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 calculation of accident risks in fitness for work assessments: diseases that can cause sudden incapacity

Risk equations have been developed to assist in determining fitness for work of people with diseases that may cause rapid loss of control. The four equations calculate the frequency of fatal injury to the person with the disease, the frequency of fatal injury to colleagues in the workplace, and the cost of fatal injury and property damage to the employer, it is suggested that the additional risk of fatal injury to the person with the disease should not exceed the fatal injury rate in high-risk industries such as forestry, fishing and mining. it is also suggested that the additional risk of fatal injury to each colleague should be no more than one-tenth of the fatal injury rate due to motor vehicle accidents in the community. Two hypothetical case examples are given, demonstrating the use of the equations. The equations highlight the need to examine the risks associated with individuals, their specific jobs and their workplaces. They also highlight significant uncertainties in the determination of fitness, which perhaps have been underestimated in the past. Wherever possible, redundant defences should be utilized to prevent accidents in the event of sudden incapacity.

Long-distance signaling and the control of branching in the rms1 mutant of peal

The ramosus (rms) mutation (rms1) of pea (Pisum sativum) causes increased branching through modification of graft-transmissible signal(s) produced in rootstock and shoot. Additional grafting techniques have led us to propose that the novel signal regulated by Rms1 moves acropetally in shoots and acts as a branching inhibitor. Epicotyl interstock grafts showed that wild-type (WT) epicotyls grafted between rms1 scions and rootstocks can revert mutant scions to a WT non-branching phenotype. Mutant scions grafted together with mutant and WT rootstocks did not branch despite a contiguous mutant root-shoot system. The primary action of Rms1 is, therefore, unlikely to be to block transport of a branching stimulus from root to shoot. Rather, Rms1 may influence a long-distance signal that functions, directly or indirectly, as a branching inhibitor. It can be deduced that this signal moves acropetally in shoots because WT rootstocks inhibit branching in rms1 shoots, and although WT scions do not branch when grafted to mutant rootstocks, they do not inhibit branching in rms1 cotyledonary shoots growing from the same rootstocks. The acropetal direction of transport of the Rms1 signal supports previous evidence that the rms1 lesion is not in an auxin biosynthesis or transport pathway. The different branching phenotypes of WT and rms1 shoots growing from the same rms1 rootstock provides further evidence that the shoot has a major role in the regulation of branching and, moreover, that root-exported cytokinin is not the only graft-transmissible signal regulating branching in intact pea plants.

Can long-distance dispersal be inferred from the New Zealand plant fossil record?

New Zealand is generally thought to have been physically isolated from the rest of the world for over 60 million years. But physical isolation may not mean biotic isolation, at least on the time scale of millions of years. Are New Zealand's present complement of plants the direct descendants of what originally rafted from Gondwana? Or has there been total extinction of this initial flora with replacement through long-distance dispersal (a complete biotic turnover)? These are two possible extremes which have come under recent discussion. Can the fossil record be used to decide the relative importance of the two endpoints, or is it simply too incomplete and too dependent on factors of chance? This paper suggests two approaches to the problem-the use of statistics to apply levels of confidence to first appearances in the fossil record and the analysis of trends based on the entire palynorecord. Statistics can suggest that the first appearance of a taxon was after New Zealand broke away from Gondwana-as long as the first appearance in the record was not due to an increase in biomass from an initially rare state. Two observations can be drawn from the overall palynorecord that are independent of changes in biomass: (1) The first appearance of palynotaxa common to both Australia and New Zealand is decidedly non-random. Most taxa occur first in Australia. This suggests a bias in air or water transport from west to east. (2) The percentage of endemic palynospecies in New Zealand shows no simple correlation with the time New Zealand drifted into isolation. The conifer macrorecord also hints at complete turnover since the Cretaceous.

The effect of channel geometry and wall boundary conditions on the formation of extrusion surface instabilities for LLDPE

It is believed that surface instabilities can occur during the extrusion of linear low density polyethylene due to high extensional stresses at the exit of the die. Local crack development can occur at a critical stress level when melt rupture is reached. This high extensional stress results from the rearrangement of the flow at the boundary transition between the wall exit and the free surface. The stress is highest at the extrudate surface and decreases into the bulk of the material. The location of the region where the critical level is reached can determine the amplitude of the extrudate surface distortion, This paper studies the effect of wall slip on the numerically simulated extensional stress level at the die exit and correlates this to the experimentally determined amplitude of the surface instability. The effect of die exit radius and die wall roughness on extrusion surface instabilities is also correlated to the exit stress level in the same way. Whereas full slip may completely suppress the surface instability, a reduction in the exit stress level and instability amplitude is also shown for a rounded die exit and a slight increase in instability is shown to result from a rough die wall. A surface instability map demonstrates how the shear rate for onset of extrusion surface instabilities can be predicted on the basis of melt strength measurements and simulated stress peaks at the exit of the die. (C) 2001 Elsevier Science B.V. All rights reserved.

Operating space diagrams: a tool for designers of wastewater treatment plants

Recent years have seen the introduction of new and varied designs of activated sludge plants. With increasing needs for higher efficiencies and lower costs, the possibility of a plant that operates more effectively has created the need for tools that can be used to evaluate and compare designs at the design stage. One such tool is the operating space diagram. It is the aim of this paper to present this tool and demonstrate its application and relevance to design using a simple case study. In the case study, use of the operating space diagram suggested changes in design that would improve the flexibility of the process. It also was useful for designing suitable control strategies.

On the fast approximation of Green's functions in MPIE formulations for planar layered media

The numerical implementation of the complex image approach for the Green's function of a mixed-potential integralequation formulation is examined and is found to be limited to low values of k(0) rho (in this context k(0) rho = 2 pirho/ lambda(0), where rho is the distance between the source and the field points of the Green's function and lambda(0) is the free space wavelength). This is a clear limitation for problems of large dimension or high frequency where this limit is easily exceeded. This paper examines the various strategies and proposes a hybrid method whereby most of the above problems can be avoided. An efficient integral method that is valid for large k(0) rho is combined with the complex image method in order to take advantage of the relative merits of both schemes. It is found that a wide overlapping region exists between the two techniques allowing a very efficient and consistent approach for accurately calculating the Green's functions. In this paper, the method developed for the computation of the Green's function is used for planar structures containing both lossless and lossy media.

Critical quantum fluctuations in the degenerate parametric oscillator

We develop a systematic theory of critical quantum fluctuations in the driven parametric oscillator. Our analytic results agree well with stochastic numerical simulations. We also compare the results obtained in the positive-P representation, as a fully quantum-mechanical calculation, with the truncated Wigner phase-space equation, also known as the semiclassical theory. We show when these results agree and differ in calculations taken beyond the linearized approximation. We find that the optimal broadband noise reduction occurs just above threshold. In this region where there are large quantum fluctuations in the conjugate variance and macroscopic quantum superposition states might be expected, we find that the quantum predictions correspond very closely to the semiclassical theory.