Unitary Representations of Unitary Groups

In this paper we review and streamline some results of Kirillov, Olshanski and Pickrell on unitary representations of the unitary group \U(\cH) of a real, complex or quaternionic separable Hilbert space and the subgroup \U_\infty(\cH), consisting of those unitary operators $g$ for which g - \1 is compact. The Kirillov--Olshanski theorem on the continuous unitary representations of the identity component \U_\infty(\cH)_0 asserts that they are direct sums of irreducible ones which can be realized in finite tensor products of a suitable complex Hilbert space. This is proved and generalized to inseparable spaces. These results are carried over to the full unitary group by Pickrell's Theorem, asserting that the separable unitary representations of \U(\cH), for a separable Hilbert space \cH, are uniquely determined by their restriction to \U_\infty(\cH)_0. For the $10$ classical infinite rank symmetric pairs $(G,K)$ of non-unitary type, such as (\GL(\cH),\U(\cH)), we also show that all separable unitary representations are trivial.Comment: 42 page

Schwinger Terms and Cohomology of Pseudodifferential Operators

We study the cohomology of the Schwinger term arising in second quantization of the class of observables belonging to the restricted general linear algebra. We prove that, for all pseudodifferential operators in 3+1 dimensions of this type, the Schwinger term is equivalent to the ``twisted'' Radul cocycle, a modified version of the Radul cocycle arising in non-commutative differential geometry. In the process we also show how the ordinary Radul cocycle for any pair of pseudodifferential operators in any dimension can be written as the phase space integral of the star commutator of their symbols projected to the appropriate asymptotic component.Comment: 19 pages, plain te

Exon-Specific QTLs Skew the Inferred Distribution of Expression QTLs Detected Using Gene Expression Array Data

Mapping of expression quantitative trait loci (eQTLs) is an important technique for studying how genetic variation affects gene regulation in natural populations. In a previous study using Illumina expression data from human lymphoblastoid cell lines, we reported that cis-eQTLs are especially enriched around transcription start sites (TSSs) and immediately upstream of transcription end sites (TESs). In this paper, we revisit the distribution of eQTLs using additional data from Affymetrix exon arrays and from RNA sequencing. We confirm that most eQTLs lie close to the target genes; that transcribed regions are generally enriched for eQTLs; that eQTLs are more abundant in exons than introns; and that the peak density of eQTLs occurs at the TSS. However, we find that the intriguing TES peak is greatly reduced or absent in the Affymetrix and RNA-seq data. Instead our data suggest that the TES peak observed in the Illumina data is mainly due to exon-specific QTLs that affect 3′ untranslated regions, where most of the Illumina probes are positioned. Nonetheless, we do observe an overall enrichment of eQTLs in exons versus introns in all three data sets, consistent with an important role for exonic sequences in gene regulation

Inference of population splits and mixtures from genome-wide allele frequency data

Many aspects of the historical relationships between populations in a species are reflected in genetic data. Inferring these relationships from genetic data, however, remains a challenging task. In this paper, we present a statistical model for inferring the patterns of population splits and mixtures in multiple populations. In this model, the sampled populations in a species are related to their common ancestor through a graph of ancestral populations. Using genome-wide allele frequency data and a Gaussian approximation to genetic drift, we infer the structure of this graph. We applied this method to a set of 55 human populations and a set of 82 dog breeds and wild canids. In both species, we show that a simple bifurcating tree does not fully describe the data; in contrast, we infer many migration events. While some of the migration events that we find have been detected previously, many have not. For example, in the human data we infer that Cambodians trace approximately 16% of their ancestry to a population ancestral to other extant East Asian populations. In the dog data, we infer that both the boxer and basenji trace a considerable fraction of their ancestry (9% and 25%, respectively) to wolves subsequent to domestication, and that East Asian toy breeds (the Shih Tzu and the Pekingese) result from admixture between modern toy breeds and "ancient" Asian breeds. Software implementing the model described here, called TreeMix, is available at http://treemix.googlecode.comComment: 28 pages, 6 figures in main text. Attached supplement is 22 pages, 15 figures. This is an updated version of the preprint available at http://precedings.nature.com/documents/6956/version/

Localizing triplet periodicity in DNA and cDNA sequences

<p>Abstract</p> <p>Background</p> <p>The protein-coding regions (coding exons) of a DNA sequence exhibit a triplet periodicity (TP) due to fact that coding exons contain a series of three nucleotide codons that encode specific amino acid residues. Such periodicity is usually not observed in introns and intergenic regions. If a DNA sequence is divided into small segments and a Fourier Transform is applied on each segment, a strong peak at frequency 1/3 is typically observed in the Fourier spectrum of coding segments, but not in non-coding regions. This property has been used in identifying the locations of protein-coding genes in unannotated sequence. The method is fast and requires no training. However, the need to compute the Fourier Transform across a segment (window) of arbitrary size affects the accuracy with which one can localize TP boundaries. Here, we report a technique that provides higher-resolution identification of these boundaries, and use the technique to explore the biological correlates of TP regions in the genome of the model organism <it>C. elegans</it>.</p> <p>Results</p> <p>Using both simulated TP signals and the real <it>C. elegans </it>sequence F56F11 as an example, we demonstrate that, (1) Modified Wavelet Transform (MWT) can better define the boundary of TP region than the conventional Short Time Fourier Transform (STFT); (2) The scale parameter (a) of MWT determines the precision of TP boundary localization: bigger values of a give sharper TP boundaries but result in a lower signal to noise ratio; (3) RNA splicing sites have weaker TP signals than coding region; (4) TP signals in coding region can be destroyed or recovered by frame-shift mutations; (5) 6 bp periodicities in introns and intergenic region can generate false positive signals and it can be removed with 6 bp MWT.</p> <p>Conclusions</p> <p>MWT can provide more precise TP boundaries than STFT and the boundaries can be further refined by bigger scale MWT. Subtraction of 6 bp periodicity signals reduces the number of false positives. Experimentally-introduced frame-shift mutations help recover TP signal that have been lost by possible ancient frame-shifts. More importantly, TP signal has the potential to be used to detect the splice junctions in fully spliced mRNA sequence.</p

