A dimension-breaking phenomenon for water waves with weak surface tension

It is well known that the water-wave problem with weak surface tension has small-amplitude line solitary-wave solutions which to leading order are described by the nonlinear Schr\"odinger equation. The present paper contains an existence theory for three-dimensional periodically modulated solitary-wave solutions which have a solitary-wave profile in the direction of propagation and are periodic in the transverse direction; they emanate from the line solitary waves in a dimension-breaking bifurcation. In addition, it is shown that the line solitary waves are linearly unstable to long-wavelength transverse perturbations. The key to these results is a formulation of the water wave problem as an evolutionary system in which the transverse horizontal variable plays the role of time, a careful study of the purely imaginary spectrum of the operator obtained by linearising the evolutionary system at a line solitary wave, and an application of an infinite-dimensional version of the classical Lyapunov centre theorem.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-015-0941-

Existence and conditional energetic stability of three-dimensional fully localised solitary gravity-capillary water waves

In this paper we show that the hydrodynamic problem for three-dimensional water waves with strong surface-tension effects admits a fully localised solitary wave which decays to the undisturbed state of the water in every horizontal direction. The proof is based upon the classical variational principle that a solitary wave of this type is a critical point of the energy subject to the constraint that the momentum is fixed. We prove the existence of a minimiser of the energy subject to the constraint that the momentum is fixed and small. The existence of a small-amplitude solitary wave is thus assured, and since the energy and momentum are both conserved quantities a standard argument may be used to establish the stability of the set of minimisers as a whole. `Stability' is however understood in a qualified sense due to the lack of a global well-posedness theory for three-dimensional water waves.Comment: 83 pages, 1 figur

Repeatability and reproducibility of multiparametric magnetic resonance imaging of the liver

As the burden of liver disease reaches epidemic levels, there is a high unmet medical need to develop robust, accurate and reproducible non-invasive methods to quantify liver tissue characteristics for use in clinical development and ultimately in clinical practice. This prospective cross-sectional study systematically examines the repeatability and reproducibility of iron-corrected T1 (cT1), T2*, and hepatic proton density fat fraction (PDFF) quantification with multiparametric MRI across different field strengths, scanner manufacturers and models. 61 adult participants with mixed liver disease aetiology and those without any history of liver disease underwent multiparametric MRI on combinations of 5 scanner models from two manufacturers (Siemens and Philips) at different field strengths (1.5T and 3T). We report high repeatability and reproducibility across different field strengths, manufacturers, and scanner models in standardized cT1 (repeatability CoV: 1.7%, bias -7.5ms, 95% LoA of -53.6 ms to 38.5 ms; reproducibility CoV 3.3%, bias 6.5 ms, 95% LoA of -76.3 to 89.2 ms) and T2* (repeatability CoV: 5.5%, bias -0.18 ms, 95% LoA -5.41 to 5.05 ms; reproducibility CoV 6.6%, bias -1.7 ms, 95% LoA -6.61 to 3.15 ms) in human measurements. PDFF repeatability (0.8%) and reproducibility (0.75%) coefficients showed high precision of this metric. Similar precision was observed in phantom measurements. Inspection of the ICC model indicated that most of the variance in cT1 could be accounted for by study participants (ICC = 0.91), with minimal contribution from technical differences. We demonstrate that multiparametric MRI is a non-invasive, repeatable and reproducible method for quantifying liver tissue characteristics across manufacturers (Philips and Siemens) and field strengths (1.5T and 3T)

Global well-posedness for the KP-I equation on the background of a non localized solution

We prove that the Cauchy problem for the KP-I equation is globally well-posed for initial data which are localized perturbations (of arbitrary size) of a non-localized (i.e. not decaying in all directions) traveling wave solution (e.g. the KdV line solitary wave or the Zaitsev solitary waves which are localized in $x$ and $y$ periodic or conversely)

Fitting the integrated Spectral Energy Distributions of Galaxies

Fitting the spectral energy distributions (SEDs) of galaxies is an almost universally used technique that has matured significantly in the last decade. Model predictions and fitting procedures have improved significantly over this time, attempting to keep up with the vastly increased volume and quality of available data. We review here the field of SED fitting, describing the modelling of ultraviolet to infrared galaxy SEDs, the creation of multiwavelength data sets, and the methods used to fit model SEDs to observed galaxy data sets. We touch upon the achievements and challenges in the major ingredients of SED fitting, with a special emphasis on describing the interplay between the quality of the available data, the quality of the available models, and the best fitting technique to use in order to obtain a realistic measurement as well as realistic uncertainties. We conclude that SED fitting can be used effectively to derive a range of physical properties of galaxies, such as redshift, stellar masses, star formation rates, dust masses, and metallicities, with care taken not to over-interpret the available data. Yet there still exist many issues such as estimating the age of the oldest stars in a galaxy, finer details ofdust properties and dust-star geometry, and the influences of poorly understood, luminous stellar types and phases. The challenge for the coming years will be to improve both the models and the observational data sets to resolve these uncertainties. The present review will be made available on an interactive, moderated web page (sedfitting.org), where the community can access and change the text. The intention is to expand the text and keep it up to date over the coming years.Comment: 54 pages, 26 figures, Accepted for publication in Astrophysics & Space Scienc

