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

GWAS of thyroid stimulating hormone highlights pleiotropic effects and inverse association with thyroid cancer

Thyroid stimulating hormone (TSH) is critical for normal development and metabolism. To better understand the genetic contribution to TSH levels, we conduct a GWAS meta-analysis at 22.4 million genetic markers in up to 119,715 individuals and identify 74 genome-wide significant loci for TSH, of which 28 are previously unreported. Functional experiments show that the thyroglobulin protein-altering variants P118L and G67S impact thyroglobulin secretion. Phenome-wide association analysis in the UK Biobank demonstrates the pleiotropic effects of TSH-associated variants and a polygenic score for higher TSH levels is associated with a reduced risk of thyroid cancer in the UK Biobank and three other independent studies. Two-sample Mendelian randomization using TSH index variants as instrumental variables suggests a protective effect of higher TSH levels (indicating lower thyroid function) on risk of thyroid cancer and goiter. Our findings highlight the pleiotropic effects of TSH-associated variants on thyroid function and growth of malignant and benign thyroid tumors

Measurements of trace gases in the tropical tropopause layer

A unique dataset of airborne in situ observations of HCl, O 3, HNO 3, H 2O, CO, CO 2 and CH 3Cl has been made in and near the tropical tropopause layer (TTL). A total of 16 profiles across the tropopause were obtained at latitudes between 10°N and 3°S from the NASA WB-57F high-altitude aircraft flying from Costa Rica. Few in situ measurements of these gases, particularly HCl and HNO 3, have been reported for the TTL. The general features of the trace gas vertical profiles are consistent with the concept of the TTL as distinct from the lower troposphere and lower stratosphere. A combination of the tracer profiles and correlations with O 3 is used to show that a measurable amount of stratospheric air is mixed into this region. The HCl measurements offer an important constraint on stratospheric mixing into the TTL because once the contribution from halocarbon decomposition is quantified, the remaining HCl (>60% in this study) must have a stratospheric source. Stratospheric HCl in the TTL brings with it a proportional amount of stratospheric O 3. Quantifying the sources of O 3 in the TTL is important because O 3 is particularly effective as a greenhouse gas in the tropopause region