Soliton solutions of noncommutative anti-self-dual Yang-Mills equations

We present exact soliton solutions of anti-self-dual Yang-Mills equations for G = GL(N) on noncommutative Euclidean spaces in four-dimension by using the Darboux transformations. Generated solutions are represented by quasideterminants of Wronski matrices in compact forms. We give special one-soliton solutions for G = GL(2) whose energy density can be real-valued. We find that the soliton solutions are the same as the commutative ones and can be interpreted as one-domain walls in four-dimension. Scattering processes of the multi-soliton solutions are also discussed

On a generalized noncommutative three-dimensional three wave resonant equation

A noncommutative version of a generalized three-dimensional three wave resonant (3D3WR) equation is presented. In the commutative case, the generalized noncommutative 3D3WR equation and its Lax pair can be transformed into the 3D3WR equations and its corresponding Lax pair due to a coordinate transformation. The Lax pair for the generalized 3D3WR equation enables us to find Darboux transformations and binary Darboux transformations easily, which are used to construct two families of quasideterminant solutions

Genome-wide and fine-resolution association analysis of malaria in West Africa

We report a genome-wide association (GWA) study of severe malaria in The Gambia. The initial GWA scan included 2,500 children genotyped on the Affymetrix 500K GeneChip, and a replication study included 3,400 children. We used this to examine the performance of GWA methods in Africa. We found considerable population stratification, and also that signals of association at known malaria resistance loci were greatly attenuated owing to weak linkage disequilibrium (LD). To investigate possible solutions to the problem of low LD, we focused on the HbS locus, sequencing this region of the genome in 62 Gambian individuals and then using these data to conduct multipoint imputation in the GWA samples. This increased the signal of association, from P = 4 × 10(-7) to P = 4 × 10(-14), with the peak of the signal located precisely at the HbS causal variant. Our findings provide proof of principle that fine-resolution multipoint imputation, based on population-specific sequencing data, can substantially boost authentic GWA signals and enable fine mapping of causal variants in African populations