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We consider compact Riemannian spin manifolds without boundary equipped with orthogonal connections. We investigate the induced Dirac operators and the associated commutative spectral triples. In case of dimension four and totally anti-symmetric torsion we compute the Chamseddine-Connes spectral action, deduce the equations of motions and discuss critical points.
Rapid decline of glomerular filtration rate estimated from creatinine (eGFRcrea) is associated with severe clinical endpoints. In contrast to cross-sectionally assessed eGFRcrea, the genetic basis for rapid eGFRcrea decline is largely unknown. To help define this, we meta-analyzed 42 genome-wide association studies from the Chronic Kidney Diseases Genetics Consortium and United Kingdom Biobank to identify genetic loci for rapid eGFRcrea decline. Two definitions of eGFRcrea decline were used: 3 mL/min/1.73m(2)/year or more ("Rapid3"; encompassing 34,874 cases, 107,090 controls) and eGFRcrea decline 25% or more and eGFRcrea under 60 mL/min/1.73m(2) at follow-up among those with eGFRcrea 60 mL/min/1.73m(2) or more at baseline ("CKDi25"; encompassing 19,901 cases, 175,244 controls). Seven independent variants were identified across six loci for Rapid3 and/or CKDi25: consisting of five variants at four loci with genome-wide significance (near UMOD-PDILT (2), PRKAG2, WDR72, OR2S2) and two variants among 265 known eGFRcrea variants (near GATM, LARP4B). All these loci were novel for Rapid3 and/or CKDi25 and our bioinformatic follow-up prioritized variants and genes underneath these loci. The OR2S2 locus is novel for any eGFRcrea trait including interesting candidates. For the five genome-wide significant lead variants, we found supporting effects for annual change in blood urea nitrogen or cystatin-based eGFR, but not for GATM or (LARP4B). Individuals at high compared to those at low genetic risk (8-14 vs. 0-5 adverse alleles) had a 1.20-fold increased risk of acute kidney injury (95% confidence interval 1.08-1.33). Thus, our identified loci for rapid kidney function decline may help prioritize therapeutic targets and identify mechanisms and individuals at risk for sustained deterioration of kidney function.
We consider orthogonal connections with arbitrary torsion on compact Riemannian manifolds. For the induced Dirac operators, twisted Dirac operators and Dirac operators of Chamseddine-Connes type we compute the spectral action. In addition to the Einstein-Hilbert action and the bosonic part of the Standard Model Lagrangian we find the Holst term from Loop Quantum Gravity, a coupling of the Holst term to the scalar curvature and a prediction for the value of the Barbero-Immirzi parameter.