Related papers: $\alpha$-Molecules
Predicting materials properties from composition or structure is of great interest to the materials science community. Deep learning has recently garnered considerable interest in materials predictive tasks with low model errors when…
In this work, we derive a generic overcomplete frame thresholding scheme based on risk minimization. Overcomplete frames being favored for analysis tasks such as classification, regression or anomaly detection, we provide a way to leverage…
We introduce an algorithm of joint approximation of a function and its first derivative by alternative orthogonal polynomials on the interval [0,1].The algorithm exhibits properties of shape preserving approximation for the function. A weak…
In this paper, we analyze the error estimate of a wavelet frame based image restoration method from degraded and incomplete measurements. We present the error between the underlying original discrete image and the approximate solution which…
We propose a novel error analysis framework for scaled generalized Laguerre and generalized Hermite approximations.This framework can be regarded as an analogue of the Nyquist-Shannon sampling theorem: It characterizes the spatial and…
This letter aims at resolving the issues raised in the recent short communication [1] and answered by [2] by proposing a systematic approximation scheme based on non-mapped shape functions, which both allows to fully exploit the unique…
In deep learning, achieving high performance on image classification tasks requires diverse training sets. However, the current best practice$\unicode{x2013}$maximizing dataset size and class balance$\unicode{x2013}$does not guarantee…
A new Hardy space Hardy space approach of Dirichlet type problem based on Tikhonov regularization and Reproducing Hilbert kernel space is discussed in this paper, which turns out to be a typical extremal problem located on the upper…
In this contribution we are interested in the quantitative homogenization properties of linear elliptic equations with homogeneous Dirichlet boundary data in polygonal domains with corners. To begin our study of this situation, we consider…
We describe S2LET, a fast and robust implementation of the scale-discretised wavelet transform on the sphere. Wavelets are constructed through a tiling of the harmonic line and can be used to probe spatially localised, scale-depended…
A new likelihood based AR approximation is given for ARMA models. The usual algorithms for the computation of the likelihood of an ARMA model require $O(n)$ flops per function evaluation. Using our new approximation, an algorithm is…
In this work, we develop an adaptive nonconforming finite element algorithm for the numerical approximation of phase-field parameterized topology optimization governed by the Stokes system. We employ the conforming linear finite element…
We present a new framework for multi-line analysis that combines kernel principal component analysis (Kernel PCA), an unsupervised machine-learning method, and Kernel SHapley Additive exPlanations (Kernel SHAP), an explainable artificial…
Condensates of active particles such as cells form almost-crystalline lattices which play a central role in many biological systems. Typically, their properties have been determined merely by analogy to the rather trivial one-dimensional…
In this paper we construct a class of random matrix ensembles labelled by a real parameter $\alpha \in (0,1)$, whose eigenvalue density near zero behaves like $|x|^\alpha$. The eigenvalue spacing near zero scales like $1/N^{1/(1+\alpha)}$…
In this article we present a modification of classical Radial Basis Function (RBF) interpolation techniques aimed at reducing oscillations near discontinuities in one and two dimensions. Our approach introduces an adaptive mechanism by…
In this paper we present results on asymptotic characteristics of multivariate function classes in the uniform norm. Our main interest is the approximation of functions with mixed smoothness parameter not larger than $1/2$. Our focus will…
In a previous paper we have introduced a new class of radial basis functions that are powerful means to approximate functions by quasi-interpolation. In this article we extend the results to create new ways of approximating functions by…
We consider the problem of characterizing the wavefront set of a tempered distribution $u\in\mathcal{S}'(\mathbb{R}^{d})$ in terms of its continuous wavelet transform, where the latter is defined with respect to a suitably chosen dilation…
In this paper we develop a general theory of metric Diophantine approximation for systems of linear forms. A new notion of `weak non-planarity' of manifolds and more generally measures on the space of $m\times n$ matrices over $\Bbb R$ is…