Nilpotent normal form for divergence-free vector fields and volume-preserving maps

We study the normal forms for incompressible flows and maps in the neighborhood of an equilibrium or fixed point with a triple eigenvalue. We prove that when a divergence free vector field in $\mathbb{R}^3$ has nilpotent linearization with maximal Jordan block then, to arbitrary degree, coordinates can be chosen so that the nonlinear terms occur as a single function of two variables in the third component. The analogue for volume-preserving diffeomorphisms gives an optimal normal form in which the truncation of the normal form at any degree gives an exactly volume-preserving map whose inverse is also polynomial inverse with the same degree.Comment: laTeX, 20 pages, 1 figur

Line versus Flux Statistics -- Considerations for the Low Redshift Lyman-alpha Forest

The flux/transmission power spectrum has become a popular statistical tool in studies of the high redshift ($z > 2$) Lyman-alpha forest. At low redshifts, where the forest has thinned out into a series of well-isolated absorption lines, the motivation for flux statistics is less obvious. Here, we study the relative merits of flux versus line correlations, and derive a simple condition under which one is favored over the other on purely statistical grounds. Systematic errors probably play an important role in this discussion, and they are outlined as well.Comment: 6 pages, to appear in "The IGM/Galaxy Connection: The Distribution of Baryons at z=0", eds. J. L. Rosenberg and M. E. Putma

Properties of Galaxies in and around Voids

Two surveys for intrinsically faint galaxies towards nearby voids have been conducted at the MPI f\"ur Astronomie, Heidelberg. One selected targets from a new diameter limited ($\Phi \ge 5''$) catalog with morphological criteria while the other used digitized objective prism Schmidt plates to select mainly HII dwarf galaxies. For some 450 galaxies, redshifts and other optical data were obtained. We studied the spatial distribution of the sample objects, their luminosity function, and their intrinsic properties. Most of the galaxies belong to already well known sheets and filaments. But we found about a dozen highly isolated galaxies in each sample (nearest neighborhood distance $\ge 3 h_{75}^{-1} Mpc$). These tend to populate additional structures and are not distributed homogeneously throughout the voids. As our results on 'void galaxies' still suffer from small sample statistics, I also tried to combine similar existing surveys of nearby voids to get further hints on the larger structure and on the luminosity function of the isolated galaxies. No differences in the luminosity function of sheet and void galaxies could be found. The optical and infrared properties of both samples are in the normal range for samples dominated by late-type dwarfs. Follow-up HI studies show that the isolated dwarfs in both samples have unusual high amount of neutral gas for a given luminosity.Comment: 10 pages, 4 figures, latex, to appear in the proceedings of the 'Ringberg workshop on Large Scale Structure', hold Sep. 23-28, 199

The characteristic blue spectra of accretion disks in quasars as uncovered in the infrared

Quasars are thought to be powered by supermassive black holes accreting surrounding gas. Central to this picture is a putative accretion disk which is believed to be the source of the majority of the radiative output. It is well known, however, that the most extensively studied disk model -- an optically thick disk which is heated locally by the dissipation of gravitational binding energy -- is apparently contradicted by observations in a few major respects. In particular, the model predicts a specific blue spectral shape asymptotically from the visible to the near-infrared, but this is not generally seen in the visible wavelength region where the disk spectrum is observable. A crucial difficulty was that, toward the infrared, the disk spectrum starts to be hidden under strong hot dust emission from much larger but hitherto unresolved scales, and thus has essentially been impossible to observe. Here we report observations of polarized light interior to the dust-emiting region that enable us to uncover this near-infrared disk spectrum in several quasars. The revealed spectra show that the near-infrared disk spectrum is indeed as blue as predicted. This indicates that, at least for the outer near-infrared-emitting radii, the standard picture of the locally heated disk is approximately correct. The model problems at shorter wavelengths should then be directed toward a better understanding of the inner parts of the revealed disk. The newly uncovered disk emission at large radii, with more future measurements, will also shed totally new light on the unanswered critical question of how and where the disk ends.Comment: published in Nature, 24 July 2008 issue. Supplementary Information can be found at http://www.mpifr-bonn.mpg.de/div/ir-interferometry/suppl_info.pdf Published version can be accessed from http://www.nature.com/nature/journal/v454/n7203/pdf/nature07114.pd

