Three-dimensional geological modelling and multivariate statistical analysis of water chemistry data to analyse and visualise aquifer structure and groundwater composition in the Wairau Plain, Marlborough District, New Zealand

Concerns regarding groundwater contamination with nitrate and the long-term sustainability of groundwater resources have prompted the development of a multi-layered three dimensional (3D) geological model to characterise the aquifer geometry of the Wairau Plain, Marlborough District, New Zealand. The 3D geological model which consists of eight litho-stratigraphic units has been subsequently used to synthesise hydrogeological and hydrogeochemical data for different aquifers in an approach that aims to demonstrate how integration of water chemistry data within the physical framework of a 3D geological model can help to better understand and conceptualise groundwater systems in complex geological settings. Multivariate statistical techniques(e.g. Principal Component Analysis and Hierarchical Cluster Analysis) were applied to groundwater chemistry data to identify hydrochemical facies which are characteristic of distinct evolutionary pathways and a common hydrologic history of groundwaters. Principal Component Analysis on hydrochemical data demonstrated that natural water-rock interactions, redox potential and human agricultural impact are the key controls of groundwater quality in the Wairau Plain. Hierarchical Cluster Analysis revealed distinct hydrochemical water quality groups in the Wairau Plain groundwater system. Visualisation of the results of the multivariate statistical analyses and distribution of groundwater nitrate concentrations in the context of aquifer lithology highlighted the link between groundwater chemistry and the lithology of host aquifers. The methodology followed in this study can be applied in a variety of hydrogeological settings to synthesise geological, hydrogeological and hydrochemical data and present them in a format readily understood by a wide range of stakeholders. This enables a more efficient communication of the results of scientific studies to the wider community.

Persistence of multiple genetic lineages within intra-host populations of Ross River virus

We examined the structure and extent of genetic diversity in intrahost populations of Ross River virus (RRV) in samples from six human patients, focusing on the nonstructural (nsP3) and structural (E2) protein genes. Strikingly, although the samples were collected from contrasting ecological settings 3,000 kilometers apart in Australia, we observed multiple viral lineages in four of the six individuals, which is indicative of widespread mixed infections. In addition, a comparison with previously published RRV sequences revealed that these distinct lineages have been in circulation for at least 5 years, and we were able to document their long-term persistence over extensive geographical distances

Linking three-dimensional geological modelling and multivariate statistical analysis to define groundwater chemistry baseline and identify inter-aquifer connectivity within the Clarence-Moreton Basin, Southeast Queensland, Australia

The Clarence-Moreton Basin (CMB) covers approximately 26000 km2 and is the only sub-basin of the Great Artesian Basin (GAB) in which there is flow to both the south-west and the east, although flow to the south-west is predominant. In many parts of the basin, including catchments of the Bremer, Logan and upper Condamine Rivers in southeast Queensland, the Walloon Coal Measures are under exploration for Coal Seam Gas (CSG). In order to assess spatial variations in groundwater flow and hydrochemistry at a basin-wide scale, a 3D hydrogeological model of the Queensland section of the CMB has been developed using GoCAD modelling software. Prior to any large-scale CSG extraction, it is essential to understand the existing hydrochemical character of the different aquifers and to establish any potential linkage. To effectively use the large amount of water chemistry data existing for assessment of hydrochemical evolution within the different lithostratigraphic units, multivariate statistical techniques were employed.

Mathematical modelling of tumour growth and interaction with host tissue and the immune system

In this thesis, three mathematical models describing the growth of solid tumour incorporating the host tissue and the immune system response are developed and investigated. The initial model describes the dynamics of the growing tumour and immune response before being extended in the second model by introducing a time-varying dendritic cell-based treatment strategy. Finally, in the third model, we present a mathematical model of a growing tumour using a hybrid cellular automata. These models can provide information to pre-experimental work to assist in designing more effective and efficient laboratory experiments related to tumour growth and interactions with the immune system and immunotherapy.

