An approximate Bayesian computation approach for estimating parameters of complex environmental processes in a cellular automata

Modelling an environmental process involves creating a model structure and parameterising the model with appropriate values to accurately represent the process. Determining accurate parameter values for environmental systems can be challenging. Existing methods for parameter estimation typically make assumptions regarding the form of the Likelihood, and will often ignore any uncertainty around estimated values. This can be problematic, however, particularly in complex problems where Likelihoods may be intractable. In this paper we demonstrate an Approximate Bayesian Computational method for the estimation of parameters of a stochastic CA. We use as an example a CA constructed to simulate a range expansion such as might occur after a biological invasion, making parameter estimates using only count data such as could be gathered from field observations. We demonstrate ABC is a highly useful method for parameter estimation, with accurate estimates of parameters that are important for the management of invasive species such as the intrinsic rate of increase and the point in a landscape where a species has invaded. We also show that the method is capable of estimating the probability of long distance dispersal, a characteristic of biological invasions that is very influential in determining spread rates but has until now proved difficult to estimate accurately.

An enriched radial point interpolation method based on weak-form and strong-form

In this article, an enriched radial point interpolation method (e-RPIM) is developed for computational mechanics. The conventional radial basis function (RBF) interpolation is novelly augmented by the suitable basis functions to reflect the natural properties of deformation. The performance of the enriched meshless RBF shape functions is first investigated using the surface fitting. The surface fitting results have proven that, compared with the conventional RBF, the enriched RBF interpolation has a much better accuracy to fit a complex surface than the conventional RBF interpolation. It has proven that the enriched RBF shape function will not only possess all advantages of the conventional RBF interpolation, but also can accurately reflect the deformation properties of problems. The system of equations for two-dimensional solids is then derived based on the enriched RBF shape function and both of the meshless strong-form and weak-form. A numerical example of a bar is presented to study the effectiveness and efficiency of e-RPIM. As an important application, the newly developed e-RPIM, which is augmented by selected trigonometric basis functions, is applied to crack problems. It has been demonstrated that the present e-RPIM is very accurate and stable for fracture mechanics problems.

Using Bayesian methods for the estimation of uncertainty in complex statistical models

The research objectives of this thesis were to contribute to Bayesian statistical methodology by contributing to risk assessment statistical methodology, and to spatial and spatio-temporal methodology, by modelling error structures using complex hierarchical models. Specifically, I hoped to consider two applied areas, and use these applications as a springboard for developing new statistical methods as well as undertaking analyses which might give answers to particular applied questions. Thus, this thesis considers a series of models, firstly in the context of risk assessments for recycled water, and secondly in the context of water usage by crops. The research objective was to model error structures using hierarchical models in two problems, namely risk assessment analyses for wastewater, and secondly, in a four dimensional dataset, assessing differences between cropping systems over time and over three spatial dimensions. The aim was to use the simplicity and insight afforded by Bayesian networks to develop appropriate models for risk scenarios, and again to use Bayesian hierarchical models to explore the necessarily complex modelling of four dimensional agricultural data. The specific objectives of the research were to develop a method for the calculation of credible intervals for the point estimates of Bayesian networks; to develop a model structure to incorporate all the experimental uncertainty associated with various constants thereby allowing the calculation of more credible credible intervals for a risk assessment; to model a single day’s data from the agricultural dataset which satisfactorily captured the complexities of the data; to build a model for several days’ data, in order to consider how the full data might be modelled; and finally to build a model for the full four dimensional dataset and to consider the timevarying nature of the contrast of interest, having satisfactorily accounted for possible spatial and temporal autocorrelations. This work forms five papers, two of which have been published, with two submitted, and the final paper still in draft. The first two objectives were met by recasting the risk assessments as directed, acyclic graphs (DAGs). In the first case, we elicited uncertainty for the conditional probabilities needed by the Bayesian net, incorporated these into a corresponding DAG, and used Markov chain Monte Carlo (MCMC) to find credible intervals, for all the scenarios and outcomes of interest. In the second case, we incorporated the experimental data underlying the risk assessment constants into the DAG, and also treated some of that data as needing to be modelled as an ‘errors-invariables’ problem [Fuller, 1987]. This illustrated a simple method for the incorporation of experimental error into risk assessments. In considering one day of the three-dimensional agricultural data, it became clear that geostatistical models or conditional autoregressive (CAR) models over the three dimensions were not the best way to approach the data. Instead CAR models are used with neighbours only in the same depth layer. This gave flexibility to the model, allowing both the spatially structured and non-structured variances to differ at all depths. We call this model the CAR layered model. Given the experimental design, the fixed part of the model could have been modelled as a set of means by treatment and by depth, but doing so allows little insight into how the treatment effects vary with depth. Hence, a number of essentially non-parametric approaches were taken to see the effects of depth on treatment, with the model of choice incorporating an errors-in-variables approach for depth in addition to a non-parametric smooth. The statistical contribution here was the introduction of the CAR layered model, the applied contribution the analysis of moisture over depth and estimation of the contrast of interest together with its credible intervals. These models were fitted using WinBUGS [Lunn et al., 2000]. The work in the fifth paper deals with the fact that with large datasets, the use of WinBUGS becomes more problematic because of its highly correlated term by term updating. In this work, we introduce a Gibbs sampler with block updating for the CAR layered model. The Gibbs sampler was implemented by Chris Strickland using pyMCMC [Strickland, 2010]. This framework is then used to consider five days data, and we show that moisture in the soil for all the various treatments reaches levels particular to each treatment at a depth of 200 cm and thereafter stays constant, albeit with increasing variances with depth. In an analysis across three spatial dimensions and across time, there are many interactions of time and the spatial dimensions to be considered. Hence, we chose to use a daily model and to repeat the analysis at all time points, effectively creating an interaction model of time by the daily model. Such an approach allows great flexibility. However, this approach does not allow insight into the way in which the parameter of interest varies over time. Hence, a two-stage approach was also used, with estimates from the first-stage being analysed as a set of time series. We see this spatio-temporal interaction model as being a useful approach to data measured across three spatial dimensions and time, since it does not assume additivity of the random spatial or temporal effects.

