Multiplicity, Invariants and Tensor Product Decomposition of Tame Representations of U(\infty)

The structure of r-fold tensor products of irreducible tame representations of the inductive limit U(\infty) of unitary groups U(n) are are described, versions of contragredient representations and invariants are realized on Bargmann-Segal-Fock spaces.Comment: 48 pages, LaTeX file, to appear in J. Math. Phy

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

Iron Age and Anglo-Saxon genomes from East England reveal British migration history

British population history has been shaped by a series of immigrations, including the early Anglo-Saxon migrations after 400 CE. It remains an open question how these events affected the genetic composition of the current British population. Here, we present whole-genome sequences from 10 individuals excavated close to Cambridge in the East of England, ranging from the late Iron Age to the middle Anglo-Saxon period. By analysing shared rare variants with hundreds of modern samples from Britain and Europe, we estimate that on average the contemporary East English population derives 38% of its ancestry from Anglo-Saxon migrations. We gain further insight with a new method, rarecoal, which infers population history and identifies fine-scale genetic ancestry from rare variants. Using rarecoal we find that the Anglo-Saxon samples are closely related to modern Dutch and Danish populations, while the Iron Age samples share ancestors with multiple Northern European populations including Britain

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

Advances in nuclear instrumentation for safeguards

This paper describes detectors, instrumentation, and analytical methods under development to address the above issues. The authors will describe work underway on room-temperature semiconductors including attempts to model the response of these detectors to improve spectrum analysis procedures and detector design. Computerized tomography is used in many medical and industrial applications; they are developing both gamma-ray and neutron tomography for improved measurements of waste and direct-use materials. Modern electronics and scintillation detectors should permit the development of fast neutron coincidence detectors with dramatically improved signal-to-noise ratios. For active measurements, they are studying several improved neutron sources, including a high-fluence, plasma-based, d-t generator. New analysis tools from information theory may permit one to better combine data from different measurement systems. This paper attempts to briefly describe a range of new sensors, electronics, and data analysis methods under study at Los Alamos and other laboratories to promote discussion of promising technology that they may bring to bear on these important global issues

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

COVID-19 vaccination uptake in people with epilepsy in Wales

Purpose People with epilepsy (PWE) are at increased risk of severe COVID-19. Assessing COVID-19 vaccine uptake is therefore important. We compared COVID-19 vaccination uptake for PWE in Wales with a matched control cohort. Methods We performed a retrospective, population, cohort study using linked, anonymised, Welsh electronic health records within the Secure Anonymised Information Linkage (SAIL) Databank (Welsh population=3.1 million).We identified PWE in Wales between 1st March 2020 and 31st December 2021 and created a control cohort using exact 5:1 matching (sex, age and socioeconomic status). We recorded 1st, 2nd and booster COVID-19 vaccinations. Results There were 25,404 adults with epilepsy (127,020 controls). 23,454 (92.3%) had a first vaccination, 22,826 (89.9%) a second, and 17,797 (70.1%) a booster. Comparative figures for controls were: 112,334 (87.8%), 109,057 (85.2%) and 79,980 (62.4%).PWE had higher vaccination rates in all age, sex and socioeconomic subgroups apart from booster uptake in older subgroups. Vaccination rates were higher in older subgroups, women and less deprived areas for both cohorts. People with intellectual disability and epilepsy had higher vaccination rates when compared with controls with intellectual disability. Conclusions COVID-19 vaccination uptake for PWE in Wales was higher than that for a matched control group