Deeply divergent mitochondrial lineages reveal patterns of local endemism in chironomids of the Australian Wet Tropics

The Wet Tropics bioregion of north-eastern Australia has been subject to extensive fluctuations in climate throughout the late Pliocene and Pleistocene. Cycles of rainforest contraction and expansion of dry sclerophyll forest associated with such climatic fluctuations are postulated to have played a major role in driving geographical endemism in terrestrial rainforest taxa. Consequences for the distributions of aquatic organisms, however, are poorly understood.The Australian non-biting midge species Echinocladius martini Cranston (Diptera: Chironomidae), although restricted to cool, well-forested freshwater streams, has been considered to be able to disperse among populations located in isolated rainforest pockets during periods of sclerophyllous forest expansion, potentially limiting the effect of climatic fluctuations on patterns of endemism. In this study, mitochondrial COI and 16S data were analysed for E. martini collected from eight sites spanning theWet Tropics bioregion to assess the scale and extent of phylogeographic structure. Analyses of genetic structure showed several highly divergent cryptic lineages with restricted geographical distributions. Within one of the identified lineages, strong genetic structure implied that dispersal among proximate (<1 km apart) streams was extremely restricted. The results suggest that vicariant processes, most likely due to the systemic drying of the Australian continent during the Plio-Pleistocene, might have fragmented historical E. martini populations and, hence, promoted divergence in allopatry.

Intelligent prognostics of machinery health utilising suspended condition monitoring data

The ability to forecast machinery failure is vital to reducing maintenance costs, operation downtime and safety hazards. Recent advances in condition monitoring technologies have given rise to a number of prognostic models for forecasting machinery health based on condition data. Although these models have aided the advancement of the discipline, they have made only a limited contribution to developing an effective machinery health prognostic system. The literature review indicates that there is not yet a prognostic model that directly models and fully utilises suspended condition histories (which are very common in practice since organisations rarely allow their assets to run to failure); that effectively integrates population characteristics into prognostics for longer-range prediction in a probabilistic sense; which deduces the non-linear relationship between measured condition data and actual asset health; and which involves minimal assumptions and requirements. This work presents a novel approach to addressing the above-mentioned challenges. The proposed model consists of a feed-forward neural network, the training targets of which are asset survival probabilities estimated using a variation of the Kaplan-Meier estimator and a degradation-based failure probability density estimator. The adapted Kaplan-Meier estimator is able to model the actual survival status of individual failed units and estimate the survival probability of individual suspended units. The degradation-based failure probability density estimator, on the other hand, extracts population characteristics and computes conditional reliability from available condition histories instead of from reliability data. The estimated survival probability and the relevant condition histories are respectively presented as “training target” and “training input” to the neural network. The trained network is capable of estimating the future survival curve of a unit when a series of condition indices are inputted. Although the concept proposed may be applied to the prognosis of various machine components, rolling element bearings were chosen as the research object because rolling element bearing failure is one of the foremost causes of machinery breakdowns. Computer simulated and industry case study data were used to compare the prognostic performance of the proposed model and four control models, namely: two feed-forward neural networks with the same training function and structure as the proposed model, but neglected suspended histories; a time series prediction recurrent neural network; and a traditional Weibull distribution model. The results support the assertion that the proposed model performs better than the other four models and that it produces adaptive prediction outputs with useful representation of survival probabilities. This work presents a compelling concept for non-parametric data-driven prognosis, and for utilising available asset condition information more fully and accurately. It demonstrates that machinery health can indeed be forecasted. The proposed prognostic technique, together with ongoing advances in sensors and data-fusion techniques, and increasingly comprehensive databases of asset condition data, holds the promise for increased asset availability, maintenance cost effectiveness, operational safety and – ultimately – organisation competitiveness.

Krylov subspace methods for approximating functions of symmetric positive definite matrices with applications to applied statistics and anomalous diffusion

Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A^(-α/2)b, where A ∈ ℝ^(n×n) is a large, sparse symmetric positive definite matrix and b ∈ ℝ^n is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LL^T is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L^(-T)z, with x = A^(-1/2)z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form ϕn = A^(-α/2)b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t^(-α/2) and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A^(-α/2)b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.

Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

In this paper, we consider the following non-linear fractional reaction–subdiffusion process (NFR-SubDP): Formula where f(u, x, t) is a linear function of u, the function g(u, x, t) satisfies the Lipschitz condition and 0Dt1–{gamma} is the Riemann–Liouville time fractional partial derivative of order 1 – {gamma}. We propose a new computationally efficient numerical technique to simulate the process. Firstly, the NFR-SubDP is decoupled, which is equivalent to solving a non-linear fractional reaction–subdiffusion equation (NFR-SubDE). Secondly, we propose an implicit numerical method to approximate the NFR-SubDE. Thirdly, the stability and convergence of the method are discussed using a new energy method. Finally, some numerical examples are presented to show the application of the present technique. This method and supporting theoretical results can also be applied to fractional integrodifferential equations.

Use of Bayesian geostatistical prediction to estimate local variations in Schistosoma haematobium infection in western Africa

Objective We aimed to predict sub-national spatial variation in numbers of people infected with Schistosoma haematobium, and associated uncertainties, in Burkina Faso, Mali and Niger, prior to implementation of national control programmes. Methods We used national field survey datasets covering a contiguous area 2,750 × 850 km, from 26,790 school-aged children (5–14 years) in 418 schools. Bayesian geostatistical models were used to predict prevalence of high and low intensity infections and associated 95% credible intervals (CrI). Numbers infected were determined by multiplying predicted prevalence by numbers of school-aged children in 1 km2 pixels covering the study area. Findings Numbers of school-aged children with low-intensity infections were: 433,268 in Burkina Faso, 872,328 in Mali and 580,286 in Niger. Numbers with high-intensity infections were: 416,009 in Burkina Faso, 511,845 in Mali and 254,150 in Niger. 95% CrIs (indicative of uncertainty) were wide; e.g. the mean number of boys aged 10–14 years infected in Mali was 140,200 (95% CrI 6200, 512,100). Conclusion National aggregate estimates for numbers infected mask important local variation, e.g. most S. haematobium infections in Niger occur in the Niger River valley. Prevalence of high-intensity infections was strongly clustered in foci in western and central Mali, north-eastern and northwestern Burkina Faso and the Niger River valley in Niger. Populations in these foci are likely to carry the bulk of the urinary schistosomiasis burden and should receive priority for schistosomiasis control. Uncertainties in predicted prevalence and numbers infected should be acknowledged and taken into consideration by control programme planners.

Numerical investigations of linear least squares methods for derivative estimation

The results of a numerical investigation into the errors for least squares estimates of function gradients are presented. The underlying algorithm is obtained by constructing a least squares problem using a truncated Taylor expansion. An error bound associated with this method contains in its numerator terms related to the Taylor series remainder, while its denominator contains the smallest singular value of the least squares matrix. Perhaps for this reason the error bounds are often found to be pessimistic by several orders of magnitude. The circumstance under which these poor estimates arise is elucidated and an empirical correction of the theoretical error bounds is conjectured and investigated numerically. This is followed by an indication of how the conjecture is supported by a rigorous argument.

Changing the rules in use? An examination of social enterprise in local governance

As multi-stakeholder entities that explicitly inhabit both social and economic domains, social enterprises pose new challenges and possibilities for local governance. In this paper, we draw on new institutional theory to examine the ways in which locally-focused social enterprises disrupt path dependencies and rules in use within local government. Rather than examining the more commonly asked question of the influence of the state on social enterprise, our purpose here is to examine the impacts of social enterprise on governmental institutions at the local level. Our discussion is based on a mixed-methods study, including an online survey of 66 local government staff, document analysis, and in-depth interviews with 24 social enterprise practitioners and local government actors working to support social enterprise development in Victoria, Australia. We find that, in some instances, the hybrid nature of social enterprise facilitates ‘joining up’ between different functional areas of local government. Beyond organisational relationships, social enterprise also influences local governance through the reinterpretation and regeneration of institutionalised public spaces.

Recruiting local public relations professionals for global relations practice : a comparative analysis between Australian and Indian public relations recruitment advertisements

The aim of this exploratory study was to gain an insight into Asian and Western public relations practices by investigating them through job advertisements and thus reflecting on what organisations expect from the public relations professionals. Grunig's (1984) four models of public relations and the concept of relationships management were used as the foundation for this study. Australia was used to represent the Western region and India was used to represent the Asian region. Sample sets of public relations recruitment advertisements from both countries were examined against Grunig's one-way communication, two-way communication and relationship management attributes.