Analysis of a stochastic chemical system close to a sniper bifurcation of its mean field model

A framework for the analysis of stochastic models of chemical systems for which the deterministic mean-field description is undergoing a saddle-node infinite period (SNIPER) bifurcation is presented. Such a bifurcation occurs for example in the modelling of cell-cycle regulation. It is shown that the stochastic system possesses oscillatory solutions even for parameter values for which the mean-field model does not oscillate. The dependence of the mean period of these oscillations on the parameters of the model (kinetic rate constants) and the size of the system (number of molecules present) is studied. Our approach is based on the chemical Fokker Planck equation. To get some insights into advantages and disadvantages of the method, a simple one-dimensional chemical switch is first analyzed, before the chemical SNIPER problem is studied in detail. First, results obtained by solving the Fokker-Planck equation numerically are presented. Then an asymptotic analysis of the Fokker-Planck equation is used to derive explicit formulae for the period of oscillation as a function of the rate constants and as a function of the system size

Radio emission from the massive stars in the Galactic Super Star Cluster Westerlund 1

Current mass-loss rate estimates imply that main sequence winds are not sufficient to strip away the H-rich envelope to yield Wolf-Rayet (WR) stars. The rich transitional population of Westerlund 1 (Wd 1) provides an ideal laboratory to observe mass-loss processes throughout the transitional phase of stellar evolution. An analysis of deep radio continuum observations of Wd 1 is presented. We detect 18 cluster members. The radio properties of the sample are diverse, with thermal, non-thermal and composite thermal/non-thermal sources present. Mass-loss rates are ~10^{-5} solar mass/year across all spectral types, insufficient to form WRs during a massive star lifetime, and the stars must undergo a period of enhanced mass loss. The sgB[e] star W9 may provide an example, with a mass-loss rate an order of magnitude higher than the other cluster members, and an extended nebula of density ~3 times the current wind. This structure is reminiscent of luminous blue variables, and one with evidence of two eras of high, possibly eruptive, mass loss. Three OB supergiants are detected, implying unusually dense winds. They also may have composite spectra, suggesting binarity. Spatially resolved nebulae are associated with three of the four RSGs and three of the six YHGs in the cluster, which are due to quiescent mass loss rather than outbursts. For some of the cool star winds, the ionizing source may be a companion star though the cluster radiation density is sufficiently high to provide the necessary ionizing radiation. Five WR stars are detected with composite spectra, interpreted as arising in colliding-wind binaries.Comment: 15 pages, 6 figures. Accepted for publication in Astronomy and Astrophysic

Radio emission from the massive stars in Westerlund 1

The diverse massive stellar population in the young massive clusterWesterlund 1 (Wd 1) provides an ideal laboratory to observe and constrain mass-loss processes throughout the transitional phase of massive star evolution. A set of high sensitivity radio observations of Wd 1 leads to the detection of 18 cluster members, a sample dominated by cool hypergiants, but with detections among hotter OB supergiants and WR stars. Here the diverse radio properties of the detected sample are briefly described. The mass-loss rates of the detected objects are surprisingly similar across the whole transitional phase of massive star evolution, at ~ 10-5 Mo yr−1. Such a rate is insufficient to strip away the H-rich mantle in a massive star lifetime, unless the stars go through a period of enhanced mass-loss. The radio luminous star W9 provides an example of such an object, with evidence for two eras of mass-loss with rates of ~ 10−4 Mo yr−1

Origins of ferromagnetism in transition-metal doped Si

We present results of the magnetic, structural and chemical characterizations of Mn<sup>+</sup>-implanted Si displaying <i>n</i>-type semiconducting behavior and ferromagnetic ordering with Curie temperature,T<sub>C</sub> well above room temperature. The temperature-dependent magnetization measured by superconducting quantum device interference (SQUID) from 5 K to 800 K was characterized by three different critical temperatures (T*<sub>C</sub>~45 K, T<sub>C1</sub>~630-650 K and T<sub>C2</sub>~805-825 K). Their origins were investigated using dynamic secondary mass ion spectroscopy (SIMS) and transmission electron microscopy (TEM) techniques, including electron energy loss spectroscopy (EELS), Z-contrast STEM (scanning TEM) imaging and electron diffraction. We provided direct evidences of the presence of a small amount of Fe and Cr impurities which were unintentionally doped into the samples together with the Mn<sup>+</sup> ions, as well as the formation of Mn-rich precipitates embedded in a Mn-poor matrix. The observed T*<sub>C</sub> is attributed to the Mn<sub>4</sub>Si<sub>7</sub> precipitates identified by electron diffraction. Possible origins of and are also discussed. Our findings raise questions regarding the origin of the high ferromagnetism reported in many material systems without a careful chemical analysis

Observation of lobes near the X-point in resonant magnetic perturbation experiments on MAST

The application of non-axisymmetric resonant magnetic perturbations (RMPs) with a toroidal mode number n=6 in the MAST tokamak produces a significant reduction in plasma energy loss associated with type-I Edge Localized Modes (ELMs), the first such observation with n>3. During the ELM mitigated stage clear lobe structures are observed in visible-light imaging of the X-point region. These lobes or manifold structures, that were predicted previously, have been observed for the first time in a range of discharges and their appearance is correlated with the effect of RMPs on the plasma i.e. they only appear above a threshold when a density pump out is observed or when the ELM frequency is increased. They appear to be correlated with the RMPs penetrating the plasma and may be important in explaining why the ELM frequency increases. The number and location of the structures observed can be well described using vacuum modelling. Differences in radial extent and poloidal width from vacuum modelling are likely to be due to a combination of transport effects and plasma screening.Comment: 15 pages, 5 figure

Comparison of alternative approaches for analysing multi-level RNA-seq data

RNA sequencing (RNA-seq) is widely used for RNA quantification in the environmental, biological and medical sciences. It enables the description of genome-wide patterns of expression and the identification of regulatory interactions and networks. The aim of RNA-seq data analyses is to achieve rigorous quantification of genes/transcripts to allow a reliable prediction of differential expression (DE), despite variation in levels of noise and inherent biases in sequencing data. This can be especially challenging for datasets in which gene expression differences are subtle, as in the behavioural transcriptomics test dataset from D. melanogaster that we used here. We investigated the power of existing approaches for quality checking mRNA-seq data and explored additional, quantitative quality checks. To accommodate nested, multi-level experimental designs, we incorporated sample layout into our analyses. We employed a subsampling without replacement-based normalization and an identification of DE that accounted for the hierarchy and amplitude of effect sizes within samples, then evaluated the resulting differential expression call in comparison to existing approaches. In a final step to test for broader applicability, we applied our approaches to a published set of H. sapiens mRNA-seq samples, The dataset-tailored methods improved sample comparability and delivered a robust prediction of subtle gene expression changes. The proposed approaches have the potential to improve key steps in the analysis of RNA-seq data by incorporating the structure and characteristics of biological experiments