Spectral Invariance of Non-Smooth Pseudodifferential Operators

In this paper we discuss some spectral invariance results for non-smooth pseudodifferential operators with coefficients in H\"older spaces. In analogy to the proof in the smooth case of Beals and Ueberberg, we use the characterization of non-smooth pseudodifferential operators to get such a result. The main new difficulties are the limited mapping properties of pseudodifferential operators with non-smooth symbols and the fact, that in general the composition of two non-smooth pseudodifferential operators is not a pseudodifferential operator. In order to improve these spectral invariance results for certain subsets of non-smooth pseudodifferential operators with coefficients in H\"older spaces, we improve the characterization of non-smooth pseudodifferential operators in a previous work by the authors.Comment: 43 page

Stress Testing German Industry Sectors: Results from a Vine Copula Based Quantile Regression

Measuring interdependence between probabilities of default (PDs) in different industry sectors of an economy plays a crucial role in financial stress testing. Thereby, regression approaches may be employed to model the impact of stressed industry sectors as covariates on other response sectors. We identify vine copula based quantile regression as an eligible tool for conducting such stress tests as this method has good robustness properties, takes into account potential nonlinearities of conditional quantile functions and ensures that no quantile crossing effects occur. We illustrate its performance by a data set of sector specific PDs for the German economy. Empirical results are provided for a rough and a fine-grained industry sector classification scheme. Amongst others, we confirm that a stressed automobile industry has a severe impact on the German economy as a whole at different quantile levels whereas e.g., for a stressed financial sector the impact is rather moderate. Moreover, the vine copula based quantile regression approach is benchmarked against both classical linear quantile regression and expectile regression in order to illustrate its methodological effectiveness in the scenarios evaluated.Comment: 12 page

Soft-gluon Resummation for High-pT Inclusive-Hadron Production at COMPASS

We study the cross section for the photoproduction reaction gamma N -> h X in fixed-target scattering at COMPASS, where the hadron h is produced at large transverse momentum. We investigate the role played by higher-order QCD corrections to the cross section. In particular we address large logarithmic "threshold" corrections to the rapidity dependent partonic cross sections, which we resum to all orders at next-to-leading accuracy. In our comparison to the experimental data we find that the threshold contributions are large and improve the agreement between data and theoretical predictions significantly.Comment: 13 pages, 7 figures, journal versio

High-field MRS

What is a high magnetic field? For in vivo MR systems using small animals like mice or rats, magnets of field-strengths as high as 11.7T/31cm (500 MHz) are available. For research in humans the highest field currently available is 9.4T/65cm (400 MHz), while in the clinic the highest field is 3-4T/95cm (130-170MHz). MR spectroscopy evolved rapidly over the last decades, and it is now an important tool in chemical and biological research focused on molecular composition, structure, and dynamics. Experiments initially conducted in cells and cell extracts, are now carried out in living animals and humans. Similarly, MRS applications in clinical diagnosis are growing steadily. The importance of field strength in such applications cannot be overemphasized. The several fold improved sensitivity at high fields enables the detailed quantitative study of both metabolic and neural signaling processes, as well as of their perturbations during disease