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March 2019

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Professor Nigel Bean
Chair of Applied Mathematics

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Associate Professor Benjamin Binder
Senior Lecturer in 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 Matthew Roughan
Professor of Applied Mathematics

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Courses matching "Models of cell-extracellular matrix interactions i"

Engineering Mathematics IIA

Mathematical models are used to understand, predict and optimise engineering systems. Many of these systems are deterministic and are modelled using differential equations. Others are random in nature and are analysed using probability theory and statistics. This course provides an introduction to differential equations and their solutions and to probability and statistics, and relates the theory to physical systems and simple real world applications. Topics covered are: Ordinary differential equations, including first and second order equations and series solutions; Fourier series; partial differential equations, including the heat equation, the wave equation, Laplace's equation and separation of variables; probability and statistical methods, including sampling and probability, descriptive statistics, random variables and probability distributions, mean and variance, linear combinations of random variables, statistical inference for means and proportions and linear regression.

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Engineering Mathematics IIB

This course provides an introduction to vector analysis and complex calculus, which is relevant to physics and engineering problems in two or more dimensions, such as solid and fluid mechanics, electromagnetism and thermodynamics. The course also introduces Laplace transform methods for solving differential equations, which have application to engineering problems such as circuit analysis and control. Topics covered are: Vector calculus: vector fields; gradient, divergence and curl; line, surface and volume integrals; integral theorems of Green, Gauss and Stokes with applications; orthogonal curvilinear coordinates. Complex analysis: elementary functions of a complex variable; complex differentiation; complex contour integrals; Laurent series; residue theorem. Laplace transforms: transforms of derivatives and integrals; shifting theorems; convolution; applications to differential equations.

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Mathematical epidemiology: Stochastic models and their statistical calibration

Mathematical models are increasingly used to inform governmental policy-makers on issues that threaten human health or which have an adverse impact on the economy. It is this real-world success combined with the wide variety of interesting mathematical problems which arise that makes mathematical epidemiology one of the most exciting topics in applied mathematics. During the summer school, you will be introduced to mathematical epidemiology and some fundamental theory required for studying and parametrising stochastic models of infection dynamics, which will provide an ideal basis for addressing key research questions in this area; several such questions will be introduced and explored in this course. Topics: An introduction to mathematical epidemiology Discrete-time and continuous-time discrete-state stochastic infection models Numerical methods for studying stochastic infection models: EXPOKIT, transforms and their inversion Methods for simulating stochastic infection models: classical (Gillespie) algorithm, more efficient exact and approximate algorithms Methods for parameterising stochastic infection models: frequentist approaches, Bayesian approaches, approximate Bayesian computation Optimal observation of stochastic infection models

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Events matching "Models of cell-extracellular matrix interactions i"

Stability of time-periodic flows
15:10 Fri 10 Mar, 2006 :: G08 Mathematics Building University of Adelaide :: Prof. Andrew Bassom, School of Mathematics and Statistics, University of Western Australia

Time-periodic shear layers occur naturally in a wide range of applications from engineering to physiology. Transition to turbulence in such flows is of practical interest and there have been several papers dealing with the stability of flows composed of a steady component plus an oscillatory part with zero mean. In such flows a possible instability mechanism is associated with the mean component so that the stability of the flow can be examined using some sort of perturbation-type analysis. This strategy fails when the mean part of the flow is small compared with the oscillatory component which, of course, includes the case when the mean part is precisely zero.

This difficulty with analytical studies has meant that the stability of purely oscillatory flows has relied on various numerical methods. Until very recently such techniques have only ever predicted that the flow is stable, even though experiments suggest that they do become unstable at high enough speeds. In this talk I shall expand on this discrepancy with emphasis on the particular case of the so-called flat Stokes layer. This flow, which is generated in a deep layer of incompressible fluid lying above a flat plate which is oscillated in its own plane, represents one of the few exact solutions of the Navier-Stokes equations. We show theoretically that the flow does become unstable to waves which propagate relative to the basic motion although the theory predicts that this occurs much later than has been found in experiments. Reasons for this discrepancy are examined by reference to calculations for oscillatory flows in pipes and channels. Finally, we propose some new experiments that might reduce this disagreement between the theoretical predictions of instability and practical realisations of breakdown in oscillatory flows.
Making tertiary mathematics more interesting
15:10 Fri 24 Mar, 2006 :: G08 Mathematics Building University of Adelaide :: Prof. Emeritus Neville de Mestre, Faculty of Information Technology, Bond University

For the past few decades, calculus and linear algebra have provided the basis for many university courses in mathematics, science or engineering. However there are other courses, which could be given to motivate the students, particularly those with only a passing love of mathematics. One possible course could show the essential features of how mathematicians solve problems using many different analytical, cerebral and computer skills. In this seminar I will describe such a one-semester course (2 lectures, 2 labs each week), which includes hands-on problem solving and students eventually creating their own problems. One or two exciting problems at first-year level will be developed in detail.
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.
A Bivariate Zero-inflated Poisson Regression Model and application to some Dental Epidemiological data
14:10 Fri 27 Oct, 2006 :: G08 Mathematics Building University of Adelaide :: University Prof Sudhir Paul

Data in the form of paired (pre-treatment, post-treatment) counts arise in the study of the effects of several treatments after accounting for possible covariate effects. An example of such a data set comes from a dental epidemiological study in Belo Horizonte (the Belo Horizonte caries prevention study) which evaluated various programmes for reducing caries. Also, these data may show extra pairs of zeros than can be accounted for by a simpler model, such as, a bivariate Poisson regression model. In such situations we propose to use a zero-inflated bivariate Poisson regression (ZIBPR) model for the paired (pre-treatment, posttreatment) count data. We develop EM algorithm to obtain maximum likelihood estimates of the parameters of the ZIBPR model. Further, we obtain exact Fisher information matrix of the maximum likelihood estimates of the parameters of the ZIBPR model and develop a procedure for testing treatment effects. The procedure to detect treatment effects based on the ZIBPR model is compared, in terms of size, by simulations, with an earlier procedure using a zero-inflated Poisson regression (ZIPR) model of the post-treatment count with the pre-treatment count treated as a covariate. The procedure based on the ZIBPR model holds level most effectively. A further simulation study indicates good power property of the procedure based on the ZIBPR model. We then compare our analysis, of the decayed, missing and filled teeth (DMFT) index data from the caries prevention study, based on the ZIBPR model with the analysis using a zero-inflated Poisson regression model in which the pre-treatment DMFT index is taken to be a covariate
Identifying the source of photographic images by analysis of JPEG quantization artifacts
15:10 Fri 27 Apr, 2007 :: G08 Mathematics Building University of Adelaide :: Dr Matthew Sorell

In a forensic context, digital photographs are becoming more common as sources of evidence in criminal and civil matters. Questions that arise include identifying the make and model of a camera to assist in the gathering of physical evidence; matching photographs to a particular camera through the camera’s unique characteristics; and determining the integrity of a digital image, including whether the image contains steganographic information. From a digital file perspective, there is also the question of whether metadata has been deliberately modified to mislead the investigator, and in the case of multiple images, whether a timeline can be established from the various timestamps within the file, imposed by the operating system or determined by other image characteristics. This talk is concerned specifically with techniques to identify the make, model series and particular source camera model given a digital image. We exploit particular characteristics of the camera’s JPEG coder to demonstrate that such identification is possible, and that even when an image has subsequently been re-processed, there are often sufficient residual characteristics of the original coding to at least narrow down the possible camera models of interest.
Flooding in the Sundarbans
15:10 Fri 18 May, 2007 :: G08 Mathematics Building University of Adelaide :: Steve Need

The Sunderbans is a region of deltaic isles formed in the mouth of the Ganges River on the border between India and Bangladesh. As the largest mangrove forest in the world it is a world heritage site, however it is also home to several remote communities who have long inhabited some regions. Many of the inhabited islands are low-lying and are particularly vulnerable to flooding, a major hazard of living in the region. Determining suitable levels of protection to be provided to these communities relies upon accurate assessment of the flood risk facing these communities. Only recently the Indian Government commissioned a study into flood risk in the Sunderbans with a view to determine where flood protection needed to be upgraded.

Flooding due to rainfall is limited due to the relatively small catchment sizes, so the primary causes of flooding in the Sunderbans are unnaturally high tides, tropical cyclones (which regularly sweep through the bay of Bengal) or some combination of the two. Due to the link between tidal anomaly and drops in local barometric pressure, the two causes of flooding may be highly correlated. I propose stochastic methods for analysing the flood risk and present the early work of a case study which shows the direction of investigation. The strategy involves linking several components; a stochastic approximation to a hydraulic flood routing model, FARIMA and GARCH models for storm surge and a stochastic model for cyclone occurrence and tracking. The methods suggested are general and should have applications in other cyclone affected regions.

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.
Moderated Statistical Tests for Digital Gene Expression Technologies
15:10 Fri 19 Oct, 2007 :: G04 Napier Building University of Adelaide :: Dr Gordon Smyth :: Walter and Eliza Hall Institute of Medical Research in Melbourne, Australia

Digital gene expression (DGE) technologies measure gene expression by counting sequence tags. They are sensitive technologies for measuring gene expression on a genomic scale, without the need for prior knowledge of the genome sequence. As the cost of DNA sequencing decreases, the number of DGE datasets is expected to grow dramatically. Various tests of differential expression have been proposed for replicated DGE data using over-dispersed binomial or Poisson models for the counts, but none of the these are usable when the number of replicates is very small. We develop tests using the negative binomial distribution to model overdispersion relative to the Poisson, and use conditional weighted likelihood to moderate the level of overdispersion across genes. A heuristic empirical Bayes algorithm is developed which is applicable to very general likelihood estimation contexts. Not only is our strategy applicable even with the smallest number of replicates, but it also proves to be more powerful than previous strategies when more replicates are available. The methodology is applicable to other counting technologies, such as proteomic spectral counts.
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.

Puzzle-based learning: Introduction to mathematics
15:10 Fri 23 May, 2008 :: LG29 Napier Building University of Adelaide :: Prof. Zbigniew Michalewicz :: School of Computer Science, University of Adelaide

The talk addresses a gap in the educational curriculum for 1st year students by proposing a new course that aims at getting students to think about how to frame and solve unstructured problems. The idea is to increase the student's mathematical awareness and problem-solving skills by discussing a variety of puzzles. The talk makes an argument that this approach - called Puzzle-Based Learning - is very beneficial for introducing mathematics, critical thinking, and problem-solving skills.

The new course has been approved by the University of Adelaide for Faculty of Engineering, Computer Science, and Mathematics. Many other universities are in the process of introducing such a course. The course will be offered in two versions: (a) full-semester course and (b) a unit within general course (e.g. Introduction to Engineering). All teaching materials (power point slides, assignments, etc.) are being prepared. The new textbook (Puzzle-Based Learning: Introduction to Critical Thinking, Mathematics, and Problem Solving) will be available from June 2008. The talk provides additional information on this development.

For further information see

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.

Elliptic equation for diffusion-advection flows
15:10 Fri 15 Aug, 2008 :: G03 Napier Building University of Adelaide :: Prof. Pavel Bedrikovsetsky :: Australian School of Petroleum Science, University of Adelaide.

The standard diffusion equation is obtained by Einstein's method and its generalisation, Fokker-Plank-Kolmogorov-Feller theory. The time between jumps in Einstein derivation is constant.

We discuss random walks with residence time distribution, which occurs for flows of solutes and suspensions/colloids in porous media, CO2 sequestration in coal mines, several processes in chemical, petroleum and environmental engineering. The rigorous application of the Einstein's method results in new equation, containing the time and the mixed dispersion terms expressing the dispersion of the particle time steps.

Usually, adding the second time derivative results in additional initial data. For the equation derived, the condition of limited solution when time tends to infinity provides with uniqueness of the Caushy problem solution.

The solution of the pulse injection problem describing a common tracer injection experiment is studied in greater detail. The new theory predicts delay of the maximum of the tracer, compared to the velocity of the flow, while its forward "tail" contains much more particles than in the solution of the classical parabolic (advection-dispersion) equation. This is in agreement with the experimental observations and predictions of the direct simulation.

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.
Hunting Non-linear Mathematical Butterflies
15:10 Fri 23 Jan, 2009 :: Napier LG29 :: Prof Nalini Joshi :: University of Sydney

The utility of mathematical models relies on their ability to predict the future from a known set of initial states. But there are non-linear systems, like the weather, where future behaviours are unpredictable unless their initial state is known to infinite precision. This is the butterfly effect. I will show how to analyse functions to overcome this problem for the classical Painleve equations, differential equations that provide archetypical non-linear models of modern physics.
What on Earth is Computational Advertising?
15:10 Wed 28 Jan, 2009 :: Napier G03 :: Dr John Tomlin :: Yahoo! Research Labs

This talk will begin with a brief introduction to, and overview of, the topic we have come to call "computational advertising", by which we mean the algorithmic techniques useful for the optimal placement, scheduling and context of on-line advertisements. Such advertisements encompass a large and growing fraction of the advertising industry, and, in the forms of display advertising, content match, and search marketing, bring in a large fraction of the income derived from the web. In addition to the overview, we give two examples of optimization models applied to problems in sponsored search and display advertising.
Boltzmann's Equations for Suspension Flow in Porous Media and Correction of the Classical Model
15:10 Fri 13 Mar, 2009 :: Napier LG29 :: Prof Pavel Bedrikovetsky :: University of Adelaide

Suspension/colloid transport in porous media is a basic phenomenon in environmental, petroleum and chemical engineering. Suspension of particles moves through porous media and particles are captured by straining or attraction. We revise the classical equations for particle mass balance and particle capture kinetics and show its non-realistic behaviour in cases of large dispersion and of flow-free filtration. In order to resolve the paradoxes, the pore-scale model is derived. The model can be transformed to Boltzmann equation with particle distribution over pores. Introduction of sink-source terms into Boltzmann equation results in much more simple calculations if compared with the traditional Chapman-Enskog averaging procedure. Technique of projecting operators in Hilbert space of Fourier images is used. The projection subspace is constructed in a way to avoid dependency of averaged equations on sink-source terms. The averaging results in explicit expressions for particle flux and capture rate. The particle flux expression describes the effect of advective particle velocity decrease if compared with the carrier water velocity due to preferential capture of "slow" particles in small pores. The capture rate kinetics describes capture from either advective or diffusive fluxes. The equations derived exhibit positive advection velocity for any dispersion and particle capture in immobile fluid that resolves the above-mentioned paradox. Finally, we discuss validation of the model for propagation of contaminants in aquifers, for filtration, for potable water production by artesian wells, for formation damage in oilfields.
Tummy troubles
12:10 Thu 9 Apr, 2009 :: Napier 210 :: Dr Ben Binder