Blazar spectral variability as explained by a twisted inhomogeneous jet

Blazars are active galactic nuclei, which are powerful sources of radiation whose central engine is located in the core of the host galaxy. Blazar emission is dominated by non-thermal radiation from a jet that moves relativistically towards us, and therefore undergoes Doppler beaming1. This beaming causes flux enhancement and contraction of the variability timescales, so that most blazars appear as luminous sources characterized by noticeable and fast changes in brightness at all frequencies. The mechanism that produces this unpredictable variability is under debate, but proposed mechanisms include injection, acceleration and cooling of particles2, with possible intervention of shock waves3,4 or turbulence5. Changes in the viewing angle of the observed emitting knots or jet regions have also been suggested as an explanation of flaring events6,7,8,9,10 and can also explain specific properties of blazar emission, such as intra-day variability11, quasi-periodicity12,13 and the delay of radio flux variations relative to optical changes14. Such a geometric interpretation, however, is not universally accepted because alternative explanations based on changes in physical conditions—such as the size and speed of the emitting zone, the magnetic field, the number of emitting particles and their energy distribution—can explain snapshots of the spectral behaviour of blazars in many cases15,16. Here we report the results of optical-to-radio-wavelength monitoring of the blazar CTA 102 and show that the observed long-term trends of the flux and spectral variability are best explained by an inhomogeneous, curved jet that undergoes changes in orientation over time. We propose that magnetohydrodynamic instabilities17 or rotation of the twisted jet6 cause different jet regions to change their orientation and hence their relative Doppler factors. In particular, the extreme optical outburst of 2016–2017 (brightness increase of six magnitudes) occurred when the corresponding emitting region had a small viewing angle. The agreement between observations and theoretical predictions can be seen as further validation of the relativistic beaming theory

Environmental chemical stressors as epigenome modifiers:a new horizon in assessment of toxicological effects

In eukaryotic cells, chromatin transformation from euchromatin into heterochromatin as a means of controlling gene expression and replication has been known as the ?accessibility hypothesis?. The interplay of epigenetic changes including histone modifications, DNA methylation, RNA interference (RNAi) and other functional epigenetic components are intricate. It is believed that these changes are well-programmed, inherited and can be modified by environmental contaminant stressors. Environmentally-driven epigenetic alterations during development, e.g. embryonic, foetal or neonatal stage, may influence disease susceptibility in adulthood. Therefore, understanding how epigenome modifications develop in response to environmental chemicals and, how epigenetic-xenobiotic interactions influence human health will shed new insights into gene-environment interactions in the epidemiology of several diseases including cancer. In this review, we consider studies of chemical modifiers including nutritional and xenobiotic effects on epigenetic components in vitro or in vivo. By examining the most-studied epigenome modifications and how their respective roles are interlinked, we highlight the central role of xenbiotic-modified epigenetic mechanisms. A major requirement will be to study and understand effects following environmentally-relevant exposures. We suggest that the study of epigenetic toxicology will open up new opportunities to devise strategies for the prevention or treatment of at-risk populations

The impact of viral mutations on recognition by SARS-CoV-2 specific T cells.

