Group theory and quasiprobability integrals of Wigner functions

The integral of the Wigner function of a quantum-mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0, 1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric discs and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in a Hilbert space carrying the positive discrete series representation of the algebra su(1, 1) approximate to so(2, 1). The explicit relation between the spectra of operators associated with discs and circles with proportional radii, is given in terms of the discrete variable Meixner polynomials.

Estimating remittance functions for Pacific island migrants

There is concern that Pacific island economies dependent on remittances of migrants will endure foreign exchange shortages and declining Living standards as remittance levels drop due to lower migration rates and the belief that migrants' willingness to remit decreases over time. The empirical validity of the remittance-decay hypothesis has never been tested. From survey data on Tongan and Western Samoan migrants in Sydney, this paper estimates remittance functions using Tobit regression analysis. It is found that the remittance-decay hypothesis has no empirical validity and migrants are motivated by factors other than altruistic family support, including asset accumulation and investment back home. (C) 1997 Elsevier Science Ltd.

Structure optimization combining soft-core interaction functions, the diffusion equation method, and molecular dynamics

Smoothing the potential energy surface for structure optimization is a general and commonly applied strategy. We propose a combination of soft-core potential energy functions and a variation of the diffusion equation method to smooth potential energy surfaces, which is applicable to complex systems such as protein structures; The performance of the method was demonstrated by comparison with simulated annealing using the refinement of the undecapeptide Cyclosporin A as a test case. Simulations were repeated many times using different initial conditions and structures since the methods are heuristic and results are only meaningful in a statistical sense.

Tubular eyes of deep-sea fishes: A comparative study of retinal topography

The world's deep oceans are home to a number of teleosts with asymmetrical or tubular eyes. These immobile eyes possess large spherical lenses and subtend a large binocular visual field directed either dorsally or rostrally. Derived from a lateral non-tubular eye, the tubular eye is comprised of a thick main retina, subserving the rostrally or dorsally directed binocular visual field, and a thin accessory retina subserving, the lateral, monocular visual field. The main retina is thought to receive a focussed image, while the accessory retina is too close to the lens for a focussed image to be received. Several species also possess retinal diverticula, which are small evaginations of differentiated retina located in the rostrolateral wall of the eye and thought to increase the visual field. In order to investigate the spatial resolving power of these retinae (main, accessory and diverticulum), the distribution of cells within the ganglion cell layer was analysed from retinal wholemounts and sectioned material in ten species representing four genera. In all species, the main retina possesses a marked increase in cell density towards a specialised retinal region (area centralis), with a centro-peripheral gradient range between 7.1 and 60:1 and a peak density range of between 30 and 55 x 10(3) cells per mm(2). The accessory retinae and the transitional zone between the main and accessory retinae possess relatively low cell densities (between 1 and 10 x 10(3) cells per mm(2)) and lack an area centralis. Retinal diverticula examined in four species possess mean ganglion cell densities of between 7.2 and 109.4 x 10(3) cells per mm(2). Analyses of soma areas show that the ganglion cell layer of most species possesses cells with areas in a range of 8.0 to 15.4 mu m(2) in the main retina and between 15.1 and 17.4 mu m(2) in the accessory retina. The peak spatial resolving power of the main retina of the ten species varies from 4.1 to 9.1 cycles per degree. The positions of the retinal areae centrales relative to each species' binocular visual field are discussed in relation to what is known of feeding behaviour of these fishes in the deep-sea.

Introduction to Discounted Cash Flow Analysis and Financial Functions in Excel

The financial and economic analysis of investment projects is typically carried out using the technique of discounted cash flow (DCF) analysis. This module introduces concepts of discounting and DCF analysis for the derivation of project performance criteria such as net present value (NPV), internal rate of return (IRR) and benefit to cost (B/C) ratios. These concepts and criteria are introduced with respect to a simple example, for which calculations using MicroSoft Excel are demonstrated.

Retinal neurons: cell types and coupled networks

Retinal neurons with distinct dendritic morphologies are likely to comprise different cell types, subject to three important caveats. First, it is necessary to avoid creating “artificial” cell types based on arbitrary criteria—for example, the presence of two or three primary dendrites. Second, it is essential to take into account changes in morphology with retinal eccentricity and cell density. Third, the retina contains imperfections like any natural system and a significant number of retinal neurons display aberrant morphologies or make aberrant connections that are not typical of the population as a whole. Many types of retinal ganglion cells show diverse patterns of tracer coupling, with the simplest pattern represented by the homologous coupling shown by On-Off direction-selective (DS) ganglion cells in the rabbit retina. Neighboring DS ganglion cells with a common preferred direction have regularly spaced somata and territorial dendritic fields, whereas DS ganglion cells with different preferred directions may have closely spaced somata and overlapping dendritic fields.

Differential perturbation of neuronal and glial glutamate transport systems in retinal ischaemia

Glutamate is the major excitatory neurotransmitter in the retina and is removed from the extracellular space by an energy-dependent process involving neuronal and glial cell transporters. The radial glial Muller cells express the glutamate transporter, GLAST, and preferentially accumulate glutamate. However, during an ischaemic episode, extracellular glutamate concentrations may rise to excitotoxic levels. Is this catastrophic rise in extracellular glutamate due to a failure of GLAST? Using immunocytochemistry, we monitored the transport of the glutamate transporter substrate, D-aspartate, in the retina under normal and ischaemic conditions. Two models of compromised retinal perfusion were compared: (1) Anaesthetised rats had their carotid arteries occluded for 7 days to produce a chronic reduction in retinal blood flow. Retinal function was assessed by electroretinography. D-aspartate was injected into the eye for 45 min, Following euthanasia, the retina was processed for D-aspartate. GLAST and glutamate immunocytochemistry. Although reduced retinal perfusion suppresses the electroretinogram b-wave, neither retinal histology, GLAST expression, nor the ability of Muller cells to uptake D-aspartate is affected. As this insult does not appear to cause excitotoxic neuronal damage, these data suggest that GLAST function and glutamate clearance are maintained during periods of reduced retinal perfusion. (2) Occlusion of the central retinal artery for 60 min abolishes retinal perfusion, inducing histological damage and electroretinogram suppression. Although GLAST expression appears to be normal. its ability to transport D-aspartate into Muller cells is greatly reduced. Interestingly, D-aspartate is transported into neuronal cells, i.e. photoreceptors, bipolar and ganglion cells. This suggests that while GLAST is vitally important for the clearance of excess extracellular glutamate, its capability to sustain inward transport is particularly susceptible to an acute ischaemic attack. Manipulation of GLAST function could alleviate the degeneration and blindness that result from ischaemic retinal disease. (C) 2001 Elsevier Science Ltd, All rights reserved.

Ataxia-telangiectasia: chronic activation of damage-responsive functions is reduced by alpha-lipoic acid

Cells from patients with the genetic disorder ataxia-telangiectasia (A-T) are hypersensitive to ionizing radiation and radiomimetic agents, both of which generate reactive oxygen species capable of causing oxidative damage to DNA and other macromolecules. We describe in A-T cells constitutive activation of pathways that normally respond to genotoxic stress, Basal levels of p53 and p21(WAF1/CIP1), phosphorylation on serine 15 of p53, and the Tyr15-phosphorylated form of cdc2 are chronically elevated in these cells. Treatment of A-T cells with the antioxidant alpha -lipoic acid significantly reduced the levels of these proteins, pointing to the involvement of reactive oxygen species in their chronic activation. These findings suggest that the absence of functional ATM results in a mild but continuous state of oxidative stress, which could account for several features of the pleiotropic phenotype of A-T.