Preconditioning techniques for the coupled Stokes–Darcy problem: spectral and field-of-values analysis

We study the performance of some preconditioning techniques for a class of block three-by-three linear systems of equations arising from finite element discretizations of the coupled Stokes–Darcy flow problem. In particular, we investigate preconditioning techniques including block preconditioners, constraint preconditioners, and augmented Lagrangian-based ones. Spectral and field-of-value analyses are established for the exact versions of these preconditioners. The result of numerical experiments are reported to illustrate the performance of inexact variants of the various preconditioners used with flexible GMRES in the solution of a 3D test problem with large jumps in the permeability

Genetic and Epigenetic Fine-Mapping of Causal Autoimmune Disease Variants

Summary Genome-wide association studies have identified loci underlying human diseases, but the causal nucleotide changes and mechanisms remain largely unknown. Here we developed a fine-mapping algorithm to identify candidate causal variants for 21 autoimmune diseases from genotyping data. We integrated these predictions with transcription and cis-regulatory element annotations, derived by mapping RNA and chromatin in primary immune cells, including resting and stimulated CD4+ T-cell subsets, regulatory T-cells, CD8+ T-cells, B-cells, and monocytes. We find that ~90% of causal variants are noncoding, with ~60% mapping to immune-cell enhancers, many of which gain histone acetylation and transcribe enhancer-associated RNA upon immune stimulation. Causal variants tend to occur near binding sites for master regulators of immune differentiation and stimulus-dependent gene activation, but only 10–20% directly alter recognizable transcription factor binding motifs. Rather, most noncoding risk variants, including those that alter gene expression, affect non-canonical sequence determinants not well-explained by current gene regulatory models