Three-dimensional geological modelling of the Galilee and central Eromanga basins, Australia: New insights into aquifer/aquitard geometry and potential influence of faults on inter-connectivity

Study region The Galilee and Eromanga basins are located in central Queensland, Australia. Both basins are components of the Great Artesian Basin which host some of the most significant groundwater resources in Australia. Study focus This study evaluates the influence of regional faults on groundwater flow in an aquifer/aquitard interbedded succession that form one of the largest Artesian Basins in the world. In order to assess the significance of regional faults as potential barriers or conduits to groundwater flow, vertical displacements of the major aquifers and aquitards were studied at each major fault and the general hydraulic relationship of units that are juxtaposed by the faults were considered. A three-dimensional (3D) geological model of the Galilee and Eromanga basins was developed based on integration of well log data, seismic surfaces, surface geology and elevation data. Geological structures were mapped in detail and major faults were characterised. New hydrological insights for the region Major faults that have been described in previous studies have been confirmed within the 3D geological model domain and a preliminary assessment of their hydraulic significance has been conducted. Previously unknown faults such as the Thomson River Fault (herein named) have also been identified in this study.

Atheroma: Is calcium important or not? A modelling study of stress within the atheromatous fibrous cap in relation to position and size of calcium deposits

Atheromatous plaque rupture h the cause of the majority of strokes and heart attacks in the developed world. The role of calcium deposits and their contribution to plaque vulnerability are controversial. Some studies have suggested that calcified plaque tends to be more stable whereas others have suggested the opposite. This study uses a finite element model to evaluate the effect of calcium deposits on the stress within the fibrous cap by varying their location and size. Plaque fibrous cap, lipid pool and calcification were modeled as hyperelastic, Isotropic, (nearly) incompressible materials with different properties for large deformation analysis by assigning time-dependent pressure loading on the lumen wall. The stress and strain contours were illustrated for each condition for comparison. Von Mises stress only increases up to 1.5% when varying the location of calcification in the lipid pool distant to the fibrous cap. Calcification in the fibrous cap leads to a 43% increase of Von Mises stress when compared with that in the lipid pool. An increase of 100% of calcification area leads to a 15% stress increase in the fibrous cap. Calcification in the lipid pool does not increase fibrous cap stress when it is distant to the fibrous cap, whilst large areas of calcification close to or in the fibrous cap may lead to a high stress concentration within the fibrous cap, which may cause plaque rupture. This study highlights the application of a computational model on a simulation of clinical problems, and it may provide insights into the mechanism of plaque rupture.

Using ontology for the representational analysis of process modelling techniques

Selecting an appropriate business process modelling technique forms an important task within the methodological challenges of a business process management project. While a plethora of available techniques has been developed over the last decades, there is an obvious shortage of well-accepted reference frameworks that can be used to evaluate and compare the capabilities of the different techniques. Academic progress has been made at least in the area of representational analyses that use ontology as a benchmark for such evaluations. This paper reflects on the comprehensive experiences with the application of a model based on the Bunge ontology in this context. A brief overview of the underlying research model characterizes the different steps in such a research project. A comparative summary of previous representational analyses of process modelling techniques over time gives insights into the relative maturity of selected process modelling techniques. Based on these experiences suggestions are made as to where ontology-based representational analyses could be further developed and what limitations are inherent to such analyses.

Life cycle modelling and design knowledge development in 3D virtual environments : final report