Hirschsprung's disease is relatively common, affecting roughly 1 in 5000 newly born babies each year in Australia. The disease occurs when there is an incomplete formation of the nervous system in the gut. Mathematical models can help in determining the underlying mechanisms that cause the disease. Comparisons between theoretical predictions and experimental results will be made.
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.
Sloshing in tanks of liquefied natural gas (LNG) vessels
15:10 Wed 22 Apr, 2009 :: Napier LG29 :: Prof. Frederic Dias :: ENS, Cachan

The last scientific conversation I had with Ernie Tuck was on liquid impact. As a matter of fact, we discussed the paper by J.H. Milgram, Journal of Fluid Mechanics 37 (1969), entitled "The motion of a fluid in a cylindrical container with a free surface following vertical impact." Liquid impact is a key issue in sloshing and in particular in sloshing in tanks of LNG vessels. Numerical simulations of sloshing have been performed by various groups, using various types of numerical methods. In terms of the numerical results, the outcome is often impressive, but the question remains of how relevant these results are when it comes to determining impact pressures. The numerical models are too simplified to reproduce the high variability of the measured pressures. In fact, for the time being, it is not possible to simulate accurately both global and local effects. Unfortunately it appears that local effects predominate over global effects when the behaviour of pressures is considered. Having said this, it is important to point out that numerical studies can be quite useful to perform sensitivity analyses in idealized conditions such as a liquid mass falling under gravity on top of a horizontal wall and then spreading along the lateral sides. Simple analytical models inspired by numerical results on idealized problems can also be useful to predict trends. The talk is organized as follows: After a brief introduction on the sloshing problem and on scaling laws, it will be explained to what extent numerical studies can be used to improve our understanding of impact pressures. Results on a liquid mass hitting a wall obtained by a finite-volume code with interface reconstruction as well as results obtained by a simple analytical model will be shown to reproduce the trends of experiments on sloshing. This is joint work with L. Brosset (GazTransport & Technigaz), J.-M. Ghidaglia (ENS Cachan) and J.-P. Braeunig (INRIA).
Wall turbulence: from the laboratory to the atmosphere
15:00 Fri 29 May, 2009 :: Napier LG29 :: Prof Ivan Marusic :: The University of Melbourne

The study of wall-bounded turbulent flows has received great attention over the past few years as a result of high Reynolds number experiments conducted in new high Reynolds number facilities such as the Princeton "superpipe", the NDF facility in Chicago and the HRNBLWT at the University of Melbourne. These experiments have brought into question the fundamental scaling laws of the turbulence and mean flow quantities as well as revealed high Reynolds number phenomena, which make extrapolation of low Reynolds number results highly questionable. In this talk these issues will be reviewed and new results from the HRNBLWT and atmospheric surface layer on the salt-flats of Utah will be presented documenting unique high Reynolds number phenomena. The implications for skin-friction drag reduction technologies and improved near-wall models for large-eddy simulation will be discussed.
Chern-Simons classes on loop spaces and diffeomorphism groups
13:10 Fri 12 Jun, 2009 :: School Board Room :: Prof Steve Rosenberg :: Boston University

The loop space LM of a Riemannian manifold M comes with a family of Riemannian metrics indexed by a Sobolev parameter. We can construct characteristic classes for LM using the Wodzicki residue instead of the usual matrix trace. The Pontrjagin classes of LM vanish, but the secondary or Chern-Simons classes may be nonzero and may distinguish circle actions on M. There are similar results for diffeomorphism groups of manifolds.
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.
Understanding hypersurfaces through tropical geometry
12:10 Fri 25 Sep, 2009 :: Napier 102 :: Dr Mohammed Abouzaid :: Massachusetts Institute of Technology

Given a polynomial in two or more variables, one may study the zero locus from the point of view of different mathematical subjects (number theory, algebraic geometry, ...). I will explain how tropical geometry allows to encode all topological aspects by elementary combinatorial objects called "tropical varieties." Mohammed Abouzaid received a B.S. in 2002 from the University of Richmond, and a Ph.D. in 2007 from the University of Chicago under the supervision of Paul Seidel. He is interested in symplectic topology and its interactions with algebraic geometry and differential topology, in particular the homological mirror symmetry conjecture. Since 2007 he has been a postdoctoral fellow at MIT, and a Clay Mathematics Institute Research Fellow.
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.
Eigen-analysis of fluid-loaded compliant panels
15:10 Wed 9 Dec, 2009 :: Santos Lecture Theatre :: Prof Tony Lucey :: Curtin University of Technology

This presentation concerns the fluid-structure interaction (FSI) that occurs between a fluid flow and an arbitrarily deforming flexible boundary considered to be a flexible panel or a compliant coating that comprises the wetted surface of a marine vehicle. We develop and deploy an approach that is a hybrid of computational and theoretical techniques. The system studied is two-dimensional and linearised disturbances are assumed. Of particular novelty in the present work is the ability of our methods to extract a full set of fluid-structure eigenmodes for systems that have strong spatial inhomogeneity in the structure of the flexible wall.

We first present the approach and some results of the system in which an ideal, zero-pressure gradient, flow interacts with a flexible plate held at both its ends. We use a combination of boundary-element and finite-difference methods to express the FSI system as a single matrix equation in the interfacial variable. This is then couched in state-space form and standard methods used to extract the system eigenvalues. It is then shown how the incorporation of spatial inhomogeneity in the stiffness of the plate can be either stabilising or destabilising. We also show that adding a further restraint within the streamwise extent of a homogeneous panel can trigger an additional type of hydroelastic instability at low flow speeds. The mechanism for the fluid-to-structure energy transfer that underpins this instability can be explained in terms of the pressure-signal phase relative to that of the wall motion and the effect on this relationship of the added wall restraint.

We then show how the ideal-flow approach can be conceptually extended to include boundary-layer effects. The flow field is now modelled by the continuity equation and the linearised perturbation momentum equation written in velocity-velocity form. The near-wall flow field is spatially discretised into rectangular elements on an Eulerian grid and a variant of the discrete-vortex method is applied. The entire fluid-structure system can again be assembled as a linear system for a single set of unknowns - the flow-field vorticity and the wall displacements - that admits the extraction of eigenvalues. We then show how stability diagrams for the fully-coupled finite flow-structure system can be assembled, in doing so identifying classes of wall-based or fluid-based and spatio-temporal wave behaviour.

A solution to the Gromov-Vaserstein problem
15:10 Fri 29 Jan, 2010 :: Engineering North N 158 Chapman Lecture Theatre :: Prof Frank Kutzschebauch :: University of Berne, Switzerland

Any matrix in $SL_n (\mathbb C)$ can be written as a product of elementary matrices using the Gauss elimination process. If instead of the field of complex numbers, the entries in the matrix are elements of a more general ring, this becomes a delicate question. In particular, rings of complex-valued functions on a space are interesting cases. A deep result of Suslin gives an affirmative answer for the polynomial ring in $m$ variables in case the size $n$ of the matrix is at least 3. In the topological category, the problem was solved by Thurston and Vaserstein. For holomorphic functions on $\mathbb C^m$, the problem was posed by Gromov in the 1980s. We report on a complete solution to Gromov's problem. A main tool is the Oka-Grauert-Gromov h-principle in complex analysis. Our main theorem can be formulated as follows: In the absence of obvious topological obstructions, the Gauss elimination process can be performed in a way that depends holomorphically on the matrix. This is joint work with Bj\"orn Ivarsson.
Nonlinear time series econometrics and financial econometrics: a personal overview
15:10 Fri 12 Mar, 2010 :: Napier G04 :: Prof Jiti Gao :: University of Adelaide

Through using ten examples, the talk focuses on the recent development on nonlinear time series econometrics and financial econometrics. Such examples cover the following models: 1. Nonlinear time series trend model; 2. Partially linear autoregressive model; 3. Nonlinear capital asset pricing model; 4. Additive capital asset pricing model; 5. Varying-coefficient capital asset pricing model; 6. Semiparametric error-term model; 7. Nonlinear and nonstationary model; 8. Partially linear ARCH model; 9. Continuous-time financial model; and 10. Stochastic volatility model.
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.
The fluid mechanics of gels used in tissue engineering
15:10 Fri 9 Apr, 2010 :: Santos Lecture Theatre :: Dr Edward Green :: University of Western Australia

Tissue engineering could be called 'the science of spare parts'. Although currently in its infancy, its long-term aim is to grow functional tissues and organs in vitro to replace those which have become defective through age, trauma or disease. Recent experiments have shown that mechanical interactions between cells and the materials in which they are grown have an important influence on tissue architecture, but in order to understand these effects, we first need to understand the mechanics of the gels themselves.

Many biological gels (e.g. collagen) used in tissue engineering have a fibrous microstructure which affects the way forces are transmitted through the material, and which in turn affects cell migration and other behaviours. I will present a simple continuum model of gel mechanics, based on treating the gel as a transversely isotropic viscous material. Two canonical problems are considered involving thin two-dimensional films: extensional flow, and squeezing flow of the fluid between two rigid plates. Neglecting inertia, gravity and surface tension, in each regime we can exploit the thin geometry to obtain a leading-order problem which is sufficiently tractable to allow the use of analytical methods. I discuss how these results could be exploited practically to determine the mechanical properties of real gels. If time permits, I will also talk about work currently in progress which explores the interaction between gel mechanics and cell behaviour.

Mathematical epidemiology with a focus on households
15:10 Fri 23 Apr, 2010 :: Napier G04 :: Dr Joshua Ross :: University of Adelaide

Mathematical models are now used routinely to inform national and global policy-makers on issues that threaten human health or which have an adverse impact on the economy. In the first part of this talk I will provide an overview of mathematical epidemiology starting with the classical deterministic model and leading to some of the current challenges. I will then present some of my recently published work which provides computationally-efficient methods for studying a mathematical model incorporating household structure. We will conclude by briefly discussing some "work-in-progess" which utilises these methods to address the issues of inference, and mixing pattern and contact structure, for emerging infections.
Meteorological drivers of extreme bushfire events in southern Australia
15:10 Fri 2 Jul, 2010 :: Benham Lecture Theatre :: Prof Graham Mills :: Centre for Australian Weather and Climate Research, Melbourne

Bushfires occur regularly during summer in southern Australia, but only a few of these fires become iconic due to their effects, either in terms of loss of life or economic and social cost. Such events include Black Friday (1939), the Hobart fires (1967), Ash Wednesday (1983), the Canberra bushfires (2003), and most recently Black Saturday in February 2009. In most of these events the weather of the day was statistically extreme in terms of heat, (low) humidity, and wind speed, and in terms of antecedent drought. There are a number of reasons for conducting post-event analyses of the meteorology of these events. One is to identify any meteorological circulation systems or dynamic processes occurring on those days that might not be widely or hitherto recognised, to document these, and to develop new forecast or guidance products. The understanding and prediction of such features can be used in the short term to assist in effective management of fires and the safety of firefighters and in the medium range to assist preparedness for the onset of extreme conditions. The results of such studies can also be applied to simulations of future climates to assess the likely changes in frequency of the most extreme fire weather events, and their documentary records provide a resource that can be used for advanced training purposes. In addition, particularly for events further in the past, revisiting these events using reanalysis data sets and contemporary NWP models can also provide insights unavailable at the time of the events. Over the past few years the Bushfire CRC's Fire Weather and Fire Danger project in CAWCR has studied the mesoscale meteorology of a number of major fire events, including the days of Ash Wednesday 1983, the Dandenong Ranges fire in January 1997, the Canberra fires and the Alpine breakout fires in January 2003, the Lower Eyre Peninsula fires in January 2005 and the Boorabbin fire in December 2007-January 2008. Various aspects of these studies are described below, including the structures of dry cold frontal wind changes, the particular character of the cold fronts associated with the most damaging fires in southeastern Australia, and some aspects of how the vertical temperature and humidity structure of the atmosphere may affect the fire weather at the surface. These studies reveal much about these major events, but also suggest future research directions, and some of these will be discussed.
Eynard-Orantin invariants and enumerative geometry
13:10 Fri 6 Aug, 2010 :: Ingkarni Wardli B20 (Suite 4) :: Dr Paul Norbury :: University of Melbourne

As a tool for studying enumerative problems in geometry Eynard and Orantin associate multilinear differentials to any plane curve. Their work comes from matrix models but does not require matrix models (for understanding or calculations). In some sense they describe deformations of complex structures of a curve and conjectural relationships to deformations of Kahler structures of an associated object. I will give an introduction to their invariants via explicit examples, mainly to do with the moduli space of Riemann surfaces, in which the plane curve has genus zero.
A spatial-temporal point process model for fine resolution multisite rainfall data from Roma, Italy
14:10 Thu 19 Aug, 2010 :: Napier G04 :: A/Prof Paul Cowpertwait :: Auckland University of Technology

A point process rainfall model is further developed that has storm origins occurring in space-time according to a Poisson process. Each storm origin has a random radius so that storms occur as circular regions in two-dimensional space, where the storm radii are taken to be independent exponential random variables. Storm origins are of random type z, where z follows a continuous probability distribution. Cell origins occur in a further spatial Poisson process and have arrival times that follow a Neyman-Scott point process. Cell origins have random radii so that cells form discs in two-dimensional space. Statistical properties up to third order are derived and used to fit the model to 10 min series taken from 23 sites across the Roma region, Italy. Distributional properties of the observed annual maxima are compared to equivalent values sampled from series that are simulated using the fitted model. The results indicate that the model will be of use in urban drainage projects for the Roma region.
Compound and constrained regression analyses for EIV models
15:05 Fri 27 Aug, 2010 :: Napier LG28 :: Prof Wei Zhu :: State University of New York at Stony Brook

In linear regression analysis, randomness often exists in the independent variables and the resulting models are referred to errors-in-variables (EIV) models. The existing general EIV modeling framework, the structural model approach, is parametric and dependent on the usually unknown underlying distributions. In this work, we introduce a general non-parametric EIV modeling framework, the compound regression analysis, featuring an intuitive geometric representation and a 1-1 correspondence to the structural model. Properties, examples and further generalizations of this new modeling approach are discussed in this talk.
A polyhedral model for boron nitride nanotubes
15:10 Fri 3 Sep, 2010 :: Napier G04 :: Dr Barry Cox :: University of Adelaide

The conventional rolled-up model of nanotubes does not apply to the very small radii tubes, for which curvature effects become significant. In this talk an existing geometric model for carbon nanotubes proposed by the authors, which accommodates this deficiency and which is based on the exact polyhedral cylindrical structure, is extended to a nanotube structure involving two species of atoms in equal proportion, and in particular boron nitride nanotubes. This generalisation allows the principle features to be included as the fundamental assumptions of the model, such as equal bond length but distinct bond angles and radii between the two species. The polyhedral model is based on the five simple geometric assumptions: (i) all bonds are of equal length, (ii) all bond angles for the boron atoms are equal, (iii) all boron atoms lie at an equal distance from the nanotube axis, (iv) all nitrogen atoms lie at an equal distance from the nanotube axis, and (v) there exists a fixed ratio of pyramidal height H, between the boron species compared with the corresponding height in a symmetric single species nanotube. Working from these postulates, expressions are derived for the various structural parameters such as radii and bond angles for the two species for specific values of the chiral vector numbers (n,m). The new model incorporates an additional constant of proportionality H, which we assume applies to all nanotubes comprising the same elements and is such that H = 1 for a single species nanotube. Comparison with `ab initio' studies suggest that this assumption is entirely reasonable, and in particular we determine the value H = 0.56\pm0.04 for boron nitride, based on computational results in the literature. This talk relates to work which is a couple of years old and given time at the end we will discuss some newer results in geometric models developed with our former student Richard Lee (now also at the University of Adelaide as a post doc) and some work-in-progress on carbon nanocones. Note: pyramidal height is our own terminology and will be explained in the talk.
Simultaneous confidence band and hypothesis test in generalised varying-coefficient models
15:05 Fri 10 Sep, 2010 :: Napier LG28 :: Prof Wenyang Zhang :: University of Bath

