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People matching "Modelling the South Australian garfish population "

Professor Nigel Bean
Chair of Applied Mathematics


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Professor Robert Elliott
Adjunct Professor


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Dr David Green
Lecturer in Applied Mathematics


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Professor Tony Roberts
Professor of Applied Mathematics


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Associate Professor Joshua Ross
Senior Lecturer in Applied Mathematics


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Professor Matthew Roughan
Professor of Applied Mathematics


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Courses matching "Modelling the South Australian garfish population "

Financial Modelling: Tools and Techniques

The growth of the range of financial products that are traded on financial markets or are available at other financial institutions, is a notable feature of the finance industry. A major factor contributing to this growth has been the development of sophisticated methods to price these products. The significance to the finance industry of developing a method for pricing options (financial derivatives) was recognized by the awarding of the Nobel Prize in Economics to Myron Scholes and Robert Merton in 1997. The mathematics upon which their method is built is stochastic calculus in continuous time. Binomial lattice type models provide another approach for pricing options. These models are formulated in discrete time and the examination of their structure and application in various financial settings takes place in a mathematical context that is less technically demanding than when time is continuous. This course discusses the binomial framework, shows how discrete-time models currently used in the financial industry are formulated within this framework and uses the models to compute prices and construct hedges to manage financial risk. Spreadsheets are used to facilitate computations where appropriate. Topics covered are: The no-arbitrage assumption for financial markets; no-arbitrage inequalities; formulation of the one-step binomial model; basic pricing formula; the Cox-Ross-Rubinstein (CRR) model; application to European style options, exchange rates and interest rates; formulation of the n-step binomial model; backward induction formula; forward induction formula; n-step CRR model; relationship to Black-Scholes; forward and future contracts; exotic options; path dependent options; implied volatility trees; implied binomial trees; interest rate models; hedging; real options; implementing the models using EXCEL spreadsheets.

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Modelling and Simulation of Stochastic Systems

The course provides students with the skills to analyse and design systems using modelling and simulation techniques. Case studies will be undertaken involving hands-on use of simulation packages. The application of simulation in areas such as manufacturing, telecommunications and transport will be investigated. At the end of this course, students will be capable of identifying practical situations where simulation modelling can be helpful, reporting to management on how they would undertake such a project, collecting relevant data, building and validating a model, analysing the output and reporting their findings to management. Students complete a project in groups of two or three, write a concise summary of what they have done and report their findings to the class. The project report at the end of this course should be a substantial document that is a record of a student's practical ability in simulation modelling, which can also become part of a portfolio or CV. Topics covered are: Introduction to simulation, hand simulation, introduction to a simulation package, review of basic probabilty theory, introduction to random number generation, generation of random variates, anaylsis of simulation output, variance reduction techniques and basic analytic queeing models.

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Statistical Analysis and Modelling 1

This is a first course in Statistics for mathematically inclined students. It will address the key principles underlying commonly used statistical methods such as confidence intervals, hypothesis tests, inference for means and proportions, and linear regression. It will develop a deeper mathematical understanding of these ideas, many of which will be familiar from studies in secondary school. The application of basic and more advanced statistical methods will be illustrated on a range of problems from areas such as medicine, science, technology, government, commerce and manufacturing. The use of the statistical package SPSS will be developed through a sequence of computer practicals. Topics covered will include: basic probability and random variables, fundamental distributions, inference for means and proportions, comparison of independent and paired samples, simple linear regression, diagnostics and model checking, multiple linear regression, simple factorial models, models with factors and continuous predictors.

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Statistical Modelling and Inference

Statistical methods are important to all areas that rely on data including science, technology, government and commerce. To deal with the complex problems that arise in practice requires a sound understanding of fundamental statistical principles together with a range of suitable modelling techniques. Computing using a high level statistical package is also an essential element of modern statistical practice. This course provides an introduction to the principles of statistical inference and the development of linear statistical models with the statistical package R. Topics covered are: Point estimates, unbiasedness, mean-squared error, confidence intervals, tests of hypotheses, power calculations, derivation of one and two-sample procedures; simple linear regression, regression diagnostics, prediction; linear models, ANOVA, multiple regression, factorial experiments, analysis of covariance models, model building; likelihood based methods for estimation and testing, goodness of fit tests; sample surveys, population means, totals and proportions, simple random samples, stratified random samples. Topics covered are: point estimates, unbiasedness, mean-squared error, confidence intervals, tests of hypotheses, power calculations, derivation of one and two-sample procedures: simple linear regression, regression diagnostics, prediction: linear models, analysis of variance (ANOVA), multiple regression, factorial experiments, analysis of covariance models, model building; likelihood-based methods for estimation and testing and goodness-of-fit tests.

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Statistical Modelling III

One of the key requirements of an applied statistician is the ability to formulate appropriate statistical models and then apply them to data in order to answer the questions of interest. Most often, such models can be seen as relating a response variable to one or more explanatory variables. For example, in a medical experiment we may seek to evaluate a new treatment by relating patient outcome to treatment received while allowing for background variables such as age, sex and disease severity. In this course, a rigorous discussion of the linear model is given and various extensions are developed. There is a strong practical emphasis and the statistical package R is used extensively. Topics covered are: the linear model, least squares estimation, generalised least squares estimation, properties of estimators, the Gauss-Markov theorem; geometry of least squares, subspace formulation of linear models, orthogonal projections; regression models, factorial experiments, analysis of covariance and model formulae; regression diagnostics, residuals, influence diagnostics, transformations, Box-Cox models, model selection and model building strategies; models with complex error structure, split-plot experiments; logistic regression models.

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Events matching "Modelling the South Australian garfish population "

Watching evolution in real time; problems and potential research areas.
15:10 Fri 26 May, 2006 :: G08. Mathematics Building University of Adelaide :: Prof Alan Cooper (Federation Fellow)

Recent studies (1) have indicated problems with our ability to use the genetic distances between species to estimate the time since their divergence (so called molecular clocks). An exponential decay curve has been detected in comparisons of closely related taxa in mammal and bird groups, and rough approximations suggest that molecular clock calculations may be problematic for the recent past (eg <1 million years). Unfortunately, this period encompasses a number of key evolutionary events where estimates of timing are critical such as modern human evolutionary history, the domestication of animals and plants, and most issues involved in conservation biology. A solution (formulated at UA) will be briefly outlined. A second area of active interest is the recent suggestion (2) that mitochondrial DNA diversity does not track population size in several groups, in contrast to standard thinking. This finding has been interpreted as showing that mtDNA may not be evolving neutrally, as has long been assumed.
Large ancient DNA datasets provide a means to examine these issues, by revealing evolutionary processes in real time (3). The data also provide a rich area for mathematical investigation as temporal information provides information about several parameters that are unknown in serial coalescent calculations (4).
References:
  1. Ho SYW et al. Time dependency of molecular rate estimates and systematic overestimation of recent divergence times. Mol. Biol. Evol. 22, 1561-1568 (2005);
    Penny D, Nature 436, 183-184 (2005).
  2. Bazin E., et al. Population size does not influence mitochondrial genetic diversity in animals. Science 312, 570 (2006);
    Eyre-Walker A. Size does not matter for mitochondrial DNA, Science 312, 537 (2006).
  3. Shapiro B, et al. Rise and fall of the Beringian steppe bison. Science 306: 1561-1565 (2004);
    Chan et al. Bayesian estimation of the timing and severity of a population bottleneck from ancient DNA. PLoS Genetics, 2 e59 (2006).
  4. Drummond et al. Measurably evolving populations, Trends in Ecol. Evol. 18, 481-488 (2003);
    Drummond et al. Bayesian coalescent inference of past population dynamics from molecular sequences. Molecular Biology Evolution 22, 1185-92 (2005).
Mathematical modelling of multidimensional tissue growth
16:10 Tue 24 Oct, 2006 :: Benham Lecture Theatre :: Prof John King

Some simple continuum-mechanics-based models for the growth of biological tissue will be formulated and their properties (particularly with regard to stability) described.
Modelling gene networks: the case of the quorum sensing network in bacteria.
15:10 Fri 1 Jun, 2007 :: G08 Mathematics Building University of Adelaide :: Dr Adrian Koerber

The quorum sensing regulatory gene-network is employed by bacteria to provide a measure of their population-density and switch their behaviour accordingly. I will present an overview of quorum sensing in bacteria together with some of the modelling approaches I\'ve taken to describe this system. I will also discuss how this system relates to virulence and medical treatment, and the insights gained from the mathematics.
Insights into the development of the enteric nervous system and Hirschsprung's disease
15:10 Fri 24 Aug, 2007 :: G08 Mathematics building University of Adelaide :: Assoc. Prof. Kerry Landman :: Department of Mathematics and Statistics, University of Melbourne

During the development of the enteric nervous system, neural crest (NC) cells must first migrate into and colonise the entire gut from stomach to anal end. The migratory precursor NC cells change type and differentiate into neurons and glia cells. These cells form the enteric nervous system, which gives rise to normal gut function and peristaltic contraction. Failure of the NC cells to invade the whole gut results in a lack of neurons in a length of the terminal intestine. This potentially fatal condition, marked by intractable constipation, is called Hirschsprung's Disease. The interplay between cell migration, cell proliferation and embryonic gut growth are important to the success of the NC cell colonisation process. Multiscale models are needed in order to model the different spatiotemporal scales of the NC invasion. For example, the NC invasion wave moves into unoccupied regions of the gut with a wave speed of around 40 microns per hour. New time-lapse techniques have shown that there is a web-like network structure within the invasion wave. Furthermore, within this network, individual cell trajectories vary considerably. We have developed a population-scale model for basic rules governing NC cell invasive behaviour incorporating the important mechanisms. The model predictions were tested experimentally. Mathematical and experimental results agreed. The results provide an understanding of why many of the genes implicated in Hirschsprung's Disease influence NC population size. Our recently developed individual cell-based model also produces an invasion wave with a well-defined wave speed; however, in addition Individual cell trajectories within the invasion wave can be extracted. Further challenges in modeling the various scales of the developmental system will be discussed.
Groundwater: using mathematics to solve our water crisis
13:10 Wed 9 Apr, 2008 :: Napier 210 :: Dr Michael Teubner

'The driest state in the driest continent' is how South Australia used to be described. And that was before the drought! Now we have severe water restrictions, dead lawns, and dying gardens. But this need not be the case. Mathematics to the rescue! Groundwater exists below much of the Adelaide metro area. We can store winter stormwater in the ground and use it when we need it in summer. But we need mathematical models to understand where groundwater exists, where we can inject stormwater and how much can be stored, and where we can extract it: all through mathematical models. Come along and see that we don't have a water problem, we have a water management problem.
Global and Local stationary modelling in finance: Theory and empirical evidence
14:10 Thu 10 Apr, 2008 :: G04 Napier Building University of Adelaide :: Prof. Dominique Guégan :: Universite Paris 1 Pantheon-Sorbonne

To model real data sets using second order stochastic processes imposes that the data sets verify the second order stationarity condition. This stationarity condition concerns the unconditional moments of the process. It is in that context that most of models developed from the sixties' have been studied; We refer to the ARMA processes (Brockwell and Davis, 1988), the ARCH, GARCH and EGARCH models (Engle, 1982, Bollerslev, 1986, Nelson, 1990), the SETAR process (Lim and Tong, 1980 and Tong, 1990), the bilinear model (Granger and Andersen, 1978, Guégan, 1994), the EXPAR model (Haggan and Ozaki, 1980), the long memory process (Granger and Joyeux, 1980, Hosking, 1981, Gray, Zang and Woodward, 1989, Beran, 1994, Giraitis and Leipus, 1995, Guégan, 2000), the switching process (Hamilton, 1988). For all these models, we get an invertible causal solution under specific conditions on the parameters, then the forecast points and the forecast intervals are available.

Thus, the stationarity assumption is the basis for a general asymptotic theory for identification, estimation and forecasting. It guarantees that the increase of the sample size leads to more and more information of the same kind which is basic for an asymptotic theory to make sense.

Now non-stationarity modelling has also a long tradition in econometrics. This one is based on the conditional moments of the data generating process. It appears mainly in the heteroscedastic and volatility models, like the GARCH and related models, and stochastic volatility processes (Ghysels, Harvey and Renault 1997). This non-stationarity appears also in a different way with structural changes models like the switching models (Hamilton, 1988), the stopbreak model (Diebold and Inoue, 2001, Breidt and Hsu, 2002, Granger and Hyung, 2004) and the SETAR models, for instance. It can also be observed from linear models with time varying coefficients (Nicholls and Quinn, 1982, Tsay, 1987).

Thus, using stationary unconditional moments suggest a global stationarity for the model, but using non-stationary unconditional moments or non-stationary conditional moments or assuming existence of states suggest that this global stationarity fails and that we only observe a local stationary behavior.

The growing evidence of instability in the stochastic behavior of stocks, of exchange rates, of some economic data sets like growth rates for instance, characterized by existence of volatility or existence of jumps in the variance or on the levels of the prices imposes to discuss the assumption of global stationarity and its consequence in modelling, particularly in forecasting. Thus we can address several questions with respect to these remarks.

1. What kinds of non-stationarity affect the major financial and economic data sets? How to detect them?

2. Local and global stationarities: How are they defined?

3. What is the impact of evidence of non-stationarity on the statistics computed from the global non stationary data sets?

4. How can we analyze data sets in the non-stationary global framework? Does the asymptotic theory work in non-stationary framework?

5. What kind of models create local stationarity instead of global stationarity? How can we use them to develop a modelling and a forecasting strategy?

These questions began to be discussed in some papers in the economic literature. For some of these questions, the answers are known, for others, very few works exist. In this talk I will discuss all these problems and will propose 2 new stategies and modelling to solve them. Several interesting topics in empirical finance awaiting future research will also be discussed.

Computational Methods for Phase Response Analysis of Circadian Clocks
15:10 Fri 18 Jul, 2008 :: G04 Napier Building University of Adelaide. :: Prof. Linda Petzold :: Dept. of Mechanical and Environmental Engineering, University of California, Santa Barbara

Circadian clocks govern daily behaviors of organisms in all kingdoms of life. In mammals, the master clock resides in the suprachiasmatic nucleus (SCN) of the hypothalamus. It is composed of thousands of neurons, each of which contains a sloppy oscillator - a molecular clock governed by a transcriptional feedback network. Via intercellular signaling, the cell population synchronizes spontaneously, forming a coherent oscillation. This multi-oscillator is then entrained to its environment by the daily light/dark cycle.

Both at the cellular and tissular levels, the most important feature of the clock is its ability not simply to keep time, but to adjust its time, or phase, to signals. We present the parametric impulse phase response curve (pIPRC), an analytical analog to the phase response curve (PRC) used experimentally. We use the pIPRC to understand both the consequences of intercellular signaling and the light entrainment process. Further, we determine which model components determine the phase response behavior of a single oscillator by using a novel model reduction technique. We reduce the number of model components while preserving the pIPRC and then incorporate the resultant model into a couple SCN tissue model. Emergent properties, including the ability of the population to synchronize spontaneously are preserved in the reduction. Finally, we present some mathematical tools for the study of synchronization in a network of coupled, noisy oscillators.

Betti's Reciprocal Theorem for Inclusion and Contact Problems
15:10 Fri 1 Aug, 2008 :: G03 Napier Building University of Adelaide :: Prof. Patrick Selvadurai :: Department of Civil Engineering and Applied Mechanics, McGill University

Enrico Betti (1823-1892) is recognized in the mathematics community for his pioneering contributions to topology. An equally important contribution is his formulation of the reciprocity theorem applicable to elastic bodies that satisfy the classical equations of linear elasticity. Although James Clerk Maxwell (1831-1879) proposed a law of reciprocal displacements and rotations in 1864, the contribution of Betti is acknowledged for its underlying formal mathematical basis and generality. The purpose of this lecture is to illustrate how Betti's reciprocal theorem can be used to full advantage to develop compact analytical results for certain contact and inclusion problems in the classical theory of elasticity. Inclusion problems are encountered in number of areas in applied mechanics ranging from composite materials to geomechanics. In composite materials, the inclusion represents an inhomogeneity that is introduced to increase either the strength or the deformability characteristics of resulting material. In geomechanics, the inclusion represents a constructed material region, such as a ground anchor, that is introduced to provide load transfer from structural systems. Similarly, contact problems have applications to the modelling of the behaviour of indentors used in materials testing to the study of foundations used to distribute loads transmitted from structures. In the study of conventional problems the inclusions and the contact regions are directly loaded and this makes their analysis quite straightforward. When the interaction is induced by loads that are placed exterior to the indentor or inclusion, the direct analysis of the problem becomes inordinately complicated both in terns of formulation of the integral equations and their numerical solution. It is shown by a set of selected examples that the application of Betti's reciprocal theorem leads to the development of exact closed form solutions to what would otherwise be approximate solutions achievable only through the numerical solution of a set of coupled integral equations.
Probabilistic models of human cognition
15:10 Fri 29 Aug, 2008 :: G03 Napier Building University of Adelaide :: Dr Daniel Navarro :: School of Psychology, University of Adelaide

Over the last 15 years a fairly substantial psychological literature has developed in which human reasoning and decision-making is viewed as the solution to a variety of statistical problems posed by the environments in which we operate. In this talk, I briefly outline the general approach to cognitive modelling that is adopted in this literature, which relies heavily on Bayesian statistics, and introduce a little of the current research in this field. In particular, I will discuss work by myself and others on the statistical basis of how people make simple inductive leaps and generalisations, and the links between these generalisations and how people acquire word meanings and learn new concepts. If time permits, the extensions of the work in which complex concepts may be characterised with the aid of nonparametric Bayesian tools such as Dirichlet processes will be briefly mentioned.
Mathematical modelling of blood flow in curved arteries
15:10 Fri 12 Sep, 2008 :: G03 Napier Building University of Adelaide :: Dr Jennifer Siggers :: Imperial College London

Atherosclerosis, characterised by plaques, is the most common arterial disease. Plaques tend to develop in regions of low mean wall shear stress, and regions where the wall shear stress changes direction during the course of the cardiac cycle. To investigate the effect of the arterial geometry and driving pressure gradient on the wall shear stress distribution we consider an idealised model of a curved artery with uniform curvature. We assume that the flow is fully-developed and seek solutions of the governing equations, finding the effect of the parameters on the flow and wall shear stress distribution. Most previous work assumes the curvature ratio is asymptotically small; however, many arteries have significant curvature (e.g. the aortic arch has curvature ratio approx 0.25), and in this work we consider in particular the effect of finite curvature.

