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.

Impact of music therapy to promote positive parenting and child development

The effectiveness of a 10-week group music therapy program for marginalized parents and their children aged 0–5 years was examined. Musical activities were used to promote positive parent–child relationships and children’s behavioral, communicative and social development. Participants were 358 parents and children from families facing social disadvantage, young parents or parents of a child with a disability. Significant improvements were found for therapist-observed parent and child behaviors, and parent-reported irritable parenting, educational activities in the home, parent mental health and child communication and social play skills. This study provides evidence of the potential effectiveness of music therapy for early intervention.

A general approach to control a positive buck-boost converter to achieve robustness against input voltage fluctuations and load changes

A Positive Buck-Boost converter is a known DC-DC converter which may be controlled to act as Buck or Boost converter with same polarity of the input voltage. This converter has four switching states which include all the switching states of the above mentioned DC-DC converters. In addition there is one switching state which provides a degree of freedom for the positive Buck-Boost converter in comparison to the Buck, Boost, and inverting Buck-Boost converters. In other words the Positive Buck-Boost Converter shows a higher level of flexibility for its inductor current control compared to the other DC-DC converters. In this paper this extra degree of freedom is utilised to increase the robustness against input voltage fluctuations and load changes. To address this capacity of the positive Buck-Boost converter, two different control strategies are proposed which control the inductor current and output voltage against any fluctuations in input voltage and load changes. Mathematical analysis for dynamic and steady state conditions are presented in this paper and simulation results verify the proposed method.

The oral health of critically ill children

Introduction. In adults, oral health has been shown to worsen during critical illness as well as influence systemic health. There is a paucity of paediatric critical care research in the area of oral health; hence the purpose of the Critically ill Children’s Oral Health (CCOH) study is to describe the status of oral health of critically ill children over time spent in the paediatric intensive care unit (PICU). The study will also examine the relationship between poor oral health and a variety of patient characteristics and PICU therapies and explore the relationship between dysfunctional oral health and PICU related Healthcare-Associated Infections (HAI). Method. An observational study was undertaken at a single tertiary-referral PICU. Oral health was measured using the Oral Assessment Scale (OAS) and culturing oropharyngeal flora. Information was also collected surrounding the use of supportive therapies, clinical characteristics of the children and the occurrence of PICU related HAI. Results. Forty-six participants were consecutively recruited to the CCOH study. Of the participants 63% (n=32) had oral dysfunction while 41% (n=19) demonstrated pathogenic oropharyngeal colonisation during their critical illness. The potential systemic pathogens isolated from the oropharynx and included Candida sp., Staphylococcus aureus, Haemophilus influenzae, Enterococcus sp. and Pseudomonas aeruginosa. The severity of critical illness had a significant positive relationship (p=0.046) with pathogenic and absent colonisation of the oropharynx. Sixty-three percent of PICU-related HAI involved the preceding or simultaneous colonisation of the oropharynx by the causative pathogen. Conclusion. Given the prevalence of poor oral health during childhood critical illness and the subsequent potential systemic consequences, evidence based oral hygiene practices should be developed and validated to guide clinicians when nursing critically ill children.

Continuous infusion of ticarcillin-clavulanate for home treatment of serious infections : clinical efficacy, safety, pharmacokinetics and pharmacodynamics

Continuous infusion (CI) ticarcillin–clavulanate is a potential therapeutic improvement over conventional intermittent dosing because the major pharmacodynamic (PD) predictor of efficacy of β-lactams is the time that free drug levels exceed the MIC. This study incorporated a 6-year retrospective arm evaluating efficacy and safety of CI ticarcillin–clavulanate in the home treatment of serious infections and a prospective arm additionally evaluating pharmacokinetics (PK) and PD. In the prospective arm, steady-state serum ticarcillin and clavulanate levels and MIC testing of significant pathogens were performed. One hundred and twelve patients (median age, 56 years) were treated with a CI dose of 9.3–12.4 g/day and mean CI duration of 18.0 days. Infections treated included osteomyelitis (50 patients), septic arthritis (6), cellulitis (17), pulmonary infections (12), febrile neutropenia (7), vascular infections (7), intra-abdominal infections (2), and Gram-negative endocarditis (2); 91/112 (81%) of patients were cured, 14 (13%) had partial response and 7 (6%) failed therapy. Nine patients had PICC line complications and five patients had drug adverse events. Eighteen patients had prospective PK/PD assessment although only four patients had sufficient data for a full PK/PD evaluation (both serum steady-state drug levels and ticarcillin and clavulanate MICs from a bacteriological isolate), as this was difficult to obtain in home-based patients, particularly as serum clavulanate levels were found to deteriorate rapidly on storage. Three of four patients with matched PK/PD assessment had free drug levels exceeding the MIC of the pathogen. Home CI of ticarcillin–clavulanate is a safe, effective, convenient and practical therapy and is a therapeutic advance over traditional intermittent dosing when used in the home setting.

