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

On a Theorem of T. Gneiting on α-Symmetric Multivariate Characteristic Functions

AbstractT. Gneiting (1998, J. Multivariate Analysis64, 131–147) proved a relation between the primitives of the classes Φd(2) and Φd(1) of 2- and 1-symmetric characteristic functions on Rd, respectively. We will give a straightforward proof of his relation, answering a question of his. To do this we use the calculus of generalized hypergeometric functions

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.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS302 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Ces\`aro means of Jacobi expansions on the parabolic biangle

We study Ces\`aro $(C,\delta)$ 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 Ces\`aro operator can be interpreted as a convolution operator. We then show that the Ces\`aro $(C,\delta)$ means of the orthogonal expansion on the biangle are uniformly bounded if $\delta>\alpha+\beta+1$, $\alpha-\frac 12\geq\beta\geq 0$. Furthermore, for $\delta\geq\alpha+2\beta+\frac 32$ the means define positive linear operators

Machine learning models to predict myocardial infarctions from past climatic and environmental conditions

Myocardial infarctions (MIs) are a major cause of death worldwide, and both high and low temperatures (i.e. heat and cold) may increase the risk of MI. The relationship between health impacts and climate is complex and influenced by a multitude of climatic, environmental, sociodemographic and behavioural factors. Here, we present a machine learning (ML) approach for predicting MI events based on multiple environmental and demographic variables. We derived data on MI events from the KORA MI registry dataset for Augsburg, Germany, between 1998 and 2015.Multivariable predictors include weather and climate, air pollution (PM10, NO, NO2, SO2 and O3), surrounding vegetation and demographic data. We tested the following ML regression algorithms: decision tree, random forest, multi-layer perceptron, gradient boosting and ridge regression. The models are able to predict the total annual number of MIs reasonably well (adjusted R2 = 0.62–0.71). Inter-annual variations and long-term trends are captured. Across models the most important predictors are air pollution and daily temperatures. Variables not related to environmental conditions, such as demographics need to be considered as well. This ML approachprovides a promising basis to model future MI under changing environmental conditions, as projected by scenarios for climate and other environmental changes

Helmholtz Open Science Workshop „Zugang zu und Nachnutzung von wissenschaftlicher Software“ #hgfos16, Report; November 2016

Der Report des Helmholtz Open Science Workshops „Zugang zu und Nachnutzung von wissenschaftlicher Software“ #hgfos16 behandelt die Themen Standards und Qualitätssicherung; Reproduzierbarkeit; Lizenzierung und weitere rechtliche Aspekte; Zitation und Anerkennung; Sichtbarkeit und Modularität; Geschäftsmodelle; Personal, Ausbildung, Karrierewege. Diese Themen sind eng miteinander verzahnt. Für jeden Themenbereich werden jeweils die Relevanz, Fragestellungen, Herausforderungen, mögliche Lösungsansätze und Handlungsempfehlungen betrachtet