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.

New insights into appetite, inflammation and the use of fish oil in hemodialysis patients

Protein-energy wasting (PEW) is commonly seen in patients with chronic kidney disease (CKD). The condition is characterised by chronic, systemic low-grade inflammation which affects nutritional status by a variety of mechanisms including reducing appetite and food intake and increasing muscle catabolism. PEW is linked with co-morbidities such as cardiovascular disease, and is associated with lower quality of life, increased hospitalisations and a 6-fold increase in risk of death1. Significant gender differences have been found in the severity and effects of several markers of PEW. There have been limited studies testing the ability of anti-inflammatory agents or nutritional interventions to reduce the effects of PEW in dialysis patients. This thesis makes a significant contribution to the understanding of PEW in dialysis patients. It advances understanding of measurement techniques for two of the key components, appetite and inflammation, and explores the effect of fish oil, an anti-inflammatory agent, on markers of PEW in dialysis patients. The first part of the thesis consists of two methodological studies conducted using baseline data. The first study aims to validate retrospective ratings of hunger, desire to eat and fullness on visual analog scales (VAS) (paper and pen and electronic) as a new method of measuring appetite in dialysis patients. The second methodological study aims to assess the ability of a variety of methods available in routine practice to detect the presence of inflammation. The second part of the thesis aims to explore the effect of 12 weeks supplementation with 2g per day of Eicosapentaenoic Acid (EPA), a longchain fatty acid found in fish oil, on markers of PEW. A combination of biomarkers and psychomarkers of appetite and inflammation are the main outcomes being explored, with nutritional status, dietary intake and quality of life included as secondary outcomes. A lead in phase of 3 months prior to baseline was used so that each person acts as their own historical control. The study also examines whether there are gender differences in response to the treatment. Being an exploratory study, an important part of the work is to test the feasibility of the intervention, thus the level of adherence and factors associated with adherence are also presented. The studies were conducted at the hemodialysis unit of the Wesley Hospital. Participants met the following criteria: adult, stage 5 CKD on hemodialysis for at least 3 months, not expected to receive a transplant or switch to another dialysis modality during the study, absence of intellectual impairment or mental illness impairing ability to follow instructions or complete the intervention. A range of intermediate, clinical and patient-centred outcome measures were collected at baseline and 12 weeks. Inflammation was measured using five biomarkers: c-reactive protein (CRP), interleukin-6 (IL6), intercellular adhesion molecule (sICAM-1), vascular cell adhesion molecule (sVCAM-1) and white cell count (WCC). Subjective appetite was measured using the first question from the Appetite and Dietary Assessment (ADAT) tool and VAS for measurements of hunger, desire to eat and fullness. A novel feature of the study was the assessment of the appetite peptides leptin, ghrelin and peptide YY as biomarkers of appetite. Nutritional status/inflammation was assessed using the Malnutrition-Inflammation Score (MIS) and the Patient-Generated Subjective Global Assessment (PG-SGA). Dietary intake was measured using 3-day records. Quality of life was measured using the Kidney Disease Quality of Life Short Form version 1.3 (KDQOL-SF™ v1.3 © RAND University), which combines the Short-Form 36 (SF36) with a kidney-disease specific module2. A smaller range of these variables was available for analysis during the control phase (CRP, ADAT, dietary intake and nutritional