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Asymptotic stability of small solitons in one dimension is proved in the framework of a discrete nonlinear Schr¨odinger equation with septic and higher power-law nonlinearities and an external potenti...
Most business processes are, by nature, multivariate and autocorrelated. Highdimensionality is rooted in processes where more than one variable is considered simultaneously to provide a more comprehen...
We show that the even- resp. odd-dimensional Schoenberg coefficients in Gegenbauer expansions of isotropic positive definite functions on the d-sphere can be expressed as linear combinations of Fourie...
This paper revisits the classical inference results for profile quasi maximum likelihood estimators (profile MLE) in the semiparametric estimation problem. We mainly focus on two prominent theorems: t...
We introduce a new approach to variable selection, called Predictive Correlation Screening, for predictor design. Predictive Correlation Screening (PCS) implements false positive control on the select...
What is the response of the climate system to anthropogenic forcings? This question is addressed typically using projections from climate models. The uncertainty surrounding current climate projection...
We consider the problem of identifying whether findings replicate from one study of high dimension to another, when the primary study guides the selection of hy-potheses to be examined in the follow-u...
We consider dimension reduction for regression or classification in which the predictors are matrix- or array-valued. This type of pre- dictor arises when measurements are obtained for each combinat...
Mouvements browniens asymetriques modifies en dimension finie et operateurs differentiels a coefficients discontinus。
Suppose that X is a two-dimensional Brownian motion. The trace X[O, I] contains a self-avoiding continuous path whose Hausdorff dimension is equal to 2.
Let X(t) (ts R,) be an u-self-similar Markov process on Rd or Rd+. The Hausdorff dimension of the image, graph and zero set of X(t) are obtained under certain mild conditions. Similar results are a...
We prove that under a general condition interpolation dimensions of H-sssi process converge in probabiIity to 2-H. The result can be applied to a wide class of H-sssi processes which includes fract...
We consider a $l_1$-penalization procedure in the non-parametric Gaussian regression model. In many concrete examples, the dimension $d$ of the input variable $X$ is very large (sometimes depending on...
We analyse the properties of the Principal Fitted Components (PFC) algorithm proposed by Cook. We derive theoretical properties of the resulting estimators, including sufficient conditions under which...
In a system made up of independent random walks fluctuations of order 1/4 n from the hydrodynamic limit come from particle current across characteristics. We show that a two-parameter space-time par...

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