Relaxing the Parity Conditions of Asymptotically Flat Gravity

Four-dimensional asymptotically flat spacetimes at spatial infinity are defined from first principles without imposing parity conditions or restrictions on the Weyl tensor. The Einstein-Hilbert action is shown to be a correct variational principle when it is supplemented by an anomalous counter-term which breaks asymptotic translation, supertranslation and logarithmic translation invariance. Poincar\'e transformations as well as supertranslations and logarithmic translations are associated with finite and conserved charges which represent the asymptotic symmetry group. Lorentz charges as well as logarithmic translations transform anomalously under a change of regulator. Lorentz charges are generally non-linear functionals of the asymptotic fields but reduce to well-known linear expressions when parity conditions hold. We also define a covariant phase space of asymptotically flat spacetimes with parity conditions but without restrictions on the Weyl tensor. In this phase space, the anomaly plays classically no dynamical role. Supertranslations are pure gauge and the asymptotic symmetry group is the expected Poincar\'e group.Comment: Four equations corrected. Two references adde

Germline Variation in Cancer-Susceptibility Genes in a Healthy, Ancestrally Diverse Cohort: Implications for Individual Genome Sequencing

<div><p>Technological advances coupled with decreasing costs are bringing whole genome and whole exome sequencing closer to routine clinical use. One of the hurdles to clinical implementation is the high number of variants of unknown significance. For cancer-susceptibility genes, the difficulty in interpreting the clinical relevance of the genomic variants is compounded by the fact that most of what is known about these variants comes from the study of highly selected populations, such as cancer patients or individuals with a family history of cancer. The genetic variation in known cancer-susceptibility genes in the general population has not been well characterized to date. To address this gap, we profiled the nonsynonymous genomic variation in 158 genes causally implicated in carcinogenesis using high-quality whole genome sequences from an ancestrally diverse cohort of 681 healthy individuals. We found that all individuals carry multiple variants that may impact cancer susceptibility, with an average of 68 variants per individual. Of the 2,688 allelic variants identified within the cohort, most are very rare, with 75% found in only 1 or 2 individuals in our population. Allele frequencies vary between ancestral groups, and there are 21 variants for which the minor allele in one population is the major allele in another. Detailed analysis of a selected subset of 5 clinically important cancer genes, <i>BRCA1</i>, <i>BRCA2</i>, <i>KRAS</i>, <i>TP53</i>, and <i>PTEN</i>, highlights differences between germline variants and reported somatic mutations. The dataset can serve a resource of genetic variation in cancer-susceptibility genes in 6 ancestry groups, an important foundation for the interpretation of cancer risk from personal genome sequences.</p></div