From Fourier to Gegenbauer: Dimension walks on spheres

We show that the even- resp. odd-dimensional Schoenberg coefficients in Gegenbauer expansions of isotropic positive definite functions on the d-sphere can be expressed as linear combinations of Fourier resp. Legendre coefficients, and we give closed form expressions for the coefficients involved in these expansions

Distances, Gegenbauer expansions, curls, and dimples: On dependence measures for random fields

The aim of this thesis is to analyze several aspects of dependence structures for stochastic processes. To this end, new dependence measures for spatial stochastic processes will be introduced. Further, different analytical properties of correlation functions and their relation to properties of the realizations of the corresponding stochastic processes will be studied. The newly introduced dependence measures are based on the distance correlation. Thus, they are defined for larger classes of processes than the well-known Pearson correlation function. In addition, the new dependence measures allow to quantify non-linear dependencies, as well as dependencies in multivariate stochastic processes. On the one hand, the investigation of analytical properties of correlation functions considers isotropic positive definite functions on spheres of different dimensions. These functions are characterized by Gegenbauer expansions involving so-called Schoenberg coefficients. Relationships between those Schoenberg coefficients will be given. On the other hand, characterizations of correlation functions of random vector fields with almost surely divergence-free and irrotational realizations will be considered. Further, the dimple property of spatio-temporal random fields will be analyzed. This dimple corresponds to a non-monotonic temporal behaviour of the correlation function, which can be generated by so-called transport fields. These transport fields and their relation to the dimple property will be investigated

Geochemie und mikroskalige Elementverteilung in lateritischen Verwitterungsresiduen - Bohnerze

Bohnerze der oberjurassischen Kalkgebiete Süddeutschlands gelten aufgrund neuerer Studien als umgelagerte Residuen eines lateritischen Verwitterungsregimes während der Kreide und des Eozäns. Durch mineralogisch-chemische Analysen sowie der Erstellung von Elementbildern gelang eine näherungsweise Zuordnung von morphologisch unterscheidbaren Bohnerzformen zu den einzelnen Bereichen eines Lateritprofils. Dabei entsprechen pisoidische Bohnerze lateritischen Konkretionen aus dem Degradationsbereich am Übergang einer Eisenkruste (eigentlicher Laterit/Ferricrete) zum Bereich der Oberflächenverwitterung. Bei den nodulären Bohnerze handelt es sich zum Einen um Goethit-imprägnierte Bohnerztonaggregate und zum Anderen um Bruchstücke einer massiven Eisenkruste

Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines

In applied mathematics and related disciplines, the modeling-simulation-optimization workflow is a prominent scheme, with mathematical models and numerical algorithms playing a crucial role. For these types of mathematical research data, the Mathematical Research Data Initiative has developed, merged and implemented ontologies and knowledge graphs. This contributes to making mathematical research data FAIR by introducing semantic technology and documenting the mathematical foundations accordingly. Using the concrete example of microfracture analysis of porous media, it is shown how the knowledge of the underlying mathematical model and the corresponding numerical algorithms for its solution can be represented by the ontologies.Comment: Preprint of a Conference Paper to appear in the Proceeding of the 17th International Conference on Metadata and Semantics Researc

Seminal plasma as a source of prostate cancer peptide biomarker candidates for detection of indolent and advanced disease

Background:Extensive prostate specific antigen screening for prostate cancer generates a high number of unnecessary biopsies and over-treatment due to insufficient differentiation between indolent and aggressive tumours. We hypothesized that seminal plasma is a robust source of novel prostate cancer (PCa) biomarkers with the potential to improve primary diagnosis of and to distinguish advanced from indolent disease. <br>Methodology/Principal Findings: In an open-label case/control study 125 patients (70 PCa, 21 benign prostate hyperplasia, 25 chronic prostatitis, 9 healthy controls) were enrolled in 3 centres. Biomarker panels a) for PCa diagnosis (comparison of PCa patients versus benign controls) and b) for advanced disease (comparison of patients with post surgery Gleason score <7 versus Gleason score >>7) were sought. Independent cohorts were used for proteomic biomarker discovery and testing the performance of the identified biomarker profiles. Seminal plasma was profiled using capillary electrophoresis mass spectrometry. Pre-analytical stability and analytical precision of the proteome analysis were determined. Support vector machine learning was used for classification. Stepwise application of two biomarker signatures with 21 and 5 biomarkers provided 83% sensitivity and 67% specificity for PCa detection in a test set of samples. A panel of 11 biomarkers for advanced disease discriminated between patients with Gleason score 7 and organ-confined (<pT3a) or advanced (≥pT3a) disease with 80% sensitivity and 82% specificity in a preliminary validation setting. Seminal profiles showed excellent pre-analytical stability. Eight biomarkers were identified as fragments of N-acetyllactosaminide beta-1,3-N-acetylglucosaminyltransferase​,prostatic acid phosphatase, stabilin-2, GTPase IMAP family member 6, semenogelin-1 and -2. Restricted sample size was the major limitation of the study.</br> <br>Conclusions/Significance: Seminal plasma represents a robust source of potential peptide makers for primary PCa diagnosis. Our findings warrant further prospective validation to confirm the diagnostic potential of identified seminal biomarker candidates.</br&gt

