numbers floating across space

Mark Girolami Chair of Statistics, Imperial College London, and The Alan Turing Institute presents: Stochastic Modelling of Urban Structure

When: Monday 20 November, 11:10am

Where: Engineering North N132


Urban systems are complex in nature and comprise of a large number of individuals that act according to utility, a measure of net benefit pertaining to preferences. The actions of individuals give rise to an emergent behaviour, creating the so-called urban structure that we observe. In this talk, I develop a stochastic model of urban structure to formally account for uncertainty arising from the complex behaviour. We further use this stochastic model to infer the components of a utility function from observed urban structure. This is a more powerful modelling framework in comparison to the ubiquitous discrete choice models that are of limited use for complex systems, in which the overall preferences of individuals are difficult to ascertain. We model urban structure as a realization of a Boltzmann distribution that is the invariant distribution of a related stochastic differential equation (SDE) that describes the dynamics of the urban system. Our specification of Boltzmann distribution assigns higher probability to stable configurations, in the sense that consumer surplus (demand) is balanced with running costs (supply), as characterized by a potential function. We specify a Bayesian hierarchical model to infer the components of a utility function from observed structure. Our model is doubly-intractable and poses significant computational challenges that we overcome using recent advances in Markov chain Monte Carlo (MCMC) methods. We demonstrate our methodology with case studies on the London retail system and airports in England.
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When:Friday 27 Oct

Where: Ingkarni Wardli B17

Presented by Dr Sophie Hautphenne, University of Melbourne


Markovian binary trees form a general and tractable class of continuous-time branching processes, which makes them well-suited for real-world applications. Thanks to their appealing probabilistic and computational features, these processes have proven to be an excellent modelling tool for applications in population biology. Typical performance measures of these models include the extinction probability of a population, the distribution of the population size at a given time, the total progeny size until extinction, and the asymptotic population composition. Besides giving an overview of the main performance measures and the techniques involved to compute them, we discuss recently developed statistical methods to estimate the model parameters, depending on the accuracy of the available data. We illustrate our results in human demography and in conservation biology

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Friday 13 October

Ingkarni Wardli B17

Professor Mat Simpson, Queensland University of Technology

Scald burns from accidental exposure to hot liquids are the most common cause of burn injury in children. Over 2000 children are treated for accidental burn injuries in Australia each year. Despite the frequency of these injuries, basic questions about the physics of heat transfer in living tissues remain unanswered. For example, skin thickness varies with age and anatomical location, yet our understanding of how tissue damage from thermal injury is influenced by skin thickness is surprisingly limited. In this presentation we will consider a series of porcine experiments to study heat transfer in living tissues. We consider burning the living tissue, as well as applying various first aid treatment strategies to cool the living tissue after injury. By calibrating solutions of simple mathematical models to match the experimental data we provide insight into how thermal energy propagates through living tissues, as well as exploring different first aid strategies. We conclude by outlining some of our current work that aims to produce more realistic mathematical models.

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This Friday, 11 August, we have a School Colloquium with Dr Robyn Araujo from Queensland University of Technology. The talk is in Ingkarni Wardli B17 at 15:10. Mathematics is Biology’s Next Microscope (Only Better!) Abstract: While mathematics has long been considered “an essential tool for physics”, the foundations of biology and the life sciences have […]

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The School of Mathematical Sciences has a long history of achievement in research and postgraduate education, and a reputation for providing a stimulating and supportive environment. The School is highly respected internationally for its research strengths in geometry, statistics, stochastic modelling and operations research, and dynamics, modelling and computation. Please see our Research pages, for […]

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This Friday, 28 July, we have a School Colloquium with Prof Philip Hall from Monash University. The talk is in Ingkarni Wardli B17 at 15:10. Abstract: In recent years, there has been much interest in the relevance of nonlinear solutions of the Navier-Stokes equations to fully turbulent flows. The solutions must be calculated numerically at […]

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Elder Professor of Mathematics in the School of Mathematical Sciences, has been awarded an Australian Laureate Fellowship worth $1.64 million to advance Index Theory and its applications. The project is expected to enhance Australia’s position at the forefront of international research in geometric analysis. To find out more visit:

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Offering a range of engaging talks, informative displays and tours of world-class teaching and research facilities, the Faculty of ECMS presents an overview of study areas and career prospects in these dynamic disciplines. All schools within the faculty will be showcasing their programs in the Ingkarni Wardli atrium, with academics and current university students available […]

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Speakers: Tony Roberts 2nd May Barry Cox 22nd May

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 Napier 209 :: Jesse Gell-Redman :: University of Melbourne Abstract… The Hodge theorem on a closed Riemannian manifold identifies the deRham cohomology with the space of harmonic differential forms. Although there are various extensions of the Hodge theorem to singular or complete but non-compact spaces, when there is an identification of L^2 Harmonic forms with […]

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