Visualisation of groundwater flow using texture based visualisation techniques

Texture based techniques for visualisation of unsteady vector fields have been applied for the visualisation of a Finite volume model for variably saturated groundwater flow through porous media. This model has been developed by staff in the School of Mathematical Sciences QUT for the study of salt water intrusion into coastal aquifers. This presentation discusses the implementation and effectiveness of the IBFV algorithm in the context of visualisation of the groundwater simulation outputs.

Mathematical modelling of muscle recruitment and function in the lumbar spine

Low back pain is an increasing problem in industrialised countries and although it is a major socio-economic problem in terms of medical costs and lost productivity, relatively little is known about the processes underlying the development of the condition. This is in part due to the complex interactions between bone, muscle, nerves and other soft tissues of the spine, and the fact that direct observation and/or measurement of the human spine is not possible using non-invasive techniques. Biomechanical models have been used extensively to estimate the forces and moments experienced by the spine. These models provide a means of estimating the internal parameters which can not be measured directly. However, application of most of the models currently available is restricted to tasks resembling those for which the model was designed due to the simplified representation of the anatomy. The aim of this research was to develop a biomechanical model to investigate the changes in forces and moments which are induced by muscle injury. In order to accurately simulate muscle injuries a detailed quasi-static three dimensional model representing the anatomy of the lumbar spine was developed. This model includes the nine major force generating muscles of the region (erector spinae, comprising the longissimus thoracis and iliocostalis lumborum; multifidus; quadratus lumborum; latissimus dorsi; transverse abdominis; internal oblique and external oblique), as well as the thoracolumbar fascia through which the transverse abdominis and parts of the internal oblique and latissimus dorsi muscles attach to the spine. The muscles included in the model have been represented using 170 muscle fascicles each having their own force generating characteristics and lines of action. Particular attention has been paid to ensuring the muscle lines of action are anatomically realistic, particularly for muscles which have broad attachments (e.g. internal and external obliques), muscles which attach to the spine via the thoracolumbar fascia (e.g. transverse abdominis), and muscles whose paths are altered by bony constraints such as the rib cage (e.g. iliocostalis lumborum pars thoracis and parts of the longissimus thoracis pars thoracis). In this endeavour, a separate sub-model which accounts for the shape of the torso by modelling it as a series of ellipses has been developed to model the lines of action of the oblique muscles. Likewise, a separate sub-model of the thoracolumbar fascia has also been developed which accounts for the middle and posterior layers of the fascia, and ensures that the line of action of the posterior layer is related to the size and shape of the erector spinae muscle. Published muscle activation data are used to enable the model to predict the maximum forces and moments that may be generated by the muscles. These predictions are validated against published experimental studies reporting maximum isometric moments for a variety of exertions. The model performs well for fiexion, extension and lateral bend exertions, but underpredicts the axial twist moments that may be developed. This discrepancy is most likely the result of differences between the experimental methodology and the modelled task. The application of the model is illustrated using examples of muscle injuries created by surgical procedures. The three examples used represent a posterior surgical approach to the spine, an anterior approach to the spine and uni-lateral total hip replacement surgery. Although the three examples simulate different muscle injuries, all demonstrate the production of significant asymmetrical moments and/or reduced joint compression following surgical intervention. This result has implications for patient rehabilitation and the potential for further injury to the spine. The development and application of the model has highlighted a number of areas where current knowledge is deficient. These include muscle activation levels for tasks in postures other than upright standing, changes in spinal kinematics following surgical procedures such as spinal fusion or fixation, and a general lack of understanding of how the body adjusts to muscle injuries with respect to muscle activation patterns and levels, rate of recovery from temporary injuries and compensatory actions by other muscles. Thus the comprehensive and innovative anatomical model which has been developed not only provides a tool to predict the forces and moments experienced by the intervertebral joints of the spine, but also highlights areas where further clinical research is required.

