Lanczos subspace filter diagonalization: Homogeneous recursive filtering and a low-storage method for the calculation of matrix elements

We develop a new iterative filter diagonalization (FD) scheme based on Lanczos subspaces and demonstrate its application to the calculation of bound-state and resonance eigenvalues. The new scheme combines the Lanczos three-term vector recursion for the generation of a tridiagonal representation of the Hamiltonian with a three-term scalar recursion to generate filtered states within the Lanczos representation. Eigenstates in the energy windows of interest can then be obtained by solving a small generalized eigenvalue problem in the subspace spanned by the filtered states. The scalar filtering recursion is based on the homogeneous eigenvalue equation of the tridiagonal representation of the Hamiltonian, and is simpler and more efficient than our previous quasi-minimum-residual filter diagonalization (QMRFD) scheme (H. G. Yu and S. C. Smith, Chem. Phys. Lett., 1998, 283, 69), which was based on solving for the action of the Green operator via an inhomogeneous equation. A low-storage method for the construction of Hamiltonian and overlap matrix elements in the filtered-basis representation is devised, in which contributions to the matrix elements are computed simultaneously as the recursion proceeds, allowing coefficients of the filtered states to be discarded once their contribution has been evaluated. Application to the HO2 system shows that the new scheme is highly efficient and can generate eigenvalues with the same numerical accuracy as the basic Lanczos algorithm.

Freeform fabrication of aluminum metal-matrix composites

A series of metal-matrix composites were formed by extrusion freeform, fabrication of a sinterable aluminum alloy in combination with silicon carbide particles and whiskers, carbon fibers, alumina particles, and hollow flyash cenospheres. Silicon carbide particles were most successful in that the composites retained high density with up to 20 vol% of reinforcement and the strength approximately doubles over the strength of the metal matrix alone. Comparison with simple models suggests that this unexpectedly high degree of reinforcement can be attributed to the concentration of small silicon carbide particles around the larger metal powder. This fabrication method also allows composites to be formed with hollow spheres that cannot be formed by other powder or melt methods.

Effects of moist chilling and solid matrix priming on germination of loblolly pine (Pinus taeda L.) seeds

Loblolly pine ( Pinus taeda L.) seeds from sources with a mild climate under maritime influence (North Carolina) required shorter moist chilling to achieve maximum germination vigor than seeds from sources with a harsher continental climate (Oklahoma). Solid matrix priming (SMP) for 6 d achieved as much as 60 d of moist chilling to improve rapidity, synchrony and completeness of germination for three of the four families studied. SMP after moist chilling increased the rapidity, synchrony and completeness of germination. The benefit of SMP was greatest for non-stratified seeds and the benefit decreased with length of moist chilling. In general, delaying planting for one week after SMP had minor effects on germination when seeds were kept in the SMP matrix at 4 degreesC. Delayed planting after SMP can increase germination rapidity and synchrony of seeds that have received long moist chilling and reduce the benefit of SMP in non-moist-chilled seeds.

Inferring genome trees by using a filter to eliminate phylogenetically discordant sequences and a distance matrix based on mean normalized BLASTP scores

Darwin's paradigm holds that the diversity of present-day organisms has arisen via a process of genetic descent with modification, as on a bifurcating tree. Evidence is accumulating that genes are sometimes transferred not along lineages but rather across lineages. To the extent that this is so, Darwin's paradigm can apply only imperfectly to genomes, potentially complicating or perhaps undermining attempts to reconstruct historical relationships among genomes (i.e., a genome tree). Whether most genes in a genome have arisen via treelike (vertical) descent or by lateral transfer across lineages can be tested if enough complete genome sequences are used. We define a phylogenetically discordant sequence (PDS) as an open reading frame (ORF) that exhibits patterns of similarity relationships statistically distinguishable from those of most other ORFs in the same genome. PDSs represent between 6.0 and 16.8% (mean, 10.8%) of the analyzable ORFs in the genomes of 28 bacteria, eight archaea, and one eukaryote (Saccharomyces cerevisiae). In this study we developed and assessed a distance-based approach, based on mean pairwise sequence similarity, for generating genome trees. Exclusion of PDSs improved bootstrap support for basal nodes but altered few topological features, indicating that there is little systematic bias among PDSs. Many but not all features of the genome tree from which PDSs were excluded are consistent with the 16S rRNA tree.

Thermolysin activates equine lamellar hoof matrix metalloproteinases

Cultured equine lamellar hoof explants secrete the pro-enzymes matrix metalloproteinse-2 (MMP-2, 72 kDa) and MMP-2 (92 kDa). Untreated explants remained intact tested on a calibrated force transducer, but when treated with an NIMP activator, developed in-vitro laminitis, separating at the dermal-epidermal junction. Explants treated with the bacterial protease thermolysin separated dose-dependently; this was accompanied by activation of both MMP-2 and -9. Thermolysin-mediated NIP activation did not occur in a cell-free system and was not inhibited by the addition of the MMP inhibitor and batimastat. These findings suggest that thermolysin-mediated gelatinase activation is not dependent on membrane-bound matrix metalloproteinase (MT-MMP) activation, providing further evidence that bacteria can produce potent MMP activators that probably facilitate host invasion. (C) 2002 Harcourt Publishers Ltd.

