The Leja method revisited: backward error analysis for the matrix exponential

The Leja method is a polynomial interpolation procedure that can be used to compute matrix functions. In particular, computing the action of the matrix exponential on a given vector is a typical application. This quantity is required, e.g., in exponential integrators. The Leja method essentially depends on three parameters: the scaling parameter, the location of the interpolation points, and the degree of interpolation. We present here a backward error analysis that allows us to determine these three parameters as a function of the prescribed accuracy. Additional aspects that are required for an efficient and reliable implementation are discussed. Numerical examples that illustrate the performance of our Matlab code are included

Meshfree exponential integrators

For the numerical solution of time-dependent partial dierential equations, a class ofmeshfree exponential integrators is proposed. These methods are of particular interest in situationswhere the solution of the dierential equation concentrates on a small part of the computationaldomain which may vary in time. For the space discretization, radial basis functions with compactsupport are suggested. The reason for this choice are stability and robustness of the resultinginterpolation procedure. The time integration is performed with an exponential Rosenbrock method.The required matrix functions are computed by Newton interpolation based on Leja points. Theproposed integrators are fully adaptive in space and time. Numerical examples that illustrate therobustness and the good stability properties of the method are included

Die Freiheit des Individuums. Eine Rekonstruktion der Gesellschaftstheorie Wilhelm von Humboldts

Das zentrale sprach- und geschichtsphilosophisch sowie politiktheoretisch reflektierte Thema Humboldts ist die Möglichkeit der Freiheit des vergesellschafteten Individuums. Die Rekonstruktion seiner Philosophie weist diese als konsistente und in empirische Forschung überführbare gesellschaftstheoretische Paradigmatik aus. Auf diese gegründet, ist sein Beitrag zum Liberalismus – eine anthropologisch fundierte, historisch dimensionierte und humanistisch geprägte Staatstheorie – ein Gegenentwurf zur englischen Tradition

Comparison of software for computing the action of the matrix exponential

The implementation of exponential integrators requires the action of the matrix exponential and related functions of a large matrix. There are various methods in the literature for carrying out this task. In this paper we describe a new implementation of a method based on interpolation at Leja points. We numerically compare this method with others from the literature. As we are interested in exponential intergrators we choose the test examples from spatial discretization of time dependent partial differential equations in two and three space dimensions. The test matrices thus have large eigenvalues and can be nonnormal

A minimisation approach for computing the ground state of Gross\u2013Pitaevskii systems

In this paper, we present a minimisation method for computing the ground stateof systems of coupled Gross\u2013Pitaevskii equations. Our approach relies on a spectral decomposition of the solution into Hermite basis functions. Inserting the spectral representation into the energy functional yields a constrained nonlinear minimisation problem for the coefficients. For its numerical solution, we employ a Newton-like method with an approximate line-search strategy. We analyse this method and prove global convergence. Appropriate starting values for the minimisation process are determined by a standard continuation strategy. Numerical examples with two and three-component two-dimensional condensates are included. These experiments demonstrate the reliability of our method and nicely illustrate the effect of phase segregation

Zur Analyse von Wahlergebnissen in Parteihochburgen unter Berücksichtigung von Regressionsphänomenen

"Regelmäßige Wahlen bilden ein Kernstück jeder demokratischen Verfassungsordnung. Insbesondere in den letzten drei Jahrzehnten hat sich die Wahlforschung im Bereich der politischen Wissenschaften mehr und mehr etabliert und spielt bei den Berichterstattungen sowohl im Vorfeld von Wahlen als auch in der Analyse von Wahlergebnissen eine entscheidende Rolle. Bei der Wahlanalyse sind vor allem die Änderungen in den sogenannten 'Partei-Hochburgen' von besonderem Interesse. Dieser Artikel soll anhand von Daten der Landtagswahl in Hessen 2008 sowie der Bundestagswahl 2005 klären helfen, ob es sich bei den Verlusten, die alle großen demokratischen Parteien in ihren Hochburgen erlitten haben, tatsächlich um beunruhigende Entwicklungen oder um ein Regressionsphänomen zur Mitte handelt. Entsprechende statistische Verfahren und Modelle werden in diesem Zusammenhang vorgestellt, angewandt und diskutiert." (Autorenreferat)"Regular elections are at the heart of every democratic constitutional order. Particularly in the last three decades electoral studies have increasingly established themselves within the field of political sciences and now play an important role in media and press coverage prior to elections and in the analysis of election results. In this analysis the results in party strongholds are of particular interest to researchers. Based on data of the election to the German State Parliament of Hesse in 2008 and of the election to the German Bundestag in 2005 this article aims at answering the question whether the losses of all big democratic parties in their strongholds are a serious and alarming matter or whether to a certain extend these losses can be explained by regression-to-the-mean. Relevant statistical methods and models are introduced, applied and discussed." (author's abstract

