Distinction inside L-packets of SL(n)

If $E/F$ is a quadratic extension $p$-adic fields, we first prove that the $\mathrm{SL}_n(F)$-distinguished representations inside a distinguished unitary L-packet of $\mathrm{SL}_n(E)$ are precisely those admitting a degenerate Whittaker model with respect to a degenerate character of $N(E)/N(F)$. Then we establish a global analogue of this result. For this, let $E/F$ be a quadratic extension of number fields and let $\pi$ be an $\mathrm{SL}_n(\mathbb{A}_F)$-distinguished square integrable automorphic representation of $\mathrm{SL}_n(\mathbb{A}_E)$. Let $(\sigma,d)$ be the unique pair associated to $\pi$, where $\sigma$ is a cuspidal representation of $\mathrm{GL}_r(\mathbb{A}_E)$ with $n=dr$. Using an unfolding argument, we prove that an element of the L-packet of $\pi$ is distinguished with respect to $\mathrm{SL}_n(\mathbb{A}_F)$ if and only if it has a degenerate Whittaker model for a degenerate character $\psi$ of type $r^d:=(r,\dots,r)$ of $N_n(\mathbb{A}_E)$ which is trivial on $N_n(E+\mathbb{A}_F)$, where $N_n$ is the group of unipotent upper triangular matrices of $\mathrm{SL}_n$. As a first application, under the assumptions that $E/F$ splits at infinity and $r$ is odd, we establish a local-global principle for $\mathrm{SL}_n(\mathbb{A}_F)$-distinction inside the L-packet of $\pi$. As a second application we construct examples of distinguished cuspidal automorphic representations $\pi$ of $\mathrm{SL}_n(\mathbb{A}_E)$ such that the period integral vanishes on some canonical copy of $\pi$, and of everywhere locally distinguished representations of $\mathrm{SL}_n(\mathbb{A}_E)$ such that their L-packets do not contain any distinguished representation.Comment: Merged with withdrawn arXiv:1906.11560. We simplified some arguments and removed an unnecessary Grunwald-Wang assumptio

Semiclassical Mechanics of the Wigner 6j-Symbol

The semiclassical mechanics of the Wigner 6j-symbol is examined from the standpoint of WKB theory for multidimensional, integrable systems, to explore the geometrical issues surrounding the Ponzano-Regge formula. The relations among the methods of Roberts and others for deriving the Ponzano-Regge formula are discussed, and a new approach, based on the recoupling of four angular momenta, is presented. A generalization of the Yutsis-type of spin network is developed for this purpose. Special attention is devoted to symplectic reduction, the reduced phase space of the 6j-symbol (the 2-sphere of Kapovich and Millson), and the reduction of Poisson bracket expressions for semiclassical amplitudes. General principles for the semiclassical study of arbitrary spin networks are laid down; some of these were used in our recent derivation of the asymptotic formula for the Wigner 9j-symbol.Comment: 64 pages, 50 figure

Effector and Naturally Occurring Regulatory T Cells Display No Abnormalities in Activation Induced Cell Death in NOD Mice

BACKGROUND: Disturbed peripheral negative regulation might contribute to evolution of autoimmune insulitis in type 1 diabetes. This study evaluates the sensitivity of naïve/effector (Teff) and regulatory T cells (Treg) to activation-induced cell death mediated by Fas cross-linking in NOD and wild-type mice. PRINCIPAL FINDINGS: Both effector (CD25(-), FoxP3(-)) and suppressor (CD25(+), FoxP3(+)) CD4(+) T cells are negatively regulated by Fas cross-linking in mixed splenocyte populations of NOD, wild type mice and FoxP3-GFP trangeneess. Proliferation rates and sensitivity to Fas cross-linking are dissociated in Treg cells: fast cycling induced by IL-2 and CD3/CD28 stimulation improve Treg resistance to Fas-ligand (FasL) in both strains. The effector and suppressor CD4(+) subsets display balanced sensitivity to negative regulation under baseline conditions, IL-2 and CD3/CD28 stimulation, indicating that stimulation does not perturb immune homeostasis in NOD mice. Effective autocrine apoptosis of diabetogenic cells was evident from delayed onset and reduced incidence of adoptive disease transfer into NOD.SCID by CD4(+)CD25(-) T cells decorated with FasL protein. Treg resistant to Fas-mediated apoptosis retain suppressive activity in vitro. The only detectable differential response was reduced Teff proliferation and upregulation of CD25 following CD3-activation in NOD mice. CONCLUSION: These data document negative regulation of effector and suppressor cells by Fas cross-linking and dissociation between sensitivity to apoptosis and proliferation in stimulated Treg. There is no evidence that perturbed AICD in NOD mice initiates or promotes autoimmune insulitis

The evolving SARS-CoV-2 epidemic in Africa: Insights from rapidly expanding genomic surveillance.

