The asymptotic distribution function of the 4-dimensional shifted van der Corput sequence

Abstract Let γq(n) be the van der Corput sequence in the base q and g(x, y, z, u) be an asymptotic distribution function of the 4-dimensional sequence In this paper we find an explicit formula for g(x, x, x, x) and then as an example we find the limit for the base q = 4, 5, 6, . . . Also we find an explicit form of sth iteration T(s)(x) of the von Neumann-Kakutani transformation defined by T(γq(n)) = γq(n + 1)

Transitkunst. Studien zur Literatur 1890-2010

Die Chiffre „Transit“ vereinigt mit Aspekten wie Mobilität, Flüchtigkeit und Vorläufigkeit zentrale Begriffe des Zeiterlebens zwischen 1890 und 2010. Vor dem Hintergrund mehrerer Krisen und Katastrophen sowie tiefgreifender Umwandlungsprozesse erscheint das Leben als Durchgangsstadium, in dem sich nur noch ein temporäres, fragmentarisches Netz von Orientierungspunkten entwerfen lässt. Das Transitäre durchdringt nahezu alle Facetten des Individuums und seiner Lebensbereiche: vom Wahrnehmen der Inkohärenz in der Folge gesellschaftlicher Umwälzungen, über den Verlust ‚sicherer‘ Orte bis zum Erfahren der eigenen Identität als provisorisch. Die Reaktion auf solche Übergangszustände ist oft eine Intensivierung der Suchbewegungen nach Sicherheit, Nähe und Glück, die jedoch selbst zunehmend transitive Zwischenstellungen markieren. Die Literatur zeichnet sich unter dieser Perspektive durch die Adaptation transittypischer Themen und Inhalte aus, desgleichen durch die autoreflexive Übertragung von Konzepten wie Momenthaftigkeit, Unvollständigkeit und Flexibilität in das eigene narrative Programm. Die Beiträge des Bandes nähern sich verschiedenen Formen eines solchen inhaltlichen und/oder formalen ‚Dazwischen‘ an. Die Idee des Transits erweist sich dabei für diese vielfältigen literatur- und kulturwissenschaftlichen Untersuchungen als ebenso funktionale wie inspirierende Klammer, der es gelingt, im bewussten Einlassen auf das im Durchgang Begriffene die heterogenen Facetten des 20. Jahrhunderts zu verbinden: zu einer Art Zeitbild und Ästhetik des Transits

Genetic fine mapping and genomic annotation defines causal mechanisms at type 2 diabetes susceptibility loci.

We performed fine mapping of 39 established type 2 diabetes (T2D) loci in 27,206 cases and 57,574 controls of European ancestry. We identified 49 distinct association signals at these loci, including five mapping in or near KCNQ1. 'Credible sets' of the variants most likely to drive each distinct signal mapped predominantly to noncoding sequence, implying that association with T2D is mediated through gene regulation. Credible set variants were enriched for overlap with FOXA2 chromatin immunoprecipitation binding sites in human islet and liver cells, including at MTNR1B, where fine mapping implicated rs10830963 as driving T2D association. We confirmed that the T2D risk allele for this SNP increases FOXA2-bound enhancer activity in islet- and liver-derived cells. We observed allele-specific differences in NEUROD1 binding in islet-derived cells, consistent with evidence that the T2D risk allele increases islet MTNR1B expression. Our study demonstrates how integration of genetic and genomic information can define molecular mechanisms through which variants underlying association signals exert their effects on disease

Genome-wide meta-analysis of 241,258 adults accounting for smoking behaviour identifies novel loci for obesity traits

Few genome-wide association studies (GWAS) account for environmental exposures, like smoking, potentially impacting the overall trait variance when investigating the genetic contribution to obesity-related traits. Here, we use GWAS data from 51,080 current smokers and 190,178 nonsmokers (87% European descent) to identify loci influencing BMI and central adiposity, measured as waist circumference and waist-to-hip ratio both adjusted for BMI. We identify 23 novel genetic loci, and 9 loci with convincing evidence of gene-smoking interaction (GxSMK) on obesity-related traits. We show consistent direction of effect for all identified loci and significance for 18 novel and for 5 interaction loci in an independent study sample. These loci highlight novel biological functions, including response to oxidative stress, addictive behaviour, and regulatory functions emphasizing the importance of accounting for environment in genetic analyses. Our results suggest that tobacco smoking may alter the genetic susceptibility to overall adiposity and body fat distribution.Peer reviewe

Multi-ancestry study of blood lipid levels identifies four loci interacting with physical activity.

