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

Intermittent Fasting Confers Protection in CNS Autoimmunity by Altering the Gut Microbiota

Multiple sclerosis (MS) is more common in western countries with diet being a potential contributing factor. Here we show that intermittent fasting (IF) ameliorated clinical course and pathology of the MS model, experimental autoimmune encephalomyelitis (EAE). IF led to increased gut bacteria richness, enrichment of the Lactobacillaceae, Bacteroidaceae, and Prevotellaceae families and enhanced antioxidative microbial metabolic pathways. IF altered T cells in the gut with a reduction of IL-17 producing T cells and an increase in regulatory T cells. Fecal microbiome transplantation from mice on IF ameliorated EAE in immunized recipient mice on a normal diet, suggesting that IF effects are at least partially mediated by the gut flora. In a pilot clinical trial in MS patients, intermittent energy restriction altered blood adipokines and the gut flora resembling protective changes observed in mice. In conclusion, IF has potent immunomodulatory effects that are at least partially mediated by the gut microbiome. Intermittent fasting confers protection in the multiple sclerosis animal model through effects on the gut microbiota; similar changes to the gut microbiota were observed in relapsing multiple sclerosis patients undergoing intermittent energy restriction

Genomic variation landscape of the human gut microbiome

Whereas large-scale efforts have rapidly advanced the understanding and practical impact of human genomic variation, the practical impact of variation is largely unexplored in the human microbiome. We therefore developed a framework for metagenomic variation analysis and applied it to 252 faecal metagenomes of 207 individuals from Europe and North America. Using 7.4 billion reads aligned to 101 reference species, we detected 10.3 million single nucleotide polymorphisms (SNPs), 107,991 short insertions/deletions, and 1,051 structural variants. The average ratio of non-synonymous to synonymous polymorphism rates of 0.11 was more variable between gut microbial species than across human hosts. Subjects sampled at varying time intervals exhibited individuality and temporal stability of SNP variation patterns, despite considerable composition changes of their gut microbiota. This indicates that individual-specific strains are not easily replaced and that an individual might have a unique metagenomic genotype, which may be exploitable for personalized diet or drug intake