status). Statistical analysis was carried out using SPSS version 14 (SPSS Inc, Chicago IL, USA). Analysis of the first part of the thesis involved descriptive and bivariate statistics, as well as Bland-Altman plots to assess agreement between methods, and sensitivity analysis/ROC curves to test the ability of methods to predict the presence of inflammation. The unadjusted (paired ttests) and adjusted (linear mixed model) change over time is presented for the main outcome variables of inflammation and appetite. Results are shown for the whole group followed by analyses according to gender and adherence to treatment. Due to the exploratory nature of the study, trends and clinical significance were considered as important as statistical significance. Twenty-eight patients (mean age 61±17y, 50% male, dialysis vintage 19.5 (4- 101) months) underwent baseline assessment. Seven out of 28 patients (25%) reported sub-optimal appetite (self-reported as fair, poor or very poor) despite all being well nourished (100% SGA A). Using the VAS, ratings of hunger, but not desire to eat or fullness, were significantly (p<0.05) associated with a range of relevant clinical variables including age (r=-0.376), comorbidities (r=-0.380) nutritional status (PG-SGA score, r=-0.451), inflammatory markers (CRP r=-0.383; sICAM-1 r=-0.387) and seven domains of quality of life. Patients expressed a preference for the paper and pen method of administering VAS. None of the tools (appetite, MIS, PG-SGA, albumin or iron) showed an acceptable ability to detect patients who are inflamed. It is recommended that CRP should be tested more frequently as a matter of course rather than seeking alternative methods of measuring inflammation. 27 patients completed the 12 week intervention. 20 patients were considered adherent based on changes in % plasma EPA, which rose from 1.3 (0.94)% to 5.2 (1.1)%, p<0.001, in this group. The major barriers to adherence were forgetting to take the tablets as well as their size. At 12 weeks, inflammatory markers remained steady apart from the white cell count which decreased (7.6(2.5) vs 7.0(2.2) x109/L, p=0.058) and sVCAM-1 which increased (1685(654) vs 2249(925) ng/mL, p=0.001). Subjective appetite using VAS increased (51mm to 57mm, +12%) and there was a trend towards reduction in peptide YY (660(31) vs 600(30) pg/mL, p=0.078). There were some gender differences apparent, with the following adjusted change between baseline and week 12: CRP (males -3% vs females +17%, p=0.19), IL6 (males +17% vs females +48%, p=0.77), sICAM-1 (males -5% vs females +11%, p=0.07), sVCAM-1 (males +54% vs females +19%, p=0.08) and hunger ratings (males 20% vs females -5%, p=0.18). On balance, males experienced a maintainence or reduction in three inflammatory markers and an improvement in hunger ratings, and therefore appeared to have responded better to the intervention. Compared to those who didn’t adhere, adherent patients maintained weight (mean(SE) change: +0.5(1.6) vs - 0.8(1.2) kg, p=0.052) and fat-free mass (-0.1 (1.6) vs -1.8 (1.8) kg, p=0.045). There was no difference in change between the intervention and control phase for CRP, appetite, nutritional status or dietary intake. The thesis makes a significant contribution to the evidence base for understanding of PEW in dialysis patients. It has advanced knowledge of methods of assessing inflammation and appetite. Retrospective ratings of hunger on a VAS appear to be a valid method of assessing appetite although samples which include patients with very poor appetite are required to confirm this. Supplementation with fish oil appeared to improve subjective appetite and dampen the inflammatory response. The effectiveness of the intervention is influenced by gender and adherence. Males appear to be more responsive to the primary outcome variables than females, and the quality of response is improved with better adherence. These results provide evidence to support future interventions aimed at reducing the effects of PEW in dialysis patients.

