Algebraic Torsion in Contact Manifolds

We extract a nonnegative integer-valued invariant, which we call the "order of algebraic torsion", from the Symplectic Field Theory of a closed contact manifold, and show that its finiteness gives obstructions to the existence of symplectic fillings and exact symplectic cobordisms. A contact manifold has algebraic torsion of order zero if and only if it is algebraically overtwisted (i.e. has trivial contact homology), and any contact 3-manifold with positive Giroux torsion has algebraic torsion of order one (though the converse is not true). We also construct examples for each nonnegative k of contact 3-manifolds that have algebraic torsion of order k but not k - 1, and derive consequences for contact surgeries on such manifolds. The appendix by Michael Hutchings gives an alternative proof of our cobordism obstructions in dimension three using a refinement of the contact invariant in Embedded Contact Homology.Comment: 53 pages, 4 figures, with an appendix by Michael Hutchings; v.3 is a final update to agree with the published paper, and also corrects a minor error that appeared in the published version of the appendi

Algebraic correction methods for computational assessment of clone overlaps in DNA fingerprint mapping

<p>Abstract</p> <p>Background</p> <p>The Sulston score is a well-established, though approximate metric for probabilistically evaluating postulated clone overlaps in DNA fingerprint mapping. It is known to systematically over-predict match probabilities by various orders of magnitude, depending upon project-specific parameters. Although the exact probability distribution is also available for the comparison problem, it is rather difficult to compute and cannot be used directly in most cases. A methodology providing both improved accuracy and computational economy is required.</p> <p>Results</p> <p>We propose a straightforward algebraic correction procedure, which takes the Sulston score as a provisional value and applies a power-law equation to obtain an improved result. Numerical comparisons indicate dramatically increased accuracy over the range of parameters typical of traditional agarose fingerprint mapping. Issues with extrapolating the method into parameter ranges characteristic of newer capillary electrophoresis-based projects are also discussed.</p> <p>Conclusion</p> <p>Although only marginally more expensive to compute than the raw Sulston score, the correction provides a vastly improved probabilistic description of hypothesized clone overlaps. This will clearly be important in overlap assessment and perhaps for other tasks as well, for example in using the ranking of overlap probabilities to assist in clone ordering.</p

New obstructions to symplectic embeddings

In this paper we establish new restrictions on symplectic embeddings of certain convex domains into symplectic vector spaces. These restrictions are stronger than those implied by the Ekeland-Hofer capacities. By refining an embedding technique due to Guth, we also show that they are sharp.Comment: 80 pages, 3 figures, v2: improved exposition and minor corrections, v3: Final version, expanded and improved exposition and minor corrections. The final publication is available at link.springer.co

GenomeVIP: A cloud platform for genomic variant discovery and interpretation

Identifying genomic variants is a fundamental first step toward the understanding of the role of inherited and acquired variation in disease. The accelerating growth in the corpus of sequencing data that underpins such analysis is making the data-download bottleneck more evident, placing substantial burdens on the research community to keep pace. As a result, the search for alternative approaches to the traditional “download and analyze” paradigm on local computing resources has led to a rapidly growing demand for cloud-computing solutions for genomics analysis. Here, we introduce the Genome Variant Investigation Platform (GenomeVIP), an open-source framework for performing genomics variant discovery and annotation using cloud- or local high-performance computing infrastructure. GenomeVIP orchestrates the analysis of whole-genome and exome sequence data using a set of robust and popular task-specific tools, including VarScan, GATK, Pindel, BreakDancer, Strelka, and Genome STRiP, through a web interface. GenomeVIP has been used for genomic analysis in large-data projects such as the TCGA PanCanAtlas and in other projects, such as the ICGC Pilots, CPTAC, ICGC-TCGA DREAM Challenges, and the 1000 Genomes SV Project. Here, we demonstrate GenomeVIP's ability to provide high-confidence annotated somatic, germline, and de novo variants of potential biological significance using publicly available data sets.</jats:p

Numerical and Experimental Investigation of Circulation in Short Cylinders

In preparation for an experimental study of magnetorotational instability (MRI) in liquid metal, we explore Couette flows having height comparable to the gap between cylinders, centrifugally stable rotation, and high Reynolds number. Experiments in water are compared with numerical simulations. Simulations show that endcaps corotating with the outer cylinder drive a strong poloidal circulation that redistributes angular momentum. Predicted azimuthal flow profiles agree well with experimental measurements. Spin-down times scale with Reynolds number as expected for laminar Ekman circulation; extrapolation from two-dimensional simulations at $Re\le 3200$ agrees remarkably well with experiment at $Re\sim 10^6$. This suggests that turbulence does not dominate the effective viscosity. Further detailed numerical studies reveal a strong radially inward flow near both endcaps. After turning vertically along the inner cylinder, these flows converge at the midplane and depart the boundary in a radial jet. To minimize this circulation in the MRI experiment, endcaps consisting of multiple, differentially rotating rings are proposed. Simulations predict that an adequate approximation to the ideal Couette profile can be obtained with a few rings