We present an extensive analysis of curved-pipe flow driven by a steady and unsteady pressure gradients. Increasing the curvature causes the shear stress on the inside of the bend to rise, indicating that the risk of plaque development would be overestimated by considering only the weak curvature limit.

Assisted reproduction technology: how maths can contribute
13:10 Wed 22 Oct, 2008 :: Napier 210 :: Dr Yvonne Stokes

Media...
Most people will have heard of IVF (in vitro fertilisation), a technology for helping infertile couples have a baby. Although there are many IVF babies, many will also know that the success rate is still low for the cost and inconvenience involved. The fact that some women cannot make use of IVF because of life-threatening consequences is less well known but motivates research into other technologies, including IVM (in vitro maturation). What has all this to do with maths? Come along and find out how mathematical modelling is contributing to understanding and improvement in this important and interesting field.
Oceanographic Research at the South Australian Research and Development Institute: opportunities for collaborative research
15:10 Fri 21 Nov, 2008 :: Napier G04 :: Associate Prof John Middleton :: South Australian Research and Development Institute

Increasing threats to S.A.'s fisheries and marine environment have underlined the increasing need for soundly based research into the ocean circulation and ecosystems (phyto/zooplankton) of the shelf and gulfs. With support of Marine Innovation SA, the Oceanography Program has within 2 years, grown to include 6 FTEs and a budget of over $4.8M. The program currently leads two major research projects, both of which involve numerical and applied mathematical modelling of oceanic flow and ecosystems as well as statistical techniques for the analysis of data. The first is the implementation of the Southern Australian Integrated Marine Observing System (SAIMOS) that is providing data to understand the dynamics of shelf boundary currents, monitor for climate change and understand the phyto/zooplankton ecosystems that under-pin SA's wild fisheries and aquaculture. SAIMOS involves the use of ship-based sampling, the deployment of underwater marine moorings, underwater gliders, HF Ocean RADAR, acoustic tracking of tagged fish and Autonomous Underwater vehicles.

The second major project involves measuring and modelling the ocean circulation and biological systems within Spencer Gulf and the impact on prawn larval dispersal and on the sustainability of existing and proposed aquaculture sites. The discussion will focus on opportunities for collaborative research with both faculty and students in this exciting growth area of S.A. science.

Multi-scale tools for interpreting cell biology data
15:10 Fri 17 Apr, 2009 :: Napier LG29 :: Dr Matthew Simpson :: University of Melbourne

Trajectory data from observations of a random walk process are often used to characterize macroscopic transport coefficients and to infer motility mechanisms in cell biology. New continuum equations describing the average moments of the position of an individual agent in a population of interacting agents are derived and validated. Unlike standard noninteracting random walks, the new moment equations explicitly represent the interactions between agents as they are coupled to the macroscopic agent density. Key issues associated with the validity of the new continuum equations and the interpretation of experimental data will be explored.
Modelling fluid-structure interactions in micro-devices
15:00 Thu 3 Sep, 2009 :: School Board Room :: Dr Richard Clarke :: University of Auckland

The flows generated in many modern micro-devices possess very little convective inertia, however, they can be highly unsteady and exert substantial hydrodynamic forces on the device components. Typically these components exhibit some degree of compliance, which traditionally has been treated using simple one-dimensional elastic beam models. However, recent findings have suggested that three-dimensional effects can be important and, accordingly, we consider the elastohydrodynamic response of a rapidly oscillating three-dimensional elastic plate that is immersed in a viscous fluid. In addition, a preliminary model will be presented which incorporates the presence of a nearby elastic wall.
The proof of the Poincare conjecture
15:10 Fri 25 Sep, 2009 :: Napier 102 :: Prof Terrence Tao :: UCLA

In a series of three papers from 2002-2003, Grigori Perelman gave a spectacular proof of the Poincare Conjecture (every smooth compact simply connected three-dimensional manifold is topologically isomorphic to a sphere), one of the most famous open problems in mathematics (and one of the seven Clay Millennium Prize Problems worth a million dollars each), by developing several new groundbreaking advances in Hamilton's theory of Ricci flow on manifolds. In this talk I describe in broad detail how the proof proceeds, and briefly discuss some of the key turning points in the argument. About the speaker: Terence Tao was born in Adelaide, Australia, in 1975. He has been a professor of mathematics at UCLA since 1999, having completed his PhD under Elias Stein at Princeton in 1996. Tao's areas of research include harmonic analysis, PDE, combinatorics, and number theory. He has received a number of awards, including the Salem Prize in 2000, the Bochner Prize in 2002, the Fields Medal and SASTRA Ramanujan Prize in 2006, and the MacArthur Fellowship and Ostrowski Prize in 2007. Terence Tao also currently holds the James and Carol Collins chair in mathematics at UCLA, and is a Fellow of the Royal Society and the Australian Academy of Sciences (Corresponding Member).
Modelling and pricing for portfolio credit derivatives
15:10 Fri 16 Oct, 2009 :: MacBeth Lecture Theatre :: Dr Ben Hambly :: University of Oxford

The current financial crisis has been in part precipitated by the growth of complex credit derivatives and their mispricing. This talk will discuss some of the background to the `credit crunch', as well as the models and methods used currently. We will then develop an alternative view of large basket credit derivatives, as functions of a stochastic partial differential equation, which addresses some of the shortcomings.
Some unusual uses of usual symmetries and some usual uses of unusual symmetries
12:10 Wed 10 Mar, 2010 :: School board room :: Prof Phil Broadbridge :: La Trobe University

Ever since Sophus Lie around 1880, continuous groups of invariance transformations have been used to reduce variables and to construct special solutions of PDEs. I will outline the general ideas, then show some variations on the usual reduction algorithm that I have used to solve some practical nonlinear boundary value problems. Applications include soil-water flow, metal surface evolution and population genetics.
Modelling of the Human Skin Equivalent
15:10 Fri 26 Mar, 2010 :: Napier 102 :: Prof Graeme Pettet :: Queensland University of Technology

A brief overview will be given of the development of a so called Human Skin Equivalent Construct. This laboratory grown construct can be used for studying growth, response and the repair of human skin subjected to wounding and/or treatment under strictly regulated conditions. Details will also be provided of a series of mathematical models we have developed that describe the dynamics of the Human Skin Equivalent Construct, which can be used to assist in the development of the experimental protocol, and to provide insight into the fundamental processes at play in the growth and development of the epidermis in both healthy and diseased states.
Hugs not drugs
15:10 Mon 20 Sep, 2010 :: Ingkarni Wardli B17 :: Dr Scott McCue :: Queensland University of Technology

I will discuss a model for drug diffusion that involves a Stefan problem with a "kinetic undercooling". I like Stefan problems, so I like this model. I like drugs too, but only legal ones of course. Anyway, it turns out that in some parameter regimes, this sophisticated moving boundary problem hardly works better than a simple linear undergraduate model (there's a lesson here for mathematical modelling). On the other hand, for certain polymer capsules, the results are interesting and suggest new means for controlled drug delivery. If time permits, I may discuss certain asymptotic limits that are of interest from a Stefan problem perspective. Finally, I won't bring any drugs with me to the seminar, but I'm willing to provide hugs if necessary.
At least four doors, numerous goats, a car, a frog, four lily pads and some probability
11:10 Wed 13 Oct, 2010 :: Napier 210 :: Dr Joshua Ross :: University of Adelaide

Media...
In the process of determining, amongst other things, the optimal strategy for playing a game show, and explaining the apparent persistence of a population that can be shown to die out with certainty, we will encounter a car, numerous goats, at least four doors, a frog, four lily pads, and some applied probability.
Arbitrage bounds for weighted variance swap prices
15:05 Fri 3 Dec, 2010 :: Napier LG28 :: Prof Mark Davis :: Imperial College London

This paper builds on earlier work by Davis and Hobson (Mathematical Finance, 2007) giving model-free---except for a 'frictionless markets' assumption--- necessary and sufficient conditions for absence of arbitrage given a set of current-time put and call options on some underlying asset. Here we suppose that the prices of a set of put options, all maturing at the same time, are given and satisfy the conditions for consistency with absence of arbitrage. We now add a path-dependent option, specifically a weighted variance swap, to the set of traded assets and ask what are the conditions on its time-0 price under which consistency with absence of arbitrage is maintained. In the present work, we work under the extra modelling assumption that the underlying asset price process has continuous paths. In general, we find that there is always a non- trivial lower bound to the range of arbitrage-free prices, but only in the case of a corridor swap do we obtain a finite upper bound. In the case of, say, the vanilla variance swap, a finite upper bound exists when there are additional traded European options which constrain the left wing of the volatility surface in appropriate ways.
Heat transfer scaling and emergence of three-dimensional flow in horizontal convection
15:10 Fri 25 Feb, 2011 :: Conference Room Level 7 Ingkarni Wardli :: Dr Greg Sheard :: Monash University

Horizontal convecton refers to flows driven by uneven heating on a horizontal forcing boundary. Flows exhibiting these characteristics are prevalent in nature, and include the North-South Hadley circulation within the atmosphere between warmer and more temperate latitudes, as well as ocean currents driven by non-uniform heating via solar radiation.

Here a model for these generic convection flows is established featuring a rectangular enclosure, insulated on the side and top walls, and driven by a linear temperature gradient applied along the bottom wall. Rayleigh number dependence of heat transfer through the forcing boundary is computed and compared with theory. Attention is given to transitions in the flow, including the development of unsteady flow and three-dimensional flow: the effect of these transitions on the Nusselt-Rayleigh number scaling exponents is described.

Mathematical modelling in nanotechnology
15:10 Fri 4 Mar, 2011 :: 7.15 Ingkarni Wardli :: Prof Jim Hill :: University of Adelaide

Media...
In this talk we present an overview of the mathematical modelling contributions of the Nanomechanics Groups at the Universities of Adelaide and Wollongong. Fullerenes and carbon nanotubes have unique properties, such as low weight, high strength, flexibility, high thermal conductivity and chemical stability, and they have many potential applications in nano-devices. In this talk we first present some new results on the geometric structure of carbon nanotubes and on related nanostructures. One concept that has attracted much attention is the creation of nano-oscillators, to produce frequencies in the gigahertz range, for applications such as ultra-fast optical filters and nano-antennae. The sliding of an inner shell inside an outer shell of a multi-walled carbon nanotube can generate oscillatory frequencies up to several gigahertz, and the shorter the inner tube the higher the frequency. A C60-nanotube oscillator generates high frequencies by oscillating a C60 fullerene inside a single-walled carbon nanotube. Here we discuss the underlying mechanisms of nano-oscillators and using the Lennard-Jones potential together with the continuum approach, to mathematically model the C60-nanotube nano-oscillator. Finally, three illustrative examples of recent modelling in hydrogen storage, nanomedicine and nanocomputing are discussed.
Modelling of Hydrological Persistence in the Murray-Darling Basin for the Management of Weirs
12:10 Mon 4 Apr, 2011 :: 5.57 Ingkarni Wardli :: Aiden Fisher :: University of Adelaide

The lakes and weirs along the lower Murray River in Australia are aggregated and considered as a sequence of five reservoirs. A seasonal Markov chain model for the system will be implemented, and a stochastic dynamic program will be used to find optimal release strategies, in terms of expected monetary value (EMV), for the competing demands on the water resource given the stochastic nature of inflows. Matrix analytic methods will be used to analyse the system further, and in particular enable the full distribution of first passage times between any groups of states to be calculated. The full distribution of first passage times can be used to provide a measure of the risk associated with optimum EMV strategies, such as conditional value at risk (CVaR). The sensitivity of the model, and risk, to changing rainfall scenarios will be investigated. The effect of decreasing the level of discretisation of the reservoirs will be explored. Also, the use of matrix analytic methods facilitates the use of hidden states to allow for hydrological persistence in the inflows. Evidence for hydrological persistence of inflows to the lower Murray system, and the effect of making allowance for this, will be discussed.
On parameter estimation in population models
15:10 Fri 6 May, 2011 :: 715 Ingkarni Wardli :: Dr Joshua Ross :: The University of Adelaide

Essential to applying a mathematical model to a real-world application is calibrating the model to data. Methods for calibrating population models often become computationally infeasible when the populations size (more generally the size of the state space) becomes large, or other complexities such as time-dependent transition rates, or sampling error, are present. Here we will discuss the use of diffusion approximations to perform estimation in several scenarios, with successively reduced assumptions: (i) under the assumption of stationarity (the process had been evolving for a very long time with constant parameter values); (ii) transient dynamics (the assumption of stationarity is invalid, and thus only constant parameter values may be assumed); and, (iii) time-inhomogeneous chains (the parameters may vary with time) and accounting for observation error (a sample of the true state is observed).
Change detection in rainfall time series for Perth, Western Australia
12:10 Mon 16 May, 2011 :: 5.57 Ingkarni Wardli :: Farah Mohd Isa :: University of Adelaide

There have been numerous reports that the rainfall in south Western Australia, particularly around Perth has observed a step change decrease, which is typically attributed to climate change. Four statistical tests are used to assess the empirical evidence for this claim on time series from five meteorological stations, all of which exceed 50 years. The tests used in this study are: the CUSUM; Bayesian Change Point analysis; consecutive t-test and the Hotelling’s T²-statistic. Results from multivariate Hotelling’s T² analysis are compared with those from the three univariate analyses. The issue of multiple comparisons is discussed. A summary of the empirical evidence for the claimed step change in Perth area is given.
Statistical modelling in economic forecasting: semi-parametrically spatio-temporal approach
12:10 Mon 23 May, 2011 :: 5.57 Ingkarni Wardli :: Dawlah Alsulami :: University of Adelaide

How to model spatio-temporal variation of housing prices is an important and challenging problem as it is of vital importance for both investors and policy makersto assess any movement in housing prices. In this seminar I will talk about the proposed model to estimate any movement in housing prices and measure the risk more accurately.
Optimal experimental design for stochastic population models
15:00 Wed 1 Jun, 2011 :: 7.15 Ingkarni Wardli :: Dr Dan Pagendam :: CSIRO, Brisbane

Markov population processes are popular models for studying a wide range of phenomena including the spread of disease, the evolution of chemical reactions and the movements of organisms in population networks (metapopulations). Our ability to use these models effectively can be limited by our knowledge about parameters, such as disease transmission and recovery rates in an epidemic. Recently, there has been interest in devising optimal experimental designs for stochastic models, so that practitioners can collect data in a manner that maximises the precision of maximum likelihood estimates of the parameters for these models. I will discuss some recent work on optimal design for a variety of population models, beginning with some simple one-parameter models where the optimal design can be obtained analytically and moving on to more complicated multi-parameter models in epidemiology that involve latent states and non-exponentially distributed infectious periods. For these more complex models, the optimal design must be arrived at using computational methods and we rely on a Gaussian diffusion approximation to obtain analytical expressions for Fisher's information matrix, which is at the heart of most optimality criteria in experimental design. I will outline a simple cross-entropy algorithm that can be used for obtaining optimal designs for these models. We will also explore the improvements in experimental efficiency when using the optimal design over some simpler designs, such as the design where observations are spaced equidistantly in time.
Priority queueing systems with random switchover times and generalisations of the Kendall-Takacs equation
16:00 Wed 1 Jun, 2011 :: 7.15 Ingkarni Wardli :: Dr Andrei Bejan :: The University of Cambridge

In this talk I will review existing analytical results for priority queueing systems with Poisson incoming flows, general service times and a single server which needs some (random) time to switch between requests of different priority. Specifically, I will discuss analytical results for the busy period and workload of such systems with a special structure of switchover times. The results related to the busy period can be seen as generalisations of the famous Kendall-Tak\'{a}cs functional equation for $M|G|1$: being formulated in terms of Laplace-Stieltjes transform, they represent systems of functional recurrent equations. I will present a methodology and algorithms of their numerical solution; the efficiency of these algorithms is achieved by acceleration of the numerical procedure of solving the classical Kendall-Tak\'{a}cs equation. At the end I will identify open problems with regard to such systems; these open problems are mainly related to the modelling of switchover times.
Modelling computer network topologies through optimisation
12:10 Mon 1 Aug, 2011 :: 5.57 Ingkarni Wardli :: Mr Rhys Bowden :: University of Adelaide

The core of the Internet is made up of many different computers (called routers) in many different interconnected networks, owned and operated by many different organisations. A popular and important field of study in the past has been "network topology": for instance, understanding which routers are connected to which other routers, or which networks are connected to which other networks; that is, studying and modelling the connection structure of the Internet. Previous study in this area has been plagued by unreliable or flawed experimental data and debate over appropriate models to use. The Internet Topology Zoo is a new source of network data created from the information that network operators make public. In order to better understand this body of network information we would like the ability to randomly generate network topologies resembling those in the zoo. Leveraging previous wisdom on networks produced as a result of optimisation processes, we propose a simple objective function based on possible economic constraints. By changing the relative costs in the objective function we can change the form of the resulting networks, and we compare these optimised networks to a variety of networks found in the Internet Topology Zoo.
AustMS/AMSI Mahler Lecture: Chaos, quantum mechanics and number theory
18:00 Tue 9 Aug, 2011 :: Napier 102 :: Prof Peter Sarnak :: Institute for Advanced Study, Princeton

