7 research outputs found
Error analysis of truncated expansion solutions to high-dimensional parabolic PDEs
We study an expansion method for high-dimensional parabolic PDEs which
constructs accurate approximate solutions by decomposition into solutions to
lower-dimensional PDEs, and which is particularly effective if there are a low
number of dominant principal components. The focus of the present article is
the derivation of sharp error bounds for the constant coefficient case and a
first and second order approximation. We give a precise characterisation when
these bounds hold for (non-smooth) option pricing applications and provide
numerical results demonstrating that the practically observed convergence speed
is in agreement with the theoretical predictions
Association analyses of more than 140,000 men identify 63 new prostate cancer susceptibility loci.
Genome-wide association studies (GWAS) and fine-mapping efforts to date have identified more than 100 prostate cancer (PrCa)-susceptibility loci. We meta-analyzed genotype data from a custom high-density array of 46,939 PrCa cases and 27,910 controls of European ancestry with previously genotyped data of 32,255 PrCa cases and 33,202 controls of European ancestry. Our analysis identified 62 novel loci associated (P C, p.Pro1054Arg) in ATM and rs2066827 (OR = 1.06; P = 2.3 × 10-9; T>G, p.Val109Gly) in CDKN1B. The combination of all loci captured 28.4% of the PrCa familial relative risk, and a polygenic risk score conferred an elevated PrCa risk for men in the ninetieth to ninety-ninth percentiles (relative risk = 2.69; 95% confidence interval (CI): 2.55-2.82) and first percentile (relative risk = 5.71; 95% CI: 5.04-6.48) risk stratum compared with the population average. These findings improve risk prediction, enhance fine-mapping, and provide insight into the underlying biology of PrCa1