arXiv subjects

Wolfgang zu Castell

Publications and source records attributed to Wolfgang zu Castell.

6 recordsLinked to original sources

arXiv2024

Towards a Quality Indicator for Research Data publications and Research Software publications -- A vision from the Helmholtz Association

Research data and software are widely accepted as an outcome of scientific work. However, in comparison to text-based publications, there is not yet an established process to assess and evaluate quality of research data and research software publications. This paper presents an attempt to fill this gap. Initiated by the Working Group Open Science of the Helmholtz Association the Task Group Helmholtz Quality Indicators for Data and Software Publications currently develops a quality indicator for research data and research software publications to be used within the Association. This report summarizes the vision of the group of what all contributes to such an indicator. The proposed approach relies on generic well-established concepts for quality criteria, such as the FAIR Principles and the COBIT Maturity Model. It does - on purpose - not limit itself to technical implementation possibilities to avoid using an existing metric for a new purpose. The intention of this paper is to share the current state for further discussion with all stakeholders, particularly with other groups also working on similar metrics but also with entities that use the metrics.

cs.DL↗

arXiv2019

A direct solver for the phase retrieval problem in ptychographic imaging

Measurements achieved with ptychographic imaging are a special case of diffraction measurements. They are generated by illuminating small parts of a sample with, e.g., a focused X-ray beam. By shifting the sample, a set of far-field diffraction patterns of the whole sample are then obtained. From a mathematical point of view those measurements are the squared modulus of the windowed Fourier transform of the sample. Thus, we have a phase retrieval problem for local Fourier measurements. A direct solver for this problem was introduced by Iwen, Viswanathan and Wang in 2016 and improved by Iwen, Preskitt, Saab and Viswanathan in 2018. Motivated by the applied perspective of ptychographic imaging, we present a generalization of this method and compare the different versions in numerical experiments. The new method proposed herein turns out to be more stable, particularly in the case of missing data.

math.NA↗

arXiv2018

Thinplate Splines on the Sphere

In this paper we give explicit closed forms for the semi-reproducing kernels associated with thinplate spline interpolation on the sphere. Polyharmonic or thinplate splines for ${\mathbb R}^d$ were introduced by Duchon and have become a widely used tool in myriad applications. The analogues for ${\mathbb S}^{d-1}$ are the thin plate splines for the sphere. The topic was first discussed by Wahba in the early 1980's, for the ${\mathbb S}^2$ case. Wahba presented the associated semi-reproducing kernels as infinite series. These semi-reproducing kernels play a central role in expressions for the solution of the associated spline interpolation and smoothing problems. The main aims of the current paper are to give a recurrence for the semi-reproducing kernels, and also to use the recurrence to obtain explicit closed form expressions for many of these kernels. The closed form expressions will in many cases be significantly faster to evaluate than the series expansions. This will enhance the practicality of using these thinplate splines for the sphere in computations.

math.CA↗

arXiv2010

Feature selection guided by structural information

In generalized linear regression problems with an abundant number of features, lasso-type regularization which imposes an $\ell^1$-constraint on the regression coefficients has become a widely established technique. Deficiencies of the lasso in certain scenarios, notably strongly correlated design, were unmasked when Zou and Hastie [J. Roy. Statist. Soc. Ser. B 67 (2005) 301--320] introduced the elastic net. In this paper we propose to extend the elastic net by admitting general nonnegative quadratic constraints as a second form of regularization. The generalized ridge-type constraint will typically make use of the known association structure of features, for example, by using temporal- or spatial closeness. We study properties of the resulting "structured elastic net" regression estimation procedure, including basic asymptotics and the issue of model selection consistency. In this vein, we provide an analog to the so-called "irrepresentable condition" which holds for the lasso. Moreover, we outline algorithmic solutions for the structured elastic net within the generalized linear model family. The rationale and the performance of our approach is illustrated by means of simulated and real world data, with a focus on signal regression.

stat.AP↗

arXiv2008

Cesàro means of Jacobi expansions on the parabolic biangle

We study Cesàro $(C,δ)$ means for two-variable Jacobi polynomials on the parabolic biangle $B=\{(x_1,x_2)\in{\mathbb R}^2:0\leq x_1^2\leq x_2\leq 1\}$. Using the product formula derived by Koornwinder & Schwartz for this polynomial system, the Cesàro operator can be interpreted as a convolution operator. We then show that the Cesàro $(C,δ)$ means of the orthogonal expansion on the biangle are uniformly bounded if $δ>α+β+1$, $α-\frac 12\geqβ\geq 0$. Furthermore, for $δ\geqα+2β+\frac 32$ the means define positive linear operators.

math.CA↗

arXiv2004

Polynomial Interpolation on the Unit Sphere II

The problem of interpolation at $(n+1)^2$ points on the unit sphere $\mathbb{S}^2$ by spherical polynomials of degree at most $n$ is proved to have a unique solution for several sets of points. The points are located on a number of circles on the sphere with even number of points on each circle. The proof is based on a method of factorization of polynomials.

math.NA↗