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The correspondence principle in quantum mechanics is concerned with the relation between a mechanical system and its quantization. When the mechanical system are relatively orderly ("integrable"), then this relation is well understood. However when the system is chaotic much less is understood. The key features already appear and are well illustrated in the simplest systems which we will review. For chaotic systems defined number-theoretically, much more is understood and the basic problems are connected with central questions in number theory. The Mahler lectures are a biennial activity organised by the Australian Mathematical Society with the assistance of the Australian Mathematical Sciences Institute.
Textbooks go interactive but are they any better?
12:10 Mon 15 Aug, 2011 :: 5.57 Ingkarni Wardli :: Mr Patrick Korbel :: University of Adelaide

Textbooks remain a central part of mathematics lessons in secondary schools. However, while textbooks are still formatted in the traditional way, they are including increasingly more sophisticated software packages to assist teachers and students. I will be demonstrating the different software packages available to students included with two South Australian textbooks. I will talk about how these new features fit into the current classroom environment and some of their potential positives and negatives. I would also like to encourage people to share their own experiences with textbooks, especially if they were used in a novel way or you have experience of mathematics classes in another country.
Alignment of time course gene expression data sets using Hidden Markov Models
12:10 Mon 5 Sep, 2011 :: 5.57 Ingkarni Wardli :: Mr Sean Robinson :: University of Adelaide

Time course microarray experiments allow for insight into biological processes by measuring gene expression over a time period of interest. This project is concerned with time course data from a microarray experiment conducted on a particular variety of grapevine over the development of the grape berries at a number of different vineyards in South Australia. The aim of the project is to construct a methodology for combining the data from the different vineyards in order to obtain more precise estimates of the underlying behaviour of the genes over the development process. A major issue in doing so is that the rate of development of the grape berries is different at different vineyards. Hidden Markov models (HMMs) are a well established methodology for modelling time series data in a number of domains and have been previously used for gene expression analysis. Modelling the grapevine data presents a unique modelling issue, namely the alignment of the expression profiles needed to combine the data from different vineyards. In this seminar, I will describe our problem, review HMMs, present an extension to HMMs and show some preliminary results modelling the grapevine data.
Mathematical modelling of lobster populations in South Australia
12:10 Mon 12 Sep, 2011 :: 5.57 Ingkarni Wardli :: Mr John Feenstra :: University of Adelaide

Just how many lobsters are there hanging around the South Australian coastline? How is this number changing over time? What is the demographic breakdown of this number? And what does it matter? Find out the answers to these questions in my upcoming talk. I will provide a brief flavour of the kinds of quantitative methods involved, showcasing relevant applications of regression, population modelling, estimation, as well as simulation. A product of these analyses are biological performance indicators which are used by government to help decide on fishery controls such as yearly total allowable catch quotas. This assists in maintaining the sustainability of the fishery and hence benefits both the fishers and the lobsters they catch.
Estimating transmission parameters for the swine flu pandemic
15:10 Fri 23 Sep, 2011 :: 7.15 Ingkarni Wardli :: Dr Kathryn Glass :: Australian National University

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Following the onset of a new strain of influenza with pandemic potential, policy makers need specific advice on how fast the disease is spreading, who is at risk, and what interventions are appropriate for slowing transmission. Mathematical models play a key role in comparing interventions and identifying the best response, but models are only as good as the data that inform them. In the early stages of the 2009 swine flu outbreak, many researchers estimated transmission parameters - particularly the reproduction number - from outbreak data. These estimates varied, and were often biased by data collection methods, misclassification of imported cases or as a result of early stochasticity in case numbers. I will discuss a number of the pitfalls in achieving good quality parameter estimates from early outbreak data, and outline how best to avoid them. One of the early indications from swine flu data was that children were disproportionately responsible for disease spread. I will introduce a new method for estimating age-specific transmission parameters from both outbreak and seroprevalence data. This approach allows us to take account of empirical data on human contact patterns, and highlights the need to allow for asymmetric mixing matrices in modelling disease transmission between age groups. Applied to swine flu data from a number of different countries, it presents a consistent picture of higher transmission from children.
Estimating disease prevalence in hidden populations
14:05 Wed 28 Sep, 2011 :: B.18 Ingkarni Wardli :: Dr Amber Tomas :: The University of Oxford

Estimating disease prevalence in "hidden" populations such as injecting drug users or men who have sex with men is an important public health issue. However, traditional design-based estimation methods are inappropriate because they assume that a list of all members of the population is available from which to select a sample. Respondent Driven Sampling (RDS) is a method developed over the last 15 years for sampling from hidden populations. Similarly to snowball sampling, it leverages the fact that members of hidden populations are often socially connected to one another. Although RDS is now used around the world, there are several common population characteristics which are known to cause estimates calculated from such samples to be significantly biased. In this talk I'll discuss the motivation for RDS, as well as some of the recent developments in methods of estimation.
Understanding the dynamics of event networks
15:00 Wed 28 Sep, 2011 :: B.18 Ingkarni Wardli :: Dr Amber Tomas :: The University of Oxford

Within many populations there are frequent communications between pairs of individuals. Such communications might be emails sent within a company, radio communications in a disaster zone or diplomatic communications between states. Often it is of interest to understand the factors that drive the observed patterns of such communications, or to study how these factors are changing over over time. Communications can be thought of as events occuring on the edges of a network which connects individuals in the population. In this talk I'll present a model for such communications which uses ideas from social network theory to account for the complex correlation structure between events. Applications to the Enron email corpus and the dynamics of hospital ward transfer patterns will be discussed.
Statistical analysis of school-based student performance data
12:10 Mon 10 Oct, 2011 :: 5.57 Ingkarni Wardli :: Ms Jessica Tan :: University of Adelaide

Join me in the journey of being a statistician for 15 minutes of your day (if you are not already one) and experience the task of data cleaning without having to get your own hands dirty. Most of you may have sat the Basic Skills Tests when at school or know someone who currently has to do the NAPLAN (National Assessment Program - Literacy and Numeracy) tests. Tests like these assess student progress and can be used to accurately measure school performance. In trying to answer the research question: "what conclusions about student progress and school performance can be drawn from NAPLAN data or data of a similar nature, using mathematical and statistical modelling and analysis techniques?", I have uncovered some interesting results about the data in my initial data analysis which I shall explain in this talk.
Statistical modelling for some problems in bioinformatics
11:10 Fri 14 Oct, 2011 :: B.17 Ingkarni Wardli :: Professor Geoff McLachlan :: The University of Queensland

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In this talk we consider some statistical analyses of data arising in bioinformatics. The problems include the detection of differential expression in microarray gene-expression data, the clustering of time-course gene-expression data and, lastly, the analysis of modern-day cytometric data. Extensions are considered to the procedures proposed for these three problems in McLachlan et al. (Bioinformatics, 2006), Ng et al. (Bioinformatics, 2006), and Pyne et al. (PNAS, 2009), respectively. The latter references are available at http://www.maths.uq.edu.au/~gjm/.
On the role of mixture distributions in the modelling of heterogeneous data
15:10 Fri 14 Oct, 2011 :: 7.15 Ingkarni Wardli :: Prof Geoff McLachlan :: University of Queensland

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We consider the role that finite mixture distributions have played in the modelling of heterogeneous data, in particular for clustering continuous data via mixtures of normal distributions. A very brief history is given starting with the seminal papers by Day and Wolfe in the sixties before the appearance of the EM algorithm. It was the publication in 1977 of the latter algorithm by Dempster, Laird, and Rubin that greatly stimulated interest in the use of finite mixture distributions to model heterogeneous data. This is because the fitting of mixture models by maximum likelihood is a classic example of a problem that is simplified considerably by the EM's conceptual unification of maximum likelihood estimation from data that can be viewed as being incomplete. In recent times there has been a proliferation of applications in which the number of experimental units n is comparatively small but the underlying dimension p is extremely large as, for example, in microarray-based genomics and other high-throughput experimental approaches. Hence there has been increasing attention given not only in bioinformatics and machine learning, but also in mainstream statistics, to the analysis of complex data in this situation where n is small relative to p. The latter part of the talk shall focus on the modelling of such high-dimensional data using mixture distributions.
Likelihood-free Bayesian inference: modelling drug resistance in Mycobacterium tuberculosis
15:10 Fri 21 Oct, 2011 :: 7.15 Ingkarni Wardli :: Dr Scott Sisson :: University of New South Wales

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A central pillar of Bayesian statistical inference is Monte Carlo integration, which is based on obtaining random samples from the posterior distribution. There are a number of standard ways to obtain these samples, provided that the likelihood function can be numerically evaluated. In the last 10 years, there has been a substantial push to develop methods that permit Bayesian inference in the presence of computationally intractable likelihood functions. These methods, termed ``likelihood-free'' or approximate Bayesian computation (ABC), are now being applied extensively across many disciplines. In this talk, I'll present a brief, non-technical overview of the ideas behind likelihood-free methods. I'll motivate and illustrate these ideas through an analysis of the epidemiological fitness cost of drug resistance in Mycobacterium tuberculosis.
Forecasting electricity demand distributions using a semiparametric additive model
15:10 Fri 16 Mar, 2012 :: B.21 Ingkarni Wardli :: Prof Rob Hyndman :: Monash University

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Electricity demand forecasting plays an important role in short-term load allocation and long-term planning for future generation facilities and transmission augmentation. Planners must adopt a probabilistic view of potential peak demand levels, therefore density forecasts (providing estimates of the full probability distributions of the possible future values of the demand) are more helpful than point forecasts, and are necessary for utilities to evaluate and hedge the financial risk accrued by demand variability and forecasting uncertainty. Electricity demand in a given season is subject to a range of uncertainties, including underlying population growth, changing technology, economic conditions, prevailing weather conditions (and the timing of those conditions), as well as the general randomness inherent in individual usage. It is also subject to some known calendar effects due to the time of day, day of week, time of year, and public holidays. I will describe a comprehensive forecasting solution designed to take all the available information into account, and to provide forecast distributions from a few hours ahead to a few decades ahead. We use semi-parametric additive models to estimate the relationships between demand and the covariates, including temperatures, calendar effects and some demographic and economic variables. Then we forecast the demand distributions using a mixture of temperature simulation, assumed future economic scenarios, and residual bootstrapping. The temperature simulation is implemented through a new seasonal bootstrapping method with variable blocks. The model is being used by the state energy market operators and some electricity supply companies to forecast the probability distribution of electricity demand in various regions of Australia. It also underpinned the Victorian Vision 2030 energy strategy.
Fast-track study of viscous flow over topography using 'Smoothed Particle Hydrodynamics'
12:10 Mon 16 Apr, 2012 :: 5.57 Ingkarni Wardli :: Mr Stephen Wade :: University of Adelaide

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Motivated by certain tea room discussions, I am going to (attempt to) model the flow of a viscous fluid under gravity over conical topography. The method used is 'Smoothed Particle Hydrodynamics' (SPH), which is an easy-to-use but perhaps limited-accuracy computational method. The model could be extended to include solidification and thermodynamic effects that can also be implemented within the framework of SPH, and this has the obvious practical application to the modelling of the coverage of ice cream with ice magic, I mean, lava flows. If I fail to achieve this within the next 4 weeks, I will have to go through a talk on SPH that I gave during honours instead.
Mathematical modelling of the surface adsorption for methane on carbon nanostructures
12:10 Mon 30 Apr, 2012 :: 5.57 Ingkarni Wardli :: Mr Olumide Adisa :: University of Adelaide

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In this talk, methane (CH4) adsorption is investigated on both graphite and in the region between two aligned single-walled carbon nanotubes, which we refer to as the groove site. The Lennard–Jones potential function and the continuous approximation is exploited to determine surface binding energies between a single CH4 molecule and graphite and between a single CH4 and two aligned single-walled carbon nanotubes. The modelling indicates that for a CH4 molecule interacting with graphite, the binding energy of the system is minimized when the CH4 carbon is 3.83 angstroms above the surface of the graphitic carbon, while the binding energy of the CH4–groove site system is minimized when the CH4 carbon is 5.17 angstroms away from the common axis shared by the two aligned single-walled carbon nanotubes. These results confirm the current view that for larger groove sites, CH4 molecules in grooves are likely to move towards the outer surfaces of one of the single-walled carbon nanotubes. The results presented in this talk are computationally efficient and are in good agreement with experiments and molecular dynamics simulations, and show that CH4 adsorption on graphite and groove surfaces is more favourable at lower temperatures and higher pressures.
Multiscale models of collective cell behaviour: Linear or nonlinear diffusion?
15:10 Fri 4 May, 2012 :: B.21 Ingkarni Wardli :: Dr Matthew Simpson :: Queensland University of Technology

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Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. There is no guidance available in the mathematical biology literature with regard to which approach is more appropriate. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. We provide a link between individual-based and continuum models using a multiscale approach in which we analyse the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is a nonlinear diffusion equation related to the porous media equation. We show that there are several reasonable approaches for dealing with agent size effects, and that these different approaches are related mathematically through the concept of mean action time. We extend our results to consider proliferation and travelling waves where greater care must be taken to ensure that the continuum model replicates the discrete process. This is joint work with Dr Ruth Baker (Oxford) and Dr Scott McCue (QUT).
Are Immigrants Discriminated in the Australian Labour Market?
12:10 Mon 7 May, 2012 :: 5.57 Ingkarni Wardli :: Ms Wei Xian Lim :: University of Adelaide

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In this talk, I will present what I did in my honours project, which was to determine if immigrants, categorised as immigrants from English speaking countries and Non-English speaking countries, are discriminated in the Australian labour market. To determine if discrimination exists, a decomposition of the wage function is applied and analysed via regression analysis. Two different methods of estimating the unknown parameters in the wage function will be discussed: 1. the Ordinary Least Square method, 2. the Quantile Regression method. This is your rare chance of hearing me talk about non-nanomathematics related stuff!
Modelling protective anti-tumour immunity using a hybrid agent-based and delay differential equation approach
15:10 Fri 11 May, 2012 :: B.21 Ingkarni Wardli :: Dr Peter Kim :: University of Sydney

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Although cancers seem to consistently evade current medical treatments, the body's immune defences seem quite effective at controlling incipient tumours. Understanding how our immune systems provide such protection against early-stage tumours and how this protection could be lost will provide insight into designing next-generation immune therapies against cancer. To engage this problem, we formulate a mathematical model of the immune response against small, incipient tumours. The model considers the initial stimulation of the immune response in lymph nodes and the resulting immune attack on the tumour and is formulated as a hybrid agent-based and delay differential equation model.
Change detection in rainfall times series for Perth, Western Australia
12:10 Mon 14 May, 2012 :: 5.57 Ingkarni Wardli :: Ms Farah Mohd Isa :: University of Adelaide

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There have been numerous reports that the rainfall in south Western Australia, particularly around Perth has observed a step change decrease, which is typically attributed to climate change. Four statistical tests are used to assess the empirical evidence for this claim on time series from five meteorological stations, all of which exceed 50 years. The tests used in this study are: the CUSUM; Bayesian Change Point analysis; consecutive t-test and the Hotelling's T^2-statistic. Results from multivariate Hotelling's T^2 analysis are compared with those from the three univariate analyses. The issue of multiple comparisons is discussed. A summary of the empirical evidence for the claimed step change in Perth area is given.
Evaluation and comparison of the performance of Australian and New Zealand intensive care units
14:10 Fri 25 May, 2012 :: 7.15 Ingkarni Wardli :: Dr Jessica Kasza :: The University of Adelaide

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Recently, the Australian Government has emphasised the need for monitoring and comparing the performance of Australian hospitals. Evaluating the performance of intensive care units (ICUs) is of particular importance, given that the most severe cases are treated in these units. Indeed, ICU performance can be thought of as a proxy for the overall performance of a hospital. We compare the performance of the ICUs contributing to the Australian and New Zealand Intensive Care Society (ANZICS) Adult Patient Database, the largest of its kind in the world, and identify those ICUs with unusual performance. It is well-known that there are many statistical issues that must be accounted for in the evaluation of healthcare provider performance. Indicators of performance must be appropriately selected and estimated, investigators must adequately adjust for casemix, statistical variation must be fully accounted for, and adjustment for multiple comparisons must be made. Our basis for dealing with these issues is the estimation of a hierarchical logistic model for the in-hospital death of each patient, with patients clustered within ICUs. Both patient- and ICU-level covariates are adjusted for, with a random intercept and random coefficient for the APACHE III severity score. Given that we expect most ICUs to have similar performance after adjustment for these covariates, we follow Ohlssen et al., JRSS A (2007), and estimate a null model that we expect the majority of ICUs to follow. This methodology allows us to rigorously account for the aforementioned statistical issues, and accurately identify those ICUs contributing to the ANZICS database that have comparatively unusual performance. This is joint work with Prof. Patty Solomon and Assoc. Prof. John Moran.
The change of probability measure for jump processes
12:10 Mon 28 May, 2012 :: 5.57 Ingkarni Wardli :: Mr Ahmed Hamada :: University of Adelaide

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In financial derivatives pricing theory, it is very common to change the probability measure from historical measure "real world" into a Risk-Neutral measure as a development of the non arbitrage condition. Girsanov theorem is the most known example of this technique and is used when prices randomness is modelled by Brownian motions. Other genuine candidates for modelling market randomness that have proved efficiency in recent literature are jump process, so how can a change of measure be performed for such processes? This talk will address this question by introducing the non arbitrage condition, discussing Girsanov theorem for diffusion and jump processes and presenting a concrete example.
Model turbulent floods based upon the Smagorinski large eddy closure
12:10 Mon 4 Jun, 2012 :: 5.57 Ingkarni Wardli :: Mr Meng Cao :: University of Adelaide

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Rivers, floods and tsunamis are often very turbulent. Conventional models of such environmental fluids are typically based on depth-averaged inviscid irrotational flow equations. We explore changing such a base to the turbulent Smagorinski large eddy closure. The aim is to more appropriately model the fluid dynamics of such complex environmental fluids by using such a turbulent closure. Large changes in fluid depth are allowed. Computer algebra constructs the slow manifold of the flow in terms of the fluid depth h and the mean turbulent lateral velocities u and v. The major challenge is to deal with the nonlinear stress tensor in the Smagorinski closure. The model integrates the effects of inertia, self-advection, bed drag, gravitational forcing and turbulent dissipation with minimal assumptions. Although the resultant model is close to established models, the real outcome is creating a sound basis for the modelling so others, in their modelling of more complex situations, can systematically include more complex physical processes.
Adventures with group theory: counting and constructing polynomial invariants for applications in quantum entanglement and molecular phylogenetics
15:10 Fri 8 Jun, 2012 :: B.21 Ingkarni Wardli :: Dr Peter Jarvis :: The University of Tasmania