Generalised varying-coefficient models (GVC) are very important models. There are a considerable number of literature addressing these models. However, most of the existing literature are devoted to the estimation procedure. In this talk, I will systematically investigate the statistical inference for GVC, which includes confidence band as well as hypothesis test. I will show the asymptotic distribution of the maximum discrepancy between the estimated functional coefficient and the true functional coefficient. I will compare different approaches for the construction of confidence band and hypothesis test. Finally, the proposed statistical inference methods are used to analyse the data from China about contraceptive use there, which leads to some interesting findings.
The mathematics of smell
15:10 Wed 29 Sep, 2010 :: Ingkarni Wardli 5.57 :: Dr Michael Borgas :: CSIRO Light Metals Flagship; Marine and Atmospheric Research; Centre for Australian Weather and Clim

The sense of smell is important in nature, but the least well understood of our senses. A mathematical model of smell, which combines the transmission of volatile-organic-compound chemical signals (VOCs) on the wind, transduced by olfactory receptors in our noses into neural information, and assembled into our odour perception, is useful. Applications include regulations for odour nuisance, like German VDI protocols for calibrated noses, to the design of modern chemical sensors for extracting information from the environment and even for the perfume industry. This talk gives a broad overview of turbulent mixing in surface layers of the atmosphere, measurements of VOCs with PTR-MS (proton transfer reaction mass spectrometers), our noses, and integrated environmental models of the Alumina industry (a source of odour emissions) to help understand the science of smell.
Explicit numerical simulation of multiphase and confined flows
15:10 Fri 8 Oct, 2010 :: Napier G04 :: Prof Mark Biggs :: University of Adelaide

Simulations in which the system of interest is essentially mimicked are termed explicit numerical simulations (ENS). Direct numerical simulation (DNS) of turbulence is a well known and long-standing example of ENS. Such simulations provide a basis for elucidating fundamentals in a way that is impossible experimentally and formulating and parameterizing engineering models with reduced experimentation. In this presentation, I will first outline the concept of ENS. I will then report a number of ENS-based studies of various multiphase fluid systems and flows in porous media. In the first of these studies, which is concerned with flow of suspensions in porous media accompanied by deposition, ENS is used to demonstrate the significant inadequacies of the classical trajectory models typically used for the study of such problems. In the second study, which is concerned with elucidating the change in binary droplet collision behaviour with Capillary number (Ca) and Reynolds number (Re), a range of collision scenarios are revealed as a function of Ca and Re and it appears that the boundaries between these scenarios in the Ca-Re space are not distinct but, rather, smeared. In the final study, it is shown that ENS an be used to predict ab initio the hydrodynamic properties of single phase flow through porous media from the Darcy to the turbulent regimes.
Bioinspired computation in combinatorial optimization: algorithms and their computational complexity
15:10 Fri 11 Mar, 2011 :: 7.15 Ingkarni Wardli :: Dr Frank Neumann :: The University of Adelaide

Bioinspired computation methods, such as evolutionary algorithms and ant colony optimization, are being applied successfully to complex engineering and combinatorial optimization problems. The computational complexity analysis of this type of algorithms has significantly increased the theoretical understanding of these successful algorithms. In this talk, I will give an introduction into this field of research and present some important results that we achieved for problems from combinatorial optimization. These results can also be found in my recent textbook "Bioinspired Computation in Combinatorial Optimization -- Algorithms and Their Computational Complexity".
To which extent the model of Black-Scholes can be applied in the financial market?
12:10 Mon 21 Mar, 2011 :: 5.57 Ingkarni Wardli :: Ahmed Hamada :: University of Adelaide

Black and Scholes have introduced a new approach to model the stock price dynamics about three decades ago. The so called Black Scholes model seems to be very adapted to the nature of market prices, mainly because the usage of the Brownian motion and the mathematical properties that follow from. Like every theoretical model, put in practice, it does not appear to be flawless, that means that new adaptations and extensions should be made so that engineers and marketers could utilise the Black Scholes models to trade and hedge risk on the market. A more detailed description with application will be given in the talk.
A mathematical investigation of methane encapsulation in carbon nanotubes.
12:10 Mon 21 Mar, 2011 :: 5.57 Ingkarni Wardli :: Olumide Adisa :: University of Adelaide

I hope we don't have to wait until oil and coal run out before we tackle that." - Thomas Edison, 1931. In a bid to resolve energy issues consistent with Thomas Edison's worries, scientists have been looking at other clean and sustainable sources of energy such as natural gas - methane. In this talk, the interaction between a methane molecule and carbon nanotubes is investigated mathematically, using two different models - first discrete and second, continuous. These models are analyzed to determine the dimensions of the particular nanotubes which will readily suck-up methane molecules. The results determine the minimum and maximum interaction energies required for methane encapsulation in different tube sizes, and establish the second model of the methane molecule as a simple and elegant model which might be exploited for other problems.
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.
How round is your triangle, square, pentagon, ...?
12:10 Wed 6 Apr, 2011 :: Napier 210 :: Dr Barry Cox :: University of Adelaide

Most of us are familiar with the problem of making circular holes in wood or other material. For smaller diameter holes we typically use a drill, and for larger diameter holes a spade-bit, hole-saw or plunge router may be used. However for some applications, like mortise-and-tenon joints, what is needed is a tool that will produce a hole with a cross-section that is something other than a circle. In this talk we look at curves that may be used as the basis for a device that will produce holes with a cross-section of an equilateral triangle, square, or any regular polygon. Along the way we will touch on areas of engineering, algebra, geometry, calculus, Gothic art and architecture.
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).
Statistical challenges in molecular phylogenetics
15:10 Fri 20 May, 2011 :: Mawson Lab G19 lecture theatre :: Dr Barbara Holland :: University of Tasmania

This talk will give an introduction to the ways that mathematics and statistics gets used in the inference of evolutionary (phylogenetic) trees. Taking a model-based approach to estimating the relationships between species has proven to be an enormously effective, however, there are some tricky statistical challenges that remain. The increasingly plentiful amount of DNA sequence data is a boon, but it is also throwing a spotlight on some of the shortcomings of current best practice particularly in how we (1) assess the reliability of our phylogenetic estimates, and (2) how we choose appropriate models. This talk will aim to give a general introduction this area of research and will also highlight some results from two of my recent PhD students.
Permeability of heterogeneous porous media - experiments, mathematics and computations
15:10 Fri 27 May, 2011 :: B.21 Ingkarni Wardli :: Prof Patrick Selvadurai :: Department of Civil Engineering and Applied Mechanics, McGill University

Permeability is a key parameter important to a variety of applications in geological engineering and in the environmental geosciences. The conventional definition of Darcy flow enables the estimation of permeability at different levels of detail. This lecture will focus on the measurement of surface permeability characteristics of a large cuboidal block of Indiana Limestone, using a surface permeameter. The paper discusses the theoretical developments, the solution of the resulting triple integral equations and associated computational treatments that enable the mapping of the near surface permeability of the cuboidal region. This data combined with a kriging procedure is used to develop results for the permeability distribution at the interior of the cuboidal region. Upon verification of the absence of dominant pathways for fluid flow through the cuboidal region, estimates are obtained for the "Effective Permeability" of the cuboid using estimates proposed by Wiener, Landau and Lifschitz, King, Matheron, Journel et al., Dagan and others. The results of these estimates are compared with the geometric mean, derived form the computational estimates.
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.
Inference and optimal design for percolation and general random graph models (Part I)
09:30 Wed 8 Jun, 2011 :: 7.15 Ingkarni Wardli :: Dr Andrei Bejan :: The University of Cambridge

The problem of optimal arrangement of nodes of a random weighted graph is discussed in this workshop. The nodes of graphs under study are fixed, but their edges are random and established according to the so called edge-probability function. This function is assumed to depend on the weights attributed to the pairs of graph nodes (or distances between them) and a statistical parameter. It is the purpose of experimentation to make inference on the statistical parameter and thus to extract as much information about it as possible. We also distinguish between two different experimentation scenarios: progressive and instructive designs.

We adopt a utility-based Bayesian framework to tackle the optimal design problem for random graphs of this kind. Simulation based optimisation methods, mainly Monte Carlo and Markov Chain Monte Carlo, are used to obtain the solution. We study optimal design problem for the inference based on partial observations of random graphs by employing data augmentation technique. We prove that the infinitely growing or diminishing node configurations asymptotically represent the worst node arrangements. We also obtain the exact solution to the optimal design problem for proximity (geometric) graphs and numerical solution for graphs with threshold edge-probability functions.

We consider inference and optimal design problems for finite clusters from bond percolation on the integer lattice $\mathbb{Z}^d$ and derive a range of both numerical and analytical results for these graphs. We introduce inner-outer plots by deleting some of the lattice nodes and show that the ëmostly populatedí designs are not necessarily optimal in the case of incomplete observations under both progressive and instructive design scenarios. Some of the obtained results may generalise to other lattices.

Inference and optimal design for percolation and general random graph models (Part II)
10:50 Wed 8 Jun, 2011 :: 7.15 Ingkarni Wardli :: Dr Andrei Bejan :: The University of Cambridge

The problem of optimal arrangement of nodes of a random weighted graph is discussed in this workshop. The nodes of graphs under study are fixed, but their edges are random and established according to the so called edge-probability function. This function is assumed to depend on the weights attributed to the pairs of graph nodes (or distances between them) and a statistical parameter. It is the purpose of experimentation to make inference on the statistical parameter and thus to extract as much information about it as possible. We also distinguish between two different experimentation scenarios: progressive and instructive designs.

We adopt a utility-based Bayesian framework to tackle the optimal design problem for random graphs of this kind. Simulation based optimisation methods, mainly Monte Carlo and Markov Chain Monte Carlo, are used to obtain the solution. We study optimal design problem for the inference based on partial observations of random graphs by employing data augmentation technique. We prove that the infinitely growing or diminishing node configurations asymptotically represent the worst node arrangements. We also obtain the exact solution to the optimal design problem for proximity (geometric) graphs and numerical solution for graphs with threshold edge-probability functions.

We consider inference and optimal design problems for finite clusters from bond percolation on the integer lattice $\mathbb{Z}^d$ and derive a range of both numerical and analytical results for these graphs. We introduce inner-outer plots by deleting some of the lattice nodes and show that the ëmostly populatedí designs are not necessarily optimal in the case of incomplete observations under both progressive and instructive design scenarios. Some of the obtained results may generalise to other lattices.

Stochastic models of reaction diffusion
15:10 Fri 17 Jun, 2011 :: 7.15 Ingkarni Wardli :: Prof Jon Chapman :: Oxford University

We consider two different position jump processes: (i) a random walk on a lattice (ii) the Euler scheme for the Smoluchowski differential equation. Both of these reduce to the diffusion equation as the time step and size of the jump tend to zero. We consider the problem of adding chemical reactions to these processes, both at a surface and in the bulk. We show how the "microscopic" parameters should be chosen to achieve the correct "macroscopic" reaction rate. This choice is found to depend on which stochastic model for diffusion is used.
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.
There are no magnetically charged particle-like solutions of the Einstein-Yang-Mills equations for models with Abelian residual groups
13:10 Fri 19 Aug, 2011 :: B.19 Ingkarni Wardli :: Dr Todd Oliynyk :: Monash University

According to a conjecture from the 90's, globally regular, static, spherically symmetric (i.e. particle-like) solutions with nonzero total magnetic charge are not expected to exist in Einstein-Yang-Mills theory. In this talk, I will describe recent work done in collaboration with M. Fisher where we establish the validity of this conjecture under certain restrictions on the residual gauge group. Of particular interest is that our non-existence results apply to the most widely studied models with Abelian residual groups.
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.
Estimating transmission parameters for the swine flu pandemic
15:10 Fri 23 Sep, 2011 :: 7.15 Ingkarni Wardli :: Dr Kathryn Glass :: Australian National University

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.
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

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.
Fluid flows in microstructured optical fibre fabrication
15:10 Fri 25 Nov, 2011 :: B.17 Ingkarni Wardli :: Mr Hayden Tronnolone :: University of Adelaide

Optical fibres are used extensively in modern telecommunications as they allow the transmission of information at high speeds. Microstructured optical fibres are a relatively new fibre design in which a waveguide for light is created by a series of air channels running along the length of the material. The flexibility of this design allows optical fibres to be created with adaptable (and previously unrealised) optical properties. However, the fluid flows that arise during fabrication can greatly distort the geometry, which can reduce the effectiveness of a fibre or render it useless. I will present an overview of the manufacturing process and highlight the difficulties. I will then focus on surface-tension driven deformation of the macroscopic version of the fibre extruded from a reservoir of molten glass, occurring during fabrication, which will be treated as a two-dimensional Stokes flow problem. I will outline two different complex-variable numerical techniques for solving this problem along with comparisons of the results, both to other models and to experimental data.
Mixing, dynamics, and probability
15:10 Fri 2 Mar, 2012 :: B.21 Ingkarni Wardli :: A/Prof Gary Froyland :: University of New South Wales

Many interesting natural phenomena are hard to predict. When modelled as a dynamical system, this unpredictability is often the result of rapid separation of nearby trajectories. Viewing the dynamics as acting on a probability measure, the mixing property states that two measurements (or random variables), evaluated at increasingly separated times, become independent in the time-separation limit. Thus, the later measurement becomes increasingly difficult to predict, given the outcome of the earlier measurement. If this approach to independence occurs exponentially quickly in time, one can profitably use linear operator tools to analyse the dynamics. I will give an overview of these techniques and show how they can be applied to answer mathematical questions, describe observed behaviour in fluid mixing, and analyse models of the ocean and atmosphere.
String Theory and the Quest for Quantum Spacetime
15:10 Fri 9 Mar, 2012 :: Ligertwood 333 Law Lecture Theatre 2 :: Prof Rajesh Gopakumar :: Harish-Chandra Research Institute

