Implicit-factorization preconditioning and iterative solvers for regularized saddle-point systems

We consider conjugate-gradient like methods for solving block symmetric indefinite linear systems that arise from saddle-point problems or, in particular, regularizations thereof. Such methods require preconditioners that preserve certain sub-blocks from the original systems but allow considerable flexibility for the remaining blocks. We construct a number of families of implicit factorizations that are capable of reproducing the required sub-blocks and (some) of the remainder. These generalize known implicit factorizations for the unregularized case. Improved eigenvalue clustering is possible if additionally some of the noncrucial blocks are reproduced. Numerical experiments confirm that these implicit-factorization preconditioners can be very effective in practice.

Iron-regulated surface determinant protein a mediates adhesion of staphylococcus aureus to human corneocyte envelope proteins

The ability of Staphylococcus aureus to colonize the human nares is a crucial prerequisite for disease. IsdA is a major S. aureus surface protein that is expressed during human infection and required for nasal colonization and survival on human skin. In this work, we show that IsdA binds to involucrin, loricrin, and cytokeratin K10, proteins that are present in the cornified envelope of human desquamated epithelial cells. To measure the forces and dynamics of the interaction between IsdA and loricrin (the most abundant protein of the cornified envelope), single-molecule force spectroscopy was used, demonstrating high-specificity binding. IsdA acts as a cellular adhesin to the human ligands, promoting whole-cell binding to immobilized proteins, even in the absence of other S. aureus components (as shown by heterologous expression in Lactococcus lactis). Inhibition experiments revealed the binding of the human ligands to the same IsdA region. This region was mapped to the NEAT domain of IsdA. The NEAT domain also was found to be required for S. aureus whole-cell binding to the ligands as well as to human nasal cells. Thus, IsdA is an important adhesin to human ligands, which predominate in its primary ecological niche.

Mapping quantitative trait loci for flag leave senescence as a yield determinant in winter wheat under optimal and drought stressed environments

The timing of flag leaf senescence (FLS) is an important determinant of yield under stress and optimal environments. A doubled haploid population derived from crossing the photo period-sensitive variety Beaver,with the photo period-insensitive variety Soissons, varied significantly for this trait, measured as the percent green flag leaf area remaining at 14 days and 35 days after anthesis. This trait also showed a significantly positive correlation with yield under variable environmental regimes. QTL analysis based on a genetic map derived from 48 doubled haploid lines using amplified fragment length polymorphism (AFLP) and simple sequence repeat (SSR) markers, revealed the genetic control of this trait. The coincidence of QTL for senescence on chromosomes 2B and 2D under drought-stressed and optimal environments, respectively, indicate a complex genetic mechanism of this trait involving the re-mobilisation of resources from the source to the sink during senescence.

Large vibrational variational calculations using 'multimode' and an iterative diagonalization technique

We have favoured the variational (secular equation) method for the determination of the (ro-) vibrational energy levels of polyatomic molecules. We use predominantly the Watson Hamiltonian in normal coordinates and an associated given potential in the variational code 'Multimode'. The dominant cost is the construction and diagonalization of matrices of ever-increasing size. Here we address this problem, using pertubation theory to select dominant expansion terms within the Davidson-Liu iterative diagonalization method. Our chosen example is the twelve-mode molecule methanol, for which we have an ab initio representation of the potential which includes the internal rotational motion of the OH group relative to CH3. Our new algorithm allows us to obtain converged energy levels for matrices of dimensions in excess of 100 000.

Predicting fault inflow in iterative software development processes: an industrial evaluation

This paper addresses the need for accurate predictions on the fault inflow, i.e. the number of faults found in the consecutive project weeks, in highly iterative processes. In such processes, in contrast to waterfall-like processes, fault repair and development of new features run almost in parallel. Given accurate predictions on fault inflow, managers could dynamically re-allocate resources between these different tasks in a more adequate way. Furthermore, managers could react with process improvements when the expected fault inflow is higher than desired. This study suggests software reliability growth models (SRGMs) for predicting fault inflow. Originally developed for traditional processes, the performance of these models in highly iterative processes is investigated. Additionally, a simple linear model is developed and compared to the SRGMs. The paper provides results from applying these models on fault data from three different industrial projects. One of the key findings of this study is that some SRGMs are applicable for predicting fault inflow in highly iterative processes. Moreover, the results show that the simple linear model represents a valid alternative to the SRGMs, as it provides reasonably accurate predictions and performs better in many cases.

On the Convergence of Two-Stage Iterative Processes for Solving Linear Equations

This paper considers two-stage iterative processes for solving the linear system $Af = b$. The outer iteration is defined by $Mf^{k + 1} = Nf^k + b$, where $M$ is a nonsingular matrix such that $M - N = A$. At each stage $f^{k + 1} $ is computed approximately using an inner iteration process to solve $Mv = Nf^k + b$ for $v$. At the $k$th outer iteration, $p_k $ inner iterations are performed. It is shown that this procedure converges if $p_k \geqq P$ for some $P$ provided that the inner iteration is convergent and that the outer process would converge if $f^{k + 1} $ were determined exactly at every step. Convergence is also proved under more specialized conditions, and for the procedure where $p_k = p$ for all $k$, an estimate for $p$ is obtained which optimizes the convergence rate. Examples are given for systems arising from the numerical solution of elliptic partial differential equations and numerical results are presented.

Iterative Methods for Equality-Constrained Least Squares Problems

We consider the linear equality-constrained least squares problem (LSE) of minimizing ${\|c - Gx\|}_2 $, subject to the constraint $Ex = p$. A preconditioned conjugate gradient method is applied to the Kuhn–Tucker equations associated with the LSE problem. We show that our method is well suited for structural optimization problems in reliability analysis and optimal design. Numerical tests are performed on an Alliant FX/8 multiprocessor and a Cray-X-MP using some practical structural analysis data.