Genetic studies of blood pressure (BP) to date have mainly analyzed common variants (minor allele frequency > 0.05). In a meta-analysis of up to similar to 1.3 million participants, we... Show moreGenetic studies of blood pressure (BP) to date have mainly analyzed common variants (minor allele frequency > 0.05). In a meta-analysis of up to similar to 1.3 million participants, we discovered 106 new BP-associated genomic regions and 87 rare (minor allele frequency <= 0.01) variant BP associations (P < 5 x 10(-8)), of which 32 were in new BP-associated loci and 55 were independent BP-associated single-nucleotide variants within known BP-associated regions. Average effects of rare variants (44% coding) were similar to 8 times larger than common variant effects and indicate potential candidate causal genes at new and known loci (for example, GATA5 and PLCB3). BP-associated variants (including rare and common) were enriched in regions of active chromatin in fetal tissues, potentially linking fetal development with BP regulation in later life. Multivariable Mendelian randomization suggested possible inverse effects of elevated systolic and diastolic BP on large artery stroke. Our study demonstrates the utility of rare-variant analyses for identifying candidate genes and the results highlight potential therapeutic targets. Show less
Since its formulation by Sir Isaac Newton, the problem of solving the equations of motion for three bodies under their own gravitational force has remained practically unsolved. Currently, the... Show moreSince its formulation by Sir Isaac Newton, the problem of solving the equations of motion for three bodies under their own gravitational force has remained practically unsolved. Currently, the solution for a given initialization can only be found by performing laborious iterative calculations that have unpredictable and potentially infinite computational cost, due to the system’s chaotic nature. We show that an ensemble of converged solutions for the planar chaotic three-body problem obtained using an arbitrarily precise numerical integrator can be used to train a deep artificial neural network (ANN) that, over a bounded time interval, provides accurate solutions at a fixed computational cost and up to 100 million times faster than the numerical integrator. In addition, we demonstrate the importance of training an ANN using converged solutions from an arbitrary precise integrator, relative to solutions computed by a conventional fixed precision integrator, which can introduce errors in the training data, due to numerical round-off and time discretization, that are learned by the ANN. Our results provide evidence that, for computationally challenging regions of phase space, a trained ANN can replace existing numerical solvers, enabling fast and scalable simulations of many-body systems to shed light on outstanding phenomena such as the formation of black hole binary systems or the origin of the core collapse in dense star clusters. Show less
