Thin Sequences and Their Role in HpH^p Theory, Model Spaces, and Uniform Algebras

In this paper we revisit some facts about thin interpolating sequences in the unit disc from three perspectives: uniform algebras, model spaces, and $H^p$ spaces. We extend the notion of asymptotic interpolation to $H^p$ spaces, for $1 \leq p \leq \infty$, providing several new ways to think about these sequences.Comment: v1: 21 pages; To appear in Rev. Mat. Iberoa

Thin Sequences and Their Role in Model Spaces and Douglas Algebras

We study thin interpolating sequences $\{\lambda_n\}$ and their relationship to interpolation in the Hardy space $H^2$ and the model spaces $K_\Theta = H^2 \ominus \Theta H^2$, where $\Theta$ is an inner function. Our results, phrased in terms of the functions that do the interpolation as well as Carleson measures, show that under the assumption that $\Theta(\lambda_n) \to 0$ the interpolation properties in $H^2$ are essentially the same as those in $K_\Theta$.Comment: v1: 16 pages. v2: 18 pages, corrections and modifications based on referee comments. To appear in J. Fourier Anal. App

Partial regularity and t-analytic sets for Banach function algebras

In this note we introduce the notion of t-analytic sets. Using this concept, we construct a class of closed prime ideals in Banach function algebras and discuss some problems related to Alling’s conjecture in H infinity. A description of all closed t-analytic sets for the disk-algebra is given. Moreover, we show that some of the assertions in [8] concerning the O-analyticity and S-regularity of certain Banach function algebras are not correct. We also determine the largest set on which a Douglas algebra is pointwise regular

Applications of micro-fluidic platforms integrating packed stationary phases

To design and fabricate novel centrifugal micro-fluidic platforms integrating packed stationary phases for solid-phase micro-extraction in a wide range of (bio)analytical applications. To design and fabricate novel micro-fluidic platforms integrating packed stationary phases capable of withstanding significant high pressures

Common DNA sequence variation influences 3-dimensional conformation of the human genome.

BACKGROUND:The 3-dimensional (3D) conformation of chromatin inside the nucleus is integral to a variety of nuclear processes including transcriptional regulation, DNA replication, and DNA damage repair. Aberrations in 3D chromatin conformation have been implicated in developmental abnormalities and cancer. Despite the importance of 3D chromatin conformation to cellular function and human health, little is known about how 3D chromatin conformation varies in the human population, or whether DNA sequence variation between individuals influences 3D chromatin conformation. RESULTS:To address these questions, we perform Hi-C on lymphoblastoid cell lines from 20 individuals. We identify thousands of regions across the genome where 3D chromatin conformation varies between individuals and find that this variation is often accompanied by variation in gene expression, histone modifications, and transcription factor binding. Moreover, we find that DNA sequence variation influences several features of 3D chromatin conformation including loop strength, contact insulation, contact directionality, and density of local cis contacts. We map hundreds of quantitative trait loci associated with 3D chromatin features and find evidence that some of these same variants are associated at modest levels with other molecular phenotypes as well as complex disease risk. CONCLUSION:Our results demonstrate that common DNA sequence variants can influence 3D chromatin conformation, pointing to a more pervasive role for 3D chromatin conformation in human phenotypic variation than previously recognized

A simple device for multiplex ELISA made from melt-extruded plastic microcapillary film

We present a simple device for multiplex quantitative enzyme-linked immunosorbant assays (ELISA) made from a novel melt-extruded microcapillary film (MCF) containing a parallel array of 200µm capillaries along its length. To make ELISA devices different protein antigens or antibodies were immobilised inside individual microcapillaries within long reels of MCF extruded from fluorinated ethylene propylene (FEP). Short pieces of coated film were cut and interfaced with a pipette, allowing sequential uptake of samples and detection solutions into all capillaries from a reagent well. As well as being simple to produce, these FEP MCF devices have excellent light transmittance allowing direct optical interrogation of the capillaries for simple signal quantification. Proof of concept experiments demonstrate both quantitative and multiplex assays in FEP MCF devices using a standard direct ELISA procedure and read using a flatbed scanner. This new multiplex immunoassay platform should find applications ranging from lab detection to point-of-care and field diagnostics

Health-related quality of life after myocardial infarction is associated with level of left ventricular ejection fraction

<p>Abstract</p> <p>Background</p> <p>The objective was to explore the relationship between left ventricular ejection fraction (LVEF) assessed during hospitalization for acute myocardial infarction (MI) and later health-related quality of life (HRQoL).</p> <p>Methods</p> <p>We used multivariable linear regression to assess the relationship between LVEF and HRQoL in 256 MI patients who responded to the Kansas City Cardiomyopathy Questionnaire (KCCQ), the EQ-5D Index, and the EuroQol Visual Analogue Scale (EQ-VAS) 2.5 years after the index MI.</p> <p>Results</p> <p>167 patients had normal LVEF (>50%), 56 intermediate (40%–50%), and 33 reduced (<40%). The mean (SD) KCCQ clinical summary scores were 85 (18), 75 (22), and 68 (21) (<it>p </it><0.001) in the three groups, respectively. The corresponding EQ-5D Index scores were 0.83 (0.18), 0.72 (0.27), and 0.76 (0.14) (<it>p </it>= 0.005) and EQ-VAS scores were 72 (18), 65 (21), and 57 (20) (<it>p </it>= 0.001). In multivariable linear regression analysis age ≥ 70 years, known chronic obstructive pulmonary disease (COPD), subsequent MI, intermediate LVEF, and reduced LVEF were independent determinants for reduced KCCQ clinical summary score. Female sex, medication for angina pectoris at discharge, and intermediate LVEF were independent determinants for reduced EQ-5D Index score. Age ≥ 70 years, COPD, and reduced LVEF were associated with reduced EQ-VAS score.</p> <p>Conclusion</p> <p>LVEF measured during hospitalization for MI was a determinant for HRQoL 2.5 years later.</p

Genome-wide compendium and functional assessment of in vivo heart enhancers

Whole-genome sequencing is identifying growing numbers of non-coding variants in human disease studies, but the lack of accurate functional annotations prevents their interpretation. We describe the genome-wide landscape of distant-acting enhancers active in the developing and adult human heart, an organ whose impairment is a predominant cause of mortality and morbidity. Using integrative analysis of >35 epigenomic data sets from mouse and human pre- and postnatal hearts we created a comprehensive reference of >80,000 putative human heart enhancers. To illustrate the importance of enhancers in the regulation of genes involved in heart disease, we deleted the mouse orthologs of two human enhancers near cardiac myosin genes. In both cases, we observe in vivo expression changes and cardiac phenotypes consistent with human heart disease. Our study provides a comprehensive catalogue of human heart enhancers for use in clinical whole-genome sequencing studies and highlights the importance of enhancers for cardiac function