Billiards, scattering by rough obstacles, and optimal mass transportation

This article presents a brief exposition of recent results of the author on billiard scattering by rough obstacles. We define the notion of a rough body and give a characterization of scattering by rough bodies. Then we define the resistance of a rough body; it can be interpreted as the aerodynamic resistance of the somersaulting body moving through a rarefied medium. We solve the problems of maximum and minimum resistance for rough bodies (more precisely, for bodies obtained by roughening a prescribed convex set) in arbitrary dimension. Surprisingly, these problems are reduced to special problems of optimal mass transportation on the sphere

Pathway to the Square Kilometre Array - The German White Paper -

The Square Kilometre Array (SKA) is the most ambitious radio telescope ever planned. With a collecting area of about a square kilometre, the SKA will be far superior in sensitivity and observing speed to all current radio facilities. The scientific capability promised by the SKA and its technological challenges provide an ideal base for interdisciplinary research, technology transfer, and collaboration between universities, research centres and industry. The SKA in the radio regime and the European Extreme Large Telescope (E-ELT) in the optical band are on the roadmap of the European Strategy Forum for Research Infrastructures (ESFRI) and have been recognised as the essential facilities for European research in astronomy. This "White Paper" outlines the German science and R&D interests in the SKA project and will provide the basis for future funding applications to secure German involvement in the Square Kilometre Array.Comment: Editors: H. R. Kl\"ockner, M. Kramer, H. Falcke, D.J. Schwarz, A. Eckart, G. Kauffmann, A. Zensus; 150 pages (low resolution- and colour-scale images), published in July 2012, language English (including a foreword and an executive summary in German), the original file is available via the MPIfR homepag

First Observation of PP-odd γ\gamma Asymmetry in Polarized Neutron Capture on Hydrogen

We report the first observation of the parity-violating 2.2 MeV gamma-ray asymmetry $A^{np}_\gamma$ in neutron-proton capture using polarized cold neutrons incident on a liquid parahydrogen target at the Spallation Neutron Source at Oak Ridge National Laboratory. $A^{np}_\gamma$ isolates the $\Delta I=1$, \mbox{$^{3}S_{1}\rightarrow {^{3}P_{1}}$} component of the weak nucleon-nucleon interaction, which is dominated by pion exchange and can be directly related to a single coupling constant in either the DDH meson exchange model or pionless EFT. We measured $A^{np}_\gamma = [-3.0 \pm 1.4 (stat) \pm 0.2 (sys)]\times 10^{-8}$, which implies a DDH weak $\pi NN$ coupling of $h_{\pi}^{1} = [2.6 \pm 1.2(stat) \pm 0.2(sys)] \times 10^{-7}$ and a pionless EFT constant of $C^{^{3}S_{1}\rightarrow ^{3}P_{1}}/C_{0}=[-7.4 \pm 3.5 (stat) \pm 0.5 (sys)] \times 10^{-11}$ MeV$^{-1}$. We describe the experiment, data analysis, systematic uncertainties, and the implications of the result.Comment: 6 pages, 5 figure

Optimal Structure and Dissolution of Partnerships

We derive the optimal incentive compatible and individually rational mechanisms to reallocate arbitrary given ownership shares among a set of agents. These mechanisms are optimal in the sense that they maximize social surplus of the final allocation subject to the aforementioned constraints and a revenue constraint. We allow for the agents' types to be drawn from non-identical distributions and for interdependent values. Because outside options are type dependent, the critical types for which individual rationality binds must be determined simultaneously with the allocation rule. We show that optimality uniquely pins down the set of critical types, which allows us to fully characterize the optimal mechanisms. Moreover, we find that the value function is Schur-concave in ownership shares when types are identically distributed, so that more symmetric shares are better irrespective of size of the revenue constraint

First Observation of \u3cem\u3eP\u3c/em\u3e-Odd γ Asymmetry in Polarized Neutron Capture on Hydrogen

