Algebraic theory of affine curvature tensors

We use curvature decompositions to construct generating sets for the space of algebraic curvature tensors and for the space of tensors with the same symmetries as those of a torsion free, Ricci symmetric connection; the latter naturally appear in relative hypersurface theory.Comment: The paper is dedicated to the memory of the first author (N. Blazic) who passed away Monday 10 October 200

Statistics of Lead Changes in Popularity-Driven Systems

We study statistical properties of the highest degree, or most popular, nodes in growing networks. We show that the number of lead changes increases logarithmically with network size N, independent of the details of the growth mechanism. The probability that the first node retains the lead approaches a finite constant for popularity-driven growth, and decays as N^{-phi}(ln N)^{-1/2}, with phi=0.08607..., for growth with no popularity bias.Comment: 4 pages, 4 figures, 2 column revtex format. Minor changes in response to referee comments. For publication in PR

On the Containment Problem for Linear Sets

It is well known that the containment problem (as well as the equivalence problem) for semilinear sets is log-complete at the second level of the polynomial hierarchy (where hardness even holds in dimension 1). It had been shown quite recently that already the containment problem for multi-dimensional linear sets is log-complete at the same level of the hierarchy (where hardness even holds when numbers are encoded in unary). In this paper, we show that already the containment problem for 1-dimensional linear sets (with binary encoding of the numerical input parameters) is log-hard (and therefore also log-complete) at this level. However, combining both restrictions (dimension 1 and unary encoding), the problem becomes solvable in polynomial time

Anti-Interleukin-5-Therapie bei eosinophilen Erkrankungen

Zusammenfassung: Bei einer Reihe von Erkrankungen, die durch eine Eosinophilie charakterisiert sind, findet man erhöhte Spiegel von Interleukin- (IL-)5 im Blut und/oder Gewebe. IL-5 spielt eine wichtige Rolle in der Regulierung von Produktion, Differenzierung, Rekrutierung, Aktivierung und Überleben eosinophiler Granulozyten. Daher stellt die Neutralisation von IL-5 durch blockierende Antikörper einen vielversprechenden neuen Ansatz in der Therapie dieser Erkrankungen dar. Erste klinische Studien zeigten, dass es nach Applikation von Anti-IL-5-Antikörpern zu einem raschen Abfall der Eosinophilenzahlen im peripheren Blut kommt. Eine Abnahme der Beschwerden wurde bei der lymphozytären Form hypereosinophiler Syndrome, bei eosinophiler Ösophagitis und bei chronischer Rhinitis mit nasaler Polyposis beobachtet. Im Gegensatz dazu zeigte eine Anti-IL-5-Antikörper-Behandlung von Patienten mit Asthma bronchiale oder mit atopischem Ekzem nicht den erwarteten klinischen Effekt. Zukünftige Studien werden zeigen, bei welchen eosinophilen Erkrankungen eine Anti-IL-5-Therapie wirksam ist und welche Patientengruppen auf diese Therapie anspreche

Constrained simulations of the Antennae Galaxies: Comparison with Herschel-PACS observations

We present a set of hydro-dynamical numerical simulations of the Antennae galaxies in order to understand the origin of the central overlap starburst. Our dynamical model provides a good match to the observed nuclear and overlap star formation, especially when using a range of rather inefficient stellar feedback efficiencies (0.01 < q_EoS < 0.1). In this case a simple conversion of local star formation to molecular hydrogen surface density motivated by observations accounts well for the observed distribution of CO. Using radiative transfer post-processing we model synthetic far-infrared spectral energy distributions (SEDs) and two-dimensional emission maps for direct comparison with Herschel-PACS observations. For a gas-to-dust ratio of 62:1 and the best matching range of stellar feedback efficiencies the synthetic far-infrared SEDs of the central star forming region peak at values of ~65 - 81 Jy at 99 - 116 um, similar to a three-component modified black body fit to infrared observations. Also the spatial distribution of the far-infrared emission at 70 um, 100 um, and 160 um compares well with the observations: >50% (> 35%) of the emission in each band is concentrated in the overlap region while only < 30% (< 15%) is distributed to the combined emission from the two galactic nuclei in the simulations (observations). As a proof of principle we show that parameter variations in the feedback model result in unambiguous changes both in the global and in the spatially resolved observable far-infrared properties of Antennae galaxy models. Our results strengthen the importance of direct, spatially resolved comparative studies of matched galaxy merger simulations as a valuable tool to constrain the fundamental star formation and feedback physics.Comment: 17 pages, 8 figures, 4 tables, submitted to MNRAS, including revisions after first referee report, comments welcom