Complex modelling in the primary/middle school years

The world’s increasing complexity, competitiveness, interconnectivity, and dependence on technology generate new challenges for nations and individuals that cannot be met by continuing education as usual (Katehi, Pearson, & Feder, 2009). With the proliferation of complex systems have come new technologies for communication, collaboration, and conceptualisation. These technologies have led to significant changes in the forms of mathematical and scientific thinking that are required beyond the classroom. Modelling, in its various forms, can develop and broaden children’s mathematical and scientific thinking beyond the standard curriculum. This paper first considers future competencies in the mathematical sciences within an increasingly complex world. Next, consideration is given to interdisciplinary problem solving and models and modelling. Examples of complex, interdisciplinary modelling activities across grades are presented, with data modelling in 1st grade, model-eliciting in 4th grade, and engineering-based modelling in 7th-9th grades.

Complex learning through cognitively demanding tasks

The world’s increasing complexity, competitiveness, interconnectivity, and dependence on technology generate new challenges for nations and individuals that cannot be met by “continuing education as usual” (The National Academies, 2009). With the proliferation of complex systems have come new technologies for communication, collaboration, and conceptualization. These technologies have led to significant changes in the forms of mathematical thinking that are required beyond the classroom. This paper argues for the need to incorporate future-oriented understandings and competencies within the mathematics curriculum, through intellectually stimulating activities that draw upon multidisciplinary content and contexts. The paper also argues for greater recognition of children’s learning potential, as increasingly complex learners capable of dealing with cognitively demanding tasks.

Mathematics and complex learning

There is unprecedented worldwide demand for mathematical solutions to complex problems. That demand has generated a further call to update mathematics education in a way that develops students’ abilities to deal with complex systems.

Impact of a data warehouse model for improved decision-making process in healthcare

