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.

Design and analysis of key management schemes for distributed wireless sensor networks

Secure communications in distributed Wireless Sensor Networks (WSN) operating under adversarial conditions necessitate efficient key management schemes. In the absence of a priori knowledge of post-deployment network configuration and due to limited resources at sensor nodes, key management schemes cannot be based on post-deployment computations. Instead, a list of keys, called a key-chain, is distributed to each sensor node before the deployment. For secure communication, either two nodes should have a key in common in their key-chains, or they should establish a key through a secure-path on which every link is secured with a key. We first provide a comparative survey of well known key management solutions for WSN. Probabilistic, deterministic and hybrid key management solutions are presented, and they are compared based on their security properties and re-source usage. We provide a taxonomy of solutions, and identify trade-offs in them to conclude that there is no one size-fits-all solution. Second, we design and analyze deterministic and hybrid techniques to distribute pair-wise keys to sensor nodes before the deployment. We present novel deterministic and hybrid approaches based on combinatorial design theory and graph theory for deciding how many and which keys to assign to each key-chain before the sensor network deployment. Performance and security of the proposed schemes are studied both analytically and computationally. Third, we address the key establishment problem in WSN which requires key agreement algorithms without authentication are executed over a secure-path. The length of the secure-path impacts the power consumption and the initialization delay for a WSN before it becomes operational. We formulate the key establishment problem as a constrained bi-objective optimization problem, break it into two sub-problems, and show that they are both NP-Hard and MAX-SNP-Hard. Having established inapproximability results, we focus on addressing the authentication problem that prevents key agreement algorithms to be used directly over a wireless link. We present a fully distributed algorithm where each pair of nodes can establish a key with authentication by using their neighbors as the witnesses.

Choose wisely: Network, ontology and annotation resources for the analysis of Staphylococcus aureus omics data

Staphylococcus aureus (S. aureus) is a prominent human and livestock pathogen investigated widely using omic technologies. Critically, due to availability, low visibility or scattered resources, robust network and statistical contextualisation of the resulting data is generally under-represented. Here, we present novel meta-analyses of freely-accessible molecular network and gene ontology annotation information resources for S. aureus omics data interpretation. Furthermore, through the application of the gene ontology annotation resources we demonstrate their value and ability (or lack-there-of) to summarise and statistically interpret the emergent properties of gene expression and protein abundance changes using publically available data. This analysis provides simple metrics for network selection and demonstrates the availability and impact that gene ontology annotation selection can have on the contextualisation of bacterial omics data.

A values analysis of attitudes towards the use of law to prevent obesity: How might these values inform public health law theory and practice?

This thesis asks whether values, like government duty, individual responsibility, community and social justice, influence the way that scholars and research participants think about the use of law to prevent obesity. It explores the way participants speak about values when expressing their support for or against a variety of government regulatory interventions, including taxation, food labelling reforms and advertising restrictions. This research contributes to our understanding of theories of public health law and public health ethics. The qualitative findings also have implications for policy development, in advocating for a variety of government interventions to prevent obesity.

Brain network efficiency and topology depend on the fiber tracking method: 11 tractography algorithms compared in 536 subjects

As connectivity analyses become more popular, claims are often made about how the brain's anatomical networks depend on age, sex, or disease. It is unclear how results depend on tractography methods used to compute fiber networks. We applied 11 tractography methods to high angular resolution diffusion images of the brain (4-Tesla 105-gradient HARDI) from 536 healthy young adults. We parcellated 70 cortical regions, yielding 70×70 connectivity matrices, encoding fiber density. We computed popular graph theory metrics, including network efficiency, and characteristic path lengths. Both metrics were robust to the number of spherical harmonics used to model diffusion (4th-8th order). Age effects were detected only for networks computed with the probabilistic Hough transform method, which excludes smaller fibers. Sex and total brain volume affected networks measured with deterministic, tensor-based fiber tracking but not with the Hough method. Each tractography method includes different fibers, which affects inferences made about the reconstructed networks.

Using Bourdieu in education research: Theory and methods

This workshop will snapshot Bourdieu's sociology. In recognition of Bourdieu's work as a powerful theoretical instrument to speculate the reproduction of social orders and cultural values, the workshop will firstly discuss the core concepts of habitus, capital, and field – the foundational triad of Bourdieu's sociology. Although Bourdieu's original work was built on some quantitative studies, his sociology has been largely qualitatively used in education research. Different from the bulk of extant research, the workshop will secondly showcase some quantitative and mixed methods research that uses a Bourdieusian framework. Mindful of such a framework helping understand social practice at a macro level, the workshop will then make an attempt to think through the macro and the micro by weaving together Bourdieu's sociology with Garfinkel's ethnomethodology. The workshop will conclude with some reflections and communications in terms of how to better realise the full value of Bourdieu in education research.

