Large normal subgroup growth and large characteristic subgroup growth

The maximal normal subgroup growth type of a finitely generated group is $n^{\log n}$. Very little is known about groups with this type of growth. In particular, the following is a long standing problem: Let $\Gamma$ be a group and $\Delta$ a subgroup of finite index. Suppose $\Delta$ has normal subgroup growth of type $n^{\log n}$, does $\Gamma$ has normal subgroup growth of type $n^{\log n}$? We give a positive answer in some cases, generalizing a result of M\"uller and the second author and a result of Gerdau. For instance, suppose $G$ is a profinite group and $H$ an open subgroup of $G$. We show that if $H$ is a generalized Golod-Shafarevich group, then $G$ has normal subgroup growth of type of $n^{\log n}$. We also use our methods to show that one can find a group with characteristic subgroup growth of type $n^{\log n}$

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 $k=3$

Effect of dopants on thermal stability and self-diffusion in iron nitride thin films

We studied the effect of dopants (Al, Ti, Zr) on the thermal stability of iron nitride thin films prepared using a dc magnetron sputtering technique. Structure and magnetic characterization of deposited samples reveal that the thermal stability together with soft magnetic properties of iron nitride thin films get significantly improved with doping. To understand the observed results, detailed Fe and N self-diffusion measurements were performed. It was observed that N self-diffusion gets suppressed with Al doping whereas Ti or Zr doping results in somewhat faster N diffusion. On the other hand Fe self-diffusion seems to get suppressed with any dopant of which heat of nitride formation is significantly smaller than that of iron nitride. Importantly, it was observed that N self-diffusion plays only a trivial role, as compared to Fe self-diffusion, in affecting the thermal stability of iron nitride thin films. Based on the obtained results effect of dopants on self-diffusion process is discussed.Comment: 10 pages, 9 fig

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 $\mu$

Animal Inhalation Models to Investigate Modulation of Inflammatory Bowel Diseases

Inflammatory bowel diseases (IBDs) comprise primarily two disease manifestations, ulcerative colitis (UC) and Crohn’s disease (CD), each with distinctive clinical and pathological features. Environmental and clinical factors strongly affect the development and clinical outcomes of IBDs. Among environmental factors, cigarette smoke (CS) is considered the most important risk factor for CD, while it attenuates the disease course of UC. Various animal models have been used to assess the impact of CS on intestinal pathophysiology. This chapter examines the suitability of animal inhalation/smoke exposure models for assessing the contrary effects of CS on UC and CD. It presents an updated literature review of IBD mouse models and a description of possible mechanisms relevant to relationships between IBD and smoking. In addition, it summarises various technical inhalation approaches, in the context of mouse disease models of IBD

Intensity interferometry of single x-ray pulses from a synchrotron storage ring

We report on measurements of second-order intensity correlations at the high brilliance storage ring PETRA III using a prototype of the newly developed Adaptive Gain Integrating Pixel Detector (AGIPD). The detector recorded individual synchrotron radiation pulses with an x-ray photon energy of 14.4 keV and repetition rate of about 5 MHz. The second-order intensity correlation function was measured simultaneously at different spatial separations that allowed to determine the transverse coherence length at these x-ray energies. The measured values are in a good agreement with theoretical simulations based on the Gaussian Schell-model.Comment: 16 pages, 6 figures, 42 reference

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

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

Origin of exchange bias in [Co/Pt]ML/Fe multilayer with orthogonal magnetic anisotropies

Magnetization reversal of soft ferromagnetic Fe layer, coupled to [Co/Pt]ML multilayer [ML] with perpendicular magnetic anisotropy (PMA), has been studied in-situ with an aim to understand the origin of exchange bias (EB) in orthogonal magnetic anisotropic systems. The interface remanant state of the ML is modified by magnetic field annealing, and the effect of the same on the soft Fe layer is monitored using the in-situ magneto-optical Kerr effect (MOKE). A considerable shift in the Fe layer hysteresis loop from the centre and an unusual increase in the coercivity, similar to exchange bias phenomena, is attributed to the exchange coupling at the [Co/Pt]ML and Fe interface. The effect of the coupling on spin orientation at the interface is further explored precisely by performing an isotope selective grazing incident nuclear resonance scattering (GINRS) technique. Here, the interface selectivity is achieved by introducing a 2 nm thick Fe57 marker between [Co/Pt]ML and Fe layers. Interface sensitivity is further enhanced by performing measurements under the x-ray standing wave conditions. The combined MOKE and GINRS analysis revealed the unidirectional pinning of the Fe layer due to the net in-plane magnetic spin at the interface caused by magnetic field annealing. Unidirectional exchange coupling or pinning at the interface, which may be due to the formation of asymmetrical closure domains, is found responsible for the origin of EB with an unusual increase in coercivity.Comment: 9 figures, 1 tabl