The subgroup growth spectrum of virtually free groups

For a finitely generated group $\Gamma$ denote by $\mu(\Gamma)$ the growth coefficient of $\Gamma$, that is, the infimum over all real numbers $d$ such that $s_n(\Gamma)<n!^d$. We show that the growth coefficient of a virtually free group is always rational, and that every rational number occurs as growth coefficient of some virtually free group. Moreover, we describe an algorithm to compute $\mu$

X-ray resonant photoexcitation: line widths and energies of K{\alpha} transitions in highly charged Fe ions

Photoabsorption by and fluorescence of the K{\alpha} transitions in highly charged iron ions are essential mechanisms for X-ray radiation transfer in astrophysical environments. We study photoabsorption due to the main K{\alpha} transitions in highly charged iron ions from heliumlike to fluorinelike (Fe 24+...17+) using monochromatic X-rays around 6.6 keV at the PETRA III synchrotron photon source. Natural linewidths were determined with hitherto unattained accuracy. The observed transitions are of particular interest for the understanding of photoexcited plasmas found in X-ray binaries and active galactic nuclei.Comment: Revised versio

Quantum Imaging with Incoherently Scattered Light from a Free-Electron Laser

The advent of accelerator-driven free-electron lasers (FEL) has opened new avenues for high-resolution structure determination via diffraction methods that go far beyond conventional x-ray crystallography methods. These techniques rely on coherent scattering processes that require the maintenance of first-order coherence of the radiation field throughout the imaging procedure. Here we show that higher-order degrees of coherence, displayed in the intensity correlations of incoherently scattered x-rays from an FEL, can be used to image two-dimensional objects with a spatial resolution close to or even below the Abbe limit. This constitutes a new approach towards structure determination based on incoherent processes, including Compton scattering, fluorescence emission or wavefront distortions, generally considered detrimental for imaging applications. Our method is an extension of the landmark intensity correlation measurements of Hanbury Brown and Twiss to higher than second-order paving the way towards determination of structure and dynamics of matter in regimes where coherent imaging methods have intrinsic limitations

Construction of a computable cell proliferation network focused on non-diseased lung cells

<p>Abstract</p> <p>Background</p> <p>Critical to advancing the systems-level evaluation of complex biological processes is the development of comprehensive networks and computational methods to apply to the analysis of systems biology data (transcriptomics, proteomics/phosphoproteomics, metabolomics, etc.). Ideally, these networks will be specifically designed to capture the normal, non-diseased biology of the tissue or cell types under investigation, and can be used with experimentally generated systems biology data to assess the biological impact of perturbations like xenobiotics and other cellular stresses. Lung cell proliferation is a key biological process to capture in such a network model, given the pivotal role that proliferation plays in lung diseases including cancer, chronic obstructive pulmonary disease (COPD), and fibrosis. Unfortunately, no such network has been available prior to this work.</p> <p>Results</p> <p>To further a systems-level assessment of the biological impact of perturbations on non-diseased mammalian lung cells, we constructed a lung-focused network for cell proliferation. The network encompasses diverse biological areas that lead to the regulation of normal lung cell proliferation (Cell Cycle, Growth Factors, Cell Interaction, Intra- and Extracellular Signaling, and Epigenetics), and contains a total of 848 nodes (biological entities) and 1597 edges (relationships between biological entities). The network was verified using four published gene expression profiling data sets associated with measured cell proliferation endpoints in lung and lung-related cell types. Predicted changes in the activity of core machinery involved in cell cycle regulation (RB1, CDKN1A, and MYC/MYCN) are statistically supported across multiple data sets, underscoring the general applicability of this approach for a network-wide biological impact assessment using systems biology data.</p> <p>Conclusions</p> <p>To the best of our knowledge, this lung-focused Cell Proliferation Network provides the most comprehensive connectivity map in existence of the molecular mechanisms regulating cell proliferation in the lung. The network is based on fully referenced causal relationships obtained from extensive evaluation of the literature. The computable structure of the network enables its application to the qualitative and quantitative evaluation of cell proliferation using systems biology data sets. The network is available for public use.</p

Asymptotic stability for sets of polynomials

summary:We introduce the concept of asymptotic stability for a set of complex functions analytic around the origin, implicitly contained in an earlier paper of the first mentioned author (“Finite group actions and asymptotic expansion of $e^{P(z)}$", Combinatorica 17 (1997), 523 – 554). As a consequence of our main result we find that the collection of entire functions $\exp (\mathfrak {P})$ with $\mathfrak {P}$ the set of all real polynomials $P(z)$ satisfying Hayman’s condition $[z^n]\exp (P(z))>0\,(n\ge n_0)$ is asymptotically stable. This answers a question raised in loc. cit