Compact convex sets with prescribed facial dimensions

While faces of a polytope form a well structured lattice, in which faces of each possible dimension are present, this is not true for general compact convex sets. We address the question of what dimensional patterns are possible for the faces of general closed convex sets. We show that for any finite sequence of positive integers there exist compact convex sets which only have extreme points and faces with dimensions from this prescribed sequence. We also discuss another approach to dimensionality, considering the dimension of the union of all faces of the same dimension. We show that the questions arising from this approach are highly nontrivial and give examples of convex sets for which the sets of extreme points have fractal dimension

Compact convex sets with prescribed facial dimensions

While faces of a polytope form a well structured lattice, in which faces of each possible dimension are present, this is not true for general compact convex sets. We address the question of what dimensional patterns are possible for the faces of general closed convex sets. We show that for any finite sequence of positive integers there exist compact convex sets which only have extreme points and faces with dimensions from this prescribed sequence. We also discuss another approach to dimensionality, considering the dimension of the union of all faces of the same dimension. We show that the questions arising from this approach are highly nontrivial and give examples of convex sets for which the sets of extreme points have fractal dimension

Angular momentum transport and turbulence in laboratory models of Keplerian flows

We present angular momentum transport (torque) measurements in two recent experimental studies of the turbulent flow between independently rotating cylinders. In addition to these studies, we reanalyze prior torque measurements to expand the range of control parameters for the experimental Taylor-Couette flows. We find that the torque may be described as a product of functions that depend only on the Reynolds number, which describes the turbulent driving intensity, and the rotation number, which characterizes the effects of global rotation. For a given Reynolds number, the global angular momentum transport for Keplerian-like flow profiles is approximately 14% of the maximum achievable transport rate. We estimate that this level of transport would produce an accretion rate of $\dot{M}/\dot{M_0} \sim 10^{-3}$ in astrophysical disks. We argue that this level of transport from hydrodynamics alone could be significant.Comment: 17 pages, 7 figures, 2 tables, submitted to Astronomy & Astrophysics (2011

DNA Methylation Analysis of Chromosome 21 Gene Promoters at Single Base Pair and Single Allele Resolution

Differential DNA methylation is an essential epigenetic signal for gene regulation, development, and disease processes. We mapped DNA methylation patterns of 190 gene promoter regions on chromosome 21 using bisulfite conversion and subclone sequencing in five human cell types. A total of 28,626 subclones were sequenced at high accuracy using (long-read) Sanger sequencing resulting in the measurement of the DNA methylation state of 580427 CpG sites. Our results show that average DNA methylation levels are distributed bimodally with enrichment of highly methylated and unmethylated sequences, both for amplicons and individual subclones, which represent single alleles from individual cells. Within CpG-rich sequences, DNA methylation was found to be anti-correlated with CpG dinucleotide density and GC content, and methylated CpGs are more likely to be flanked by AT-rich sequences. We observed over-representation of CpG sites in distances of 9, 18, and 27 bps in highly methylated amplicons. However, DNA sequence alone is not sufficient to predict an amplicon's DNA methylation status, since 43% of all amplicons are differentially methylated between the cell types studied here. DNA methylation in promoter regions is strongly correlated with the absence of gene expression and low levels of activating epigenetic marks like H3K4 methylation and H3K9 and K14 acetylation. Utilizing the single base pair and single allele resolution of our data, we found that i) amplicons from different parts of a CpG island frequently differ in their DNA methylation level, ii) methylation levels of individual cells in one tissue are very similar, and iii) methylation patterns follow a relaxed site-specific distribution. Furthermore, iv) we identified three cases of allele-specific DNA methylation on chromosome 21. Our data shed new light on the nature of methylation patterns in human cells, the sequence dependence of DNA methylation, and its function as epigenetic signal in gene regulation. Further, we illustrate genotype–epigenotype interactions by showing novel examples of allele-specific methylation

Impact of gene variants on sex-specific regulation of human Scavenger receptor class B type 1 (SR-BI) expression in liver and association with lipid levels in a population-based study