Implications of faecal indicator bacteria for the microbiological assessment of roof harvested rainwater quality in Southeast Queensland, Australia

The study aimed to evaluate the suitability of Escherichia coli, enterococci and C. perfringens to assess the microbiological quality of roof harvested rainwater, and to assess whether the concentrations of these faecal indicators can be used to predict the presence or absence of specific zoonotic bacterial or protozoan pathogens. From a total of 100 samples tested, respectively 58%, 83% and 46% of samples were found to be positive for E. coli, enterococci and C. perfringens spores, as determined by traditional culture based methods. Additionally, in the samples tested, 7%, 19%, 1%, 8%, 17%, and 15% were PCR positive for A. hydrophila lip, C. coli ceuE, C. jejuni mapA, L. pneumophila mip, Salmonella invA, and G. lamblia β-giardin genes. However, none of the samples was positive for E. coli O157 LPS, VT1, VT2 and C. parvum COWP genes. The presence or absence of these potential pathogens did not correlate with any of the faecal indicator bacterial concentrations as determined by a binary logistic regression model. The roof-harvested rainwater samples tested in this study appear to be of poor microbiological quality and no significant correlation was found between the concentration of faecal indicators and pathogenic microorganisms. The use of faecal indicator bacteria raises questions regarding their reliability in assessing the microbiological quality of water and particularly their poor correlation with pathogenic microorganisms. The presence of one or more zoonotic pathogens suggests that the microbiological analysis of water should be performed, and appropriate treatment measures should be undertaken especially in tanks where the water is used for drinking.

A new pulsed power supply topology based on positive buck-boost converters concept

Improving efficiency and flexibility in pulsed power supply technologies is the most substantial concern of pulsed power systems specifically with regard to plasma generation. Recently, the improvement of pulsed power supply has become of greater concern due to the extension of pulsed power applications to environmental and industrial areas. With this respect, a current source based topology is proposed in this paper as a pulsed power supply which gives the possibility of power flow control during load supplying mode. The main contribution in this configuration is utilization of low-medium voltage semiconductor switches for high voltage generation. A number of switch-diode-capacitor units are designated at the output of topology to exchange the current source energy into voltage form and generate a pulsed power with sufficient voltage magnitude and stress. Simulations carried out in Matlab/SIMULINK platform as well as experimental tests on a prototype setup have verified the capability of this topology in performing desired duties. Being efficient and flexible are the main advantages of this topology.

Positive relationships among collaboration for innovation, past innovation abandonment and future product introduction in manufacturing SMEs

The importance of collaboration for firm level innovation has been well established but much of the research focuses on large firms, with little research on small and medium enterprises. This paper investigates the links between product innovation and external collaboration and between future product innovation and past abandonment in small and medium sized firms, analysing data from 449 manufacturing firms, collected through the Australian Business Longitudinal Database. Our findings indicate firms that sought ideas or solutions from external network such as suppliers, or business partners reported higher level of new product introduction than firms that did not have any external collaboration. Further, firms with past abandonment experiences reported higher levels of new product introduction than firms that did not have such experience. Additionally, the findings indicated that firms with external collaboration were more likely to introduce new products even if they had previously experienced abandonment of a product innovation than firms without external collaboration. Implications, limitations and future research are outlined.

Positive design and construction of mechanisms for the sustainable development in microenterprises in Africa

Enterprise development and its contribution to societal and economic outcomes are well known. However, limited research into microenterprises and the practices of microfinance and microcredit in developing countries has been carried out. This chapter presents the findings of research based on six years of engagement with the microentrepreneurs of Beira in Mozambique and suggests a model for responsible and sustainable support for enterprise development in developing economies. Building on semistructured interviews, observation, and participatory action research, this research project articulates a new approach supportive of enterprise development, as a process of cocreation with local people and based on sustainability principles. These findings are part of a longitudinal study of the successes and failures of small enterprises and their impact on social and economic activity.

