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.

Cardiac ARIA Index: Measuring Accessibility to Cardiovascular Services in Rural and Remote Australia via Applied Geographic Spatial Technology

Cardiovascular disease (CVD) continues to impose a heavy burden in terms of cost, disability and death in Australia. Evidence suggests that increasing remoteness, where cardiac services are scarce, is linked to an increased risk of dying from CVD. Fatal CVD events are reported to be between 20% and 50% higher in rural areas compared to major cities. The Cardiac ARIA project, with its extensive use of geographic Information Systems (GIS), ranks each of Australia’s 20,387 urban, rural and remote population centres by accessibility to essential services or resources for the management of a cardiac event. This unique, innovative and highly collaborative project delivers a powerful tool to highlight and combat the burden imposed by cardiovascular disease (CVD) in Australia. Cardiac ARIA is innovative. It is a model that could be applied internationally and to other acute and chronic conditions such as mental health, midwifery, cancer, respiratory, diabetes and burns services. Cardiac ARIA was designed to: 1. Determine by expert panel, what were the minimal services and resources required for the management of a cardiac event in any urban, rural or remote population locations in Australia using a single patient pathway to access care. 2. Derive a classification using GIS accessibility modelling for each of Australia’s 20,387 urban, rural and remote population locations. 3. Compare the Cardiac ARIA categories and population locations with census derived population characteristics. Key findings are as follows: • In the event of a cardiac emergency, the majority of Australians had very good access to cardiac services. Approximately 71% or 13.9 million people lived within one hour of a category one hospital. • 68% of older Australians lived within one hour of a category one hospital (Principal Referral Hospital with access to Cardiac Catheterisation). • Only 40% of indigenous people lived within one hour of the category one hospital. • 16% (74000) of indigenous people lived more than one hour from a hospital. • 3% (91,000) of people 65 years of age or older lived more than one hour from any hospital or clinic. • Approximately 96%, or 19 million, of people lived within one hour of the four key services to support cardiac rehabilitation and secondary prevention. • 75% of indigenous people lived within one hour of the four cardiac rehabilitation services to support cardiac rehabilitation and secondary prevention. Fourteen percent (64,000 persons) indigenous people had poor access to the four key services to support cardiac rehabilitation and secondary prevention. • 12% (56,000) of indigenous people were more than one hour from a hospital and only had access one the four key services (usually a medical service) to support cardiac rehabilitation and secondary prevention.

Thomas Young’s investigations in gradient-index optics

Purpose: James Clerk Maxwell is usually recognized as being the first, in 1854, to consider using inhomogeneous media in optical systems. However, some fifty years earlier Thomas Young, stimulated by his interest in the optics of the eye and accommodation, had already modeled some applications of gradient-index optics. These applications included using an axial gradient to provide spherical aberration-free optics and a spherical gradient to describe the optics of the atmosphere and the eye lens. We evaluated Young’s contributions. Method: We attempted to derive Young’s equations for axial and spherical refractive index gradients. Raytracing was used to confirm accuracy of formula. Results: We did not confirm Young’s equation for the axial gradient to provide aberration-free optics, but derived a slightly different equation. We confirmed the correctness of his equations for deviation of rays in a spherical gradient index and for the focal length of a lens with a nucleus of fixed index surrounded by a cortex of reducing index towards the edge. Young claimed that the equation for focal length applied to a lens with part of the constant index nucleus of the sphere removed, such that the loss of focal length was a quarter of the thickness removed, but this is not strictly correct. Conclusion: Young’s theoretical work in gradient-index optics received no acknowledgement from either his contemporaries or later authors. While his model of the eye lens is not an accurate physiological description of the human lens, with the index reducing least quickly at the edge, it represented a bold attempt to approximate the characteristics of the lens. Thomas Young’s work deserves wider recognition.

Can the Cardiac ARIA Index Improve Cardiac Care for Australia's Indigenous Population?

