Fractal-like Distributions over the Rational Numbers in High-throughput Biological and Clinical Data

Recent developments in extracting and processing biological and clinical data are allowing quantitative approaches to studying living systems. High-throughput sequencing, expression profiles, proteomics, and electronic health records are some examples of such technologies. Extracting meaningful information from those technologies requires careful analysis of the large volumes of data they produce. In this note, we present a set of distributions that commonly appear in the analysis of such data. These distributions present some interesting features: they are discontinuous in the rational numbers, but continuous in the irrational numbers, and possess a certain self-similar (fractal-like) structure. The first set of examples which we present here are drawn from a high-throughput sequencing experiment. Here, the self-similar distributions appear as part of the evaluation of the error rate of the sequencing technology and the identification of tumorogenic genomic alterations. The other examples are obtained from risk factor evaluation and analysis of relative disease prevalence and co-mordbidity as these appear in electronic clinical data. The distributions are also relevant to identification of subclonal populations in tumors and the study of the evolution of infectious diseases, and more precisely the study of quasi-species and intrahost diversity of viral populations

VarScan 2: Somatic mutation and copy number alteration discovery in cancer by exome sequencing

Cancer is a disease driven by genetic variation and mutation. Exome sequencing can be utilized for discovering these variants and mutations across hundreds of tumors. Here we present an analysis tool, VarScan 2, for the detection of somatic mutations and copy number alterations (CNAs) in exome data from tumor–normal pairs. Unlike most current approaches, our algorithm reads data from both samples simultaneously; a heuristic and statistical algorithm detects sequence variants and classifies them by somatic status (germline, somatic, or LOH); while a comparison of normalized read depth delineates relative copy number changes. We apply these methods to the analysis of exome sequence data from 151 high-grade ovarian tumors characterized as part of the Cancer Genome Atlas (TCGA). We validated some 7790 somatic coding mutations, achieving 93% sensitivity and 85% precision for single nucleotide variant (SNV) detection. Exome-based CNA analysis identified 29 large-scale alterations and 619 focal events per tumor on average. As in our previous analysis of these data, we observed frequent amplification of oncogenes (e.g., CCNE1, MYC) and deletion of tumor suppressors (NF1, PTEN, and CDKN2A). We searched for additional recurrent focal CNAs using the correlation matrix diagonal segmentation (CMDS) algorithm, which identified 424 significant events affecting 582 genes. Taken together, our results demonstrate the robust performance of VarScan 2 for somatic mutation and CNA detection and shed new light on the landscape of genetic alterations in ovarian cancer

Non-perturbative dynamics of hot non-Abelian gauge fields: beyond leading log approximation

Many aspects of high-temperature gauge theories, such as the electroweak baryon number violation rate, color conductivity, and the hard gluon damping rate, have previously been understood only at leading logarithmic order (that is, neglecting effects suppressed only by an inverse logarithm of the gauge coupling). We discuss how to systematically go beyond leading logarithmic order in the analysis of physical quantities. Specifically, we extend to next-to-leading-log order (NLLO) the simple leading-log effective theory due to Bodeker that describes non-perturbative color physics in hot non-Abelian plasmas. A suitable scaling analysis is used to show that no new operators enter the effective theory at next-to-leading-log order. However, a NLLO calculation of the color conductivity is required, and we report the resulting value. Our NLLO result for the color conductivity can be trivially combined with previous numerical work by G. Moore to yield a NLLO result for the hot electroweak baryon number violation rate.Comment: 20 pages, 1 figur