After a brief description of the Z-graded differential Poisson algebra, we introduce a covariant star product for exterior differential forms and give an explicit expression for it up to second order in the deformation parameter , in the case of symplectic manifolds. The graded differential Poisson algebra endows the manifold with a connection, not necessarily torsion-free, and places upon the connection various constraints.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) enters human host cells via angiotensin-converting enzyme 2 (ACE2) and causes coronavirus disease 2019 (COVID-19). Here, through a genome-wide association study, we identify a variant (rs190509934, minor allele frequency 0.2–2%) that downregulates ACE2 expression by 37% (P = 2.7 × 10−8) and reduces the risk of SARS-CoV-2 infection by 40% (odds ratio = 0.60, P = 4.5 × 10−13), providing human genetic evidence that ACE2 expression levels influence COVID-19 risk. We also replicate the associations of six previously reported risk variants, of which four were further associated with worse outcomes in individuals infected with the virus (in/near LZTFL1, MHC, DPP9 and IFNAR2). Lastly, we show that common variants define a risk score that is strongly associated with severe disease among cases and modestly improves the prediction of disease severity relative to demographic and clinical factors alone.

Human infection with SARS-CoV-2, the causative agent of COVID-19, leads to a remarkably diverse spectrum of outcomes, ranging from asymptomatic to fatal. Recent reports suggest that both clinical and genetic risk factors may contribute to COVID-19 susceptibility and severity. To investigate genetic risk factors, we collected over 500,000 COVID-19 survey responses between April and May 2020 with accompanying genetic data from the AncestryDNA database. We conducted sex-stratified and meta-analyzed genome-wide association studies (GWAS) for COVID-19 susceptibility (positive nasopharyngeal swab test, ncases=2,407) and severity (hospitalization, ncases=250). The severity GWAS replicated associations with severe COVID-19 near ABO and SLC6A20 (P<0.05). Furthermore, we identified three novel loci with P<5x10-8. The strongest association was near IVNS1ABP, a gene involved in influenza virus replication, and was associated only in males. The other two novel loci harbor genes with established roles in viral replication or immunity: SRRM1 and the immunoglobulin lambda locus. We thus present new evidence that host genetic variation likely contributes to COVID-19 outcomes and demonstrate the value of large-scale, self-reported data as a mechanism to rapidly address a health crisis.

Data availabilitySummary statistics generated by COVID-19 Host Genetics Initiative are available online (https://www.covid19hg.org/results/r6/). The analyses described here use the freeze 6 data. The COVID-19 Host Genetics Initiative continues to regularly release new data freezes. Summary statistics for samples from individuals of non-European ancestry are not currently available owing to the small individual sample sizes of these groups, but the results for 23 loci lead variants are reported in Supplementary Table 3. Individual-level data can be requested directly from the authors of the contributing studies, listed in Supplementary Table 1.

Multiple COVID-19 genome-wide association studies (GWASs) have identified reproducible genetic associations indicating that there is a genetic component to susceptibility and severity risk. To complement these studies, we collected deep coronavirus disease 2019 (COVID-19) phenotype data from a survey of 736,723 AncestryDNA research participants. With these data, we defined eight phenotypes related to COVID-19 outcomes: four phenotypes that align with previously studied COVID-19 definitions and four 'expanded' phenotypes that focus on susceptibility given exposure, mild clinical manifestations and an aggregate score of symptom severity. We performed a replication analysis of 12 previously reported COVID-19 genetic associations with all eight phenotypes in a trans-ancestry meta-analysis of AncestryDNA research participants. In this analysis, we show distinct patterns of association at the 12 loci with the eight outcomes that we assessed. We also performed a genome-wide discovery analysis of all eight phenotypes, which did not yield new genome-wide significant loci but did suggest that three of the four 'expanded' COVID-19 phenotypes have enhanced power to capture protective genetic associations relative to the previously studied phenotypes. Thus, we conclude that continued large-scale ascertainment of deep COVID-19 phenotype data would likely represent a boon for COVID-19 therapeutic target identification.