Space and time together constitute one of the most basic elements of physical reality. Since Einstein spacetime has become an active participant in the dynamics of the gravitational force. However, our notion of a quantum spacetime is still rudimentary. String theory, building upon hints provided from the physics of black holes, seems to be suggesting a very novel, "holographic" picture of what quantum spacetime might be. This relies on some very surprising connections of gravity with quantum field theories (which provide the framework for the description of the other fundamental interactions of nature). In this talk, I will try and convey some of the flavour of these connections as well as its significance.
Forecasting electricity demand distributions using a semiparametric additive model
15:10 Fri 16 Mar, 2012 :: B.21 Ingkarni Wardli :: Prof Rob Hyndman :: Monash University

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.
Instability in standing waves in inhomogeneous nonlinear Schrodinger equations
13:10 Fri 30 Mar, 2012 :: B.17 Ingkarni Wardli :: Dr Robert Marangell :: The University of Sydney

In this talk, I will describe a mechanism for determining instability of standing wave solutions to a class of inhomogeneous nonlinear Schrodinger (NLS) equations. The inhomogeneity in this case means that the equations will spatially alternate between NLS and the so-called Gross-Pitaevskii equation. Such equations are useful in 1-D models of Bose-Einstein Condensates (BECs). The mechanism is inherently topological and therefore robust, leading to its application to a number of different soliton solutions, such as gap solitons, surface gap solitons, and dark soliton among others.
The mechanics of plant root growth
15:10 Fri 30 Mar, 2012 :: B.21 Ingkarni Wardli :: Dr Rosemary Dyson :: University of Birmingham

Growing plant cells undergo rapid axial elongation with negligible radial expansion: high internal turgor pressure causes viscous stretching of the cell wall. We represent the cell wall as a thin fibre-reinforced viscous sheet, providing insight into the geometric and biomechanical parameters underlying bulk quantities such as wall extensibility and showing how either dynamical changes in material properties, achieved through changes in the cell-wall microstructure, or passive fibre reorientation may suppress cell elongation. We then investigate how the action of enzymes on the cell wall microstructure can lead to the required dynamic changes in macroscale wall material properties, and thus demonstrate a mechanism by which hormones may regulate plant growth.
Spatial-point data sets and the Polya distribution
15:10 Fri 27 Apr, 2012 :: B.21 Ingkarni Wardli :: Dr Benjamin Binder :: The University of Adelaide

Spatial-point data sets, generated from a wide range of physical systems and mathematical models, can be analyzed by counting the number of objects in equally sized bins. We find that the bin counts are related to the Polya distribution. New indexes are developed which quantify whether or not a spatial data set is at its most evenly distributed state. Using three case studies (Lagrangian fluid particles in chaotic laminar flows, cellular automata agents in discrete models, and biological cells within colonies), we calculate the indexes and predict the spatial-state of the system.
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

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).
Enhancing the Jordan canonical form
15:10 Fri 1 Jun, 2012 :: B.21 Ingkarni Wardli :: A/Prof Anthony Henderson :: The University of Sydney

In undergraduate linear algebra, we teach the Jordan canonical form theorem: that every similarity class of n x n complex matrices contains a special matrix which is block-diagonal with each block having a very simple form (a single eigenvalue repeated down the diagonal, ones on the super-diagonal, and zeroes elsewhere). This is of course very useful for matrix calculations. After explaining some of the general context of this result, I will focus on a case which, despite its close proximity to the Jordan canonical form theorem, has only recently been worked out: the classification of pairs of a vector and a matrix.
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

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.
IGA Workshop: Dendroidal sets
14:00 Tue 12 Jun, 2012 :: Ingkarni Wardli B17 :: Dr Ittay Weiss :: University of the South Pacific

A series of four 2-hour lectures by Dr. Ittay Weiss. The theory of dendroidal sets was introduced by Moerdijk and Weiss in 2007 in the study of homotopy operads in algebraic topology. In the five years that have past since then several fundamental and highly non-trivial results were established. For instance, it was established that dendroidal sets provide models for homotopy operads in a way that extends the Joyal-Lurie approach to homotopy categories. It can be shown that dendroidal sets provide new models in the study of n-fold loop spaces. And it is very recently shown that dendroidal sets model all connective spectra in a way that extends the modeling of certain spectra by Picard groupoids. The aim of the lecture series will be to introduce the concepts mentioned above, present the elementary theory, and understand the scope of the results mentioned as well as discuss the potential for further applications. Sources for the course will include the article "From Operads to Dendroidal Sets" (in the AMS volume on mathematical foundations of quantum field theory (also on the arXiv)) and the lecture notes by Ieke Moerdijk "simplicial methods for operads and algebraic geometry" which resulted from an advanced course given in Barcelona 3 years ago. No prior knowledge of operads will be assumed nor any knowledge of homotopy theory that is more advanced then what is required for the definition of the fundamental group. The basics of the language of presheaf categories will be recalled quickly and used freely.
Notions of non-commutative metric spaces; why and how
15:10 Fri 15 Jun, 2012 :: B.21 Ingkarni Wardli :: Dr Ittay Weiss :: The University of the South Pacific

The classical notion of metric space includes the axiom of symmetry: d(x,y)=d(y,x). Some applications of metric techniques to problems in computer graphics, concurrency, and physics (to mention a few) are seriously stressing the limitations imposed by symmetry, resulting in various relaxations of it. I will review some of the motivating problems that seem to require non-symmetry and then review some of the suggested models to deal with the problem. My review will be critical to the topological implications (which are often unpleasant) of some of the models and I will present metric 1-spaces, a new notion of generalized metric spaces.
2012 AMSI-SSAI Lecture: Approximate Bayesian computation (ABC): advances and limitations
11:00 Fri 13 Jul, 2012 :: Engineering South S112 :: Prof Christian Robert :: Universite Paris-Dauphine

The lack of closed form likelihoods has been the bane of Bayesian computation for many years and, prior to the introduction of MCMC methods, a strong impediment to the propagation of the Bayesian paradigm. We are now facing models where an MCMC completion of the model towards closed-form likelihoods seems unachievable and where a further degree of approximation appears unavoidable. In this talk, I will present the motivation for approximative Bayesian computation (ABC) methods, the consistency results already available, the various Monte Carlo implementations found in the current literature, as well as the inferential, rather than computational, challenges set by these methods. A recent advance based on empirical likelihood will also be discussed.
Continuous random walk models for solute transport in porous media
15:10 Fri 17 Aug, 2012 :: B.21 Ingkarni Wardli :: Prof Pavel Bedrikovetski :: The University of Adelaide

The classical diffusion (thermal conductivity) equation was derived from the Master random walk equation and is parabolic. The main assumption was a probabilistic distribution of the jump length while the jump time is constant. Distribution of the jump time along with the jump length adds the second time derivative into the averaged equations, but the equation becomes ... elliptic! Where from to take an extra initial condition? We discuss how to pose the well-posed flow problem, exact 1d solution and numerous engineering applications. This is joint work with A. Shapiro and H. Yuan.
Krylov Subspace Methods or: How I Learned to Stop Worrying and Love GMRes
12:10 Mon 17 Sep, 2012 :: B.21 Ingkarni Wardli :: Mr David Wilke :: University of Adelaide

Many problems within applied mathematics require the solution of a linear system of equations. For instance, models of arterial umbilical blood flow are obtained through a finite element approximation, resulting in a linear, n x n system. For small systems the solution is (almost) trivial, but what happens when n is large? Say, n ~ 10^6? In this case matrix inversion is expensive (read: completely impractical) and we seek approximate solutions in a reasonable time. In this talk I will discuss the basic theory underlying Krylov subspace methods; a class of non-stationary iterative methods which are currently the methods-of-choice for large, sparse, linear systems. In particular I will focus on the method of Generalised Minimum RESiduals (GMRes), which is of the most popular for nonsymmetric systems. It is hoped that through this presentation I will convince you that a) solving linear systems is not necessarily trivial, and that b) my lack of any tangible results is not (entirely) a result of my own incompetence.
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.
Towards understanding fundamental interactions for nanotechnology
15:10 Fri 5 Oct, 2012 :: B.20 Ingkarni Wardli :: Dr Doreen Mollenhauer :: MacDiarmid Institute for Advanced Materials and Nanotechnology, Wellington

Multiple simultaneous interactions show unique collective properties that are qualitatively different from properties displayed by their monovalent constituents. Multivalent interactions play an important role for the self-organization of matter, recognition processes and signal transduction. A broad understanding of these interactions is therefore crucial in order to answer central questions and make new developments in the field of biotechnology and material science. In the framework of a joint experimental and theoretical project we study the electronic effects in monovalent and multivalent interactions by doing quantum chemical calculations. The particular interest of our investigations is in organic molecules interacting with gold nanoparticles or graphene. The main purpose is to analyze the nature of multivalent bonding in comparison to monovalent interaction.
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.
Epidemic models in socially structured populations: when are simple models too simple?
14:00 Thu 25 Oct, 2012 :: 5.56 Ingkarni Wardli :: Dr Lorenzo Pellis :: The University of Warwick

Both age and household structure are recognised as important heterogeneities affecting epidemic spread of infectious pathogens, and many models exist nowadays that include either or both forms of heterogeneity. However, different models may fit aggregate epidemic data equally well and nevertheless lead to different predictions of public health interest. I will here present an overview of stochastic epidemic models with increasing complexity in their social structure, focusing in particular on households models. For these models, I will present recent results about the definition and computation of the basic reproduction number R0 and its relationship with other threshold parameters. Finally, I will use these results to compare models with no, either or both age and household structure, with the aim of quantifying the conditions under which each form of heterogeneity is relevant and therefore providing some criteria that can be used to guide model design for real-time predictions.
Epidemic models in socially structured populations: when are simple models too simple?
14:00 Thu 25 Oct, 2012 :: 5.56 Ingkarni Wardli :: Dr Lorenzo Pellis :: The University of Warwick

Both age and household structure are recognised as important heterogeneities affecting epidemic spread of infectious pathogens, and many models exist nowadays that include either or both forms of heterogeneity. However, different models may fit aggregate epidemic data equally well and nevertheless lead to different predictions of public health interest. I will here present an overview of stochastic epidemic models with increasing complexity in their social structure, focusing in particular on households models. For these models, I will present recent results about the definition and computation of the basic reproduction number R0 and its relationship with other threshold parameters. Finally, I will use these results to compare models with no, either or both age and household structure, with the aim of quantifying the conditions under which each form of heterogeneity is relevant and therefore providing some criteria that can be used to guide model design for real-time predictions.
Spatiotemporally Autoregressive Partially Linear Models with Application to the Housing Price Indexes of the United States
12:10 Mon 12 Nov, 2012 :: B.21 Ingkarni Wardli :: Ms Dawlah Alsulami :: University of Adelaide

We propose a Spatiotemporal Autoregressive Partially Linear Regression ( STARPLR) model for data observed irregularly over space and regularly in time. The model is capable of catching possible non linearity and nonstationarity in space by coefficients to depend on locations. We suggest two-step procedure to estimate both the coefficients and the unknown function, which is readily implemented and can be computed even for large spatio-temoral data sets. As an illustration, we apply our model to analyze the 51 States' House Price Indexes (HPIs) in USA.
Modern trends in dynamo theory
15:10 Fri 16 Nov, 2012 :: B.20 Ingkarni Wardli :: Prof Michael Proctor :: University of Cambridge

Dynamo action is the process by which magnetic fields in astrophysical bodies (and recently, laboratory fluids) are maintained against resistive losses by Faraday induction. For many years a favoured model of this process, known as mean-field electrodynamics, has been widely used to produce tractable models. I shall present a critique of this theory and contrast it it with another dynamo process (small scale dynamo action) that does not, unlike mean-field electrodynamics, rely on broken reflection symmetry or scale separation. Finally, I shall talk about very recent rigorous results concerning the Archontis dynamo, in which the magnetic and velocity fields are closely aligned.
Hyperplane arrangements and tropicalization of linear spaces
10:10 Mon 17 Dec, 2012 :: Ingkarni Wardli B17 :: Dr Graham Denham :: University of Western Ontario

I will give an introduction to a sequence of ideas in tropical geometry, the tropicalization of linear spaces. In the beginning, a construction due to De Concini and Procesi (wonderful models, 1995) gave a combinatorially explicit description of various iterated blowups of projective spaces along (proper transforms of) linear subspaces. A decade later, Tevelev's notion of tropical compactifications led to, in particular, a new view of the wonderful models and their intersection theory in terms of the theory of toric varieties (via work of Feichtner-Sturmfels, Feichtner-Yuzvinsky, Ardila-Klivans, and others). Recently, these ideas have played a role in Huh and Katz's proof of a long-standing conjecture in combinatorics.
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

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.
M-theory and higher gauge theory
13:10 Fri 12 Apr, 2013 :: Ingkarni Wardli B20 :: Dr Christian Saemann :: Heriot-Watt University

I will review my recent work on integrability of M-brane configurations and the description of M-brane models in higher gauge theory. In particular, I will discuss categorified analogues of instantons and present superconformal equations of motion for the non-abelian tensor multiplet in six dimensions. The latter are derived from considering non-abelian gerbes on certain twistor spaces.
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

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.
Models of cell-extracellular matrix interactions in tissue engineering
15:10 Fri 3 May, 2013 :: B.18 Ingkarni Wardli :: Dr Ed Green :: University of Adelaide

Tissue engineers hope in future to be able to grow functional tissues in vitro to replace those that are damaged by injury, disease, or simple wear and tear. They use cell culture methods, such as seeding cells within collagen gels, that are designed to mimic the cells' environment in vivo. Amongst other factors, it is clear that mechanical interactions between cells and the extracellular matrix (ECM) in which they reside play an important role in tissue development. However, the mechanics of the ECM is complex, and at present, its role is only partly understood. In this talk, I will present mathematical models of some simple cell-ECM interaction problems, and show how they can be used to gain more insight into the processes that regulate tissue development.
Neuronal excitability and canards
15:10 Fri 10 May, 2013 :: B.18 Ingkarni Wardli :: A/Prof Martin Wechselberger :: University of Sydney

The notion of excitability was first introduced in an attempt to understand firing properties of neurons. It was Alan Hodgkin who identified three basic types (classes) of excitable axons (integrator, resonator and differentiator) distinguished by their different responses to injected steps of currents of various amplitudes. Pioneered by Rinzel and Ermentrout, bifurcation theory explains repetitive (tonic) firing patterns for adequate steady inputs in integrator (type I) and resonator (type II) neuronal models. In contrast, the dynamic behavior of differentiator (type III) neurons cannot be explained by standard dynamical systems theory. This third type of excitable neuron encodes a dynamic change in the input and leads naturally to a transient response of the neuron. In this talk, I will show that "canards" - peculiar mathematical creatures - are well suited to explain the nature of transient responses of neurons due to dynamic (smooth) inputs. I will apply this geometric theory to a simple driven FitzHugh-Nagumo/Morris-Lecar type neural model and to a more complicated neural model that describes paradoxical excitation due to propofol anesthesia.
Markov decision processes and interval Markov chains: what is the connection?
12:10 Mon 3 Jun, 2013 :: B.19 Ingkarni Wardli :: Mingmei Teo :: University of Adelaide

