Restricted Isometries for Partial Random Circulant Matrices

In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to succeed when the restricted isometry constants of the sampling matrix are small. Many potential applications of compressed sensing involve a data-acquisition process that proceeds by convolution with a random pulse followed by (nonrandom) subsampling. At present, the theoretical analysis of this measurement technique is lacking. This paper demonstrates that the $s$th order restricted isometry constant is small when the number $m$ of samples satisfies $m \gtrsim (s \log n)^{3/2}$, where $n$ is the length of the pulse. This bound improves on previous estimates, which exhibit quadratic scaling

Compressed sensing for wide-field radio interferometric imaging

For the next generation of radio interferometric telescopes it is of paramount importance to incorporate wide field-of-view (WFOV) considerations in interferometric imaging, otherwise the fidelity of reconstructed images will suffer greatly. We extend compressed sensing techniques for interferometric imaging to a WFOV and recover images in the spherical coordinate space in which they naturally live, eliminating any distorting projection. The effectiveness of the spread spectrum phenomenon, highlighted recently by one of the authors, is enhanced when going to a WFOV, while sparsity is promoted by recovering images directly on the sphere. Both of these properties act to improve the quality of reconstructed interferometric images. We quantify the performance of compressed sensing reconstruction techniques through simulations, highlighting the superior reconstruction quality achieved by recovering interferometric images directly on the sphere rather than the plane.Comment: 15 pages, 8 figures, replaced to match version accepted by MNRA

Estimation in high dimensions: a geometric perspective

This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of asymptotic convex geometry, and demonstrates connections between geometric results and estimation problems. The theory is illustrated with applications to sparse recovery, matrix completion, quantization, linear and logistic regression and generalized linear models.Comment: 56 pages, 9 figures. Multiple minor change

Territorial cohesion cities: a policy recipe for achieving territorial cohesion?

This paper discusses the role of medium towns as crucial anchors in achieving the policy goal of Territorial Cohesion. It highlights the need to counterbalance market trends to favour the continuous channelling of investment and people into larger metropolitan areas by way of proactive measures focused on attracting investment into medium towns, and as an alternative to dispersing public and private investment in lagging territories. Iberian and Nordic cases are examined in order to illustrate the possibilities and challenges of using ‘Territorial Cohesion Cities’ as development hubs in lagging regions, in order to achieve Territorial Cohesion at a national level

Multipliers for p-Bessel sequences in Banach spaces

Multipliers have been recently introduced as operators for Bessel sequences and frames in Hilbert spaces. These operators are defined by a fixed multiplication pattern (the symbol) which is inserted between the analysis and synthesis operators. In this paper, we will generalize the concept of Bessel multipliers for p-Bessel and p-Riesz sequences in Banach spaces. It will be shown that bounded symbols lead to bounded operators. Symbols converging to zero induce compact operators. Furthermore, we will give sufficient conditions for multipliers to be nuclear operators. Finally, we will show the continuous dependency of the multipliers on their parameters.Comment: 17 page

New life in old churches : the missional integration of communal life, societal relevant congregational development and property estate management