Discovery and fine-mapping of glycaemic and obesity-related trait loci using high-density imputation

Reference panels from the 1000 Genomes (1000G) Project Consortium provide near complete coverage of common and low-frequency genetic variation with minor allele frequency ≥0.5% across European ancestry populations. Within the European Network for Genetic and Genomic Epidemiology (ENGAGE) Consortium, we have undertaken the first large-scale meta-analysis of genome-wide association studies (GWAS), supplemented by 1000G imputation, for four quantitative glycaemic and obesity-related traits, in up to 87,048 individuals of European ancestry. We identified two loci for body mass index (BMI) at genome-wide significance, and two for fasting glucose (FG), none of which has been previously reported in larger meta-analysis efforts to combine GWAS of European ancestry. Through conditional analysis, we also detected multiple distinct signals of association mapping to established loci for waist-hip ratio adjusted for BMI (RSPO3) and FG (GCK and G6PC2). The index variant for one association signal at the G6PC2 locus is a low-frequency coding allele, H177Y, which has recently been demonstrated to have a functional role in glucose regulation. Fine-mapping analyses revealed that the non-coding variants most likely to drive association signals at established and novel loci were enriched for overlap with enhancer elements, which for FG mapped to promoter and transcription factor binding sites in pancreatic islets, in particular. Our study demonstrates that 1000G imputation and genetic fine-mapping of common and low-frequency variant association signals at GWAS loci, integrated with genomic annotation in relevant tissues, can provide insight into the functional and regulatory mechanisms through which their effects on glycaemic and obesity-related traits are mediated

Discovery and Fine-Mapping of Glycaemic and Obesity-Related Trait Loci Using High-Density Imputation

Reference panels from the 1000 Genomes (1000G) Project Consortium provide near complete coverage of common and low-frequency genetic variation with minor allele frequency ≥0.5% across European ancestry populations. Within the European Network for Genetic and Genomic Epidemiology (ENGAGE) Consortium, we have undertaken the fi

periscope: sub-genomic RNA identification in SARS-CoV-2 genomic sequencing data

We have developed periscope, a tool for the detection and quantification of sub-genomic RNA (sgRNA) in SARS-CoV-2 genomic sequence data. The translation of the SARS-CoV-2 RNA genome for most open reading frames (ORFs) occurs via RNA intermediates termed “sub-genomic RNAs”. sgRNAs are produced through discontinuous transcription which relies on homology between transcription regulatory sequences (TRS-B) upstream of the ORF start codons and that of the TRS-L which is located in the 5’ UTR. TRS-L is immediately preceded by a leader sequence. This leader sequence is therefore found at the 5’ end of all sgRNA. We applied periscope to 1,155 SARS-CoV-2 genomes from Sheffield, UK and validated our findings using orthogonal datasets and in vitro cell systems. Using a simple local alignment to detect reads which contain the leader sequence we were able to identify and quantify reads arising from canonical and non-canonical sgRNA. We were able to detect all canonical sgRNAs at expected abundances, with the exception of ORF10. A number of recurrent non-canonical sgRNAs are detected. We show that the results are reproducible using technical replicates and determine the optimum number of reads for sgRNA analysis. In VeroE6 ACE2+/− cell lines, periscope can detect the changes in the kinetics of sgRNA in orthogonal sequencing datasets. Finally, variants found in genomic RNA are transmitted to sgRNAs with high fidelity in most cases. This tool can be applied to all sequenced COVID-19 samples worldwide to provide comprehensive analysis of SARS-CoV-2 sgRNA

Geographical and temporal distribution of SARS-CoV-2 clades in the WHO European Region, January to June 2020

We show the distribution of SARS-CoV-2 genetic clades over time and between countries and outline potential genomic surveillance objectives. We applied three available genomic nomenclature systems for SARS-CoV-2 to all sequence data from the WHO European Region available during the COVID-19 pandemic until 10 July 2020. We highlight the importance of real-time sequencing and data dissemination in a pandemic situation. We provide a comparison of the nomenclatures and lay a foundation for future European genomic surveillance of SARS-CoV-2.Peer reviewe