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

Genomewide meta-analysis identifies loci associated with IGF-I and IGFBP-3 levels with impact on age-related traits

The growth hormone/insulin-like growth factor (IGF) axis can be manipulated in animal models to promote longevity, and IGF-related proteins including IGF-I and IGF-binding protein-3 (IGFBP-3) have also been implicated in risk of human diseases including cardiovascular diseases, diabetes, and cancer. Throug

Combining Asian and European genome-wide association studies of colorectal cancer improves risk prediction across racial and ethnic populations

Polygenic risk scores (PRS) have great potential to guide precision colorectal cancer (CRC) prevention by identifying those at higher risk to undertake targeted screening. However, current PRS using European ancestry data have sub-optimal performance in non-European ancestry populations, limiting their utility among these populations. Towards addressing this deficiency, we expand PRS development for CRC by incorporating Asian ancestry data (21,731 cases; 47,444 controls) into European ancestry training datasets (78,473 cases; 107,143 controls). The AUC estimates (95% CI) of PRS are 0.63(0.62-0.64), 0.59(0.57-0.61), 0.62(0.60-0.63), and 0.65(0.63-0.66) in independent datasets including 1681-3651 cases and 8696-115,105 controls of Asian, Black/African American, Latinx/Hispanic, and non-Hispanic White, respectively. They are significantly better than the European-centric PRS in all four major US racial and ethnic groups (p-values < 0.05). Further inclusion of non-European ancestry populations, especially Black/African American and Latinx/Hispanic, is needed to improve the risk prediction and enhance equity in applying PRS in clinical practice

Genome-wide association study of classical Hodgkin lymphoma identifies key regulators of disease susceptibility

Several susceptibility loci for classical Hodgkin lymphoma (cHL) have been reported, however much of the heritable risk is unknown. Here, we perform a meta-analysis of two existing genome-wide association studies (GWAS), a new GWAS, and replication totalling 5,314 cases and 16,749 controls. We identify risk loci for all cHL at 6q22.33 (rs9482849, P=1.52 × 10-8) and for nodular sclerosis HL (NSHL) at 3q28 (rs4459895, P=9.43 × 10-17), 6q23.3 (rs6928977, P=4.62 × 10-55 11), 10p14 (rs3781093, P=9.49 × 10-13), 13q34 (rs112998813, P=4.58 × 10-8) and 16p13.13 (rs34972832, P=2.12 × 10-8). Additionally, independent loci within the HLA region are observed for NSHL (rs9269081, HLA-DPB1*03:01, Val86 in HLA-DRB1) and mixed cellularity HL (rs1633096, rs13196329, Val86 in HLA-DRB1). The new and established risk loci localise to areas of active chromatin and show an over-representation of transcription factor binding for determinants of B-cell development and immune response.In the United Kingdom, Bloodwise (LLR; 10021) provided principal funding for the study. Support from Cancer Research UK (C1298/A8362 supported by the Bobby Moore Fund) and the Lymphoma Research Trust is also acknowledged. A.S. is supported by a clinical fellowship from Cancer Research UK. For the UK-GWAS, sample and data acquisition were supported by Breast Cancer Now, the European Union and the Lymphoma Research Trust. The UK-GWAS made use of control genotyping data generated by the WTCCC. For further information, please visit the publishr's website

Identification of multiple risk loci and regulatory mechanisms influencing susceptibility to multiple myeloma

Genome-wide association studies (GWAS) have transformed our understanding of susceptibility to multiple myeloma (MM), but much of the heritability remains unexplained. We report a new GWAS, a meta-analysis with previous GWAS and a replication series, totalling 9974 MM cases and 247,556 controls of European ancestry. Collectively, these data provide evidence for six new MM risk loci, bringing the total number to 23. Integration of information from gene expression, epigenetic profiling and in situ Hi-C data for the 23 risk loci implicate disruption of developmental transcriptional regulators as a basis of MM susceptibility, compatible with altered B-cell differentiation as a key mechanism. Dysregulation of autophagy/apoptosis and cell cycle signalling feature as recurrently perturbed pathways. Our findings provide further insight

Fatigue and mechanical properties of nanostructured and conventional titania (TiO2) thermal spray coatings