Background: Timely access to appropriate cardiac care is critical for optimising outcomes. Our aim was to derive an objective, comparable, geographic measure reflecting access to cardiac services for Australia's 20,387 population locations. Methods: An expert panel defined a single patient care pathway. Using geographic information systems (GIS) the numeric/alpha index was modelled in two phases. The acute phase index (numeric) ranged from 1 (access to tertiary centre with PCI ≤1 h) to 8 (no ambulance service, >3 h to medical facility, air transport required). The aftercare index was modelled into 5 alphabetic categories; A (Access to general practitioner, pharmacy, cardiac rehabilitation, pathology ≤1 h) to E (no services available within 1 h). Results: Approximately 70% or 13.9 million people lived within a CardiacARIAindex category 1A location. Disparity continues in access to category 1A cardiac services for 5.8 million (30%) of all Australians, 60% of Aboriginal and Torres Strait Islander people and 32% of people over 65 years of age. In a cardiac emergency only 40% of the Indigenous population reside within one hour of category 1 hospital. Approximately 30% (81,491 Indigenous persons) are more than one to three hours from basic cardiac services. Conclusion: Geographically, the majority of Australian's have timely access for survival of a cardiac event. The CardiacARIAindex objectively demonstrates that the healthcare system may not be providing for the needs of 60% of Indigenous people residing outside the 1A geographic radius. Innovative clinical practice maybe required to address these disparities.

Where not to have a Heart Attack in Australia!: The Cardiac ARIA Index

Background/aims: Access to appropriate health care following an acute cardiac event is important for positive outcomes. The aim of the Cardiac ARIA index was to derive an objective, comparable, geographic measure reflecting access to cardiac services across Australia. Methods: Geographic Information Systems (GIS) were used to model a numeric-alpha index based on acute management from onset of symptoms to return to the community. Acute time frames have been calculated to include time for ambulance to arrive, assess and load patient, and travel to facility by road 40–80 kph. Results: The acute phase of the index was modelled into five categories: 1 [24/7 percutaneous cardiac intervention (PCI) ≤1 h]; 2 [24/7 PCI 1–3 h, and PCI less than an additional hour to nearest accident and emergency room (A&E)]: 3 [Nearest A&E ≤3 h (no 24/7 PCI within an extra hour)]: 4 [Nearest A&E 3–12 h (no 24/7 PCI within an extra hour)]: 5 [Nearest A&E 12–24 h (no 24/7 PCI within an extra hour)]. Discharge care was modelled into three categories based on time to a cardiac rehabilitation program, retail pharmacy, pathology services, hospital, GP or remote clinic: (A) all services ≤30 min; (B) >30 min and ≤60 min; (C) >60 min. Examples of the index indicate that the majority of population locations within capital cities were category 1A; Alice Springs and Byron Bay were 3A; and the Northern Territory town of Maningrida had minimal access to cardiac services with an index ranking of 5C. Conclusion: The Cardiac ARIA index provides an invaluable tool to inform appropriate strategies for the use of scarce cardiac resources.

Improving Indigenous women’s wellness through action research

Today in Australia, 75% of all Indigenous Australians reside in urban and peri-urban areas. In Brisbane, Indigenous Australians now number just over 45,000, and this number is rapidly increasing. Undertaking research with urban based Indigenous Australians is a relatively new phenomenon. Most past research with Indigenous people has been carried out in remote and regional areas. This paper focuses on a Participation Action Research project undertaken with Indigenous women in the highly urbanised area of North Brisbane. The project takes on the challenge of undertaking urban based Indigenous research. It opts not to centre on poor Indigenous women’s health statistics but instead centres on Indigenous women’s wellness and ways to talk about and work towards wellness. Through the cycles of dialogue with Indigenous women these concepts were teased out and manifested in two highly successful Women’s Wellness Summits. This paper will outline aspects of this project.

