Nonlinear Differential Equations Satisfied by Certain Classical Modular Forms

A unified treatment is given of low-weight modular forms on \Gamma_0(N), N=2,3,4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations, which yields a single nonlinear third-order equation, called a generalized Chazy equation. As byproducts, a table of divisor function and theta identities is generated by means of q-expansions, and a transformation law under \Gamma_0(4) for the second complete elliptic integral is derived. More generally, it is shown how Picard-Fuchs equations of triangle subgroups of PSL(2,R) which are hypergeometric equations, yield systems of nonlinear equations for weight-1 forms, and generalized Chazy equations. Each triangle group commensurable with \Gamma(1) is treated.Comment: 40 pages, final version, accepted by Manuscripta Mathematic

Geometry of WZW Orientifolds

We analyze unoriented Wess-Zumino-Witten models from a geometrical point of view. We show that the geometric interpretation of simple current crosscap states is as centre orientifold planes localized on conjugacy classes of the group manifold. We determine the locations and dimensions of these planes for arbitrary simply-connected groups and orbifolds thereof. The dimensions of the O-planes turn out to be given by the dimensions of symmetric coset manifolds based on regular embeddings. Furthermore, we give a geometrical interpretation of boundary conjugation in open unoriented WZW models; it yields D-branes together with their images under the orientifold projection. To find the agreement between O-planes and crosscap states, we find explicit answers for lattice extensions of Gaussian sums. These results allow us to express the modular P-matrix, which is directly related to the crosscap coefficient, in terms of characters of the horizontal subgroup of the affine Lie algebra. A corollary of this relation is that there exists a formal linear relation between the modular P- and the modular S-matrix.Comment: 35 pages LaTeX, 2 tables; Proof added for symmetric space relation; minor improvements; references adde

Measurement of Leading Proton and Neutron Production in Deep Inelastic Scattering at HERA

Deep--inelastic scattering events with a leading baryon have been detected by the H1 experiment at HERA using a forward proton spectrometer and a forward neutron calorimeter. Semi--inclusive cross sections have been measured in the kinematic region 2 <= Q^2 <= 50 GeV^2, 6.10^-5 <= x <= 6.10^-3 and baryon p_T <= MeV, for events with a final state proton with energy 580 <= E' <= 740 GeV, or a neutron with energy E' >= 160 GeV. The measurements are used to test production models and factorization hypotheses. A Regge model of leading baryon production which consists of pion, pomeron and secondary reggeon exchanges gives an acceptable description of both semi-inclusive cross sections in the region 0.7 <= E'/E_p <= 0.9, where E_p is the proton beam energy. The leading neutron data are used to estimate for the first time the structure function of the pion at small Bjorken--x.Comment: 30 pages, 9 figures, 2 tables, submitted to Eur. Phys.

Genetically Determined Height and Risk of Non-hodgkin Lymphoma

Although the evidence is not consistent, epidemiologic studies have suggested that taller adult height may be associated with an increased risk of some non-Hodgkin lymphoma (NHL) subtypes. Height is largely determined by genetic factors, but how these genetic factors may contribute to NHL risk is unknown. We investigated the relationship between genetic determinants of height and NHL risk using data from eight genome-wide association studies (GWAS) comprising 10,629 NHL cases, including 3,857 diffuse large B-cell lymphoma (DLBCL), 2,847 follicular lymphoma (FL), 3,100 chronic lymphocytic leukemia (CLL), and 825 marginal zone lymphoma (MZL) cases, and 9,505 controls of European ancestry. We evaluated genetically predicted height by constructing polygenic risk scores using 833 height-associated SNPs. We used logistic regression to estimate odds ratios (OR) and 95% confidence intervals (CI) for association between genetically determined height and the risk of four NHL subtypes in each GWAS and then used fixed-effect meta-analysis to combine subtype results across studies. We found suggestive evidence between taller genetically determined height and increased CLL risk (OR = 1.08, 95% CI = 1.00\u20131.17, p = 0.049), which was slightly stronger among women (OR = 1.15, 95% CI: 1.01\u20131.31, p = 0.036). No significant associations were observed with DLBCL, FL, or MZL. Our findings suggest that there may be some shared genetic factors between CLL and height, but other endogenous or environmental factors may underlie reported epidemiologic height associations with other subtypes

Charmonium Production in Deep Inelastic Scattering at HERA

The electroproduction of J/psi and psi(2S) mesons is studied in elastic, quasi-elastic and inclusive reactions for four momentum transfers 2 Q^2 80 GeV^2 and photon-proton centre of mass energies 25 W 180 GeV. The data were taken with the H1 detector at the electron proton collider HERA in the years 1995 to 1997. The total virtual photon-proton cross section for elastic J/psi production is measured as a function of Q^2 and W. The dependence of the production rates on the square of the momentum transfer from the proton (t) is extracted. Decay angular distributions are analysed and the ratio of the longitudinal and transverse cross sections is derived. The ratio of the cross sections for quasi-elastic psi(2S) and J/psi meson production is measured as a function of Q^2. The results are discussed in terms of theoretical models based upon perturbative QCD. Differential cross sections for inclusive and inelastic production of J/psi mesons are determined and predictions within two theoretical frameworks are compared with the data, the non-relativistic QCD factorization approach including colour octet and colour singlet contributions, and the model of Soft Colour Interactions

