
Search the School of Mathematical SciencesPeople matching "+Mathematical +modelling"Events matching "+Mathematical +modelling" 
Mathematical modelling of multidimensional tissue growth 16:10 Tue 24 Oct, 2006 :: Benham Lecture Theatre :: Prof John King
Some simple continuummechanicsbased 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 genenetwork is employed by bacteria to provide a measure of their populationdensity 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. 

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 PantheonSorbonne
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 nonstationarity 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 nonstationarity 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 nonstationary unconditional moments or nonstationary 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 nonstationarity 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 nonstationarity on the statistics computed from the global non stationary data sets?
4. How can we analyze data sets in the nonstationary global framework? Does the asymptotic theory work in nonstationary 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.


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 (18231892) 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 (18311879) 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 decisionmaking 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 fullydeveloped 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 curvedpipe 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 lifethreatening 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 underpin SA's wild fisheries and aquaculture. SAIMOS involves the use of shipbased 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.


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. 

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. 

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 modelfreeexcept for a 'frictionless markets' assumption
necessary and sufficient conditions for absence of arbitrage given a set of
currenttime 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 pathdependent option, specifically a weighted variance swap, to
the
set of traded assets and ask what are the conditions on its time0 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 arbitragefree 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. 

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 nanodevices. 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 nanooscillators, to produce frequencies in the gigahertz range, for applications such as ultrafast optical filters and nanoantennae. The sliding of an inner shell inside an outer shell of a multiwalled carbon nanotube can generate oscillatory frequencies up to several gigahertz, and the shorter the inner tube the higher the frequency. A C60nanotube oscillator generates high frequencies by oscillating a C60 fullerene inside a singlewalled carbon nanotube. Here we discuss the underlying mechanisms of nanooscillators and using the LennardJones potential together with the continuum approach, to mathematically model the C60nanotube nanooscillator. Finally, three illustrative examples of recent modelling in hydrogen storage, nanomedicine and nanocomputing are discussed. 

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
Media...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 agespecific 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. 

Statistical analysis of schoolbased 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. 

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
Media...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 microarraybased genomics and other highthroughput 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 highdimensional data using mixture distributions. 

Likelihoodfree 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
Media...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 ``likelihoodfree'' or approximate Bayesian computation (ABC), are now being applied extensively across many disciplines.
In this talk, I'll present a brief, nontechnical overview of the ideas behind likelihoodfree methods. I'll motivate and illustrate these ideas through an analysis of the epidemiological fitness cost of drug resistance in Mycobacterium tuberculosis. 

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
Media...In this talk, methane (CH4) adsorption is investigated on both graphite and in the region between two aligned singlewalled carbon nanotubes, which we refer to as the groove site. The LennardâJones 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 singlewalled 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 CH4âgroove site system is minimized when the CH4 carbon is 5.17 angstroms away from the common axis shared by the two aligned singlewalled 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 singlewalled 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. 

Modelling protective antitumour immunity using a hybrid agentbased and delay differential equation approach 15:10 Fri 11 May, 2012 :: B.21 Ingkarni Wardli :: Dr Peter Kim :: University of Sydney
Media...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 earlystage tumours and how this protection could be lost will provide insight into designing nextgeneration 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 agentbased and delay differential equation model. 

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
Media...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! 

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
Media...The mathematical study of humantohuman transmissible pathogens has
established itself as a complementary methodology to the traditional
epidemiological approach. The classic susceptibleinfectiousrecovered
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 withinhost dynamics of viral (or bacterial or parasite)
infections, with implications for our understanding of infection,
emergence of drug resistance and optimal druginterventions.
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.


A multiscale approach to reactiondiffusion processes in domains with microstructure 15:10 Fri 15 Mar, 2013 :: B.18 Ingkarni Wardli :: Prof Malte Peter :: University of Augsburg
Media...Reactiondiffusion 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 multiscale problems, which has proven reliable for obtaining feasible macroscopic models, is the method of periodic homogenisation.
The talk will give an introduction to multiscale 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
Media...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
Media...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 nonobservable Markov process. So in order to prices some financial product, we have to use some of the filtering theory to deal with the nonobservable process, these techniques are gaining very much of interest from practitioners and researchers in the field of financial mathematics. 

Progress in the prediction of buoyancyaffected turbulence 15:10 Fri 17 May, 2013 :: B.18 Ingkarni Wardli :: Dr Daniel Chung :: University of Melbourne
Media...Buoyancyaffected 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 buoyancyaffected
turbulence using direct and largeeddy simulations, along with implications
for the characterisation of mixing in the ocean and the lowcloud 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 subgridscale model that captures the anisotropic character of stratified
mixing will be developed for largeeddy simulation of buoyancyaffected
turbulence. Finally, the subgridscale model is utilised to perform a
systematic largeeddy simulation investigation of the archetypal lowcloud
regimes, from which the link between the lowertropospheric stability
criterion and the cloud fraction interpreted. 

