Overview of (pro-)Lie group structures on Hopf algebra character groups

Character groups of Hopf algebras appear in a variety of mathematical and physical contexts. To name just a few, they arise in non-commutative geometry, renormalisation of quantum field theory, and numerical analysis. In the present article we review recent results on the structure of character groups of Hopf algebras as infinite-dimensional (pro-)Lie groups. It turns out that under mild assumptions on the Hopf algebra or the target algebra the character groups possess strong structural properties. Moreover, these properties are of interest in applications of these groups outside of Lie theory. We emphasise this point in the context of two main examples: The Butcher group from numerical analysis and character groups which arise from the Connes--Kreimer theory of renormalisation of quantum field theories.Comment: 31 pages, precursor and companion to arXiv:1704.01099, Workshop on "New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series", May 25-28, 2015, ICMAT, Madrid, Spai

Molecular genetics of nicotine dependence and abstinence: whole genome association using 520,000 SNPs

BACKGROUND: Classical genetic studies indicate that nicotine dependence is a substantially heritable complex disorder. Genetic vulnerabilities to nicotine dependence largely overlap with genetic vulnerabilities to dependence on other addictive substances. Successful abstinence from nicotine displays substantial heritable components as well. Some of the heritability for the ability to quit smoking appears to overlap with the genetics of nicotine dependence and some does not. We now report genome wide association studies of nicotine dependent individuals who were successful in abstaining from cigarette smoking, nicotine dependent individuals who were not successful in abstaining and ethnically-matched control subjects free from substantial lifetime use of any addictive substance. RESULTS: These data, and their comparison with data that we have previously obtained from comparisons of four other substance dependent vs control samples support two main ideas: 1) Single nucleotide polymorphisms (SNPs) whose allele frequencies distinguish nicotine-dependent from control individuals identify a set of genes that overlaps significantly with the set of genes that contain markers whose allelic frequencies distinguish the four other substance dependent vs control groups (p < 0.018). 2) SNPs whose allelic frequencies distinguish successful vs unsuccessful abstainers cluster in small genomic regions in ways that are highly unlikely to be due to chance (Monte Carlo p < 0.00001). CONCLUSION: These clustered SNPs nominate candidate genes for successful abstinence from smoking that are implicated in interesting functions: cell adhesion, enzymes, transcriptional regulators, neurotransmitters and receptors and regulation of DNA, RNA and proteins. As these observations are replicated, they will provide an increasingly-strong basis for understanding mechanisms of successful abstinence, for identifying individuals more or less likely to succeed in smoking cessation efforts and for tailoring therapies so that genotypes can help match smokers with the treatments that are most likely to benefit them

Mating dynamics in a nematode with three sexes and its evolutionary implications

Nematodes have diverse reproductive strategies, which make them ideal subjects for comparative studies to address how mating systems evolve. Here we present the sex ratios and mating dynamics of the free-living nematode Rhabditis sp. SB347, in which males, females and hermaphrodites co-exist. The three sexes are produced by both selfing and outcrossing, and females tend to appear early in a mother’s progeny. Males prefer mating with females over hermaphrodites, which our results suggest is related to the female-specific production of the sex pheromones ascr#1 and ascr#9. We discuss the parallels between this system and that of parasitic nematodes that exhibit alternation between uniparental and biparental reproduction

RNAi Screen of DAF-16/FOXO Target Genes in C. elegans Links Pathogenesis and Dauer Formation