New Binding Mode to TNF-Alpha Revealed by Ubiquitin-Based Artificial Binding Protein

A variety of approaches have been employed to generate binding proteins from non-antibody scaffolds. Utilizing a beta-sheet of the human ubiquitin for paratope creation we obtained binding proteins against tumor necrosis factor (TNF)-alpha. The bioactive form of this validated pharmacological target protein is a non-covalently linked homo-trimer. This structural feature leads to the observation of a certain heterogeneity concerning the binding mode of TNF-alpha binding molecules, for instance in terms of monomer/trimer specificity. We analyzed a ubiquitin-based TNF-alpha binder, selected by ribosome display, with a particular focus on its mode of interaction. Using enzyme-linked immunosorbent assays, specific binding to TNF-alpha with nanomolar affinity was observed. In isothermal titration calorimetry we obtained comparable results regarding the affinity and detected an exothermic reaction with one ubiquitin-derived binding molecule binding one TNF-alpha trimer. Using NMR spectroscopy and other analytical methods the 1∶3 stoichiometry could be confirmed. Detailed binding analysis showed that the interaction is affected by the detergent Tween-20. Previously, this phenomenon was reported only for one other type of alternative scaffold-derived binding proteins – designed ankyrin repeat proteins – without further investigation. As demonstrated by size exclusion chromatography and NMR spectroscopy, the presence of the detergent increases the association rate significantly. Since the special architecture of TNF-alpha is known to be modulated by detergents, the access to the recognized epitope is indicated to be restricted by conformational transitions within the target protein. Our results suggest that the ubiquitin-derived binding protein targets a new epitope on TNF-alpha, which differs from the epitopes recognized by TNF-alpha neutralizing antibodies

Eddy Study to Understand Physical-Chemical-Biological Coupling and the Biological Carbon Pump as a Function of Eddy Type off West Africa, Cruise No. M160, 23.11.2019 - 20.12.2019, Mindelo (Cabo Verde) - Mindelo (Cabo Verde)

