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.

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.

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.

Evaluation of novel Streptococcus pyogenes vaccine candidates incorporating multiple conserved sequences from the C-repeat region of the M-protein

A major challenge for Streptococcus pyogenes vaccine development is the identification of epitopes that confer protection from infection by multiple S. pyogenes M-types. Here we have identified and characterised the distribution of common variant sequences from individual repeat units of the C-repeat region (CRR) of M-proteins representing 77 different M-types. Three polyvalent fusion vaccine candidates (SV1, SV2 and SV3) incorporating the most common variants were subsequently expressed and purified, and demonstrated to be alpha-helical by Circular Dichroism (CD), a secondary conformational characteristic of the CRR in the M-protein. Antibodies raised against each of these constructs recognise M-proteins that vary in their CRR, and bind to the surface of multiple S. pyogenes isolates. Antibodies raised against SV1, containing five variant sequences, also kill heterologous S. pyogenes isolates in in vitro bactericidal assays. Further structural characterisation of this construct demonstrated the conformation of SV1 was stable at different pHs, and thermal unfolding of SV1 a reversible process. Our findings demonstrate that linkage of multiple variant sequences into a single recombinant construct overcomes the need to embed the variant sequences in foreign helix promoting flanking sequences for conformational stability, and demonstrates the viability of the polyvalent candidates as global S. pyogenes vaccine candidates.

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.

The social orders of family mealtime

This study examined the everyday practices of families within the context of family mealtime to investigate how members accomplished mealtime interactions. Using an ethnomethodological approach, conversation analysis and membership categorization analysis, the study investigated the interactional resources that family members used to assemble their social orders moment by moment during family mealtimes. While there is interest in mealtimes within educational policy, health research and the media, there remain few studies that provide fine-grained detail about how members produce the social activity of having a family meal. Findings from this study contribute empirical understandings about families and family mealtime. Two families with children aged 2 to 10 years were observed as they accomplished their everyday mealtime activities. Data collection took place in the family homes where family members video recorded their naturally occurring mealtimes. Each family was provided with a video camera for a one-month period and they decided which mealtimes they recorded, a method that afforded participants greater agency in the data collection process and made available to the analyst a window into the unfolding of the everyday lives of the families. A total of 14 mealtimes across the two families were recorded, capturing 347 minutes of mealtime interactions. Selected episodes from the data corpus, which includes centralised breakfast and dinnertime episodes, were transcribed using the Jeffersonian system. Three data chapters examine extended sequences of family talk at mealtimes, to show the interactional resources used by members during mealtime interactions. The first data chapter explores multiparty talk to show how the uniqueness of the occasion of having a meal influences turn design. It investigates the ways in which members accomplish two-party talk within a multiparty setting, showing how one child "tells" a funny story to accomplish the drawing together of his brothers as an audience. As well, this chapter identifies the interactional resources used by the mother to cohort her children to accomplish the choralling of grace. The second data chapter draws on sequential and categorical analysis to show how members are mapped to a locally produced membership category. The chapter shows how the mapping of members into particular categories is consequential for social order; for example, aligning members who belong to the membership category "had haircuts" and keeping out those who "did not have haircuts". Additional interactional resources such as echoing, used here to refer to the use of exactly the same words, similar prosody and physical action, and increasing physical closeness, are identified as important to the unfolding talk particularly as a way of accomplishing alignment between the grandmother and grand-daughter. The third and final data analysis chapter examines topical talk during family mealtimes. It explicates how members introduce topics of talk with an orientation to their co-participant and the way in which the take up of a topic is influenced both by the sequential environment in which it is introduced and the sensitivity of the topic. Together, these three data chapters show aspects of how family members participated in family mealtimes. The study contributes four substantive themes that emerged during the analytic process and, as such, the themes reflect what the members were observed to be doing. The first theme identified how family knowledge was relevant and consequential for initiating and sustaining interaction during mealtime with, for example, members buying into the talk of other members or being requested to help out with knowledge about a shared experience. Knowledge about members and their activities was evident with the design of questions evidencing an orientation to coparticipant’s knowledge. The second theme found how members used topic as a resource for social interaction. The third theme concerned the way in which members utilised membership categories for producing and making sense of social action. The fourth theme, evident across all episodes selected for analysis, showed how children’s competence is an ongoing interactional accomplishment as they manipulated interactional resources to manage their participation in family mealtime. The way in which children initiated interactions challenges previous understandings about children’s restricted rights as conversationalists. As well as making a theoretical contribution, the study offers methodological insight by working with families as research participants. The study shows the procedures involved as the study moved from one where the researcher undertook the decisions about what to videorecord to offering this decision making to the families, who chose when and what to videorecord of their mealtime practices. Evident also are the ways in which participants orient both to the video-camera and to the absent researcher. For the duration of the mealtime the video-camera was positioned by the adults as out of bounds to the children; however, it was offered as a "treat" to view after the mealtime was recorded. While situated within family mealtimes and reporting on the experiences of two families, this study illuminates how mealtimes are not just about food and eating; they are social. The study showed the constant and complex work of establishing and maintaining social orders and the rich array of interactional resources that members draw on during family mealtimes. The family’s interactions involved members contributing to building the social orders of family mealtime. With mealtimes occurring in institutional settings involving young children, such as long day care centres and kindergartens, the findings of this study may help educators working with young children to see the rich interactional opportunities mealtimes afford children, the interactional competence that children demonstrate during mealtimes, and the important role/s that adults may assume as co-participants in interactions with children within institutional settings.

