Department of Mathematics and Computing Seminars

Dynamics of solid particles and gaseous bubbles in viscous density stratified fluid is studied analytically and numerically within the framework of creeping flow approximation. Equations of motion for particles and bubbles include the consideration of the buoyancy force, Stokes drag force and memory integral drag force. Expressions for the drag forces exerted on solid particles and gaseous bubbles are different. The problem studied is applicable to many practical situations where particle and bubble motion may be experienced in viscous fluids, which include aerosol and dust transport in the atmosphere, drop dynamics in pharmaceuticals and perfume, sediment and bubble motions in oceans and cavitation processes in technology. Exact analytical solutions for both the homogeneous surrounding fluid and density stratified fluid are obtained; they are analysed against numerical solutions. Results obtained are particularly relevant to the physical processes that may occur in the cooling system of the Open Pool Australian Light-water research reactor OPAL at Lucas Heights.

Yury Stepanyants is a member of the Computational Engineering and Science Research Centre (CESRC).

In this talk, I will discuss the problem of projected outlier detection in high dimensional data streams. I will first discuss the formulation of this problem and the changes we will face when addressing this problem. I will also dwell on a new technique, called Stream Projected Ouliter deTector (SPOT), to identify outliers embedded in subspaces. SPOT devises Sparse Subspace Template (SST), a set of subspaces obtained by unsupervised and/or supervised learning processes, to detect projected outliers effectively. Multi-Objective Genetic Algorithm (MOGA) is employed as an effective search method for finding outlying subspaces from training data to construct SST. The experimental results demonstrate the efficiency and effectiveness of SPOT in detecting outliers in high-dimensional data streams.

In this talk I will discuss modelling anomalous subdiffusion with application to modelling potential propagation in spiny dendrites. Most of the brain is composed of dendrites and dendritic trees that relay postsynaptic potentials to a soma for processing and possible nerve cell firing. The mathematical description of the electrotonic properties of neuronal dendrites and dendritic trees is based on the cable equation, which models a dendrite as a homogeneous membrane cylinder with membrane capacitance, membrane resistance, and axial resistance as model parameters. In recent years advances in imaging technologies and experimental techniques have enabled detailed studies of the local structure and the distribution of dendritic spines - small protrusions that decorate typical dendrites of excitary nerve cells in the neocortex. The dendritic spines act as local traps that result in anomalous diffusion of molecules along the axial direction of dendrites. In an effort to model the electrotonic properties of neuronal dendrites with spines we have introduced a new fractional cable equation that incorporates anomalous electro-diffusion of ions. The model equations predict that larger spine densities can serve to enhance both the arrival time and the persistence of postsynaptic potentials that propagate along spiny dendrites to the soma. We describe a fractional cable equation to model anomalously slow electrodiffusion of ions in nerve cells. Fundamental solutions of this model are presented and results for firing rates and voltage attenuation are obtained in terms of the anomalous diffusion parameters. A particular application to model the passive propagation of a postsynaptic potential along a spiny dendrite is described. An interesting special case of this model is equivalent to a particular example of a fractional reaction-diffusion equation formulated by Henry and Wearne (2000, p.448-455). The solution in this example predicts negative solutions contrary to the physical reality for chemical reactions. This result has sparked new research into modelling reactions in the presence of anomalous subdiffusion and will form the second half of the this talk where we shall discuss potential alternative models for single and multi-species reactions in the case of linear reaction dynamics. These model equations are derived from a mesoscopic continuous time random walk formulation of anomalously diffusing species with linear mean field reaction kinetics. The effect of reactions is manifest in reaction modified spatio-temporal diffusion operators as well as in additive mean field reaction terms. One consequence of the non-separability of reaction and subdiffusion terms is that the governing evolution equation for the concentration of one particular species may include both reactive and diffusive contributions from other species. The general solution is derived for the multi-species system and some particular special cases involving both irreversible and reversible reaction dynamics are analyzed in detail. We have carried out Monte Carlo simulations corresponding to these special cases and we find excellent agreement with theory. The impact of this new research on the modelling of spiny dendrites will be discussed.

This seminar will be targeted to an audience without specific mathematical knowledge.

