Lexicographic decomposition of chains and the concept of a planar chain

In an earlier paper [Journal of Mathematical Economics, 37 (2002) 17-38], we proved that if a preference relation on a commodity space is non-representable by a real-valued function then that chain is necessarily a long chain, a planar chain, an Aronszajn-like chain or a Souslin chain. In this paper, we study the class of planar chains, the simplest example of which is the Debreu chain (R-2, <(l)). (C) 2002 Elsevier Science B.V. All rights reserved.

Linear ketenimines. Variable structures of C,C-dicyanoketenimines and C,C-bis-sulfonylketenimines

C,C-Dicyanoketenimines 10a-c were generated by flash vacuum thermolysis of ketene NS-acetals 9a-c or by thermal or photochemical decomposition of alpha-azido-,beta-cyanocinnamonitrile 11. In the latter reaction, 3,3-dicyano-2-phenyl-1-azirine 12 is also formed. IR spectroscopy of the keteniminines isolated in Ar matrixes or as neat films, NMR spectroscopy of 10c, and theoretical calculations (B3LYP/6-31G*) demonstrate that these ketenimines have variable geometry, being essentially linear along the CCN-R framework in polar media (neat films and solution), but in the gas phase or Ar matrix they are bent, as is usual for ketenimines. Experiments and calculations agree that a single CN substituent as in 13 is not enough to enforce linearity, and sulfonyl groups are less effective that cyano groups in causing linearity. C,C-Bis(methylsulfonyl)ketenimines 4-5 and a C-cyano-C-(methylsulfonyl)ketenimine 15 are not linear. The compound p-O2NC6H4N=C= C(COOMe)2 previously reported in the literature is probably somewhat linearized along the CCNR moiety. A computational survey (B3LYP/6-31G*) of the inversion barrier at nitrogen indicates that electronegative C-substituents dramatically lower the barrier; this is also true of N-acyl substituents. Increasing polarity causes lower barriers. Although N-alkylbis(methylsulfonyl)ketenimines are not calculated to be linear, the barriers are so low that crystal lattice forces can induce planarity in N-methylbis(methylsulfonyl)ketenimine 3.

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.

Conditional simulation of random fields by successive residuals

This paper presents a new approach to the LU decomposition method for the simulation of stationary and ergodic random fields. The approach overcomes the size limitations of LU and is suitable for any size simulation. The proposed approach can facilitate fast updating of generated realizations with new data, when appropriate, without repeating the full simulation process. Based on a novel column partitioning of the L matrix, expressed in terms of successive conditional covariance matrices, the approach presented here demonstrates that LU simulation is equivalent to the successive solution of kriging residual estimates plus random terms. Consequently, it can be used for the LU decomposition of matrices of any size. The simulation approach is termed conditional simulation by successive residuals as at each step, a small set (group) of random variables is simulated with a LU decomposition of a matrix of updated conditional covariance of residuals. The simulated group is then used to estimate residuals without the need to solve large systems of equations.

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.

Leaf litter decomposition of Piper aduncum, Gliricidia sepium and Imperata cylindrica in the humid lowlands of Papua New Guinea

No information is available on the decomposition and nutrient release pattern of Piper aduncum and Imperata cylindrica despite their importance in shifting cultivation systems of Papua New Guinea and other tropical regions. We conducted a litter bag study (24 weeks) on a Typic Eutropepts in the humid lowlands to assess the rate of decomposition of Piper aduncum, Imperata cylindrica and Gliricidia sepium leaves under sweet potato (Ipomoea batatas). Decomposition rates of piper leaf litter were fastest followed closely by gliricidia, and both lost 50% of the leaf biomass within 10 weeks. Imperata leaf litter decomposed much slower and half-life values exceeded the period of observation. The decomposition patterns were best explained by the lignin plus polyphenol over N ratio which was lowest for piper (4.3) and highest for imperata (24.7). Gliricidia leaf litter released 79 kg N ha(-1), whereas 18 kg N ha(-1) was immobilised in the imperata litter. The mineralization of P was similar for the three species, but piper litter released large amounts of K. The decomposition and nutrient release patterns had significant effects on the soil. The soil contained significantly more water in the previous imperata plots at 13 weeks due to the relative slow decomposition of the leaves. Soil N levels were significantly reduced in the previous imperata plots due to immobilisation of N. Levels of exchangeable K were significantly increased in the previous piper plots due to the large addition of K. It can be concluded that piper leaf litter is a significant and easily decomposable source of K which is an important nutrient for sweet potato. Gliricidia leaf litter contained much N, whereas imperata leaf litter releases relatively little nutrients and keeps the soil more moist. Gliricidia fallow is more attractive than an imperata fallow for it improves the soil fertility and produces fuelwood as additional saleable products.

Fast, scalable master equation solution algorithms. IV. Lanczos iteration with diffusion approximation preconditioned iterative inversion

In this paper we propose a second linearly scalable method for solving large master equations arising in the context of gas-phase reactive systems. The new method is based on the well-known shift-invert Lanczos iteration using the GMRES iteration preconditioned using the diffusion approximation to the master equation to provide the inverse of the master equation matrix. In this way we avoid the cubic scaling of traditional master equation solution methods while maintaining the speed of a partial spectral decomposition. The method is tested using a master equation modeling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long-lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Fast, scalable master equation solution algorithms. III. Direct time propagation accelerated by a diffusion approximation preconditioned iterative solver

In this paper we propose a novel fast and linearly scalable method for solving master equations arising in the context of gas-phase reactive systems, based on an existent stiff ordinary differential equation integrator. The required solution of a linear system involving the Jacobian matrix is achieved using the GMRES iteration preconditioned using the diffusion approximation to the master equation. In this way we avoid the cubic scaling of traditional master equation solution methods and maintain the low temperature robustness of numerical integration. The method is tested using a master equation modelling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long lived isomerizing intermediates. (C) 2003 American Institute of Physics.