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In many modelling problems in mathematics and physics, a standard challenge is dealing with several repeated instances of a system under study. If linear transformations are involved, then the machinery of tensor products steps in, and it is the job of group theory to control how the relevant symmetries lift from a single system, to having many copies. At the level of group characters, the construction which does this is called PLETHYSM. In this talk all this will be contextualised via two case studies: entanglement invariants for multipartite quantum systems, and Markov invariants for tree reconstruction in molecular phylogenetics. By the end of the talk, listeners will have understood why Alice, Bob and Charlie love Cayley's hyperdeterminant, and they will know why the three squangles -- polynomial beasts of degree 5 in 256 variables, with a modest 50,000 terms or so -- can tell us a lot about quartet trees!
The Four Colour Theorem
11:10 Mon 23 Jul, 2012 :: B.17 Ingkarni Wardli :: Mr Vincent Schlegel :: University of Adelaide

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Arguably the most famous problem in discrete mathematics, the Four Colour Theorem was first conjectured in 1852 by South African mathematician Francis Guthrie. For 124 years, it defied many attempts to prove and disprove it. I will talk briefly about some of the rich history of this result, including some of the graph-theoretic techniques used in the 1976 Appel-Haken proof.
Air-cooled binary Rankine cycle performance with varying ambient temperature
12:10 Mon 13 Aug, 2012 :: B.21 Ingkarni Wardli :: Ms Josephine Varney :: University of Adelaide

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Next month, I have to give a presentation in Reno, Nevada to a group of geologists, engineers and geophysicists. So, for this talk, I am going to ask you to pretend you know very little about maths (and perhaps a lot about geology) and give me some feedback on my proposed talk. The presentation itself, is about the effect of air-cooling on geothermal power plant performance. Air-cooling is necessary for geothermal plays in dry areas, and ambient air temperature significantly affects the power output of air-cooled geothermal power plants. Hence, a method for determining the effect of ambient air temperature on geothermal power plants is presented. Using the ambient air temperature distribution from Leigh Creek, South Australia, this analysis shows that an optimally designed plant produces 6% more energy annually than a plant designed using the mean ambient temperature.
Infectious diseases modelling: from biology to public health policy
15:10 Fri 24 Aug, 2012 :: B.20 Ingkarni Wardli :: Dr James McCaw :: The University of Melbourne

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The mathematical study of human-to-human transmissible pathogens has established itself as a complementary methodology to the traditional epidemiological approach. The classic susceptible--infectious--recovered model paradigm has been used to great effect to gain insight into the epidemiology of endemic diseases such as influenza and pertussis, and the emergence of novel pathogens such as SARS and pandemic influenza. The modelling paradigm has also been taken within the host and used to explain the within-host dynamics of viral (or bacterial or parasite) infections, with implications for our understanding of infection, emergence of drug resistance and optimal drug-interventions. In this presentation I will provide an overview of the mathematical paradigm used to investigate both biological and epidemiological infectious diseases systems, drawing on case studies from influenza, malaria and pertussis research. I will conclude with a summary of how infectious diseases modelling has assisted the Australian government in developing its pandemic preparedness and response strategies.
Electrokinetics of concentrated suspensions of spherical particles
15:10 Fri 28 Sep, 2012 :: B.21 Ingkarni Wardli :: Dr Bronwyn Bradshaw-Hajek :: University of South Australia

Electrokinetic techniques are used to gather specific information about concentrated dispersions such as electronic inks, mineral processing slurries, pharmaceutical products and biological fluids (e.g. blood). But, like most experimental techniques, intermediate quantities are measured, and consequently the method relies explicitly on theoretical modelling to extract the quantities of experimental interest. A self-consistent cell-model theory of electrokinetics can be used to determine the electrical conductivity of a dense suspension of spherical colloidal particles, and thereby determine the quantities of interest (such as the particle surface potential). The numerical predictions of this model compare well with published experimental results. High frequency asymptotic analysis of the cell-model leads to some interesting conclusions.
Rescaling the coalescent
12:30 Mon 8 Oct, 2012 :: B.21 Ingkarni Wardli :: Mr Adam Rohrlach :: University of Adelaide

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Recently I gave a short talk about how researchers use mathematics to estimate the time since a species' most recent common ancestor. I also pointed out why this generally doesn't work when a population hasn't had a constant population size. Then I quickly changed the subject. In this talk I aim to reintroduce the Coalescent Model, show how it works in general, and finally how researcher's deal with varying a population size.
Multi-scale models of evolutionary epidemiology: where is HIV going?
14:00 Fri 19 Oct, 2012 :: Napier 205 :: Dr Lorenzo Pellis :: The University of Warwick

An important component of pathogen evolution at the population level is evolution within hosts, which can alter the composition of genotypes available for transmission as infection progresses. I will present a deterministic multi-scale model, linking the within-host competition dynamics with the transmission dynamics at a population level. I will take HIV as an example of how this framework can help clarify the conflicting evolutionary pressure an infectious disease might be subject to.
AD Model Builder and the estimation of lobster abundance
12:10 Mon 22 Oct, 2012 :: B.21 Ingkarni Wardli :: Mr John Feenstra :: University of Adelaide

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Determining how many millions of lobsters reside in our waters and how it changes over time is a central aim of lobster stock assessment. ADMB is powerful optimisation software to model and solve complex non-linear problems using automatic differentiation and plays a major role in SA and worldwide in fisheries stock assessment analyses. In this talk I will provide a brief description of an example modelling problem, key features and use of ADMB.
Thin-film flow in helically-wound channels with small torsion
15:10 Fri 26 Oct, 2012 :: B.21 Ingkarni Wardli :: Dr Yvonne Stokes :: University of Adelaide

The study of flow in open helically-wound channels has application to many natural and industrial flows. We will consider laminar flow down helically-wound channels of rectangular cross section and with small torsion, in which the fluid depth is small. Assuming a steady-state flow that is independent of position along the axis of the channel, the flow solution may be determined in the two-dimensional cross section of the channel. A thin-film approximation yields explicit expressions for the fluid velocity in terms of the free-surface shape. The latter satisfies an interesting non-linear ordinary differential equation that, for a channel of rectangular cross section, has an analytical solution. The predictions of the thin-film model are shown to be in good agreement with much more computationally intensive solutions of the small-helix-torsion Navier-Stokes equations. This work has particular relevance to spiral particle separators used in the minerals processing industry. Early work on modelling of particle-laden thin-film flow in spiral channels will also be discussed.
Thin-film flow in helically-wound channels with small torsion
15:10 Fri 26 Oct, 2012 :: B.21 Ingkarni Wardli :: Dr Yvonne Stokes :: University of Adelaide

The study of flow in open helically-wound channels has application to many natural and industrial flows. We will consider laminar flow down helically-wound channels of rectangular cross section and with small torsion, in which the fluid depth is small. Assuming a steady-state flow that is independent of position along the axis of the channel, the flow solution may be determined in the two-dimensional cross section of the channel. A thin-film approximation yields explicit expressions for the fluid velocity in terms of the free-surface shape. The latter satisfies an interesting non-linear ordinary differential equation that, for a channel of rectangular cross section, has an analytical solution. The predictions of the thin-film model are shown to be in good agreement with much more computationally intensive solutions of the small-helix-torsion Navier-Stokes equations. This work has particular relevance to spiral particle separators used in the minerals processing industry. Early work on modelling of particle-laden thin-film flow in spiral channels will also be discussed.
Fair and Loathing in State Parliament
12:10 Mon 29 Oct, 2012 :: B.21 Ingkarni Wardli :: Mr Casey Briggs :: University of Adelaide

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The South Australian electoral system has a history of bias, malapportionment and perceived unfairness. These days, it is typical of most systems across Australia, except with one major difference - a specific legislated criterion designed to force the system to be 'fair'. In reality, fairness is a hard concept to define, and an even harder concept to enforce. In this talk I will briefly take you through the history of South Australian electoral reform, the current state of affairs and my proposed research. There will be very little in the way of rigorous mathematics. No knowledge of politics is assumed, but an understanding of the process of voting would be useful.
Dynamics of microbial populations from a copper sulphide leaching heap
12:30 Mon 12 Nov, 2012 :: B.21 Ingkarni Wardli :: Ms Susana Soto Rojo :: University of Adelaide

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We are interested in the dynamics of the microbial population from a copper sulphide bioleaching heap. The composition of the microbial consortium is closely related to the kinetics of the oxidation processes that lead to copper recovery. Using a non-linear model, which considers the effect of substrate depletion and incorporates spatial dependence, we analyse adjacent strips correlation, patterns of microbial succession, relevance of pertinent physic-chemical parameters and the implications of the absence of barriers between the three lifts of the heap. We also explore how the dynamics of the microbial community relate to the mineral composition of the individual strips of the bioleaching pile.
A multiscale approach to reaction-diffusion processes in domains with microstructure
15:10 Fri 15 Mar, 2013 :: B.18 Ingkarni Wardli :: Prof Malte Peter :: University of Augsburg

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Reaction-diffusion processes occur in many materials with microstructure such as biological cells, steel or concrete. The main difficulty in modelling and simulating accurately such processes is to account for the fine microstructure of the material. One method of upscaling multi-scale problems, which has proven reliable for obtaining feasible macroscopic models, is the method of periodic homogenisation. The talk will give an introduction to multi-scale modelling of chemical mechanisms in domains with microstructure as well as to the method of periodic homogenisation. Moreover, a few aspects of solving the resulting systems of equations numerically will also be discussed.
The boundary conditions for macroscale modelling of a discrete diffusion system with periodic diffusivity
12:10 Mon 29 Apr, 2013 :: B.19 Ingkarni Wardli :: Chen Chen :: University of Adelaide

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Many mathematical and engineering problems have a multiscale nature. There are a vast of theories supporting multiscale modelling on infinite domain, such as homogenization theory and centre manifold theory. To date, there are little consideration of the correct boundary conditions to be used at the edge of macroscale model. In this seminar, I will present how to derive macroscale boundary conditions for the diffusion system.
Filtering Theory in Modelling the Electricity Market
12:10 Mon 6 May, 2013 :: B.19 Ingkarni Wardli :: Ahmed Hamada :: University of Adelaide

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In mathematical finance, as in many other fields where applied mathematics is a powerful tool, we assume that a model is good enough when it captures different sources of randomness affecting the quantity of interests, which in this case is the electricity prices. The power market is very different from other markets in terms of the randomness sources that can be observed in the prices feature and evolution. We start from suggesting a new model that simulates the electricity prices, this new model is constructed by adding a periodicity term, a jumps terms and a positives mean reverting term. The later term is driven by a non-observable Markov process. So in order to prices some financial product, we have to use some of the filtering theory to deal with the non-observable process, these techniques are gaining very much of interest from practitioners and researchers in the field of financial mathematics.
Progress in the prediction of buoyancy-affected turbulence
15:10 Fri 17 May, 2013 :: B.18 Ingkarni Wardli :: Dr Daniel Chung :: University of Melbourne

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Buoyancy-affected turbulence represents a significant challenge to our understanding, yet it dominates many important flows that occur in the ocean and atmosphere. The presentation will highlight some recent progress in the characterisation, modelling and prediction of buoyancy-affected turbulence using direct and large-eddy simulations, along with implications for the characterisation of mixing in the ocean and the low-cloud feedback in the atmosphere. Specifically, direct numerical simulation data of stratified turbulence will be employed to highlight the importance of boundaries in the characterisation of turbulent mixing in the ocean. Then, a subgrid-scale model that captures the anisotropic character of stratified mixing will be developed for large-eddy simulation of buoyancy-affected turbulence. Finally, the subgrid-scale model is utilised to perform a systematic large-eddy simulation investigation of the archetypal low-cloud regimes, from which the link between the lower-tropospheric stability criterion and the cloud fraction interpreted.
Multiscale modelling couples patches of wave-like simulations
12:10 Mon 27 May, 2013 :: B.19 Ingkarni Wardli :: Meng Cao :: University of Adelaide

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A multiscale model is proposed to significantly reduce the expensive numerical simulations of complicated waves over large spatial domains. The multiscale model is built from given microscale simulations of complicated physical processes such as sea ice or turbulent shallow water. Our long term aim is to enable macroscale simulations obtained by coupling small patches of simulations together over large physical distances. This initial work explores the coupling of patch simulations of wave-like pdes. With the line of development being to water waves we discuss the dynamics of two complementary fields called the 'depth' h and 'velocity' u. A staggered grid is used for the microscale simulation of the depth h and velocity u. We introduce a macroscale staggered grid to couple the microscale patches. Linear or quadratic interpolation provides boundary conditions on the field in each patch. Linear analysis of the whole coupled multiscale system establishes that the resultant macroscale dynamics is appropriate. Numerical simulations support the linear analysis. This multiscale method should empower the feasible computation of large scale simulations of wave-like dynamics with complicated underlying physics.
An Overview of Mathematics in the Australian Curriculum
12:10 Mon 5 Aug, 2013 :: B.19 Ingkarni Wardli :: Patrick Korbel :: University of Adelaide

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I will be doing an overview of mathematics in the new Australian Curriculum from Foundation (Reception) to Year 12 for those not familiar with new curriculum.
Thin-film flow in helical channels
12:10 Mon 9 Sep, 2013 :: B.19 Ingkarni Wardli :: David Arnold :: University of Adelaide

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Spiral particle separators are used in the mineral processing industry to refine ores. A slurry, formed by mixing crushed ore with a fluid, is run down a helical channel and at the end of the channel, the particles end up sorted in different sections of the channel. Design of such devices is largely experimentally based, and mathematical modelling of flow in helical channels is relatively limited. In this talk, I will outline some of the work that I have been doing on thin-film flow in helical channels.
Controlling disease, one household at a time.
12:10 Mon 23 Sep, 2013 :: B.19 Ingkarni Wardli :: Michael Lydeamore :: University of Adelaide

Pandemics and Epidemics have always caused significant disruption to society. Attempting to model each individual in any reasonable sized population is unfeasible at best, but we can get surprisingly good results just by looking at a single household in a population. In this talk, I'll try to guide you through the logic I've discovered this year, and present some of the key results we've obtained so far, as well as provide a brief indication of what's to come.
Modelling the South Australian garfish population slice by slice.
12:10 Mon 14 Oct, 2013 :: B.19 Ingkarni Wardli :: John Feenstra :: University of Adelaide

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In this talk I will provide a taste of how South Australian garfish populations are modelled. The role and importance of garfish 'slices' will be explained and how these help produce important reporting quantities of yearly recruitment, legal-size biomass, and exploitation rate within a framework of an age and length based population model.
Classification Using Censored Functional Data
15:10 Fri 18 Oct, 2013 :: B.18 Ingkarni Wardli :: A/Prof Aurore Delaigle :: University of Melbourne

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We consider classification of functional data. This problem has received a lot of attention in the literature in the case where the curves are all observed on the same interval. A difficulty in applications is that the functional curves can be supported on quite different intervals, in which case standard methods of analysis cannot be used. We are interested in constructing classifiers for curves of this type. More precisely, we consider classification of functions supported on a compact interval, in cases where the training sample consists of functions observed on other intervals, which may differ among the training curves. We propose several methods, depending on whether or not the observable intervals overlap by a significant amount. In the case where these intervals differ a lot, our procedure involves extending the curves outside the interval where they were observed. We suggest a new nonparametric approach for doing this. We also introduce flexible ways of combining potential differences in shapes of the curves from different populations, and potential differences between the endpoints of the intervals where the curves from each population are observed.
Modelling and optimisation of group dose-response challenge experiments
12:10 Mon 28 Oct, 2013 :: B.19 Ingkarni Wardli :: David Price :: University of Adelaide

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An important component of scientific research is the 'experiment'. Effective design of these experiments is important and, accordingly, has received significant attention under the heading 'optimal experimental design'. However, until recently, little work has been done on optimal experimental design for experiments where the underlying process can be modelled by a Markov chain. In this talk, I will discuss some of the work that has been done in the field of optimal experimental design for Markov Chains, and some of the work that I have done in applying this theory to dose-response challenge experiments for the bacteria Campylobacter jejuni in chickens.
A gentle introduction to bubble evolution in Hele-Shaw flows
15:10 Fri 22 Nov, 2013 :: 5.58 (Ingkarni Wardli) :: Dr Scott McCue :: QUT

A Hele-Shaw cell is easy to make and serves as a fun toy for an applied mathematician to play with. If we inject air into a Hele-Shaw cell that is otherwise filled with viscous fluid, we can observe a bubble of air growing in size. The process is highly unstable, and the bubble boundary expands in an uneven fashion, leading to striking fingering patterns (look up Hele-Shaw cell or Saffman-Taylor instability on YouTube). From a mathematical perspective, modelling these Hele-Shaw flows is interesting because the governing equations are sufficiently ``simple'' that a considerable amount of analytical progress is possible. Indeed, there is no other context in which (genuinely) two-dimensional moving boundary problems are so tractable. More generally, Hele-Shaw flows are important as they serve as prototypes for more complicated (and important) physical processes such as crystal growth and diffusion limited aggregation. I will give an introduction to some of the main ideas and summarise some of my present research in this area.
The effects of pre-existing immunity
15:10 Fri 7 Mar, 2014 :: B.18 Ingkarni Wardli :: Associate Professor Jane Heffernan :: York University, Canada

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Immune system memory, also called immunity, is gained as a result of primary infection or vaccination, and can be boosted after vaccination or secondary infections. Immunity is developed so that the immune system is primed to react and fight a pathogen earlier and more effectively in secondary infections. The effects of memory, however, on pathogen propagation in an individual host (in-host) and a population (epidemiology) are not well understood. Mathematical models of infectious diseases, employing dynamical systems, computer simulation and bifurcation analysis, can provide projections of pathogen propagation, show outcomes of infection and help inform public health interventions. In the Modelling Infection and Immunity (MI^2) lab, we develop and study biologically informed mathematical models of infectious diseases at both levels of infection, and combine these models into comprehensive multi-scale models so that the effects of individual immunity in a population can be determined. In this talk we will discuss some of the interesting mathematical phenomenon that arise in our models, and show how our results are directly applicable to what is known about the persistence of infectious diseases.
Outlier removal using the Bayesian information criterion for group-based trajectory modelling
12:10 Mon 28 Apr, 2014 :: B.19 Ingkarni Wardli :: Chris Davies :: University of Adelaide

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Attributes measured longitudinally can be used to define discrete paths of measurements, or trajectories, for each individual in a given population. Group-based trajectory modelling methods can be used to identify subgroups of trajectories within a population, such that trajectories that are grouped together are more similar to each other than to trajectories in distinct groups. Existing methods generally allocate every individual trajectory into one of the estimated groups. However this does not allow for the possibility that some individuals may be following trajectories so different from the rest of the population that they should not be included in a group-based trajectory model. This results in these outlying trajectories being treated as though they belong to one of the groups, distorting the estimated trajectory groups and any subsequent analyses that use them. We have developed an algorithm for removing outlying trajectories based on the maximum change in Bayesian information criterion (BIC) due to removing a single trajectory. As well as deciding which trajectory to remove, the number of groups in the model can also change. The decision to remove an outlying trajectory is made by comparing the log-likelihood contributions of the observations to those of simulated samples from the estimated group-based trajectory model. In this talk the algorithm will be detailed and an application of its use will be demonstrated.
Group meeting
15:10 Fri 6 Jun, 2014 :: 5.58 Ingkarni Wardli :: Meng Cao and Trent Mattner :: University of Adelaide

Meng Cao:: Multiscale modelling couples patches of nonlinear wave-like simulations :: Abstract: The multiscale gap-tooth scheme is built from given microscale simulations of complicated physical processes to empower macroscale simulations. By coupling small patches of simulations over unsimulated physical gaps, large savings in computational time are possible. So far the gap-tooth scheme has been developed for dissipative systems, but wave systems are also of great interest. This article develops the gap-tooth scheme to the case of nonlinear microscale simulations of wave-like systems. Classic macroscale interpolation provides a generic coupling between patches that achieves arbitrarily high order consistency between the multiscale scheme and the underlying microscale dynamics. Eigen-analysis indicates that the resultant gap-tooth scheme empowers feasible computation of large scale simulations of wave-like dynamics with complicated underlying physics. As an pilot study, we implement numerical simulations of dam-breaking waves by the gap-tooth scheme. Comparison between a gap-tooth simulation, a microscale simulation over the whole domain, and some published experimental data on dam breaking, demonstrates that the gap-tooth scheme feasibly computes large scale wave-like dynamics with computational savings. Trent Mattner :: Coupled atmosphere-fire simulations of the Canberra 2003 bushfires using WRF-Sfire :: Abstract: The Canberra fires of January 18, 2003 are notorious for the extreme fire behaviour and fire-atmosphere-topography interactions that occurred, including lee-slope fire channelling, pyrocumulonimbus development and tornado formation. In this talk, I will discuss coupled fire-weather simulations of the Canberra fires using WRF-SFire. In these simulations, a fire-behaviour model is used to dynamically predict the evolution of the fire front according to local atmospheric and topographic conditions, as well as the associated heat and moisture fluxes to the atmosphere. It is found that the predicted fire front and heat flux is not too bad, bearing in mind the complexity of the problem and the severe modelling assumptions made. However, the predicted moisture flux is too low, which has some impact on atmospheric dynamics.
Modelling the mean-field behaviour of cellular automata
12:10 Mon 4 Aug, 2014 :: B.19 Ingkarni Wardli :: Kale Davies :: University of Adelaide

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Cellular automata (CA) are lattice-based models in which agents fill the lattice sites and behave according to some specified rule. CA are particularly useful when modelling cell behaviour and as such many people consider CA model in which agents undergo motility and proliferation type events. We are particularly interested in predicting the average behaviour of these models. In this talk I will show how a system of differential equations can be derived for the system and discuss the difficulties that arise in even the seemingly simple case of a CA with motility and proliferation.
Modelling biological gel mechanics
12:10 Mon 8 Sep, 2014 :: B.19 Ingkarni Wardli :: James Reoch :: University of Adelaide

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The behaviour of gels such as collagen is the result of complex interactions between mechanical and chemical forces. In this talk, I will outline the modelling approaches we are looking at in order to incorporate the influence of cell behaviour alongside chemical potentials, and the various circumstances which lead to gel swelling and contraction.
Inferring absolute population and recruitment of southern rock lobster using only catch and effort data
12:35 Mon 22 Sep, 2014 :: B.19 Ingkarni Wardli :: John Feenstra :: University of Adelaide

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Abundance estimates from a data-limited version of catch survey analysis are compared to those from a novel one-parameter deterministic method. Bias of both methods is explored using simulation testing based on a more complex data-rich stock assessment population dynamics fishery operating model, exploring the impact of both varying levels of observation error in data as well as model process error. Recruitment was consistently better estimated than legal size population, the latter most sensitive to increasing observation errors. A hybrid of the data-limited methods is proposed as the most robust approach. A more statistically conventional error-in-variables approach may also be touched upon if enough time.
A Hybrid Markov Model for Disease Dynamics
12:35 Mon 29 Sep, 2014 :: B.19 Ingkarni Wardli :: Nicolas Rebuli :: University of Adelaide

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Modelling the spread of infectious diseases is fundamental to protecting ourselves from potentially devastating epidemics. Among other factors, two key indicators for the severity of an epidemic are the size of the epidemic and the time until the last infectious individual is removed. To estimate the distribution of the size and duration of an epidemic (within a realistic population) an epidemiologist will typically use Monte Carlo simulations of an appropriate Markov process. However, the number of states in the simplest Markov epidemic model, the SIR model, is quadratic in the population size and so Monte Carlo simulations are computationally expensive. In this talk I will discuss two methods for approximating the SIR Markov process and I will demonstrate the approximation error by comparing probability distributions and estimates of the distributions of the final size and duration of an SIR epidemic.
Happiness and social information flow: Computational social science through data.
15:10 Fri 7 Nov, 2014 :: EM G06 (Engineering & Maths Bldg) :: Dr Lewis Mitchell :: University of Adelaide

The recent explosion in big data coming from online social networks has led to an increasing interest in bringing quantitative methods to bear on questions in social science. A recent high-profile example is the study of emotional contagion, which has led to significant challenges and controversy. This talk will focus on two issues related to emotional contagion, namely remote-sensing of population-level wellbeing and the problem of information flow across a social network. We discuss some of the challenges in working with massive online data sets, and present a simple tool for measuring large-scale happiness from such data. By combining over 10 million geolocated messages collected from Twitter with traditional census data we uncover geographies of happiness at the scale of states and cities, and discuss how these patterns may be related to traditional wellbeing measures and public health outcomes. Using tools from information theory we also study information flow between individuals and how this may relate to the concept of predictability for human behaviour.
Happiness and social information flow: Computational social science through data.
15:10 Fri 7 Nov, 2014 :: EM G06 (Engineering & Maths Bldg) :: Dr Lewis Mitchell :: University of Adelaide

The recent explosion in big data coming from online social networks has led to an increasing interest in bringing quantitative methods to bear on questions in social science. A recent high-profile example is the study of emotional contagion, which has led to significant challenges and controversy. This talk will focus on two issues related to emotional contagion, namely remote-sensing of population-level wellbeing and the problem of information flow across a social network. We discuss some of the challenges in working with massive online data sets, and present a simple tool for measuring large-scale happiness from such data. By combining over 10 million geolocated messages collected from Twitter with traditional census data we uncover geographies of happiness at the scale of states and cities, and discuss how these patterns may be related to traditional wellbeing measures and public health outcomes. Using tools from information theory we also study information flow between individuals and how this may relate to the concept of predictability for human behaviour.
Modelling segregation distortion in multi-parent crosses
15:00 Mon 17 Nov, 2014 :: 5.57 Ingkarni Wardli :: Rohan Shah (joint work with B. Emma Huang and Colin R. Cavanagh) :: The University of Queensland

Construction of high-density genetic maps has been made feasible by low-cost high-throughput genotyping technology; however, the process is still complicated by biological, statistical and computational issues. A major challenge is the presence of segregation distortion, which can be caused by selection, difference in fitness, or suppression of recombination due to introgressed segments from other species. Alien introgressions are common in major crop species, where they have often been used to introduce beneficial genes from wild relatives. Segregation distortion causes problems at many stages of the map construction process, including assignment to linkage groups and estimation of recombination fractions. This can result in incorrect ordering and estimation of map distances. While discarding markers will improve the resulting map, it may result in the loss of genomic regions under selection or containing beneficial genes (in the case of introgression). To correct for segregation distortion we model it explicitly in the estimation of recombination fractions. Previously proposed methods introduce additional parameters to model the distortion, with a corresponding increase in computing requirements. This poses difficulties for large, densely genotyped experimental populations. We propose a method imposing minimal additional computational burden which is suitable for high-density map construction in large multi-parent crosses. We demonstrate its use modelling the known Sr36 introgression in wheat for an eight-parent complex cross.
Multiscale modelling of multicellular biological systems: mechanics, development and disease
03:10 Fri 6 Mar, 2015 :: Lower Napier LG24 :: Dr James Osborne :: University of Melbourne

When investigating the development and function of multicellular biological systems it is not enough to only consider the behaviour of individual cells in isolation. For example when studying tissue development, how individual cells interact, both mechanically and biochemically, influences the resulting tissues form and function. In this talk we present a multiscale modelling framework for simulating the development and function of multicellular biological systems (in particular tissues). Utilising the natural structural unit of the cell, the framework consists of three main scales: the tissue level (macro-scale); the cell level (meso-scale); and the sub-cellular level (micro-scale), with multiple interactions occurring between all scales. The cell level is central to the framework and cells are modelled as discrete interacting entities using one of a number of possible modelling paradigms, including lattice based models (cellular automata and cellular Potts) and off-lattice based models (cell centre and vertex based representations). The sub-cellular level concerns numerous metabolic and biochemical processes represented by interaction networks rendered stochastically or into ODEs. The outputs from such systems influence the behaviour of the cell level affecting properties such as adhesion and also influencing cell mitosis and apoptosis. At the tissue level we consider factors or restraints that influence the cells, for example the distribution of a nutrient or messenger molecule, which is represented by field equations, on a growing domain, with individual cells functioning as sinks and/or sources. The modular approach taken within the framework enables more realistic behaviour to be considered at each scale. This framework is implemented within the Open Source Chaste library (Cancer Heart and Soft Tissue Environment, (http://www.cs.ox.ac.uk/chaste/) and has been used to model biochemical and biomechanical interactions in various biological systems. In this talk we present the key ideas of the framework along with applications within the fields of development and disease.
How do we quantify the filamentous growth in yeast colony?
12:10 Mon 30 Mar, 2015 :: Ingkarni Wardli 715 Conference Room :: Dr. Benjamin Binder :: School of Mathematical Sciences

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In this talk we will develop a systematic method to measure the spatial patterning of colony morphology. A hybrid modelling approach of the growth process will also be discussed.
Group Meeting
15:10 Fri 24 Apr, 2015 :: N218 Engineering North :: Dr Ben Binder :: University of Adelaide

Talk (Dr Ben Binder): How do we quantify the filamentous growth in a yeast colony? Abstract: In this talk we will develop a systematic method to measure the spatial patterning of yeast colony morphology. The methods are applicable to other physical systems with circular spatial domains, for example, batch mixing fluid devices. A hybrid modelling approach of the yeast growth process will also be discussed. After the seminar, Ben will start a group discussion by sharing some information and experiences on attracting honours/PhD students to the group.
Did the Legend of Zelda unfold in our Solar System?
12:10 Mon 27 Apr, 2015 :: Napier LG29 :: Adam Rohrlach :: University of Adelaide

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Well, obviously not. We can see the other planets, and they're not terribly conducive to Elven based life. Still, I aim to exhaustively explore the topic, all the while avoiding conventional logic and reasoning. Clearly, one could roll out any number of 'telescope' based proofs, and 'video game characters aren't really real, even after a million wishes' arguments, but I want to tackle this hotly debated issue using physics (the ugly cousin of actual mathematics). Armed with a remedial understanding of year 12 physics, from the acclaimed 2000 South Australian syllabus, I can think of no one better qualified, or possibly willing, to give this talk.
Haven't I seen you before? Accounting for partnership duration in infectious disease modeling
15:10 Fri 8 May, 2015 :: Level 7 Conference Room Ingkarni Wardli :: Dr Joel Miller :: Monash University

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Our ability to accurately predict and explain the spread of an infectious disease is a significant factor in our ability to implement effective interventions. Our ability to accurately model disease spread depends on how accurately we capture the various effects. This is complicated by the fact that infectious disease spread involves a number of time scales. Four that are particularly relevant are: duration of infection in an individual, duration of partnerships between individuals, the time required for an epidemic to spread through the population, and the time required for the population structure to change (demographic or otherwise).

Mathematically simple models of disease spread usually make the implicit assumption that the duration of partnerships is by far the shortest time scale in the system. Thus they miss out on the tendency for infected individuals to deplete their local pool of susceptibles. Depending on the details of the disease in question, this effect may be significant.

I will discuss work done to reduce these assumptions for "SIR" (Susceptible-Infected-Recovered) diseases, which allows us to interpolate between populations which are static and populations which change partners rapidly in closed populations (no entry/exit). I will then discuss early results in applying these methods to diseases such as HIV in which the population time scales are relevant.

People smugglers and statistics
12:10 Mon 25 May, 2015 :: Ingkarni Wardli 715 Conference Room :: Prof. Patty Solomon :: School of Mathematical Sciences

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In 2012 the Commonwealth Chief Scientist asked for my advice on the statistics being used in people smuggling prosecutions. Many defendants come from poor fishing villages in Indonesia, where births are not routinely recorded and the age of the defendant is not known. However mandatory jail sentences apply in Australia for individuals convicted of people smuggling which do not apply to children less than 18 years old - so assessing the age of each defendant is very important. Following an Australian Human Rights Commission inquiry into the treatment of individuals suspected of people smuggling, the Attorney-General's department sought advice from the Chief Scientist, which is where I come in. I'll present the methods used by the prosecution and defence, which are both wrong, and introduce the prosecutor's fallacy.
Group Meeting
15:10 Fri 29 May, 2015 :: EM 213 :: Dr Judy Bunder :: University of Adelaide

Talk : Patch dynamics for efficient exascale simulations Abstract Massive parallelisation has lead to a dramatic increase in available computational power. However, data transfer speeds have failed to keep pace and are the major limiting factor in the development of exascale computing. New algorithms must be developed which minimise the transfer of data. Patch dynamics is a computational macroscale modelling scheme which provides a coarse macroscale solution of a problem defined on a fine microscale by dividing the domain into many nonoverlapping, coupled patches. Patch dynamics is readily adaptable to massive parallelisation as each processor core can evaluate the dynamics on one, or a few, patches. However, patch coupling conditions interpolate across the unevaluated parts of the domain between patches and require almost continuous data transfer. We propose a modified patch dynamics scheme which minimises data transfer by only reevaluating the patch coupling conditions at `mesoscale' time scales which are significantly larger than the microscale time of the microscale problem. We analyse and quantify the error arising from patch dynamics with mesoscale temporal coupling.
Complex Systems, Chaotic Dynamics and Infectious Diseases
15:10 Fri 5 Jun, 2015 :: Engineering North N132 :: Prof Michael Small :: UWA

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In complex systems, the interconnection between the components of the system determine the dynamics. The system is described by a very large and random mathematical graph and it is the topological structure of that graph which is important for understanding of the dynamical behaviour of the system. I will talk about two specific examples - (1) spread of infectious disease (where the connection between the agents in a population, rather than epidemic parameters, determine the endemic state); and, (2) a transformation to represent a dynamical system as a graph (such that the "statistical mechanics" of the graph characterise the dynamics).
Dynamics on Networks: The role of local dynamics and global networks on hypersynchronous neural activity
15:10 Fri 31 Jul, 2015 :: Ingkarni Wardli B21 :: Prof John Terry :: University of Exeter, UK

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Graph theory has evolved into a useful tool for studying complex brain networks inferred from a variety of measures of neural activity, including fMRI, DTI, MEG and EEG. In the study of neurological disorders, recent work has discovered differences in the structure of graphs inferred from patient and control cohorts. However, most of these studies pursue a purely observational approach; identifying correlations between properties of graphs and the cohort which they describe, without consideration of the underlying mechanisms. To move beyond this necessitates the development of mathematical modelling approaches to appropriately interpret network interactions and the alterations in brain dynamics they permit.

In the talk we introduce some of these concepts with application to epilepsy, introducing a dynamic network approach to study resting state EEG recordings from a cohort of 35 people with epilepsy and 40 adult controls. Using this framework we demonstrate a strongly significant difference between networks inferred from the background activity of people with epilepsy in comparison to normal controls. Our findings demonstrate that a mathematical model based analysis of routine clinical EEG provides significant additional information beyond standard clinical interpretation, which may ultimately enable a more appropriate mechanistic stratification of people with epilepsy leading to improved diagnostics and therapeutics.