Markov decision processes are a way to model processes which involve some sort of decision making and interval Markov chains are a way to incorporate uncertainty in the transition probability matrix. How are these two concepts related? In this talk, I will give an overview of these concepts and discuss how they relate to each other.
Birational geometry of M_g
12:10 Fri 21 Jun, 2013 :: Ingkarni Wardli B19 :: Dr Jarod Alper :: Australian National University

In 1969, Deligne and Mumford introduced a beautiful compactification of the moduli space of smooth curves which has proved extremely influential in geometry, topology and physics. Using recent advances in higher dimensional geometry and the minimal model program, we study the birational geometry of M_g. In particular, in an effort to understand the canonical model of M_g, we study the log canonical models as well as the associated divisorial contractions and flips by interpreting these models as moduli spaces of particular singular curves.
The search for the exotic - subfactors and conformal field theory
13:10 Fri 26 Jul, 2013 :: Engineering-Maths 212 :: Prof David E. Evans :: Cardiff University

Subfactor theory provides a framework for studying modular invariant partition functions in conformal field theory, and candidates for exotic modular tensor categories. I will describe work with Terry Gannon on the search for exotic theories beyond those from symmetries based on loop groups, Wess-Zumino-Witten models and finite groups.
Fire-Atmosphere Models
12:10 Mon 29 Jul, 2013 :: B.19 Ingkarni Wardli :: Mika Peace :: University of Adelaide

Fire behaviour models are increasingly being used to assist in planning and operational decisions for bush fires and fuel reduction burns. Rate of spread (ROS) of the fire front is a key output of such models. The ROS value is typically calculated from a formula which has been derived from empirical data, using very simple meteorological inputs. We have used a coupled fire-atmosphere model to simulate real bushfire events. The results show that complex interactions between a fire and the atmosphere can have a significant influence on fire spread, thus highlighting the limitations of a model that uses simple meteorological inputs.
The Hamiltonian Cycle Problem and Markov Decision Processes
15:10 Fri 2 Aug, 2013 :: B.18 Ingkarni Wardli :: Prof Jerzy Filar :: Flinders University

We consider the famous Hamiltonian cycle problem (HCP) embedded in a Markov decision process (MDP). More specifically, we consider a moving object on a graph G where, at each vertex, a controller may select an arc emanating from that vertex according to a probabilistic decision rule. A stationary policy is simply a control where these decision rules are time invariant. Such a policy induces a Markov chain on the vertices of the graph. Therefore, HCP is equivalent to a search for a stationary policy that induces a 0-1 probability transition matrix whose non-zero entries trace out a Hamiltonian cycle in the graph. A consequence of this embedding is that we may consider the problem over a number of, alternative, convex - rather than discrete - domains. These include: (a) the space of stationary policies, (b) the more restricted but, very natural, space of doubly stochastic matrices induced by the graph, and (c) the associated spaces of so-called "occupational measures". This approach to the HCP has led to both theoretical and algorithmic approaches to the underlying HCP problem. In this presentation, we outline a selection of results generated by this line of research.
K-theory and solid state physics
12:10 Fri 13 Sep, 2013 :: Ingkarni Wardli B19 :: Dr Keith Hannabuss :: Balliol College, Oxford

More than 50 years ago Dyson showed that there is a nine-fold classification of random matrix models, the classes of which are each associated with Riemannian symmetric spaces. More recently it was realised that a related argument enables one to classify the insulating properties of fermionic systems (with the addition of an extra class to give 10 in all), and can be described using K-theory. In this talk I shall give a survey of the ideas, and a brief outline of work with Guo Chuan Thiang.
How the leopard got his spots
14:10 Mon 14 Oct, 2013 :: 7.15 Ingkarni Wardli :: Dr Ed Green :: School of Mathematical Sciences

Patterns are everywhere in nature, whether they be the spots and stripes on animals' coats, or the intricate arrangement of different cell types in a tissue. But how do these patterns arise? Whilst every cell contains a plan of the organism in its genes, the cells need to organise themselves so that each knows what it should do to achieve this plan. Mathematics can help biologists explore how different types of signals might be used to control the patterning process. In this talk, I will introduce two simple mathematical theories of biological pattern formation: Turing patterns where, surprisingly, the essential ingredient for producing the pattern is diffusion, which usually tends to make things more uniform; and the Keller-Segel model, which provides a simple mechanism for the formation of multicellular structures from isolated single cells. These mathematical models can be used to explain how tissues develop, and why there are many spotted animals with a stripy tail, but no stripy animals with a spotted tail.
Model Misspecification due to Site Specific Rate Heterogeneity: how is tree inference affected?
12:10 Mon 21 Oct, 2013 :: B.19 Ingkarni Wardli :: Stephen Crotty :: University of Adelaide

In this talk I'll answer none of the questions you ever had about phylogenetics, but hopefully some you didn't. I'll be giving this presentation at a phylogenetics conference in 3 weeks, so sorry it is a little light on background. You've been warned! Phlyogeneticists have long recognised that different sites in a DNA sequence can experience different rates of nucleotide substitution, and many models have been developed to accommodate this rate heterogeneity. But what happens when a single site exhibits rate heterogeneity along different branches of an evolutionary tree? In this talk I'll introduce the notion of Site Specific Rate Heterogeneity (SSRH) and investigate a simple case, looking at the impact of SSRH on inference via maximum parsimony, neighbour joining and maximum likelihood.
Developing Multiscale Methodologies for Computational Fluid Mechanics
12:10 Mon 11 Nov, 2013 :: B.19 Ingkarni Wardli :: Hammad Alotaibi :: University of Adelaide

Recently the development of multiscale methods is one of the most fertile research areas in mathematics, physics, engineering and computer science. The need for multiscale modeling comes usually from the fact that the available macroscale models are not accurate enough, and the microscale models are not efficient enough. By combining both viewpoints, one hopes to arrive at a reasonable compromise between accuracy and efficiency. In this seminar I will give an overview of the recent efforts on developing multiscale methods such as patch dynamics scheme which is used to address an important class of time dependent multiscale problems.
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.
A few flavours of optimal control of Markov chains
11:00 Thu 12 Dec, 2013 :: B18 :: Dr Sam Cohen :: Oxford University

In this talk we will outline a general view of optimal control of a continuous-time Markov chain, and how this naturally leads to the theory of Backward Stochastic Differential Equations. We will see how this class of equations gives a natural setting to study these problems, and how we can calculate numerical solutions in many settings. These will include problems with payoffs with memory, with random terminal times, with ergodic and infinite-horizon value functions, and with finite and infinitely many states. Examples will be drawn from finance, networks and electronic engineering.
Integrability of infinite-dimensional Lie algebras and Lie algebroids
12:10 Fri 7 Feb, 2014 :: Ingkarni Wardli B20 :: Christoph Wockel :: Hamburg University

Lie's Third Theorem states that each finite-dimensional Lie algebra is the Lie algebra of a Lie group (we also say "integrates to a Lie group"). The corresponding statement for infinite-dimensional Lie algebras or Lie algebroids is false and we will explain geometrically why this is the case. The underlying pattern is that of integration of central extensions of Lie algebras and Lie algebroids. This also occurs in other contexts, and we will explain some aspects of string group models in these terms. In the end we will sketch how the non-integrability of Lie algebras and Lie algebroids can be overcome by passing to higher categorical objects (such as smooth stacks) and give a panoramic (but still conjectural) perspective on the precise relation of the various integrability problems.
The effects of pre-existing immunity
15:10 Fri 7 Mar, 2014 :: B.18 Ingkarni Wardli :: Associate Professor Jane Heffernan :: York University, Canada

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.
Dynamical systems approach to fluid-plasma turbulence
15:10 Fri 14 Mar, 2014 :: 5.58 Ingkarni Wardli :: Professor Abraham Chian

Sun-Earth system is a complex, electrodynamically coupled system dominated by multiscale interactions. The complex behavior of the space environment is indicative of a state driven far from equilibrium whereby instabilities, nonlinear waves, and turbulence play key roles in the system dynamics. First, we review the fundamental concepts of nonlinear dynamics in fluids and plasmas and discuss their relevance to the study of the Sun-Earth relation. Next, we show how Lagrangian coherent structures identify the transport barriers of plasma turbulence modeled by 3-D solar convective dynamo. Finally, we show how Lagrangian coherent structures can be detected in the solar photospheric turbulence using satellite observations.
Ice floe collisions in the Marginal Ice Zone
12:10 Mon 12 May, 2014 :: B.19 Ingkarni Wardli :: Lucas Yiew :: University of Adelaide

In an era of climate change, it is becoming increasingly important to model the dynamics of sea-ice cover in the polar regions. The Marginal Ice Zone represents a vast region of ice cover strongly influenced by the effects of ocean waves. As ocean waves penetrate this region, wave energy is progressively dispersed through energy dissipative mechanisms such as collisions between ice floes (discrete chunks of ice). In this talk I will discuss the mathematical models required to build a collision model, and the validation of these models with experimental results.
Stochastic models of evolution: Trees and beyond
15:10 Fri 16 May, 2014 :: B.18 Ingkarni Wardli :: Dr Barbara Holland :: The University of Tasmania

In the first part of the talk I will give a general introduction to phylogenetics, and discuss some of the mathematical and statistical issues that arise in trying to infer evolutionary trees. In particular, I will discuss how we model the evolution of DNA along a phylogenetic tree using a continuous time Markov process. In the second part of the talk I will discuss how to express the two-state continuous-time Markov model on phylogenetic trees in such a way that allows its extension to more general models. In this framework we can model convergence of species as well as divergence (speciation). I will discuss the identifiability (or otherwise) of the models that arise in some simple cases. Use of a statistical framework means that we can use established techniques such as the AIC or likelihood ratio tests to decide if datasets show evidence of convergent evolution.
Computing with groups
15:10 Fri 30 May, 2014 :: B.21 Ingkarni Wardli :: Dr Heiko Dietrich :: Monash University

Groups are algebraic structures which show up in many branches of mathematics and other areas of science; Computational Group Theory is on the cutting edge of pure research in group theory and its interplay with computational methods. In this talk, we consider a practical aspect of Computational Group Theory: how to represent a group in a computer, and how to work with such a description efficiently. We will first recall some well-established methods for permutation group; we will then discuss some recent progress for matrix groups.
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

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

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.
Spectral asymptotics on random Sierpinski gaskets
12:10 Fri 26 Sep, 2014 :: Ingkarni Wardli B20 :: Uta Freiberg :: Universitaet Stuttgart

Self similar fractals are often used in modeling porous media. Hence, defining a Laplacian and a Brownian motion on such sets describes transport through such materials. However, the assumption of strict self similarity could be too restricting. So, we present several models of random fractals which could be used instead. After recalling the classical approaches of random homogenous and recursive random fractals, we show how to interpolate between these two model classes with the help of so called V-variable fractals. This concept (developed by Barnsley, Hutchinson & Stenflo) allows the definition of new families of random fractals, hereby the parameter V describes the degree of `variability' of the realizations. We discuss how the degree of variability influences the geometric, analytic and stochastic properties of these sets. - These results have been obtained with Ben Hambly (University of Oxford) and John Hutchinson (ANU Canberra).
Optimally Chosen Quadratic Forms for Partitioning Multivariate Data
13:10 Tue 14 Oct, 2014 :: Ingkarni Wardli 715 Conference Room :: Assoc. Prof. Inge Koch :: School of Mathematical Sciences

Quadratic forms are commonly used in linear algebra. For d-dimensional vectors they have a matrix representation, Q(x) = x'Ax, for some symmetric matrix A. In statistics quadratic forms are defined for d-dimensional random vectors, and one of the best-known quadratic forms is the Mahalanobis distance of two random vectors. In this talk we want to partition a quadratic form Q(X) = X'MX, where X is a random vector, and M a symmetric matrix, that is, we want to find a d-dimensional random vector W such that Q(X) = W'W. This problem has many solutions. We are interested in a solution or partition W of X such that pairs of corresponding variables (X_j, W_j) are highly correlated and such that W is simpler than the given X. We will consider some natural candidates for W which turn out to be suboptimal in the sense of the above constraints, and we will then exhibit the optimal solution. Solutions of this type are useful in the well-known T-square statistic. We will see in examples what these solutions look like.
Geometric singular perturbation theory and canard theory to study travelling waves in: 1) a model for tumor invasion; and 2) a model for wound healing angiogenesis.
15:10 Fri 17 Oct, 2014 :: EM 218 Engineering & Mathematics Building :: Dr Petrus (Peter) van Heijster :: QUT

In this talk, I will present results on the existence of smooth and shock-like travelling wave solutions for two advection-reaction-diffusion models. The first model describes malignant tumour (i.e. skin cancer) invasion, while the second one is a model for wound healing angiogenesis. Numerical solutions indicate that both smooth and shock-fronted travelling wave solutions exist for these two models. I will verify the existence of both type of these solutions using techniques from geometric singular perturbation theory and canard theory. Moreover, I will provide numerical results on the stability of the waves and the actual observed wave speeds. This is joint work with K. Harley, G. Pettet, R. Marangell and M. Wechselberger.
Topology Tomography with Spatial Dependencies
15:00 Tue 25 Nov, 2014 :: Engineering North N132 :: Darryl Veitch :: The University of Melbourne

There has been quite a lot of tomography inference work on measurement networks with a tree topology. Here observations are made, at the leaves of the tree, of `probes' sent down from the root and copied at each branch point. Inference can be performed based on loss or delay information carried by probes, and used in order to recover loss parameters, delay parameters, or the topology, of the tree. In all of these a strong assumption of spatial independence between links in the tree has been made in prior work. I will describe recent work on topology inference, based on loss measurement, which breaks that assumption. In particular I will introduce a new model class for loss with non trivial spatial dependence, the `Jump Independent Models', which are well motivated, and prove that within this class the topology is identifiable.
Predicting pressure drops in pipelines due to pump trip events
12:10 Mon 2 Mar, 2015 :: Napier LG29 :: David Arnold :: University of Adelaide

Sunwater is a Queensland company that designs, builds and manages large-scale water infrastructure such as dams, weirs and pipelines. In this talk, I will discuss one of the aspects that is crucial in the design stage of long pipelines, the pipelines ability to withstand large pressure disturbances caused by pump trip events. A pump trip is a sudden, unplanned shutdown of a pump, which causes potentially destructive pressure waves to propagate through the pipe network. Accurate simulation of such events is time consuming and costly, so rules of thumb and intuition are used during initial planning and design of a pipeline project. I will discuss some simple mathematical models for pump trip events, show some results, and discuss how they could be used in the initial design process.
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, ( 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.
IGA Workshop on Symmetries and Spinors: Interactions Between Geometry and Physics
09:30 Mon 13 Apr, 2015 :: Conference Room 7.15 on Level 7 of the Ingkarni Wardli building :: J. Figueroa-O'Farrill (University of Edinburgh), M. Zabzine (Uppsala University), et al

The interplay between physics and geometry has lead to stunning advances and enriched the internal structure of each field. This is vividly exemplified in the theory of supergravity, which is a supersymmetric extension of Einstein's relativity theory to the small scales governed by the laws of quantum physics. Sophisticated mathematics is being employed for finding solutions to the generalised Einstein equations and in return, they provide a rich source for new exotic geometries. This workshop brings together world-leading scientists from both, geometry and mathematical physics, as well as young researchers and students, to meet and learn about each others work.
A Model to Represent the Propagation of a Wave Over a Bovine Oocyte
12:10 Mon 20 Apr, 2015 :: Napier LG29 :: Amelia Thomas :: University of Adelaide

When the fertilization of egg cells is studied experimentally, generally the cumulus cells surrounding the egg are removed, for easier visualization of the egg itself. However, interesting phenomena are observed in the cumulus cells if they are left intact. In this talk I will present some models that can be used to describe the travelling wavelike movement of the cumulus cells away from the egg cell which occurs post-fertilisation.
A Collision Algorithm for Sea Ice
12:10 Mon 4 May, 2015 :: Napier LG29 :: Lucas Yiew :: University of Adelaide

The wave-induced collisions between sea ice are highly complex and nonlinear, and involves a multitude of subprocesses. Several collision models do exist, however, to date, none of these models have been successfully integrated into sea-ice forecasting models. A key component of a collision model is the development of an appropriate collision algorithm. In this seminar I will present a time-stepping, event-driven algorithm to detect, analyse and implement the pre- and post-collision processes.
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


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.

