On the alleged simplicity of impure proof

Roughly, a proof of a theorem, is “pure” if it draws only on what is “close” or “intrinsic” to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is “extrinsic,” “extraneous,” “distant,” “remote,” “alien,” or “foreign” to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical statements and proofs. Mathematicians have paid little attention to specifying such distance measures precisely because in practice certain methods of proof have seemed self- evidently impure by design: think for instance of analytic geometry and analytic number theory. By contrast, mathematicians have paid considerable attention to whether such impurities are a good thing or to be avoided, and some have claimed that they are valuable because generally impure proofs are simpler than pure proofs. This article is an investigation of this claim, formulated more precisely by proof- theoretic means. After assembling evidence from proof theory that may be thought to support this claim, we will argue that on the contrary this evidence does not support the claim

Retrospective evaluation of whole exome and genome mutation calls in 746 cancer samples

Funder: NCI U24CA211006Abstract: The Cancer Genome Atlas (TCGA) and International Cancer Genome Consortium (ICGC) curated consensus somatic mutation calls using whole exome sequencing (WES) and whole genome sequencing (WGS), respectively. Here, as part of the ICGC/TCGA Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium, which aggregated whole genome sequencing data from 2,658 cancers across 38 tumour types, we compare WES and WGS side-by-side from 746 TCGA samples, finding that ~80% of mutations overlap in covered exonic regions. We estimate that low variant allele fraction (VAF < 15%) and clonal heterogeneity contribute up to 68% of private WGS mutations and 71% of private WES mutations. We observe that ~30% of private WGS mutations trace to mutations identified by a single variant caller in WES consensus efforts. WGS captures both ~50% more variation in exonic regions and un-observed mutations in loci with variable GC-content. Together, our analysis highlights technological divergences between two reproducible somatic variant detection efforts

The Evolution of Environmental Policy in the People’s Republic of China

This paper outlines how the evolution of China’s policy and study of the environment are reflected in the scholarly literature, paying special attention to the impact of the country’s environmental developments on international relations. In particular, it examines accounts of how China has moved from an isolated national scientific and environmental control infrastructure into the centre of international environmental debates as its society has opened and the geographical scale of ecological problems has expanded. The paper also identifies the continuing inhibitors to China’s ability to control environmental degradation – including lack of transparency, elite manipulation, and bureaucratic weaknesses – despite the opening of China’s system to limited participation of civil society in its environmental debates

The Evolution of Environmental Policy in the People’s Republic of China

This paper outlines how the evolution of China’s policy and study of the environment are reflected in the scholarly literature, paying special attention to the impact of the country’s environmental developments on international relations. In particular, it examines accounts of how China has moved from an isolated national scientific and environmental control infrastructure into the centre of international environmental debates as its society has opened and the geographical scale of ecological problems has expanded. The paper also identifies the continuing inhibitors to China’s ability to control environmental degradation – including lack of transparency, elite manipulation, and bureaucratic weaknesses – despite the opening of China’s system to limited participation of civil society in its environmental debates

The Evolution of Environmental Policy in the People’s Republic of China

This paper outlines how the evolution of China’s policy and study of the environment are reflected in the scholarly literature, paying special attention to the impact of the country’s environmental developments on international relations. In particular, it examines accounts of how China has moved from an isolated national scientific and environmental control infrastructure into the centre of international environmental debates as its society has opened and the geographical scale of ecological problems has expanded. The paper also identifies the continuing inhibitors to China’s ability to control environmental degradation – including lack of transparency, elite manipulation, and bureaucratic weaknesses – despite the opening of China’s system to limited participation of civil society in its environmental debates