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.

Revealing common attributes of organizational identities using performance measurement systems

Identity is unique, multiple and dynamic. This paper explores common attributes of organisational identities, and examines the role of performance management systems (PMSs) on revealing identity attributes. One of the influential PMSs, the balanced scorecard, is used to illustrate the arguments. A case study of a public-sector organisation suggests that PMSs now place a value on the intangible aspects of organisational life as well as the financial, periodically revealing distinctiveness, relativity, visibility, fluidity and manageability of public-sector identities that sustain their viability. This paper contributes to a multi-disciplinary approach and its practical application, demonstrating an alternative pathway to identity-making using PMSs.

Female genital mutilation : legal, attitudinal and practical reform

Female genital mutilation (FGM) is a cultural practice common in many Islamic societies. It involves the deliberate, non-therapeutic physical modification of young girls’ genitalia. FGM can take several forms, ranging from less damaging incisions to actual removal of genitalia and narrowing or even closing of the vagina. While often thought to be required by religion, FGM both predates and has no basis in the Koran. Rather, it is a cultural tradition, motivated by a patriarchal social desire to control female bodies to ensure virginity at marriage (preserving family honour), and to prevent infidelity by limiting sexual desire. In the USA and Australia in 2010, peak medical bodies considered endorsing the medical administration of a ‘lesser’ form of FGM. The basis for this was pragmatic: it would be preferable to satisfy patients’ desire for FGM in medically-controlled conditions, rather than have these patients seek it, possibly in more severe forms, under less safe conditions. While arguments favouring medically-administered FGM were soon overcome, the prospect of endorsing FGM illuminated the issue in these two Western countries and beyond. This paper will review the nature of FGM, its physical and psychological health consequences, and Australian laws prohibiting FGM. Then, it will scan recent developments in Africa, where FGM has been made illegal by a growing number of nations and by the Protocol to the African Charter on Human and Peoples’ Rights 2003 (the Maputo Protocol), but is still proving difficult to eradicate. Finally, based on arguments derived from theories of rights, health evidence, and the historical and religious contexts, this paper will ask whether an absolute human right against FGM can be developed.

Using cost-effective multimedia to create engaging learning experiences in law and other disciplines

This is the final report of an Australian Learning and Teaching Council Teaching Fellowship which addressed the needs of two separate groups of learners: (1) final year law students studying ethics and (2) law academics and other interested educators in higher education wishing to use information and communication technologies (ICT) to create engaging learning environments for their students but lacking the capacity to do so. The Fellowship resulted in final year law students being infused with an improved appreciation of ethical practice than they receive from traditional lecture/tutorial means by the development of an integrated program of blended learning including an online program entitled "Entry into Valhalla". This "ethics capstone‟ utilises multimedia produced using cost effective resources (including the "Second Life" virtual environment) to create engaging, contextualised learning experiences. The Fellowship also constructed the knowledge of producing cost-effective multimedia projects in other law academics and other educators in higher education by staff development activities comprising workshops, conference presentations and an interactive website using the "Entry into Valhalla" program as a case study exemplar.

Developing a transition pedagogy : intentional curriculum design in first and final year law programs

This chapter will first consider the rationale for a transition pedagogy for first and final year law students. It then discusses the elements of a transition pedagogy for both years, noting the synergies and differences between programs designed to assist transition into and out of a law degree. In doing so, the authors attempt to explore the extent to which the first year curriculum principles identified by Sally Kift under an Australian Learning and Teaching Council (ALTC) Senior Fellowship may also be applied to the final year university experience. During the course of the discussion, examples are drawn from universities and Law Schools in Australia and internationally which seek to address these imperatives...

The capstone experience in law

An effective capstone experience provides closure through: Supporting students to synthesise their learning in the program by building upon the knowledge, skills and capability development that has taken place over the entirety of the curriculum; Providing enhanced opportunities for students to reflect on their personal and professional development over the course of their legal education experience and how that prepares them for their future professional and personal lives; Assisting students to attain an understanding of what it means to be a graduate of the discipline and begin to develop a professional identity.

