Robust algorithms for solving stochastic partial differential equations

A robust semi-implicit central partial difference algorithm for the numerical solution of coupled stochastic parabolic partial differential equations (PDEs) is described. This can be used for calculating correlation functions of systems of interacting stochastic fields. Such field equations can arise in the description of Hamiltonian and open systems in the physics of nonlinear processes, and may include multiplicative noise sources. The algorithm can be used for studying the properties of nonlinear quantum or classical field theories. The general approach is outlined and applied to a specific example, namely the quantum statistical fluctuations of ultra-short optical pulses in chi((2)) parametric waveguides. This example uses a non-diagonal coherent state representation, and correctly predicts the sub-shot noise level spectral fluctuations observed in homodyne detection measurements. It is expected that the methods used wilt be applicable for higher-order correlation functions and other physical problems as well. A stochastic differencing technique for reducing sampling errors is also introduced. This involves solving nonlinear stochastic parabolic PDEs in combination with a reference process, which uses the Wigner representation in the example presented here. A computer implementation on MIMD parallel architectures is discussed. (C) 1997 Academic Press.

Differential disease reactions on lucerne genotypes inoculated with Phytophthora medicaginis isolates from lucerne and chickpea

Stem inoculation of clonally propagated lucerne genotypes was used to assess levels of host species and genotype specialisation in Phytophthora medicaginis. A quantitative assessment of pathogenic aggressiveness of 29 P. medicaginis isolates (from lucerne and chickpea) on 9 different clonally propagated lucerne genotypes revealed no significant difference in aggressiveness between isolates from lucerne and those from chickpea on all of the lucerne genotypes. This supported previous studies which showed that P. medicaginis isolates from lucerne and chickpea were indistinguishable using random amplified polymorphic DNA (RAPD) analysis. Analysis of pathogenic aggressiveness towards individual lucerne genotypes revealed, for the first time, specificity of individual P. medicaginis isolates. This has implications for breeding for resistance to P. medicaginis in lucerne, where screening should be done using the widest range of pathogen specificity obtainable.

Local dispersion of the Eucalyptus leaf beetle Chrysophtharta bimaculata (Coleoptera: Chrysomelidae), and implications for forest protection

1. Chrysophtharta bimaculata is a native chrysomelid species that can cause chronic defoliation of plantation and regrowth Eucalyptus forests in Tasmania, Australia. Knowledge of the dispersion pattern of C. bimaculata was needed in order to assess the efficiency of an integrated pest management (IPM) programme currently used for its control. 2. Using data from yellow flight traps, local populations of C. bimaculata adults were monitored over a season at spatial scales relevant to commercial forestry: within a 50-ha operational management unit (a forestry 'coupe') and between coupes. In addition, oviposition was monitored over a season at a subset of the between-coupe sites. 3. Dispersion indices (Taylor's Power Law and Iwao's Mean Crowding regression method) demonstrated that C. bimaculata adults were spatially aggregated within and between coupes, although the number of egg-batches laid at the between-coupe scale was uniform. Spatial autocorrelation analysis showed that trap-catches at the within-coupe level were similar (positively autocorrelated) to a radius distance of approximately 110 m, and then dissimilar (negatively autocorrelated) at approximately 250 m. At the between-coupe scale, no repeatable spatial autocorrelation patterns were observed. 4. For any individual site, rapid changes in beetle density were observed to be associated with loosely aggregated flights of beetles into and out of that site. Peak adult catches (> the weekly mean plus standard deviation trap-catch) for a site occurred for a period of 2.0 +/- 0.22 weeks at a time (n = 37), with normally only one or two peaks per site per season. Peak oviposition events for a site occurred on average 1.4 +/- 0.11 times per season and lasted 1.5 +/- 0.12 weeks. 5. Analysis of an extensive data set (n = 417) demonstrated that adult abundance at a site was positively correlated with egg density, but negatively correlated with tree damage (caused by conspecifics) and the presence of conspecific larvae. There was no relationship between adult abundance and a visual estimate of the amount of young foliage on trees. 6. Adults of C. bimaculata are show n to occur in relatively small, mobile aggregations. This means that pest surveys must be both regular (less than 2 weeks apart) and intensive (with sampling points no more than 150 m apart) if beetle populations are to be monitored with confidence. Further refinement of the current IPM strategy must recognize the problems posed by this temporal and spatial patchiness, particularly with regard to the use of biological insecticides, such as Bacillus thuringiensis, for which only a very short operational window exists.

Differential expression of mitochondrial NADH dehydrogenase in ethanol-treated rat brain: Revealed by differential display

The technique of polymerase chain reaction (PCR) differential display was used to detect alterations in gene expression after chronic alcohol administration. Male Wistar rats were treated with ethanol vapor for 14 days. The cDNA generated from mRNA isolated from the hippocampi of ethanol-treated and control animals was compared by PCR differential display. A differentially expressed cDNA fragment was used to screen mRNA samples by Northern analysis. The level of a mRNA was significantly elevated (x 2.5) in the hippocampus, but not the cortex of alcohol-treated rats up to 48 hr after withdrawal. Sequence analysis of the cDNA fragment revealed an almost perfect homology to rat mitochondrial NADH dehydrogenase subunit 4 mRNA. The selective induction of this mRNA in alcohol-treated rat brain areas suggests altered metabolic processes and possible dysfunction of the mitochondria. The technique of PCR differential display may prove useful in further analysis of gene expression during alcohol dependence and withdrawal.

Differential expression of Egr-1-like DNA-binding activities in the naive rat brain and after excitatory stimulation

Egr-1 and related proteins are inducible transcription factors within the brain recognizing the same consensus DNA sequence. Three Egr DNA-binding activities were observed in regions of the naive rat brain. Egr-1 was present in all brain regions examined. Bands composed, at least in part, of Egr-2 and Egr-3 were present in different relative amounts in the cerebral cortex, striatum, hippocampus, thalamus, and midbrain. All had similar affinity and specificity for the Egr consensus DNA recognition sequence. Administration of the convulsants NMDA, kainate, and pentylenetetrazole differentially induced Egr-1 and Egr-2/3 DNA-binding activities in the cerebral cortex, hippocampus, and cerebellum. All convulsants induced Egr-1 and Egr-2 immunoreactivity in the cerebral cortex and hippocampus. These data indicate that the members of the Egr family are regulated at different levels and may interact at promoters containing the Egr consensus sequence to fine tune a program of gene expression resulting from excitatory stimuli.