In this chapter we discuss numerical software for linear algebra problems on parallel computers. We focus on some of the most common numerical operations: linear system solving and eigenvalue computations. Numerical operations such as linear system solving and eigenvalue calculations can be applied to two di erent kinds of matrix: dense and sparse. In dense systems, essentially every matrix ele...

The purpose of this paper is to introduce a class of numerical algorithms designed for rapid application of dense matrices (or integral operators) to vectors. As is well-known, applying directly a dense N×N− matrix to a vector requires roughly N operations, and this simple fact is a cause of serious difficulties encountered in large-scale computations. For example, the main reason for the limit...

Concentration gradients of morphogenic proteins pattern the embryonic axes of Drosophila by activating different genes at different concentrations. The neurogenic ectoderm enhancers (NEEs) activate different genes at different threshold levels of the Dorsal (Dl) morphogen, which patterns the dorsal/ventral axis. NEEs share a unique arrangement of highly constrained DNA-binding sites for Dl, Twi...

Enrichment of FLI1 and RUNX1 mutations in families with excessive bleeding and platelet dense granule secretion defects Jacqueline Stockley, Neil V. Morgan, Danai Bem, Gillian C. Lowe, Marie Lordkipanidzé, Ban Dawood, Michael A. Simpson, Kirsty Macfarlane, Kevin Horner, Vincenzo C. Leo, Katherine Talks, Jayashree Motwani, Jonathan T. Wilde, Peter W. Collins, Michael Makris, Steve P. Watson, and...

cattle syndrome absent in MKs from CHS cattle at all stages of maturation. MKs in bone marrow samples from two control (n = 91) five and two CHS (n = 61 ) cattle that had been processed for were the uranaffin reaction were also evaluated. The clear microsvesicles were replaced by uranaffin-positive granules in in MKs from control cattle. but positive uranaffin granules clear were not observed i...

Abstract Decadal changes in land use/land cover for Balachaur watershed in Nawanshahar district, Punjab, India were studied using black and white aerial photographs for March 1984 on approximately 1:20,000 scale and multidate geocoded false colour composites (FCC) of IRS-1D LISS-III on 1:50,000 scale for March 2002, September 2002, and May 2003 and interpreted visually to prepare land use/land...

Pietro Corvaja §1 Introduction. A general principle in the theory of diophantine equations asserts that if an equation admits " many " rational solutions, there should be a geometric reason explaining such abundance. We consider here a (multiplicative) semigroup of N ×N matrices with rational entries: we suppose that all of them admit rational eigenvalues and deduce the natural geometrical cons...

Random graph theory is used to examine the “smallworld phenomenon” – any two strangers are connected through a short chain of mutual acquaintances. We will show that for certain families of random graphs with given expected degrees, the average distance is almost surely of order log n/ log d̃ where d̃ is the weighted average of the sum of squares of the expected degrees. Of particular interest ar...

In many communities there is an elite, a relatively small group of participants that is well connected and highly influential. In order to understand the whole community and the underlying mechanisms it is hence very helpful to study the characteristics and the emergence of the elite. In the past it has been shown that various social networks exhibit surprisingly similar properties, like power ...