Adaptive Finite Element Approximations for Kohn-Sham Models

The Kohn-Sham equation is a powerful, widely used approach for computation of ground state electronic energies and densities in chemistry, materials science, biology, and nanosciences. In this paper, we study the adaptive finite element approximations for the Kohn-Sham model. Based on the residual type a posteriori error estimators proposed in this paper, we introduce an adaptive finite element algorithm with a quite general marking strategy and prove the convergence of the adaptive finite element approximations. Using D{\" o}rfler's marking strategy, we then get the convergence rate and quasi-optimal complexity. We also carry out several typical numerical experiments that not only support our theory,but also show the robustness and efficiency of the adaptive finite element computations in electronic structure calculations.Comment: 38pages, 7figure

Dissecting the causal effect between gut microbiota, DHA, and urate metabolism: A large-scale bidirectional Mendelian randomization

ObjectivesOur aim was to investigate the interactive causal effects between gut microbiota and host urate metabolism and explore the underlying mechanism using genetic methods.MethodsWe extracted summary statistics from the abundance of 211 microbiota taxa from the MiBioGen (N =18,340), 205 microbiota metabolism pathways from the Dutch Microbiome Project (N =7738), gout from the Global Biobank Meta-analysis Initiative (N =1,448,128), urate from CKDGen (N =288,649), and replication datasets from the Global Urate Genetics Consortium (N gout =69,374; N urate =110,347). We used linkage disequilibrium score regression and bidirectional Mendelian randomization (MR) to detect genetic causality between microbiota and gout/urate. Mediation MR and colocalization were performed to investigate potential mediators in the association between microbiota and urate metabolism.ResultsTwo taxa had a common causal effect on both gout and urate, whereas the Victivallaceae family was replicable. Six taxa were commonly affected by both gout and urate, whereas the Ruminococcus gnavus group genus was replicable. Genetic correlation supported significant results in MR. Two microbiota metabolic pathways were commonly affected by gout and urate. Mediation analysis indicated that the Bifidobacteriales order and Bifidobacteriaceae family had protective effects on urate mediated by increasing docosahexaenoic acid. These two bacteria shared a common causal variant rs182549 with both docosahexaenoic acid and urate, which was located within MCM6/LCT locus.ConclusionsGut microbiota and host urate metabolism had a bidirectional causal association, implicating the critical role of host-microbiota crosstalk in hyperuricemic patients. Changes in gut microbiota can not only ameliorate host urate metabolism but also become a foreboding indicator of urate metabolic diseases

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements