GMRES and the minimal polynomial

We present a qualitative model for the convergence behaviour of the Generalised Minimal Residual (GMRES) method for solving nonsingular systems of linear equationsAx =b in finite and infinite dimensional spaces. One application of our methods is the solution of discretised infinite dimensional problems, such as integral equations, where the constants in the asymptotic bounds are independent of the mesh size.Our model provides simple, general bounds that explain the convergence of GMRES as follows: If the eigenvalues ofA consist of a single cluster plus outliers then the convergence factor is bounded by the cluster radius, while the asymptotic error constant reflects the non-normality ofA and the distance of the outliers from the cluster. If the eigenvalues ofA consist of several close clusters, then GMRES treats the clusters as a single big cluster, and the convergence factor is the radius of this big cluster. We exhibit matrices for which these bounds are tight.Our bounds also lead to a simpler proof of existing r-superlinear convergence results in Hilbert space.This research was partially supported by National Science Foundation grants DMS-9122745, DMS-9423705, CCR-9102853, CCR-9400921, DMS-9321938, DMS-9020915, and DMS-9403224.     

A nonrigid registration algorithm for longitudinal breast MR images and the analysis of breast tumor response

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) can estimate parameters relating to blood flow and tissue volume fractions and therefore may be used to characterize the response of breast tumors to treatment. To assess treatment response, values of these DCE-MRI parameters are observed at different time points during the course of treatment. We propose a method whereby DCE-MRI data sets obtained in separate imaging sessions can be co-registered to a common image space, thereby retaining spatial information so that serial DCE-MRI parameter maps can be compared on a voxel-by-voxel basis. In performing inter-session breast registration, one must account for patient repositioning and breast deformation, as well as changes in tumor shape and volume relative to other imaging sessions. One challenge is to optimally register the normal tissues while simultaneously preventing tumor distortion. We accomplish this by extending the adaptive bases algorithm through adding a tumor-volume preserving constraint in the cost function. We also propose a novel method to generate the simulated breast magnetic resonance (MR) images, which can be used to evaluate the proposed registration algorithm quantitatively. The proposed nonrigid registration algorithm is applied to both simulated and real longitudinal 3D high resolution MR images and the obtained transformations are then applied to lower resolution physiological parameter maps obtained via DCE-MRI. The registration results demonstrate the proposed algorithm can successfully register breast MR images acquired at different time points and allow for analysis of the registered parameter maps.     

Copper and iron interactions with angiotensin-converting enzyme inhibitors. A study by fast-atom bombardment tandem mass spectrometry

Fast atom bombardment, combined with high-energy collision-induced tandem mass spectrometry, has been used to investigate gas-phase metal-ion interactions with captopril, enalaprilat and lisinopril, all angiotensin-converting enzyme inhibitors.Suggestions for the location of metal-binding sites are presented. For captopril, metal binding occurs most likely at both the sulphur and the nitrogen atom. For enalaprilat and lisinopril, binding preferably occurs at the amine nitrogen. Copyright 1999 John Wiley & Sons, Ltd.     

Correlation of surface segregation with bulk diffusion for binary metal alloys

Previous treatments of surface segregation in metal alloys have all failed in some systems, due either to inadequacies in the theories or in the thermochemical data. A new model is proposed here using only alloy diffusion data. Predicted surface compositions agree quantitatively with ISS measurements and qualitatively AES results.     

Observation of radio-wave-induced red hydroxyl emission at low altitude in the ionosphere

We report the discovery of radio-wave-induced red emission of OH Meinel rotation-vibrational bands at 629.79 nm. These are the first measurements of artificial aurora below 100 km. We believe that the 629.79-nm OH emission was due to radio-wave focusing by sporadic ionization clouds near 80-85 km altitude, thus giving a technique to visualize the low-altitude sporadic ionization and providing insight into ionospheric interactions at these low altitudes.     

Coaxially gated in-wire thin-film transistors made by template assembly

Nanowire field effect transistors were prepared by a wet chemical template replication method using anodic aluminum oxide membranes. The membrane pores were first lined with a thin SiO2 layer by the surface sol-gel method. Au, CdS (or CdSe), and Au wire segments were then sequentially electrodeposited within the pores, and the resulting nanowires were released by dissolution of the membrane. Electrofluidic alignment of these nanowires between source and drain leads and evaporation of gold over the central CdS (CdSe) stripe affords a "wrap-around gate" structure. At VDS = -2 V, the Au/CdS/Au devices had an ON/OFF current ratio of 103, a threshold voltage of 2.4 V, and a subthreshold slope of 2.2 V/decade. A 3-fold decrease in the subthreshold slope relative to that of planar nanocrystalline CdSe devices can be attributed to coaxial gating. The control of dimensions afforded by template synthesis should make it possible to reduce the gate dielectric thickness, channel length, and diameter of the semiconductor segment to sublithographic dimensions while retaining the simplicity of the wet chemical synthetic method.