Many genetic loci affect circulating lipid levels, but it remains unknown whether lifestyle factors, such as physical activity, modify these genetic effects. To identify lipid loci interacting with physical activity, we performed genome-wide analyses of circulating HDL cholesterol, LDL cholesterol, and triglyceride levels in up to 120,979 individuals of European, African, Asian, Hispanic, and Brazilian ancestry, with follow-up of suggestive associations in an additional 131,012 individuals. We find four loci, in/near CLASP1, LHX1, SNTA1, and CNTNAP2, that are associated with circulating lipid levels through interaction with physical activity; higher levels of physical activity enhance the HDL cholesterol-increasing effects of the CLASP1, LHX1, and SNTA1 loci and attenuate the LDL cholesterol-increasing effect of the CNTNAP2 locus. The CLASP1, LHX1, and SNTA1 regions harbor genes linked to muscle function and lipid metabolism. Our results elucidate the role of physical activity interactions in the genetic contribution to blood lipid levels

A principal component meta-analysis on multiple anthropometric traits identifies novel loci for body shape

Large consortia have revealed hundreds of genetic loci associated with anthropometric traits, one trait at a time. We examined whether genetic variants affect body shape as a composite phenotype that is represented by a combination of anthropometric traits. We developed an approach that calculates averaged PCs (AvPCs) representing body shape derived from six anthropometric traits (body mass index, height, weight, waist and hip circumference, waist-to-hip ratio). The first four AvPCs explain >99% of the variability, are heritable, and associate with cardiometabolic outcomes. We performed genome-wide association analyses for each body shape composite phenotype across 65 studies and meta-analysed summary statistics. We identify six novel loci: LEMD2 and CD47 for AvPC1, RPS6KA5/C14orf159 and GANAB for AvPC3, and ARL15 and ANP32 for AvPC4. Our findings highlight the value of using multiple traits to define complex phenotypes for discovery, which are not captured by single-trait analyses, and may shed light onto new pathways

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

New genetic loci link adipose and insulin biology to body fat distribution.

Body fat distribution is a heritable trait and a well-established predictor of adverse metabolic outcomes, independent of overall adiposity. To increase our understanding of the genetic basis of body fat distribution and its molecular links to cardiometabolic traits, here we conduct genome-wide association meta-analyses of traits related to waist and hip circumferences in up to 224,459 individuals. We identify 49 loci (33 new) associated with waist-to-hip ratio adjusted for body mass index (BMI), and an additional 19 loci newly associated with related waist and hip circumference measures (P < 5 × 10(-8)). In total, 20 of the 49 waist-to-hip ratio adjusted for BMI loci show significant sexual dimorphism, 19 of which display a stronger effect in women. The identified loci were enriched for genes expressed in adipose tissue and for putative regulatory elements in adipocytes. Pathway analyses implicated adipogenesis, angiogenesis, transcriptional regulation and insulin resistance as processes affecting fat distribution, providing insight into potential pathophysiological mechanisms

Fine-mapping type 2 diabetes loci to single-variant resolution using high-density imputation and islet-specific epigenome maps

We expanded GWAS discovery for type 2 diabetes (T2D) by combining data from 898,130 European-descent individuals (9% cases), after imputation to high-density reference panels. With these data, we (i) extend the inventory of T2D-risk variants (243 loci,135 newly implicated in T2D predisposition, comprising 403 distinct association signals); (ii) enrich discovery of lower-frequency risk alleles (80 index variants with minor allele frequency 2); (iii) substantially improve fine-mapping of causal variants (at 51 signals, one variant accounted for >80% posterior probability of association (PPA)); (iv) extend fine-mapping through integration of tissue-specific epigenomic information (islet regulatory annotations extend the number of variants with PPA >80% to 73); (v) highlight validated therapeutic targets (18 genes with associations attributable to coding variants); and (vi) demonstrate enhanced potential for clinical translation (genome-wide chip heritability explains 18% of T2D risk; individuals in the extremes of a T2D polygenic risk score differ more than ninefold in prevalence).Peer reviewe