Thinfilm flow in helical channels 12:10 Mon 9 Sep, 2013 :: B.19 Ingkarni Wardli :: David Arnold :: University of Adelaide
Media...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 thinfilm flow in helical channels. 

A gentle introduction to bubble evolution in HeleShaw flows 15:10 Fri 22 Nov, 2013 :: 5.58 (Ingkarni Wardli) :: Dr Scott McCue :: QUT
A HeleShaw cell is easy to make and serves as a fun toy for an applied mathematician to play with. If we inject air into a HeleShaw 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 HeleShaw cell or SaffmanTaylor instability on YouTube). From a mathematical perspective, modelling these HeleShaw 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) twodimensional moving boundary problems are so tractable. More generally, HeleShaw 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 preexisting immunity 15:10 Fri 7 Mar, 2014 :: B.18 Ingkarni Wardli :: Associate Professor Jane Heffernan :: York University, Canada
Media...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 (inhost) 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 multiscale 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. 

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 (macroscale); the cell level (mesoscale); and the subcellular level (microscale), 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 offlattice based models (cell centre and vertex based representations). The subcellular 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. 

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
Media...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. 

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
Media...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 householdstratified infection data. A design decision involves making a tradeoff between the number of households to enrol and the sampling frequency. Two commonly used study designs are considered: crosssectional and cohort. The search for an optimal design uses Bayesian methods to explore the joint parameterdesign space combined with Shannon entropy of the posteriors to estimate the amount of information for each design. We found that for the crosssectional designs, the amount of information increases with the sampling intensity while the cohort design often exhibits a tradeoff between the number of households sampled and the intensity of followup. Our results broadly support the choices made in existing data collection studies. 

Mathematical modelling of the immune response to influenza 15:00 Thu 12 May, 2016 :: Ingkarni Wardli B20 :: Ada Yan :: University of Melbourne
Media...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 crossreactivity in resolving infection. Our model provides a mechanistic explanation for the observed variation in viruses' abilities to protect against subsequent infection at short interexposure 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 crossreactive cellular adaptive immune responses. To account for intersubject as well as intervirus 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.


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
Media...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 agentbased models realized on empirical social networks, and ending up with populationlevel 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 populationlevel 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 centurylong 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 postmenopausal human longevity: The Grandmother Hypothesis 15:10 Fri 2 Sep, 2016 :: Napier G03 :: Dr Peter Kim :: University of Sydney
Media...Human postmenopausal 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 agentbased model that incorporates two sexes and mating, fertilitylongevity 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 lifehistories, one humanlike 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
Media...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 divideandconquer strategies, by determining efficient subsamples. 

Measuring and mapping carbon dioxide from remote sensing satellite data 15:10 Fri 21 Oct, 2016 :: Napier G03 :: Prof Noel Cressie :: University of Wollongong
Media...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 groundbased locations at somewhat regular time intervals. In contrast, satellitebased 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 Observatory2 (OCO2), whose principal objective is to retrieve a geographical distribution of CO2 sources and sinks. OCO2's measurement of columnaveraged mole fraction, XCO2, is designed to achieve this, through a dataassimilation 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 spatialstatistical modelling. 

How oligomerisation impacts steady state gradient in a morphogenreceptor 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 multiprotein 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 continuoustime branching processes, which makes them wellsuited for realworld 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. 

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 constraintbased 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 cellcell adhesion
and on predatorprey 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 highlevel reasoning and modelling of the processes that created this data. The 0th order aspect of shape is the number pieces: "connected components" to a topologist; "clustering" to a statistician. Higherorder topological aspects of shape are holes, quantified as "nonbounding cycles" in homology theory. These signal the existence of some type of constraint on the datagenerating 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 spacetime 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 "+Mathematical +modelling" 
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. 

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.More information... 

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 trafficmatrix 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 matrixanalytic 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. 

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. 

Topup 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 postPhD 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.More information... 
Publications matching "+Mathematical +modelling"Publications 

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  The mathematical modelling of rotating capillary tubes for holeyfibre manufacture Voyce, Christopher; Fitt, A; Monro, Tanya, Journal of Engineering Mathematics 60 (69–87) 2008  Mathematical modelling of oxygen concentration in bovine and murine cumulusoocyte complexes Clark, Alys; Stokes, Yvonne; Lane, Michelle; Thompson, Jeremy, Reproduction 131 (999–1006) 2006  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  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 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  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  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  A mathematical study of peristaltic transport of a Casson fluid Mernone, Anacleto; Mazumdar, Jagan; Lucas, S, Mathematical and Computer Modelling 35 (895–912) 2002  Statistical modelling and prediction associated with the HIV/AIDS epidemic Solomon, Patricia; Wilson, Susan, The Mathematical Scientist 26 (87–102) 2001  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 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 batchmovement queueing systems Hunt, Emma, Mathematical and Computer Modelling 31 (299–305) 2000  Maximal profit dimensioning and tariffing of loss networks with crossconnects Bean, Nigel; Brown, Deborah; Taylor, Peter, Mathematical and Computer Modelling 31 (21–30) 2000  Quasireversibility 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 
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