In vitro models of colorectal cancer: why and how?
15:10 Fri 7 Aug, 2015 :: B19 Ingkarni Wardli :: Dr Tamsin Lannagan :: Gastrointestinal Cancer Biology Group, University of Adelaide / SAHMRI

1 in 20 Australians will develop colorectal cancer (CRC) and it is the second most common cause of cancer death. Similar to many other cancer types, it is the metastases rather than the primary tumour that are lethal, and prognosis is defined by “how far” the tumour has spread at time of diagnosis. Modelling in vivo behavior through rapid and relatively inexpensive in vitro assays would help better target therapies as well as help develop new treatments. One such new in vitro tool is the culture of 3D organoids. Organoids are a biologically stable means of growing, storing and testing treatments against bowel cancer. To this end, we have just set up a human colorectal organoid bank across Australia. This consortium will help us to relate in vitro growth patterns to in vivo behaviour and ultimately in the selection of patients for personalized therapies. Organoid growth, however, is complex. There appears to be variable growth rates and growth patterns. Together with members of the ECMS we recently gained funding to better quantify and model spatial structures in these colorectal organoids. This partnership will aim to directly apply the expertise within the ECMS to patient care.
Modelling terrorism risk - can we predict future trends?
12:10 Mon 10 Aug, 2015 :: Benham Labs G10 :: Stephen Crotty :: University of Adelaide

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As we are all aware, the incidence of terrorism is increasing in the world today. This is confirmed when viewing terrorism events since 1970 as a time series. Can we model this increasing trend and use it to predict terrorism events in the future? Probably not, but we'll give it a go anyway.
Modelling Directionality in Stationary Geophysical Time Series
12:10 Mon 12 Oct, 2015 :: Benham Labs G10 :: Mohd Mahayaudin Mansor :: University of Adelaide

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Many time series show directionality inasmuch as plots again-st time and against time-to-go are qualitatively different, and there is a range of statistical tests to quantify this effect. There are two strategies for allowing for directionality in time series models. Linear models are reversible if and only if the noise terms are Gaussian, so one strategy is to use linear models with non-Gaussian noise. The alternative is to use non-linear models. We investigate how non-Gaussian noise affects directionality in a first order autoregressive process AR(1) and compare this with a threshold autoregressive model with two thresholds. The findings are used to suggest possible improvements to an AR(9) model, identified by an AIC criterion, for the average yearly sunspot numbers from 1700 to 1900. The improvement is defined in terms of one-step-ahead forecast errors from 1901 to 2014.
Typhoons and Tigers
12:10 Fri 23 Oct, 2015 :: Hughes Lecture Room 322 :: Assoc. Prof. Andrew Metcalfe :: School of Mathematical Sciences

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The Sundarbans, situated on the north coast of India and south west Bangladesh, are one of the world's largest mangrove regions (4100 square kilometres). In India, there are over 4 million inhabitants on the deltaic islands in the region. There is a diverse flora and fauna, and it is the only remaining habitat of the Bengal tiger. The Sundarbans is an UNESCO World Heritage Site and International Biodiversity Reserve. However, the Sundarbans are prone to flooding from the cyclones that regularly develop in the Bay of Bengal. In this talk I shall describe a stochastic model for the flood risk and explain how this can be used to make decisions about flood mitigation strategies and to provide estimates of the increase in flood risk due to rising sea levels and climate change.
Ocean dynamics of Gulf St Vincent: a numerical study
12:10 Mon 2 Nov, 2015 :: Benham Labs G10 :: Henry Ellis :: University of Adelaide

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The aim of this research is to determine the physical dynamics of ocean circulation within Gulf St. Vincent, South Australia, and the exchange of momentum, nutrients, heat, salt and other water properties between the gulf and shelf via Investigator Strait and Backstairs Passage. The project aims to achieve this through the creation of high-resolution numerical models, combined with new and historical observations from a moored instrument package, satellite data, and shipboard surveys. The quasi-realistic high-resolution models are forced using boundary conditions generated by existing larger scale ROMS models, which in turn are forced at the boundary by a global model, creating a global to regional to local model network. Climatological forcing is done using European Centres for Medium range Weather Forecasting (ECMWF) data sets and is consistent over the regional and local models. A series of conceptual models are used to investigate the relative importance of separate physical processes in addition to fully forced quasi-realistic models. An outline of the research to be undertaken is given: • Connectivity of Gulf St. Vincent with shelf waters including seasonal variation due to wind and thermoclinic patterns; • The role of winter time cooling and formation of eddies in flushing the gulf; • The formation of a temperature front within the gulf during summer time; and • The connectivity and importance of nutrient rich, cool, water upwelling from the Bonney Coast with the gulf via Backstairs Passage during summer time.
Modelling Coverage in RNA Sequencing
09:00 Mon 9 Nov, 2015 :: Ingkarni Wardli 5.57 :: Arndt von Haeseler :: Max F Perutz Laboratories, University of Vienna

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RNA sequencing (RNA-seq) is the method of choice for measuring the expression of RNAs in a cell population. In an RNA-seq experiment, sequencing the full length of larger RNA molecules requires fragmentation into smaller pieces to be compatible with limited read lengths of most deep-sequencing technologies. Unfortunately, the issue of non-uniform coverage across a genomic feature has been a concern in RNA-seq and is attributed to preferences for certain fragments in steps of library preparation and sequencing. However, the disparity between the observed non-uniformity of read coverage in RNA-seq data and the assumption of expected uniformity elicits a query on the read coverage profile one should expect across a transcript, if there are no biases in the sequencing protocol. We propose a simple model of unbiased fragmentation where we find that the expected coverage profile is not uniform and, in fact, depends on the ratio of fragment length to transcript length. To compare the non-uniformity proposed by our model with experimental data, we extended this simple model to incorporate empirical attributes matching that of the sequenced transcript in an RNA-seq experiment. In addition, we imposed an experimentally derived distribution on the frequency at which fragment lengths occur.

We used this model to compare our theoretical prediction with experimental data and with the uniform coverage model. If time permits, we will also discuss a potential application of our model.
Weak globularity in homotopy theory and higher category theory
12:10 Thu 12 Nov, 2015 :: Ingkarni Wardli B19 :: Simona Paoli :: University of Leicester

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Spaces and homotopy theories are fundamental objects of study of algebraic topology. One way to study these objects is to break them into smaller components with the Postnikov decomposition. To describe such decomposition purely algebraically we need higher categorical structures. We describe one approach to modelling these structures based on a new paradigm to build weak higher categories, which is the notion of weak globularity. We describe some of their connections to both homotopy theory and higher category theory.
Use of epidemic models in optimal decision making
15:00 Thu 19 Nov, 2015 :: Ingkarni Wardli 5.57 :: Tim Kinyanjui :: School of Mathematics, The University of Manchester

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Epidemic models have proved useful in a number of applications in epidemiology. In this work, I will present two areas that we have used modelling to make informed decisions. Firstly, we have used an age structured mathematical model to describe the transmission of Respiratory Syncytial Virus in a developed country setting and to explore different vaccination strategies. We found that delayed infant vaccination has significant potential in reducing the number of hospitalisations in the most vulnerable group and that most of the reduction is due to indirect protection. It also suggests that marked public health benefit could be achieved through RSV vaccine delivered to age groups not seen as most at risk of severe disease. The second application is in the optimal design of studies aimed at collection of household-stratified infection data. A design decision involves making a trade-off between the number of households to enrol and the sampling frequency. Two commonly used study designs are considered: cross-sectional and cohort. The search for an optimal design uses Bayesian methods to explore the joint parameter-design space combined with Shannon entropy of the posteriors to estimate the amount of information for each design. We found that for the cross-sectional designs, the amount of information increases with the sampling intensity while the cohort design often exhibits a trade-off between the number of households sampled and the intensity of follow-up. Our results broadly support the choices made in existing data collection studies.
Connecting within-host and between-host dynamics to understand how pathogens evolve
15:10 Fri 1 Apr, 2016 :: Engineering South S112 :: A/Prof Mark Tanaka :: University of New South Wales

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Modern molecular technologies enable a detailed examination of the extent of genetic variation among isolates of bacteria and viruses. Mathematical models can help make inferences about pathogen evolution from such data. Because the evolution of pathogens ultimately occurs within hosts, it is influenced by dynamics within hosts including interactions between pathogens and hosts. Most models of pathogen evolution focus on either the within-host or the between-host level. Here I describe steps towards bridging the two scales. First, I present a model of influenza virus evolution that incorporates within-host dynamics to obtain the between-host rate of molecular substitution as a function of the mutation rate, the within-host reproduction number and other factors. Second, I discuss a model of viral evolution in which some hosts are immunocompromised, thereby extending opportunities for within-host virus evolution which then affects population-level evolution. Finally, I describe a model of Mycobacterium tuberculosis in which multi-drug resistance evolves within hosts and spreads by transmission between hosts.
Mathematical modelling of the immune response to influenza
15:00 Thu 12 May, 2016 :: Ingkarni Wardli B20 :: Ada Yan :: University of Melbourne

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The immune response plays an important role in the resolution of primary influenza infection and prevention of subsequent infection in an individual. However, the relative roles of each component of the immune response in clearing infection, and the effects of interaction between components, are not well quantified.

We have constructed a model of the immune response to influenza based on data from viral interference experiments, where ferrets were exposed to two influenza strains within a short time period. The changes in viral kinetics of the second virus due to the first virus depend on the strains used as well as the interval between exposures, enabling inference of the timing of innate and adaptive immune response components and the role of cross-reactivity in resolving infection. Our model provides a mechanistic explanation for the observed variation in viruses' abilities to protect against subsequent infection at short inter-exposure intervals, either by delaying the second infection or inducing stochastic extinction of the second virus. It also explains the decrease in recovery time for the second infection when the two strains elicit cross-reactive cellular adaptive immune responses. To account for inter-subject as well as inter-virus variation, the model is formulated using a hierarchical framework. We will fit the model to experimental data using Markov Chain Monte Carlo methods; quantification of the model will enable a deeper understanding of the effects of potential new treatments.
Behavioural Microsimulation Approach to Social Policy and Behavioural Economics
15:10 Fri 20 May, 2016 :: S112 Engineering South :: Dr Drew Mellor :: Ernst & Young

SIMULAIT is a general purpose, behavioural micro-simulation system designed to predict behavioural trends in human populations. This type of predictive capability grew out of original research initially conducted in conjunction with the Defence Science and Technology Group (DSTO) in South Australia, and has been fully commercialised and is in current use by a global customer base. To our customers, the principal value of the system lies in its ability to predict likely outcomes to scenarios that challenge conventional approaches based on extrapolation or generalisation. These types of scenarios include: the impact of disruptive technologies, such as the impact of wide-spread adoption of autonomous vehicles for transportation or batteries for household energy storage; and the impact of effecting policy elements or interventions, such as the impact of imposing water usage restrictions. SIMULAIT employs a multi-disciplinary methodology, drawing from agent-based modelling, behavioural science and psychology, microeconomics, artificial intelligence, simulation, game theory, engineering, mathematics and statistics. In this seminar, we start with a high-level view of the system followed by a look under the hood to see how the various elements come together to answer questions about behavioural trends. The talk will conclude with a case study of a recent application of SIMULAIT to a significant policy problem - how to address the deficiency of STEM skilled teachers in the Victorian teaching workforce.
Time series analysis of paleo-climate proxies (a mathematical perspective)
15:10 Fri 27 May, 2016 :: Engineering South S112 :: Dr Thomas Stemler :: University of Western Australia

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In this talk I will present the work my colleagues from the School of Earth and Environment (UWA), the "trans disciplinary methods" group of the Potsdam Institute for Climate Impact Research, Germany, and I did to explain the dynamics of the Australian-South East Asian monsoon system during the last couple of thousand years. From a time series perspective paleo-climate proxy series are more or less the monsters moving under your bed that wake you up in the middle of the night. The data is clearly non-stationary, non-uniform sampled in time and the influence of stochastic forcing or the level of measurement noise are more or less unknown. Given these undesirable properties almost all traditional time series analysis methods fail. I will highlight two methods that allow us to draw useful conclusions from the data sets. The first one uses Gaussian kernel methods to reconstruct climate networks from multiple proxies. The coupling relationships in these networks change over time and therefore can be used to infer which areas of the monsoon system dominate the complex dynamics of the whole system. Secondly I will introduce the transformation cost time series method, which allows us to detect changes in the dynamics of a non-uniform sampled time series. Unlike the frequently used interpolation approach, our new method does not corrupt the data and therefore avoids biases in any subsequence analysis. While I will again focus on paleo-climate proxies, the method can be used in other applied areas, where regular sampling is not possible.
Approaches to modelling cells and remodelling biological tissues
14:10 Wed 10 Aug, 2016 :: Ingkarni Wardli 5.57 :: Professor Helen Byrne :: University of Oxford

Biological tissues are complex structures, whose evolution is characterised by multiple biophysical processes that act across diverse space and time scales. For example, during normal wound healing, fibroblast cells located around the wound margin exert contractile forces to close the wound while those located in the surrounding tissue synthesise new tissue in response to local growth factors and mechanical stress created by wound contraction. In this talk I will illustrate how mathematical modelling can provide insight into such complex processes, taking my inspiration from recent studies of cell migration, vasculogenesis and wound healing.
Mathematical modelling of social spreading processes
15:10 Fri 19 Aug, 2016 :: Napier G03 :: Prof Hans De Sterck :: Monash University

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Social spreading processes are intriguing manifestations of how humans interact and shape each others' lives. There is great interest in improving our understanding of these processes, and the increasing availability of empirical information in the era of big data and online social networks, combined with mathematical and computational modelling techniques, offer compelling new ways to study these processes. I will first discuss mathematical models for the spread of political revolutions on social networks. The influence of online social networks and social media on the dynamics of the Arab Spring revolutions of 2011 are of particular interest in our work. I will describe a hierarchy of models, starting from agent-based models realized on empirical social networks, and ending up with population-level models that summarize the dynamical behaviour of the spreading process. We seek to understand quantitatively how political revolutions may be facilitated by the modern online social networks of social media. The second part of the talk will describe a population-level model for the social dynamics that cause cigarette smoking to spread in a population. Our model predicts that more individualistic societies will show faster adoption and cessation of smoking. Evidence from a newly composed century-long composite data set on smoking prevalence in 25 countries supports the model, with potential implications for public health interventions around the world. Throughout the talk, I will argue that important aspects of social spreading processes can be revealed and understood via quantitative mathematical and computational models matched to empirical data. This talk describes joint work with John Lang and Danny Abrams.
Modelling evolution of post-menopausal human longevity: The Grandmother Hypothesis
15:10 Fri 2 Sep, 2016 :: Napier G03 :: Dr Peter Kim :: University of Sydney

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Human post-menopausal longevity makes us unique among primates, but how did it evolve? One explanation, the Grandmother Hypothesis, proposes that as grasslands spread in ancient Africa displacing foods ancestral youngsters could effectively exploit, older females whose fertility was declining left more descendants by subsidizing grandchildren and allowing mothers to have new babies sooner. As more robust elders could help more descendants, selection favoured increased longevity while maintaining the ancestral end of female fertility. We develop a probabilistic agent-based model that incorporates two sexes and mating, fertility-longevity tradeoffs, and the possibility of grandmother help. Using this model, we show how the grandmother effect could have driven the evolution of human longevity. Simulations reveal two stable life-histories, one human-like and the other like our nearest cousins, the great apes. The probabilistic formulation shows how stochastic effects can slow down and prevent escape from the ancestral condition, and it allows us to investigate the effect of mutation rates on the trajectory of evolution.
A principled experimental design approach to big data analysis
15:10 Fri 23 Sep, 2016 :: Napier G03 :: Prof Kerrie Mengersen :: Queensland University of Technology

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Big Datasets are endemic, but they are often notoriously difficult to analyse because of their size, complexity, history and quality. The purpose of this paper is to open a discourse on the use of modern experimental design methods to analyse Big Data in order to answer particular questions of interest. By appeal to a range of examples, it is suggested that this perspective on Big Data modelling and analysis has wide generality and advantageous inferential and computational properties. In particular, the principled experimental design approach is shown to provide a flexible framework for analysis that, for certain classes of objectives and utility functions, delivers equivalent answers compared with analyses of the full dataset. It can also provide a formalised method for iterative parameter estimation, model checking, identification of data gaps and evaluation of data quality. Finally it has the potential to add value to other Big Data sampling algorithms, in particular divide-and-conquer strategies, by determining efficient sub-samples.
SIR epidemics with stages of infection
12:10 Wed 28 Sep, 2016 :: EM218 :: Matthieu Simon :: Universite Libre de Bruxelles

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This talk is concerned with a stochastic model for the spread of an epidemic in a closed homogeneously mixing population. The population is subdivided into three classes of individuals: the susceptibles, the infectives and the removed cases. In short, an infective remains infectious during a random period of time. While infected, it can contact all the susceptibles present, independently of the other infectives. At the end of the infectious period, it becomes a removed case and has no further part in the infection process.

We represent an infectious period as a set of different stages that an infective can go through before being removed. The transitions between stages are ruled by either a Markov process or a semi-Markov process. In each stage, an infective makes contaminations at the epochs of a Poisson process with a specific rate.

Our purpose is to derive closed expressions for a transform of different statistics related to the end of the epidemic, such as the final number of susceptibles and the area under the trajectories of all the infectives. The analysis is performed by using simple matrix analytic methods and martingale arguments. Numerical illustrations will be provided at the end of the talk.
Transmission Dynamics of Visceral Leishmaniasis: designing a test and treat control strategy
12:10 Thu 29 Sep, 2016 :: EM218 :: Graham Medley :: London School of Hygiene & Tropical Medicine

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Visceral Leishmaniasis (VL) is targeted for elimination from the Indian Sub-Continent. Progress has been much better in some areas than others. Current control is based on earlier diagnosis and treatment and on insecticide spraying to reduce the density of the vector. There is a surprising dearth of specific information on the epidemiology of VL, which makes modelling more difficult. In this seminar, I describe a simple framework that gives some insight into the transmission dynamics. We conclude that the majority of infection comes from cases prior to diagnosis. If this is the case then, early diagnosis will be advantageous, but will require a test with high specificity. This is a paradox for many clinicians and public health workers, who tend to prioritise high sensitivity.