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


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.

Mathematical Modeling and Analysis of Active Suspensions
14:10 Mon 3 Aug, 2015 :: Napier 209 :: Professor Michael Shelley :: Courant Institute of Mathematical Sciences, New York University

Complex fluids that have a 'bio-active' microstructure, like suspensions of swimming bacteria or assemblies of immersed biopolymers and motor-proteins, are important examples of so-called active matter. These internally driven fluids can have strange mechanical properties, and show persistent activity-driven flows and self-organization. I will show how first-principles PDE models are derived through reciprocal coupling of the 'active stresses' generated by collective microscopic activity to the fluid's macroscopic flows. These PDEs have an interesting analytic structures and dynamics that agree qualitatively with experimental observations: they predict the transitions to flow instability and persistent mixing observed in bacterial suspensions, and for microtubule assemblies show the generation, propagation, and annihilation of disclination defects. I'll discuss how these models might be used to study yet more complex biophysical systems.
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.
Non-crossing quantiles
15:10 Fri 14 Aug, 2015 :: Ingkarni Wardli B21 :: Dr Yanan Fan :: UNSW

Quantile regression has received increased attention in the statistics community in recent years. However, since the quantile regression curves are estimated separately, the curves can cross, leading to invalid response distribution. Many authors have proposed remedies for this in the context of frequentist estimation. In this talk, I will explain some of the existing approaches, and then describe a new Bayesian semi-parametric approach for fitting non-crossing quantile regression models simultaneously.
Queues and cooperative games
15:00 Fri 18 Sep, 2015 :: Ingkarni Wardli B21 :: Moshe Haviv :: Department of Statistics and the Federmann Center for the Study of Rationality, The Hebrew Universit

The area of cooperative game theory deals with models in which a number of individuals, called players, can form coalitions so as to improve the utility of its members. In many cases, the formation of the grand coalition is a natural result of some negotiation or a bargaining procedure. The main question then is how the players should split the gains due to their cooperation among themselves. Various solutions have been suggested among them the Shapley value, the nucleolus and the core.

Servers in a queueing system can also join forces. For example, they can exchange service capacity among themselves or serve customers who originally seek service at their peers. The overall performance improves and the question is how they should split the gains, or, equivalently, how much each one of them needs to pay or be paid in order to cooperate with the others. Our major focus is in the core of the resulting cooperative game and in showing that in many queueing games the core is not empty.

Finally, customers who are served by the same server can also be looked at as players who form a grand coalition, now inflicting damage on each other in the form of additional waiting time. We show how cooperative game theory, specifically the Aumann-Shapley prices, leads to a way in which this damage can be attributed to individual customers or groups of customers.
Modelling Directionality in Stationary Geophysical Time Series
12:10 Mon 12 Oct, 2015 :: Benham Labs G10 :: Mohd Mahayaudin Mansor :: University of Adelaide

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.
Chern-Simons classes on loop spaces and diffeomorphism groups
12:10 Fri 16 Oct, 2015 :: Ingkarni Wardli B17 :: Steve Rosenberg :: Boston University

Not much is known about the topology of the diffeomorphism group Diff(M) of manifolds M of dimension four and higher. We'll show that for a class of manifolds of dimension 4k+1, Diff(M) has infinite fundamental group. This is proved by translating the problem into a question about Chern-Simons classes on the tangent bundle to the loop space LM. To build the CS classes, we use a family of metrics on LM associated to a Riemannian metric on M. The curvature of these metrics takes values in an algebra of pseudodifferential operators. The main technical step in the CS construction is to replace the ordinary matrix trace in finite dimensions with the Wodzicki residue, the unique trace on this algebra. The moral is that some techniques in finite dimensional Riemannian geometry can be extended to some examples in infinite dimensional geometry.
Ocean dynamics of Gulf St Vincent: a numerical study
12:10 Mon 2 Nov, 2015 :: Benham Labs G10 :: Henry Ellis :: University of Adelaide

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

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.
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

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.
Chaos in dimensions 2 and 3
15:10 Fri 18 Mar, 2016 :: Engineering South S112 :: Dr Andy Hammerlindl :: Monash University

I will talk about known models of chaotic dynamical systems in dimensions two and three, and results which classify the types of chaotic dynamics that are robust under perturbation. I will also talk about my own work towards understanding chaotic dynamics for discrete-time systems in dimension three. This is joint work with C. Bonatti, A. Gogolev, and R. Potrie.
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

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.
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.
Multi-scale modeling in biofluids and particle aggregation
15:10 Fri 17 Jun, 2016 :: B17 Ingkarni Wardli :: Dr Sarthok Sircar :: University of Adelaide

In today's seminar I will give 2 examples in mathematical biology which describes the multi-scale organization at 2 levels: the meso/micro level and the continuum/macro level. I will then detail suitable tools in statistical mechanics to link these different scales. The first problem arises in mathematical physiology: swelling-de-swelling mechanism of mucus, an ionic gel. Mucus is packaged inside cells at high concentration (volume fraction) and when released into the extracellular environment, it expands in volume by two orders of magnitude in a matter of seconds. This rapid expansion is due to the rapid exchange of calcium and sodium that changes the cross-linked structure of the mucus polymers, thereby causing it to swell. Modeling this problem involves a two-phase, polymer/solvent mixture theory (in the continuum level description), together with the chemistry of the polymer, its nearest neighbor interaction and its binding with the dissolved ionic species (in the micro-scale description). The problem is posed as a free-boundary problem, with the boundary conditions derived from a combination of variational principle and perturbation analysis. The dynamics of neutral gels and the equilibrium-states of the ionic gels are analyzed. In the second example, we numerically study the adhesion fragmentation dynamics of rigid, round particles clusters subject to a homogeneous shear flow. In the macro level we describe the dynamics of the number density of these cluster. The description in the micro-scale includes (a) binding/unbinding of the bonds attached on the particle surface, (b) bond torsion, (c) surface potential due to ionic medium, and (d) flow hydrodynamics due to shear flow.
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

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.
Predicting turbulence
14:10 Tue 30 Aug, 2016 :: Napier 209 :: Dr Trent Mattner :: School of Mathematical Sciences

Turbulence is characterised by three-dimensional unsteady fluid motion over a wide range of spatial and temporal scales. It is important in many problems of technological and scientific interest, such as drag reduction, energy production and climate prediction. Turbulent flows are governed by the Navier--Stokes equations, which are a nonlinear system of partial differential equations. Typically, numerical methods are needed to find solutions to these equations. In turbulent flows, however, the resulting computational problem is usually intractable. Filtering or averaging the Navier--Stokes equations mitigates the computational problem, but introduces new quantities into the equations. Mathematical models of turbulence are needed to estimate these quantities. One promising turbulence model consists of a random collection of fluid vortices, which are themselves approximate solutions of the Navier--Stokes equations.
The mystery of colony collapse: Mathematics and honey bee loss
15:10 Fri 16 Sep, 2016 :: Napier G03 :: Prof Mary Myerscough :: University of Sydney

Honey bees are vital to the production of many foods which need to be pollinated by insects. Yet in many parts of the world honey bee colonies are in decline. A crucial contributor to hive well-being is the health, productivity and longevity of its foragers. When forager numbers are depleted due to stressors in the colony (such as disease or malnutrition) or in the environment (such as pesticides) there is a significant effect, not only on the amount of food (nectar and pollen) that can be collected but also on the colony's capacity to raise brood (eggs, larvae and pupae) to produce new adult bees to replace lost or aged bees. We use a set of differential equation models to explore the effect on the hive of high forager death rates. In particular we examine what happens when bees become foragers at a comparatively young age and how this can lead to a sudden rapid decline of adult bees and the death of the colony.
SIR epidemics with stages of infection
12:10 Wed 28 Sep, 2016 :: EM218 :: Matthieu Simon :: Universite Libre de Bruxelles

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.
Symmetric functions and quantum integrability
15:10 Fri 30 Sep, 2016 :: Napier G03 :: Dr Paul Zinn-Justin :: University of Melbourne/Universite Pierre et Marie Curie

We'll discuss an approach to studying families of symmetric polynomials which is based on ''quantum integrability'', that is, on the use of exactly solvable two-dimensional lattice models. We'll first explain the general strategy on the simplest case, namely Schur polynomials, with the introduction of a model of lattice paths (a.k.a. five-vertex model). We'll then discuss recent work (in collaboration with M. Wheeler) that extends this approach to Hall--Littlewood polynomials and Grothendieck polynomials, and some applications of it.
On the Willmore energy
15:10 Fri 7 Oct, 2016 :: Napier G03 :: Dr Yann Bernard :: Monash University

The Willmore energy of a surface captures its bending. Originally discovered 200 years ago by Sophie Germain in the context of elasticity theory, it has since then been rediscovered numerous times in several areas of science: general relativity, optics, string theory, conformal geometry, and cell biology. For example, our red blood cells assume a peculiar shape that minimises the Willmore energy. In this talk, I will present the thrilling history of the Willmore energy, its applications, and its main properties. The presentation will be accessible to all mathematicians as well as to advanced undergraduate students.
Collective and aneural foraging in biological systems
15:10 Fri 3 Mar, 2017 :: Lower Napier LG14 :: Dr Jerome Buhl and Dr David Vogel :: The University of Adelaide

The field of collective behaviour uses concepts originally adapted from statistical physics to study how complex collective phenomena such as mass movement or swarm intelligence emerge from relatively simple interactions between individuals. Here we will focus on two applications of this framework. First we will have look at new insights into the evolution of sociality brought by combining models of nutrition and social interactions to explore phenomena such as collective foraging decisions, emergence of social organisation and social immunity. Second, we will look at the networks built by slime molds under exploration and foraging context.
Fast approximate inference for arbitrarily large statistical models via message passing
15:10 Fri 17 Mar, 2017 :: Engineering South S111 :: Prof Matt Wand :: University of Technology Sydney

We explain how the notion of message passing can be used to streamline the algebra and computer coding for fast approximate inference in large Bayesian statistical models. In particular, this approach is amenable to handling arbitrarily large models of particular types once a set of primitive operations is established. The approach is founded upon a message passing formulation of mean field variational Bayes that utilizes factor graph representations of statistical models. The notion of factor graph fragments is introduced and is shown to facilitate compartmentalization of the required algebra and coding.
Poisson-Lie T-duality and integrability
11:10 Thu 13 Apr, 2017 :: Engineering & Math EM213 :: Ctirad Klimcik :: Aix-Marseille University, Marseille

The Poisson-Lie T-duality relates sigma-models with target spaces symmetric with respect to mutually dual Poisson-Lie groups. In the special case if the Poisson-Lie symmetry reduces to the standard non-Abelian symmetry one of the corresponding mutually dual sigma-models is the standard principal chiral model which is known to enjoy the property of integrability. A natural question whether this non-Abelian integrability can be lifted to integrability of sigma model dualizable with respect to the general Poisson-Lie symmetry has been answered in the affirmative by myself in 2008. The corresponding Poisson-Lie symmetric and integrable model is a one-parameter deformation of the principal chiral model and features a remarkable explicit appearance of the standard Yang-Baxter operator in the target space geometry. Several distinct integrable deformations of the Yang-Baxter sigma model have been then subsequently uncovered which turn out to be related by the Poisson-Lie T-duality to the so called lambda-deformed sigma models. My talk gives a review of these developments some of which found applications in string theory in the framework of the AdS/CFT correspondence.
Serotonin Movement Through the Human Colonic Mucosa
15:10 Fri 19 May, 2017 :: Ingkarni Wardli 5.57 :: Helen Dockrell :: Flinders University / Flinders Medical Centre

The control of gut motility remains poorly defined and this makes it difficult to treat disorders associated with dysmotility in patient populations. Intestinal serotonin can elicit and modulate colonic motor patterns and is released in response to a variety of stimuli including nutrient ingestion and pressure change. I will describe a computational model of intestinal tissue and the predicted movement of serotonin through this tissue by advection and diffusion following pressure-dependent release. I have developed this model as a PhD candidate under the supervision of Associate Professor Phil Dinning, Professor Damien Keating and Dr Lukasz Wilendt.
Stokes' Phenomenon in Translating Bubbles
15:10 Fri 2 Jun, 2017 :: Ingkarni Wardli 5.57 :: Dr Chris Lustri :: Macquarie University

This study of translating air bubbles in a Hele-Shaw cell containing viscous fluid reveals the critical role played by surface tension in these systems. The standard zero-surface-tension model of Hele-Shaw flow predicts that a continuum of bubble solutions exists for arbitrary flow translation velocity. The inclusion of small surface tension, however, eliminates this continuum of solutions, instead producing a discrete, countably infinite family of solutions, each with distinct translation speeds. We are interested in determining this discrete family of solutions, and understanding why only these solutions are permitted. Studying this problem in the asymptotic limit of small surface tension does not seem to give any particular reason why only these solutions should be selected. It is only by using exponential asymptotic methods to study the Stokes’ structure hidden in the problem that we are able to obtain a complete picture of the bubble behaviour, and hence understand the selection mechanism that only permits certain solutions to exist. In the first half of my talk, I will explain the powerful ideas that underpin exponential asymptotic techniques, such as analytic continuation and optimal truncation. I will show how they are able to capture behaviour known as Stokes' Phenomenon, which is typically invisible to classical asymptotic series methods. In the second half of the talk, I will introduce the problem of a translating air bubble in a Hele-Shaw cell, and show that the behaviour can be fully understood by examining the Stokes' structure concealed within the problem. Finally, I will briefly showcase other important physical applications of exponential asymptotic methods, including submarine waves and particle chains.
Aggregation patterns from local and non-local interactions
15:10 Fri 30 Jun, 2017 :: Ingkarni Wardli 5.57 :: Dr Emily Hackett-Jones :: Centre for Cancer Biology, University of South Australia

