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.

The application of Bowen’s family system theory (BFST) to the Malay population in Malaysia

The rapid economic development and social changes in Malaysia recently have led to many psychosocial problems in young people, such as drug addiction, child sexual abuse and mental illness. The Malaysian government is beginning to focus more attention on its social welfare and human service needs in order to alleviate these psychosocial problems. Although counselling is accepted and widespread in Malaysia, the practice of family therapy is not as accepted as it is still a widely held belief that family problems need to be kept within the family. However, changes are imminent and thus the theoretical basis of family therapy needs to be culturally relevant. Bowen‟s Family Systems Theory (BFST) is already one of the major theories taught to tertiary counselling students in Malaysian universities. The main tenet of Bowen‟s theory is that the family as a system may be unstable unless each member of the family is well differentiated. High differentiation levels in the family allow a person to both leave the family‟s boundaries in search of uniqueness and to continually return to the family fold in order to establish a more mature sense of belonging. The difficulty, however, is that while Bowen has claimed that his theory is universal nearly all of the research confirming the theory has been conducted in the United States of America. The only known study outside America, however, did show that Bowen‟s theory applied to a Filipino population but, one of the theory‟s propositions that differentiation is intergenerational was not supported in this non-American sample. The American sample that was compared to the Malay sample was taken from Skowron and Friedlander‟s (1998) study. One hundred and twenty-seven faculty staff in an American university completed the Differentiation of Self Inventory (DSI) to measure level of differentiation of self. This thesis therefore, set out to determine whether Bowen‟s theory applied to another non-American sample, the Malaysian community. The research also investigated if the intergenerational effect was present in the Malaysian sample as well as explored the role of socio-economic status on Bowen‟s theory of differentiation and gender effect. Three hundred and seventy-four families completed four measures to examine these research questions: the Differentiation of Self Inventory (DSI), the Family Inventory of Life Event (FILE), the Depression Anxiety and Stress Scale (DASS) and the Connor-Davidson Resilience Scale (CD-RISC). The results of the study showed that differentiation of self is a valid construct for the Malay population. However, all four subscales of the Differentiation of Self Inventory (DSI); emotional reactivity (ER), emotional cut-off (EC), fusion with other (FO) and I position (IP), showed significant differences compared to the American sample from Skowron and Friedlander‟s (1998) study. The Malay sample scored higher in emotional reaction (ER), fusion with other (FO), but lower on emotional cut-off (EC) and I position (IP) than the American sample. The intergenerational effect was found in the Malay population as the parent‟s level of differentiation correlated with their children‟s level of differentiation. It was found that stress as measured by the Family Inventory of Life Event (FILE) and as measured by the Depression Anxiety and Stress Scale (DASS) were not correlated with the level of differentiation of self in parents. However, gender had a significant effect in predicting the level of differentiation among parents in Malay population with females scores higher on emotional reactivity (ER) and fusion with other (FO) than males. An additional finding was that resilience can be predicted from the level of differentiation of self in children in the Malay sample. There was also a positive correlation between the level of differentiation of self in parents and resilience in their children. Findings from this study indicate that the concept of differentiation of self is applicable to a Malay sample; however, the implementation of the theory should be applied with cultural sensitivity.

Infrastructure transitions toward sustainability : a complex adaptive systems perspective

To ensure infrastructure assets are procured and maintained by government on behalf of citizens, appropriate policy and institutional architecture is needed, particularly if a fundamental shift to more sustainable infrastructure is the goal. The shift in recent years from competitive and resource-intensive procurement to more collaborative and sustainable approaches to infrastructure governance is considered a major transition in infrastructure procurement systems. In order to better understand this transition in infrastructure procurement arrangements, the concept of emergence from Complex Adaptive Systems (CAS) theory is offered as a key construct. Emergence holds that micro interactions can result in emergent macro order. Applying the concept of emergence to infrastructure procurement, this research examines how interaction of agents in individual projects can result in different industry structural characteristics. The paper concludes that CAS theory, and particularly the concept of ‘emergence’, provides a useful construct to understand infrastructure procurement dynamics and progress towards sustainability.

Industry-school partnerships : an ecological approach

Internationally, Industry-School Partnerships (ISPs) are a ubiquitous government approach for enabling school to work transitions. Significant benefits of ISPs for centralised bureaucracies that are seeking to address common educational problems include: i) cost reduction; ii) supply to geographically dispersed locations, and; iii) industry access to innovative education solutions. In Queensland, there exists a government led ISP, the Gateway to Industry Schools Program. Under this initiative is the Queensland Minerals and Energy Academy, a lead industry organisation for 34 schools and 17 multinational sponsor companies. Acquiring an understanding of this strategic ISP is critical, given the current Resources Industry boom, and the workforce skills shortage experienced in Australia. This review paper adopts Ecological Systems Theory as a lens to understand the inner workings of ISPs. Acknowledging that ISPs will remain a key feature of government policy, this paper seeks to further illuminate the role of ISPs in transitioning young people from school to the working world.