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.

Multifractal characterisation and analysis of complex networks

Complex networks have been studied extensively due to their relevance to many real-world systems such as the world-wide web, the internet, biological and social systems. During the past two decades, studies of such networks in different fields have produced many significant results concerning their structures, topological properties, and dynamics. Three well-known properties of complex networks are scale-free degree distribution, small-world effect and self-similarity. The search for additional meaningful properties and the relationships among these properties is an active area of current research. This thesis investigates a newer aspect of complex networks, namely their multifractality, which is an extension of the concept of selfsimilarity. The first part of the thesis aims to confirm that the study of properties of complex networks can be expanded to a wider field including more complex weighted networks. Those real networks that have been shown to possess the self-similarity property in the existing literature are all unweighted networks. We use the proteinprotein interaction (PPI) networks as a key example to show that their weighted networks inherit the self-similarity from the original unweighted networks. Firstly, we confirm that the random sequential box-covering algorithm is an effective tool to compute the fractal dimension of complex networks. This is demonstrated on the Homo sapiens and E. coli PPI networks as well as their skeletons. Our results verify that the fractal dimension of the skeleton is smaller than that of the original network due to the shortest distance between nodes is larger in the skeleton, hence for a fixed box-size more boxes will be needed to cover the skeleton. Then we adopt the iterative scoring method to generate weighted PPI networks of five species, namely Homo sapiens, E. coli, yeast, C. elegans and Arabidopsis Thaliana. By using the random sequential box-covering algorithm, we calculate the fractal dimensions for both the original unweighted PPI networks and the generated weighted networks. The results show that self-similarity is still present in generated weighted PPI networks. This implication will be useful for our treatment of the networks in the third part of the thesis. The second part of the thesis aims to explore the multifractal behavior of different complex networks. Fractals such as the Cantor set, the Koch curve and the Sierspinski gasket are homogeneous since these fractals consist of a geometrical figure which repeats on an ever-reduced scale. Fractal analysis is a useful method for their study. However, real-world fractals are not homogeneous; there is rarely an identical motif repeated on all scales. Their singularity may vary on different subsets; implying that these objects are multifractal. Multifractal analysis is a useful way to systematically characterize the spatial heterogeneity of both theoretical and experimental fractal patterns. However, the tools for multifractal analysis of objects in Euclidean space are not suitable for complex networks. In this thesis, we propose a new box covering algorithm for multifractal analysis of complex networks. This algorithm is demonstrated in the computation of the generalized fractal dimensions of some theoretical networks, namely scale-free networks, small-world networks, random networks, and a kind of real networks, namely PPI networks of different species. Our main finding is the existence of multifractality in scale-free networks and PPI networks, while the multifractal behaviour is not confirmed for small-world networks and random networks. As another application, we generate gene interactions networks for patients and healthy people using the correlation coefficients between microarrays of different genes. Our results confirm the existence of multifractality in gene interactions networks. This multifractal analysis then provides a potentially useful tool for gene clustering and identification. The third part of the thesis aims to investigate the topological properties of networks constructed from time series. Characterizing complicated dynamics from time series is a fundamental problem of continuing interest in a wide variety of fields. Recent works indicate that complex network theory can be a powerful tool to analyse time series. Many existing methods for transforming time series into complex networks share a common feature: they define the connectivity of a complex network by the mutual proximity of different parts (e.g., individual states, state vectors, or cycles) of a single trajectory. In this thesis, we propose a new method to construct networks of time series: we define nodes by vectors of a certain length in the time series, and weight of edges between any two nodes by the Euclidean distance between the corresponding two vectors. We apply this method to build networks for fractional Brownian motions, whose long-range dependence is characterised by their Hurst exponent. We verify the validity of this method by showing that time series with stronger correlation, hence larger Hurst exponent, tend to have smaller fractal dimension, hence smoother sample paths. We then construct networks via the technique of horizontal visibility graph (HVG), which has been widely used recently. We confirm a known linear relationship between the Hurst exponent of fractional Brownian motion and the fractal dimension of the corresponding HVG network. In the first application, we apply our newly developed box-covering algorithm to calculate the generalized fractal dimensions of the HVG networks of fractional Brownian motions as well as those for binomial cascades and five bacterial genomes. The results confirm the monoscaling of fractional Brownian motion and the multifractality of the rest. As an additional application, we discuss the resilience of networks constructed from time series via two different approaches: visibility graph and horizontal visibility graph. Our finding is that the degree distribution of VG networks of fractional Brownian motions is scale-free (i.e., having a power law) meaning that one needs to destroy a large percentage of nodes before the network collapses into isolated parts; while for HVG networks of fractional Brownian motions, the degree distribution has exponential tails, implying that HVG networks would not survive the same kind of attack.

