ANTHRALIN-DERIVED TRANSIENTS–I. THE TRIPLET STATE AND THE PRODUCTS OF ITS REACTION WITH OXYGEN IN BENZENE

Direct laser excitation in benzene of 1,8-dihydroxy-9-anthrone (anthralin) does not lead to transient species with lifetimes in the nanosecond time regime or longer. The triplet state has been produced in benzene by pulse radiolysis and characterised in terms of its absorption spectrum (lambda max 560 nm), natural lifetime (11 microseconds), self-quenching properties (kmicrosecond = 2.6 x 10(7) l mol-1 s-1) and triplet energy (234 kJ mol-1). There is no tendency in the non-polar medium for production of either the triplet or ground state in a tautomeric form. The observed triplet state reacts with oxygen with a typical rate constant, 2.2 x 10(9) l mol-1 s-1. The products of this reaction are singlet oxygen (approximately 64%) and the anthralin radical (approximately 14%).     

NAPHTHYL- AND QUINOLYLLUCIFERIN: GREEN AND RED LIGHT EMITTING FIREFLY LUCIFERIN ANALOGUES

In the course of investigations on the possible involvement of the CIEEL (chemically initiated electron-exchange luminescence) mechanism in firefly bioluminescence, we have synthesized two novel firefly luciferin substrate analogues. D-Naphthylluciferin and D-quinolylluciferin were prepared by condensing D-cysteine with 2-cyano-6-hydroxynaphthalene and 2-cyano-6-hydroxyquinoline, respectively. These analogues are the first examples of bioluminescent substrates for firefly luciferase that do not contain a benzothiazole moiety. Firefly luciferase-catalyzed bioluminescence emission spectra revealed that compared to the normal yellow-green light of luciferin (lambda max = 559 nm), the emission from naphthylluciferin is significantly blue-shifted (lambda max = 524 nm); whereas quinolylluciferin emits orange-red light (lambda max = 608 nm). The fluorescence emission spectra, reaction pH optima, relative light yields, light emission kinetics and KM values of the analogues also were measured and compared to those of luciferin. Neither of the analogues produced the characteristic flash kinetics observed for the natural substrate. Instead, slower rise times to peak emission intensity were recorded. It appears that the formation of an intermediate from the analogue adenylates prior to the addition of oxygen is responsible for the slow rise times. The synthetic substrate analogues described here should be useful for future mechanistic studies.     

PIGS,PARTIES, AND NOISE: HOW STOCHASTICITY IMPACTS THE ROBUSTNESS OF THE TSEMBAGA CULTURAL PRACTICES

Abstract We present a probabilistic perspective on sustainable resource usage. A mathematical model is introduced to describe the interplay between a population and its renewable resource base. The amount of effort a society chooses to exert in harvesting its resource is formalized in the model. Using an indigenous population of slash and burn farmers as a case study, we derive a system of stochastic differential equations from a system of ordinary differential equations introduced by another author. The cultural mechanisms that help to stabilize the population in the deterministic system actually decrease the expected survival time in the stochastic system.     

ANALYSIS OF SENSITIVITY AND UNCERTAINTY IN AN INDIVIDUAL‐BASED MODEL OF A THREATENED WILDLIFE SPECIES

Sensitivity analysis—determination of how prediction variables affect response variables—of individual‐based models (IBMs) are few but important to the interpretation of model output. We present sensitivity analysis of a spatially explicit IBM (HexSim) of a threatened species, the Northern Spotted Owl (NSO; Strix occidentalis caurina) in Washington, USA. We explored sensitivity to HexSim variables representing habitat quality, movement, dispersal, and model architecture; previous NSO studies have well established sensitivity of model output to vital rate variation. We developed “normative” (expected) model settings from field studies, and then varied the values of ≥ 1 input parameter at a time by ±10% and ±50% of their normative values to determine influence on response variables of population size and trend. We determined time to population equilibration and dynamics of populations above and below carrying capacity. Recovery time from small population size to carrying capacity greatly exceeded decay time from an overpopulated condition, suggesting lag time required to repopulate newly available habitat. Response variables were most sensitive to input parameters of habitat quality which are well‐studied for this species and controllable by management. HexSim thus seems useful for evaluating potential NSO population responses to landscape patterns for which good empirical information is available.     

Automatic Hessians by reverse accumulation

Let n be the number of independent variables of a function f,and let W and S respectively be the time and space bounds forthe joint evaluation of {f, f} using automatic differentiationwith reverse accumulation. In this note, we examine an extensionof the technique of reverse accumulation which allows the automaticextraction of the Hessian of f. The method allows the parallelevaluation of all rows of the Hessian matrix in about 2W timeunits and 3S space units on each of n processors, or sequentialrow-by-row evaluation in about 2nW time units and 3S space unitson a single processor. The approach described here is intendedfor use with operator overloading (for example in Ada) and allowsthe conventional coding of the target function f.     

Neural networks and finite-order approximations

Email: Curry{at}Cardiff.ac.uk This paper investigates the approximation properties of standardfeedforward neural networks (NNs) through the application ofmultivanate Thylor-series expansions. The capacity to approximatearbitrary functional forms is central to the NN philosophy,but is usually proved by allowing the number of hidden nodesto increase to infinity. The Thylor-series approach does notdepend on such limiting cases, lie paper shows how the seriesapproximation depends on individual network weights. The roleof the bias term is taken as an example. We are also able tocompare the sigmoid and hyperbolic-tangent activation functions,with particular emphasis on their impact on the bias term. Thepaper concludes by discussing the potential importance of ourresults for NN modelling: of particular importance is the trainingprocess.     

A Sine-Collocation Method for the Computation of the Eigenvalues of the Radial Schr?dinger Equation

A collocation scheme using sine function basis elements is developedand used to approximate the eigenvalues of the radial Schr?dingerequation. The method is shown to apply to problems with singulareigensolutions and error bounds for the approximate eigenvaluesare given. The method is applied to a few test examples to indicateboth the accuracy and the implementation of the method.