Medley, G.F., Hollingsworth, T.D., Olliaro, P.L. & Adams, E.R. (2015) Health-seeking, diagnostics and transmission in the control of visceral leishmaniasis. Nature 528, S102-S108 (3 December 2015), DOI: 10.1038/nature16042
Measuring and mapping carbon dioxide from remote sensing satellite data
15:10 Fri 21 Oct, 2016 :: Napier G03 :: Prof Noel Cressie :: University of Wollongong

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This talk is about environmental statistics for global remote sensing of atmospheric carbon dioxide, a leading greenhouse gas. An important compartment of the carbon cycle is atmospheric carbon dioxide (CO2), where it (and other gases) contribute to climate change through a greenhouse effect. There are a number of CO2 observational programs where measurements are made around the globe at a small number of ground-based locations at somewhat regular time intervals. In contrast, satellite-based programs are spatially global but give up some of the temporal richness. The most recent satellite launched to measure CO2 was NASA's Orbiting Carbon Observatory-2 (OCO-2), whose principal objective is to retrieve a geographical distribution of CO2 sources and sinks. OCO-2's measurement of column-averaged mole fraction, XCO2, is designed to achieve this, through a data-assimilation procedure that is statistical at its basis. Consequently, uncertainty quantification is key, starting with the spectral radiances from an individual sounding to borrowing of strength through spatial-statistical modelling.
Segregation of particles in incompressible flows due to streamline topology and particle-boundary interaction
15:10 Fri 2 Dec, 2016 :: Ingkarni Wardli 5.57 :: Professor Hendrik C. Kuhlmann :: Institute of Fluid Mechanics and Heat Transfer, TU Wien, Vienna, Austria

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The incompressible flow in a number of classical benchmark problems (e.g. lid-driven cavity, liquid bridge) undergoes an instability from a two-dimensional steady to a periodic three-dimensional flow, which is steady or in form of a traveling wave, if the Reynolds number is increased. In the supercritical regime chaotic as well as regular (quasi-periodic) streamlines can coexist for a range of Reynolds numbers. The spatial structures of the regular regions in three-dimensional Navier-Stokes flows has received relatively little attention, partly because of the high numerical effort required for resolving these structures. Particles whose density does not differ much from that of the liquid approximately follow the chaotic or regular streamlines in the bulk. Near the boundaries, however, their trajectories strongly deviate from the streamlines, in particular if the boundary (wall or free surface) is moving tangentially. As a result of this particle-boundary interaction particles can rapidly segregate and be attracted to periodic or quasi-periodic orbits, yielding particle accumulation structures (PAS). The mechanism of PAS will be explained and results from experiments and numerical modelling will be presented to demonstrate the generic character of the phenomenon.
How oligomerisation impacts steady state gradient in a morphogen-receptor system
15:10 Fri 20 Oct, 2017 :: Ingkarni Wardli 5.57 :: Mr Phillip Brown :: University of Adelaide

In developmental biology an important process is cell fate determination, where cells start to differentiate their form and function. This is an element of the broader concept of morphogenesis. It has long been held that cell differentiation can occur by a chemical signal providing positional information to 'undecided' cells. This chemical produces a gradient of concentration that indicates to a cell what path it should develop along. More recently it has been shown that in a particular system of this type, the chemical (protein) does not exist purely as individual molecules, but can exist in multi-protein complexes known as oligomers. Mathematical modelling has been performed on systems of oligomers to determine if this concept can produce useful gradients of concentration. However, there are wide range of possibilities when it comes to how oligomer systems can be modelled and most of them have not been explored. In this talk I will introduce a new monomer system and analyse it, before extending this model to include oligomers. A number of oligomer models are proposed based on the assumption that proteins are only produced in their oligomer form and can only break apart once they have left the producing cell. It will be shown that when oligomers are present under these conditions, but only monomers are permitted to bind with receptors, then the system can produce robust, biologically useful gradients for a significantly larger range of model parameters (for instance, degradation, production and binding rates) compared to the monomer system. We will also show that when oligomers are permitted to bind with receptors there is negligible difference compared to the monomer system.
The Markovian binary tree applied to demography and conservation biology
15:10 Fri 27 Oct, 2017 :: Ingkarni Wardli B17 :: 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.
Stochastic Modelling of Urban Structure
11:10 Mon 20 Nov, 2017 :: Engineering Nth N132 :: Mark Girolami :: Imperial College London, and The Alan Turing Institute

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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.
Calculating optimal limits for transacting credit card customers
15:10 Fri 2 Mar, 2018 :: Horace Lamb 1022 :: Prof Peter Taylor :: University of Melbourne

Credit card users can roughly be divided into `transactors', who pay off their balance each month, and `revolvers', who maintain an outstanding balance, on which they pay substantial interest. In this talk, we focus on modelling the behaviour of an individual transactor customer. Our motivation is to calculate an optimal credit limit from the bank's point of view. This requires an expression for the expected outstanding balance at the end of a payment period. We establish a connection with the classical newsvendor model. Furthermore, we derive the Laplace transform of the outstanding balance, assuming that purchases are made according to a marked point process and that there is a simplified balance control policy which prevents all purchases in the rest of the payment period when the credit limit is exceeded. We then use the newsvendor model and our modified model to calculate bounds on the optimal credit limit for the more realistic balance control policy that accepts all purchases that do not exceed the limit. We illustrate our analysis using a compound Poisson process example and show that the optimal limit scales with the distribution of the purchasing process, while the probability of exceeding the optimal limit remains constant. Finally, we apply our model to some real credit card purchase data.
Models, machine learning, and robotics: understanding biological networks
15:10 Fri 16 Mar, 2018 :: Horace Lamb 1022 :: Prof Steve Oliver :: University of Cambridge

The availability of complete genome sequences has enabled the construction of computer models of metabolic networks that may be used to predict the impact of genetic mutations on growth and survival. Both logical and constraint-based models of the metabolic network of the model eukaryote, the ale yeast Saccharomyces cerevisiae, have been available for some time and are continually being improved by the research community. While such models are very successful at predicting the impact of deleting single genes, the prediction of the impact of higher order genetic interactions is a greater challenge. Initial studies of limited gene sets provided encouraging results. However, the availability of comprehensive experimental data for the interactions between genes involved in metabolism demonstrated that, while the models were able to predict the general properties of the genetic interaction network, their ability to predict interactions between specific pairs of metabolic genes was poor. I will examine the reasons for this poor performance and demonstrate ways of improving the accuracy of the models by exploiting the techniques of machine learning and robotics. The utility of these metabolic models rests on the firm foundations of genome sequencing data. However, there are two major problems with these kinds of network models - there is no dynamics, and they do not deal with the uncertain and incomplete nature of much biological data. To deal with these problems, we have developed the Flexible Nets (FNs) modelling formalism. FNs were inspired by Petri Nets and can deal with missing or uncertain data, incorporate both dynamics and regulation, and also have the potential for model predictive control of biotechnological processes.
Modelling phagocytosis
15:10 Fri 25 May, 2018 :: Horace Lamb 1022 :: Prof Ngamta (Natalie) Thamwattana :: University of Wollongong

Phagocytosis refers to a process in which one cell type fully encloses and consumes unwanted cells, debris or particulate matter. It plays an important role in immune systems through the destruction of pathogens and the inhibiting of cancerous cells. In this study, we combine models on cell-cell adhesion and on predator-prey modelling to generate a new model for phagocytosis that is capable of relating the interaction between cells in both space and time. Numerical results are presented, demonstrating the behaviours of cells during the process of phagocytosis.
Topological Data Analysis
15:10 Fri 31 Aug, 2018 :: Napier 208 :: Dr Vanessa Robins :: Australian National University

Topological Data Analysis has grown out of work focussed on deriving qualitative and yet quantifiable information about the shape of data. The underlying assumption is that knowledge of shape - the way the data are distributed - permits high-level reasoning and modelling of the processes that created this data. The 0-th order aspect of shape is the number pieces: "connected components" to a topologist; "clustering" to a statistician. Higher-order topological aspects of shape are holes, quantified as "non-bounding cycles" in homology theory. These signal the existence of some type of constraint on the data-generating process. Homology lends itself naturally to computer implementation, but its naive application is not robust to noise. This inspired the development of persistent homology: an algebraic topological tool that measures changes in the topology of a growing sequence of spaces (a filtration). Persistent homology provides invariants called the barcodes or persistence diagrams that are sets of intervals recording the birth and death parameter values of each homology class in the filtration. It captures information about the shape of data over a range of length scales, and enables the identification of "noisy" topological structure. Statistical analysis of persistent homology has been challenging because the raw information (the persistence diagrams) are provided as sets of intervals rather than functions. Various approaches to converting persistence diagrams to functional forms have been developed recently, and have found application to data ranging from the distribution of galaxies, to porous materials, and cancer detection.
Mathematical modelling of the emergence and spread of antimalarial drug resistance
15:10 Fri 14 Sep, 2018 :: Napier 208 :: Dr Jennifer Flegg :: University of Melbourne

Malaria parasites have repeatedly evolved resistance to antimalarial drugs, thwarting efforts to eliminate the disease and contributing to an increase in mortality. In this talk, I will introduce several statistical and mathematical models for monitoring the emergence and spread of antimalarial drug resistance. For example, results will be presented from Bayesian geostatistical models that have quantified the space-time trends in drug resistance in Africa and Southeast Asia. I will discuss how the results of these models have been used to update public health policy.

News matching "Modelling the South Australian garfish population "

ARC success
The School of Mathematical Sciences was again very successful in attracting Australian Research Council funding for 2008. Recipients of ARC Discovery Projects are (with staff from the School highlighted):

Prof NG Bean; Prof PG Howlett; Prof CE Pearce; Prof SC Beecham; Dr AV Metcalfe; Dr JW Boland: WaterLog - A mathematical model to implement recommendations of The Wentworth Group.

2008-2010: $645,000

Prof RJ Elliott: Dynamic risk measures. (Australian Professorial Fellowship)

2008-2012: $897,000

Dr MD Finn: Topological Optimisation of Fluid Mixing.

2008-2010: $249,000

Prof PG Bouwknegt; Prof M Varghese; A/Prof S Wu: Dualities in String Theory and Conformal Field Theory in the context of the Geometric Langlands Program.

2008-2010: $240,000

The latter grant is held through the ANU Posted Wed 26 Sep 07.

Potts Medal Winner
Professor Charles Pearce, the Elder Profesor of Mathematics, was awarded the Ren Potts Medal by the Australian Society for Operations Research at its annual meeting in December. This is a national award for outstanding contributions to Operations Research in Australia. Posted Tue 22 Jan 08.
Success in Learning and Teaching Grants
The School of Mathematical Sciences has been awarded two Faculty L&T awards. Congratulations to Dr David Green for his successful grant "One Simulation Modelling Instruction Module" and to Drs Adrian Koerber, Paul McCann and Jim Denier for their successful grant "Graphics Calculators and beyond". Posted Tue 11 Mar 08.
ICTAM 2008
The 2008 IUTAM International Congress of Theoretical and Applied Mechanics was hosted by the South Australian theoretical and applied mechanics community. Visit the congress web-site for full details. Posted Mon 25 Aug 08.
Australian Research Council Discovery Project Successes

Congratulations to the following members of the School for their success in the ARC Discovery Grants which were announced recently.

  • A/Prof M Roughan; Prof H Shen $315K Network Management in a World of Secrets
  • Prof AJ Roberts; Dr D Strunin $315K Effective and accurate model dynamics, deterministic and stochastic, across multiple space and time scales
  • A/Prof J Denier; Prof AP Bassom $180K A novel approach to controlling boundary-layer separation
Posted Wed 17 Sep 08.
2008 ANZICS-CORE Best Publication
The paper "Mortality and length-of-stay outcomes, 1993-2003, in the binational Australian and New Zealand intensive care adult patient database" by J.L. Moran, P. Bristow, P.J. Solomon, et al. published in Critical Care Medicine. Vol. 36, 46-61, 2008 has been awarded the "2008 ANZICS-CORE Best Publication" award at the 2008 ANZICS/ACCCN Intensive Care ASM in Sydney. Posted Wed 20 May 09.
Adelaide becomes full member of the Australian Mathematical Sciences Institute
The University of Adelaide, through the School of Mathematical Sciences, has recently become a full member of the Australian Mathematical Sciences Institute. AMSI undertakes wide ranging activities to support the Mathematical Sciences within Australia. Full details of AMSI and their activities can be found on their website Posted Wed 29 Jul 09.
Prizegiving photographs now available
Congratulations again to all of the 2008 School of Mathematical Sciences student prizewinners. A selection of photographs from the prizegiving evening at the Museum of South Australia is now available. Posted Wed 26 Aug 09.

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Sam Cohen wins prize for best student talk at Aust MS 2009
Congratulations to Mr Sam Cohen, a PhD student within the School, who was awarded the B. H. Neumann Prize for the best student paper at the 2009 meeting of the Australian Mathematical Society for his talk on Dynamic Risk Measures and Nonlinear Expectations with Markov Chain noise. Posted Tue 6 Oct 09.
Welcome to Dr Joshua Ross
We welcome Dr Joshua Ross as a new lecturer in the School of Mathematical Sciences. Joshua has moved over to Adelaide from the University of Cambridge. His research interests are mathematical modelling (especially mathematical biology) and operations research. Posted Mon 15 Mar 10.

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Maths by Email has arrived
Maths by Email is an initiative of CSIRO and the Australian Mathematical Sciences Institute. It is a free fortnightly email newsletter featuring maths news and events. To find out more, including how to subscribe, go to the Maths by Email website. Posted Thu 8 Apr 10.

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Prize Giving Dinner
The School of Mathematical Sciences Prize Giving Dinner was held on 29th of July in the Pacific Cultures Gallery of the South Australian Museum. Photos from the evening can be found here. Posted Thu 29 Jul 10.
ARC Grant successes
The School of Mathematical Sciences has again had outstanding success in the ARC Discovery and Linkage Projects schemes. Congratulations to the following staff for their success in the Discovery Project scheme: Prof Nigel Bean, Dr Josh Ross, Prof Phil Pollett, Prof Peter Taylor, New methods for improving active adaptive management in biological systems, $255,000 over 3 years; Dr Josh Ross, New methods for integrating population structure and stochasticity into models of disease dynamics, $248,000 over three years; A/Prof Matt Roughan, Dr Walter Willinger, Internet traffic-matrix synthesis, $290,000 over three years; Prof Patricia Solomon, A/Prof John Moran, Statistical methods for the analysis of critical care data, with application to the Australian and New Zealand Intensive Care Database, $310,000 over 3 years; Prof Mathai Varghese, Prof Peter Bouwknegt, Supersymmetric quantum field theory, topology and duality, $375,000 over 3 years; Prof Peter Taylor, Prof Nigel Bean, Dr Sophie Hautphenne, Dr Mark Fackrell, Dr Malgorzata O'Reilly, Prof Guy Latouche, Advanced matrix-analytic methods with applications, $600,000 over 3 years. Congratulations to the following staff for their success in the Linkage Project scheme: Prof Simon Beecham, Prof Lee White, A/Prof John Boland, Prof Phil Howlett, Dr Yvonne Stokes, Mr John Wells, Paving the way: an experimental approach to the mathematical modelling and design of permeable pavements, $370,000 over 3 years; Dr Amie Albrecht, Prof Phil Howlett, Dr Andrew Metcalfe, Dr Peter Pudney, Prof Roderick Smith, Saving energy on trains - demonstration, evaluation, integration, $540,000 over 3 years Posted Fri 29 Oct 10.
New Fellow of the Australian Academy of Science
Professor Mathai Varghese, Professor of Pure Mathematics and ARC Professorial Fellow within the School of Mathematical Sciences, was elected to the Australian Academy of Science. Professor Varghese's citation read "for his distinguished for his work in geometric analysis involving the topology of manifolds, including the Mathai-Quillen formalism in topological field theory.". Posted Tue 30 Nov 10.
Bushfire CRC post-graduate scholarship success
Congratulations to Mika Peace who has been awarded a PhD scholarship from the Bushfire Cooperative Research Centre. Mika is working with Trent Mattner and Graham Mills (from the Bureau of Meteorology) on coupled fire-weather modelling Posted Wed 6 Apr 11.
ARC Future Fellowship success
Associate Professor Zudi Lu has been awarded an ARC Future Fellowship. Associate Professor Lu, and Associate Professor in Statistics, will use the support provided by his Future Fellowship to further improve the theory and practice of econometric modelling of nonlinear spatial time series. Congratulations Zudi. Posted Thu 12 May 11.
Hydrological Society of SA Ian Liang Prize
Congratulations to Hayden Tronnolone who has been awarded the 2011 Ian Laing Prize by the Hydrological Society of South Australia. The annual prize, awarded to a student undertaking the final year of an ordinary or honours degree course or post graduate diploma course which involves some study of hydrology, water resource management, or related sciences, was awarded to Hayden for the work he undertook in his honours project on the study of flow in spiral particle separators. Hayden ins currently undertaking a PhD under the supervision of Dr Yvonne Stokes and Dr Matt Finn. Posted Mon 30 May 11.
Inaugural winner of the Alf van der Poorten Travelling Fellowship
Congratulations to Dr Ray Vozzo who has been awarded the inaugural Alf van der Poorten Travelling Fellowship from the Australian Mathematical Society. Ray will use the fellowship to attend a meeting in Potsdam and visit colleagues in the United Kingdom. Posted Wed 20 Jul 11.
First Australian-New Zealand Rotating Flows Workshop
The first Australian-New Zealand Rotating Flow Workshop will be held from 9th to 11th of January 2012. The workshop, organised by the School of Mathematical Sciences at the University of Adelaide and the Department of Engineering Science at the University of Auckland, will bring together world leading researchers in the broad field of rotating flows. The workshop is sponsored by AMSI, the School of Mathematical Sciences, the University of Auckland and the Royal Society of New Zealand. Please visit the workshop website for further details. Posted Sat 24 Sep 11.
ARC Grant Success
Congratulations to the following staff who were successful in securing funding from the Australian Research Council Discovery Projects Scheme. Associate Professor Finnur Larusson awarded $270,000 for his project Flexibility and symmetry in complex geometry; Dr Thomas Leistner, awarded $303,464 for his project Holonomy groups in Lorentzian geometry, Professor Michael Murray Murray and Dr Daniel Stevenson (Glasgow), awarded $270,000 for their project Bundle gerbes: generalisations and applications; Professor Mathai Varghese, awarded $105,000 for his project Advances in index theory and Prof Anthony Roberts and Professor Ioannis Kevrekidis (Princeton) awarded $330,000 for their project Accurate modelling of large multiscale dynamical systems for engineering and scientific simulation and analysis Posted Tue 8 Nov 11.
Best paper prize at Membrane Symposium
Congratulations to Wei Xian Lim who was awarded the prize for the best student presentation at the Membrane Society of Australasia 2011 ECR Membrane Symposium for her talk on "Mathematical modelling of gas capture in porous materials". Xian is working on her PhD with Jim Hill and Barry Cox. Posted Mon 28 Nov 11.
Two contract positions are available
As a result of the School's success in securing two prestigious Australian Research Council Future Fellowships, we now have two limited term positions available, one in Pure Mathematics and one in Statistics. Posted Wed 14 Dec 11.
Top-up scholarship available
A PhD opportunity is available to help in mathematical modelling of the interaction of ocean waves and sea ice. For information, see this advertisement. Posted Thu 1 Nov 12.
A/Prof Joshua Ross, 2017 Moran Medal recipient
Congratulations to Associate Professor Joshua Ross who has won the 2017 Moran Medal, awarded by the Australian Academy of Science. The Moran Medal recognises outstanding research by scientists up to 10 years post-PhD in applied probability, biometrics, mathematical genetics, psychometrics and statistics. Associate Professor Ross has made influential contributions to public health and conservation biology using mathematical modelling and statistics to help in decision making. Posted Fri 23 Dec 16.

