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.

On the beach : exploring the complex egalitarianism of the Australian beach

Australia, internationally, is known as a beach loving country, particularly in popular culture. The beach did not figure significantly in academic discussion before the 1980s when Fiske, Hodge, and Turner (1987, 54) researched the beach as a space of myth, seeing it as an integral part of the modern Australian identity. One common myth in Australia is that the beach is an equaliser, a place of multiple ethnicities, shapes, sizes, and genders (Dutton, 1985). I agree that the beach remains a significant aspect of Australian identity; however, limiting its meaning to a mythic space contributing to a homogenous national identity is not adequate. This paper will explore how Australian texts comment on or challenge the myth of the beach as an egalitarian space. I argue that recent Australian texts show a more complex, layered representation of this concept; and that the beach also in this respect can no longer be understood as a myth transcending difference.

Allergen capture by IgE and IgG enhanced cell-binding by allergen multimers: How complex is it?

Allergic diseases are the most common chronic disease of the western world, costing $7.8 billion per year in lost productivity and medical care in Australia alone.1 IgE is central to the immunopathogenesis of allergic diseases and important advances are now being made on multiple fronts of IgE research. In particular, two groups independently invested in the generation of IgE reporter mice to address the vexing question of the route of development of the elusive IgE+ B cell.2, 3 Two new anti-IgE mAb targeting membrane IgE and cell-bound IgE have the potential to deplete the cellular source of IgE.4, 5 These could be candidates for alternative anti-IgE treatment options with advantages over current anti-IgE therapy (OmalizumAb), which depletes free serum IgE. Researchers are still intrigued by the modes of interaction of IgE with allergen, and with both its receptors; the high affinity FcεR1 on mast cells and basophils, and the low affinity, C-type lectin, IgE receptor, CD23,6 on B cells and monocytes (Figure 1a and b). A new approach to the study of the complexity of these interactions was recently reported by Reginald et al.7 on page 167 of this issue.

Raman spectroscopy of some complex arsenate minerals—implications for soil remediation

The application of spectroscopy to the study of contaminants in soils is important. Among the many contaminants is arsenic, which is highly labile and may leach to non-contaminated areas. Minerals of arsenate may form depending upon the availability of specific cations for example calcium and iron. Such minerals include carminite, pharmacosiderite and talmessite. Each of these arsenate minerals can be identified by its characteristic Raman spectrum enabling identification.

Abstracting and correlating heterogeneous events to detect complex scenarios

The research presented in this thesis addresses inherent problems in signaturebased intrusion detection systems (IDSs) operating in heterogeneous environments. The research proposes a solution to address the difficulties associated with multistep attack scenario specification and detection for such environments. The research has focused on two distinct problems: the representation of events derived from heterogeneous sources and multi-step attack specification and detection. The first part of the research investigates the application of an event abstraction model to event logs collected from a heterogeneous environment. The event abstraction model comprises a hierarchy of events derived from different log sources such as system audit data, application logs, captured network traffic, and intrusion detection system alerts. Unlike existing event abstraction models where low-level information may be discarded during the abstraction process, the event abstraction model presented in this work preserves all low-level information as well as providing high-level information in the form of abstract events. The event abstraction model presented in this work was designed independently of any particular IDS and thus may be used by any IDS, intrusion forensic tools, or monitoring tools. The second part of the research investigates the use of unification for multi-step attack scenario specification and detection. Multi-step attack scenarios are hard to specify and detect as they often involve the correlation of events from multiple sources which may be affected by time uncertainty. The unification algorithm provides a simple and straightforward scenario matching mechanism by using variable instantiation where variables represent events as defined in the event abstraction model. The third part of the research looks into the solution to address time uncertainty. Clock synchronisation is crucial for detecting multi-step attack scenarios which involve logs from multiple hosts. Issues involving time uncertainty have been largely neglected by intrusion detection research. The system presented in this research introduces two techniques for addressing time uncertainty issues: clock skew compensation and clock drift modelling using linear regression. An off-line IDS prototype for detecting multi-step attacks has been implemented. The prototype comprises two modules: implementation of the abstract event system architecture (AESA) and of the scenario detection module. The scenario detection module implements our signature language developed based on the Python programming language syntax and the unification-based scenario detection engine. The prototype has been evaluated using a publicly available dataset of real attack traffic and event logs and a synthetic dataset. The distinct features of the public dataset are the fact that it contains multi-step attacks which involve multiple hosts with clock skew and clock drift. These features allow us to demonstrate the application and the advantages of the contributions of this research. All instances of multi-step attacks in the dataset have been correctly identified even though there exists a significant clock skew and drift in the dataset. Future work identified by this research would be to develop a refined unification algorithm suitable for processing streams of events to enable an on-line detection. In terms of time uncertainty, identified future work would be to develop mechanisms which allows automatic clock skew and clock drift identification and correction. The immediate application of the research presented in this thesis is the framework of an off-line IDS which processes events from heterogeneous sources using abstraction and which can detect multi-step attack scenarios which may involve time uncertainty.

Managing infrastructure transitions : a complex adaptive systems perspective

Engineering assets such as roads, rail, bridges and other forms of public works are vital to the effective functioning of societies {Herder, 2006 #128}. Proficient provision of this physical infrastructure is therefore one of the key activities of government {Lædre, 2006 #123}. In order to ensure engineering assets are procured and maintained on behalf of citizens, government needs to devise the appropriate policy and institutional architecture for this purpose. The changing institutional arrangements around the procurement of engineering assets are the focus of this paper. The paper describes and analyses the transition to new, more collaborative forms of procurement arrangements which are becoming increasingly prevalent in Australia and other OECD countries. Such fundamental shifts from competitive to more collaborative approaches to project governance can be viewed as a major transition in procurement system arrangements. In many ways such changes mirror the shift from New Public Management, with its emphasis on the use of market mechanisms to achieve efficiencies {Hood, 1991 #166}, towards more collaborative approaches to service delivery, such as those under network governance arrangements {Keast, 2007 #925}. However, just as traditional forms of procurement in a market context resulted in unexpected outcomes for industry, such as a fragmented industry afflicted by chronic litigation {Dubois, 2002 #9}, the change to more collaborative forms of procurement is unlikely to be a panacea to the problems of procurement, and may well also have unintended consequences. This paper argues that perspectives from complex adaptive systems (CAS) theory can contribute to the theory and practice of managing system transitions. In particular the concept of emergence provides a key theoretical construct to understand the aggregate effect that individual project governance arrangements can have upon the structure of specific industries, which in turn impact individual projects. Emergence is understood here as the macro structure that emerges out of the interaction of agents in the system {Holland, 1998 #100; Tang, 2006 #51}.