic preserving and accurate methods, in order to guarantee high efficiency and accuracy in all regimes. The numerical scheme is validated and its performances are analyzed by numerical simulations. © 2014 Elsevier Inc.

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