Possible effects of gigantic internal waves on underwater navigation are discussed. It has been shown that under certain conditions, intense internal waves may dangerously effect on coastal engineering constructions and submarine navigation. The possible role of large amplitude internal solitary waves in the wrecks of American submarines in 1960s will also be discussed.

Typical models describing internal waves in density stratified oceans are outlined. Among them, the Korteweg−de Vries, Benjamin−Ono, Gardner, Ostrovsky, Kadomtsev−Petvialshvili and other equations. Solutions of these equations in the form of stationary propagating periodic or solitary waves are discussed. Characteristic parameters of waves are presented for shallow and deep basins. Experimental observations of giant solitary waves in different places of the World Ocean are summarized. The main cause of gigantic wave appearance is the barotropic tide which transforms into baroclininc perturbations and gives birth to internal waves. An example of such transformation of nonlinear internal tide with the consequent development of internal solitary waves on the Australian North West Shelf is discussed in detail. Influence of various factors such as nonlinearity, dispersion, the Coriolis effect due to Earth rotation, depth variation and horizontal variability of density stratification, on wave propagation are demonstrated through the numerical simulation. Simulations show that a wide variety of nonlinear wave shapes can be explained by a synergetic action of nonlinearity and variability of hydrology along the wave path.

The Progress Bar is a new tool you can use in Moodle (StudyDesk) within your courses. It's easy to set up and helpful to your students.

This seminar will discuss:

• why such a tool is needed,
• results of evaluation and student feedback,
• impact on student progression, and
• how you can set up the Progress Bar in your course.

For the p (> 1) simple linear models, the problem of testing the intercepts following a preliminary test on the suspected equality of slopes is considered. The unrestricted test (UT), restricted test (RT) and pre-test test (PTT) are proposed from the M-tests using the M-estimation methodology. The asymptotic distributions of the test statistics are obtained and used to derive the asymptotic power functions of the tests. Analytical and computational comparisons of the three tests are provided. The PTT achieves a reasonable dominance over the others asymptotically.

The odds ratio (OR) is one of the most popular and frequently used indices for measuring the extent of association between exposure and its outcomes in randomised controlled trials (RCTs). Meta-analysis combines data from various independent trials in estimating OR for binary outcomes to make the sample size larger so that the inference based on meta-analysis is reliable. However, there are situations in which the outcomes are on an ordinal scale with more than two cate- gories. The OR can not directly be used without arbitrarily grouping multiple levels of response into two categories. Moreover, the col- lapsing of data may cause a loss of efficiency. The generalised odds ratio (GOR) (Agresti, 1980) is used for summarising the difference between two stochastically ordered distributions of an ordinal cate- gorical variable without the need to assume any specific parametric models (Hosmer and Lemeshow, 1989). In this study, GOR is used for combining the treatment effect in meta-analysis for ordered categori- cal outcomes. A quasi-empirical Bayes method is developed for RCTs using GOR under independent multinomial sampling procedure. This method will help identifying the extreme trials, hence improve the meta-analysis with heterogeneous trials. Both fixed effects and ran- dom effects model are employed and compared.

Traditional postoperative management following gastrointestinal surgery mandates that patients do not receive nutrition until resumption of bowel function has occurred. However, as this may not occur for a number of days in a patient population who are frequently malnourished prior to surgery, delay in nutritional provision may further compromise the patient and contribute to a prolonged postoperative course. The concept of early postoperative feeding, in which patients receive nutrition before bowel function has returned has been investigated in a growing number of randomised controlled trials without evidence of adverse outcomes. Three other meta-analyses on this topic exist but these contain a number of limitations that potentially limit the validity of the outcomes and conclusions reported.

Objectives: To conduct a meta-analysis of randomized controlled trials evaluating the effect on surgical outcomes of providing nutrition within 24-hours following gastrointestinal surgery compared with traditional postoperative management.

Methods: A search of Cochrane, Medline, PubMed and EMBASE electronic databases was conducted to identify randomized controlled trials published in English language between1966 and 2008 comparing the outcomes of early and traditional post-operative feeding. All trials involving resection of the portions of the gastrointestinal tract followed by patients receiving nutritionally significant oral or enteral intake within 24-hours after surgery were included for analysis. Random effects meta-analyses were performed. Outcome variables analysed were complications, mortality, anastomotic leak, nasogastric reinsertion, days to passing flatus, days to first bowel motion, days to consumption of solid diet and length of stay.