Biological aggregations are ubiquitous in nature and may arise from a number of different mechanisms - both local and non-local. I will discuss two such mechanisms with particular application to the enteric nervous system; the nervous system in the gut responsible for peristalsis. Aggregates of neurons with a particular form are necessary for normal gut development. Our work suggests possible explanations for observations in normal and abnormal gut development.
In space there is no-one to hear you scream
12:10 Tue 12 Sep, 2017 :: Inkgarni Wardli 5.57 :: A/Prof Gary Glonek :: School of Mathematical Sciences

Modern data problems often involve data in very high dimensions. For example, gene expression profiles, used to develop cancer screening models, typically have at least 30,000 dimensions. When dealing with such data, it is natural to apply intuition from low dimensional cases. For example, in a sample of normal observations, a typical data point will be near the centre of the distribution with only a small number of points at the edges. In this talk, simple probability theory will be used to show that the geometry of data in high dimensional space is very different from what we can see in one and two-dimensional examples. We will show that the typical data point is at the edge of the distribution, a long way from its centre and even further from any other points.
Understanding burn injuries and first aid treatment using simple mathematical models
15:10 Fri 13 Oct, 2017 :: Ingkarni Wardli B17 :: Prof Mat Simpson :: Queensland University of Technology

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

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.
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.
Quantifying language change
15:10 Fri 1 Jun, 2018 :: Horace Lamb 1022 :: A/Prof Eduardo Altmann :: University of Sydney

Mathematical methods to study natural language are increasingly important because of the ubiquity of textual data in the Internet. In this talk I will discuss mathematical models and statistical methods to quantify the variability of language, with focus on two problems: (i) How the vocabulary of languages changed over the last centuries? (ii) How the language of scientific disciplines relate to each other and evolved in the last decades? One of the main challenges of these analyses stem from universal properties of word frequencies, which show high temporal variability and are fat-tailed distributed. The later feature dramatically affects the statistical properties of entropy-based estimators, which motivates us to compare vocabularies using a generalized Jenson-Shannon divergence (obtained from entropies of order alpha).
Quantifying language change
15:10 Fri 1 Jun, 2018 :: Napier 208 :: A/Prof Eduardo Altmann :: University of Sydney

Mathematical methods to study natural language are increasingly important because of the ubiquity of textual data in the Internet. In this talk I will discuss mathematical models and statistical methods to quantify the variability of language, with focus on two problems: (i) How the vocabulary of languages changed over the last centuries? (ii) How the language of scientific disciplines relate to each other and evolved in the last decades? One of the main challenges of these analyses stem from universal properties of word frequencies, which show high temporal variability and are fat-tailed distributed. The later feature dramatically affects the statistical properties of entropy-based estimators, which motivates us to compare vocabularies using a generalized Jenson-Shannon divergence (obtained from entropies of order alpha).
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.
Exceptional quantum symmetries
11:10 Fri 5 Oct, 2018 :: Barr Smith South Polygon Lecture theatre :: Scott Morrison :: Australian National University

I will survey our current understanding of "quantum symmetries", the mathematical models of topological order, in particular through the formalism of fusion categories. Our very limited classification results to date point to nearly all examples being built out of data coming from finite groups, quantum groups at roots of unity, and cohomological data. However, there are a small number of "exceptional" quantum symmetries that so far appear to be disconnected from the world of classical symmetries as studied in representation theory and group theory. I'll give an update on recent progress understanding these examples.
Interactive theorem proving for mathematicians
15:10 Fri 5 Oct, 2018 :: Napier 208 :: A/Prof Scott Morrison :: Australian National University

Mathematicians use computers to write their proofs (LaTeX), and to do their calculations (Sage, Mathematica, Maple, Matlab, etc, as well as custom code for simulations or searches). However today we rarely use computers to help us to construct and understand proofs. There is a long tradition in computer science of interactive and automatic theorem proving; particularly today these are important tools in engineering correct software, as well as in optimisation and compilation. There have been some notable examples of formalisation of modern mathematics (e.g. the odd order theorem, the Kepler conjecture, and the four-colour theorem). Even in these cases, huge engineering efforts were required to translate the mathematics to a form a computer could understand. Moreover, in most areas of research there is a huge gap between the interests of human mathematicians and the abilities of computer provers. Nevertheless, I think it's time for mathematicians to start getting interested in interactive theorem provers! It's now possible to write proofs, and write tools that help write proofs, in languages which are expressive enough to encompass most of modern mathematics, and ergonomic enough to use for general purpose programming. I'll give an informal introduction to dependent type theory (the logical foundation of many modern theorem provers), some examples of doing mathematics in such a system, and my experiences working with mathematics students in these systems.
Random walks
15:10 Fri 12 Oct, 2018 :: Napier 208 :: A/Prof Kais Hamza :: Monash University

A random walk is arguably the most basic stochastic process one can define. It is also among the most intuitive objects in the theory of probability and stochastic processes. For these and other reasons, it is one of the most studied processes or rather family of processes, finding applications in all areas of science, technology and engineering. In this talk, I will start by recalling some of the classical results for random walks and then discuss some of my own recent explorations in this area of research that has maintained relevance for decades.
Bayesian Synthetic Likelihood
15:10 Fri 26 Oct, 2018 :: Napier 208 :: A/Prof Chris Drovandi :: Queensland University of Technology

Complex stochastic processes are of interest in many applied disciplines. However, the likelihood function associated with such models is often computationally intractable, prohibiting standard statistical inference frameworks for estimating model parameters based on data. Currently, the most popular simulation-based parameter estimation method is approximate Bayesian computation (ABC). Despite the widespread applicability and success of ABC, it has some limitations. This talk will describe an alternative approach, called Bayesian synthetic likelihood (BSL), which overcomes some limitations of ABC and can be much more effective in certain classes of applications. The talk will also describe various extensions to the standard BSL approach. This project has been a joint effort with several academic collaborators, post-docs and PhD students.
Some advances in the formulation of analytical methods for linear and nonlinear dynamics
15:10 Tue 20 Nov, 2018 :: EMG07 :: Dr Vladislav Sorokin :: University of Auckland

In the modern engineering, it is often necessary to solve problems involving strong parametric excitation and (or) strong nonlinearity. Dynamics of micro- and nanoscale electro-mechanical systems, wave propagation in structures made of corrugated composite materials are just examples of those. Numerical methods, although able to predict systems behavior for specific sets of parameters, fail to provide an insight into underlying physics. On the other hand, conventional analytical methods impose severe restrictions on the problem parameters space and (or) on types of the solutions. Thus, the quest for advanced tools to deal with linear and nonlinear structural dynamics still continues, and the lecture is concerned with an advanced formulation of an analytical method. The principal novelty aspect is that the presence of a small parameter in governing equations is not requested, so that dynamic problems involving strong parametric excitation and (or) strong nonlinearity can be considered. Another advantage of the method is that it is free from conventional restrictions on the excitation frequency spectrum and applicable for problems involving combined multiple parametric and (or) direct excitations with incommensurate frequencies, essential for some applications. A use of the method will be illustrated in several examples, including analysis of the effects of corrugation shapes on dispersion relation and frequency band-gaps of structures and dynamics of nonlinear parametric amplifiers.
The role of microenvironment in regulation of cell infiltration and bortezomib-OV therapy in glioblastoma
15:10 Fri 11 Jan, 2019 :: IW 5.57 :: Professor Yangjin Kim :: Konkuk University, South Korea

Tumor microenvironment (TME) plays a critical role in regulation of tumor cell invasion in glioblastoma. Many microenvironmental factors such as extracllular matrix, microglia and astrocytes can either block or enhance this critical infiltration step in brain [4]. Oncolytic viruses such as herpes simplex virus-1 (oHSV) are genetically modified to target and kill cancer cells while not harming healthy normal cells and are currently under multiple clinical trials for safety and efficacy [1]. Bortezomib is a peptide-based proteasome inhibitor and is an FDA-approved drug for myeloma and mantle cell lymphoma. Yoo et al (2) have previously demonstrated that bortezomibinduced unfolded protein response (UPR) in many tumor cell lines (glioma, ovarian, and head and neck) up-regulated expression of heat shock protein 90 (HSP90), which then enhanced viral replication through promotion of nuclear localization of the viral polymerase in vitro. This led to synergistic tumor cell killing in vitro, and a combination treatment of mice with oHSV and bortezomib showed improved anti-tumor efficacy in vivo [2]. This combination therapy also increased the surface expression levels of NK cell activating markers and enhanced pro-inflammatory cytokine secretion. These findings demonstrated that the synergistic interaction between oHSV and bortezomib, a clinically relevant proteasome inhibitor, augments the cancer cell killing and promotes overall therapeutic efficacy. We investigated the role of NK cells in combination therapy with oncolytic virus (OV) and bortezomib. NK cells display rapid and potent immunity to metastasis and hematological cancers, and they overcome immunosuppressive effects of tumor microenvironment. We developed a mathematical model, a system of PDEs, in order to address the question of how the density of NK cells affects the growth of the tumor [3]. We found that the anti-tumor efficacy increases when the endogenous NKs are depleted, and also when exogenous NK cells are injected into the tumor. We also show that the TME plays a significant role in anti-tumor efficacy in OV combination therapy, and illustrate the effect of different spatial patterns of OV injection [5]. The results illustrate a possible phenotypic switch within tumor populations in a given microenvironment, and suggest new anti-invasion therapies. These predictions were validated by our in vivo and in vitro experiments. References 1]  Kanai R, … Rabkin SD, “Oncolytic herpes simplex virus vectors and chemotherapy: are combinatorial strategies more effective for cancer?”, Future Oncology, 6(4), 619–634, 2010. 
 [2]  Yoo J, et al., “Bortezomib-induced unfolded protein response increases oncolytic hsv-1 replication resulting in synergistic antitumor effect”, Clin Cancer Res , Vol. 20(14), 2014, pp. 3787-3798. 
 [3]  Yangjin Kim,..Balveen Kaur and Avner Friedman, “Complex role of NK cells in regulation of oncolytic virus-bortezomib therapy”, PNAS, 115 (19), pp. 4927-4932, 2018. 
 [4] Yangjin Kim, ..Sean Lawler, and Mark Chaplain, “Role of extracellular matrix and microenvironment in regulation of tumor growth and LAR-mediated invasion in glioblastoma”, PLoS One, 13(10):e0204865, 2018. 
 [5] Yangjin Kim, …, Hans G. Othmer, “Synergistic effects of bortezomib-OV therapy and anti-invasive
strategies in glioblastoma: A mathematical model”, Special issue, submitted, 2018.

News matching "Models of cell-extracellular matrix interactions i"

Mathematics Building to be demolished
The existing mathematics building will be demolished to make way for a new 8-storey, 6-star building. The new building, which is expected to be completed for the start of semester 1, 2010, will house the Schools of Electrical and Electronic Engineering, Computer Science and Mathematical Sciences. The demolition will begin on 10th December 2007. See the Building Life Impact web-site for more details. Posted Mon 12 Nov 07.
Recent PhD's
At the December graduation ceremony Mr Raymond Kennington was awarded the degree of Doctor of Philosophy for his thesis entitled "Random allocations: new and extended models and techniques with applications and numerics". Congratulations to Ray and his supervisor, Professor Charles Pearce. Posted Wed 2 Jan 08.
ARC Grant successes
Congratulations to Tony Roberts, Charles Pearce, Robert Elliot, Andrew Metcalfe and all their collaborators on their success in the current round of ARC grants. The projects are "Development of innovative technologies for oil production based on the advanced theory of suspension flows in porous media" (Tony Roberts et al.), "Perturbation and approximation methods for linear operators with applications to train control, water resource management and evolution of physical systems" (Charles Pearce et al.), "Risk Measures and Management in Finance and Actuarial Science Under Regime-Switching Models" (Robert Elliott et al.) and "A new flood design methodology for a variable and changing climate" (Andrew Metcalfe et al.) Posted Mon 26 Oct 09.
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.
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.
AMSI-ANZIAM Lecture Tour - Public Lecture

AMSI-ANZIAM Lecture Tour, Public Lecture

The Role of Embedded Optimisation in Smart Systems and Products
September 23, 6:00pm Horace Lamb Lecture Theatre

Professor Stephen Boyd, Stanford University, Samsung Professor of Engineering, Professor of Electrical Engineering

Further details here

Posted Mon 23 Sep 13.

Publications matching "Models of cell-extracellular matrix interactions i"