Metal-organic framework nanofibers via electrospinning

A hierarchical system of highly porous nanofibers has been prepared by electrospinning MOF (metal-organic framework) nanoparticles with suitable carrier polymers. Nitrogen adsorption proved the MOF nanoparticles to be fully accessible inside the polymeric fibers. © 2011 The Royal Society of Chemistry

Electrospun antimony doped tin oxide (ATO) nanofibers as a versatile conducting matrix

Nanoparticles of ATO (antimony doped tin oxide) were used to produce thick conductive, free standing mats of nanofibers via electrospinning. These fibrous mats were incorporated into polymer films to produce a transparent conducting polymer foil. Moreover, the fiber mats can serve as porous electrodes for electrodeposition of Prussian Blue and TiO2 and were tested in dye-sensitized solar cells

GVC: efficient random access compression for gene sequence variations

Background: In recent years, advances in high-throughput sequencing technologies have enabled the use of genomic information in many fields, such as precision medicine, oncology, and food quality control. The amount of genomic data being generated is growing rapidly and is expected to soon surpass the amount of video data. The majority of sequencing experiments, such as genome-wide association studies, have the goal of identifying variations in the gene sequence to better understand phenotypic variations. We present a novel approach for compressing gene sequence variations with random access capability: the Genomic Variant Codec (GVC). We use techniques such as binarization, joint row- and column-wise sorting of blocks of variations, as well as the image compression standard JBIG for efficient entropy coding. Results: Our results show that GVC provides the best trade-off between compression and random access compared to the state of the art: it reduces the genotype information size from 758 GiB down to 890 MiB on the publicly available 1000 Genomes Project (phase 3) data, which is 21% less than the state of the art in random-access capable methods. Conclusions: By providing the best results in terms of combined random access and compression, GVC facilitates the efficient storage of large collections of gene sequence variations. In particular, the random access capability of GVC enables seamless remote data access and application integration. The software is open source and available at https://github.com/sXperfect/gvc/

Critical Review Effects of Yoga Interventions on Pain and Pain-Associated Disability: A Meta-Analysis

Abstract: We searched databases for controlled clinical studies, and performed a meta-analysis on the effectiveness of yoga interventions on pain and associated disability. Five randomized studies reported single-blinding and had a higher methodological quality; 7 studies were randomized but not blinded and had moderate quality; and 4 nonrandomized studies had low quality. In 6 studies, yoga was used to treat patients with back pain; in 2 studies to treat rheumatoid arthritis; in 2 studies to treat patients with headache/migraine; and 6 studies enrolled individuals for other indications. All studies reported positive effects in favor of the yoga interventions. With respect to pain, a random effect meta-analysis estimated the overall treatment effect at SMD = À.74 (CI: À.97; À.52, P < .0001), and an overall treatment effect at SMD = À.79 (CI: À1.02; À.56, P < .0001) for pain-related disability. Despite some limitations, there is evidence that yoga may be useful for several pain-associated disorders. Moreover, there are hints that even short-term interventions might be effective. Nevertheless, large-scale further studies have to identify which patients may benefit from the respective interventions. Perspective: This meta-analysis suggests that yoga is a useful supplementary approach with moderate effect sizes on pain and associated disability