Building the toolkit of quality monitoring clinical outcomes as a means of assessing quality in residential care

Residential aged care in Australia does not have a system of quality assessment related to clinical outcomes, creating a significant gap in quality monitoring. Clinical outcomes represent the results of all inputs into care, thus providing an indication of the success of those inputs. To fill this gap, an assessment tool based on resident outcomes (the ResCareQA) was developed and evaluated in collaboration with residential care providers. A useful output of the ResCareQA is a profile of resident clinical status, and this paper will use such outputs to present a snapshot of nine residential facilities. Such comprehensive data has not yet been available within Australia, so this will provide an important insight. ResCareQA data was collected from all residents (N=498) of nine aged care facilities from two major aged care providers. For each facility, numerator–denominator data were calculated to assess the degree of potential clinical problems. Results varied across clinical areas and across facilities, and rank-ordered facility results for selected clinical areas are reviewed and discussed. Use of the ResCareQA to generate clinical outcome data provides a concrete means of monitoring care quality within residential facilities; regular use of the ResCareQA could thus contribute to improved care outcomes within residential aged care.

Market access of Papua New Guinea bananas (Musa spp.) with particular respect to banana fly (Bactrocera musae (Tryon)) (Diptera: Tephritidae)

International market access for fresh commodities is regulated by international accepted phytosanitary guidelines, the objectives of which are to reduce the biosecurity risk of plant pest and disease movement. Papua New Guinea (PNG) has identified banana as a potential export crop and to help meet international market access requirements, this thesis provides information for the development of a pest risk analysis (PRA) for PNG banana fruit. The PRA is a three step process which first identifies the pests associated with a particular commodity or pathway, then assesses the risk associated with those pests, and finally identifies risk management options for those pests if required. As the first step of the PRA process, I collated a definitive list on the organisms associated with the banana plant in PNG using formal literature, structured interviews with local experts, grey literature and unpublished file material held in PNG field research stations. I identified 112 organisms (invertebrates, vertebrate, pathogens and weeds) associated with banana in PNG, but only 14 of these were reported as commonly requiring management. For these 14 I present detailed information summaries on their known biology and pest impact. A major finding of the review was that of the 14 identified key pests, some research information occurs for 13. The single exception for which information was found to be lacking was Bactrocera musae (Tryon), the banana fly. The lack of information for this widely reported ‘major pest on PNG bananas’ would hinder the development of a PNG banana fruit PRA. For this reason the remainder of the thesis focused on this organism, particularly with respect to generation of information required by the PRA process. Utilising an existing, but previously unanalysed fruit fly trapping database for PNG, I carried out a Geographic Information System analysis of the distribution and abundance of banana in four major regions of PNG. This information is required for a PRA to determine if banana fruit grown in different parts of the country are at different risks from the fly. Results showed that the fly was widespread in all cropping regions and that temperature and rainfall were not significantly correlated with banana fly abundance. Abundance of the fly was significantly correlated (albeit weakly) with host availability. The same analysis was done with four other PNG pest fruit flies and their responses to the environmental factors differed to banana fly and each other. This implies that subsequent PRA analyses for other PNG fresh commodities will need to investigate the risk of each of these flies independently. To quantify the damage to banana fruit caused by banana fly in PNG, local surveys and one national survey of banana fruit infestation were carried out. Contrary to expectations, infestation was found to be very low, particularly in the widely grown commercial cultivar, Cavendish. Infestation of Cavendish fingers was only 0.41% in a structured, national survey of over 2 700 banana fingers. Follow up laboratory studies showed that fingers of Cavendish, and another commercial variety Lady-finger, are very poor hosts for B. musae, with very low host selection rates by female flies and very poor immature survival. An analysis of a recent (within last decade) incursion of B. musae into the Gazelle Peninsula of East New Britain Province, PNG, provided the final set of B. musae data. Surveys of the fly on the peninsular showed that establishment and spread of the fly in the novel environment was very rapid and thus the fly should be regarded as being of high biosecurity concern, at least in tropical areas. Supporting the earlier impact studies, however, banana fly has not become a significant banana fruit problem on the Gazelle, despite bananas being the primary starch staple of the region. The results of the research chapters are combined in the final Discussion in the form of a B. musae focused PRA for PNG banana fruit. Putting the thesis in a broader context, the Discussion also deals with the apparent discrepancy between high local abundance of banana fly and very low infestation rates. This discussion focuses on host utilisation patterns of specialist herbivores and suggests that local pest abundance, as determined by trapping or monitoring, need not be good surrogate for crop damage, despite this linkage being implicit in a number of international phytosanitary protocols.

Design and deployment of a remote robust sensor network : experiences from an outdoor water quality monitoring network

This paper investigates a wireless sensor network deployment - monitoring water quality, e.g. salinity and the level of the underground water table - in a remote tropical area of northern Australia. Our goal is to collect real time water quality measurements together with the amount of water being pumped out in the area, and investigate the impacts of current irrigation practice on the environments, in particular underground water salination. This is a challenging task featuring wide geographic area coverage (mean transmission range between nodes is more than 800 meters), highly variable radio propagations, high end-to-end packet delivery rate requirements, and hostile deployment environments. We have designed, implemented and deployed a sensor network system, which has been collecting water quality and flow measurements, e.g., water flow rate and water flow ticks for over one month. The preliminary results show that sensor networks are a promising solution to deploying a sustainable irrigation system, e.g., maximizing the amount of water pumped out from an area with minimum impact on water quality.