Structural damage identification with noise polluted Frequency Response Functions (FRFs)

Damage detection in structures has become increasingly important in recent years. While a number of damage detection and localization methods have been proposed, very few attempts have been made to explore the structure damage with noise polluted data which is unavoidable effect in real world. The measurement data are contaminated by noise because of test environment as well as electronic devices and this noise tend to give error results with structural damage identification methods. Therefore it is important to investigate a method which can perform better with noise polluted data. This paper introduces a new damage index using principal component analysis (PCA) for damage detection of building structures being able to accept noise polluted frequency response functions (FRFs) as input. The FRF data are obtained from the function datagen of MATLAB program which is available on the web site of the IASC-ASCE (International Association for Structural Control– American Society of Civil Engineers) Structural Health Monitoring (SHM) Task Group. The proposed method involves a five-stage process: calculation of FRFs, calculation of damage index values using proposed algorithm, development of the artificial neural networks and introducing damage indices as input parameters and damage detection of the structure. This paper briefly describes the methodology and the results obtained in detecting damage in all six cases of the benchmark study with different noise levels. The proposed method is applied to a benchmark problem sponsored by the IASC-ASCE Task Group on Structural Health Monitoring, which was developed in order to facilitate the comparison of various damage identification methods. The illustrated results show that the PCA-based algorithm is effective for structural health monitoring with noise polluted FRFs which is of common occurrence when dealing with industrial structures.

Physical effect in patent law

This thesis addresses one of the fundamental issues that remains unresolved in patent law today. It is a question that strikes at the heart of what a patent is and what it is supposed to protect. That question is whether an invention must produce a physical effect or cause a physical transformation of matter to be patentable, or whether it is sufficient that an invention involves a specific practical application of an idea or principle to achieve a useful result. In short, the question is whether patent law contains a physicality requirement. Resolving this issue will determine whether only traditional mechanical, industrial and manufacturing processes are patent eligible, or whether patent eligibility extends to include purely intangible, or non-physical, products and processes. To this end, this thesis seeks to identify where the dividing line lies between patentable subject matter and the recognised categories of excluded matter, namely, fundamental principles of nature, physical phenomena, and abstract ideas. It involves determining which technological advances are worth the inconvenience monopoly protection causes the public at large, and which should remain free for all to use without restriction. This is an issue that has important ramifications for innovation in the ‘knowledge economy’ of the Information Age. Determining whether patent law contains a physicality requirement is integral to deciding whether much of the valuable innovation we are likely to witness, in what are likely to be the emerging areas of technology in the near future, will receive the same encouragement as industrial and manufacturing advances of previous times.

The nature of juristic paradigms : exploring the theoretical and conceptual relationship between adversarialism and therapeutic jurisprudence

Problem solving courts appear to achieve outcomes which are not common in mainstream courts. There are increasing calls for the adoption of more “therapeutic” and “problem solving” practices by mainstream judges in civil and criminal courts in a number of jurisdictions, most notably in the United States and Australia. Currently, a judge who sets out to exercise a significant therapeutic function is quite likely to be doing so in a specialist court or jurisdiction, outside the mainstream court system, and, arguably, from outside the adversarial paradigm itself. To some extent, his work is tolerated but marginalized. But do therapeutic and problem solving functions have the potential to define, rather than complement, the role of judicial officers? The basic question addressed in this paper is, therefore, whether the judicial role could evolve to be not just less adversarial, but fundamentally non-adversarial. In other words, could we see--or are we seeing--a paradigm shift not just in the colloquial, casual sense of the word, but in the strong, worldview changing sense meant by Thomas Kuhn?

Group law computations on Jacobians of hyperelliptic Curves

We derive an explicit method of computing the composition step in Cantor’s algorithm for group operations on Jacobians of hyperelliptic curves. Our technique is inspired by the geometric description of the group law and applies to hyperelliptic curves of arbitrary genus. While Cantor’s general composition involves arithmetic in the polynomial ring F_q[x], the algorithm we propose solves a linear system over the base field which can be written down directly from the Mumford coordinates of the group elements. We apply this method to give more efficient formulas for group operations in both affine and projective coordinates for cryptographic systems based on Jacobians of genus 2 hyperelliptic curves in general form.