We report the first observation of the parity-violating gamma-ray asymmetry Anpγ in neutron-proton capture using polarized cold neutrons incident on a liquid parahydrogen target at the Spallation Neutron Source at Oak Ridge National Laboratory. Anpγ isolates the ΔI = 1, 3S1 → 3P1 component of the weak nucleon-nucleon interaction, which is dominated by pion exchange and can be directly related to a single coupling constant in either the DDH meson exchange model or pionless effective field theory. We measured Anpγ = [−3.0 ± 1.4(stat )± 0.2(syst)] × 10−8, which implies a DDH weak πNN coupling of h1π = [2.6 ± 1.2(stat) ± 0.2(syst)] × 10−7 and a pionless EFT constant of C3S1 → 3P1/C0 = [−7.4 ± 3.5(stat) ± 0.5(syst)] × 10−11  MeV−1. We describe the experiment, data analysis, systematic uncertainties, and implications of the result

Pyrosequencing of Bacterial Symbionts within Axinella corrugata Sponges: Diversity and Seasonal Variability

Background: Marine sponge species are of significant interest to many scientific fields including marine ecology, conservation biology, genetics, host-microbe symbiosis and pharmacology. One of the most intriguing aspects of the sponge ‘‘holobiont’’ system is the unique physiology, interaction with microbes from the marine environment and the development of a complex commensal microbial community. However, intraspecific variability and temporal stability of sponge-associated bacterial symbionts remain relatively unknown. Methodology/Principal Findings: We have characterized the bacterial symbiont community biodiversity of seven different individuals of the Caribbean reef sponge Axinella corrugata, from two different Florida reef locations during variable seasons using multiplex 454 pyrosequencing of 16 S rRNA amplicons. Over 265,512 high-quality 16 S rRNA sequences were generated and analyzed. Utilizing versatile bioinformatics methods and analytical software such as the QIIME and CloVR packages, we have identified 9,444 distinct bacterial operational taxonomic units (OTUs). Approximately 65,550 rRNA sequences (24%) could not be matched to bacteria at the class level, and may therefore represent novel taxa. Differentially abundant classes between seasonal Axinella communities included Gammaproteobacteria, Flavobacteria, Alphaproteobacteria, Cyanobacteria, Acidobacter and Nitrospira. Comparisons with a proximal outgroup sponge species (Amphimedon compressa), and the growing sponge symbiont literature, indicate that this study has identified approximately 330 A. corrugata-specific symbiotic OTUs, many of which are related to the sulfur-oxidizing Ectothiorhodospiraceae. This family appeared exclusively within A. corrugata, comprising \u3e34.5% of all sequenced amplicons. Other A. corrugata symbionts such as Deltaproteobacteria, Bdellovibrio, and Thiocystis among many others are described. Conclusions/Significance: Slight shifts in several bacterial taxa were observed between communities sampled during spring and fall seasons. New 16 S rDNA sequences and concomitant identifications greatly expand the microbial community profile for this model reef sponge, and will likely be useful as a baseline for any future comparisons regarding sponge microbial community dynamics

Assessing the complex sponge microbiota: core, variable and species-specific bacterial communities in marine sponges

Marine sponges are well known for their associations with highly diverse, yet very specific and often highly similar microbiota. The aim of this study was to identify potential bacterial sub-populations in relation to sponge phylogeny and sampling sites and to define the core bacterial community. 16S ribosomal RNA gene amplicon pyrosequencing was applied to 32 sponge species from eight locations around the world's oceans, thereby generating 2567 operational taxonomic units (OTUs at the 97% sequence similarity level) in total and up to 364 different OTUs per sponge species. The taxonomic richness detected in this study comprised 25 bacterial phyla with Proteobacteria, Chloroflexi and Poribacteria being most diverse in sponges. Among these phyla were nine candidate phyla, six of them found for the first time in sponges. Similarity comparison of bacterial communities revealed no correlation with host phylogeny but a tropical sub-population in that tropical sponges have more similar bacterial communities to each other than to subtropical sponges. A minimal core bacterial community consisting of very few OTUs (97%, 95% and 90%) was found. These microbes have a global distribution and are probably acquired via environmental transmission. In contrast, a large species-specific bacterial community was detected, which is represented by OTUs present in only a single sponge species. The species-specific bacterial community is probably mainly vertically transmitted. It is proposed that different sponges contain different bacterial species, however, these bacteria are still closely related to each other explaining the observed similarity of bacterial communities in sponges in this and previous studies. This global analysis represents the most comprehensive study of bacterial symbionts in sponges to date and provides novel insights into the complex structure of these unique associations