Improving automatic speaker verification using SVM techniques

Automatic recognition of people is an active field of research with important forensic and security applications. In these applications, it is not always possible for the subject to be in close proximity to the system. Voice represents a human behavioural trait which can be used to recognise people in such situations. Automatic Speaker Verification (ASV) is the process of verifying a persons identity through the analysis of their speech and enables recognition of a subject at a distance over a telephone channel { wired or wireless. A significant amount of research has focussed on the application of Gaussian mixture model (GMM) techniques to speaker verification systems providing state-of-the-art performance. GMM's are a type of generative classifier trained to model the probability distribution of the features used to represent a speaker. Recently introduced to the field of ASV research is the support vector machine (SVM). An SVM is a discriminative classifier requiring examples from both positive and negative classes to train a speaker model. The SVM is based on margin maximisation whereby a hyperplane attempts to separate classes in a high dimensional space. SVMs applied to the task of speaker verification have shown high potential, particularly when used to complement current GMM-based techniques in hybrid systems. This work aims to improve the performance of ASV systems using novel and innovative SVM-based techniques. Research was divided into three main themes: session variability compensation for SVMs; unsupervised model adaptation; and impostor dataset selection. The first theme investigated the differences between the GMM and SVM domains for the modelling of session variability | an aspect crucial for robust speaker verification. Techniques developed to improve the robustness of GMMbased classification were shown to bring about similar benefits to discriminative SVM classification through their integration in the hybrid GMM mean supervector SVM classifier. Further, the domains for the modelling of session variation were contrasted to find a number of common factors, however, the SVM-domain consistently provided marginally better session variation compensation. Minimal complementary information was found between the techniques due to the similarities in how they achieved their objectives. The second theme saw the proposal of a novel model for the purpose of session variation compensation in ASV systems. Continuous progressive model adaptation attempts to improve speaker models by retraining them after exploiting all encountered test utterances during normal use of the system. The introduction of the weight-based factor analysis model provided significant performance improvements of over 60% in an unsupervised scenario. SVM-based classification was then integrated into the progressive system providing further benefits in performance over the GMM counterpart. Analysis demonstrated that SVMs also hold several beneficial characteristics to the task of unsupervised model adaptation prompting further research in the area. In pursuing the final theme, an innovative background dataset selection technique was developed. This technique selects the most appropriate subset of examples from a large and diverse set of candidate impostor observations for use as the SVM background by exploiting the SVM training process. This selection was performed on a per-observation basis so as to overcome the shortcoming of the traditional heuristic-based approach to dataset selection. Results demonstrate the approach to provide performance improvements over both the use of the complete candidate dataset and the best heuristically-selected dataset whilst being only a fraction of the size. The refined dataset was also shown to generalise well to unseen corpora and be highly applicable to the selection of impostor cohorts required in alternate techniques for speaker verification.

Efficient simulation of unsaturated flow using exponential time integration

We assess the performance of an exponential integrator for advancing stiff, semidiscrete formulations of the unsaturated Richards equation in time. The scheme is of second order and explicit in nature but requires the action of the matrix function φ(A) where φ(z) = [exp(z) - 1]/z on a suitability defined vector v at each time step. When the matrix A is large and sparse, φ(A)v can be approximated by Krylov subspace methods that require only matrix-vector products with A. We prove that despite the use of this approximation the scheme remains second order. Furthermore, we provide a practical variable-stepsize implementation of the integrator by deriving an estimate of the local error that requires only a single additional function evaluation. Numerical experiments performed on two-dimensional test problems demonstrate that this implementation outperforms second-order, variable-stepsize implementations of the backward differentiation formulae.

Matrix regularization techniques for online multitask learning

In this paper we examine the problem of prediction with expert advice in a setup where the learner is presented with a sequence of examples coming from different tasks. In order for the learner to be able to benefit from performing multiple tasks simultaneously, we make assumptions of task relatedness by constraining the comparator to use a lesser number of best experts than the number of tasks. We show how this corresponds naturally to learning under spectral or structural matrix constraints, and propose regularization techniques to enforce the constraints. The regularization techniques proposed here are interesting in their own right and multitask learning is just one application for the ideas. A theoretical analysis of one such regularizer is performed, and a regret bound that shows benefits of this setup is reported.