The role of law in responding to climate change : emerging regulatory, liability and market approaches

Climate change presents as the archetypal environmental problem with short-term economic self-interest operating to the detriment of the long-term sustainability of our society. The scientific reports of the Intergovernmental Panel on Climate Change strongly assert that the stabilisation of emissions in the atmosphere, to avoid the adverse impacts of climate change, requires significant and rapid reductions in ‘business as usual’ global greenhouse gas emissions. The sheer magnitude of emissions reductions required, within this urgent timeframe, will necessitate an unprecedented level of international, multi-national and intra-national cooperation and will challenge conventional approaches to the creation and implementation of international and domestic legal regimes. To meet this challenge, existing international, national and local legal systems must harmoniously implement a strong international climate change regime through a portfolio of traditional and innovative legal mechanisms that swiftly transform current behavioural practices in emitting greenhouse gases. These include the imposition of strict duties to reduce emissions through the establishment of strong command and control regulation (the regulatory approach); mechanisms for the creation and distribution of liabilities for greenhouse gas emissions and climaterelated harm (the liability approach) and the use of innovative regulatory tools in the form of the carbon trading scheme (the market approach). The legal relations between these various regulatory, liability and market approaches must be managed to achieve a consistent, compatible and optimally effective legal regime to respond to the threat of climate change. The purpose of this thesis is to analyse and evaluate the emerging legal rules and frameworks, both international and Australian, required for the effective regulation of greenhouse gas emissions to address climate change in the context of the urgent and deep emissions reductions required to minimise the adverse impacts of climate change. In doing so, this thesis will examine critically the existing and potential role of law in effectively responding to climate change and will provide recommendations on the necessary reforms to achieve a more effective legal response to this global phenomenon in the future.

Murray-Darling basin governance : the focus of the law

The legal arrangements for the management of the Murray-Darling Basin in Australia have changed significantly over the years. The Constitution of the Commonwealth has led to the legal arrangements for the management of the Murray-Darling Basin. The Water Act 2000 of Queensland aimed at advancing sustainable management and efficient use of water and other resources by establishing a system for the planning, allocation and use of water. The Water Management Act 2000 of New South Wales ensures the sustainable and integrated management of the water resources of the state benefiting the present and future generations. The Natural Resources Management Act 2004 of South Australia applies to water resources and to other natural resources. The Act aimed at assisting the achievement of ecologically sustainable development in the state.

Exploring ethical dilemmas for principals arising from role conflict with school counsellors

Acting in the best interests of students is central to the moral and ethical work of schools. Yet tensions can arise between principals and school counsellors as they work from at times opposing professional paradigms. In this article we report on principals’ and counsellors’ responses to scenarios covering confidentiality and the law, student/teacher relationships, student welfare and psychological testing of students. This discussion takes place against an examination of ethics, ethical dilemmas and professional codes of ethics. While there were a number of commonalities among principals and school counsellors that arose from their common belief in education as a moral venture, there were also some key differences among them. These differences centred on the principals’ focus on the school as a whole and counsellors’ focus on the welfare of the individual student. A series of recommendations is offered to assist principals to navigate ethical dilemmas such as those considered in this article.

A requirements and capability discussion : UAS for SAR and law enforcement

This presentation explores the requirements and capabilities of Unmanned Aircraft Systems (UAS) for applications in Law Enforcement and Search and Rescue.

Models of South-East Asian organised crime drug operations in Queensland

In 2002, the United Nations Office on Drugs and Crime (UNODC) issued a report entitled Results of a pilot survey of forty selected organized criminal groups in sixteen countries which established five models of organised crime. This paper reviews these and other common organised crime models and drug trafficking models, and applies them to cases of South East Asian drug trafficking in the Australian state of Queensland. The study tests the following hypotheses: (1) South-East Asian drug trafficking groups in Queensland will operate within a criminal network or core group; (2) Wholesale drug distributors in Queensland will not fit consistently under any particular UN organised crime model; and (3) Street dealers will have no organisational structure. The study concluded that drug trafficking or importation closely resembles a criminal network or core group structure. Wholesale dealers did not fit consistently into any UN organised crime model. Street dealers had no organisational structure as an organisational structure is typically found in mid- to high-level drug trafficking.