Dr. Kevin Minors, MMath PhD

Dr. Kevin Minors, MMath PhD

Hamilton, Bermuda
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Kevin is a 6X-certified AWS and Azure Machine Learning Specialist with numerous years of…

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    Bermuda

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    Leeds, England, United Kingdom

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    Leeds, England, United Kingdom

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Publications

  • Simulating Crowds in Real Time with Agent-Based Modelling and a Particle Filter

    arXiv

    Agent-based modelling is a valuable approach for systems whose behaviour is driven by the interactions between distinct entities. They have shown particular promise as a means of modelling crowds of people in streets, public transport terminals, stadiums, etc. However, the methodology faces a fundamental difficulty: there are no established mechanisms for dynamically incorporating real-time data into models. This limits simulations that are inherently dynamic, such as pedestrian movements, to…

    Agent-based modelling is a valuable approach for systems whose behaviour is driven by the interactions between distinct entities. They have shown particular promise as a means of modelling crowds of people in streets, public transport terminals, stadiums, etc. However, the methodology faces a fundamental difficulty: there are no established mechanisms for dynamically incorporating real-time data into models. This limits simulations that are inherently dynamic, such as pedestrian movements, to scenario testing of, for example, the potential impacts of new architectural configurations on movements. This paper begins to address this fundamental gap by demonstrating how a particle filter could be used to incorporate real data into an agent-based model of pedestrian movements at run time. The experiments show that it is indeed possible to use a particle filter to perform online (real time) model optimisation. However, as the number of agents increases, the number of individual particles (and hence the computational complexity) required increases exponentially. By laying the groundwork for the real-time simulation of crowd movements, this paper has implications for the management of complex environments (both nationally and internationally) such as transportation hubs, hospitals, shopping centres, etc.

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  • Noise-driven bias in the non-local voter model

    Europhysics Letters

    Is it more effective to have a strong influence over a small domain, or a weaker influence over a larger one? Here, we introduce and analyse an off-lattice generalisation of the voter model, in which the range and strength of agents' influence are control parameters. We consider both low- and high-density regimes and, using distinct mathematical approaches, derive analytical predictions for the evolution of agent densities. We find that, even when the agents are equally persuasive on average…

    Is it more effective to have a strong influence over a small domain, or a weaker influence over a larger one? Here, we introduce and analyse an off-lattice generalisation of the voter model, in which the range and strength of agents' influence are control parameters. We consider both low- and high-density regimes and, using distinct mathematical approaches, derive analytical predictions for the evolution of agent densities. We find that, even when the agents are equally persuasive on average, those whose influence is wider but weaker have an overall noise-driven advantage allowing them to reliably dominate the entire population. We discuss the implications of our results and the potential of our model (or adaptations thereof) to improve the understanding of political campaign strategies and the evolution of disease.

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  • Invasions Slow Down or Collapse in the Presence of Reactive Boundaries

    Bulletin of Mathematical Biology

    Motivated by the propagation of thin bacterial films around planar obstacles, this paper considers the dynamics of travelling wave solutions to the Fisher–KPP equation ut=u(1−u)+uxx+uyy in a planar strip −∞<x<∞, 0≤y≤L. We examine the propagation of fronts in the presence of a mixed boundary condition (also referred to as a ‘partially absorbing’ or ‘reactive’ boundary) uy=αu, with α>0, at y=0. The presence of boundary conditions of this kind leads to the development of front solutions…

    Motivated by the propagation of thin bacterial films around planar obstacles, this paper considers the dynamics of travelling wave solutions to the Fisher–KPP equation ut=u(1−u)+uxx+uyy in a planar strip −∞<x<∞, 0≤y≤L. We examine the propagation of fronts in the presence of a mixed boundary condition (also referred to as a ‘partially absorbing’ or ‘reactive’ boundary) uy=αu, with α>0, at y=0. The presence of boundary conditions of this kind leads to the development of front solutions that propagate in x but contain transverse structure in y. Motivated by the observation that the speed of propagation in the Fisher–KPP equation is determined (for exponentially decaying initial conditions) by the behaviour at the leading edge, we analyse the linearised Fisher–KPP equation in order to estimate the speed of the stable travelling front, a function of the width L and the imposed boundary conditions. For wide strips the speed estimate based on the linearised equation agrees well with the results of numerical simulations. For narrow channels numerical simulations indicate that the stable front propagates more slowly, and for sufficiently small L or sufficiently large α the front speed falls to zero and the front collapses. The reason for the collapse is the non-existence, far behind the front, of a stable positive equilibrium solution u(x, y). While existence of these equilibrium states can be demonstrated via phase plane arguments, the investigation of stability is similar to calculations of critical patch sizes carried out in similar ecological models.

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Honors & Awards

  • Best Presentation

    Leeds Data Science Society

    Best Presentation at the Leeds Data Science Engagement and Employability Conference 2019

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