Polynomial Identities, Indices, and Duality for the N=1 Superconformal Model SM(2,4\nu)

We prove polynomial identities for the N=1 superconformal model SM(2,4\nu) which generalize and extend the known Fermi/Bose character identities. Our proof uses the q-trinomial coefficients of Andrews and Baxter on the bosonic side and a recently introduced very general method of producing recursion relations for q-series on the fermionic side. We use these polynomials to demonstrate a dual relation under q \rightarrow q^{-1} between SM(2,4\nu) and M(2\nu-1,4\nu). We also introduce a generalization of the Witten index which is expressible in terms of the Rogers false theta functions.Comment: 41 pages, harvmac, no figures; new identities, proofs and comments added; misprints eliminate

LSST Science Book, Version 2.0

A survey that can cover the sky in optical bands over wide fields to faint magnitudes with a fast cadence will enable many of the exciting science opportunities of the next decade. The Large Synoptic Survey Telescope (LSST) will have an effective aperture of 6.7 meters and an imaging camera with field of view of 9.6 deg^2, and will be devoted to a ten-year imaging survey over 20,000 deg^2 south of +15 deg. Each pointing will be imaged 2000 times with fifteen second exposures in six broad bands from 0.35 to 1.1 microns, to a total point-source depth of r~27.5. The LSST Science Book describes the basic parameters of the LSST hardware, software, and observing plans. The book discusses educational and outreach opportunities, then goes on to describe a broad range of science that LSST will revolutionize: mapping the inner and outer Solar System, stellar populations in the Milky Way and nearby galaxies, the structure of the Milky Way disk and halo and other objects in the Local Volume, transient and variable objects both at low and high redshift, and the properties of normal and active galaxies at low and high redshift. It then turns to far-field cosmological topics, exploring properties of supernovae to z~1, strong and weak lensing, the large-scale distribution of galaxies and baryon oscillations, and how these different probes may be combined to constrain cosmological models and the physics of dark energy.Comment: 596 pages. Also available at full resolution at http://www.lsst.org/lsst/sciboo

Genomic organisation analysis of novel immunoglobulin-like transcripts in Atlantic salmon (Salmo salar) reveals a tightly clustered and multigene family

Copyright 2011 Elsevier B.V., All rights reserved.Peer reviewedPublisher PD

Evolutionary Convergence on Highly-Conserved 3′ Intron Structures in Intron-Poor Eukaryotes and Insights into the Ancestral Eukaryotic Genome

The presence of spliceosomal introns in eukaryotes raises a range of questions about genomic evolution. Along with the fundamental mysteries of introns' initial proliferation and persistence, the evolutionary forces acting on intron sequences remain largely mysterious. Intron number varies across species from a few introns per genome to several introns per gene, and the elements of intron sequences directly implicated in splicing vary from degenerate to strict consensus motifs. We report a 50-species comparative genomic study of intron sequences across most eukaryotic groups. We find two broad and striking patterns. First, we find that some highly intron-poor lineages have undergone evolutionary convergence to strong 3′ consensus intron structures. This finding holds for both branch point sequence and distance between the branch point and the 3′ splice site. Interestingly, this difference appears to exist within the genomes of green alga of the genus Ostreococcus, which exhibit highly constrained intron sequences through most of the intron-poor genome, but not in one much more intron-dense genomic region. Second, we find evidence that ancestral genomes contained highly variable branch point sequences, similar to more complex modern intron-rich eukaryotic lineages. In addition, ancestral structures are likely to have included polyT tails similar to those in metazoans and plants, which we found in a variety of protist lineages. Intriguingly, intron structure evolution appears to be quite different across lineages experiencing different types of genome reduction: whereas lineages with very few introns tend towards highly regular intronic sequences, lineages with very short introns tend towards highly degenerate sequences. Together, these results attest to the complex nature of ancestral eukaryotic splicing, the qualitatively different evolutionary forces acting on intron structures across modern lineages, and the impressive evolutionary malleability of eukaryotic gene structures

Expanded encyclopaedias of DNA elements in the human and mouse genomes

All data are available on the ENCODE data portal: www.encodeproject. org. All code is available on GitHub from the links provided in the methods section. Code related to the Registry of cCREs can be found at https:// github.com/weng-lab/ENCODE-cCREs. Code related to SCREEN can be found at https://github.com/weng-lab/SCREEN.© The Author(s) 2020. The human and mouse genomes contain instructions that specify RNAs and proteins and govern the timing, magnitude, and cellular context of their production. To better delineate these elements, phase III of the Encyclopedia of DNA Elements (ENCODE) Project has expanded analysis of the cell and tissue repertoires of RNA transcription, chromatin structure and modification, DNA methylation, chromatin looping, and occupancy by transcription factors and RNA-binding proteins. Here we summarize these efforts, which have produced 5,992 new experimental datasets, including systematic determinations across mouse fetal development. All data are available through the ENCODE data portal (https://www.encodeproject.org), including phase II ENCODE1 and Roadmap Epigenomics2 data. We have developed a registry of 926,535 human and 339,815 mouse candidate cis-regulatory elements, covering 7.9 and 3.4% of their respective genomes, by integrating selected datatypes associated with gene regulation, and constructed a web-based server (SCREEN; http://screen.encodeproject.org) to provide flexible, user-defined access to this resource. Collectively, the ENCODE data and registry provide an expansive resource for the scientific community to build a better understanding of the organization and function of the human and mouse genomes.This work was supported by grants from the NIH under U01HG007019, U01HG007033, U01HG007036, U01HG007037, U41HG006992, U41HG006993, U41HG006994, U41HG006995, U41HG006996, U41HG006997, U41HG006998, U41HG006999, U41HG007000, U41HG007001, U41HG007002, U41HG007003, U54HG006991, U54HG006997, U54HG006998, U54HG007004, U54HG007005, U54HG007010 and UM1HG009442

Active Composite Membrane Mirrors

Abstract Fabrication of composite sandwich panel mirrors has advanced sufficiently in surface accuracy and thermal stability to consider a thin composite membrane supported by rigid active supports for a large space mirror. We are carrying out a technology development with a 0.5-meter diameter, 0.5-mm thick composite membrane on a 36-actuator support. Measurements will be made of the controlled figure at ambient and low temperatures to determine the figure accuracy and stability and the validity of the mathematical performance analysis