The health system is one sector dealing with a deluge of complex data. Many healthcare organisations struggle to utilise these volumes of health data effectively and efficiently. Also, there are many healthcare organisations, which still have stand-alone systems, not integrated for management of information and decision-making. This shows, there is a need for an effective system to capture, collate and distribute this health data. Therefore, implementing the data warehouse concept in healthcare is potentially one of the solutions to integrate health data. Data warehousing has been used to support business intelligence and decision-making in many other sectors such as the engineering, defence and retail sectors. The research problem that is going to be addressed is, "how can data warehousing assist the decision-making process in healthcare". To address this problem the researcher has narrowed an investigation focusing on a cardiac surgery unit. This research used the cardiac surgery unit at the Prince Charles Hospital (TPCH) as the case study. The cardiac surgery unit at TPCH uses a stand-alone database of patient clinical data, which supports clinical audit, service management and research functions. However, much of the time, the interaction between the cardiac surgery unit information system with other units is minimal. There is a limited and basic two-way interaction with other clinical and administrative databases at TPCH which support decision-making processes. The aims of this research are to investigate what decision-making issues are faced by the healthcare professionals with the current information systems and how decision-making might be improved within this healthcare setting by implementing an aligned data warehouse model or models. As a part of the research the researcher will propose and develop a suitable data warehouse prototype based on the cardiac surgery unit needs and integrating the Intensive Care Unit database, Clinical Costing unit database (Transition II) and Quality and Safety unit database [electronic discharge summary (e-DS)]. The goal is to improve the current decision-making processes. The main objectives of this research are to improve access to integrated clinical and financial data, providing potentially better information for decision-making for both improved from the questionnaire and by referring to the literature, the results indicate a centralised data warehouse model for the cardiac surgery unit at this stage. A centralised data warehouse model addresses current needs and can also be upgraded to an enterprise wide warehouse model or federated data warehouse model as discussed in the many consulted publications. The data warehouse prototype was able to be developed using SAS enterprise data integration studio 4.2 and the data was analysed using SAS enterprise edition 4.3. In the final stage, the data warehouse prototype was evaluated by collecting feedback from the end users. This was achieved by using output created from the data warehouse prototype as examples of the data desired and possible in a data warehouse environment. According to the feedback collected from the end users, implementation of a data warehouse was seen to be a useful tool to inform management options, provide a more complete representation of factors related to a decision scenario and potentially reduce information product development time. However, there are many constraints exist in this research. For example the technical issues such as data incompatibilities, integration of the cardiac surgery database and e-DS database servers and also, Queensland Health information restrictions (Queensland Health information related policies, patient data confidentiality and ethics requirements), limited availability of support from IT technical staff and time restrictions. These factors have influenced the process for the warehouse model development, necessitating an incremental approach. This highlights the presence of many practical barriers to data warehousing and integration at the clinical service level. Limitations included the use of a small convenience sample of survey respondents, and a single site case report study design. As mentioned previously, the proposed data warehouse is a prototype and was developed using only four database repositories. Despite this constraint, the research demonstrates that by implementing a data warehouse at the service level, decision-making is supported and data quality issues related to access and availability can be reduced, providing many benefits. Output reports produced from the data warehouse prototype demonstrated usefulness for the improvement of decision-making in the management of clinical services, and quality and safety monitoring for better clinical care. However, in the future, the centralised model selected can be upgraded to an enterprise wide architecture by integrating with additional hospital units’ databases.

Navigating a complex organizational landscape : leadership challenges and practices

This paper discusses exploratory research to identify the reported leadership challenges faced by leaders in the public sector in Australia and what specific leadership practices they engage in to deal with these challenges. Emerging is a sense that leadership in these complex work environments is not about controlling or mandating action but about engaging in conversation, building relationships and empowering staff to engage in innovative ways to solve complex problems. In addition leaders provide a strong sense of purpose and identity to guide behaviour and decisions to overcome being overwhelmed by the sheer volume of demands in a unpredictable and often unsupportive environment. Questions are raised as to the core competencies leaders need to develop to drive and underpin these leadership practices and the implications this has for the focus on future leadership development programmes. The possible direction of a future research programme will be put forward for further discussion.

Event-related brain potentials dissociate the developmental time-course of automatic numerical magnitude analysis and cognitive control functions during the first three years of primary school

In this study we set out to dissociate the developmental time course of automatic symbolic number processing and cognitive control functions in grade 1-3 British primary school children. Event-related potential (ERP) and behavioral data were collected in a physical size discrimination numerical Stroop task. Task-irrelevant numerical information was processed automatically already in grade 1. Weakening interference and strengthening facilitation indicated the parallel development of general cognitive control and automatic number processing. Relationships among ERP and behavioral effects suggest that control functions play a larger role in younger children and that automaticity of number processing increases from grade 1 to 3.

Complexity, evolution, and the structure of demand

This chapter argues that evolutionary economics should be founded upon complex systems theory rather than neo-Darwinian analogies concerning natural selection, which focus on supply side considerations and competition amongst firms and technologies. It suggests that conceptions such as production and consumption functions should be replaced by network representations, in which the preferences or, more correctly, the aspirations of consumers are fundamental and, as such, the primary drivers of economic growth. Technological innovation is viewed as a process that is intermediate between these aspirational networks, and the organizational networks in which goods and services are produced. Consumer knowledge becomes at least as important as producer knowledge in determining how economic value is generated. It becomes clear that the stability afforded by connective systems of rules is essential for economic flexibility to exist, but that too many rules result in inert and structurally unstable states. In contrast, too few rules result in a more stable state, but at a low level of ordered complexity. Economic evolution from this perspective is explored using random and scale free network representations of complex systems.

Charting the system : the integrated master schedule as a multi-level and poly-temporal boundary object in complex projects

This paper investigates the use of visual artifacts to represent a complex adaptive system (CAS). The integrated master schedule (IMS) is one of those visuals widely used in complex projects for scheduling, budgeting, and project management. In this paper, we discuss how the IMS outperforms the traditional timelines and acts as a ‘multi-level and poly-temporal boundary object’ that visually represents the CAS. We report the findings of a case study project on the way the IMS mapped interactions, interdependencies, constraints and fractal patterns in a complex project. Finally, we discuss how the IMS was utilised as a complex boundary object by eliciting commitment and development of shared mental models, and facilitating negotiation through the layers of multiple interpretations from stakeholders.

A multi-level model of leadership in complex project management

Management (or perceived mismanagement) of large-scale, complex projects poses special problems and often results in spectacular failures, cost overruns, time blowouts and stakeholder dissatisfaction. While traditional project management responds with increasingly administrative constraints, we argue that leaders of such projects also need to display adaptive and enabling behaviours to foster adaptive processes, such as opportunity recognition, which requires an interaction of cognitive and affective processes of individual, project, and team leader attributes and behaviours. At the core of this model we propose is an interaction of cognitive flexibility, affect and emotional intelligence. The result of this interaction is enhanced leader opportunity recognition that, in turn, facilitates multilevel outcomes.

Person-environment fit: project leader-stakeholder relationships in a complex project environment

In this paper, we develop a conceptual model to explore the perceived complementary congruence between complex project leaders and the demands of the complex project environment to understand how leaders’ affective and behavioural performance at work might be impacted by this fit. We propose that complex project leaders high in emotional intelligence and cognitive flexibility should report a higher level of fit between themselves and the complex project environment. This abilities-demands measure of fit should then relate to affective and behavioural performance outcomes, such that leaders who perceive a higher level of fit should establish and maintain more effective, higher quality project stakeholder relationships than leaders who perceive a lower level of fit.

Fuzzy methods for analysis of microarrays and networks

Bioinformatics involves analyses of biological data such as DNA sequences, microarrays and protein-protein interaction (PPI) networks. Its two main objectives are the identification of genes or proteins and the prediction of their functions. Biological data often contain uncertain and imprecise information. Fuzzy theory provides useful tools to deal with this type of information, hence has played an important role in analyses of biological data. In this thesis, we aim to develop some new fuzzy techniques and apply them on DNA microarrays and PPI networks. We will focus on three problems: (1) clustering of microarrays; (2) identification of disease-associated genes in microarrays; and (3) identification of protein complexes in PPI networks. The first part of the thesis aims to detect, by the fuzzy C-means (FCM) method, clustering structures in DNA microarrays corrupted by noise. Because of the presence of noise, some clustering structures found in random data may not have any biological significance. In this part, we propose to combine the FCM with the empirical mode decomposition (EMD) for clustering microarray data. The purpose of EMD is to reduce, preferably to remove, the effect of noise, resulting in what is known as denoised data. We call this method the fuzzy C-means method with empirical mode decomposition (FCM-EMD). We applied this method on yeast and serum microarrays, and the silhouette values are used for assessment of the quality of clustering. The results indicate that the clustering structures of denoised data are more reasonable, implying that genes have tighter association with their clusters. Furthermore we found that the estimation of the fuzzy parameter m, which is a difficult step, can be avoided to some extent by analysing denoised microarray data. The second part aims to identify disease-associated genes from DNA microarray data which are generated under different conditions, e.g., patients and normal people. We developed a type-2 fuzzy membership (FM) function for identification of diseaseassociated genes. This approach is applied to diabetes and lung cancer data, and a comparison with the original FM test was carried out. Among the ten best-ranked genes of diabetes identified by the type-2 FM test, seven genes have been confirmed as diabetes-associated genes according to gene description information in Gene Bank and the published literature. An additional gene is further identified. Among the ten best-ranked genes identified in lung cancer data, seven are confirmed that they are associated with lung cancer or its treatment. The type-2 FM-d values are significantly different, which makes the identifications more convincing than the original FM test. The third part of the thesis aims to identify protein complexes in large interaction networks. Identification of protein complexes is crucial to understand the principles of cellular organisation and to predict protein functions. In this part, we proposed a novel method which combines the fuzzy clustering method and interaction probability to identify the overlapping and non-overlapping community structures in PPI networks, then to detect protein complexes in these sub-networks. Our method is based on both the fuzzy relation model and the graph model. We applied the method on several PPI networks and compared with a popular protein complex identification method, the clique percolation method. For the same data, we detected more protein complexes. We also applied our method on two social networks. The results showed our method works well for detecting sub-networks and give a reasonable understanding of these communities.