Bunch-Kaufman factorization for real symmetric indefinite banded matrices

The Bunch-Kaufman algorithm for factoring symmetric indefinite matrices was rejected for banded matrices because it destroys the banded structure of the matrix. Herein, it is shown that for a subclass of real symmetric matrices which arise in solving the generalized eigenvalue problem using Lanczos's method, the Bunch-Kaufman algorithm does not result in major destruction of the bandwidth. Space time complexities of the algorithm are given and used to show that the Bunch-Kaufman algorithm is a significant improvement over LU factorization

The use of Lanczos's method to solve the large generalized symmetric definite eigenvalue problem

The generalized eigenvalue problem, Kx = Lambda Mx, is of significant practical importance, especially in structural enginering where it arises as the vibration and buckling problem. A new algorithm, LANZ, based on Lanczos's method is developed. LANZ uses a technique called dynamic shifting to improve the efficiency and reliability of the Lanczos algorithm. A new algorithm for solving the tridiagonal matrices that arise when using Lanczos's method is described. A modification of Parlett and Scott's selective orthogonalization algorithm is proposed. Results from an implementation of LANZ on a Convex C-220 show it to be superior to a subspace iteration code

A language comparison for scientific computing on MIMD architectures

Choleski's method for solving banded symmetric, positive definite systems is implemented on a multiprocessor computer using three FORTRAN based parallel programming languages, the Force, PISCES and Concurrent FORTRAN. The capabilities of the language for expressing parallelism and their user friendliness are discussed, including readability of the code, debugging assistance offered, and expressiveness of the languages. The performance of the different implementations is compared. It is argued that PISCES, using the Force for medium-grained parallelism, is the appropriate choice for programming Choleski's method on the multiprocessor computer, Flex/32

Helicobacter pylori-Induced Histone Modification, Associated Gene Expression in Gastric Epithelial Cells, and Its Implication in Pathogenesis

Histone modifications are critical in regulating gene expression, cell cycle, cell proliferation, and development. Relatively few studies have investigated whether Helicobacter pylori, the major cause of human gastric diseases, affects histone modification. We therefore investigated the effects of H. pylori infection on histone modifications in a global and promoter-specific manner in gastric epithelial cells. Infection of gastric epithelial cells by wild-type H. pylori induced time- and dose-dependent dephosphorylation of histone H3 at serine 10 (H3 Ser10) and decreased acetylation of H3 lysine 23, but had no effects on seven other specific modifications. Different cag pathogenicity island (PAI)-containing-clinical isolates showed similar abilities to induce H3 Ser10 dephosphorylation. Mutation of cagA, vacA, nonphosphorylateable CagA mutant cagAEPISA, or disruption of the flagella showed no effects, while deletion of the entire cagPAI restored the H3 Ser10 phosphorylation to control levels. Analysis of 27 cagPAI mutants indicated that the genes that caused H3 Ser10 dephosphorylation were similar to those that were previously found to induce interleukin-8, irrespective of CagA translocation. This effect was independent of ERK or p38 pathways and type I interferon signaling. Additionally, c-Jun and hsp70 gene expression was associated with this histone modification. These results demonstrate that H. pylori alters histone modification and host response via a cagA-, vacA-independent, but cagPAI-dependent mechanisms, which contribute to its persistent infection and pathogenesis

Data Traffic Reduction Schemes for Cholesky Factorization on Asynchronous Multiprocessor Systems

Communication requirements of Cholesky factorization of dense and sparse symmetric, positive definite matrices are analyzed. The communication requirement is characterized by the data traffic generated on multiprocessor systems with local and shared memory. Lower bound proofs are given to show that when the load is uniformly distributed the data traffic associated with factoring an n x n dense matrix using n to the alpha power (alpha less than or equal 2) processors is omega(n to the 2 + alpha/2 power). For n x n sparse matrices representing a square root of n x square root of n regular grid graph the data traffic is shown to be omega(n to the 1 + alpha/2 power), alpha less than or equal 1. Partitioning schemes that are variations of block assignment scheme are described and it is shown that the data traffic generated by these schemes are asymptotically optimal. The schemes allow efficient use of up to O(n to the 2nd power) processors in the dense case and up to O(n) processors in the sparse case before the total data traffic reaches the maximum value of O(n to the 3rd power) and O(n to the 3/2 power), respectively. It is shown that the block based partitioning schemes allow a better utilization of the data accessed from shared memory and thus reduce the data traffic than those based on column-wise wrap around assignment schemes