An Asymptotically Optimal Minimum Degree Ordering of Regular Grids

It has previously been shown that there exists a minimum degree ordering for regular grids that is considerably worse than nested dissection in terms of fill-in and operations for factorization [1]. This paper proves the existence of a minimum degree ordering for regular grids that has the same optimal asymptotic order complexity for fill-in and operation count as nested dissection. The analysis is verified by showing exact match between analytical prediction and experimental measurement. The analysis motivates a peripheral preordering strategy for use with the popular multiple minimum degree (MMD) algorithm, and is shown to consistently reduce fill-in and operation count for regular grids. Keywords: Sparse Matrices, Finite Element Grids, Minimum Degree Ordering, Computational Complexity. AMS(MOS) subject classifications: 65F05, 65F50, 68R10 1 Introduction The solution of large sparse systems of equations is commonly required in many scientific and engineering applications such as C..

A Tensor Product Formulation of Strassen's Matrix Multiplication Algorithm

In this paper, we present a program generation strategy of Strassen's matrix multiplication algorithm using a programming methodology based on tensor product formulas. In this methodology, block recursive programs such as the fast Fourier Transforms and Strassen's matrix multiplication algorithm are expressed as algebraic formulas involving tensor products and other matrix operations. Such formulas can be systematically translated to high-performance parallel/vector codes for various architectures. In this paper, we present a non-recursive implementation of Strassen's algorithm for shared memory vector processors such as the Cray Y-MP. A previous implementation of Strassen's algorithm synthesized from tensor product formulas required working storage of size O(7 n ) for multiplying 2 n \Theta 2 n matrices. We present a modified formulation in which the working storage requirement is reduced to O(4 n ). The modified formulation exhibits sufficient parallelism for efficient implem..

Myofilament Alterations Associated with Human R14del-Phospholamban Cardiomyopathy

Phospholamban (PLN) is a major regulator of cardiac contractility, and human mutations in this gene give rise to inherited cardiomyopathies. The deletion of Arginine 14 is the most-prevalent cardiomyopathy-related mutation, and it has been linked to arrhythmogenesis and early death. Studies in PLN-humanized mutant mice indicated an increased propensity to arrhythmias, but the underlying cellular mechanisms associated with R14del-PLN cardiac dysfunction in the absence of any apparent structural remodeling remain unclear. The present study addressed the specific role of myofilaments in the setting of R14del-PLN and the long-term effects of R14del-PLN in the heart. Maximal force was depressed in skinned cardiomyocytes from both left and right ventricles, but this effect was more pronounced in the right ventricle of R14del-PLN mice. In addition, the Ca2+ sensitivity of myofilaments was increased in both ventricles of mutant mice. However, the depressive effects of R14del-PLN on contractile parameters could be reversed with the positive inotropic drug omecamtiv mecarbil, a myosin activator. At 12 months of age, corresponding to the mean symptomatic age of R14del-PLN patients, contractile parameters and Ca2+ transients were significantly depressed in the right ventricular R14del-PLN cardiomyocytes. Echocardiography did not reveal any alterations in cardiac function or remodeling, although histological and electron microscopy analyses indicated subtle alterations in mutant hearts. These findings suggest that both aberrant myocyte calcium cycling and aberrant contractility remain specific to the right ventricle in the long term. In addition, altered myofilament activity is an early characteristic of R14del-PLN mutant hearts and the positive inotropic drug omecamtiv mecarbil may be beneficial in treating R14del-PLN cardiomyopathy