An augmented Lanczos algorithm for the efficient computation of a dot-product of a function of a large sparse symmetric matrix

The Lanczos algorithm is appreciated in many situations due to its speed. and economy of storage. However, the advantage that the Lanczos basis vectors need not be kept is lost when the algorithm is used to compute the action of a matrix function on a vector. Either the basis vectors need to be kept, or the Lanczos process needs to be applied twice. In this study we describe an augmented Lanczos algorithm to compute a dot product relative to a function of a large sparse symmetric matrix, without keeping the basis vectors.

Abnormal extracellular matrix protein transport associated with increased apoptosis of vascular smooth muscle cells in Marfan syndrome and bicuspid aortic valve thoracic aortic aneurysm

Background - Marfan syndrome (MS) is a genetic disorder caused by a mutation in the fibrillin gene FBN1. Bicuspid aortic valve (BAV) is a congenital heart malformation of unknown cause. Both conditions are associated with ascending aortic aneurysm and premature death. This study examined the relationship among the secretion of extracellular matrix proteins fibrillin, fibronectin, tenascin, and vascular smooth muscle cell (VSMC) apoptosis. The role of matrix metalloproteinase (MMP)- 2 in VSMC apoptosis was studied in MS aneurysm. Methods and Results - Aneurysm tissue was obtained from patients undergoing surgery ( MS: 4 M, 1 F, age 27 - 45 years; BAV: 3 M, 2 F, age 28 - 65 years). Normal aorta from subjects with nonaneurysm disease was also collected ( 4 M, 1 F, age 23 - 93 years). MS and BAV aneurysm histology showed areas of cystic medial necrosis (CMN) without inflammatory infiltrate. Immunohistochemical study of cultured MS and BAV VSMC showed intracellular accumulation and reduction of extracellular distribution of fibrillin, fibronectin, and tenascin. Western blot showed no increase in expression of fibrillin, fibronectin, or tenascin in MS or BAV VSMC and increased expression of MMP-2 in MS VSMCs. There was 4-fold increase in loss of cultured VSMC incubated in serum-free medium for 24 hours in both MS ( 27 +/- 8%) and BAV ( 32 +/- 14%) compared with control ( 7 +/- 5%). Conclusions - In MS and BAV there is alteration in both the amount and quality of secreted proteins and an increased degree of VSMC apoptosis. Up-regulation of MMP-2 might play a role in VSMC apoptosis in MS VSMC. The findings suggest the presence of a fundamental cellular abnormality in BAV thoracic aorta, possibly of genetic origin.

Matrix metalloproteinase-2 and-9 involvement in canine tumors

Matrix metalloproteinases (MMPs) are a family of enzymes implicated in the degradation and remodeling of extracellular matrix and in vascularization. They are also involved in pathologic processes such as tumor invasion and metastasis in experimental cancer models and in human malignancies. We used gelatin zymography and inummohistochemistry to determine whether MMP-2 and MMP-9 are present in canine tumors and normal tissues and whether MMP production correlates with clinicopathologic parameters of prognostic importance. High levels of pro-MMP-9, pro-MMP-2, and active MMP-2 were detected in most canine tumors. Significantly higher MMP levels were measured in canine tumors than in nontumors, malignancies had higher MMP levels than benign tumors, and sarcomas had higher active MMP-2 than carcinomas. Cartilaginous tumors produced higher MMP levels than did nonsarcomatous malignancies, benign tumors, and normal tissues, and significantly greater MMP-2 than osteosarcomas and fibrosarcomas. Pro-MMP-9 production correlated with the histologic grade of osteosarcomas. The 62-kd form of active MMP-2 was detected only in high-grade, p53-positive, metastatic malignancies. Zymography proved to be a sensitive and quantitative technique for the assessment of MMP presence but has the limitation of requiring fresh tissue; inummohistochemistry is qualitative and comparatively insensitive but could be of value in archival studies. MMP presence was shown in a range of canine tumors, and their link to tumor type and grade was demonstrated for the first time. This study will allow a substantially improved evaluation of veterinary cancer patients and provides baseline information necessary for the design of clinical trials targeting MMPs.

One-sided Radial-Fundamental Matrix Estimation

For modern consumer cameras often approximate calibration data is available, making applications such as 3D reconstruction or photo registration easier as compared to the pure uncalibrated setting. In this paper we address the setting with calibrateduncalibrated image pairs: for one image intrinsic parameters are assumed to be known, whereas the second view has unknown distortion and calibration parameters. This situation arises e.g. when one would like to register archive imagery to recently taken photos. A commonly adopted strategy for determining epipolar geometry is based on feature matching and minimal solvers inside a RANSAC framework. However, only very few existing solutions apply to the calibrated-uncalibrated setting. We propose a simple and numerically stable two-step scheme to first estimate radial distortion parameters and subsequently the focal length using novel solvers. We demonstrate the performance on synthetic and real datasets.