Health risk from the use of roof-harvested rainwater in Southeast Queensland, Australia, as potable or nonpotable water, determined using quantitative microbial risk assessment

A total of 214 rainwater samples from 82 tanks were collected in urban Southeast Queensland (SEQ) in Australia and analysed for the zoonotic bacterial and protozoan pathogen using real-time binary PCR and quantitative PCR (qPCR). Quantitative Microbial Risk Assessment (QMRA) analysis was used to quantify the risk of infection associated with the exposure to potential pathogens from potable and non-potable uses of roof-harvested rainwater. Of the 214 samples tested, 10.7%, 9.8%, and 5.6%, and 0.4% samples were positive for Salmonella invA, Giardia lamblia β-giardin , Legionella pneumophila mip, and Campylobacter jejuni mapA genes. Cryptosporidium parvum could not be detected. The estimated numbers of viable Salmonella spp., G. lamblia β-giradin, and L. pneumophila genes ranged from 1.6 × 101 to 9.5 × 101 cells, 1.4 × 10-1 to 9.0 × 10-1 cysts, and 1.5 × 101 to 4.3 × 101 per 1000 ml of water, respectively. Six risk scenarios were considered from exposure to Salmonella spp., G. lamblia and L. pneumophila. For Salmonella spp., and G. lamblia, these scenarios were: (1) liquid ingestion due to drinking of rainwater on a daily basis (2) accidental liquid ingestion due to garden hosing twice a week (3) aerosol ingestion due to showering on a daily basis, and (4) aerosol ingestion due to hosing twice a week. For L. pneumophila, these scenarios were: (5) aerosol inhalation due to showering on a daily basis, and (6) aerosol inhalation due to hosing twice a week. The risk of infection from Salmonella spp., G. lamblia, and L. pneumophila associated with the use of rainwater for showering and garden hosing was calculated to be well below the threshold value of one extra infection per 10,000 persons per year in urban SEQ. However, the risk of infection from ingesting Salmonella spp. and G. lamblia via drinking exceeds this threshold value, and indicates that if undisinfected rainwater were ingested by drinking, then the gastrointestinal diseases of Salmonellosis and Giardiasis is expected to range from 5.0 × 100 to 2.8 × 101 (Salmonellosis) and 1.0 × 101 to 6.4 × 101 (Giardiasis) cases per 10,000 persons per year, respectively. Since this health risk seems higher than that expected from the reported incidences of gastroenteritis, the assumptions used to estimate these infection risks are critically examined. Nonetheless, it would seem prudent to disinfect rainwater for potable use.

Characterisation of the tritrophic interactions between tobacco yellow dwarf virus, its vector and host-plants

