Wavelets in function spaces on cellular domains

Nowadays the theory and application of wavelet decompositions plays an important role not only for the study of function spaces (of Lebesgue, Hardy, Sobolev, Besov, Triebel-Lizorkin type) but also for its applications in signal and numerical analysis, partial differential equations and image processing. In this context it it a hard problem to construct wavelet bases for suitable function spaces on domains, e. g. the unit cube. A big step in this direction are the contributions of Hans Triebel from 2006 to 2008 where he constructed Riesz bases for classes of Besov- and Triebel-Lizorkin spaces on domains, starting with Daubechies wavelets. But there was a problem coming from the method: He had to exclude a big number of function spaces, in particular a large class of classical Sobolev spaces. The main goal of this thesis is a construction of Riesz bases of wavelet systems also for the exceptional cases using a modification of the function spaces - the so-called reinforced function spaces.Comment: 109 pages, my thesis for becoming a Dr. rer. nat. at Friedrich-Schiller-Universitaet Jen

Sparse Control of Alignment Models in High Dimension

For high dimensional particle systems, governed by smooth nonlinearities depending on mutual distances between particles, one can construct low-dimensional representations of the dynamical system, which allow the learning of nearly optimal control strategies in high dimension with overwhelming confidence. In this paper we present an instance of this general statement tailored to the sparse control of models of consensus emergence in high dimension, projected to lower dimensions by means of random linear maps. We show that one can steer, nearly optimally and with high probability, a high-dimensional alignment model to consensus by acting at each switching time on one agent of the system only, with a control rule chosen essentially exclusively according to information gathered from a randomly drawn low-dimensional representation of the control system.Comment: 39 page

Besov regularity of solutions to the p-Poisson equation

In this paper, we study the regularity of solutions to the $p$-Poisson equation for all $1<p<\infty$. In particular, we are interested in smoothness estimates in the adaptivity scale $B^\sigma_{\tau}(L_{\tau}(\Omega))$, $1/\tau = \sigma/d+1/p$, of Besov spaces. The regularity in this scale determines the order of approximation that can be achieved by adaptive and other nonlinear approximation methods. It turns out that, especially for solutions to $p$-Poisson equations with homogeneous Dirichlet boundary conditions on bounded polygonal domains, the Besov regularity is significantly higher than the Sobolev regularity which justifies the use of adaptive algorithms. This type of results is obtained by combining local H\"older with global Sobolev estimates. In particular, we prove that intersections of locally weighted H\"older spaces and Sobolev spaces can be continuously embedded into the specific scale of Besov spaces we are interested in. The proof of this embedding result is based on wavelet characterizations of Besov spaces.Comment: 45 pages, 2 figure

An XMM and Chandra view of massive clusters of galaxies to z=1

The X-ray properties of a sample of high redshift (z>0.6), massive clusters observed with XMM-Newton and Chandra are described, including two exceptional systems. One, at z=0.89, has an X-ray temperature of T=11.5 (+1.1, -0.9) keV (the highest temperature of any cluster known at z>0.6), an estimated mass of (1.4+/-0.2)x10^15 solar masses and appears relaxed. The other, at z=0.83, has at least three sub-clumps, probably in the process of merging, and may also show signs of faint filamentary structure at large radii,observed in X-rays. In general there is a mix of X-ray morphologies, from those clusters which appear relaxed and containing little substructure to some highly non-virialized and probably merging systems. The X-ray gas metallicities and gas mass fractions of the relaxed systems are similar to those of low redshift clusters of the same temperature, suggesting that the gas was in place, and containing its metals, by z=0.8. The evolution of the mass-temperature relation may be consistent with no evolution or with the ``late formation'' assumption. The effect of point source contamination in the ROSAT survey from which these clusters were selected is estimated, and the implications for the ROSAT X-ray luminosity function discussed.Comment: 9 pages, in Carnegie Observatories Astrophysics Series, Vol. 3: Clusters of Galaxies: Probes of Cosmological Structure and Galaxy Evolution, ed. J. S. Mulchaey, A. Dressler, and A. Oemler. See http://www.ociw.edu/ociw/symposia/series/symposium3/proceedings.html for a full-resolution versio

Using an Immersive Video Environment to Assess Pedestrians’ Compliance With COVID Distance Keeping Interventions

