‎We provide a uniform estimate for the $L^1$-norm (over any interval of bounded length) of the logarithmic derivatives‎ ‎of global normalizing factors associated to intertwining operators for the following reductive groups over number fields‎: ‎inner forms of $operatorname{GL}(n)$; quasi-split classical groups and their similitude groups; the exceptional group $G_2$‎. ‎This estimate is a key in...

The robust estimation of the low-dimensional subspace that spans the data from a set of high-dimensional, possibly corrupted by gross errors and outliers observations is fundamental in many computer vision problems. The state-of-the-art robust principal component analysis (PCA) methods adopt convex relaxations of `0 quasi-norm-regularised rank minimisation problems. That is, the nuclear norm an...

The aim of a phase I oncology trial is to identify a dose with an acceptable safety profile. Most phase I designs use the dose-limiting toxicity, a binary endpoint, to assess the unacceptable level of toxicity. The dose-limiting toxicity might be incomplete for investigating molecularly targeted therapies as much useful toxicity information is discarded. In this work, we propose a quasi-continu...

We analyze low rank tensor completion (TC) using noisy measurements of a subset of the tensor. Assuming a rank-$r$, order-$d$, $N \times N \times \cdots \times N$ tensor where $r=O(1)$, the best sampling complexity that was achieved is $O(N^{\frac{d}{2}})$, which is obtained by solving a tensor nuclear-norm minimization problem. However, this bound is significantly larger than the number of fre...

Recently, Brezis, Van Schaftingen and the second author [4] established a new formula for W ? 1 , p norm of function in C c ? ( R N ) . The was obtained by replacing L 2 Gagliardo semi-norm s with weak- quasi-norm setting = This provides characterization such norms, which complements celebrated Bourgain-Brezis-Mironescu (BBM) [1] In this paper, we obtain an analog case 0 particular, present any...

We generalize the a posteriori techniques for the linear heat equation in [Ver03] to the case of the nonlinear parabolic p-Laplace problem thereby proving reliable and efficient a posteriori error estimates for a fully discrete implicite Euler Galerkin finite element scheme. The error is analyzed using the so-called quasi-norm and a related dual error expression. This leads to equivalence of th...

D epartement de math ematiques Universit e du Qu ebec a Montr eal 0 PRELIMINARIES 1 Abstract One important challenge in non{parametric density and regression{function estimation is spatially inhomogeneous smoothness. This is often modelled by Besov-and Triebel{type smoothness constraints. Donoho and Johnstone (1992), Delyon and Juditsky (1993) studied minimax rates of convergence for wavelet es...

Properties of first-order Sobolev-type spaces on abstract metric measure spaces, so-called Newtonian spaces, based on quasi-Banach function lattices are investigated. The set of all weak upper gradients of a Newtonian function is of particular interest. Existence of minimal weak upper gradients in this general setting is proven and corresponding representation formulae are given. Furthermore, t...