On the multiple Borsuk numbers of sets

The Borsuk number of a set S of diameter d >0 in Euclidean n-space is the smallest value of m such that S can be partitioned into m sets of diameters less than d. Our aim is to generalize this notion in the following way: The k-fold Borsuk number of such a set S is the smallest value of m such that there is a k-fold cover of S with m sets of diameters less than d. In this paper we characterize the k-fold Borsuk numbers of sets in the Euclidean plane, give bounds for those of centrally symmetric sets, smooth bodies and convex bodies of constant width, and examine them for finite point sets in the Euclidean 3-space.Comment: 16 pages, 3 figure

Crossing media boundaries: adaptations and new media forms of the book

t is necessary to continuously review the definition of the book moving from one bound by its material form to one determined by its function as a means of communication. The book’s social function as the high status vehicle for communicating new ideas and cultural expressions is being challenged by sophisticated systems of conveying meaning in other media. In this article, we report on two projects: electronic book (e-book) publication and reader forum for Nature Mage and the transmedia augmented reality (AR) fiction Sherwood Rise, which investigate these issues. Claudio Pires Franco’s work is based on the adaptation of a source work: Duncan Pile’s Nature Mage. The project aims to develop the book from e-book to a fan-produced enhanced digital book. Through this practice-based research, Franco investigates the definitions and classification of the e and i forms of the book and adaptation in new media; the role of the author in creative collaboration with readers through online forums; the extension of the story world through creative collaboration and reader participation while respecting and safeguarding creative properties. One remove from the traditional book, David Miller’s Sherwood Rise, research the user experience with AR to examine narrative problems and explore new storytelling aesthetics. These new media forms define the outer borders of the book system within which content is formed and moulded, and around which society is shaped

Technical Design Report for the PANDA Solenoid and Dipole Spectrometer Magnets

This document is the Technical Design Report covering the two large spectrometer magnets of the PANDA detector set-up. It shows the conceptual design of the magnets and their anticipated performance. It precedes the tender and procurement of the magnets and, hence, is subject to possible modifications arising during this process.Comment: 10 pages, 14MB, accepted by FAIR STI in May 2009, editors: Inti Lehmann (chair), Andrea Bersani, Yuri Lobanov, Jost Luehning, Jerzy Smyrski, Technical Coordiantor: Lars Schmitt, Bernd Lewandowski (deputy), Spokespersons: Ulrich Wiedner, Paola Gianotti (deputy

Elevated extinction rates as a trigger for diversification rate shifts: early amniotes as a case study

Tree shape analyses are frequently used to infer the location of shifts in diversification rate within the Tree of Life. Many studies have supported a causal relationship between shifts and temporally coincident events such as the evolution of “key innovations”. However, the evidence for such relationships is circumstantial. We investigated patterns of diversification during the early evolution of Amniota from the Carboniferous to the Triassic, subjecting a new supertree to analyses of tree balance in order to infer the timing and location of diversification shifts. We investigated how uneven origination and extinction rates drive diversification shifts, and use two case studies (herbivory and an aquatic lifestyle) to examine whether shifts tend to be contemporaneous with evolutionary novelties. Shifts within amniotes tend to occur during periods of elevated extinction, with mass extinctions coinciding with numerous and larger shifts. Diversification shifts occurring in clades that possess evolutionary innovations do not coincide temporally with the appearance of those innovations, but are instead deferred to periods of high extinction rate. We suggest such innovations did not cause increases in the rate of cladogenesis, but allowed clades to survive extinction events. We highlight the importance of examining general patterns of diversification before interpreting specific shifts

Forward modeling of collective Thomson scattering for Wendelstein 7-X plasmas: Electrostatic approximation

In this paper, we present a method for numerical computation of collective Thomson scattering (CTS). We developed a forward model, eCTS, in the electrostatic approximation and benchmarked it against a full electromagnetic model. Differences between the electrostatic and the electromagnetic models are discussed. The sensitivity of the results to the ion temperature and the plasma composition is demonstrated. We integrated the model into the Bayesian data analysis framework Minerva and used it for the analysis of noisy synthetic data sets produced by a full electromagnetic model. It is shown that eCTS can be used for the inference of the bulk ion temperature. The model has been used to infer the bulk ion temperature from the first CTS measurements on Wendelstein 7-X

Towards a new image processing system at Wendelstein 7-X: From spatial calibration to characterization of thermal events

Wendelstein 7-X (W7-X) is the most advanced fusion experiment in the stellarator line and is aimed at proving that the stellarator concept is suitable for a fusion reactor. One of the most important issues for fusion reactors is the monitoring of plasma facing components when exposed to very high heat loads, through the use of visible and infrared (IR) cameras. In this paper, a new image processing system for the analysis of the strike lines on the inboard limiters from the first W7-X experimental campaign is presented. This system builds a model of the IR cameras through the use of spatial calibration techniques, helping to characterize the strike lines by using the information given by real spatial coordinates of each pixel. The characterization of the strike lines is made in terms of position, size, and shape, after projecting the camera image in a 2D grid which tries to preserve the curvilinear surface distances between points. The description of the strike-line shape is made by means of the Fourier Descriptors

Dynamic Energy Landscapes of Riboswitches Help Interpret Conformational Rearrangements and Function

Riboswitches are RNAs that modulate gene expression by ligand-induced conformational changes. However, the way in which sequence dictates alternative folding pathways of gene regulation remains unclear. In this study, we compute energy landscapes, which describe the accessible secondary structures for a range of sequence lengths, to analyze the transcriptional process as a given sequence elongates to full length. In line with experimental evidence, we find that most riboswitch landscapes can be characterized by three broad classes as a function of sequence length in terms of the distribution and barrier type of the conformational clusters: low-barrier landscape with an ensemble of different conformations in equilibrium before encountering a substrate; barrier-free landscape in which a direct, dominant “downhill” pathway to the minimum free energy structure is apparent; and a barrier-dominated landscape with two isolated conformational states, each associated with a different biological function. Sharing concepts with the “new view” of protein folding energy landscapes, we term the three sequence ranges above as the sensing, downhill folding, and functional windows, respectively. We find that these energy landscape patterns are conserved in various riboswitch classes, though the order of the windows may vary. In fact, the order of the three windows suggests either kinetic or thermodynamic control of ligand binding. These findings help understand riboswitch structure/function relationships and open new avenues to riboswitch design