An improved method to detect damage using modal strain energy based damage index

This paper presents two novel concepts to enhance the accuracy of damage detection using the Modal Strain Energy based Damage Index (MSEDI) with the presence of noise in the mode shape data. Firstly, the paper presents a sequential curve fitting technique that reduces the effect of noise on the calculation process of the MSEDI, more effectively than the two commonly used curve fitting techniques; namely, polynomial and Fourier’s series. Secondly, a probability based Generalized Damage Localization Index (GDLI) is proposed as a viable improvement to the damage detection process. The study uses a validated ABAQUS finite-element model of a reinforced concrete beam to obtain mode shape data in the undamaged and damaged states. Noise is simulated by adding three levels of random noise (1%, 3%, and 5%) to the mode shape data. Results show that damage detection is enhanced with increased number of modes and samples used with the GDLI.

The health and cost implications of high body mass index in Australian Defence Force personnel.

BACKGROUND: Frequent illness and injury among workers with high body mass index (BMI) can raise the costs of employee healthcare and reduce workforce maintenance and productivity. These issues are particularly important in vocational settings such as the military, which require good physical health, regular attendance and teamwork to operate efficiently. The purpose of this study was to compare the incidence of injury and illness, absenteeism, productivity, healthcare usage and administrative outcomes among Australian Defence Force personnel with varying BMI. METHODS: Personnel were grouped into cohorts according to the following ranges for (BMI): normal (18.5-24.9 kg/m²; n = 197), overweight (25-29.9 kg/m²; n = 154) and obese (≥30 kg/m²) with restricted body fat (≤28 % for females, ≤24 % for males) (n = 148) and with no restriction on body fat (n = 180). Medical records for each individual were audited retrospectively to record the incidence of injury and illness, absenteeism, productivity, healthcare usage (i.e., consultation with medical specialists, hospital stays, medical investigations, prescriptions) and administrative outcomes (e.g., discharge from service) over one year. These data were then grouped and compared between the cohorts. RESULTS: The prevalence of injury and illness, cost of medical specialist consultations and cost of medical scans were all higher (p <0.05) in both obese cohorts compared with the normal cohort. The estimated productivity losses from restricted work days were also higher (p <0.05) in the obese cohort with no restriction on body fat compared with the normal cohort. Within the obese cohort, the prevalence of injury and illness, healthcare usage and productivity were not significantly greater in the obese cohort with no restriction on body fat compared with the cohort with restricted body fat. The number of restricted work days, the rate of re-classification of Medical Employment Classification and the rate of discharge from service were similar between all four cohorts. CONCLUSIONS: High BMI in the military increases healthcare usage, but does not disrupt workforce maintenance. The greater prevalence of injury and illness, greater healthcare usage and lower productivity in obese Australian Defence Force personnel is not related to higher levels of body fat.

History behind the IVF egg: Are women's comprehensive histories associated with the number of eggs collected, or fertilised normally, from repeated IVF cycles? [abstract]

Most studies of in vitro fertilisation (IVF) outcomes use cycle-based data and fail to account for women who use repeated IVF cycles. The objective of this study was to examine the association between the number of eggs collected (EC) and the percentage fertilised normally, and women’s self-reported medical, personal and social histories. This study involved a crosssectional survey of infertile women (aged 27-46 years) recruited from four privately-owned fertility clinics located in major cities of Australia. Regression modeling was used to estimate the mean EC and mean percentage of eggs fertilised normally: adjusted for age at EC. Appropriate statistical methods were used to take account of repeated IVF cycles by the same women. Among 121 participants who returned the survey and completed 286 IVF cycles, the mean age at EC was 35.2 years (SD 4.5). Women’s age at EC was strongly associated with the number of EC: <30 years, 11.7 EC; 30.0-< 35 years, 10.6 EC; 35.0-<40.0 years, 7.3 EC; 40.0+ years, 8.1 EC; p<.0001. Prolonged use of oral contraceptives was associated with lower numbers of EC: never used, 14.6 EC; 0-2 years, 11.7 EC; 3-5 years, 8.5 EC; 6þ years, 8.2 EC; p=.04. Polycystic ovary syndrome (PCOS) was associated with more EC: have PCOS, 11.5 EC; no, 8.3 EC; p=.01. Occupational exposures may be detrimental to normal fertilisation: professional roles, 58.8%; trade and service roles, 51.8%; manual and other roles, 63.3%; p=.02. In conclusion, women’s age remains the most significant characteristic associated with EC but not the percentage of eggs fertilised normally.