Experience plays an important role in building management. “How often will this asset need repair?” or “How much time is this repair going to take?” are types of questions that project and facility managers face daily in planning activities. Failure or success in developing good schedules, budgets and other project management tasks depend on the project manager's ability to obtain reliable information to be able to answer these types of questions. Young practitioners tend to rely on information that is based on regional averages and provided by publishing companies. This is in contrast to experienced project managers who tend to rely heavily on personal experience. Another aspect of building management is that many practitioners are seeking to improve available scheduling algorithms, estimating spreadsheets and other project management tools. Such “micro-scale” levels of research are important in providing the required tools for the project manager's tasks. However, even with such tools, low quality input information will produce inaccurate schedules and budgets as output. Thus, it is also important to have a broad approach to research at a more “macro-scale.” Recent trends show that the Architectural, Engineering, Construction (AEC) industry is experiencing explosive growth in its capabilities to generate and collect data. There is a great deal of valuable knowledge that can be obtained from the appropriate use of this data and therefore the need has arisen to analyse this increasing amount of available data. Data Mining can be applied as a powerful tool to extract relevant and useful information from this sea of data. Knowledge Discovery in Databases (KDD) and Data Mining (DM) are tools that allow identification of valid, useful, and previously unknown patterns so large amounts of project data may be analysed. These technologies combine techniques from machine learning, artificial intelligence, pattern recognition, statistics, databases, and visualization to automatically extract concepts, interrelationships, and patterns of interest from large databases. The project involves the development of a prototype tool to support facility managers, building owners and designers. This final report presents the AIMMTM prototype system and documents how and what data mining techniques can be applied, the results of their application and the benefits gained from the system. The AIMMTM system is capable of searching for useful patterns of knowledge and correlations within the existing building maintenance data to support decision making about future maintenance operations. The application of the AIMMTM prototype system on building models and their maintenance data (supplied by industry partners) utilises various data mining algorithms and the maintenance data is analysed using interactive visual tools. The application of the AIMMTM prototype system to help in improving maintenance management and building life cycle includes: (i) data preparation and cleaning, (ii) integrating meaningful domain attributes, (iii) performing extensive data mining experiments in which visual analysis (using stacked histograms), classification and clustering techniques, associative rule mining algorithm such as “Apriori” and (iv) filtering and refining data mining results, including the potential implications of these results for improving maintenance management. Maintenance data of a variety of asset types were selected for demonstration with the aim of discovering meaningful patterns to assist facility managers in strategic planning and provide a knowledge base to help shape future requirements and design briefing. Utilising the prototype system developed here, positive and interesting results regarding patterns and structures of data have been obtained.

Life Cycle Modelling and Design Knowledge Development in 3D Virtual Environments

Experience plays an important role in building management. “How often will this asset need repair?” or “How much time is this repair going to take?” are types of questions that project and facility managers face daily in planning activities. Failure or success in developing good schedules, budgets and other project management tasks depend on the project manager's ability to obtain reliable information to be able to answer these types of questions. Young practitioners tend to rely on information that is based on regional averages and provided by publishing companies. This is in contrast to experienced project managers who tend to rely heavily on personal experience. Another aspect of building management is that many practitioners are seeking to improve available scheduling algorithms, estimating spreadsheets and other project management tools. Such “micro-scale” levels of research are important in providing the required tools for the project manager's tasks. However, even with such tools, low quality input information will produce inaccurate schedules and budgets as output. Thus, it is also important to have a broad approach to research at a more “macro-scale.” Recent trends show that the Architectural, Engineering, Construction (AEC) industry is experiencing explosive growth in its capabilities to generate and collect data. There is a great deal of valuable knowledge that can be obtained from the appropriate use of this data and therefore the need has arisen to analyse this increasing amount of available data. Data Mining can be applied as a powerful tool to extract relevant and useful information from this sea of data. Knowledge Discovery in Databases (KDD) and Data Mining (DM) are tools that allow identification of valid, useful, and previously unknown patterns so large amounts of project data may be analysed. These technologies combine techniques from machine learning, artificial intelligence, pattern recognition, statistics, databases, and visualization to automatically extract concepts, interrelationships, and patterns of interest from large databases. The project involves the development of a prototype tool to support facility managers, building owners and designers. This Industry focused report presents the AIMMTM prototype system and documents how and what data mining techniques can be applied, the results of their application and the benefits gained from the system. The AIMMTM system is capable of searching for useful patterns of knowledge and correlations within the existing building maintenance data to support decision making about future maintenance operations. The application of the AIMMTM prototype system on building models and their maintenance data (supplied by industry partners) utilises various data mining algorithms and the maintenance data is analysed using interactive visual tools. The application of the AIMMTM prototype system to help in improving maintenance management and building life cycle includes: (i) data preparation and cleaning, (ii) integrating meaningful domain attributes, (iii) performing extensive data mining experiments in which visual analysis (using stacked histograms), classification and clustering techniques, associative rule mining algorithm such as “Apriori” and (iv) filtering and refining data mining results, including the potential implications of these results for improving maintenance management. Maintenance data of a variety of asset types were selected for demonstration with the aim of discovering meaningful patterns to assist facility managers in strategic planning and provide a knowledge base to help shape future requirements and design briefing. Utilising the prototype system developed here, positive and interesting results regarding patterns and structures of data have been obtained.