<p>Abstract</p> <p>Background</p> <p>Several studies have noted that genetic variants of <it>SCARB1</it>, a lipoprotein receptor involved in reverse cholesterol transport, are associated with serum lipid levels in a sex-dependent fashion. However, the mechanism underlying this gene by sex interaction has not been explored.</p> <p>Methods</p> <p>We utilized both epidemiological and molecular methods to study how estrogen and gene variants interact to influence <it>SCARB1 </it>expression and lipid levels. Interaction between 35 <it>SCARB1 </it>haplotype-tagged polymorphisms and endogenous estradiol levels was assessed in 498 postmenopausal Caucasian women from the population-based Rancho Bernardo Study. We further examined associated variants with overall and <it>SCARB1 </it>splice variant (SR-BI and SR-BII) expression in 91 human liver tissues using quantitative real-time PCR.</p> <p>Results</p> <p>Several variants on a haplotype block spanning intron 11 to intron 12 of <it>SCARB1 </it>showed significant gene by estradiol interaction affecting serum lipid levels, the strongest for rs838895 with HDL-cholesterol (p = 9.2 × 10^-4) and triglycerides (p = 1.3 × 10^-3) and the triglyceride:HDL cholesterol ratio (p = 2.7 × 10^-4). These same variants were associated with expression of the SR-BI isoform in a sex-specific fashion, with the strongest association found among liver tissue from 52 young women <45 years old (p = 0.002).</p> <p>Conclusions</p> <p>Estrogen and <it>SCARB1 </it>genotype may act synergistically to regulate expression of <it>SCARB1 </it>isoforms and impact serum levels of HDL cholesterol and triglycerides. This work highlights the importance of considering sex-dependent effects of gene variants on serum lipid levels.</p

Search for gravitational-lensing signatures in the full third observing run of the LIGO-Virgo network

Gravitational lensing by massive objects along the line of sight to the source causes distortions of gravitational wave-signals; such distortions may reveal information about fundamental physics, cosmology and astrophysics. In this work, we have extended the search for lensing signatures to all binary black hole events from the third observing run of the LIGO--Virgo network. We search for repeated signals from strong lensing by 1) performing targeted searches for subthreshold signals, 2) calculating the degree of overlap amongst the intrinsic parameters and sky location of pairs of signals, 3) comparing the similarities of the spectrograms amongst pairs of signals, and 4) performing dual-signal Bayesian analysis that takes into account selection effects and astrophysical knowledge. We also search for distortions to the gravitational waveform caused by 1) frequency-independent phase shifts in strongly lensed images, and 2) frequency-dependent modulation of the amplitude and phase due to point masses. None of these searches yields significant evidence for lensing. Finally, we use the non-detection of gravitational-wave lensing to constrain the lensing rate based on the latest merger-rate estimates and the fraction of dark matter composed of compact objects

Search for eccentric black hole coalescences during the third observing run of LIGO and Virgo

Despite the growing number of confident binary black hole coalescences observed through gravitational waves so far, the astrophysical origin of these binaries remains uncertain. Orbital eccentricity is one of the clearest tracers of binary formation channels. Identifying binary eccentricity, however, remains challenging due to the limited availability of gravitational waveforms that include effects of eccentricity. Here, we present observational results for a waveform-independent search sensitive to eccentric black hole coalescences, covering the third observing run (O3) of the LIGO and Virgo detectors. We identified no new high-significance candidates beyond those that were already identified with searches focusing on quasi-circular binaries. We determine the sensitivity of our search to high-mass (total mass M&gt;70 M⊙) binaries covering eccentricities up to 0.3 at 15 Hz orbital frequency, and use this to compare model predictions to search results. Assuming all detections are indeed quasi-circular, for our fiducial population model, we place an upper limit for the merger rate density of high-mass binaries with eccentricities 0&lt;e≤0.3 at 0.33 Gpc−3 yr−1 at 90\% confidence level