Matrix-vector multiplication and triangular linear solver using GPGPU for symmetric positive definite matrices derived from elliptic equations

The modern GPUs are well suited for intensive computational tasks and massive parallel computation. Sparse matrix multiplication and linear triangular solver are the most important and heavily used kernels in scientific computation, and several challenges in developing a high performance kernel with the two modules is investigated. The main interest it to solve linear systems derived from the elliptic equations with triangular elements. The resulting linear system has a symmetric positive definite matrix. The sparse matrix is stored in the compressed sparse row (CSR) format. It is proposed a CUDA algorithm to execute the matrix vector multiplication using directly the CSR format. A dependence tree algorithm is used to determine which variables the linear triangular solver can determine in parallel. To increase the number of the parallel threads, a coloring graph algorithm is implemented to reorder the mesh numbering in a pre-processing phase. The proposed method is compared with parallel and serial available libraries. The results show that the proposed method improves the computation cost of the matrix vector multiplication. The pre-processing associated with the triangular solver needs to be executed just once in the proposed method. The conjugate gradient method was implemented and showed similar convergence rate for all the compared methods. The proposed method showed significant smaller execution time.

Differentiability of bizonal positive definite kernels on complex spheres

We prove that any continuous function with domain {z ∈ C: |z| ≤ 1} that generates a bizonal positive definite kernel on the unit sphere in 'C POT.Q' , q ⩾ 3, is continuously differentiable in {z ∈ C: |z| < 1} up to order q − 2, with respect to both z and 'Z BARRA'. In particular, the partial derivatives of the function with respect to x = Re z and y = Im z exist and are continuous in {z ∈ C: |z| < 1} up to the same order.

Workplace drug testing, different matrices different objectives

Drug testing is used by employers to detect drug use by employees or job candidates. It can identify recent use of alcohol, prescription drugs, and illicit drugs as a screening tool for potential health and safety and performance issues. Urine is the most commonly used sample for illicit drugs. It detects the use of a drug within the last few days and as such is evidence of recent use; but a positive test does not necessarily mean that the individual was impaired at the time of the test. Abstention from use for three days will often produce a negative test result. Analysis of hair provides a much longer window of detection, typically 1 to 3 months. Hence the likelihood of a falsely negative test using hair is very much less than with a urine test. Conversely, a negative hair test is a substantially stronger indicator of a non-drug user than a negative urine test. Oral fluid (saliva) is also easy to collect. Drugs remain in oral fluid for a similar time as in blood. The method is a good way of detecting current use and is more likely to reflect current impairment. It offers promise as a test in post-accident, for cause, and on-duty situations. Studies have shown that within the same industrial settings, hair testing can detect twice as many drug users as urine testing. Copyright (C) 2012 John Wiley & Sons, Ltd.