Modelling ideal turbulent vortex breakdown

In this computational study we investigate the role of turbulence in ideal axisymmetric vortex breakdown. A pipe geometry with a slight constriction near the inlet is used to stabilise the location of the breakdown within the computed domain. Eddy-viscosity and differential Reynolds stress models are used to model the turbulence. Changes in upstream turbulence levels, flow Reynolds and Swirl numbers are considered. The different computed solutions are monitored for indications of different breakdown flow configurations. Trends in vortex breakdown due to turbulent flow conditions are identified and discussed.

Promoting interdisciplinarity through mathematical modelling

This article presents one approach to addressing the important issue of interdisciplinarity in the primary school mathematics curriculum, namely, through realistic mathematical modelling problems. Such problems draw upon other disciplines for their contexts and data. The article initially considers the nature of modelling with complex systems and discusses how such experiences differ from existing problem-solving activities in the primary mathematics curriculum. Principles for designing interdisciplinary modelling problems are then addressed, with reference to two mathematical modelling problems— one based in the scientific domain and the other in the literary domain. Examples of the models children have created in solving these problems follow. A reflection on the differences in the diversity and sophistication of these models raises issues regarding the design of interdisciplinary modelling problems. The article concludes with suggested opportunities for generating multidisciplinary projects within the regular mathematics curriculum.

Host searching behaviour of Diachasmimorpha kraussii (Fullaway) (Hymenoptera: Braconidae: Opiinae), a polyphagous parasitoid of Dacinae fruit flies (Diptera: Tephritidae)

Diachasmimorpha kraussii (Hymenoptera: Braconidae: Opiinae) is a koinobiont larval parasitoid of dacine fruit flies of the genus Bactrocera (Diptera: Tephritidae) in its native range (Australia, Papua New Guinea, Solomon Islands). The wasp is a potentially important control agent for pest fruit flies, having been considered for both classical and inundative biological control releases. I investigated the host searching, selection and utilisation mechanisms of the wasp against native host flies within its native range (Australia). Such studies are rare in opiine research where the majority of studies, because of the applied nature of the research, have been carried out using host flies and environments which are novel to the wasps. Diachasmimorpha kraussii oviposited equally into maggots of four fruit fly species, all of which coexist with the wasp in its native range (Australia), when tested in a choice trial using a uniform artificial diet media. While eggs laid into Bactrocera tryoni and B. jarvisi developed successfully through to adult wasps, eggs laid into B. cucumis and B. cacuminata were encapsulated. These results suggest that direct larval cues are not an important element in host selection by D. kraussii. Further exploring how D. kraussii locates suitable host larvae, I investigated the role of plant cues in host searching and selection. This was examined in a laboratory choice trial using uninfested fruit or fruit infested with either B. tryoni or B. jarvisi maggots. The results showed a consistent preference ranking among infested fruits by the wasp, with guava and peach most preferred, but with no response to uninfested fruits. Thus, it appears the wasp uses chemical cues emitted in response to fruit fly larval infestation for host location, but does not use cues from uninfested fruits. To further tease apart the role of (i) suitable and non-suitable maggots, (ii) infested and uninfested fruits of different plant species, and (iii) adult flies, in wasp host location and selection, I carried out a series of behavioural tests where I manipulated these attributes in a field cage. These trials confirmed that D. kraussii did not respond to cues in uninfested fruits, that there were consistent preferences by the wasps for different maggot infested fruits, that fruit preference did not vary depending on whether the maggots were physiologically suitable or not suitable for wasp offspring development, and finally, that adult flies appear to play a secondary role as indicators of larval infestation. To investigate wasp behaviour in an unrestrained environment, I concurrently observed diurnal foraging behaviours of both the wasp and one of its host fly in a small nectarine orchard. Wasp behaviour, both spatially and temporally, was not correlated with adult fruit fly behaviour or abundance. This study reinforced the point that infested fruit seems to be the primary cue used by foraging wasps. Wasp and fly feeding and mating was not observed in the orchard, implying these activities are occurring elsewhere. It is highly unlikely that these behaviours were happening within the orchard during the night as both insects are diurnal. As the final component of investigating host location, I carried out a habitat preference study for the wasp at the landscape scale. Using infested sentinel fruits, I tested the parasitism rate of B. tryoni in eucalyptus sclerophyll forest, rainforest and suburbia in South East Queensland. Although, rainforest is the likely endemic habitat of both B. tryoni and D. kraussii, B. tryoni abundance is significantly greater in suburban environments followed by eucalyptus sclerophyll forest. Parasitism rate was found to be higher in suburbia than in the eucalyptus sclerophyll forest, while no parasitism was recorded in the rainforest. This result suggests that wasps orient within the landscape towards areas of high host density and are not restricted by habitat types. Results from the different experiments suggest that host searching, selection and utilisation behaviour of D. kraussii are strongly influenced by cues associated with fruit fly larval feeding. Cues from uninfested fruits, the host larvae themselves, and the adult host flies play minimal roles. The discussion focuses on the fit of D. kraussii to Vinson’s classical parasitoid host location model and the implications of results for biological control, including recommendations for host and plant preference screening protocols and release regimes.

