Semigroup expansions using the derived category, kernel, and Malcev products

AbstractThree new classes of expansions are defined in this paper. More precisely, three different expansions are associated to each semigroup variety V. It is shown that several previously defined expansions can be viewed as specific examples of these constructions, or slight variants there of. This method is then used to “smooth” an already existing expansion to one which is guaranteed to be functorial and is maximal in a sense that will be made precise. Perhaps more importantly, this method of construction provides a large resource of expansions to be used as needed in the future

Holonomy Embedding for Arbitrary Stable Semigroups

Original article can be found at: http://ejournals.wspc.com.sg/journals/ijac/mkt/archive.shtml Copyright World Scientific Publishing Company. DOI: 10.1142/S0218196702001206 [Full text of this article is not available in the UHRA]We show how the Rhodes expansion Ŝ of any stable semigroup S embeds into the cascade integral (a natural generalization of the wreath product) of permutation-reset transformation semigroups with zero adjoined. The permutation groups involved are exactly the Schützenberger groups of the -classes of S. Since S ←← Ŝ is an aperiodic map via which all subgroups of S lift to Ŝ, this results in a strong Krohn–Rhodes–Zeiger decomposition for the entire class of stable semigroups. This class includes all semigroups that are finite, torsion, finite -above, compact Hausdorff, or relatively free profinite, as well as many other semigroups. Even if S is not stable, one can expand it using Henckell's expansion and then apply our embedding. This gives a simplified proof of the Holonomy Embedding theorem for all semigroups.Peer reviewe

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