Gauge Poisson representations for birth/death master equations

Poisson representation techniques provide a powerful method for mapping master equations for birth/death processes -- found in many fields of physics, chemistry and biology -- into more tractable stochastic differential equations. However, the usual expansion is not exact in the presence of boundary terms, which commonly occur when the differential equations are nonlinear. In this paper, a gauge Poisson technique is introduced that eliminates boundary terms, to give an exact representation as a weighted rate equation with stochastic terms. These methods provide novel techniques for calculating and understanding the effects of number correlations in systems that have a master equation description. As examples, correlations induced by strong mutations in genetics, and the astrophysical problem of molecule formation on microscopic grain surfaces are analyzed. Exact analytic results are obtained that can be compared with numerical simulations, demonstrating that stochastic gauge techniques can give exact results where standard Poisson expansions are not able to.

Stochastic delay differential equations for genetic regulatory networks

Time delay is an important aspect in the modelling of genetic regulation due to slow biochemical reactions such as gene transcription and translation, and protein diffusion between the cytosol and nucleus. In this paper we introduce a general mathematical formalism via stochastic delay differential equations for describing time delays in genetic regulatory networks. Based on recent developments with the delay stochastic simulation algorithm, the delay chemical masterequation and the delay reaction rate equation are developed for describing biological reactions with time delay, which leads to stochastic delay differential equations derived from the Langevin approach. Two simple genetic regulatory networks are used to study the impact of' intrinsic noise on the system dynamics where there are delays. (c) 2006 Elsevier B.V. All rights reserved.

Relationship between ash content and R-70 self-heating rate of Callide Coal

Borecore samples from the Trap Gully pit at Callide have been assessed using the R-70 self-heating test. The highest R-70 self-heating rate value was 16.22 degrees C/h, which is consistent with the subbituminous rank of the coal. R-70 decreases significantly with increasing mineral matter content, as defined by the ash content of the coal. This effect is due to the mineral matter in the coal acting as a heat sink. A trendline equation has been fitted to the borecore data from the Trap Gully pit: R-70 = 0.0029 x ash(2) - 0.4889 x ash + 20.644, where all parameters are on a dry-basis. This relationship can be used to model the self-heating hazard of the pit, both vertically and laterally. (c) 2005 Elsevier B.V All rights reserved.