The DAF-16/FOXO transcription factor is the major downstream output of the insulin/IGF1R signaling pathway controlling C. elegans dauer larva development and aging. To identify novel downstream genes affecting dauer formation, we used RNAi to screen candidate genes previously identified to be regulated by DAF-16. We used a sensitized genetic background [eri-1(mg366); sdf-9(m708)], which enhances both RNAi efficiency and constitutive dauer formation (Daf-c). Among 513 RNAi clones screened, 21 displayed a synthetic Daf-c (SynDaf) phenotype with sdf-9. One of these genes, srh-100, was previously identified to be SynDaf, but twenty have not previously been associated with dauer formation. Two of the latter genes, lys-1 and cpr-1, are known to participate in innate immunity and six more are predicted to do so, suggesting that the immune response may contribute to the dauer decision. Indeed, we show that two of these genes, lys-1 and clc-1, are required for normal resistance to Staphylococcus aureus. clc-1 is predicted to function in epithelial cohesion. Dauer formation exhibited by daf-8(m85), sdf-9(m708), and the wild-type N2 (at 27°C) were all enhanced by exposure to pathogenic bacteria, while not enhanced in a daf-22(m130) background. We conclude that knockdown of the genes required for proper pathogen resistance increases pathogenic infection, leading to increased dauer formation in our screen. We propose that dauer larva formation is a behavioral response to pathogens mediated by increased dauer pheromone production

Integrative Genomic Analyses Identify BRF2 as a Novel Lineage-Specific Oncogene in Lung Squamous Cell Carcinoma

William Lockwood and colleagues show that the focal amplification of a gene, BRF2, on Chromosome 8p12 plays a key role in squamous cell carcinoma of the lung

Clinical characteristics with inflammation profiling of long COVID and association with 1-year recovery following hospitalisation in the UK: a prospective observational study

Background No effective pharmacological or non-pharmacological interventions exist for patients with long COVID. We aimed to describe recovery 1 year after hospital discharge for COVID-19, identify factors associated with patient-perceived recovery, and identify potential therapeutic targets by describing the underlying inflammatory profiles of the previously described recovery clusters at 5 months after hospital discharge. Methods The Post-hospitalisation COVID-19 study (PHOSP-COVID) is a prospective, longitudinal cohort study recruiting adults (aged ≥18 years) discharged from hospital with COVID-19 across the UK. Recovery was assessed using patient-reported outcome measures, physical performance, and organ function at 5 months and 1 year after hospital discharge, and stratified by both patient-perceived recovery and recovery cluster. Hierarchical logistic regression modelling was performed for patient-perceived recovery at 1 year. Cluster analysis was done using the clustering large applications k-medoids approach using clinical outcomes at 5 months. Inflammatory protein profiling was analysed from plasma at the 5-month visit. This study is registered on the ISRCTN Registry, ISRCTN10980107, and recruitment is ongoing. Findings 2320 participants discharged from hospital between March 7, 2020, and April 18, 2021, were assessed at 5 months after discharge and 807 (32·7%) participants completed both the 5-month and 1-year visits. 279 (35·6%) of these 807 patients were women and 505 (64·4%) were men, with a mean age of 58·7 (SD 12·5) years, and 224 (27·8%) had received invasive mechanical ventilation (WHO class 7–9). The proportion of patients reporting full recovery was unchanged between 5 months (501 [25·5%] of 1965) and 1 year (232 [28·9%] of 804). Factors associated with being less likely to report full recovery at 1 year were female sex (odds ratio 0·68 [95% CI 0·46–0·99]), obesity (0·50 [0·34–0·74]) and invasive mechanical ventilation (0·42 [0·23–0·76]). Cluster analysis (n=1636) corroborated the previously reported four clusters: very severe, severe, moderate with cognitive impairment, and mild, relating to the severity of physical health, mental health, and cognitive impairment at 5 months. We found increased inflammatory mediators of tissue damage and repair in both the very severe and the moderate with cognitive impairment clusters compared with the mild cluster, including IL-6 concentration, which was increased in both comparisons (n=626 participants). We found a substantial deficit in median EQ-5D-5L utility index from before COVID-19 (retrospective assessment; 0·88 [IQR 0·74–1·00]), at 5 months (0·74 [0·64–0·88]) to 1 year (0·75 [0·62–0·88]), with minimal improvements across all outcome measures at 1 year after discharge in the whole cohort and within each of the four clusters. Interpretation The sequelae of a hospital admission with COVID-19 were substantial 1 year after discharge across a range of health domains, with the minority in our cohort feeling fully recovered. Patient-perceived health-related quality of life was reduced at 1 year compared with before hospital admission. Systematic inflammation and obesity are potential treatable traits that warrant further investigation in clinical trials. Funding UK Research and Innovation and National Institute for Health Research