Darboux Coordinates and Liouville-Arnold Integration in Loop Algebras

Darboux coordinates are constructed on rational coadjoint orbits of the positive frequency part \wt{\frak{g}}^+ of loop algebras. These are given by the values of the spectral parameters at the divisors corresponding to eigenvector line bundles over the associated spectral curves, defined within a given matrix representation. A Liouville generating function is obtained in completely separated form and shown, through the Liouville-Arnold integration method, to lead to the Abel map linearization of all Hamiltonian flows induced by the spectral invariants. Serre duality is used to define a natural symplectic structure on the space of line bundles of suitable degree over a permissible class of spectral curves, and this is shown to be equivalent to the Kostant-Kirillov symplectic structure on rational coadjoint orbits. The general construction is given for $\frak{g}=\frak{gl}(r)$ or $\frak{sl}(r)$, with reductions to orbits of subalgebras determined as invariant fixed point sets under involutive automorphisms. The case $\frak{g=sl}(2)$ is shown to reproduce the classical integration methods for finite dimensional systems defined on quadrics, as well as the quasi-periodic solutions of the cubically nonlinear Schr\"odinger equation. For $\frak{g=sl}(3)$, the method is applied to the computation of quasi-periodic solutions of the two component coupled nonlinear Schr\"odinger equation.Comment: 61 pg

European Union enlargement, post-accession migration and imaginative geographies of the ‘New Europe’: media discourses in Romania and the United Kingdom.

This paper is concerned with re-imaginings of ‘Europe’ following the accession to the European Union (EU) of former ‘Eastern European’ countries. In particular it explores media representations of post-EU accession migration from Romania to the United Kingdom in the UK and Romanian newspaper press. Todorova’s (1997) notion of Balkanism is deployed as a theoretical construct to facilitate the analysis of these representations as first, the continuation of long-standing and deeply embedded imaginings of the ‘East’ of Europe and, second, as a means of contesting these discourses. The paper explores the way in which the UK press construct Balkanist discourses about Romania and Romanian migrants, and then analyses how the Romanian press has contested such discourses. The paper argues that the idea of the ‘East’ remains important in constructing notions of ‘Europe’ within popular media geographies

Small BGK waves and nonlinear Landau damping

Consider 1D Vlasov-poisson system with a fixed ion background and periodic condition on the space variable. First, we show that for general homogeneous equilibria, within any small neighborhood in the Sobolev space W^{s,p} (p>1,s<1+(1/p)) of the steady distribution function, there exist nontrivial travelling wave solutions (BGK waves) with arbitrary minimal period and traveling speed. This implies that nonlinear Landau damping is not true in W^{s,p}(s<1+(1/p)) space for any homogeneous equilibria and any spatial period. Indeed, in W^{s,p} (s<1+(1/p)) neighborhood of any homogeneous state, the long time dynamics is very rich, including travelling BGK waves, unstable homogeneous states and their possible invariant manifolds. Second, it is shown that for homogeneous equilibria satisfying Penrose's linear stability condition, there exist no nontrivial travelling BGK waves and unstable homogeneous states in some W^{s,p} (p>1,s>1+(1/p)) neighborhood. Furthermore, when p=2,we prove that there exist no nontrivial invariant structures in the H^{s} (s>(3/2)) neighborhood of stable homogeneous states. These results suggest the long time dynamics in the W^{s,p} (s>1+(1/p)) and particularly, in the H^{s} (s>(3/2)) neighborhoods of a stable homogeneous state might be relatively simple. We also demonstrate that linear damping holds for initial perturbations in very rough spaces, for linearly stable homogeneous state. This suggests that the contrasting dynamics in W^{s,p} spaces with the critical power s=1+(1/p) is a trully nonlinear phenomena which can not be traced back to the linear level

Opening a Can of Worms: Leprosy Reactions and Complicit Soil-Transmitted Helminths

Immunogenetics and cellular immunology of bacterial infectious disease

Measurement of \Gamma_{ee}(J/\psi)*Br(J/\psi->e^+e^-) and \Gamma_{ee}(J/\psi)*Br(J/\psi->\mu^+\mu^-)

