Rush-Larsen time-stepping methods of high order for stiff problems in cardiac electrophysiology

To address the issues of stability and accuracy for reaction-diffusion equations, the development of high order and stable time-stepping methods is necessary. This is particularly true in the context of cardiac electrophysiology, where reaction-diffusion equations are coupled with stiff ODE systems. Many research have been led in that way in the past 15 years concerning implicit-explicit methods and exponential integrators. In 2009, Perego and Veneziani proposed an innovative time-stepping method of order 2. In this paper we present the extension of this method to the orders 3 and 4 and introduce the Rush-Larsen schemes of order k (shortly denoted RL\_k). The RL\_k schemes are explicit multistep exponential integrators. They display a simple general formulation and an easy implementation. The RL\_k schemes are shown to be stable under perturbation and convergent of order k. Their Dahlquist stability analysis is performed. They have a very large stability domain provided that the stabilizer associated with the method captures well enough the stiff modes of the problem. The RL\_k method is numerically studied as applied to the membrane equation in cardiac electrophysiology. The RL k schemes are shown to be stable under perturbation and convergent oforder k. Their Dahlquist stability analysis is performed. They have a very large stability domain provided that the stabilizer associated with the method captures well enough the stiff modes of the problem. The RL k method is numerically studied as applied to the membrane equation in cardiac electrophysiology

Pointwise adaptive estimation for robust and quantile regression

A nonparametric procedure for robust regression estimation and for quantile regression is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each point M-estimators over different local neighbourhoods and by a local model selection procedure based on sequential testing. Non-asymptotic risk bounds are obtained, which yield rate-optimality for large sample asymptotics under weak conditions. Simulations for different univariate median regression models show good finite sample properties, also in comparison to traditional methods. The approach is extended to image denoising and applied to CT scans in cancer research

Pointwise adaptive estimation for quantile regression

A nonparametric procedure for quantile regression, or more generally nonparametric M-estimation, is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each point M-estimators over different local neighbourhoods and by a local model selection procedure based on sequential testing. Non-asymptotic risk bounds are obtained, which yield rate-optimality for large sample asymptotics under weak conditions. Simulations for different univariate median regression models show good finite sample properties, also in comparison to traditional methods. The approach is the basis for denoising CT scans in cancer research.M-estimation, median regression, robust estimation, local model selection, unsupervised learning, local bandwidth selection, median filter, Lepski procedure, minimax rate, image denoising

The question of empire today

Y.C. Zarka, tomando como referencia la política exterior de Estados Unidos, presenta una reflexión en perspectiva histórica, política y filosófica sobre la idea contemporánea de imperio. Los modelos del imperio romano y del imperio colonial han sido abandonados. El imperialismo contemporáneo impone su hegemonía por las vías económica y cultural. Partiendo de la dialéctica imperio-imperialismo, desde los conceptos de soberanía y democracia, el autor muestra las contradicciones internas y externas de lo que denomina repúblicas imperiales. Desde la primera perspectiva, la hegemonía imperial puede ser interpretada al mismo tiempo como la expresión y la crisis de la soberanía. Desde la segunda, la contradicción se encuentra en la justificación de una política internacional intervencionista en nombre de las ideas de libertad, república y democracia.Y.C. Zarka, has taking the foreign policy of the United States as a reference, presenting a reflection on the contemporary idea of empire in historical, political and philosophical perspective. The models of the Roman Empire and the colonial empire have been left behind. The contemporary imperialism enforces its hegemony by economy and culture. Due the empire-imperialism dialectic, the author shows the internal and external contradictions of what he names "imperial republics". For instance: the imperial hegemony can be interpreted as expression and crisis of the idea sovereignty; the interventionist international policy is justified on behalf of freedom, republic and democracy ideas.Publicad

La tolerancia o cómo coexistir en un mundo desgarrado

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Loi de position?

La loi de position tire sa force de son imprécision, de son refus d’examiner avec rigueur les faits du passé et de son recours au futur pour ignorer les cas les plus récalcitrants. Spence (1988) se porte néanmoins à sa rescousse dans ce numéro. Son argumentation, cependant, est minée par de nombreuses généralisations hâtives, pour ne pas dire fausses. Il concède à mes remarques antérieures (Morin 1986) que la longueur pourrait avoir eu une influence, mais déforme souvent mes propos. En particulier, il m’attribue à tord la thèse que « la qualité des voyelles contemporaines [du français] se rattacherait […] à leur longueur en français moyen »— une thèse qui est clairement farfelue et qu’il n’a aucun mal à discréditer.The loi de position draws its strength from its lack of precision, its cursory concern for historical facts, and its appeal to future evolution to set aside recalcitrant data. Spence (1988) will nevertheless champion its cause in this journal. His argumentation, however, suffers from being based on numerous hasty—not to say false—generalizations. He will concede that vocalic length might have had some influence, but to much less an extent than he claims I proposed (Morin 1986). He presents a distorted view of my analysis; in particular, he imputes me the thesis that "vowel quality in modern French would derive from vocalic length in middle French"—which is so obviously false that he has no difficulty in falsifying it