A survey and analysis of the GNSS spoofing threat and countermeasures

Detection and prevention of global network satellite system (GNSS) “spoofing” attacks, or the broadcast of false global navigation satellite system services, has recently attracted much research interest. This survey aims to fill three gaps in the literature: first, to assess in detail the exact nature of threat scenarios posed by spoofing against the most commonly cited targets; second, to investigate the many practical impediments, often underplayed, to carrying out GNSS spoofing attacks in the field; and third, to survey and assess the effectiveness of a wide range of proposed defences against GNSS spoofing. Our conclusion lists promising areas of future research.

New insights into rebound effects : theory and empirical evidence

The main objective of the thesis is to seek insights into the theory, and provide empirical evidence of rebound effects. Rebound effects reduce the environmental benefits of environmental policies and household behaviour changes. In particular, win-win demand side measures, in the form of energy efficiency and household consumption pattern changes, are seen as ways for households and businesses to save money and the environment. However, these savings have environmental impacts when spent, which are known as rebound effects. This is an area that has been widely neglected by policy makers. This work extends the rebound effect literature in three important ways, (1) it incorporates the potential for variation of rebound effects with household income level, (2) it enables the isolation of direct and indirect effects for cases of energy efficient technology adoption, and examines the relationship between these two component effects, and (3) it expands the scope of rebound effect analysis to include government taxes and subsidies. MACROBUTTON HTMLDirect Using a case study approach it is found that the rebound effect from household consumption pattern changes targeted at electricity is between 5 and 10%. For consumption pattern changes with reduced vehicle fuel use, the rebound effect is in the order of 20 to 30%. Higher income households in general are found to have a lower total rebound effect; however the indirect effect becomes relatively more significant at higher household income levels. In the win-lose case of domestic photovoltaic electricity generation, it is demonstrated that negative rebound effects can occur, which can potentially amplify the environmental benefits of this action. The rebound effect from a carbon tax, which occurs due to the re-spending of raised revenues, was found to be in the range of 11-32%. Taxes and transfers between households of different income levels also have environmental implications. For example, a more progressive tax structure, with increased low income welfare payments is likely to increase greenhouse gas emissions. Subsidies aimed at encouraging environmentally friendly consumption habits are also subject to rebound effects, as they constitute a substitution of government expenditure for household expenditure. For policy makers, these findings point to the need to incorporate rebound effects in the environmental policy evaluation process.’

Southern theory and its dynamics for postcolonial education

This paper discusses how the exploration of social texts and historical contexts from the global 'South', as put forward in Raewyn Connell's study 'Southern Theory' (2007), can improve the theoretical tools used in postcolonial education analysis. Connell analyses a selection of excellent and compelling social theory texts written by scholars in Africa, India, Iran, Latin America and Australia to show how they challenge and counter the silences, distortions and plain lies of dominant Western social theory. These texts of the global South do not mince words in laying bare the role of the institutions and elites of the West in the destruction, dispossession, and bloodshed involved in creating the world in which we live, and in perpetuating its catastrophes. The texts also reveal intense debates between scholars over their conceptualisations of local, national and global society. My paper argues that this kind of work is of vital importance to postcolonial studies in education. It helps education scholars to uncover the problematic assumptions and distortions of dominant education thought, and understand different ways of seeing. Postcolonial educators could use this to help both students and teacher unlearn many of our taught perceptions of the world, whether in the global North or the global South. Developing a countervailing social theory in education would sharpen our questioning of the structures of schooling as they relate to society, and tease out new dimensions of postcolonial leadership for education.

Boys 'doing' and 'undoing' media education : new possibilities for theory and practice