The products of the electron width of the J/\psi meson and the branching fraction of its decays to the lepton pairs were measured using data from the KEDR experiment at the VEPP-4M electron-positron collider. The results are \Gamma_{ee}(J/\psi)*Br(J/\psi->e^+e^-)=(0.3323\pm0.0064\pm0.0048) keV, \Gamma_{ee}(J/\psi)*Br(J/\psi->\mu^+\mu^-)=(0.3318\pm0.0052\pm0.0063) keV. Their combinations \Gamma_{ee}\times(\Gamma_{ee}+\Gamma_{\mu\mu})/\Gamma=(0.6641\pm0.0082\pm0.0100) keV, \Gamma_{ee}/\Gamma_{\mu\mu}=1.002\pm0.021\pm0.013 can be used to improve theaccuracy of the leptonic and full widths and test leptonic universality. Assuming e\mu universality and using the world average value of the lepton branching fraction, we also determine the leptonic \Gamma_{ll}=5.59\pm0.12 keV and total \Gamma=94.1\pm2.7 keV widths of the J/\psi meson.Comment: 7 pages, 6 figure

A Single-Dose Intranasal ChAd Vaccine Protects Upper and Lower Respiratory Tracts against SARS-CoV-2

The coronavirus disease 2019 pandemic has made deployment of an effective vaccine a global health priority. We evaluated the protective activity of a chimpanzee adenovirus-vectored vaccine encoding a prefusion stabilized spike protein (ChAd-SARS-CoV-2-S) in challenge studies with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and mice expressing the human angiotensin-converting enzyme 2 receptor. Intramuscular dosing of ChAd-SARS-CoV-2-S induces robust systemic humoral and cell-mediated immune responses and protects against lung infection, inflammation, and pathology but does not confer sterilizing immunity, as evidenced by detection of viral RNA and induction of anti-nucleoprotein antibodies after SARS-CoV-2 challenge. In contrast, a single intranasal dose of ChAd-SARS-CoV-2-S induces high levels of neutralizing antibodies, promotes systemic and mucosal immunoglobulin A (IgA) and T cell responses, and almost entirely prevents SARS-CoV-2 infection in both the upper and lower respiratory tracts. Intranasal administration of ChAd-SARS-CoV-2-S is a candidate for preventing SARS-CoV-2 infection and transmission and curtailing pandemic spread

Potential Genetic Overlap Between Insomnia and Sleep Symptoms in Major Depressive Disorder: A Polygenic Risk Score Analysis

Background: The prevalence of insomnia and hypersomnia in depressed individuals is substantially higher than that found in the general population. Unfortunately, these concurrent sleep problems can have profound effects on the disease course. Although the full biology of sleep remains to be elucidated, a recent genome-wide association (GWAS) of insomnia, and other sleep traits in over 1 million individuals was recently published and provides many promising hits for genetics of insomnia in a population-based sample. Methods: Using data from the largest available GWAS of insomnia and other sleep traits, we sought to test if sleep variable PRS scores derived from population-based studies predicted sleep variables in samples of depressed cases [Psychiatric Genomics Consortium - Major Depressive Disorder subjects (PGC MDD)]. A leave-one-out analysis was performed to determine the effects that each individual study had on our results. Results: The only significant finding was for insomnia, where p-value threshold, p = 0.05 was associated with insomnia in our PGC MDD sample (R2 = 1.75−3, p = 0.006). Conclusion: Our results reveal that <1% of variance is explained by the variants that cover the two significant p-value thresholds, which is in line with the fact that depression and insomnia are both polygenic disorders. To the best of our knowledge, this is the first study to investigate genetic overlap between the general population and a depression sample for insomnia, which has important treatment implications, such as leading to novel drug targets in future research efforts

Identification of common genetic risk variants for autism spectrum disorder

Autism spectrum disorder (ASD) is a highly heritable and heterogeneous group of neurodevelopmental phenotypes diagnosed in more than 1% of children. Common genetic variants contribute substantially to ASD susceptibility, but to date no individual variants have been robustly associated with ASD. With a marked sample-size increase from a unique Danish population resource, we report a genome-wide association meta-analysis of 18,381 individuals with ASD and 27,969 controls that identified five genome-wide-significant loci. Leveraging GWAS results from three phenotypes with significantly overlapping genetic architectures (schizophrenia, major depression, and educational attainment), we identified seven additional loci shared with other traits at equally strict significance levels. Dissecting the polygenic architecture, we found both quantitative and qualitative polygenic heterogeneity across ASD subtypes. These results highlight biological insights, particularly relating to neuronal function and corticogenesis, and establish that GWAS performed at scale will be much more productive in the near term in ASD.Peer reviewe

Track D Social Science, Human Rights and Political Science

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138414/1/jia218442.pd