Investment in severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) sequencing in Africa over the past year has led to a major increase in the number of sequences that have been generated and used to track the pandemic on the continent, a number that now exceeds 100,000 genomes. Our results show an increase in the number of African countries that are able to sequence domestically and highlight that local sequencing enables faster turnaround times and more-regular routine surveillance. Despite limitations of low testing proportions, findings from this genomic surveillance study underscore the heterogeneous nature of the pandemic and illuminate the distinct dispersal dynamics of variants of concern-particularly Alpha, Beta, Delta, and Omicron-on the continent. Sustained investment for diagnostics and genomic surveillance in Africa is needed as the virus continues to evolve while the continent faces many emerging and reemerging infectious disease threats. These investments are crucial for pandemic preparedness and response and will serve the health of the continent well into the 21st century

Abstracts from the 20th International Symposium on Signal Transduction at the Blood-Brain Barriers

https://deepblue.lib.umich.edu/bitstream/2027.42/138963/1/12987_2017_Article_71.pd

The evolving SARS-CoV-2 epidemic in Africa: Insights from rapidly expanding genomic surveillance

INTRODUCTION Investment in Africa over the past year with regard to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) sequencing has led to a massive increase in the number of sequences, which, to date, exceeds 100,000 sequences generated to track the pandemic on the continent. These sequences have profoundly affected how public health officials in Africa have navigated the COVID-19 pandemic. RATIONALE We demonstrate how the first 100,000 SARS-CoV-2 sequences from Africa have helped monitor the epidemic on the continent, how genomic surveillance expanded over the course of the pandemic, and how we adapted our sequencing methods to deal with an evolving virus. Finally, we also examine how viral lineages have spread across the continent in a phylogeographic framework to gain insights into the underlying temporal and spatial transmission dynamics for several variants of concern (VOCs). RESULTS Our results indicate that the number of countries in Africa that can sequence the virus within their own borders is growing and that this is coupled with a shorter turnaround time from the time of sampling to sequence submission. Ongoing evolution necessitated the continual updating of primer sets, and, as a result, eight primer sets were designed in tandem with viral evolution and used to ensure effective sequencing of the virus. The pandemic unfolded through multiple waves of infection that were each driven by distinct genetic lineages, with B.1-like ancestral strains associated with the first pandemic wave of infections in 2020. Successive waves on the continent were fueled by different VOCs, with Alpha and Beta cocirculating in distinct spatial patterns during the second wave and Delta and Omicron affecting the whole continent during the third and fourth waves, respectively. Phylogeographic reconstruction points toward distinct differences in viral importation and exportation patterns associated with the Alpha, Beta, Delta, and Omicron variants and subvariants, when considering both Africa versus the rest of the world and viral dissemination within the continent. Our epidemiological and phylogenetic inferences therefore underscore the heterogeneous nature of the pandemic on the continent and highlight key insights and challenges, for instance, recognizing the limitations of low testing proportions. We also highlight the early warning capacity that genomic surveillance in Africa has had for the rest of the world with the detection of new lineages and variants, the most recent being the characterization of various Omicron subvariants. CONCLUSION Sustained investment for diagnostics and genomic surveillance in Africa is needed as the virus continues to evolve. This is important not only to help combat SARS-CoV-2 on the continent but also because it can be used as a platform to help address the many emerging and reemerging infectious disease threats in Africa. In particular, capacity building for local sequencing within countries or within the continent should be prioritized because this is generally associated with shorter turnaround times, providing the most benefit to local public health authorities tasked with pandemic response and mitigation and allowing for the fastest reaction to localized outbreaks. These investments are crucial for pandemic preparedness and response and will serve the health of the continent well into the 21st century