The purpose of this study is to investigate how secondary school media educators might best meet the needs of students who prefer practical production work to ‘theory’ work in media studies classrooms. This is a significant problem for a curriculum area that claims to develop students’ media literacies by providing them with critical frameworks and a metalanguage for thinking about the media. It is a problem that seems to have become more urgent with the availability of new media technologies and forms like video games. The study is located in the field of media education, which tends to draw on structuralist understandings of the relationships between young people and media and suggests that students can be empowered to resist media’s persuasive discourses. Recent theoretical developments suggest too little emphasis has been placed on the participatory aspects of young people playing with, creating and gaining pleasure from media. This study contributes to this ‘participatory’ approach by bringing post structuralist perspectives to the field, which have been absent from studies of secondary school media education. I suggest theories of media learning must take account of the ongoing formation of students’ subjectivities as they negotiate social, cultural and educational norms. Michel Foucault’s theory of ‘technologies of the self’ and Judith Butler’s theories of performativity and recognition are used to develop an argument that media learning occurs in the context of students negotiating various ‘ethical systems’ as they establish their social viability through achieving recognition within communities of practice. The concept of ‘ethical systems’ has been developed for this study by drawing on Foucault’s theories of discourse and ‘truth regimes’ and Butler’s updating of Althusser’s theory of interpellation. This post structuralist approach makes it possible to investigate the ways in which students productively repeat and vary norms to creatively ‘do’ and ‘undo’ the various media learning activities with which they are required to engage. The study focuses on a group of year ten students in an all boys’ Catholic urban school in Australia who undertook learning about video games in a three-week intensive ‘immersion’ program. The analysis examines the ethical systems operating in the classroom, including formal systems of schooling, informal systems of popular cultural practice and systems of masculinity. It also examines the students’ use of semiotic resources to repeat and/or vary norms while reflecting on, discussing, designing and producing video games. The key findings of the study are that students are motivated to learn technology skills and production processes rather than ‘theory’ work. This motivation stems from the students’ desire to become recognisable in communities of technological and masculine practice. However, student agency is not only possible through critical responses to media, but through performative variation of norms through creative ethical practices as students participate with new media technologies. Therefore, the opportunities exist for media educators to create the conditions for variation of norms through production activities. The study offers several implications for media education theory and practice including: the productive possibilities of post structuralism for informing ways of doing media education; the importance of media teachers having the autonomy to creatively plan curriculum; the advantages of media and technology teachers collaborating to draw on a broad range of resources to develop curriculum; the benefits of placing more emphasis on students’ creative uses of media; and the advantages of blending formal classroom approaches to media education with less formal out of school experiences.

Contradictions : Genre, causal layered analysis and analysis of institutional change

In what follows, I put forward an argument for an analytical method for social science that operates at the level of genre. I argue that generic convergence, generic hybridity, and generic instability provide us with a powerful perspectives on changes in political, cultural, and economic relationships, most specifically at the level of institutions. Such a perspective can help us identify the transitional elements, relationships, and trajectories that define the place of our current system in history, thereby grounding our understanding of possible futures.1 In historically contextualising our present with this method, my concern is to indicate possibilities for the future. Systemic contradictions indicate possibility spaces within which systemic change must and will emerge. We live in a system currently dominated by many fully-expressed contradictions, and so in the presence of many possible futures. The contradictions of the current age are expressed most overtly in the public genres of power politics. Contemporary public policy—indeed politics in general-is an excellent focus for any investigation of possible futures, precisely because of its future-oriented function. It is overtly hortatory; it is designed ‘to get people to do things’ (Muntigl in press: 147). There is no point in trying to get people to do things in the past. Consequently, policy discourse is inherently oriented towards creating some future state of affairs (Graham in press), along with concomitant ways of being, knowing, representing, and acting (Fairclough 2000).

The impact of institutional, instrumental and interpersonal underpinnings on network dynamics and outcomes

Networks form a key part of the infrastructure of contemporary governance arrangements and, as such, are likely to continue for some time. Networks can take many forms and be formed for many reasons. Some networks have been explicitly designed to generate a collective response to an issue; some arise from a top down perspective through mandate or coercion; while others rely more heavily on interpersonal relations and doing the right thing. In this paper, these three different perspectives are referred to as the “3I”s: Instrumental, Institutional or Interpersonal. It is proposed that these underlying motivations will affect the process dynamics within the different types of networks in different ways and therefore influence the type of outcomes achieved. This proposition is tested through a number of case studies. An understanding of these differences will lead to more effective design, management and clearer expectations of what can be achieved through networks.

Info-gap theory and robust design of surveillance for invasive species : the case study of Barrow Island

Surveillance for invasive non-indigenous species (NIS) is an integral part of a quarantine system. Estimating the efficiency of a surveillance strategy relies on many uncertain parameters estimated by experts, such as the efficiency of its components in face of the specific NIS, the ability of the NIS to inhabit different environments, and so on. Due to the importance of detecting an invasive NIS within a critical period of time, it is crucial that these uncertainties be accounted for in the design of the surveillance system. We formulate a detection model that takes into account, in addition to structured sampling for incursive NIS, incidental detection by untrained workers. We use info-gap theory for satisficing (not minimizing) the probability of detection, while at the same time maximizing the robustness to uncertainty. We demonstrate the trade-off between robustness to uncertainty, and an increase in the required probability of detection. An empirical example based on the detection of Pheidole megacephala on Barrow Island demonstrates the use of info-gap analysis to select a surveillance strategy.