Orthogonality defect and reduced search-space size for solving integer least-squares problems

In the context of ambiguity resolution (AR) of Global Navigation Satellite Systems (GNSS), decorrelation among entries of an ambiguity vector, integer ambiguity search and ambiguity validations are three standard procedures for solving integer least-squares problems. This paper contributes to AR issues from three aspects. Firstly, the orthogonality defect is introduced as a new measure of the performance of ambiguity decorrelation methods, and compared with the decorrelation number and with the condition number which are currently used as the judging criterion to measure the correlation of ambiguity variance-covariance matrix. Numerically, the orthogonality defect demonstrates slightly better performance as a measure of the correlation between decorrelation impact and computational efficiency than the condition number measure. Secondly, the paper examines the relationship of the decorrelation number, the condition number, the orthogonality defect and the size of the ambiguity search space with the ambiguity search candidates and search nodes. The size of the ambiguity search space can be properly estimated if the ambiguity matrix is decorrelated well, which is shown to be a significant parameter in the ambiguity search progress. Thirdly, a new ambiguity resolution scheme is proposed to improve ambiguity search efficiency through the control of the size of the ambiguity search space. The new AR scheme combines the LAMBDA search and validation procedures together, which results in a much smaller size of the search space and higher computational efficiency while retaining the same AR validation outcomes. In fact, the new scheme can deal with the case there are only one candidate, while the existing search methods require at least two candidates. If there are more than one candidate, the new scheme turns to the usual ratio-test procedure. Experimental results indicate that this combined method can indeed improve ambiguity search efficiency for both the single constellation and dual constellations respectively, showing the potential for processing high dimension integer parameters in multi-GNSS environment.

State cycles, initialization and the Trivium stream cipher

Trivium is a keystream generator for a binary additive synchronous stream cipher. It was selected in the final portfolio for the Profile 2 category of the eSTREAM project. The keystream generator is constructed using bit- based shift registers. In this paper we present an alternate representation of Trivium using word-based shift registers, with a word size of three bits. This representation is useful for determining cycles of internal state values. Under this representation it is clear that the state space can be partitioned into subspaces and that over some of these subspaces the state update function is effectively linear. The role of the initialization process is critical in ensuring the states used for generating keystream are updated nonlinearly at some point, as the state update function alone does not provide this.

Using the index for inclusion to develop inclusive school communities

This chapter provides an overview of how school communities can work together in processes or review and development to strive towards a more inclusive approach to education. The writers of this chapter have been using a resource called the Index for Inclusion (Booth & Ainscow, 2005, 2011) for a number of years in Australia and in a pilot trail in New Zealand to support education staff in processes of review, with the aim to increase the participation and learning of all students. The resource supports the development of collaborative community processes and defines inclusion as ‘putting values into action’ (Booth & Ainscow, 2011, p.18). The process of review and development for more inclusive and socially just schools supports the development of a school culture, policy and practice where people are valued and treated with respect for their varied knowledge and experiences. In our experience, this resource has been useful to challenge our thinking about education in school communities and in region/districts about inclusive school development. We suggest the Index framework is broad enough to be used in a range of settings and countries. The resource is also useful for pre-service and in-service teacher development to provoke reflection and discussion about inclusion. This chapter provides an overview of the dimensions and framework that inform the Index of Inclusion. We discuss how the Index can be used in school contexts and draw on our own experience to give real examples of how teachers, paraprofessionals, students, principals and parents have experienced the Index when used in their local school communities in Australia and New Zealand. The chapter concludes with some points for discussion to challenge the status quo in schools and to inspire teachers to work towards a more socially just society through making changes at a school level.