My System of Career Influences MSCI (Adult) Facilitator's Guide

Career development in the 21st century presents many challenges and opportunities to adults. They must now navigate a complex and rapidly changing world of work influenced by technology, globalisation and fluctuating economic conditions. The My System of Career Influences (MSCI) (Adult) is a qualitative career assessment tool based on the constructivist theory from cognitive psychology. Acknowledged as the third wave in cognitive science after psychoanalysis and behaviourism, constructivism emphasises the individual in the assessment and counselling process. Individuals actively participate in the construction of their own reality and are encouraged to respond to and deal with both anticipated and unanticipated events that influence their careers. The tool comprises a facilitator guide and participant workbooks. The guide describes the Systems Theory Framework of career development that provides the theoretical background to the MSCI as well as a step-by-step user guide to conducting the MSCI (Adult) process with individuals and groups. Each participant uses the accompanying MSCI (Adult) Workbook (sold separately) which they can complete and keep for later reference. With its attention to an holistic and storied approach to career intervention My System of Career Influences (MSCI) (Adult) is an essential resource for all career practitioners working with adults in today's workplaces.

A framework for qualitative analysis of focus group data in information systems

Focus groups are a popular qualitative research method for information systems researchers. However, compared with the abundance of research articles and handbooks on planning and conducting focus groups, surprisingly, there is little research on how to analyse focus group data. Moreover, those few articles that specifically address focus group analysis are all in fields other than information systems, and offer little specific guidance for information systems researchers. Further, even the studies that exist in other fields do not provide a systematic and integrated procedure to analyse both focus group ‘content’ and ‘interaction’ data. As the focus group is a valuable method to answer the research questions of many IS studies (in the business, government and society contexts), we believe that more attention should be paid to this method in the IS research. This paper offers a systematic and integrated procedure for qualitative focus group data analysis in information systems research.

Optimal management of agricultural systems

To remain competitive, many agricultural systems are now being run along business lines. Systems methodologies are being incorporated, and here evolutionary computation is a valuable tool for identifying more profitable or sustainable solutions. However, agricultural models typically pose some of the more challenging problems for optimisation. This chapter outlines these problems, and then presents a series of three case studies demonstrating how they can be overcome in practice. Firstly, increasingly complex models of Australian livestock enterprises show that evolutionary computation is the only viable optimisation method for these large and difficult problems. On-going research is taking a notably efficient and robust variant, differential evolution, out into real-world systems. Next, models of cropping systems in Australia demonstrate the challenge of dealing with competing objectives, namely maximising farm profit whilst minimising resource degradation. Pareto methods are used to illustrate this trade-off, and these results have proved to be most useful for farm managers in this industry. Finally, land-use planning in the Netherlands demonstrates the size and spatial complexity of real-world problems. Here, GIS-based optimisation techniques are integrated with Pareto methods, producing better solutions which were acceptable to the competing organizations. These three studies all show that evolutionary computation remains the only feasible method for the optimisation of large, complex agricultural problems. An extra benefit is that the resultant population of candidate solutions illustrates trade-offs, and this leads to more informed discussions and better education of the industry decision-makers.

Macroscopically Dissipative Systems with Underlying Microscopic Dynamics : Properties and Limits of Measurement

While some of the deepest results in nature are those that give explicit bounds between important physical quantities, some of the most intriguing and celebrated of such bounds come from fields where there is still a great deal of disagreement and confusion regarding even the most fundamental aspects of the theories. For example, in quantum mechanics, there is still no complete consensus as to whether the limitations associated with Heisenberg's Uncertainty Principle derive from an inherent randomness in physics, or rather from limitations in the measurement process itself, resulting from phenomena like back action. Likewise, the second law of thermodynamics makes a statement regarding the increase in entropy of closed systems, yet the theory itself has neither a universally-accepted definition of equilibrium, nor an adequate explanation of how a system with underlying microscopically Hamiltonian dynamics (reversible) settles into a fixed distribution.

Motivated by these physical theories, and perhaps their inconsistencies, in this thesis we use dynamical systems theory to investigate how the very simplest of systems, even with no physical constraints, are characterized by bounds that give limits to the ability to make measurements on them. Using an existing interpretation, we start by examining how dissipative systems can be viewed as high-dimensional lossless systems, and how taking this view necessarily implies the existence of a noise process that results from the uncertainty in the initial system state. This fluctuation-dissipation result plays a central role in a measurement model that we examine, in particular describing how noise is inevitably injected into a system during a measurement, noise that can be viewed as originating either from the randomness of the many degrees of freedom of the measurement device, or of the environment. This noise constitutes one component of measurement back action, and ultimately imposes limits on measurement uncertainty. Depending on the assumptions we make about active devices, and their limitations, this back action can be offset to varying degrees via control. It turns out that using active devices to reduce measurement back action leads to estimation problems that have non-zero uncertainty lower bounds, the most interesting of which arise when the observed system is lossless. One such lower bound, a main contribution of this work, can be viewed as a classical version of a Heisenberg uncertainty relation between the system's position and momentum. We finally also revisit the murky question of how macroscopic dissipation appears from lossless dynamics, and propose alternative approaches for framing the question using existing systematic methods of model reduction.

