Improving Inversions of the Overlap Operator

We present relaxation and preconditioning techniques which accelerate the inversion of the overlap operator by a factor of four on small lattices, with larger gains as the lattice size increases. These improvements can be used in both propagator calculations and dynamical simulations.Comment: lattice2004(machines

Numerical Methods for the QCD Overlap Operator: I. Sign-Function and Error Bounds

The numerical and computational aspects of the overlap formalism in lattice quantum chromodynamics are extremely demanding due to a matrix-vector product that involves the sign function of the hermitian Wilson matrix. In this paper we investigate several methods to compute the product of the matrix sign-function with a vector, in particular Lanczos based methods and partial fraction expansion methods. Our goal is two-fold: we give realistic comparisons between known methods together with novel approaches and we present error bounds which allow to guarantee a given accuracy when terminating the Lanczos method and the multishift-CG solver, applied within the partial fraction expansion methods.Comment: 30 pages, 2 figure

A comparative study of numerical methods for the overlap Dirac operator--a status report

Improvements of various methods to compute the sign function of the hermitian Wilson-Dirac matrix within the overlap operator are presented. An optimal partial fraction expansion (PFE) based on a theorem of Zolotarev is given. Benchmarks show that this PFE together with removal of converged systems within a multi-shift CG appears to approximate the sign function times a vector most efficiently. A posteriori error bounds are given.Comment: 3 pages, poster contribution to Lattice2001(algorithms

A Mutation in Amino Acid Permease AAP6 Reduces the Amino Acid Content of the Arabidopsis Sieve Elements but Leaves Aphid Herbivores Unaffected.

The aim of this study was to investigate the role of the amino acid permease gene AAP6 in regulating phloem amino acid composition and then to determine the effects of this altered diet on aphid performance. A genotype of Arabidopsis thaliana (L.) was produced in which the function of the amino acid permease gene AAP6 (At5g49630) was abolished. Plants homozygous for the insertionally inactivated AAP6 gene had a significantly larger mean rosette width than the wild type and a greater number of cauline leaves. Seeds from the aap6 mutant were also significantly larger than those from the wild-type plants. Sieve element (SE) sap was collected by aphid stylectomy and the amino acids derivatized, separated, and quantified using Capillary Electrophoresis with Laser Induced Fluorescence (CE-LIF). In spite of the large variation across samples, the total amino acid concentration of SE sap of the aap6 mutant plants was significantly lower than that of the wild-type plants. The concentrations of lysine, phenylalanine, leucine, and aspartic acid were all significantly lower in concentration in the aap6 mutant plants compared with wild-type plants. This is the first direct demonstration of a physiological role for an amino acid transporter in regulating SE composition in vivo. The amino acid availability in sieve element sap is thought to be the major limiting factor for aphid growth and reproduction. Despite the changes in their diet, the aphid Myzus persicae(Sulzer) displayed only small changes in feeding behaviour on mutant plants when measured using the Electronic Penetration Graph (EPG) technique. Salivation by the aphid into the SE (E1 phase) was increased on mutant plants but there was no significant effect on other feeding EPG behaviours, or in the rate of honeydew production. Consistent with the small effect on aphid feeding behaviour, there was only a small effect of reduced sieve element amino acid concentration on aphid reproduction. The data are discussed in relation to the regulation of phloem composition and the role of phloem amino acids in regulating aphid performance

One-Flavour Hybrid Monte Carlo with Wilson Fermions

The Wilson fermion determinant can be written as product of the determinants of two hermitian positive definite matrices. This formulation allows to simulate non-degenerate quark flavors by means of the hybrid Monte Carlo algorithm. A major numerical difficulty is the occurrence of nested inversions. We construct a Uzawa iteration scheme which treats the nested system within one iterative process.Comment: 11 pages, to appear in proceedings of the workshop "Numerical Challenges in Lattice QCD", Springer Verla