Generalised Elliptic Functions

We consider multiply periodic functions, sometimes called Abelian functions, defined with respect to the period matrices associated with classes of algebraic curves. We realise them as generalisations of the Weierstras P-function using two different approaches. These functions arise naturally as solutions to some of the important equations of mathematical physics and their differential equations, addition formulae, and applications have all been recent topics of study. The first approach discussed sees the functions defined as logarithmic derivatives of the sigma-function, a modified Riemann theta-function. We can make use of known properties of the sigma function to derive power series expansions and in turn the properties mentioned above. This approach has been extended to a wide range of non hyperelliptic and higher genus curves and an overview of recent results is given. The second approach defines the functions algebraically, after first modifying the curve into its equivariant form. This approach allows the use of representation theory to derive a range of results at lower computational cost. We discuss the development of this theory for hyperelliptic curves and how it may be extended in the future.Comment: 16 page

Senescence of the cellular immune response in Drosophila melanogaster

Immune system effectiveness generally declines as animals age, compromising disease resistance. In Drosophila, expression of a variety of immune-related genes elevates during ageing; however how this is linked to increasing pathogen susceptibility in older flies has remained unclear. We investigated whether changes in the Drosophila cellular immune response might contribute to immunosenescence. Experiments studied fly cohorts of different ages and compared the numbers and activity of the circulating haemocytes involved in pathogen defence. In female wildtype Samarkand and Oregon R flies the haemocyte population fell by 31.8% and 10.2% respectively during the first four weeks of adulthood. Interestingly we detected no such decline in male flies. The impact of ageing on the phagocytic activity of haemocytes was investigated by injecting flies with fluorescently labelled microbes or latex beads and assessing the ability of haemocytes to engulf them. For all immune challenges the proportion of actively phagocytosing haemocytes decreased as flies aged. Whilst 24.3% ± 1.15% of haemocytes in one-week-old flies phagocytosed Escherichia coli bacteria or Beauveria bassiana fungal spores, this decreased to 16.7% ± 0.99% in four-week-old flies. This clear senescence of the Drosophila cellular immune response may underpin increased disease susceptibility in older flies

Trans-ancestry genome-wide association meta-analysis of prostate cancer identifies new susceptibility loci and informs genetic risk prediction.

Prostate cancer is a highly heritable disease with large disparities in incidence rates across ancestry populations. We conducted a multiancestry meta-analysis of prostate cancer genome-wide association studies (107,247 cases and 127,006 controls) and identified 86 new genetic risk variants independently associated with prostate cancer risk, bringing the total to 269 known risk variants. The top genetic risk score (GRS) decile was associated with odds ratios that ranged from 5.06 (95% confidence interval (CI), 4.84-5.29) for men of European ancestry to 3.74 (95% CI, 3.36-4.17) for men of African ancestry. Men of African ancestry were estimated to have a mean GRS that was 2.18-times higher (95% CI, 2.14-2.22), and men of East Asian ancestry 0.73-times lower (95% CI, 0.71-0.76), than men of European ancestry. These findings support the role of germline variation contributing to population differences in prostate cancer risk, with the GRS offering an approach for personalized risk prediction

Genetic Drivers of Heterogeneity in Type 2 Diabetes Pathophysiology

Type 2 diabetes (T2D) is a heterogeneous disease that develops through diverse pathophysiological processes1,2 and molecular mechanisms that are often specific to cell type3,4. Here, to characterize the genetic contribution to these processes across ancestry groups, we aggregate genome-wide association study data from 2,535,601 individuals (39.7% not of European ancestry), including 428,452 cases of T2D. We identify 1,289 independent association signals at genome-wide significance (P \u3c 5 × 10-8) that map to 611 loci, of which 145 loci are, to our knowledge, previously unreported. We define eight non-overlapping clusters of T2D signals that are characterized by distinct profiles of cardiometabolic trait associations. These clusters are differentially enriched for cell-type-specific regions of open chromatin, including pancreatic islets, adipocytes, endothelial cells and enteroendocrine cells. We build cluster-specific partitioned polygenic scores5 in a further 279,552 individuals of diverse ancestry, including 30,288 cases of T2D, and test their association with T2D-related vascular outcomes. Cluster-specific partitioned polygenic scores are associated with coronary artery disease, peripheral artery disease and end-stage diabetic nephropathy across ancestry groups, highlighting the importance of obesity-related processes in the development of vascular outcomes. Our findings show the value of integrating multi-ancestry genome-wide association study data with single-cell epigenomics to disentangle the aetiological heterogeneity that drives the development and progression of T2D. This might offer a route to optimize global access to genetically informed diabetes care