Results: Fifteen studies involving a total of 1240 patients were analysed. A statistically significant forty-five percent reduction in relative odds of developing post operative complications were seen in patients receiving early postoperative feeding (OR 0.55 CI 0.35, 0.87, p=0.01). Trends favouring early feeding were seen with relation to reduction in anastomotic breakdown (OR 0.75, CI 0.39, 1.4, p=0.39), mortality (OR 0.71, CI 0.32,1.56, p= 0.39), resumption of bowel function as evidenced by days to passage of flatus (WMD -0.42, CI -1.12, 0.28, p=0.23) and first bowel motion (WMD -0.28, CI -1.20, 0.64, p=0.55), and reduced length of stay (WMD -1.28, CI -2.94, 0.38, p=0.13), however these were not statistically significant. A forty-eight percent relative reduction in nasogastric tube reinsertion was seen for traditional feeding practices (OR 1.48, CI 0.93, 2.35, p=0.10). The early feeding group had a significantly earlier resumption of solid diet (WMD -3.48, CI -4.72, -2.24, p<0.0001).

Conclusions: Early provision of nutritionally significant oral or enteral intake appear to be associated with a significant reduction in reported complications when compared with traditional postoperative feeding practices and may confer reductions in mortality, anastomotic leak, and resumption of GI function as evidenced by passage of flatus, however these results need to be interpreted in the context of the heterogeneity detected within the analysis. The current work highlights areas requiring further research including the need for multidisciplinary collaboration in this clinical area, and the need for further research and modelling to better match meta-analysis methodology with the clinical contexts to which they are being applied such as methods to deal more robustly with small study numbers, and the more sensitive detection of heterogeneity and publication bias.

Bio: Emma completed a Bachelor of Health Science at QUT with majors in Nutrition and Dietetics, and Public Health in 2001, graduating with first class honours and since then has worked a clinical dietitian in a variety of medical and surgical speciality areas within the positions she has held at the Princess Alexandra Hospital in Brisbane, and in her current role as the Clinical Specialist Dietitian at the Ipswich Hospital. After several years of increasing involvement with clinical audits within her workplace she commenced her MPhil with USQ in 2008, investigating the outcomes of early versus traditional postoperative feeding in gastrointestinal resectional surgery patients using meta-analysis. Her research interests lie in translating research into clinical practice with a view to improving patient outcomes.

Margrabe provides a pricing formula for an exchange option where the distributions of both stock prices are log-normal with correlated Wiener components. Merton has provided a formula for the price of a European call option on a single stock where the stock price process contains a compound Poisson jump component, in addition to a continuous log-normally distributed component. We use Merton's analysis to extend Margrabe's results to the case of exchange options where both stock price processes also contain compound Poisson jump components. A Radon-Nikodym derivative process that induces the change of measure from the market measure to an equivalent martingale measure is introduced. The choice of parameters in the Radon-Nikodym derivative allows us to price the option under different financial-economic scenarios. We also consider American style exchange options and provide a probabilistic intepretation of the early exercise premium.

Academic numeracy is a critical awareness that allows students to become confident and competent in using mathematics and to be able to situate, interpret, critique, use, communicate and even create mathematics within their discipline’s setting. Academic numeracy is usually based on both the mathematics learnt at school and the mathematics needed in disciplines such as nursing or economics. Many students at both school and university are opting to study easier types of mathematics; universities are removing mathematical pre-requisites from award programs and not recognising the embedded mathematics within many of their courses. These trends ensure that initiatives which allow students to bridge the mathematical gaps to university are still necessary. Yet while research into mathematics at university does exist, it is still in its infancy. There are many questions not fully answered and as universities move into the culture of quality and performance matched funding, it is essential that we continue to address the following questions:

• What academic numeracy is needed by students at university?
• What are students' academic numeracy skills on entering university?
• What are the most effective ways to develop the academic numeracy skills of university students?

This presentation will highlight some of the research undertaken and the curricula and resources developed by myself and others at USQ.