Adaptively varying-coefficient spatiotemporal models
Lu, Zudi; Steinskog, D; Tjostheim, D; Yao, Q, Journal of the Royal Statistical Society Series B-Statistical Methodology 71 (859–880) 2009
Hitting probabilities and hitting times for stochastic fluid flows the bounded model
Bean, Nigel; O'Reilly, Malgorzata; Taylor, P, Probability in the Engineering and Informational Sciences 23 (121–147) 2009
On some contact problems for inhomogeneous anisotropic elastic materials
Clements, David; Ang, W, International Journal of Engineering Science In Press (–) 2009
On the beneficial impact of strong correlations for anomaly detection
Roughan, Matthew, Stochastic Models (1–27) 2009
The decay of suddenly blocked flow in a curved pipe
Clarke, Robert; Denier, James, Journal of Engineering Mathematics 63 (241–257) 2009
GATEway: Symbiotic inter-domain traffic engineering
Roughan, Matthew; Zhang, Y, Internet Measurement Conference 08, Greece 20/10/08
Characterization of matrix-exponential distributions
Bean, Nigel; Fackrell, Mark; Taylor, Peter, Stochastic Models 24 (339–363) 2008
Mathematical modeling of glucose supply toward successful in vitro maturation of mammalian oocytes
Stokes, Yvonne; Clark, Alys; Thompson, Jeremy, Tissue Engineering. Part A. Tissue Engineering 14 (1539–1547) 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
Nonlinear transient heat conduction problems for a class of inhomogeneous anisotropic materials by BEM
Azis, Mohammad; Clements, David, Engineering Analysis With Boundary Elements 32 (1054–1060) 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
The mir-200 family and mir-205 regulate epithelial to mesenchymal transition by targeting ZEB1 and SIP1
Gregory, P; Bert, A; Paterson, Emily; Barry, Simon; Tsykin, Anna; Farshid, Gelareh; Vadas, Matthew Alexander; Khew-Goodall, Yeesim; Goodall, Gregory, Nature Cell Biology 10 (593–601) 2008
Model subgrid microscale interactions to accurately discretise stochastic partial differential equations.
Roberts, Anthony John,
Gene expression analysis of multiple gastrointestinal regions reveals activation of common cell regulatory pathways following cytotoxic chemotherapy
Bowen, Joanne; Gibson, Rachel; Tsykin, Anna; Stringer, Andrea Marie; Logan, Richard; Keefe, Dorothy, International Journal of Cancer 121 (1847–1856) 2007
New models for old questions: generalized linear models for cost prediction
Moran, John; Solomon, Patricia; Peisach, Aaron; Martin, J, Journal of Evaluation in Clinical Practice 13 (381–389) 2007
Statistics in review; Part 1: graphics, data summary and linear models
Moran, John; Solomon, Patricia, Critical care and Resuscitation 9 (81–90) 2007
Statistics in review; Part 2: Generalised linear models, time-to-event and time-series analysis, evidence synthesis and clinical trials
Moran, John; Solomon, Patricia, Critical care and Resuscitation 9 (187–197) 2007
The difference between hazard and risk in the relation between bone density and fracture
Nordin, Borje; Baghurst, Peter; Metcalfe, Andrew, Calcified Tissue International 80 (349–352) 2007
A biography of J. N. Newman
Tuck, Ernest, Journal of Engineering Mathematics 58 (1–5) 2007
Subgrid and interelement interactions affect discretisations of stochastically forced diffusion
Roberts, Anthony John, The ANZIAM Journal - On-line full-text 48 (C168–C188) 2007
Traffic matrix estimation method and apparatus
Duffield, N; Greenberg, A; Klincewicz, J; Roughan, Matthew; Zhang, Y,
Computer algebra models dynamics on a multigrid across multiple length and time scales
Roberts, Anthony John,
Computer algebra models the inertial dynamics of a thin film flow of power law fluids and other non-Newtonian fluids (Unpublished)
Roberts, Anthony John,
Binomial Models in Finance
Van Der Hoek, John; Elliott, Robert, (Springer) 2006
A simulation method for calibrating cluster-process rainfall models
Leonard, Michael; Lambert, Martin; Metcalfe, Andrew; Kuczera, George, 30th Hydrology and Water Resources Symposium, Launceston, Tasmania 04/12/06
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
Numerical studies on the approximation of horizontal diffusion using sigma coordinate system
Lee, Jong; Teubner, Michael; Nixon, John; Cho, Y-S, KSCE Journal of Civil Engineering 10 (145–149) 2006
On a generalised plane strain crack problem for inhomogeneous anisotropic elastic materials
Clements, David; Ang, W, International Journal of Engineering Science 44 (273–284) 2006
On the indentation of an inhomogeneous anisotropic elastic material by multiple straight rigid punches
Clements, David; Ang, W, Engineering Analysis With Boundary Elements 30 (284–291) 2006
Option pricing for GARCH models with Markov switching
Elliott, Robert; Siu, T; Chan, L, International Journal of Theoretical and Applied Finance 9 (825–841) 2006
Reduced models of chemical reaction in chaotic flows
Vikhansky, A; Cox, Stephen, Physics of Fluids 18 (37102–37102) 2006
Computation of short-crested deepwater waves
Ioualalen, M; Okamura, M; Cornier, S; Kharif, C; Roberts, Anthony John, Journal of Waterway Port Coastal and Ocean Engineering-ASCE 132 (157–165) 2006
Resolving the multitude of microscale interactions accurately models stochastic partial differential equations
Roberts, Anthony John, London Mathematical Society. Journal of Computation and Mathematics 9 (193–221) 2006
Three-dimensional flow due to a microcantilever oscillating near a wall: an unsteady slender-body analysis
Clarke, Richard; Jensen, O; Billingham, J; Williams, P, Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 462 (913–933) 2006
Adaptive battle agents: Emergence in artificial life combat models
Baker, Thomas; Botting, Matthew Craig; Berryman, Matthew; Ryan, Alex; Grisogono, A; Abbott, Derek, The SPIE International Symposium on Smart Structures, Devices, and Systems II, Sydney, Australia 13/12/04
Best approximation of nonlinear systems: Optimal causal feedback models
Torokhti, Anatoli; Howlett, P; Pearce, Charles, The 9th world multi-conference on systemics, cybernetics and informatics, Orlando, Florida, USA 10/07/05
Simulating catchment-scale monthly rainfall with classes of hidden Markov models
Whiting, Julian; Thyer, M; Lambert, Martin; Metcalfe, Andrew, The 29th Hydrology and Water Resources Symposium, Rydges Lakeside, Canberra, Australia 20/02/05
Algorithms for return probabilities for stochastic fluid flows
Bean, Nigel; O'Reilly, Malgorzata; Taylor, Peter, Stochastic Models 21 (149–184) 2005
Best causal mathematical models for a nonlinear system
Torokhti, Anatoli; Howlett, P; Pearce, Charles, IEEE Transactions on Circuits and Systems I - regular papers 52 (1013–1020) 2005
Ramaswami's duality and probabilistic algorithms for determining the rate matrix for a structured GI/M/1 Markov chain
Hunt, Emma, The ANZIAM Journal 46 (485–493) 2005
Reliability of supply between production lines
Green, David; Metcalfe, Andrew, Stochastic Models 21 (449–464) 2005
Traffic matrix reloaded: Impact of routing changes
Teixeira, R; Duffield, N; Rexford, J; Roughan, Matthew, Lecture Notes in Computer Science/Lecture Notes in Artificial Intelligence 3431 (251–264) 2005
Expression profiling of a myeloid cell line model to identify novel transcription factors influencing myeloid cell differentiation, proliferation and leukaemia
Wilkinson, Christopher; Brown, Anna; Kok, Chung; Solomon, Patricia; Goodall, Gregory; Gonda, Thomas; D'Andrea, M, 5th Australian Microarray Conference 2005, Barossa Valley, South Australia 29/09/05
Nonlinear analysis of rubber-based polymeric materials with thermal relaxation models
Melnik, R; Strunin, D; Roberts, Anthony John, Numerical Heat Transfer Part A-Applications 47 (549–569) 2005
Preface to the Proceedings of the 7th Biennial Engineering Mathematics and Applications Conference, EMAC-2005
Stacey, A; Blyth, B; Shepherd, J; Roberts, Anthony John, The ANZIAM Journal 47 (–) 2005
Load balancing techniques for inter-domain traffic engineering
Chandrayana, K; Zhang, Y; Roughan, Matthew; Sen, S,
Computer algebra resolves a multitude of microscale interactions to model stochastic partial differential equations
Roberts, Anthony John,
A fundamental solution for linear second-order elliptic systems with variable coefficients
Clements, David, Journal of Engineering Mathematics 49 (209–216) 2004
A probabilistic algorithm for finding the rate matrix of a block-GI/M/1 Markov chain
Hunt, Emma, The ANZIAM Journal 45 (457–475) 2004
Macrophage-tumour interactions: In vivo dynamics
Byrne, H; Cox, Stephen; Kelly, C, Discrete and Continuous Dynamical Systems-Series B 4 (81–98) 2004
Mixing measures for a two-dimensional chaotic Stokes flow
Finn, Matthew; Cox, Stephen; Byrne, H, Journal of Engineering Mathematics 48 (129–155) 2004
Modern approach of design of welded components subjected to fatigue loading
Ghosh, Abir, Journal of Structural Engineering-ASCE 130 (812–820) 2004
On the boundary-layer equations for power-law fluids
Denier, James; Dabrowski, Paul, Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 460 (3143–3158) 2004
Reynolds number effects in a simple planetary mixer
Clifford, M; Cox, Stephen; Finn, Matthew, Chemical Engineering Science 59 (3371–3379) 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
Second moments of a matrix analytic model of machine maintenance
Green, David; Metcalfe, Andrew, IMA International Conference on Modelling in Industrial Maintenance and Reliability (5th: 2004), Salford, United Kingdom 05/04/04
Cell-signalling repression in bacterial quorum sensing
Ward, J; King, J; Koerber, Adrian; Croft, J; Sockett, R; Williams, P, Mathematical Medicine and Biology (Print Edition) 21 (169–204) 2004
Arborescences, matrix-trees and the accumulated sojourn time in a Markov process
Pearce, Charles; Falzon, L, chapter in Stochastic analysis and applications Volume 3 (Nova Science Publishers) 147–168, 2003
Identification of probability distributions within hidden state models of rainfall
Whiting, Julian; Lambert, Martin; Metcalfe, Andrew, 28th International Hydrology and Water Resources Symposium, Wollongong, NWS, 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 dual-reciprocity boundary element method for a class of elliptic boundary value problems for non-homogenous anisotropic media
Ang, W; Clements, David; Vahdati, N, Engineering Analysis With Boundary Elements 27 (49–55) 2003
A genetic algorithm based on nearest neighbour classification to breast cancer diagnosis
Jain, R; Mazumdar, Jagan, Australasian Physical and Engineering Sciences in Medicine 26 (6–11) 2003
Dynamics of the cell and its extracellular matrix - A simple mathematical approach
Saha, Asit; Mazumdar, Jagan, IEEE Transactions on NanoBioscience 2 (89–93) 2003
Numerical model of electrical potential within the human head
Nixon, John; Rasser, Paul; Teubner, Michael; Clark, C; Bottema, M, International Journal for Numerical Methods in Engineering 56 (2353–2366) 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
Robust parameter estimation for asset price models with Markov modulated volatilities
Elliott, Robert; Malcolm, William; Tsoi, A, Journal of Economic Dynamics & Control 27 (1391–1409) 2003
The tree cut and merge algorithm for estimation of network reliability
Hui, Kin-Ping; Bean, Nigel; Kraetzl, Miro; Kroese, D, Probability in the Engineering and Informational Sciences 17 (23–45) 2003
An Information-Theoretic Approach to Traffic Matrix Estimation
Zhang, Y; Roughan, Matthew; Lund, C; Donoho, D, Ulrich, Karlsruche, Germany 25/08/03
Experience in measuring backbone traffic variability: models, metrics, measurements and meaning
Roughan, Matthew; Greenberg, A; Kalmaned, C; Rumsewicz, Michael; Yates, J; Zhang, Y, 2nd ACM SIGCOMM Workshop on Internet measurment, Marseille, France 06/11/02
Experience in measuring internet backbone traffic variability: Models, metrics, measurements and meaning
Roughan, Matthew; Greenberg, A; Kalmanek, C; Rumsewicz, Michael; Yates, J; Zhang, Y, 18th International Teletraffic Congress (ICT-18), Berlin, Germanay 31/08/03
Performance of estimated traffic matrices in traffic engineering
Roughan, Matthew; Thorup, M; Zhang, Y, 003 ACM SIGMETRICS international conference on Measurement and modeling of computer systems, San Diego, CA, USA 10/06/03
Traffic engineering with estimated traffic matrices
Roughan, Matthew; Thorup, M; Zhang, Y, 3rd ACM SIGCOMM conference on Internet measurement, Miami Beach, Florida USA 27/10/03
A holistic finite difference approach models linear dynamics consistently
Roberts, Anthony John, Mathematics of Computation 72 (247–262) 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
A comparison of models for catchment runoff
Metcalfe, Andrew; Heneker, Theresa; Lambert, Martin; Kuczera, George; Atan, I, 27th Hydrology and Water Resources Symposium 2002, Hilton on the Park, Melbourne 20/05/02
A matrix analytic model for machine maintenance
Green, David; Metcalfe, Andrew; Swailes, D, Matrix-Analytic Methods: Theory and Applications, Adelaide, Australia 14/07/02
A comparison of linear and nonlinear computations of waves made by slender submerged bodies
Tuck, Ernest; Scullen, David, Journal of Engineering Mathematics 42 (255–264) 2002
Higher-order statistical moments of wave-induced response of offshore structures via efficient sampling techniques
Najafian, G; Burrows, R; Tickell, R; Metcalfe, Andrew, International Offshore and Polar Engineering Conference 3 (465–470) 2002
Portfolio optimization, hidden Markov models, and technical analysis of P&F-charts
Elliott, Robert; Hinz, J, International Journal of Theoretical and Applied Finance 5 (385–399) 2002
Supporting maintenance strategies using Markov models
Al-Hassan, K; Swailes, D; Chan, J; Metcalfe, Andrew, IMA Journal of Management Mathematics 13 (17–27) 2002
What is a unit of capacity worth?
Chiera, Belinda; Taylor, Peter, Probability in the Engineering and Informational Sciences 16 (513–522) 2002
Computational models for materials with shape memory: towards a systematic description of coupled phenomena.
Melnik, R; Roberts, Anthony John, chapter in Computational science-ICCS 2002 (Springer) 490–499, 2002
Deterministic models
Metcalfe, Andrew, chapter in Research methods for postgraduates (Oxford University Press) 279–291, 2002
Price interactions of baseload supply changes and electricity demand shocks
Sick, G; Stein, M; Elliott, Robert, chapter in Real Options and Energy Management (Risk Books) 371–391, 2002
Stochastic models and simulation
Metcalfe, Andrew, chapter in Research methods for postgraduates (Oxford University Press) 292–299, 2002
The value of mathematical models
Metcalfe, Andrew, chapter in Research methods for postgraduates (Oxford University Press) 269–278, 2002
Phase transitions in shape memory alloys with hyperbolic heat conduction and differential-algebraic models
Melnik, R; Roberts, Anthony John; Thomas, K, Computational Mechanics 29 (16–26) 2002
Some new bounds for singular values and eigenvalues of matrix products
Lu, L-Z; Pearce, Charles, Annals of Operations Research 98 (141–148) 2001
Hidden state Markov chain time series models for arid zone hydrology
Cigizoglu, K; Adamson, Peter; Lambert, Martin; Metcalfe, Andrew, International Symposium on Water Resources and Environmental Impact Assessment (2001), Istanbul, Turkey 11/07/01
TCP congestion controls: Algorithms and models
Low, S; Roughan, Matthew, IEEE Infocom 2001, Anchorage, Alaska USA 22/04/01
White noise approach to interest rate models
Filinkov, Alexei; Van Der Hoek, John, Quantitative Methods in Finance Conference (2001), Sydney, Australia 12/12/01
The convergence of genetic learning algorithms, with particular reference to recent cobweb models
Pearce, Charles, chapter in Commerce, Complexity and Evolution (Cambridge University Press) 277–288, 2000
A triangular coastal element developed for use in finite difference tidal models
McInerney, David; Noye, Brian, The ANZIAM Journal 42 (C936–C953) 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
Deformations of carbon-fiber-reinforced yacht masts
Clements, David; Cooke, Tristrom, Journal of Engineering Mathematics 37 (11–25) 2000
Flowing windowpanes: a comparison of Newtonian and Maxwell fluid models
Stokes, Yvonne, Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 456 (1861–1864) 2000
Quasistationary distributions for level-dependent quasi-birth-and-death processes
Bean, Nigel; Pollett, P; Taylor, Peter, Stochastic Models 16 (511–541) 2000
The paradox of Parrondo's games
Harmer, Gregory; Abbott, Derek; Taylor, Peter, Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 456 (247–259) 2000
Unsteady stenosis flow prediction: a comparative study of non-Newtonian models with operator splitting scheme
Siauw, W; Ng, E; Mazumdar, Jagan, Medical Engineering & Physics 22 (265–277) 2000

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