Uniform algebras and approximation on manifolds

Let $\Omega \subset \mathbb{C}^n$ be a bounded domain and let $\mathcal{A} \subset \mathcal{C}(\bar{\Omega})$ be a uniform algebra generated by a set $F$ of holomorphic and pluriharmonic functions. Under natural assumptions on $\Omega$ and $F$ we show that the only obstruction to $\mathcal{A} = \mathcal{C}(\bar{\Omega})$ is that there is a holomorphic disk $D \subset \bar{\Omega}$ such that all functions in $F$ are holomorphic on $D$, i.e., the only obstruction is the obvious one. This generalizes work by A. Izzo. We also have a generalization of Wermer's maximality theorem to the (distinguished boundary of the) bidisk

Integrating sequence and array data to create an improved 1000 Genomes Project haplotype reference panel

A major use of the 1000 Genomes Project (1000GP) data is genotype imputation in genome-wide association studies (GWAS). Here we develop a method to estimate haplotypes from low-coverage sequencing data that can take advantage of single-nucleotide polymorphism (SNP) microarray genotypes on the same samples. First the SNP array data are phased to build a backbone (or 'scaffold') of haplotypes across each chromosome. We then phase the sequence data 'onto' this haplotype scaffold. This approach can take advantage of relatedness between sequenced and non-sequenced samples to improve accuracy. We use this method to create a new 1000GP haplotype reference set for use by the human genetic community. Using a set of validation genotypes at SNP and bi-allelic indels we show that these haplotypes have lower genotype discordance and improved imputation performance into downstream GWAS samples, especially at low-frequency variants. © 2014 Macmillan Publishers Limited. All rights reserved

Mendelian randomization supports bidirectional causality between telomere length and clonal hematopoiesis of indeterminate potential

Human genetic studies support an inverse causal relationship between leukocyte telomere length (LTL) and coronary artery disease (CAD), but directionally mixed effects for LTL and diverse malignancies. Clonal hematopoiesis of indeterminate potential (CHIP), characterized by expansion of hematopoietic cells bearing leukemogenic mutations, predisposes both hematologic malignancy and CAD. TERT (which encodes telomerase reverse transcriptase) is the most significantly associated germline locus for CHIP in genome-wide association studies. Here, we investigated the relationship between CHIP, LTL, and CAD in the Trans-Omics for Precision Medicine (TOPMed) program (n = 63,302) and UK Biobank (n = 47,080). Bidirectional Mendelian randomization studies were consistent with longer genetically imputed LTL increasing propensity to develop CHIP, but CHIP then, in turn, hastens to shorten measured LTL (mLTL). We also demonstrated evidence of modest mediation between CHIP and CAD by mLTL. Our data promote an understanding of potential causal relationships across CHIP and LTL toward prevention of CAD