How useful is expert opinion for predicting the distribution of a species within and beyond the region of expertise? A case study using brush-tailed rock-wallabiesPetrogale penicillata

1. Species' distribution modelling relies on adequate data sets to build reliable statistical models with high predictive ability. However, the money spent collecting empirical data might be better spent on management. A less expensive source of species' distribution information is expert opinion. This study evaluates expert knowledge and its source. In particular, we determine whether models built on expert knowledge apply over multiple regions or only within the region where the knowledge was derived. 2. The case study focuses on the distribution of the brush-tailed rock-wallaby Petrogale penicillata in eastern Australia. We brought together from two biogeographically different regions substantial and well-designed field data and knowledge from nine experts. We used a novel elicitation tool within a geographical information system to systematically collect expert opinions. The tool utilized an indirect approach to elicitation, asking experts simpler questions about observable rather than abstract quantities, with measures in place to identify uncertainty and offer feedback. Bayesian analysis was used to combine field data and expert knowledge in each region to determine: (i) how expert opinion affected models based on field data and (ii) how similar expert-informed models were within regions and across regions. 3. The elicitation tool effectively captured the experts' opinions and their uncertainties. Experts were comfortable with the map-based elicitation approach used, especially with graphical feedback. Experts tended to predict lower values of species occurrence compared with field data. 4. Across experts, consensus on effect sizes occurred for several habitat variables. Expert opinion generally influenced predictions from field data. However, south-east Queensland and north-east New South Wales experts had different opinions on the influence of elevation and geology, with these differences attributable to geological differences between these regions. 5. Synthesis and applications. When formulated as priors in Bayesian analysis, expert opinion is useful for modifying or strengthening patterns exhibited by empirical data sets that are limited in size or scope. Nevertheless, the ability of an expert to extrapolate beyond their region of knowledge may be poor. Hence there is significant merit in obtaining information from local experts when compiling species' distribution models across several regions.