Nanostructured and conventional titania (TiO2) coatings were thermally sprayed using air plasma spray (APS) and high velocity oxy-fuel (HVOF) processes. The fatigue and mechanical properties of these coatings were investigated. A previous study characterized these coatings by scanning electron microscopy (SEM) to investigate the microstructural features and Vickers indentation to determine the hardness and crack propagation resistance. This current complementary SEM work examined fracture surfaces of fatigue-tested samples to assess crack nucleation and to study mechanisms of deformations. The fatigue strength of coatings deposited onto low-carbon steel (AISI 1018) showed that the nanostructured titania coated specimens exhibited significantly higher fatigue strength compared to the conventionally sprayed titania. The strain–time curve of AISI 1018 coated with TiO2 indicated that the strain amplitude of the HVOF-sprayed nanostructured TiO2 coating was much lower than the corresponding data of APS conventional TiO2. SEM analysis of fracture surfaces revealed valuable information regarding the influence of these coatings on the performance of the coated component. This investigation gives new understanding to the nature of fatigue and deformation of the nanostructured and conventional titania (TiO2) coatings

Properties and microstructures of nanostructured partially stabilized zirconia coatings

Results concerning micro hardness, elastic modulus and roughness (Ra) of plasma sprayed coatings fabricated from nanostructured partially stabilized zirconia (PSZ) feedstock are presented. Nanostructured zirconia particles were plasma sprayed (Ar/H2) at three power levels, with two different argon flow rates at two spray distances. The results indicate that the microhardness, elastic modulus and roughness of the nanostructured zirconia coatings exhibit a trend whereby smoother coatings exhibit higher microhardness and elastic modulus. This correlation implies that a roughness gage can be used to estimate the coating microhardness and elastic modulus; i.e., a simple non-destructive and in situ test is proposed for these coatings. The powder particle distribution is similar to the commercial materials, with average particle size close to 30 J..Lm (Fig. I). By SEM, each powder particle is formed by the agglomeration of many tiny particles (Fig. 2). When the sprayed particles are examined by SEM, the agglomerated nanostructured particles apparently split up or explode inside the plasma flame becoming a large group of very tiny particles, having an opposite effect to the initial agglomeration (Fig. 3). This phenomenon probably is associated with the low roughness (Ra) presented by coatings (up to 3.8 J..Lm). The nanostructured coatings present only the nontransformable tetragonal t' phase of zirconia, which is the one with the highest thermal shock resistence of all the zirconia phases (Fig. 4). microhardness (up to 750 HV50o, Fig. 5) and high values of elastic modulus (up to 95 GPa, Fig. 6) but still having high porosity (8-10%)

Does Retrogression Always Account for the Large Volume of Submarine Megaslides? Evidence to the Contrary From the Tampen Slide, Offshore Norway

Submarine landslides can be several orders of magnitude larger than their terrestrial counterparts and can pose significant hazards across entire ocean basins. The landslide failure mechanism strongly controls the associated tsunami hazard. The Tampen Slide offshore Norway is one of the largest landslides on Earth but remains poorly understood due to its subsequent burial beneath up to 450 m of sediments. Here, we use laterally extensive (16,000 km2), high-resolution processed 3-D seismic reflection data to characterize the upper Tampen Slide. We identify longitudinal (downslope, movement-parallel) chutes and ridges that are up to 40 m high, as well as extensional and compressional (cross-slope) ridges. This is the first time that longitudinal ridges of such size have been imaged in a deep marine setting. The first phase of the Tampen Slide involved the simultaneous translation of over 720 km3 of sediments along a single failure plane. This was followed by spreading along the head- and sidewall, and the formation of a retrogressive debris flow and slump, the volumes of which are insignificant compared to the first failure. The process responsible for movement of such a large sediment volume along a single glide plane differs significantly from that of other passive margin megaslides, which typically comprise numerous smaller landslides that fail retrogressively along multiple glide planes. The trigger mechanism (e.g., an earthquake), the presence of mechanically strong obstructions (e.g., volcanic structural high), and the number and location of weak layers may be key factors that determine whether megaslides develop along a single plane or retrogressively