Tobacco yellow dwarf virus (TbYDV, family Geminiviridae, genus Mastrevirus) is an economically important pathogen causing summer death and yellow dwarf disease in bean (Phaseolus vulgaris L.) and tobacco (Nicotiana tabacum L.), respectively. Prior to the commencement of this project, little was known about the epidemiology of TbYDV, its vector and host-plant range. As a result, disease control strategies have been restricted to regular poorly timed insecticide applications which are largely ineffective, environmentally hazardous and expensive. In an effort to address this problem, this PhD project was carried out in order to better understand the epidemiology of TbYDV, to identify its host-plant and vectors as well as to characterise the population dynamics and feeding physiology of the main insect vector and other possible vectors. The host-plants and possible leafhopper vectors of TbYDV were assessed over three consecutive growing seasons at seven field sites in the Ovens Valley, Northeastern Victoria, in commercial tobacco and bean growing properties. Leafhoppers and plants were collected and tested for the presence of TbYDV by PCR. Using sweep nets, twenty-three leafhopper species were identified at the seven sites with Orosius orientalis the predominant leafhopper. Of the 23 leafhopper species screened for TbYDV, only Orosius orientalis and Anzygina zealandica tested positive. Forty-two different plant species were also identified at the seven sites and tested. Of these, TbYDV was only detected in four dicotyledonous species, Amaranthus retroflexus, Phaseolus vulgaris, Nicotiana tabacum and Raphanus raphanistrum. Using a quadrat survey, the temporal distribution and diversity of vegetation at four of the field sites was monitored in order to assess the presence of, and changes in, potential host-plants for the leafhopper vector(s) and the virus. These surveys showed that plant composition and the climatic conditions at each site were the major influences on vector numbers, virus presence and the subsequent occurrence of tobacco yellow dwarf and bean summer death diseases. Forty-two plant species were identified from all sites and it was found that sites with the lowest incidence of disease had the highest proportion of monocotyledonous plants that are non hosts for both vector and the virus. In contrast, the sites with the highest disease incidence had more host-plant species for both vector and virus, and experienced higher temperatures and less rainfall. It is likely that these climatic conditions forced the leafhopper to move into the irrigated commercial tobacco and bean crop resulting in disease. In an attempt to understand leafhopper species diversity and abundance, in and around the field borders of commercially grown tobacco crops, leafhoppers were collected from four field sites using three different sampling techniques, namely pan trap, sticky trap and sweep net. Over 51000 leafhopper samples were collected, which comprised 57 species from 11 subfamilies and 19 tribes. Twentythree leafhopper species were recorded for the first time in Victoria in addition to several economically important pest species of crops other than tobacco and bean. The highest number and greatest diversity of leafhoppers were collected in yellow pan traps follow by sticky trap and sweep nets. Orosius orientalis was found to be the most abundant leafhopper collected from all sites with greatest numbers of this leafhopper also caught using the yellow pan trap. Using the three sampling methods mentioned above, the seasonal distribution and population dynamics of O. orientalis was studied at four field sites over three successive growing seasons. The population dynamics of the leafhopper was characterised by trimodal peaks of activity, occurring in the spring and summer months. Although O. orientalis was present in large numbers early in the growing season (September-October), TbYDV was only detected in these leafhoppers between late November and the end of January. The peak in the detection of TbYDV in O. orientalis correlated with the observation of disease symptoms in tobacco and bean and was also associated with warmer temperatures and lower rainfall. To understand the feeding requirements of Orosius orientalis and to enable screening of potential control agents, a chemically-defined artificial diet (designated PT-07) and feeding system was developed. This novel diet formulation allowed survival for O. orientalis for up to 46 days including complete development from first instar through to adulthood. The effect of three selected plant derived proteins, cowpea trypsin inhibitor (CpTi), Galanthus nivalis agglutinin (GNA) and wheat germ agglutinin (WGA), on leafhopper survival and development was assessed. Both GNA and WGA were shown to reduce leafhopper survival and development significantly when incorporated at a 0.1% (w/v) concentration. In contrast, CpTi at the same concentration did not exhibit significant antimetabolic properties. Based on these results, GNA and WGA are potentially useful antimetabolic agents for expression in genetically modified crops to improve the management of O. orientalis, TbYDV and the other pathogens it vectors. Finally, an electrical penetration graph (EPG) was used to study the feeding behaviour of O. orientalis to provide insights into TbYDV acquisition and transmission. Waveforms representing different feeding activity were acquired by EPG from adult O. orientalis feeding on two plant species, Phaseolus vulgaris and Nicotiana tabacum and a simple sucrose-based artificial diet. Five waveforms (designated O1-O5) were observed when O. orientalis fed on P. vulgaris, while only four (O1-O4) and three (O1-O3) waveforms were observed during feeding on N. tabacum and the artificial diet, respectively. The mean duration of each waveform and the waveform type differed markedly depending on the food source. This is the first detailed study on the tritrophic interactions between TbYDV, its leafhopper vector, O. orientalis, and host-plants. The results of this research have provided important fundamental information which can be used to develop more effective control strategies not only for O. orientalis, but also for TbYDV and other pathogens vectored by the leafhopper.

Positive correlation of male and female Bactrocera tryoni (Froggatt) (Diptera: Tephritidae) catches in orange-ammonia traps

Populations of the Queensland fruit fly, Bactrocera tryoni, are routinely monitored using cue-lure, a male-only attractant. Such monitoring provides no information about females and there is little information available to show if male and female B. tryoni numbers are correlated in the field. Using a data set of 1 148 weekly clearances of orange-ammonia baited traps, which catch both males and females, the correlation between male and female numbers was tested for 48 weeks of the year (four weeks each month) and for the combined data set. Weekly male and female trap catches were almost entirely highly correlated, regardless of mean population size or time of year. For the whole year, the correlation between male and female numbers was r = 0.722, significant at p<0.001. Results suggest that changes in the number if male B. tryoni, as detected through cue-lure sampling, will reflect changes in numbers of female B. tryoni.