Genetic drivers of heterogeneity in type 2 diabetes pathophysiology

Type 2 diabetes (T2D) is a heterogeneous disease that develops through diverse pathophysiological processes1,2 and molecular mechanisms that are often specific to cell type3,4. Here, to characterize the genetic contribution to these processes across ancestry groups, we aggregate genome-wide association study data from 2,535,601 individuals (39.7% not of European ancestry), including 428,452 cases of T2D. We identify 1,289 independent association signals at genome-wide significance (P &lt; 5 × 10-8) that map to 611 loci, of which 145 loci are, to our knowledge, previously unreported. We define eight non-overlapping clusters of T2D signals that are characterized by distinct profiles of cardiometabolic trait associations. These clusters are differentially enriched for cell-type-specific regions of open chromatin, including pancreatic islets, adipocytes, endothelial cells and enteroendocrine cells. We build cluster-specific partitioned polygenic scores5 in a further 279,552 individuals of diverse ancestry, including 30,288 cases of T2D, and test their association with T2D-related vascular outcomes. Cluster-specific partitioned polygenic scores are associated with coronary artery disease, peripheral artery disease and end-stage diabetic nephropathy across ancestry groups, highlighting the importance of obesity-related processes in the development of vascular outcomes. Our findings show the value of integrating multi-ancestry genome-wide association study data with single-cell epigenomics to disentangle the aetiological heterogeneity that drives the development and progression of T2D. This might offer a route to optimize global access to genetically informed diabetes care.</p

Ancestral diversity improves discovery and fine-mapping of genetic loci for anthropometric traits - the Hispanic/Latino Anthropometry Consortium

Hispanic/Latinos have been underrepresented in genome-wide association studies (GWAS) for anthropometric traits despite their notable anthropometric variability, ancestry proportions, and high burden of growth stunting and overweight/obesity. To address this knowledge gap, we analyzed densely-imputed genetic data in a sample of Hispanic/Latino adults to identify and fine-map genetic variants associated with body mass index (BMI), height, and BMI-adjusted waist-to-hip ratio (WHRadjBMI). We conducted a GWAS of 18 studies/consortia as part of the Hispanic/Latino Anthropometry (HISLA) Consortium (Stage 1, n=59,771) and generalized our findings in 9 additional studies (HISLA Stage 2, n=10,538). We conducted a trans-ancestral GWAS with summary statistics from HISLA Stage 1 and existing consortia of European and African ancestries. In our HISLA Stage 1+2 analyses, we discovered one BMI locus, as well as two BMI signals and another height signal each within established anthropometric loci. In our trans-ancestral meta-analysis, we discovered three BMI loci, one height locus, and one WHRadjBMI locus. We also identified three secondary signals for BMI, 28 for height, and two for WHRadjBMI in established loci. We show that 336 known BMI, 1,177 known height, and 143 known WHRadjBMI (combined) SNPs demonstrated suggestive transferability (nominal significance and effect estimate directional consistency) in Hispanic/Latino adults. Of these, 36 BMI, 124 height, and 11 WHRadjBMI SNPs were significant after trait-specific Bonferroni correction. Trans-ancestral meta-analysis of the three ancestries showed a small-to-moderate impact of uncorrected population stratification on the resulting effect size estimates. Our findings demonstrate that future studies may also benefit from leveraging diverse ancestries and differences in linkage disequilibrium patterns to discover novel loci and additional signals with less residual population stratification