We identify amino acid variants within dominant SARS-CoV-2 T cell epitopes by interrogating global sequence data. Several variants within nucleocapsid and ORF3a epitopes have arisen independently in multiple lineages and result in loss of recognition by epitope-specific T cells assessed by IFN-γ and cytotoxic killing assays. Complete loss of T cell responsiveness was seen due to Q213K in the A∗01:01-restricted CD8+ ORF3a epitope FTSDYYQLY207-215; due to P13L, P13S, and P13T in the B∗27:05-restricted CD8+ nucleocapsid epitope QRNAPRITF9-17; and due to T362I and P365S in the A∗03:01/A∗11:01-restricted CD8+ nucleocapsid epitope KTFPPTEPK361-369. CD8+ T cell lines unable to recognize variant epitopes have diverse T cell receptor repertoires. These data demonstrate the potential for T cell evasion and highlight the need for ongoing surveillance for variants capable of escaping T cell as well as humoral immunity.This work is supported by the UK Medical Research Council (MRC); Chinese Academy of Medical Sciences(CAMS) Innovation Fund for Medical Sciences (CIFMS), China; National Institute for Health Research (NIHR)Oxford Biomedical Research Centre, and UK Researchand Innovation (UKRI)/NIHR through the UK Coro-navirus Immunology Consortium (UK-CIC). Sequencing of SARS-CoV-2 samples and collation of data wasundertaken by the COG-UK CONSORTIUM. COG-UK is supported by funding from the Medical ResearchCouncil (MRC) part of UK Research & Innovation (UKRI),the National Institute of Health Research (NIHR),and Genome Research Limited, operating as the Wellcome Sanger Institute. T.I.d.S. is supported by a Well-come Trust Intermediate Clinical Fellowship (110058/Z/15/Z). L.T. is supported by the Wellcome Trust(grant number 205228/Z/16/Z) and by theUniversity of Liverpool Centre for Excellence in Infectious DiseaseResearch (CEIDR). S.D. is funded by an NIHR GlobalResearch Professorship (NIHR300791). L.T. and S.C.M.are also supported by the U.S. Food and Drug Administration Medical Countermeasures Initiative contract75F40120C00085 and the National Institute for Health Research Health Protection Research Unit (HPRU) inEmerging and Zoonotic Infections (NIHR200907) at University of Liverpool inpartnership with Public HealthEngland (PHE), in collaboration with Liverpool School of Tropical Medicine and the University of Oxford.L.T. is based at the University of Liverpool. M.D.P. is funded by the NIHR Sheffield Biomedical ResearchCentre (BRC – IS-BRC-1215-20017). ISARIC4C is supported by the MRC (grant no MC_PC_19059). J.C.K.is a Wellcome Investigator (WT204969/Z/16/Z) and supported by NIHR Oxford Biomedical Research Centreand CIFMS. The views expressed are those of the authors and not necessarily those of the NIHR or MRC

Evaluating the Effects of SARS-CoV-2 Spike Mutation D614G on Transmissibility and Pathogenicity.

Global dispersal and increasing frequency of the SARS-CoV-2 spike protein variant D614G are suggestive of a selective advantage but may also be due to a random founder effect. We investigate the hypothesis for positive selection of spike D614G in the United Kingdom using more than 25,000 whole genome SARS-CoV-2 sequences. Despite the availability of a large dataset, well represented by both spike 614 variants, not all approaches showed a conclusive signal of positive selection. Population genetic analysis indicates that 614G increases in frequency relative to 614D in a manner consistent with a selective advantage. We do not find any indication that patients infected with the spike 614G variant have higher COVID-19 mortality or clinical severity, but 614G is associated with higher viral load and younger age of patients. Significant differences in growth and size of 614G phylogenetic clusters indicate a need for continued study of this variant

Investigation of hospital discharge cases and SARS-CoV-2 introduction into Lothian care homes

Background The first epidemic wave of severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) in Scotland resulted in high case numbers and mortality in care homes. In Lothian, over one-third of care homes reported an outbreak, while there was limited testing of hospital patients discharged to care homes. Aim To investigate patients discharged from hospitals as a source of SARS-CoV-2 introduction into care homes during the first epidemic wave. Methods A clinical review was performed for all patients discharges from hospitals to care homes from 1st March 2020 to 31st May 2020. Episodes were ruled out based on coronavirus disease 2019 (COVID-19) test history, clinical assessment at discharge, whole-genome sequencing (WGS) data and an infectious period of 14 days. Clinical samples were processed for WGS, and consensus genomes generated were used for analysis using Cluster Investigation and Virus Epidemiological Tool software. Patient timelines were obtained using electronic hospital records. Findings In total, 787 patients discharged from hospitals to care homes were identified. Of these, 776 (99%) were ruled out for subsequent introduction of SARS-CoV-2 into care homes. However, for 10 episodes, the results were inconclusive as there was low genomic diversity in consensus genomes or no sequencing data were available. Only one discharge episode had a genomic, time and location link to positive cases during hospital admission, leading to 10 positive cases in their care home. Conclusion The majority of patients discharged from hospitals were ruled out for introduction of SARS-CoV-2 into care homes, highlighting the importance of screening all new admissions when faced with a novel emerging virus and no available vaccine