Stochastic modelling of financial time series with memory and multifractal scaling

Financial processes may possess long memory and their probability densities may display heavy tails. Many models have been developed to deal with this tail behaviour, which reflects the jumps in the sample paths. On the other hand, the presence of long memory, which contradicts the efficient market hypothesis, is still an issue for further debates. These difficulties present challenges with the problems of memory detection and modelling the co-presence of long memory and heavy tails. This PhD project aims to respond to these challenges. The first part aims to detect memory in a large number of financial time series on stock prices and exchange rates using their scaling properties. Since financial time series often exhibit stochastic trends, a common form of nonstationarity, strong trends in the data can lead to false detection of memory. We will take advantage of a technique known as multifractal detrended fluctuation analysis (MF-DFA) that can systematically eliminate trends of different orders. This method is based on the identification of scaling of the q-th-order moments and is a generalisation of the standard detrended fluctuation analysis (DFA) which uses only the second moment; that is, q = 2. We also consider the rescaled range R/S analysis and the periodogram method to detect memory in financial time series and compare their results with the MF-DFA. An interesting finding is that short memory is detected for stock prices of the American Stock Exchange (AMEX) and long memory is found present in the time series of two exchange rates, namely the French franc and the Deutsche mark. Electricity price series of the five states of Australia are also found to possess long memory. For these electricity price series, heavy tails are also pronounced in their probability densities. The second part of the thesis develops models to represent short-memory and longmemory financial processes as detected in Part I. These models take the form of continuous-time AR(∞) -type equations whose kernel is the Laplace transform of a finite Borel measure. By imposing appropriate conditions on this measure, short memory or long memory in the dynamics of the solution will result. A specific form of the models, which has a good MA(∞) -type representation, is presented for the short memory case. Parameter estimation of this type of models is performed via least squares, and the models are applied to the stock prices in the AMEX, which have been established in Part I to possess short memory. By selecting the kernel in the continuous-time AR(∞) -type equations to have the form of Riemann-Liouville fractional derivative, we obtain a fractional stochastic differential equation driven by Brownian motion. This type of equations is used to represent financial processes with long memory, whose dynamics is described by the fractional derivative in the equation. These models are estimated via quasi-likelihood, namely via a continuoustime version of the Gauss-Whittle method. The models are applied to the exchange rates and the electricity prices of Part I with the aim of confirming their possible long-range dependence established by MF-DFA. The third part of the thesis provides an application of the results established in Parts I and II to characterise and classify financial markets. We will pay attention to the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX), the NASDAQ Stock Exchange (NASDAQ) and the Toronto Stock Exchange (TSX). The parameters from MF-DFA and those of the short-memory AR(∞) -type models will be employed in this classification. We propose the Fisher discriminant algorithm to find a classifier in the two and three-dimensional spaces of data sets and then provide cross-validation to verify discriminant accuracies. This classification is useful for understanding and predicting the behaviour of different processes within the same market. The fourth part of the thesis investigates the heavy-tailed behaviour of financial processes which may also possess long memory. We consider fractional stochastic differential equations driven by stable noise to model financial processes such as electricity prices. The long memory of electricity prices is represented by a fractional derivative, while the stable noise input models their non-Gaussianity via the tails of their probability density. A method using the empirical densities and MF-DFA will be provided to estimate all the parameters of the model and simulate sample paths of the equation. The method is then applied to analyse daily spot prices for five states of Australia. Comparison with the results obtained from the R/S analysis, periodogram method and MF-DFA are provided. The results from fractional SDEs agree with those from MF-DFA, which are based on multifractal scaling, while those from the periodograms, which are based on the second order, seem to underestimate the long memory dynamics of the process. This highlights the need and usefulness of fractal methods in modelling non-Gaussian financial processes with long memory.

Interdisciplinary modelling

This article examines one approach to promoting creative and flexible use of mathematical ideas within an interdisciplinary context in the primary curriculum, namely, through modelling. Three classes of fifth-grade children worked on a modelling problem, The First Fleet (Australia’s settlement), situated within the curriculum domains of science and studies of society and environment. Reported here are the cycles of development displayed by one group of children as they worked the problem, together with the range of models created across the classes. Children developed mathematisation processes that extended beyond their regular curriculum, including identifying and prioritising key problem elements, exploring relationships among elements, quantifying qualitative data, ranking and aggregating data, and creating and working with weighted scores. Aspects of Goldin’s (2000, 2007) affective structures also appeared to play an important role in the children's mathematical developments.