Harmonic Spline-Wavelets on the 3-dimensional Ball and their Application to the Reconstruction of the Earth´s Density Distribution from Gravitational Data at Arbitrarily Shaped Satellite Orbits

We introduce splines for the approximation of harmonic functions on a 3-dimensional ball. Those splines are combined with a multiresolution concept. More precisely, at each step of improving the approximation we add more data and, at the same time, reduce the hat-width of the used spline basis functions. Finally, a convergence theorem is proved. One possible application, that is discussed in detail, is the reconstruction of the Earth´s density distribution from gravitational data obtained at a satellite orbit. This is an exponentially ill-posed problem where only the harmonic part of the density can be recovered since its orthogonal complement has the potential 0. Whereas classical approaches use a truncated singular value decomposition (TSVD) with the well-known disadvantages like the non-localizing character of the used spherical harmonics and the bandlimitedness of the solution, modern regularization techniques use wavelets allowing a localized reconstruction via convolutions with kernels that are only essentially large in the region of interest. The essential remaining drawback of a TSVD and the wavelet approaches is that the integrals (i.e. the inner product in case of a TSVD and the convolution in case of wavelets) are calculated on a spherical orbit, which is not given in reality. Thus, simplifying modelling assumptions, that certainly include a modelling error, have to be made. The splines introduced here have the important advantage, that the given data need not be located on a sphere but may be (almost) arbitrarily distributed in the outer space of the Earth. This includes, in particular, the possibility to mix data from different satellite missions (different orbits, different derivatives of the gravitational potential) in the calculation of the Earth´s density distribution. Moreover, the approximating splines can be calculated at varying resolution scales, where the differences for increasing the resolution can be computed with the introduced spline-wavelet technique

Spreading out: covid-19 and the changing geography of consumption

Lockdowns change where consumers spend their money; expenditures are more evenly spread in space, write Martin Brown, Matthias Fengler, Rafael Lalive, Robert Rohrkemper, and Thomas Spyche

Will the Sustainable Development Goals be fulfilled? Assessing present and future global poverty

Monitoring progress towards the fulfillment of the Sustainable Development Goals (SDGs) requires the assessment of potential future trends in poverty. This paper presents an econometric tool that provides a methodological framework to carry out projections of poverty rates worldwide and aims at assessing absolute poverty changes at the global level under different scenarios. The model combines country-specific historical estimates of the distribution of income, using Beta–Lorenz curves, with projections of population changes by age and education attainment level, as well as GDP projections to provide the first set of internally consistent poverty projections for all countries of the world. Making use of demographic and economic projections developed in the context of the Intergovernmental Panel on Climate Change’s Shared Socioeconomic Pathways, we create poverty paths by country up to the year 2030. The differences implied by different global scenarios span worldwide poverty rates ranging from 4.5% (around 375 million persons) to almost 6% (over 500 million persons) by the end of our projection period. The largest differences in poverty headcount and poverty rates across scenarios appear for Sub-Saharan Africa, where the projections for the most optimistic scenario imply over 300 million individuals living in extreme poverty in 2030. The results of the comparison of poverty scenarios point towards the difficulty of fulfilling the first goal of the SDGs unless further development policy efforts are enacted

Die „tiefe Internationalisierung“ der deutschen Kommunikationswissenschaft?: Eine Evaluation der Personal- und Forschungsstrukturen sowie der Lehrprogramme deutscher Hochschulen

Der Beitrag präsentiert und diskutiert die Ergebnisse einer umfassenden Befragung und mehrerer Dokumentenanalysen zu Personal-und Forschungsstrukturen sowie Lehrprogrammen in der deutschen Kommunikationswissenschaft im Hinblick auf deren „tiefe Internationalisierung“ bzw. kosmopolitische Ausrichtung. Darunter verstehen wir eine umfassende Anerkennung und Einbindung globaler Vielfalt in die Wissensproduktion und messen dies entlang der Inhalts-und Raumdimension des Forschungs-und Lehroutputs der Professuren und der mit ihnen verbundenen Stellenstrukturen. Die Befunde zeigen, dass die deutsche Kommunikationswissenschaft einen großen Nachholbedarf hat, was eine kosmopolitische Wissensproduktion angeht. Vor dem Hintergrund der Relevanz globaler Werte, globalen Wissens und Global Governance werden aber auch Potentiale aufgezeigt sowie hochschulpolitische Maßnahmen diskutiert, die eine inhaltliche Internationalisierung der deutschen Kommunikationswissenschaft vorantreiben können.This paper presents and discusses the results of a comprehensive survey and several document analyses on personnel and research structures as well as teaching programs in German communication studies regarding their “deep internationalization” or cosmopolitan orientation. By this, we mean a comprehensive recognition and integration of global diversity into knowledge production. We measure this through the content and spatial dimension of the research and teaching output of professors, as well as the teaching and research staff linked tothem. The findings show that German communication studies is lagging a truly cosmopolitan knowledge production. Against the backdrop of the relevance of global values, global knowledge, and global governance, however, the study also points out potentials and discusses higher education policy measures that could advance the internationalization of German communication studies

Variance-of-variance risk premium

This article explores the premium for bearing the variance risk of the VIX index, called the variance-of-variance risk premium. I find that during the sample period from 2006 until 2014 trading strategies exploiting the difference between the implied and realized variance of the VIX index yield average excess returns of − 24.16% per month, with an alpha of − 16.98% after adjusting for Fama–French and Carhart risk factors as well as accounting for variance risk (both highly significant). The article provides further evidence of risk premium characteristics using corridor variance swaps and compares empirical results with the predictions of reduced-form and structural benchmark models

A Nonlinear Galerkin Scheme Involving Vector and Tensor Spherical Harmonics for Solving the Incompressible Navier-Stokes Equation on the Sphere

This work is concerned with a nonlinear Galerkin method for solving the incompressible Navier-Stokes equation on the sphere. It extends the work of Debussche, Marion,Shen, Temam et al. from one-dimensional or toroidal domains to the spherical geometry. In the first part, the method based on type 3 vector spherical harmonics is introduced and convergence is indicated. Further it is shown that the occurring coupling terms involving three vector spherical harmonics can be expressed algebraically in terms of Wigner-3j coefficients. To improve the numerical efficiency and economy we introduce an FFT based pseudo spectral algorithm for computing the Fourier coefficients of the nonlinear advection term. The resulting method scales with O(N^3), if N denotes the maximal spherical harmonic degree. The latter is demonstrated in an extensive numerical example