Physical distancing is a key measure to slow the spread of many highly infectious diseases, e.g. COVID-19. Streetscape interventions such as pedestrian signage can contribute to ensuring distances are kept, but it is unclear to what extent people comply with these in practice. This paper tackles this question using an immersive video environment to realistically simulate real-life streetscapes in the lab. In a controlled user study, we augmented panoramic video footage with pedestrian one-way street signage and recorded route decisions to assess compliance with distance keeping measures. Our results indicate that such signage affects routing decisions and can thus help pedestrians to avoid crowded situations where distance keeping is difficult. We also identified further factors affecting decisions and a correlation between intention to comply and actual compliance. The experimental method we used enabled us to effectively and safely carry out a study of a phenomenon that in the real world depends on interaction with the physical environment. This method may have applications in other areas in which simulations of physical environments are important

Rare Copy Number Variants in \u3cem\u3eNRXN1\u3c/em\u3e and \u3cem\u3eCNTN6\u3c/em\u3e Increase Risk for Tourette Syndrome

Tourette syndrome (TS) is a model neuropsychiatric disorder thought to arise from abnormal development and/or maintenance of cortico-striato-thalamo-cortical circuits. TS is highly heritable, but its underlying genetic causes are still elusive, and no genome-wide significant loci have been discovered to date. We analyzed a European ancestry sample of 2,434 TS cases and 4,093 ancestry-matched controls for rare (\u3c 1% frequency) copy-number variants (CNVs) using SNP microarray data. We observed an enrichment of global CNV burden that was prominent for large (\u3e 1 Mb), singleton events (OR = 2.28, 95% CI [1.39–3.79], p = 1.2 × 10−3) and known, pathogenic CNVs (OR = 3.03 [1.85–5.07], p = 1.5 × 10−5). We also identified two individual, genome-wide significant loci, each conferring a substantial increase in TS risk (NRXN1 deletions, OR = 20.3, 95% CI [2.6–156.2]; CNTN6 duplications, OR = 10.1, 95% CI [2.3–45.4]). Approximately 1% of TS cases carry one of these CNVs, indicating that rare structural variation contributes significantly to the genetic architecture of TS

Exoplanet Diversity in the Era of Space-based Direct Imaging Missions

This whitepaper discusses the diversity of exoplanets that could be detected by future observations, so that comparative exoplanetology can be performed in the upcoming era of large space-based flagship missions. The primary focus will be on characterizing Earth-like worlds around Sun-like stars. However, we will also be able to characterize companion planets in the system simultaneously. This will not only provide a contextual picture with regards to our Solar system, but also presents a unique opportunity to observe size dependent planetary atmospheres at different orbital distances. We propose a preliminary scheme based on chemical behavior of gases and condensates in a planet's atmosphere that classifies them with respect to planetary radius and incident stellar flux.Comment: A white paper submitted to the National Academy of Sciences Exoplanet Science Strateg

Animal-related factors associated with moderate-to-severe diarrhea in children younger than five years in western Kenya: A matched case-control study

Background Diarrheal disease remains among the leading causes of global mortality in children younger than 5 years. Exposure to domestic animals may be a risk factor for diarrheal disease. The objectives of this study were to identify animal-related exposures associated with cases of moderate-to-severe diarrhea (MSD) in children in rural western Kenya, and to identify the major zoonotic enteric pathogens present in domestic animals residing in the homesteads of case and control children. Methodology/Principal findings We characterized animal-related exposures in a subset of case and control children (n = 73 pairs matched on age, sex and location) with reported animal presence at home enrolled in the Global Enteric Multicenter Study in western Kenya, and analysed these for an association with MSD. We identified potentially zoonotic enteric pathogens in pooled fecal specimens collected from domestic animals resident at children’s homesteads. Variables that were associated with decreased risk of MSD were washing hands after animal contact (matched odds ratio [MOR] = 0.2; 95% CI 0.08–0.7), and presence of adult sheep that were not confined in a pen overnight (MOR = 0.1; 0.02–0.5). Variables that were associated with increased risk of MSD were increasing number of sheep owned (MOR = 1.2; 1.0–1.5), frequent observation of fresh rodent excreta (feces/urine) outside the house (MOR = 7.5; 1.5–37.2), and participation of the child in providing water to chickens (MOR = 3.8; 1.2–12.2). Of 691 pooled specimens collected from 2,174 domestic animals, 159 pools (23%) tested positive for one or more potentially zoonotic enteric pathogens (Campylobacter jejuni, C. coli, non-typhoidal Salmonella, diarrheagenic E. coli, Giardia, Cryptosporidium, or rotavirus). We did not find any association between the presence of particular pathogens in household animals, and MSD in children. Conclusions and significance Public health agencies should continue to promote frequent hand washing, including after animal contact, to reduce the risk of MSD. Future studies should address specific causal relations of MSD with sheep and chicken husbandry practices, and with the presence of rodents