Matrix-product codes over Fq

Codes C-1,...,C-M of length it over F-q and an M x N matrix A over F-q define a matrix-product code C = [C-1 (...) C-M] (.) A consisting of all matrix products [c(1) (...) c(M)] (.) A. This generalizes the (u/u + v)-, (u + v + w/2u + v/u)-, (a + x/b + x/a + b + x)-, (u + v/u - v)- etc. constructions. We study matrix-product codes using Linear Algebra. This provides a basis for a unified analysis of /C/, d(C), the minimum Hamming distance of C, and C-perpendicular to. It also reveals an interesting connection with MDS codes. We determine /C/ when A is non-singular. To underbound d(C), we need A to be 'non-singular by columns (NSC)'. We investigate NSC matrices. We show that Generalized Reed-Muller codes are iterative NSC matrix-product codes, generalizing the construction of Reed-Muller codes, as are the ternary 'Main Sequence codes'. We obtain a simpler proof of the minimum Hamming distance of such families of codes. If A is square and NSC, C-perpendicular to can be described using C-1(perpendicular to),...,C-M(perpendicular to) and a transformation of A. This yields d(C-perpendicular to). Finally we show that an NSC matrix-product code is a generalized concatenated code.

Development and implementation of the population Fisher information matrix for the evaluation of population pharmacokinetic designs.

In population pharmacokinetic studies, the precision of parameter estimates is dependent on the population design. Methods based on the Fisher information matrix have been developed and extended to population studies to evaluate and optimize designs. In this paper we propose simple programming tools to evaluate population pharmacokinetic designs. This involved the development of an expression for the Fisher information matrix for nonlinear mixed-effects models, including estimation of the variance of the residual error. We implemented this expression as a generic function for two software applications: S-PLUS and MATLAB. The evaluation of population designs based on two pharmacokinetic examples from the literature is shown to illustrate the efficiency and the simplicity of this theoretic approach. Although no optimization method of the design is provided, these functions can be used to select and compare population designs among a large set of possible designs, avoiding a lot of simulations.

Relationship of glycosaminoglycan and matrix changes to vascular smooth cell phenotype modulation in rabbit arteries after acute injury

Purpose: The phenotype of vascular smooth muscle cells (SMCs) is altered in several arterial pathologies, including the neointima formed after acute arterial injury. This study examined the time course of this phenotypic change in relation to changes in the amount and distribution of matrix glycosaminoglycans. Methods: The immunochemical staining of heparan sulphates (HS) and chondroitin sulphates (CS) in the extracellular matrix of the arterial wall was examined at early points after balloon catheter injury of the rabbit carotid artery. SMC phenotype was assessed by means of ultrastructural morphometry of the cytoplasmic volume fraction of myofilaments. The proportions of cell and matrix components in the media were analyzed with similar morphometric techniques. Results: HS and CS were shown in close association with SMCs of the uninjured arterial media as well as being more widespread within the matrix. Within 6 hours after arterial injury, there was loss of the regular pericellular distribution of both HS and CS, which was associated with a significant expansion in the extracellular space. This preceded the change in ultrastructural phenotype of the SMCs. The glycosaminoglycan loss was most exaggerated at 4 days, after which time the HS and CS reappeared around the medial SMCs. SMCs of the recovering media were able to rapidly replace their glycosaminoglycans, whereas SMCs of the developing neointima failed to produce HS as readily as they produced CS. Conclusions: These studies indicate that changes in glycosaminoglycans of the extracellular matrix precede changes in SMC phenotype after acute arterial injury. In the recovering arterial media, SMCs replace their matrix glycosaminoglycans rapidly, whereas the newly established neointima fails to produce similar amounts of heparan sulphates.

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.

Foraging by the endangered black-breasted button-quail (Turnix melanogaster) within fragmented rainforest of an agricultural landscape

We studied the foraging habitat of the endangered black-breasted button-quail (Turnix melanogaster) in 13 rainforest patches of an agricultural landscape (23.4 km(2)) in eastern Australia to assess its use of fragmented habitats outside conservation reserves. The species foraged only in the three largest patches (17.4, 40.0, 63.8 ha in size), all of which were connected to open eucalypt forest, and in intact rainforest. Occurrence of birds was greatest in the largest patch. The maximum number of individuals within the study area was estimated to be 22. Radio-tracking of nine birds revealed that three were resident in the largest patch for periods of over 100 days; no movements between patches were detected. Three radio-tagged birds were taken by avian and mammalian predators. Our results indicated that the long-term future of the species in agricultural landscapes is bleak and that management action is urgently needed to arrest its decline in these ecosystems, (C) 2001 Elsevier Science Ltd. All rights reserved.

Mapping glider habitat in dry eucalypt forests for Montreal Process indicator 1.1: Fragmentation of forest types

Accurate habitat mapping is critical to landscape ecological studies such as required for developing and testing Montreal Process indicator 1.1e, fragmentation of forest types. This task poses a major challenge to remote sensing, especially in mixedspecies, variable-age forests such as dry eucalypt forests of subtropical eastern Australia. In this paper, we apply an innovative approach that uses a small section of one-metre resolution airborne data to calibrate a moderate spatial resolution model (30 m resolution; scale 1:50 000) based on Landsat Thematic Mapper data to estimate canopy structural properties in St Marys State Forest, near Maryborough, south-eastern Queensland. The approach applies an image-processing model that assumes each image pixel is significantly larger than individual tree crowns and gaps to estimate crown-cover percentage, stem density and mean crown diameter. These parameters were classified into three discrete habitat classes to match the ecology of four exudivorous arboreal species (yellowbellied glider Petaurus australis, sugar glider P. breviceps, squirrel glider P. norfolcensis , and feathertail glider Acrobates pygmaeus), and one folivorous arboreal marsupial, the greater glider Petauroides volans. These species were targeted due to the known ecological preference for old trees with hollows, and differences in their home range requirements. The overall mapping accuracy, visually assessed against transects (n = 93) interpreted from a digital orthophoto and validated in the field, was 79% (KHAT statistic = 0.72). The KHAT statistic serves as an indicator of the extent that the percentage correct values of the error matrix are due to ‘true’ agreement verses ‘chance’ agreement. This means that we are able to reliably report on the effect of habitat loss on target species, especially those with a large home range size (e.g. yellow-bellied glider). However, the classified habitat map failed to accurately capture the spatial patterning (e.g. patch size and shape) of stands with a trace or sub-dominance of senescent trees. This outcome makes the reporting of the effects of habitat fragmentation more problematic, especially for species with a small home range size (e.g. feathertail glider). With further model refinement and validation, however, this moderateresolution approach offers an important, cost eff e c t i v e advancement in mapping the age of dry eucalypt forests in the region.

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.