Monitoring and analysis of internet traffic targeting unused address spaces

Today’s evolving networks are experiencing a large number of different attacks ranging from system break-ins, infection from automatic attack tools such as worms, viruses, trojan horses and denial of service (DoS). One important aspect of such attacks is that they are often indiscriminate and target Internet addresses without regard to whether they are bona fide allocated or not. Due to the absence of any advertised host services the traffic observed on unused IP addresses is by definition unsolicited and likely to be either opportunistic or malicious. The analysis of large repositories of such traffic can be used to extract useful information about both ongoing and new attack patterns and unearth unusual attack behaviors. However, such an analysis is difficult due to the size and nature of the collected traffic on unused address spaces. In this dissertation, we present a network traffic analysis technique which uses traffic collected from unused address spaces and relies on the statistical properties of the collected traffic, in order to accurately and quickly detect new and ongoing network anomalies. Detection of network anomalies is based on the concept that an anomalous activity usually transforms the network parameters in such a way that their statistical properties no longer remain constant, resulting in abrupt changes. In this dissertation, we use sequential analysis techniques to identify changes in the behavior of network traffic targeting unused address spaces to unveil both ongoing and new attack patterns. Specifically, we have developed a dynamic sliding window based non-parametric cumulative sum change detection techniques for identification of changes in network traffic. Furthermore we have introduced dynamic thresholds to detect changes in network traffic behavior and also detect when a particular change has ended. Experimental results are presented that demonstrate the operational effectiveness and efficiency of the proposed approach, using both synthetically generated datasets and real network traces collected from a dedicated block of unused IP addresses.

Gender equity in the professoriate : a cohort study of new women professors in Australia

According to statistics and trend data, women continue to be substantially under- represented in the Australian professoriate, and growth in their representation has been slow despite the plethora of equity programs. While not disputing these facts, we propose that examining gender equity by cohort provides a complementary perspective on the status of gender equity in the professoriate. Based on over 500 survey responses, we detected substantial similarities between women and men who were appointed as professors or associate professors between 2005 and 2008. There were similar proportions of women and men appointed via external or internal processes or by invitation. Additionally, similar proportions of women and men professors expressed a marked preference for research over teaching. Furthermore, there were similar distributions between the genders in the age of appointment to the professoriate. However, a notable gender difference was that women were appointed to the professoriate on average 1.9 years later than mens. This later appointment provides one reason for the lower representation of women compared to men in the professoriate. It also raises questions of the typical length of time that women and men remain in the (paid) professoriate and reasons why they might leave it. A further similarity between women and men in this cohort was their identification of motivation and circumstances as key factors in their career orientation. However, substantially more women identified motivation than circumstances and the situation was reversed for men. The open-ended survey responses also provided confirmation that affirmative action initiatives make a difference to women’s careers.

Theory and development of GPS integrity monitoring system

This thesis discusses various aspects of the integrity monitoring of GPS applied to civil aircraft navigation in different phases of flight. These flight phases include en route, terminal, non-precision approach and precision approach. The thesis includes four major topics: probability problem of GPS navigation service, risk analysis of aircraft precision approach and landing, theoretical analysis of Receiver Autonomous Integrity Monitoring (RAIM) techniques and RAIM availability, and GPS integrity monitoring at a ground reference station. Particular attention is paid to the mathematical aspects of the GPS integrity monitoring system. The research has been built upon the stringent integrity requirements defined by civil aviation community, and concentrates on the capability and performance investigation of practical integrity monitoring systems with rigorous mathematical and statistical concepts and approaches. Major contributions of this research are: • Rigorous integrity and continuity risk analysis for aircraft precision approach. Based on the joint probability density function of the affecting components, the integrity and continuity risks of aircraft precision approach with DGPS were computed. This advanced the conventional method of allocating the risk probability. • A theoretical study of RAIM test power. This is the first time a theoretical study on RAIM test power based on the probability statistical theory has been presented, resulting in a new set of RAIM criteria. • Development of a GPS integrity monitoring and DGPS quality control system based on GPS reference station. A prototype of GPS integrity monitoring and DGPS correction prediction system has been developed and tested, based on the A USN A V GPS base station on the roof of QUT ITE Building.

