Characters of the W3 algebra

Traces of powers of the zero mode in the W3 Algebra have recently been found to be of interest, for example in relation to Black Hole thermodynamics, and arise as the terms in an expansion of the full characters of the algebra. We calculate the first few such powers in two cases. Firstly, we find the traces in the 3-state Potts model by using null vectors to derive modular differential equations for the traces. Secondly, we calculate the exact results for Verma module representations. We compare our two methods with each other and the result of brute-force diagonalisation for low levels and find complete agreement.Comment: v2: Numerous small changes, version to appear in JHEP, 22 pages. v3: Typos corrected, matches published version, 22 page

Modular properties of characters of the W3 algebra

In a previous work, exact formulae and differential equations were found for traces of powers of the zero mode in the W3 algebra. In this paper we investigate their modular properties, in particular we find the exact result for the modular transformations of traces of $W_0^n$ for n = 1, 2, 3, solving exactly the problem studied approximately by Gaberdiel, Hartman and Jin. We also find modular differential equations satisfied by traces with a single $W_0$ inserted, and relate them to differential equations studied by Mathur et al. We find that, remarkably, these all seem to be related to weight 0 modular forms with expansions with non-negative integer coefficients.Comment: 20 pages. v2: 23 pages. v3: 23 pages, published in JHE

PARP regulates nonhomologous end joining through retention of Ku at double-strand breaks

Poly ADP-ribosylation polymerases are necessary for recruitment and/or retention of Ku at double-strand breaks during nonhomologous end-joining DNA repair

The Genetic Interpretation of Area under the ROC Curve in Genomic Profiling

Genome-wide association studies in human populations have facilitated the creation of genomic profiles which combine the effects of many associated genetic variants to predict risk of disease. The area under the receiver operator characteristic (ROC) curve is a well established measure for determining the efficacy of tests in correctly classifying diseased and non-diseased individuals. We use quantitative genetics theory to provide insight into the genetic interpretation of the area under the ROC curve (AUC) when the test classifier is a predictor of genetic risk. Even when the proportion of genetic variance explained by the test is 100%, there is a maximum value for AUC that depends on the genetic epidemiology of the disease, i.e. either the sibling recurrence risk or heritability and disease prevalence. We derive an equation relating maximum AUC to heritability and disease prevalence. The expression can be reversed to calculate the proportion of genetic variance explained given AUC, disease prevalence, and heritability. We use published estimates of disease prevalence and sibling recurrence risk for 17 complex genetic diseases to calculate the proportion of genetic variance that a test must explain to achieve AUC = 0.75; this varied from 0.10 to 0.74. We provide a genetic interpretation of AUC for use with predictors of genetic risk based on genomic profiles. We provide a strategy to estimate proportion of genetic variance explained on the liability scale from estimates of AUC, disease prevalence, and heritability (or sibling recurrence risk) available as an online calculator

Genome-wide meta-analysis identifies five new susceptibility loci for cutaneous malignant melanoma.

Thirteen common susceptibility loci have been reproducibly associated with cutaneous malignant melanoma (CMM). We report the results of an international 2-stage meta-analysis of CMM genome-wide association studies (GWAS). This meta-analysis combines 11 GWAS (5 previously unpublished) and a further three stage 2 data sets, totaling 15,990 CMM cases and 26,409 controls. Five loci not previously associated with CMM risk reached genome-wide significance (P < 5 × 10(-8)), as did 2 previously reported but unreplicated loci and all 13 established loci. Newly associated SNPs fall within putative melanocyte regulatory elements, and bioinformatic and expression quantitative trait locus (eQTL) data highlight candidate genes in the associated regions, including one involved in telomere biology.[Please see the Supplementary Note for acknowledgments.]This is the author accepted manuscript. The final version is available from NPG via http://dx.doi.org/10.1038/ng.337

Localization of type 1 diabetes susceptibility to the MHC class I genes HLA-B and HLA-A

The major histocompatibility complex (MHC) on chromosome 6 is associated with susceptibility to more common diseases than any other region of the human genome, including almost all disorders classified as autoimmune. In type 1 diabetes the major genetic susceptibility determinants have been mapped to the MHC class II genes HLA-DQB1 and HLA-DRB1 (refs 1-3), but these genes cannot completely explain the association between type 1 diabetes and the MHC region. Owing to the region's extreme gene density, the multiplicity of disease-associated alleles, strong associations between alleles, limited genotyping capability, and inadequate statistical approaches and sample sizes, which, and how many, loci within the MHC determine susceptibility remains unclear. Here, in several large type 1 diabetes data sets, we analyse a combined total of 1,729 polymorphisms, and apply statistical methods - recursive partitioning and regression - to pinpoint disease susceptibility to the MHC class I genes HLA-B and HLA-A (risk ratios >1.5; Pcombined = 2.01 × 10-19 and 2.35 × 10-13, respectively) in addition to the established associations of the MHC class II genes. Other loci with smaller and/or rarer effects might also be involved, but to find these, future searches must take into account both the HLA class II and class I genes and use even larger samples. Taken together with previous studies, we conclude that MHC-class-I-mediated events, principally involving HLA-B*39, contribute to the aetiology of type 1 diabetes. ©2007 Nature Publishing Group

Limits to the Rate of Adaptive Substitution in Sexual Populations

In large populations, many beneficial mutations may be simultaneously available and may compete with one another, slowing adaptation. By finding the probability of fixation of a favorable allele in a simple model of a haploid sexual population, we find limits to the rate of adaptive substitution, , that depend on simple parameter combinations. When variance in fitness is low and linkage is loose, the baseline rate of substitution is , where is the population size, is the rate of beneficial mutations per genome, and is their mean selective advantage. Heritable variance in log fitness due to unlinked loci reduces by under polygamy and under monogamy. With a linear genetic map of length Morgans, interference is yet stronger. We use a scaling argument to show that the density of adaptive substitutions depends on , , , and only through the baseline density: . Under the approximation that the interference due to different sweeps adds up, we show that , implying that interference prevents the rate of adaptive substitution from exceeding one per centimorgan per 200 generations. Simulations and numerical calculations confirm the scaling argument and confirm the additive approximation for ; for higher , the rate of adaptation grows above , but only very slowly. We also consider the effect of sweeps on neutral diversity and show that, while even occasional sweeps can greatly reduce neutral diversity, this effect saturates as sweeps become more common—diversity can be maintained even in populations experiencing very strong interference. Our results indicate that for some organisms the rate of adaptive substitution may be primarily recombination-limited, depending only weakly on the mutation supply and the strength of selection

Genome-wide association study in 176,678 Europeans reveals genetic loci for tanning response to sun exposure

The skin's tendency to sunburn rather than tan is a major risk factor for skin cancer. Here we report a large genome-wide association study of ease of skin tanning in 176,678 subjects of European ancestry. We identify significant associa