Global periodicity conditions for maps and recurrences via Normal Forms

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences.Comment: 25 page

Identifying Elements of \u3cem\u3eKinder- und Jugendliteratur\u3c/em\u3e

Kinder- und Jugendliteratur, children’s literature written for the purpose of teaching or entertaining young people, has been present in German literature since the Middle Ages. This genre has changed as German literature progressed, reflecting the developments of each era, including such periods as the Romantic, the Biedermeier, Realism, Modernism and Postmodernism. As such, we examined individual works of German Kinder- und Jugendliteratur for the purpose of identifying distinctive features which situate them within children’s literature as well as in the respective historical genre. The works examined were Nußknacker und Mausekönig (1816) by E. T. A. Hoffmann, Emil und die Detektive (1929) by Erich Kästner, Försters Pucki (1935) by Madge Trott, Jan und das Wildpferd (1957) by Heinrich Denneborg, Die Wolke (1987) by Gudrun Pausewang, and Tintenherz (2003) by Cornelia Funke. We present our findings in the form of a Wimmelbuch, a typical form of German Kinder- und Jugendliteratur made popular during the Biedermeier period of the mid-1800s

The genetic aetiology of cannabis use initiation: a meta-analysis of genome-wide association studies and a SNP-based heritability estimation

While initiation of cannabis use is around 40% heritable, not much is known about the underlying genetic aetiology. Here, we meta-analysed two genome-wide association studies of initiation of cannabis use with >10000 individuals. None of the genetic variants reached genome-wide significance. We also performed a gene-based association test, which also revealed no significant effects of individual genes. Finally, we estimated that only approximately 6% of the variation in cannabis initiation is due to common genetic variants. Future genetic studies using larger sample sizes and different methodologies (including sequencing) might provide more insight in the complex genetic aetiology of cannabis use

HumMeth27QCReport: an R package for quality control and primary analysis of Illumina Infinium methylation data

<p>Abstract</p> <p>Background</p> <p>The study of the human DNA methylome has gained particular interest in the last few years. Researchers can nowadays investigate the potential role of DNA methylation in common disorders by taking advantage of new high-throughput technologies. Among these, Illumina Infinium assays can interrogate the methylation levels of hundreds of thousands of CpG sites, offering an ideal solution for genome-wide methylation profiling. However, like for other high-throughput technologies, the main bottleneck remains at the stage of data analysis rather than data production.</p> <p>Findings</p> <p>We have developed <it>HumMeth27QCReport</it>, an R package devoted to researchers wanting to quickly analyse their Illumina Infinium methylation arrays. This package automates quality control steps by generating a report including sample-independent and sample-dependent quality plots, and performs primary analysis of raw methylation calls by computing data normalization, statistics, and sample similarities. This package is available at CRAN repository, and can be integrated in any Galaxy instance through the implementation of ad-hoc scripts accessible at Galaxy Tool Shed.</p> <p>Conclusions</p> <p>Our package provides users of the Illumina Infinium Methylation assays with a simplified, automated, open-source quality control and primary analysis of their methylation data. Moreover, to enhance its use by experimental researchers, the tool is being distributed along with the scripts necessary for its implementation in the Galaxy workbench. Finally, although it was originally developed for HumanMethylation27, we proved its compatibility with data generated with the HumanMethylation450 Bead Chip.</p

Parent-of-origin-specific allelic associations among 106 genomic loci for age at menarche.

Age at menarche is a marker of timing of puberty in females. It varies widely between individuals, is a heritable trait and is associated with risks for obesity, type 2 diabetes, cardiovascular disease, breast cancer and all-cause mortality. Studies of rare human disorders of puberty and animal models point to a complex hypothalamic-pituitary-hormonal regulation, but the mechanisms that determine pubertal timing and underlie its links to disease risk remain unclear. Here, using genome-wide and custom-genotyping arrays in up to 182,416 women of European descent from 57 studies, we found robust evidence (P < 5 × 10(-8)) for 123 signals at 106 genomic loci associated with age at menarche. Many loci were associated with other pubertal traits in both sexes, and there was substantial overlap with genes implicated in body mass index and various diseases, including rare disorders of puberty. Menarche signals were enriched in imprinted regions, with three loci (DLK1-WDR25, MKRN3-MAGEL2 and KCNK9) demonstrating parent-of-origin-specific associations concordant with known parental expression patterns. Pathway analyses implicated nuclear hormone receptors, particularly retinoic acid and γ-aminobutyric acid-B2 receptor signalling, among novel mechanisms that regulate pubertal timing in humans. Our findings suggest a genetic architecture involving at least hundreds of common variants in the coordinated timing of the pubertal transition

Single-cell longitudinal analysis of SARS-CoV-2 infection in human airway epithelium identifies target cells, alterations in gene expression, and cell state changes.

There are currently limited Food and Drug Administration (FDA)-approved drugs and vaccines for the treatment or prevention of Coronavirus Disease 2019 (COVID-19). Enhanced understanding of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) infection and pathogenesis is critical for the development of therapeutics. To provide insight into viral replication, cell tropism, and host-viral interactions of SARS-CoV-2, we performed single-cell (sc) RNA sequencing (RNA-seq) of experimentally infected human bronchial epithelial cells (HBECs) in air-liquid interface (ALI) cultures over a time course. This revealed novel polyadenylated viral transcripts and highlighted ciliated cells as a major target at the onset of infection, which we confirmed by electron and immunofluorescence microscopy. Over the course of infection, the cell tropism of SARS-CoV-2 expands to other epithelial cell types including basal and club cells. Infection induces cell-intrinsic expression of type I and type III interferons (IFNs) and interleukin (IL)-6 but not IL-1. This results in expression of interferon-stimulated genes (ISGs) in both infected and bystander cells. This provides a detailed characterization of genes, cell types, and cell state changes associated with SARS-CoV-2 infection in the human airway

Hundreds of variants clustered in genomic loci and biological pathways affect human height

Most common human traits and diseases have a polygenic pattern of inheritance: DNA sequence variants at many genetic loci influence the phenotype. Genome-wide association (GWA) studies have identified more than 600 variants associated with human traits, but these typically explain small fractions of phenotypic variation, raising questions about the use of further studies. Here, using 183,727 individuals, we show that hundreds of genetic variants, in at least 180 loci, influence adult height, a highly heritable and classic polygenic trait. The large number of loci reveals patterns with important implications for genetic studies of common human diseases and traits. First, the 180 loci are not random, but instead are enriched for genes that are connected in biological pathways (P = 0.016) and that underlie skeletal growth defects (P < 0.001). Second, the likely causal gene is often located near the most strongly associated variant: in 13 of 21 loci containing a known skeletal growth gene, that gene was closest to the associated variant. Third, at least 19 loci have multiple independently associated variants, suggesting that allelic heterogeneity is a frequent feature of polygenic traits, that comprehensive explorations of already-discovered loci should discover additional variants and that an appreciable fraction of associated loci may have been identified. Fourth, associated variants are enriched for likely functional effects on genes, being over-represented among variants that alter amino-acid structure of proteins and expression levels of nearby genes. Our data explain approximately 10% of the phenotypic variation in height, and we estimate that unidentified common variants of similar effect sizes would increase this figure to approximately 16% of phenotypic variation (approximately 20% of heritable variation). Although additional approaches are needed to dissect the genetic architecture of polygenic human traits fully, our findings indicate that GWA studies can identify large numbers of loci that implicate biologically relevant genes and pathways.