Probability and statistics

Now in its sixth edition, the Traffic Engineering Handbook continues to be a must have publication in the transportation industry, as it has been for the past 60 years. The new edition provides updated information for people entering the practice and for those already practicing. The handbook is a convenient desk reference, as well as an all in one source of principles and proven techniques in traffic engineering. Most chapters are presented in a new format, which divides the chapters into four areas-basics, current practice, emerging trends and information sources. Chapter topics include road users, vehicle characteristics, statistics, planning for operations, communications, safety, regulations, traffic calming, access management, geometrics, signs and markings, signals, parking, traffic demand, maintenance and studies. In addition, as the focus in transportation has shifted from project based to operations based, two new chapters have been added-"Planning for Operations" and "Managing Traffic Demand to Address Congestion: Providing Travelers with Choices." The Traffic Engineering Handbook continues to be one of the primary reference sources for study to become a certified Professional Traffic Operations Engineer™. Chapters are authored by notable and experienced authors, and reviewed and edited by a distinguished panel of traffic engineering experts.

An investigation of rail condition monitoring by Fibre Bragg Grating sensors

Condition monitoring on rails and train wheels is vitally important to the railway asset management and the rail-wheel interactions provide the crucial information of the health state of both rails and wheels. Continuous and remote monitoring is always a preference for operators. With a new generation of strain sensing devices in Fibre Bragg Grating (FBG) sensors, this study explores the possibility of continuous monitoring of the health state of the rails; and investigates the required signal processing techniques and their limitations.

Monitoring of the vertical movements of rail sleepers with the passage of trains

Due to an ever increasing demand for more frequent and higher volume of train service, the physical conditions of tracks in modem railways are deteriorating more quickly when compared to tracks built decades ago. There are incidences in both the UK and Hong Kong indicating there are needs for a more stringent checks on the rail conditions using suitable and effective non-invasive and nondestructive condition monitoring system.

A comprehensive condition monitoring of modern railway

The demand for high quality rail services in the twenty-first century has put an ever increasing demand on all rail operators. In order to meet the expectation of their patrons, the maintenance regime of railway systems has to be tightened up, the track conditions have to be well looked after, the rolling stock must be designed to withstand heavy duty. In short, in an ideal world where resources are unlimited, one needs to implement a very rigorous inspection regime in order to take care of the modem needs of a railway system [1]. If cost were not an issue, the maintenance engineers could inspect the train body by the most up-to-date techniques such as ultra-sound examination, x-ray inspection, magnetic particle inspection, etc. on a regular basis. However it is inconceivable to have such a perfect maintenance regime in any commercial railway. Likewise, it is impossible to have a perfect rolling stock which can weather all the heavy duties experienced in a modem railway. Hence it is essential that some condition monitoring schemes are devised to pick up potential defects which could manifest into safety hazards. This paper introduces an innovative condition monitoring system for track profile and, together with an instrumented car to carry out surveillance of the track, will provide a comprehensive railway condition monitoring system which is free from the usual difficulty of electromagnetic compatibility issues in a typical railway environment

Advances in vegetation management for power line corridor monitoring using aerial remote sensing techniques

This paper presents a comprehensive discussion of vegetation management approaches in power line corridors based on aerial remote sensing techniques. We address three issues 1) strategies for risk management in power line corridors, 2) selection of suitable platforms and sensor suite for data collection and 3) the progress in automated data processing techniques for vegetation management. We present initial results from a series of experiments and, challenges and lessons learnt from our project.