Journal Articles

Permanent URI for this collectionhttps://mro.massey.ac.nz/handle/10179/7915

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    Pattern Formation in a Spatially Extended Model of Pacemaker Dynamics in Smooth Muscle Cells.
    (Springer Nature Switzerland AG on behalf of the Society for Mathematical Biology, 2022-07-08) Fatoyinbo HO; Brown RG; Simpson DJW; van Brunt B
    Spatiotemporal patterns are common in biological systems. For electrically coupled cells, previous studies of pattern formation have mainly used applied current as the primary bifurcation parameter. The purpose of this paper is to show that applied current is not needed to generate spatiotemporal patterns for smooth muscle cells. The patterns can be generated solely by external mechanical stimulation (transmural pressure). To do this we study a reaction-diffusion system involving the Morris-Lecar equations and observe a wide range of spatiotemporal patterns for different values of the model parameters. Some aspects of these patterns are explained via a bifurcation analysis of the system without coupling - in particular Type I and Type II excitability both occur. We show the patterns are not due to a Turing instability and that the spatially extended model exhibits spatiotemporal chaos. We also use travelling wave coordinates to analyse travelling waves.
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    Factorizations of theta function identities
    (New Zealand Mathematical Society & University of Auckland, 28/08/2017) Cooper S; Lam HY
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    Who is most likely to offend in my store now? Statistical steps towards retail crime prevention with Auror
    (Australian Mathematical Society, 14/08/2017) McDonald BW; Hall L; Zhang XP
    Auror is establishing itself both locally and internationally as a leader in retail crime solutions. In mid-2015 a study group of mathematicians and statisticians teamed up with Auror to analyse data from the first two and a half years of their venture to identify and prevent retail theft. The aim was to explore methods for nominating the top ten individuals most likely to offend in a particular store at a particular time. Various methods were employed to explore the relationships between retail crime incidents, including generalised linear models, regression trees and similarity matrices. The relationships identified were then used to inform predictions on individuals most likely to reoffend. The focus of the current analysis is to model the behaviour of reoffenders. At the time of the study group the project was still in the early phases of data collection. As data collection proceeds, prediction methods will likely give better and better intelligence to aid crime prevention efforts.