Bayesian mixtures for modelling complex medical data : a case study in Parkinson’s disease

Mixture models are a flexible tool for unsupervised clustering that have found popularity in a vast array of research areas. In studies of medicine, the use of mixtures holds the potential to greatly enhance our understanding of patient responses through the identification of clinically meaningful clusters that, given the complexity of many data sources, may otherwise by intangible. Furthermore, when developed in the Bayesian framework, mixture models provide a natural means for capturing and propagating uncertainty in different aspects of a clustering solution, arguably resulting in richer analyses of the population under study. This thesis aims to investigate the use of Bayesian mixture models in analysing varied and detailed sources of patient information collected in the study of complex disease. The first aim of this thesis is to showcase the flexibility of mixture models in modelling markedly different types of data. In particular, we examine three common variants on the mixture model, namely, finite mixtures, Dirichlet Process mixtures and hidden Markov models. Beyond the development and application of these models to different sources of data, this thesis also focuses on modelling different aspects relating to uncertainty in clustering. Examples of clustering uncertainty considered are uncertainty in a patient’s true cluster membership and accounting for uncertainty in the true number of clusters present. Finally, this thesis aims to address and propose solutions to the task of comparing clustering solutions, whether this be comparing patients or observations assigned to different subgroups or comparing clustering solutions over multiple datasets. To address these aims, we consider a case study in Parkinson’s disease (PD), a complex and commonly diagnosed neurodegenerative disorder. In particular, two commonly collected sources of patient information are considered. The first source of data are on symptoms associated with PD, recorded using the Unified Parkinson’s Disease Rating Scale (UPDRS) and constitutes the first half of this thesis. The second half of this thesis is dedicated to the analysis of microelectrode recordings collected during Deep Brain Stimulation (DBS), a popular palliative treatment for advanced PD. Analysis of this second source of data centers on the problems of unsupervised detection and sorting of action potentials or "spikes" in recordings of multiple cell activity, providing valuable information on real time neural activity in the brain.