The Ext algebra and a new generalisation of D-Koszul algebras

We generalise Koszul and D-Koszul algebras by introducing a class of graded algebras called (D,A)-stacked algebras. We give a characterisation of (D,A)-stacked algebras and show that their Ext algebra is finitely generated as an algebra in degrees 0, 1, 2 and 3. In the monomial case, we give an explicit description of the Ext algebra by quiver and relations, and show that the ideal of relations has a quadratic Gr\"obner basis; this enables us to give a regrading of the Ext algebra under which the regraded Ext algebra is a Koszul algebra.Comment: New title; minor changes; 25 page

Multiple novel prostate cancer susceptibility signals identified by fine-mapping of known risk loci among Europeans

Genome-wide association studies (GWAS) have identified numerous common prostate cancer (PrCa) susceptibility loci. We have fine-mapped 64 GWAS regions known at the conclusion of the iCOGS study using large-scale genotyping and imputation in 25 723 PrCa cases and 26 274 controls of European ancestry. We detected evidence for multiple independent signals at 16 regions, 12 of which contained additional newly identified significant associations. A single signal comprising a spectrum of correlated variation was observed at 39 regions; 35 of which are now described by a novel more significantly associated lead SNP, while the originally reported variant remained as the lead SNP only in 4 regions. We also confirmed two association signals in Europeans that had been previously reported only in East-Asian GWAS. Based on statistical evidence and linkage disequilibrium (LD) structure, we have curated and narrowed down the list of the most likely candidate causal variants for each region. Functional annotation using data from ENCODE filtered for PrCa cell lines and eQTL analysis demonstrated significant enrichment for overlap with bio-features within this set. By incorporating the novel risk variants identified here alongside the refined data for existing association signals, we estimate that these loci now explain ∼38.9% of the familial relative risk of PrCa, an 8.9% improvement over the previously reported GWAS tag SNPs. This suggests that a significant fraction of the heritability of PrCa may have been hidden during the discovery phase of GWAS, in particular due to the presence of multiple independent signals within the same regio

Finite Generation of Ext and (D,A)-stacked Algebras

We introduce the class of (D,A)-stacked algebras, which generalise the classes of Koszul algebras, d-Koszul algebras and (D,A)-stacked monomial algebras. We show that the Ext algebra of a (D,A)-stacked algebra is finitely generated in degrees 0, 1, 2 and 3. After investigating some general properties of E(Ʌ) for this class of algebras, we look at a regrading of E(Ʌ) and give examples for which the regraded Ext algebra is a Koszul algebra. Following this we give a general construction of a (D,A)-stacked algebra ~Ʌ from a d-Koszul algebra Ʌ, setting D = dA, with A ≥ 1. From this construction we relate the homological properties of ~Ʌ and Ʌ, including the projective resolutions and the structure of the Ext algebra

Identification of seven new prostate cancer susceptibility loci through a genome-wide association study

Prostate cancer (PrCa) is the most frequently diagnosed male cancer in developed countries. To identify common PrCa susceptibility alleles, we have previously conducted a genome-wide association study in which 541, 129 SNPs were genotyped in 1,854 PrCa cases with clinically detected disease and 1,894 controls. We have now evaluated promising associations in a second stage, in which we genotyped 43,671 SNPs in 3,650 PrCa cases and 3,940 controls, and a third stage, involving an additional 16,229 cases and 14,821 controls from 21 studies. In addition to previously identified loci, we identified a further seven new prostate cancer susceptibility loci on chromosomes 2, 4, 8, 11, and 22 (P=1.6×10−8 to P=2.7×10−33)

Multiple loci on 8q24 associated with prostate cancer susceptibility

Previous studies have identified multiple loci on 8q24 associated with prostate cancer risk. We performed a comprehensive analysis of SNP associations across 8q24 by genotyping tag SNPs in 5,504 prostate cancer cases and 5,834 controls. We confirmed associations at three previously reported loci and identified additional loci in two other linkage disequilibrium blocks (rs1006908: per-allele OR = 0.87, P = 7.9 x 10(-8); rs620861: OR = 0.90, P = 4.8 x 10(-8)). Eight SNPs in five linkage disequilibrium blocks were independently associated with prostate cancer susceptibility

Whole-genome sequencing reveals host factors underlying critical COVID-19

Altres ajuts: Department of Health and Social Care (DHSC); Illumina; LifeArc; Medical Research Council (MRC); UKRI; Sepsis Research (the Fiona Elizabeth Agnew Trust); the Intensive Care Society, Wellcome Trust Senior Research Fellowship (223164/Z/21/Z); BBSRC Institute Program Support Grant to the Roslin Institute (BBS/E/D/20002172, BBS/E/D/10002070, BBS/E/D/30002275); UKRI grants (MC_PC_20004, MC_PC_19025, MC_PC_1905, MRNO2995X/1); UK Research and Innovation (MC_PC_20029); the Wellcome PhD training fellowship for clinicians (204979/Z/16/Z); the Edinburgh Clinical Academic Track (ECAT) programme; the National Institute for Health Research, the Wellcome Trust; the MRC; Cancer Research UK; the DHSC; NHS England; the Smilow family; the National Center for Advancing Translational Sciences of the National Institutes of Health (CTSA award number UL1TR001878); the Perelman School of Medicine at the University of Pennsylvania; National Institute on Aging (NIA U01AG009740); the National Institute on Aging (RC2 AG036495, RC4 AG039029); the Common Fund of the Office of the Director of the National Institutes of Health; NCI; NHGRI; NHLBI; NIDA; NIMH; NINDS.Critical COVID-19 is caused by immune-mediated inflammatory lung injury. Host genetic variation influences the development of illness requiring critical care or hospitalization after infection with SARS-CoV-2. The GenOMICC (Genetics of Mortality in Critical Care) study enables the comparison of genomes from individuals who are critically ill with those of population controls to find underlying disease mechanisms. Here we use whole-genome sequencing in 7,491 critically ill individuals compared with 48,400 controls to discover and replicate 23 independent variants that significantly predispose to critical COVID-19. We identify 16 new independent associations, including variants within genes that are involved in interferon signalling (IL10RB and PLSCR1), leucocyte differentiation (BCL11A) and blood-type antigen secretor status (FUT2). Using transcriptome-wide association and colocalization to infer the effect of gene expression on disease severity, we find evidence that implicates multiple genes-including reduced expression of a membrane flippase (ATP11A), and increased expression of a mucin (MUC1)-in critical disease. Mendelian randomization provides evidence in support of causal roles for myeloid cell adhesion molecules (SELE, ICAM5 and CD209) and the coagulation factor F8, all of which are potentially druggable targets. Our results are broadly consistent with a multi-component model of COVID-19 pathophysiology, in which at least two distinct mechanisms can predispose to life-threatening disease: failure to control viral replication; or an enhanced tendency towards pulmonary inflammation and intravascular coagulation. We show that comparison between cases of critical illness and population controls is highly efficient for the detection of therapeutically relevant mechanisms of disease