A comparison of low-storage strategies for spectral analysis in dissipative systems: filter diagonalisation in the Lanczos representation and harmonic inversion of the Chebychev-order-domain autocorrelation function

We compare the performance of two different low-storage filter diagonalisation (LSFD) strategies in the calculation of complex resonance energies of the HO2, radical. The first is carried out within a complex-symmetric Lanczos subspace representation [H. Zhang, S.C. Smith, Phys. Chem. Chem. Phys. 3 (2001) 2281]. The second involves harmonic inversion of a real autocorrelation function obtained via a damped Chebychev recursion [V.A. Mandelshtam, H.S. Taylor, J. Chem. Phys. 107 (1997) 6756]. We find that while the Chebychev approach has the advantage of utilizing real algebra in the time-consuming process of generating the vector recursion, the Lanczos, method (using complex vectors) requires fewer iterations, especially for low-energy part of the spectrum. The overall efficiency in calculating resonances for these two methods is comparable for this challenging system. (C) 2001 Elsevier Science B.V. All rights reserved.

Calculation of product state distributions from resonance decay via Lanczos subspace filter diagonalization: Application to HO2

Resonance phenomena associated with the unimolecular dissociation of HO2 have been investigated quantum-mechanically by the Lanczos homogeneous filter diagonalization (LHFD) method. The calculated resonance energies, rates (widths), and product state distributions are compared to results from an autocorrelation function-based filter diagonalization (ACFFD) method. For calculating resonance wave functions via ACFFD, an analytical expression for the expansion coefficients of the modified Chebyshev polynomials is introduced. Both dissociation rates and product state distributions of O-2 show strong fluctuations, indicating the dissociation of HO2 is essentially irregular. (C) 2001 American Institute of Physics.

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.

Linear models of simple cells: Correspondence to real cell responses and space spanning properties

Despite their limitations, linear filter models continue to be used to simulate the receptive field properties of cortical simple cells. For theoreticians interested in large scale models of visual cortex, a family of self-similar filters represents a convenient way in which to characterise simple cells in one basic model. This paper reviews research on the suitability of such models, and goes on to advance biologically motivated reasons for adopting a particular group of models in preference to all others. In particular, the paper describes why the Gabor model, so often used in network simulations, should be dropped in favour of a Cauchy model, both on the grounds of frequency response and mutual filter orthogonality.

The filter system for tertiary treatment of sewage effluent by land application - its performance in a subtropical environment

FILTER is an innovative, CSIRO developed system for treating effluent using high rate land application and subsequent effluent recapture via a closely spaced, subsurface drainage network. We report on the summer performance of a FILTER system established in a subtropical environment on a relatively impermeable swelling clay soil underlain by a deep regional water table. Using secondary treated sewage effluent, the FILTER system produced effluent of tertiary nutrient standards (less than or equal to5 mg/L TN; less than or equal to1 mg/L TP), with salinity levels suitable for subsequent irrigation reuse (EC less than or equal to2.5 dS/m). Removal of faecal coliforms was considerably less effective. The hydraulic loading rate achieved was about two and a half times larger than conventional irrigation demand, but this was associated with high deep percolation losses (e 3 mm/day). Comparisons are made with the original FILTER system developed and tested by Jayawardane et al. in temperate Australia. Suggestions are made for modifications to, and further testing of FILTER in a subtropical environment.

ReoPro rules: results from the 'DoTirofiban and ReoPro give similar efficacy trial' (TARGET) - A Key Paper Evaluation (Topol, Ej et al)

In the treatment of atherosclerotic disease, stenting in the presence of a glycoprotein (GP) IIb/IIIa antagonist is becoming an increasingly common procedure. The ‘Do Tirofiban and ReoPro Give Similar Efficacy Trial’ (TARGET) was designed to determine whether the cheaper tirofiban was as effective and safe as abciximab in the prevention of ischaemic events with stenting. Unexpectedly, abciximab was shown to be superior to tirofiban. Tirofiban is a selective GP IIb/IIIa antagonist whereas abciximab has additional anti-inflammatory actions, which may contribute to its superiority.

Is bucindolol BEST? (A Key Paper Evaluation)

Carvedilol, a non-selective β-adrenoceptor blocker with ancillary properties, and metoprolol and bisoprolol, selective β1-blockers without ancillary properties, have been shown to reduce mortality and morbidity in heart failure. In the Beta-blocker Evaluation of Survival Trial (BEST), bucindolol, a non-selective β-adrenoceptor blocker with different ancillary properties to carvedilol, did not reduce overall survival in heart failure. Possible explanations for this include: more Blacks being included in the trial, bucindolol being more ‘sympatholytic’ than the other β-blockers and more advanced heart failure in BEST. Another possible explanation is that bucindolol is stimulating cardiac β2-adrenoceptors to counter the effects of inhibiting cardiac β1-adrenoceptors. Bucindolol is not the best treatment and carvedilol, metoprolol and bisoprolol should be preferred in heart failure.