Cruise M160 is part of concerted MOSES/REEBUS Eddy Study featuring three major research expeditions (M156, M160, MSM104). It aims to develop both a qualitative and quantitative understanding of the role of physical-chemical-biological coupling in eddies for the biological pump. The study is part of the MOSES “Ocean Eddies” event chain, which follows three major hypotheses to be addressed by the MOSES/REEBUS field campaigns: (1) Mesoscale and sub-mesoscale eddies play an important role in transferring energy along the energy cascade from the large-scale circulation to dissipation at the molecular level. (2) Mesoscale and sub-mesoscale eddies are important drivers in determining onset, magnitude and characteristics of biological productivity in the ocean and contribute significantly to global primary production and particle export and transfer to the deep ocean. (3) Mesoscale and sub-mesoscale eddies are important for shaping extreme biogeochemical environments (e.g., pH, oxygen) in the oceans, thus acting as a source/sink function for greenhouse gases. In contrast to the other two legs, MOSES Eddy Study II during M160 did not include any benthic work but focused entirely on the pelagic dynamics within eddies. It accomplished a multi-disciplinary, multi-parameter and multi-platform study of two discrete cyclonic eddies in an unprecedented complexity. The pre-cruise search for discrete eddies suitable for detailed study during M160 had already started a few months prior to the cruise. Remote sensing data products (sea surface height, sea surface temperature, ocean color/chlorophyll a) were used in combination with eddy detection algorithms and numerical modelling to identify and track eddies in the entire eddy field off West Africa. In addition, 2 gliders and 1 waveglider had been set out from Mindelo/Cabo Verde for pre-cruise mapping of the potential working area north of the Cabo Verdean archipelago. At the start of M160, a few suitable eddies – mostly of cyclonic type – had been identified, some of which were outside the safe operation range of the motorglider plane. As technical problems delayed the flight operations, the first eddy (center at 14.5°N/25°W) for detailed study was chosen to the southwest of the island of Fogo. It was decided to carry out a first hydrographic survey there followed by the deployment of a suite of instruments (gliders, waveglider, floats, drifter short-term mooring). Such instrumented, we left this first eddy and transited – via a strong anticyclonic feature southwest of the island of Santiago – to the region northeast of the island of Sal, i.e. in the working range of the glider plane. During the transit, a full suite of underway measurements as well as CTD/RO section along 22°W (16°-18.5°N) were carried in search for sub-surface expressions of anticyclonic eddy features. In the northeast, we had identified the second strong cyclonic eddy (center at 18°N/22.5°W) which was chosen for detailed study starting with a complete hydrographic survey (ADCP, CTD/RO, other routine station work). After completion of the mesoscale work program, we identified a strong frontal region at the southwestern rim of the cyclonic eddy, which was chosen for the first sub-mesoscale study with aerial observation component. There, the first dye release experiment was carried out which consisted of the dye release itself followed by an intense multi-platforms study of the vertical and horizontal spreading of the initial dye streak. This work was METEOR-Berichte, Cruise M160, Mindelo – Mindelo, 23.11.2019 4 – 20.12.2019 supported and partly guided by aerial observation of the research motorglider Stemme, which was still somewhat compromised by technical issues and meteorological conditions (high cloud cover, Saharan dust event). Nevertheless, this first dye release experiment was successful and showed rapid movement of the dynamic meandering front. After completion of work on this second eddy and execution of a focused sampling program at the Cape Verde Ocean Observation, RV METEOR returned to the first eddy for continuation of the work started there in the beginning of the cruise. This was accompanied by a relocation of the airbase of Stemme from the international airport of Sal to the domestic airport of Fogo. The further execution of the eddy study at this first eddy, which again included a complete hydrographic survey followed by a mesoscale eddy study with dye release, was therefore possible with aerial observations providing important guidance for work on RV METEOR. Overall, M160 accomplished an extremely intense and complex work program with 212 instrument deployments during station work, 137 h of observation with towed instruments and a wide range of underway measurements throughout the cruise. Up to about 30 individually tracked platforms (Seadrones, glider, wavegliders, drifters, floats) were in the water at the same time providing unprecedented and orchestrated observation capabilities in an eddy. All planned work components were achieved and all working groups acquired the expected numbers of instrument deployments and sampling opportunities

National and subnational short-term forecasting of COVID-19 in Germany and Poland during early 2021

We compare forecasts of weekly case and death numbers for COVID-19 in Germany and Poland based on 15 different modelling approaches. These cover the period from January to April 2021 and address numbers of cases and deaths one and two weeks into the future, along with the respective uncertainties. We find that combining different forecasts into one forecast can enable better predictions. However, case numbers over longer periods were challenging to predict. Additional data sources, such as information about different versions of the SARS-CoV-2 virus present in the population, might improve forecasts in the future

NOX1 loss-of-function genetic variants in patients with inflammatory bowel disease.

Genetic defects that affect intestinal epithelial barrier function can present with very early-onset inflammatory bowel disease (VEOIBD). Using whole-genome sequencing, a novel hemizygous defect in NOX1 encoding NAPDH oxidase 1 was identified in a patient with ulcerative colitis-like VEOIBD. Exome screening of 1,878 pediatric patients identified further seven male inflammatory bowel disease (IBD) patients with rare NOX1 mutations. Loss-of-function was validated in p.N122H and p.T497A, and to a lesser degree in p.Y470H, p.R287Q, p.I67M, p.Q293R as well as the previously described p.P330S, and the common NOX1 SNP p.D360N (rs34688635) variant. The missense mutation p.N122H abrogated reactive oxygen species (ROS) production in cell lines, ex vivo colonic explants, and patient-derived colonic organoid cultures. Within colonic crypts, NOX1 constitutively generates a high level of ROS in the crypt lumen. Analysis of 9,513 controls and 11,140 IBD patients of non-Jewish European ancestry did not reveal an association between p.D360N and IBD. Our data suggest that loss-of-function variants in NOX1 do not cause a Mendelian disorder of high penetrance but are a context-specific modifier. Our results implicate that variants in NOX1 change brush border ROS within colonic crypts at the interface between the epithelium and luminal microbes

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements