Essential Norms of Weighted Composition Operators Between Bloch Type Spaces

We compute the essential norm of a weighted composition operator uCϕ acting from an analytic Lipschitz space into a weighted Bloch-type space on the disk, and give estimates for the essential norm of uCϕ when it maps the standard Bloch space into a weighted Bloch-type space. We also study boundedness and compactness of weighted composition operators on analytic Lipschitz spaces from a geometric perspective

Isolation and component structure in spaces of composition operators

We establish a condition that guarantees isolation in the space of composition operators acting between H p (B N ) and H q (B N ), for 0 \u3c p ≤ ∞, 0 \u3c q \u3c ∞, and N ≥ 1. This result will allow us, in certain cases where 0 \u3c q \u3c p ≤ ∞, completely to characterize the component structure of this space of operators

The association of genetic variants of type 2 diabetes with kidney function

Type 2 diabetes is highly prevalent and is the major cause of progressive chronic kidney disease in American Indians. Genome wide association studies identified several loci associated with diabetes but their impact on susceptibility to diabetic complications is unknown. To measure this we studied the association of 18 type 2 diabetes genome wide association single nucleotide polymorphisms (SNPs) with the estimated glomerular filtration rate (eGFR) (MDRD equation) and urine albumin to creatinine ratio in 6,958 individuals in the Strong Heart Study family and cohort participants. Center specific residuals of eGFR and the log urine albumin to creatinine ratio, obtained from linear regression models adjusted for age, sex and body mass index, were regressed onto SNP dosage using variance component in family data and linear regression models in unrelated individuals. Estimates were then combined across centers. Four diabetic loci were associated with eGFR and one locus with the urine albumin to creatinine ratio. A SNP in the WFS1 gene (rs10010131) was associated with higher eGFR in younger individuals and with increased albuminuria. The SNPs of the FTO, KCNJ11 and TCF7L2 genes were associated with lower eGFR, not albuminuria, and were not significant in prospective analyses. Our findings suggest a shared genetic risk for type 2 diabetes, its kidney complications, and a potential role for WFS1 in early onset diabetic nephropathy in American Indian populations

Genetic Determinants of Lipid Traits in Diverse Populations from the Population Architecture using Genomics and Epidemiology (PAGE) Study

For the past five years, genome-wide association studies (GWAS) have identified hundreds of common variants associated with human diseases and traits, including high-density lipoprotein cholesterol (HDL-C), low-density lipoprotein cholesterol (LDL-C), and triglyceride (TG) levels. Approximately 95 loci associated with lipid levels have been identified primarily among populations of European ancestry. The Population Architecture using Genomics and Epidemiology (PAGE) study was established in 2008 to characterize GWAS–identified variants in diverse population-based studies. We genotyped 49 GWAS–identified SNPs associated with one or more lipid traits in at least two PAGE studies and across six racial/ethnic groups. We performed a meta-analysis testing for SNP associations with fasting HDL-C, LDL-C, and ln(TG) levels in self-identified European American (∼20,000), African American (∼9,000), American Indian (∼6,000), Mexican American/Hispanic (∼2,500), Japanese/East Asian (∼690), and Pacific Islander/Native Hawaiian (∼175) adults, regardless of lipid-lowering medication use. We replicated 55 of 60 (92%) SNP associations tested in European Americans at p<0.05. Despite sufficient power, we were unable to replicate ABCA1 rs4149268 and rs1883025, CETP rs1864163, and TTC39B rs471364 previously associated with HDL-C and MAFB rs6102059 previously associated with LDL-C. Based on significance (p<0.05) and consistent direction of effect, a majority of replicated genotype-phentoype associations for HDL-C, LDL-C, and ln(TG) in European Americans generalized to African Americans (48%, 61%, and 57%), American Indians (45%, 64%, and 77%), and Mexican Americans/Hispanics (57%, 56%, and 86%). Overall, 16 associations generalized across all three populations. For the associations that did not generalize, differences in effect sizes, allele frequencies, and linkage disequilibrium offer clues to the next generation of association studies for these traits

New genetic loci link adipose and insulin biology to body fat distribution.

Body fat distribution is a heritable trait and a well-established predictor of adverse metabolic outcomes, independent of overall adiposity. To increase our understanding of the genetic basis of body fat distribution and its molecular links to cardiometabolic traits, here we conduct genome-wide association meta-analyses of traits related to waist and hip circumferences in up to 224,459 individuals. We identify 49 loci (33 new) associated with waist-to-hip ratio adjusted for body mass index (BMI), and an additional 19 loci newly associated with related waist and hip circumference measures (P < 5 × 10(-8)). In total, 20 of the 49 waist-to-hip ratio adjusted for BMI loci show significant sexual dimorphism, 19 of which display a stronger effect in women. The identified loci were enriched for genes expressed in adipose tissue and for putative regulatory elements in adipocytes. Pathway analyses implicated adipogenesis, angiogenesis, transcriptional regulation and insulin resistance as processes affecting fat distribution, providing insight into potential pathophysiological mechanisms