Application of operations research techniques to improve efficiency in the emergency department

The main aim of this thesis is to analyse and optimise a public hospital Emergency Department. The Emergency Department (ED) is a complex system with limited resources and a high demand for these resources. Adding to the complexity is the stochastic nature of almost every element and characteristic in the ED. The interaction with other functional areas also complicates the system as these areas have a huge impact on the ED and the ED is powerless to change them. Therefore it is imperative that OR be applied to the ED to improve the performance within the constraints of the system. The main characteristics of the system to optimise included tardiness, adherence to waiting time targets, access block and length of stay. A validated and verified simulation model was built to model the real life system. This enabled detailed analysis of resources and flow without disruption to the actual ED. A wide range of different policies for the ED and a variety of resources were able to be investigated. Of particular interest was the number and type of beds in the ED and also the shift times of physicians. One point worth noting was that neither of these resources work in isolation and for optimisation of the system both resources need to be investigated in tandem. The ED was likened to a flow shop scheduling problem with the patients and beds being synonymous with the jobs and machines typically found in manufacturing problems. This enabled an analytic scheduling approach. Constructive heuristics were developed to reactively schedule the system in real time and these were able to improve the performance of the system. Metaheuristics that optimised the system were also developed and analysed. An innovative hybrid Simulated Annealing and Tabu Search algorithm was developed that out-performed both simulated annealing and tabu search algorithms by combining some of their features. The new algorithm achieves a more optimal solution and does so in a shorter time.

Strategic project evaluation for open pit mining ventures using real options and allied econometric techniques

Open pit mine operations are complex businesses that demand a constant assessment of risk. This is because the value of a mine project is typically influenced by many underlying economic and physical uncertainties, such as metal prices, metal grades, costs, schedules, quantities, and environmental issues, among others, which are not known with much certainty at the beginning of the project. Hence, mining projects present a considerable challenge to those involved in associated investment decisions, such as the owners of the mine and other stakeholders. In general terms, when an option exists to acquire a new or operating mining project, , the owners and stock holders of the mine project need to know the value of the mining project, which is the fundamental criterion for making final decisions about going ahead with the venture capital. However, obtaining the mine project’s value is not an easy task. The reason for this is that sophisticated valuation and mine optimisation techniques, which combine advanced theories in geostatistics, statistics, engineering, economics and finance, among others, need to be used by the mine analyst or mine planner in order to assess and quantify the existing uncertainty and, consequently, the risk involved in the project investment. Furthermore, current valuation and mine optimisation techniques do not complement each other. That is valuation techniques based on real options (RO) analysis assume an expected (constant) metal grade and ore tonnage during a specified period, while mine optimisation (MO) techniques assume expected (constant) metal prices and mining costs. These assumptions are not totally correct since both sources of uncertainty—that of the orebody (metal grade and reserves of mineral), and that about the future behaviour of metal prices and mining costs—are the ones that have great impact on the value of any mining project. Consequently, the key objective of this thesis is twofold. The first objective consists of analysing and understanding the main sources of uncertainty in an open pit mining project, such as the orebody (in situ metal grade), mining costs and metal price uncertainties, and their effect on the final project value. The second objective consists of breaking down the wall of isolation between economic valuation and mine optimisation techniques in order to generate a novel open pit mine evaluation framework called the ―Integrated Valuation / Optimisation Framework (IVOF)‖. One important characteristic of this new framework is that it incorporates the RO and MO valuation techniques into a single integrated process that quantifies and describes uncertainty and risk in a mine project evaluation process, giving a more realistic estimate of the project’s value. To achieve this, novel and advanced engineering and econometric methods are used to integrate financial and geological uncertainty into dynamic risk forecasting measures. The proposed mine valuation/optimisation technique is then applied to a real gold disseminated open pit mine deposit to estimate its value in the face of orebody, mining costs and metal price uncertainties.

An example of cognitive obstacles in advanced integration: the case of scalar line integrals

Cognitive obstacles that arise in the teaching and learning of scalar line integrals, derived from cognitive aids provided to students when first learning about integration of single variable functions are described. A discussion of how and why the obstacles cause students problems is presented and possible strategies to overcome the obstacles are outlined.