Cis and Trans Effects of Human Genomic Variants on Gene Expression

This work was funded by the Louis-Jeantet Foundation (http://www.jeantet.ch/), the European Research Council (Grant ID: 260927 http://erc.europa.eu/), the Swiss National Foundation (Grant ID: 130342 http://www.snf.ch), NCCR Frontiers In Genetics (http://www.frontiers-in-genetics.org), the UK Medical Research Council (http://www.mrc.ac.uk) and the Wellcome Trust (Grant ID: 092731).

Continued 26S proteasome dysfunction in mouse brain cortical neurons impairs autophagy and the Keap1-Nrf2 oxidative defence pathway

The ubiquitin–proteasome system (UPS) and macroautophagy (autophagy) are central to normal proteostasis and interdependent in that autophagy is known to compensate for the UPS to alleviate ensuing proteotoxic stress that impairs cell function. UPS and autophagy dysfunctions are believed to have a major role in the pathomechanisms of neurodegenerative disease. Here we show that continued 26S proteasome dysfunction in mouse brain cortical neurons causes paranuclear accumulation of fragmented dysfunctional mitochondria, associated with earlier recruitment of Parkin and lysine 48-linked ubiquitination of mitochondrial outer membrane (MOM) proteins, including Mitofusin-2. Early events also include phosphorylation of p62/SQSTM1 (p62) and increased optineurin, as well as autophagosomal LC3B and removal of some mitochondria, supporting the induction of selective autophagy. Inhibition of the degradation of ubiquitinated MOM proteins with continued 26S proteasome dysfunction at later stages may impede efficient mitophagy. However, continued 26S proteasome dysfunction also decreases the levels of essential autophagy proteins ATG9 and LC3B, which is characterised by decreases in their gene expression, ultimately leading to impaired autophagy. Intriguingly, serine 351 phosphorylation of p62 did not enhance its binding to Keap1 or stabilise the nuclear factor erythroid 2-related factor 2 (Nrf2) transcription factor in this neuronal context. Nrf2 protein levels were markedly decreased despite transcriptional activation of the Nrf2 gene. Our study reveals novel insights into the interplay between the UPS and autophagy in neurons and is imperative to understanding neurodegenerative disease where long-term proteasome inhibition has been implicated

Quality of medication use in primary care - mapping the problem, working to a solution: a systematic review of the literature

Background: The UK, USA and the World Health Organization have identified improved patient safety in healthcare as a priority. Medication error has been identified as one of the most frequent forms of medical error and is associated with significant medical harm. Errors are the result of the systems that produce them. In industrial settings, a range of systematic techniques have been designed to reduce error and waste. The first stage of these processes is to map out the whole system and its reliability at each stage. However, to date, studies of medication error and solutions have concentrated on individual parts of the whole system. In this paper we wished to conduct a systematic review of the literature, in order to map out the medication system with its associated errors and failures in quality, to assess the strength of the evidence and to use approaches from quality management to identify ways in which the system could be made safer. Methods: We mapped out the medicines management system in primary care in the UK. We conducted a systematic literature review in order to refine our map of the system and to establish the quality of the research and reliability of the system. Results: The map demonstrated that the proportion of errors in the management system for medicines in primary care is very high. Several stages of the process had error rates of 50% or more: repeat prescribing reviews, interface prescribing and communication and patient adherence. When including the efficacy of the medicine in the system, the available evidence suggested that only between 4% and 21% of patients achieved the optimum benefit from their medication. Whilst there were some limitations in the evidence base, including the error rate measurement and the sampling strategies employed, there was sufficient information to indicate the ways in which the system could be improved, using management approaches. The first step to improving the overall quality would be routine monitoring of adherence, clinical effectiveness and hospital admissions. Conclusion: By adopting the whole system approach from a management perspective we have found where failures in quality occur in medication use in primary care in the UK, and where weaknesses occur in the associated evidence base. Quality management approaches have allowed us to develop a coherent change and research agenda in order to tackle these, so far, fairly intractable problems

Genome-wide Polygenic Burden of Rare Deleterious Variants in Sudden Unexpected Death in Epilepsy

Peer reviewe

Scans for signatures of selection in Russian cattle breed genomes reveal new candidate genes for environmental adaptation and acclimation

Domestication and selective breeding has resulted in over 1000 extant cattle breeds. Many of these breeds do not excel in important traits but are adapted to local environments. These adaptations are a valuable source of genetic material for efforts to improve commercial breeds. As a step toward this goal we identified candidate regions to be under selection in genomes of nine Russian native cattle breeds adapted to survive in harsh climates. After comparing our data to other breeds of European and Asian origins we found known and novel candidate genes that could potentially be related to domestication, economically important traits and environmental adaptations in cattle. The Russian cattle breed genomes contained regions under putative selection with genes that may be related to adaptations to harsh environments (e.g., AQP5, RAD50, and RETREG1). We found genomic signatures of selective sweeps near key genes related to economically important traits, such as the milk production (e.g., DGAT1, ABCG2), growth (e.g., XKR4), and reproduction (e.g., CSF2). Our data point to candidate genes which should be included in future studies attempting to identify genes to improve the extant breeds and facilitate generation of commercial breeds that fit better into the environments of Russia and other countries with similar climates