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Key messagesMathematical modelling is intrinsically difficult given the complexity of relationships between parameters and difficulty quantifying those parametersModelling needs input from a much wider range of sources including domain expertsData sharing and communication of results could be improvedPolicy makers and the public often had poor understanding of key concepts such as exponential growth and the limitations of long-term forecasting

In this paper, we investigate a generalised model of $N$ particles undergoing second-order non-local interactions on a lattice. Our results have applications across many research areas, including the modelling of migration, information dynamics and Muller's ratchet -- the irreversible accumulation of deleterious mutations in an evolving population. Strikingly, numerical simulations of the model are observed to deviate significantly from its mean-field approximation even for large population sizes. We show that the disagreement between deterministic and stochastic solutions stems from finite-size effects that change the propagation speed and cause the position of the wave to fluctuate. These effects are shown to decay anomalously as $(\log N)^{-2}$ and $(\log N)^{-3}$, respectively -- much slower than the usual $N^{-1/2}$ factor. Our results suggest that the accumulation of deleterious mutations in a Muller's ratchet and the loss of awareness in a population may occur much faster than predicted by the corresponding deterministic models. The general applicability of our model suggests that this unexpected scaling could be important in a wide range of real-world applications., Comment: 14 pages, 9 figures

This dissertation is comprised of two components: a critical thesis and a creative response in the form of a poetry collection. The thesis seeks to identify and chart surrealism’s ongoing influence within Australian poetry and literary history: starting with Angry Penguins journal of the 1940s; followed by the radical renewal of style in selected figures of the Generation of ’68 of the seventies and eighties; and the close study of individual poets of the contemporary period. My own poetry manuscript, Ultraviolet, supplements this thesis and continues its traditions, as a contemporary example immersed in surrealist aesthetics and literary techniques.

The probability hypothesis density (PHD) filter from the theory of random finite sets is a well-known method for multitarget tracking. We present the Gaussian mixture (GM) and improved sequential Monte Carlo implementations of the PHD filter for visual tracking. These implementations are shown to provide advantages over previous PHD filter implementations on visual data by removing complications such as clustering and data association and also having beneficial computational characteristics. The GM-PHD filter is deployed on microscopic visual data to extract trajectories of free-swimming bacteria in order to analyze their motion. Using this method, a significantly larger number of tracks are obtained than was previously possible. This permits calculation of reliable distributions for parameters of bacterial motion. The PHD filter output was tested by checking agreement with a careful manual analysis. A comparison between the PHD filter and alternative tracking methods was carried out using simulated data, demonstrating superior performance by the PHD filter in a range of realistic scenarios. © 2012 IEEE.