technical report Fourier analysis of stochastic simulations


Simulation is a simple means to investigate chemically reacting systems. In a deterministic framework, the evolution of concentration in time produced by numerically solving a set of differential equations can be seen to directly characterize an average behaviour. In a stochastic context, multiple simulation traces are required to produce an average with reasonable confidence, however the noise contains other useful information about the system. This report presents a new technique to extract useful information from simulation traces using Fourier analysis. The technique may be used with deterministic traces but is particularly effective when applied to stochastic simulations. Three statistical measures are defined over the frequency spectra of accumulated simulation traces, which may be used to characterise typical simulated behaviour. Two are independent measures of stochasticity while the third measures the distance between simulations, thus creating a space which may be used to compare models or simulation algorithms, for example. Concrete instances of the use of these techniques are presented in relation to characterising the viability of various mutant strains of budding yeast

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S. Sedwards