Clopidogrel: A CURE in acute coronary syndromes? (A Key Paper Evaluation)

The standard approach to preventing acute coronary syndromes (ACSs)has been to inhibit platelet aggregation with aspirin and to inhibit blood coagulation with low molecular-weight heparin (LMWH). Even with this combination there is still a substantial short and long-term cardiovascular risk. The Clopidogrel in Unstable angina to prevent Recurrent Events (CURE) trial [1] compared clopidogrel plus aspirin against aspirin alone in patients with ACSs. The clopidogrel regimen was a loading dose of 300 mg p.o. followed by 75 mg/day and the recommended dose of aspirin was 75 - 325 mg/day. The first primary outcome was a composite of death from cardiovascular causes, non-fatal myocardial infarction (MI) or stroke and this occurred significantly less often in the clopidogrel than the placebo group (9.3 vs. 11.4%). Although there were more clopidogrel patients with life-threatening bleeding (clopidogrel 2.2%, placebo 1.8%), this represented GI haemorrhages and bleeding at sites of arterial puncture rather than fatal bleeding. This trial suggests a role for clopidogrel in the long-term treatment of ACSs

The influence of calcium on granular sludge in a full-scale UASB treating paper mill wastewater

Calcium precipitation can have a number of effects on the performance of high-rate anaerobic performance including cementing of the sludge bed, limiting diffusion, and diluting the active biomass. The aim of this study was to observe the influence of precipitation in a stable full-scale system fed with high-calcium paper factory wastewater. Granules were examined from an upflow anaerobic sludge blanket reactor (volume 1,805 m(3)) at a recycled paper mill with a loading rate of 5.7-6.6 kgCOD.m(-3).d(-1) and influent calcium concentration of 400-700 gCa(.)m(-3). The granules were relatively small (1 mm), with a 200-400 mum core of calcium precipitate as observed with energy dispersive X-ray spectroscopy. Compared to other granules, Methanomicrobiales not Methanobacteriales were the dominant hydrogen or formate utilisers, and putative acidogens were filamentous. The strength of the paper mill fed granules was very high when compared to granules from other full-scale reactors, and a partial linear correlation between granule strength and calcium concentration was identified.

Riddling and invariance for discontinuous maps preserving Lebesgue measure

In this paper we use the mixture of topological and measure-theoretic dynamical approaches to consider riddling of invariant sets for some discontinuous maps of compact regions of the plane that preserve two-dimensional Lebesgue measure. We consider maps that are piecewise continuous and with invertible except on a closed zero measure set. We show that riddling is an invariant property that can be used to characterize invariant sets, and prove results that give a non-trivial decomposion of what we call partially riddled invariant sets into smaller invariant sets. For a particular example, a piecewise isometry that arises in signal processing (the overflow oscillation map), we present evidence that the closure of the set of trajectories that accumulate on the discontinuity is fully riddled. This supports a conjecture that there are typically an infinite number of periodic orbits for this system.

Lanczos subspace time-independent wave packet calculations of S(D-1)+H-2 reactive scattering

In this paper. we present the results of quantum dynamical simulations of the S (D-1) + H-2 insertion reaction on a newly developed potential energy surface (J. Chem. Phys. 2001, 114, 320). State-to-state reaction probabilities. product state distributions, and initial-state resolved cumulative reaction probabilities from a given incoming reactant channel are obtained from a time-independent wave packet analysis, performed within a single Lanczos subspace. Integral reaction cross sections are then estimated by J-shifting method and compared with the results from molecular beam experiment and QCT calculations.

Chebyshev real wave packet propagation: H+O-2 (J=0) state-to-state reactive scattering calculations

In this paper we explore the relative performance of two recently developed wave packet methodologies for reactive scattering, namely the real wave packet Chebyshev domain propagation of Gray and Balint-Kurti [J. Chem. Phys. 108, 950 (1998)] and the Lanczos subspace wave packet approach of Smith [J. Chem. Phys. 116, 2354 (2002); Chem. Phys. Lett. 336, 149 (2001)]. In the former method, a modified Schrodinger equation is employed to propagate the real part of the wave packet via the well-known Chebyshev iteration. While the time-dependent wave packet from the modified Schrodinger equation is different from that obtained using the standard Schrodinger equation, time-to-energy Fourier transformation yields wave functions which differ only trivially by normalization. In the Lanczos subspace approach the linear system of equations defining the action of the Green operator may be solved via either time-dependent or time-independent methods, both of which are extremely efficient due to the simple tridiagonal structure of the Hamiltonian in the Lanczos representation. The two different wave packet methods are applied to three dimensional reactive scattering of H+O-2 (total J=0). State-to-state reaction probabilities, product state distributions, as well as initial-state-resolved cumulative reaction probabilities are examined. (C) 2002 American Institute of Physics.

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.