German textAusgehend von dem konkreten mehrdimensionalen missionalen Kirchenprojekt REFOmoabit ist es Ziel dieser Masterarbeit, eine Antwort auf die Frage zu geben, wie eine fruchtbare Integration von (1) gemeinschaftlichem Leben, (2) gesellschaftsrelevantem Gemeindebau und (3) Immobilienmanagement gelingen kann. Die aktuelle ekklesiologische Praxis und Erfahrung zeigt jedoch, dass es zu Spannungen zwischen dem Prinzip des gaben- und konsensbasierten Miteinanders, einerseits und der Entwicklung eines gesellschaftsrelevanten Gemeindebaus und einem die ersten beiden Bereiche unterstützenden Immobilienmanagements andererseits kommt. Infolgedessen soll im Rahmen dieser Arbeit die Frage nach der genauen Art und Ausprägung dieser Spannungen, ihren Ursachen und möglichen Lösungen, die eine wirklich fruchtbare Integration dieser drei Bereiche ermöglichen, untersucht und beantwortet werden. Dies erfolgt mit einem interdisziplinären Dreischritt, indem (a) soziologisch Art, Ausprägung und Ursache der vorfindlichen Spannungen analysiert werden, diese (b) theologisch reflektiert werden und abschließend (c) praktisch-theologische Handlungsmöglichkeiten als ekklesiologische Hilfestellungen für eine fruchtbare Integration entwickelt werden.Based on the multidimensional church planting project REFOmoabit this dissertation aims to answer the question how a fruitful integration of (1) communal life, (2) societal relevant congregational development and (3) property estate management is possible. Current ecclesiological practice and experience has shown that tensions arise between the principle of gift- and consensus-based cooperation and transformative church planting as well as the real estate management that is supposed to support the other two areas. Therefore this dissertation aims to examine and answer questions about the exact nature and extent of these tensions, their causes and possible solutions that make a truly fruitful integration of these three areas possible. This takes place within an interdisciplinary approach by (a) analyzing the nature, extent and reason of the tensions sociologically, (b) examining them from a theological viewpoint and (c) offering practical theological courses of action as an ecclesiological aid for a fruitful integration.Philosophy, Practical and Systematic TheologyM. Th. (Practical Theology

A new rhynchocephalian from the late jurassic of Germany with a dentition that is unique amongst tetrapods.

Rhynchocephalians, the sister group of squamates (lizards and snakes), are only represented by the single genus Sphenodon today. This taxon is often considered to represent a very conservative lineage. However, rhynchocephalians were common during the late Triassic to latest Jurassic periods, but rapidly declined afterwards, which is generally attributed to their supposedly adaptive inferiority to squamates and/or Mesozoic mammals, which radiated at that time. New finds of Mesozoic rhynchocephalians can thus provide important new information on the evolutionary history of the group. A new fossil relative of Sphenodon from the latest Jurassic of southern Germany, Oenosaurus muehlheimensis gen. et sp. nov., presents a dentition that is unique amongst tetrapods. The dentition of this taxon consists of massive, continuously growing tooth plates, probably indicating a crushing dentition, thus representing a previously unknown trophic adaptation in rhynchocephalians. The evolution of the extraordinary dentition of Oenosaurus from the already highly specialized Zahnanlage generally present in derived rhynchocephalians demonstrates an unexpected evolutionary plasticity of these animals. Together with other lines of evidence, this seriously casts doubts on the assumption that rhynchocephalians are a conservative and adaptively inferior lineage. Furthermore, the new taxon underlines the high morphological and ecological diversity of rhynchocephalians in the latest Jurassic of Europe, just before the decline of this lineage on this continent. Thus, selection pressure by radiating squamates or Mesozoic mammals alone might not be sufficient to explain the demise of the clade in the Late Mesozoic, and climate change in the course of the fragmentation of the supercontinent of Pangaea might have played a major role

Ambivalence of the influence of nitrogen supply on o-aminoacetophenone in 'Riesling' wine

AAP (o-aminoacetophenone) is the aroma substance responsible for the untypical ageing off-flavour (UTA). The impact of nitrogen supply on the formation of AAP was investigated between 1994 and 1999. The experiment was carried out in the Rheingau (Germany) with six fertigation treatments of annual quantities of N (0, 30, 60, 90, 150 kg·N·ha-1). Results indicated that the long-term varied N fertilization affected AAP concentration in wine as much as the year. Whereas a better N supply of the grapes due to effects of the year coincided with lower AAP values, the fertilization effect was reversal: higher N fertilization increased the concentrations of AAP. AAP did not correlate with its precursor IAA and only slightly with antioxidative capacity. Neither varying yield nor soluble solids could explain the high variance of AAP. An indicator for potential AAP formation could not be found, neither in must nor in wine.