Associations of autozygosity with a broad range of human phenotypes

In many species, the offspring of related parents suffer reduced reproductive success, a phenomenon known as inbreeding depression. In humans, the importance of this effect has remained unclear, partly because reproduction between close relatives is both rare and frequently associated with confounding social factors. Here, using genomic inbreeding coefficients (F-ROH) for >1.4 million individuals, we show that F-ROH is significantly associated (p <0.0005) with apparently deleterious changes in 32 out of 100 traits analysed. These changes are associated with runs of homozygosity (ROH), but not with common variant homozygosity, suggesting that genetic variants associated with inbreeding depression are predominantly rare. The effect on fertility is striking: F-ROH equivalent to the offspring of first cousins is associated with a 55% decrease [95% CI 44-66%] in the odds of having children. Finally, the effects of F-ROH are confirmed within full-sibling pairs, where the variation in F-ROH is independent of all environmental confounding.Peer reviewe

Two high-risk susceptibility loci at 6p25.3 and 14q32.13 for Waldenström macroglobulinemia

Waldenström macroglobulinemia (WM)/lymphoplasmacytic lymphoma (LPL) is a rare, chronic B-cell lymphoma with high heritability. We conduct a two-stage genome-wide association study of WM/LPL in 530 unrelated cases and 4362 controls of European ancestry and identify two high-risk loci associated with WM/LPL at 6p25.3 (rs116446171, near EXOC2 and IRF4; OR = 21.14, 95% CI: 14.40–31.03, P = 1.36 × 10−54) and 14q32.13 (rs117410836, near TCL1; OR = 4.90, 95% CI: 3.45–6.96, P = 8.75 × 10−19). Both risk alleles are observed at a low frequency among controls (~2–3%) and occur in excess in affected cases within families. In silico data suggest that rs116446171 may have functional importance, and in functional studies, we demonstrate increased reporter transcription and proliferation in cells transduced with the 6p25.3 risk allele. Although further studies are needed to fully elucidate underlying biological mechanisms, together these loci explain 4% of the familial risk and provide insights into genetic susceptibility to this malignancy

Distinct germline genetic susceptibility profiles identified for common non-Hodgkin lymphoma subtypes

Lymphoma risk is elevated for relatives with common non-Hodgkin lymphoma (NHL) subtypes, suggesting shared genetic susceptibility across subtypes. To evaluate the extent of mutual heritability among NHL subtypes and discover novel loci shared among subtypes, we analyzed data from eight genome-wide association studies within the InterLymph Consortium, including 10,629 cases and 9505 controls. We utilized Association analysis based on SubSETs (ASSET) to discover loci for subsets of NHL subtypes and evaluated shared heritability across the genome using Genome-wide Complex Trait Analysis (GCTA) and polygenic risk scores. We discovered 17 genome-wide significant loci (P &lt; 5 × 10−8) for subsets of NHL subtypes, including a novel locus at 10q23.33 (HHEX) (P = 3.27 × 10−9). Most subset associations were driven primarily by only one subtype. Genome-wide genetic correlations between pairs of subtypes varied broadly from 0.20 to 0.86, suggesting substantial heterogeneity in the extent of shared heritability among subtypes. Polygenic risk score analyses of established loci for different lymphoid malignancies identified strong associations with some NHL subtypes (P &lt; 5 × 10−8), but weak or null associations with others. Although our analyses suggest partially shared heritability and biological pathways, they reveal substantial heterogeneity among NHL subtypes with each having its own distinct germline genetic architecture

Female chromosome X mosaicism is age-related and preferentially affects the inactivated X chromosome

To investigate large structural clonal mosaicism of chromosome X, we analysed the SNP microarray intensity data of 38,303 women from cancer genome-wide association studies (20,878 cases and 17,425 controls) and detected 124 mosaic X events42Mb in 97 (0.25%) women. Here we show rates for X-chromosome mosaicism are four times higher than mean autosomal rates; X mosaic events more often include the entire chromosome and participants with X events more likely harbour autosomal mosaic events. X mosaicism frequency increases with age (0.11% in 50-year olds; 0.45% in 75-year olds), as reported for Y and autosomes. Methylation array analyses of 33 women with X mosaicism indicate events preferentially involve the inactive X chromosome. Our results provide further evidence that the sex chromosomes undergo mosaic events more frequently than autosomes, which could have implications for understanding the underlying mechanisms of mosaic events and their possible contribution to risk for chronic diseases

Detectable clonal mosaicism and its relationship to aging and cancer

In an analysis of 31,717 cancer cases and 26,136 cancer-free controls from 13 genome-wide association studies, we observed large chromosomal abnormalities in a subset of clones in DNA obtained from blood or buccal samples. We observed mosaic abnormalities, either aneuploidy or copy-neutral loss of heterozygosity, of >2 Mb in size in autosomes of 517 individuals (0.89%), with abnormal cell proportions of between 7% and 95%. In cancer-free individuals, frequency increased with age, from 0.23% under 50 years to 1.91% between 75 and 79 years (P = 4.8 × 10(-8)). Mosaic abnormalities were more frequent in individuals with solid tumors (0.97% versus 0.74% in cancer-free individuals; odds ratio (OR) = 1.25; P = 0.016), with stronger association with cases who had DNA collected before diagnosis or treatment (OR = 1.45; P = 0.0005). Detectable mosaicism was also more common in individuals for whom DNA was collected at least 1 year before diagnosis with leukemia compared to cancer-free individuals (OR = 35.4; P = 3.8 × 10(-11)). These findings underscore the time-dependent nature of somatic events in the etiology of cancer and potentially other late-onset diseases