The irrationality of a number theoretical series

Denote by $\sigma_k(n)$ the sum of the $k$-th powers of the divisors of $n$, and let $S_k=\sum_{n\geq 1}\frac{\sigma_k(n)}{n!}$. We prove that Schinzel's conjecture H implies that $S_k$ is irrational, and give an unconditional proof for the case $k=3$

Coherent control of collective nuclear quantum states via transient magnons

Ultrafast and precise control of quantum systems at x-ray energies involves photons with oscillation periods below 1 as. Coherent dynamic control of quantum systems at these energies is one of the major challenges in hard x-ray quantum optics. Here, we demonstrate that the phase of a quantum system embedded in a solid can be coherently controlled via a quasi-particle with subattosecond accuracy. In particular, we tune the quantum phase of a collectively excited nuclear state via transient magnons with a precision of 1 zs and a timing stability below 50 ys. These small temporal shifts are monitored interferometrically via quantum beats between different hyperfine-split levels. The experiment demonstrates zeptosecond interferometry and shows that transient quasi-particles enable accurate control of quantum systems embedded in condensed matter environments

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

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

Epithelial Tissues Have Varying Degrees of Susceptibility to KrasG12D-Initiated Tumorigenesis in a Mouse Model

Activating mutations in the Kras gene are commonly found in some but not all epithelial cancers. In order to understand the susceptibility of different epithelial tissues to Kras-induced tumorigenesis, we introduced one of the most common Kras mutations, KrasG12D, broadly in epithelial tissues. We used a mouse model in which the G12D mutation is placed in the endogenous Kras locus controlled by inducible, Cre-mediated recombination in tissues expressing cytokeratin 19 including the oral cavity, GI tract, lungs, and ducts of the liver, kidney, and the pancreas. Introduction of the KrasG12D mutation in adult mouse tissues led to neoplastic changes in some but not all of these tissues. Notably, many hyperplasias, metaplasias and adenomas were observed in the oral cavity, stomach, colon and lungs, suggesting that exposure to products of the outside environment promotes KrasG12D-initiated tumorigenesis. However, environmental exposure did not consistently correlate with tumor formation, such as in the small intestine, suggesting that there are also intrinsic differences in susceptibility to Kras activation. The pancreas developed small numbers of mucinous metaplasias with characteristics of early stage pancreatic intraepithelial neoplasms (PanINs), supporting the hypothesis that pancreatic ducts have the potential to give rise pancreatic cancer

Enhancement of COPD biological networks using a web-based collaboration interface

The construction and application of biological network models is an approach that offers a holistic way to understand biological processes involved in disease. Chronic obstructive pulmonary disease (COPD) is a progressive inflammatory disease of the airways for which therapeutic options currently are limited after diagnosis, even in its earliest stage. COPD network models are important tools to better understand the biological components and processes underlying initial disease development. With the increasing amounts of literature that are now available, crowdsourcing approaches offer new forms of collaboration for researchers to review biological findings, which can be applied to the construction and verification of complex biological networks. We report the construction of 50 biological network models relevant to lung biology and early COPD using an integrative systems biology and collaborative crowd-verification approach. By combining traditional literature curation with a data-driven approach that predicts molecular activities from transcriptomics data, we constructed an initial COPD network model set based on a previously published non-diseased lung-relevant model set. The crowd was given the opportunity to enhance and refine the networks on a website ( https://bionet.sbvimprover.com/) and to add mechanistic detail, as well as critically review existing evidence and evidence added by other users, so as to enhance the accuracy of the biological representation of the processes captured in the networks. Finally, scientists and experts in the field discussed and refined the networks during an in-person jamboree meeting. Here, we describe examples of the changes made to three of these networks: Neutrophil Signaling, Macrophage Signaling, and Th1-Th2 Signaling. We describe an innovative approach to biological network construction that combines literature and data mining and a crowdsourcing approach to generate a comprehensive set of COPD-relevant models that can be used to help understand the mechanisms related to lung pathobiology. Registered users of the website can freely browse and download the networks