Parallel minimum norm solution of sparse block diagonal column overlapped underdetermined systems

Underdetermined systems of equations in which the minimum norm solution needs to be computed arise in many applications, such as geophysics, signal processing, and biomedical engineering. In this article, we introduce a new parallel algorithm for obtaining the minimum 2-norm solution of an underdetermined system of equations. The proposed algorithm is based on the Balance scheme, which was originally developed for the parallel solution of banded linear systems. The proposed scheme assumes a generalized banded form where the coefficient matrix has column overlapped block structure in which the blocks could be dense or sparse. In this article, we implement the more general sparse case. The blocks can be handled independently by any existing sequential or parallel QR factorization library. A smaller reduced system is formed and solved before obtaining the minimum norm solution of the original system in parallel. We experimentally compare and confirm the error bound of the proposed method against the QR factorization based techniques by using true single-precision arithmetic. We implement the proposed algorithm by using the message passing paradigm. We demonstrate numerical effectiveness as well as parallel scalability of the proposed algorithm on both shared and distributed memory architectures for solving various types of problems. © 2017 ACM

Short report. The AIDIT and IMPACT conference 2006: Outcomes and future directions

IMPACT (Identification of Men with a genetic predisposition to ProstAte Cancer: Targeted screening in BRCA1/2 mutation carriers and controls) is an international collaboration investigating the utility of targeted prostate-specific antigen (PSA) screening for men at increased risk of prostate cancer due to inherited predisposition. Although the majority of prostate cancer occurs sporadically, it is recognized that family history plays a role in a significant number of cases: a family history either of prostate cancer alone, or of other cancers including breast and ovarian cancer. Evidence of the link between single genes and prostate cancer risk is strongest for the BRCA1 and BRCA2 genes, with BRCA2 in particular thought to lead to a relative risk of 4.65 (95%CI 3.48-6.22). This relative risk may be as high as 7.33 in men under the age of 65 years

Lack of association between RNASEL Arg462Gln variant and the risk of breast cancer

Background: The RNASEL G1385A variant was recently found to be implicated in the development of prostate cancer. Considering the function of RNase L and the pleiotropic effects of mutations associated with cancer, we sought to investigate whether the RNASEL G1385A variant is a risk factor for breast cancer. Patients and Methods: A total of 453 breast cancer patients and 382 age- and sex-matched controls from Greece and Turkey were analyzed. Genotyping for the RNASEL G1385A variant was performed using an Amplification Refractory Mutation System (ARMS). Results: Statistical evaluation of the RNASEL G1385A genotype distribution among breast cancer patients and controls revealed no significant association between the presence of the risk genotype and the occurrence of breast cancer. Conclusion: Although an increasing number of studies report an association between the RNASEL G1385A variant and prostate cancer risk, this variant does not appear to be implicated in the development of breast cancer

Hybrid Solver for Quasi Block Diagonal Linear Systems

We present a solver for a class of sparse linear systems that we call quasi block diagonal. The solver combines multi-processors and multi-threaded parallelisms using MPI and OpenMP to implement preconditioned Jacobi. Specific formats for sparse matrices are exploited in order to reduce memory storage requirements. Our experiments show that communication costs are negligible, so as that speed-up and efficiency with respect to the sequential implementation are very high. Our hybrid implementation is tested on a cluster and compared to Intel MKL PARDISO linear solver

Flux approximation scheme for the incompressible Navier-Stokes equations using local boundary value problems

We present a flux approximation scheme for the incompressible Navier- Stokes equations, that is based on a flux approximation scheme for the scalar advection-diffusion-reaction equation that we developed earlier. The flux is computed from local boundary value problems (BVPs) and is expressed as a sum of a homogeneous and an inhomogeneous part. The homogeneous part depends on the balance of the convective and viscous forces and the inhomogeneous part depends on source terms included in the local BVP

Complete flux scheme for conservation laws containing a linear source

We present an extension of the complete flux scheme for conservation laws containing a linear source. In our new scheme, we split off the linear part of the source and incorporate this term in the homogeneous flux, the remaining nonlinear part is included in the inhomogeneous flux. This approach gives rise to modified homogeneous and inhomogeneous fluxes, which reduce to the classical fluxes for vanishing linear source. On the other hand, if the linear source is large, the solution of the underlying boundary value problem is oscillatory, resulting in completely different numerical fluxes. We demonstrate the performance of the homogeneous flux approximation

Infantile spasms is associated with deletion of the MAGI2 gene on chromosome 7q11.23-q21.11.

Infantile spasms (IS) is the most severe and common form of epilepsy occurring in the first year of life. At least half of IS cases are idiopathic in origin, with others presumed to arise because of brain insult or malformation. Here, we identify a locus for IS by high-resolution mapping of 7q11.23-q21.1 interstitial deletions in patients. The breakpoints delineate a 500 kb interval within the MAGI2 gene (1.4 Mb in size) that is hemizygously disrupted in 15 of 16 participants with IS or childhood epilepsy, but remains intact in 11 of 12 participants with no seizure history. MAGI2 encodes the synaptic scaffolding protein membrane-associated guanylate kinase inverted-2 that interacts with Stargazin, a protein also associated with epilepsy in the stargazer mouse