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Elder Professor Mathai Varghese Awarded Australian Laureate Fellowship
Professor Mathai Varghese, 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. Posted Thu 15 Jun 17.

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Elder Professor Mathai Varghese Awarded Australian Laureate Fellowship
Professor Mathai Varghese, 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 will enhance Australia's position at the forefront of international research in geometric analysis. Posted Thu 15 Jun 17.

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Publications matching "Modelling the South Australian garfish population "

Publications
Evaluation of the impact of breast cancer screening in South Australia
Tallis, George; O'Neill, Terence, Internal Medicine Journal 39 (174–178) 2009
A high resolution large-scale gaussian random field rainfall model for Australian monthly rainfall
Osti, Alexander; Leonard, Michael; Lambert, Martin; Metcalfe, Andrew, Water Down Under 2008, Adelaide 14/04/08
A temporally heterogeneous high-resolution large-scale gaussian random field model for Australian rainfall
Osti, Alexander; Leonard, Michael; Lambert, Martin; Metcalfe, Andrew, 17th IASTED International Conference on Applied Simulation and Modelling, Greece 23/06/08
Modelling Water Blending-Sensitivity of Optimal Policies
Webby, Roger; Green, David; Metcalfe, Andrew, 17th Biennial Congress on Modeling and Simulation, New Zealand 01/12/08
Stochastic cyclone modelling in the Bay of Bengal
Need, Steven; Lambert, Martin; Metcalfe, Andrew; Sen, D, Water Down Under 2008, Adelaide 14/04/08
Conditional expectation formulae for copulas
Crane, Glenis Jayne; Van Der Hoek, John, Australian & New Zealand Journal of Statistics 50 (53–67) 2008
Evolving gene frequencies in a population with three possible alleles at a locus
Hajek, Bronwyn; Broadbridge, P; Williams, G, Mathematical and Computer Modelling 47 (210–217) 2008
Modelling survival in acute severe illness: Cox versus accelerated failure time models
Moran, John; Bersten, A; Solomon, Patricia; Edibam, C; Hunt, T, Journal of Evaluation in Clinical Practice 14 (83–93) 2008
Mortality and length-of-stay outcomes, 1993-2003, in the binational Australian and New Zealand intensive care adult patient database
Moran, John; Bristow, P; Solomon, Patricia; George, C; Hatt, G, Critical Care Medicine 36 (46–61) 2008
On spatiotemporal drought classification in New South Wales: Development and evaluation of alternative techniques
Osti, Alexander; Lambert, Martin; Metcalfe, Andrew, Australian Journal of Water Resources 12 (21–35) 2008
The development of an Australian database of wood dust exposures: Issues and future directions
Pearce, Charles; Leipnik, R, Journal of Occupational Health and Safety 24 (417–424) 2008
The mathematical modelling of rotating capillary tubes for holey-fibre manufacture
Voyce, Christopher; Fitt, A; Monro, Tanya, Journal of Engineering Mathematics 60 (69–87) 2008
Computer algebra derives discretisations via self-adjoint multiscale modelling (Unpublished)
Roberts, Anthony John,
A note on N-k configurations and theorems in projective space
Glynn, David, Bulletin of the Australian Mathematical Society 76 (15–31) 2007
Inverse groundwater modelling in the Willunga Basin, South Australia
Knowles, I; Teubner, Michael; Yan, A; Rasser, Paul; Lee, Jong, Hydrogeology Journal 15 (1107–1118) 2007
The Mekong-applications of value at risk (VAR) and conditional value at risk (CVAR) simulation to the benefits, costs and consequences of water resources development in a large river basin
Webby, Roger; Adamson, Peter; Boland, J; Howlett, P; Metcalfe, Andrew; Piantadosi, J, Ecological Modelling 201 (89–96) 2007
Numerical simulation of circulation and thermal stratification in Torrens Lake, Adelaide, South Australia
Nixon, J; Lee, Jong; Teubner, Michael; Gill, Peter, Ozwater Convention & Exhibiton (24th : 2007 : Sydney, New South Wales), Sydney, New South Wales 04/03/07
El Nino effects and upwelling off South Australia
Middleton, Susan; Middleton, J; Van Ruth, Paul; Ward, Timothy; Arthur, C; McClean, J; Maltrud, M; Gill, P; Levings, A, Journal of Physical Oceanography 37 (2458–2477) 2007
Laguerre geometries and some connections to generalized quadrangles
Brown, Matthew, Journal of the Australian Mathematical Society 83 (335–355) 2007
Drought forecasting using adaptive stochastic models in New South Wales
Wong, Hui; Osti, Alexander; Lambert, Martin; Metcalfe, Andrew, 30th Hydrology and Water Resources Symposium, Launceston, Tasmania 04/12/06
Modelling extreme rainfall and tidal anomaly
Need, Steven; Lambert, Martin; Metcalfe, Andrew, 30th Hydrology and Water Resources Symposium, Launceston, Tasmania 04/12/06
Modelling multivariate extreme flood events
Wong, Hui; Need, Steven; Adamson, Peter; Lambert, Martin; Metcalfe, Andrew, 30th Hydrology and Water Resources Symposium, Launceston, Tasmania 04/12/06
Consumption of untreated tank rainwater and gastroenteritis among young children in South Australia
Heyworth, J; Glonek, Garique; Maynard, E; Baghurst, Peter; Finlay-Jones, J, International Journal of Epidemiology 35 (1051–1058) 2006
Does dog or cat ownership lead to increased gastroenteritis in young children in South Australia?
Heyworth, J; Cutt, H; Glonek, Garique, Epidemiology and Infection 134 (926–934) 2006
Incidence, impact on the family and cost of gastroenteritis among 4 to 6-year-old children in South Australia
Heyworth, J; Jardine, A; Glonek, Garique; Maynard, E, Journal of Gastroenterology and Hepatology 21 (1320–1325) 2006
Mathematical modelling of oxygen concentration in bovine and murine cumulus-oocyte complexes
Clark, Alys; Stokes, Yvonne; Lane, Michelle; Thompson, Jeremy, Reproduction 131 (999–1006) 2006
The effect on survival of early detection of breast cancer in South Australia
Tallis, George; Leppard, Phillip; O'Neill, Terence, Model Assisted Statistics and Applications 1 (115–123) 2006
An analytic modelling approach for network routing algorithms that use "ant-like" mobile agents
Bean, Nigel; Costa, Andre, Computer Networks-The International Journal of Computer and Telecommunications Networking 49 (243–268) 2005
An inverse modelling technique for glass forming by gravity sagging
Agnon, Y; Stokes, Yvonne, European Journal of Mechanics B-Fluids 24 (275–287) 2005
Effect of social networks on 10 year survival in very old Australians: the Australian longitudinal study of aging
Giles, Lynne Catherine; Glonek, Garique; Luszcz, M; Andrews, G, Journal of Epidemiology and Community Health 59 (574–579) 2005
Riemann-Siegel sums via stationary phase
Tuck, Ernest, Bulletin of the Australian Mathematical Society 72 (325–328) 2005
Deterministic and stochastic modelling of endosome escape by Staphylococcus aureus: "quorum" sensing by a single bacterium
Koerber, Adrian; King, J; Williams, P, Journal of Mathematical Biology 50 (440–488) 2005
Investigation and modelling of traffic issues in immersive audio environments
McMahon, Jeremy; Rumsewicz, Michael; Boustead, P; Safaei, F, 2004 IEEE International Conference on Communications, Paris, France 20/06/04
Optimal quantization for energy-efficient information transfer in a population of neuron-like devices
McDonnell, Mark; Stocks, N; Pearce, Charles; Abbott, Derek, Fluctuations and Noise 2004, Gran Canaria Islands, Spain 26/05/04
Expected lifetime in South Australia 1841-1996
Leppard, Phillip; Tallis, George; Pearce, Charles, Transactions of the Royal Society of South Australia 128 (37–42) 2004
Modelling thirty-day mortality in the acute respiratory distress syndrome (ARDS) in an adult ICU
Moran, John; Solomon, Patricia; Fox, V; Salagaras, M; Williams, P; Quinlan, K; Bersten, A, Anaesthesia and Intensive Care 32 (317–329) 2004
The effect of World War 1 and the 1918 influenza pandemic on cohort life expectancy of South Australian males born in 1881-1900
Leppard, Phillip; Tallis, George; Pearce, Charles, Journal of Population Research 21 (161–176) 2004
Development of Non-Homogeneous and Hierarchical Hidden Markov Models for Modelling Monthly Rainfall and Streamflow Time Series
Whiting, Julian; Lambert, Martin; Metcalfe, Andrew; Kuczera, George, World Water and Environmental Resources Congress (2004), Salt Lake City, Utah, USA 27/06/04
Euler and his contribution to number theory
Glen, Amy; Scott, Paul, Australian Mathematics Teacher 1 (2–5) 2004
Stochastic modelling of tidal anomaly for estimation of flood risk in coastal areas
Ahmer, Ingrid; Lambert, Martin; Leonard, Michael; Metcalfe, Andrew, 28th International Hydrology and Water Resources Symposium, Wollongong, NSW, Australia 10/11/03
A Probabilistic algorithm for determining the fundamental matrix of a block M/G/1 Markov chain
Hunt, Emma, Mathematical and Computer Modelling 38 (1203–1209) 2003
A note on the sensitivities of self-reporting and screen detection of primary breast tumours
Tallis, George; Leppard, Phillip; O'Neill, Terence, Australian & New Zealand Journal of Statistics 45 (7–18) 2003
A philosophy for the modelling of realistic nonlinear systems
Howlett, P; Torokhti, Anatoli; Pearce, Charles, Proceedings of the American Mathematical Society 132 (353–363) 2003
An approximate formula for the stress intensity factor for the pressurized star crack
Clements, David; Widana, Inyoman, Mathematical and Computer Modelling 37 (689–694) 2003
Method of hybrid approximations for modelling of multidimensional nonlinear systems
Torokhti, Anatoli; Howlett, P; Pearce, Charles, Multidimensional Systems and Signal Processing 14 (397–410) 2003
Modelling persistence in annual Australian point rainfall
Whiting, Julian; Lambert, Martin; Metcalfe, Andrew, Hydrology and Earth System Sciences 7 (197–211) 2003
Optimal mathematical models for nonlinear dynamical systems
Torokhti, Anatoli; Howlett, P; Pearce, Charles, Mathematical and Computer Modelling of Dynamical Systems 9 (327–343) 2003
Rumours, epidemics, and processes of mass action: Synthesis and analysis
Dickinson, Rowland; Pearce, Charles, Mathematical and Computer Modelling 38 (1157–1167) 2003
The generalised Hadamard inequality, g-convexity and functional Stolarsky means
Neuman, E; Pearce, Charles; Pecaric, Josip; Simic, V, Bulletin of the Australian Mathematical Society 68 (303–316) 2003
Low-dimensional modelling of dynamical systems applied to some dissipative fluid mechanics
Roberts, Anthony John, chapter in Nonlinear dynamics: from lasers to butterflies (World Scientific Publishing) 257–313, 2003
Modelling host tissue degradation by extracellular bacterial pathogens
King, J; Koerber, Adrian; Croft, J; Ward, J; Williams, P; Sockett, R, Mathematical Medicine and Biology (Print Edition) 20 (227–260) 2003
Modelling nonlinear dynamics of shape-memory-alloys with approximate models of coupled thermoelasticity
Melnik, R; Roberts, Anthony John, Zeitschrift fur Angewandte Mathematik und Mechanik 83 (93–104) 2003
Modelling the dynamics of turbulent floods
Mei, Z; Roberts, Anthony John; Li, Z, Siam Journal on Applied Mathematics 63 (423–458) 2003
Australian Premiere of The Deepest Desire [duration ca. 25 min] by Jake Heggie
Campbell, Elizabeth; Koch, Elizabeth; Hanysz, Alexander,
Coastal flood modelling: Allowing for dependence between rainfall and tidal anomaly
Ahmer, Ingrid; Metcalfe, Andrew; Lambert, Martin; Deans, J, EMAC 2002, Brisbane, Australia 29/09/02
A mathematical study of peristaltic transport of a Casson fluid
Mernone, Anacleto; Mazumdar, Jagan; Lucas, S, Mathematical and Computer Modelling 35 (895–912) 2002
Bivariate stochastic modelling of ephemeral streamflow
Cigizoglu, H; Adamson, Peter; Metcalfe, Andrew, Hydrological Processes 16 (1451–1465) 2002
Reanalysis of Travelling Speed and the Risk of Crash Involvement in Adelaide South Australia
Kloeden, Craig; McLean, Alexander; Glonek, Garique,
Fractional Brownian motion and financial modelling
Elliott, Robert; Van Der Hoek, John, chapter in Mathematical Finance (Birkhauser) 140–151, 2001
Integrated solutions of stochastic evolution equations with additive noise
Filinkov, Alexei; Maizurna, Isna, Bulletin of the Australian Mathematical Society 64 (281–290) 2001
Linearised cavity theory with smooth detachment
Haese, Peter, Australian Mathematical Society Gazette 28 (187–193) 2001
Poisson manifolds in generalised Hamiltonian biomechanics
Ivancevic, V; Pearce, Charles, Bulletin of the Australian Mathematical Society 64 (515–526) 2001
Statistical modelling and prediction associated with the HIV/AIDS epidemic
Solomon, Patricia; Wilson, Susan, The Mathematical Scientist 26 (87–102) 2001
The modelling and numerical simulation of causal non-linear systems
Howlett, P; Torokhti, Anatoli; Pearce, Charles, Nonlinear Analysis-Theory Methods & Applications 47 (5559–5572) 2001
Modelling Overflow Traffic from Terrestrial Networks into Satellite Networks
Green, David, 8th International Conference on Telecommunications (June 2001), Bucharest, Romania 04/06/01
Modelling Service Time Distribution in Cellular Networks Using Phase-Type Service Distributions
Green, David; Asenstorfer, J; Jayasuriya, A,
Mathematical modelling of quorum sensing in bacteria
Ward, J; King, J; Koerber, Adrian; Williams, P; Croft, J; Sockett, R, Mathematical Medicine and Biology (Print Edition) 18 (263–292) 2001
A brief survey and synthesis of the roles of time in petri nets
Bowden, Fred David John, Mathematical and Computer Modelling 31 (55–68) 2000
A family of 2-dimensional laguerre planes of generalised shear type
Polster, Burkhard; Steinke, G, Bulletin of the Australian Mathematical Society 61 (69–83) 2000
A new perspective on the normalization of invariant measures for loss networks and other product form systems
Bean, Nigel; Stewart, Mark, Mathematical and Computer Modelling 31 (47–54) 2000
Algorithms for second moments in batch-movement queueing systems
Hunt, Emma, Mathematical and Computer Modelling 31 (299–305) 2000
Biomathematical modelling of physiological fluids using a Casson fluid with emphasis to peristalsis
Mernone, Anacleto; Mazumdar, Jagan, Australasian Physical and Engineering Sciences in Medicine 23 (94–100) 2000
Cauchy-Schwarz functionals
Cho, Y; Dragomir, S; Kim, S-S; Pearce, Charles, Bulletin of the Australian Mathematical Society 62 (479–491) 2000
Disease surveillance and data collection issues in epidemic modelling
Solomon, Patricia; Isham, V, Statistical Methods in Medical Research 9 (259–277) 2000
Maximal profit dimensioning and tariffing of loss networks with cross-connects
Bean, Nigel; Brown, Deborah; Taylor, Peter, Mathematical and Computer Modelling 31 (21–30) 2000
Positive random variables and the A-G-H inequality
Pearce, Charles, Australian Mathematical Society Gazette 27 (91–95) 2000
Quasi-reversibility and networks of queues with nonstandard batch movements
Taylor, Peter, Mathematical and Computer Modelling 31 (335–341) 2000
The exact solution of the general stochastic rumour
Pearce, Charles, Mathematical and Computer Modelling 31 (289–298) 2000
When is a MAP poisson?
Bean, Nigel; Green, David, Mathematical and Computer Modelling 31 (31–46) 2000
More on the pizza theorem
Pearce, Charles, Australian Mathematical Society Gazette 27 (4–5) 2000

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