Da impossibilidade da lucidez: a dissolução do Século XX em O arco-íris da gravidade, de Thomas Pynchon

Esta tese analisa a relação entre a ficcionalização da História Moderna e o desenvolvimento de uma ética da vida cotidiana no romance O arco-íris da gravidade, do norte-americano Thomas Pynchon. Para a sua análise e interpretação, será desenvolvido, no primeiro capítulo, um aporte teórico-metodológico que coteje a complexidade formal da narrativa (que dificulta a sua síntese temática) para se estabelecer, a partir daí, as condições de possibilidade de detecção de núcleos temáticos recorrentes que, numa rede de interconexões não-concêntrica ou dispersiva , perspectivizam no romance uma totalização fraturada do sistema-mundo moderno e contemporâneo. No segundo capítulo a ficcionalização do século XX é apresentada em suas configurações metafísica e intra-mundana, e no capítulo final são analisadas as condições que ela impõe para a formação, dentro do real ficcional, de rotinas e modos de vida eticamente positivos

On differentially dissipative dynamical systems

Dissipativity is an essential concept of systems theory. The paper provides an extension of dissipativity, named differential dissipativity, by lifting storage functions and supply rates to the tangent bundle. Differential dissipativity is connected to incremental stability in the same way as dissipativity is connected to stability. It leads to a natural formulation of differential passivity when restricting to quadratic supply rates. The paper also shows that the interconnection of differentially passive systems is differentially passive, and provides preliminary examples of differentially passive electrical systems. © IFAC.

The Bifurcation Interpreter: A Step Towards the Automatic Analysis of Dynamical Systems

The Bifurcation Interpreter is a computer program that autonomously explores the steady-state orbits of one-parameter families of periodically- driven oscillators. To report its findings, the Interpreter generates schematic diagrams and English text descriptions similar to those appearing in the science and engineering research literature. Given a system of equations as input, the Interpreter uses symbolic algebra to automatically generate numerical procedures that simulate the system. The Interpreter incorporates knowledge about dynamical systems theory, which it uses to guide the simulations, to interpret the results, and to minimize the effects of numerical error.

Divergent Paths of Development: The Modern World-System and Democratization in South Africa and Zambia

This article examines whether a Modern World- Systems (MWS) perspective can provide an improved understanding of the processes of democratization in Africa (and other developing regions of the world) by conducting a comparative case study of South Africa and Zambia in the 1990s, examining the transitions to democracy and divergent processes of democratic consolidation in each country. Semiperipheral South Africa has, due to its more advantageous position in the world-system, been better equipped than peripheral Zambia to safeguard democracy against erosion and reversal. Th e central irony of the MWS is that the weakest states in the MWS can be pushed around by core powers and are more easily forced to democratize while at the same time they are least likely to possess the resources necessary for democratic consolidation. Semiperipheral states can maintain their independence vis-à-vis the core to a higher degree, but if the decision is made to undertake a democratic transition they are more likely to possess the resources necessary for successful consolidation. Th e MWS perspective allows for an improved understanding of the causal pathway of how position in the MWS translates into the ability to consolidate democracy than does approaches that emphasize domestic factors.

Collaborative Planning in an Uncollaborative World

The purpose of this paper is to expose the concept of collaborative planning to the reality of planning, thereby assessing its efficacy for informing and explaining what planners 'really' do and can do. In this systematic appraisal, collaborative planning is disaggregated into four elements that can enlighten such conceptual frameworks: ontology, epistemology, ideology and methodology. These four lenses help delimit and clarify collaborative planning's strengths and weaknesses. The conceptual debate is related to an empirical investigation of planning processes, ranging from region-wide to local and from statutory to visionary in an arena where special care has been invested in participatory deliberation processes. The final analysis provides a systematic gauge of collaborative planning in light of the extensive empirical evidence, deploying the four conceptual dimensions introduced in part one. This exposes a range of problems not only with the concept itself but also regarding its affinity with the uncollaborative world within which it has to operate. The former shed light on those aspects where collaborative planning as a conceptual tool for practitioners needs to be renovated, while the latter highlight inconsistencies in a political framework that struggles to accommodate both global competitiveness and local democratic collaboration.

Appropriate complexity for the prediction of coastal and estuarine geomorphic behaviour at decadal to centennial scales

Coastal and estuarine landforms provide a physical template that not only accommodates diverse ecosystem functions and human activities, but also mediates flood and erosion risks that are expected to increase with climate change. In this paper, we explore some of the issues associated with the conceptualisation and modelling of coastal morphological change at time and space scales relevant to managers and policy makers. Firstly, we revisit the question of how to define the most appropriate scales at which to seek quantitative predictions of landform change within an age defined by human interference with natural sediment systems and by the prospect of significant changes in climate and ocean forcing. Secondly, we consider the theoretical bases and conceptual frameworks for determining which processes are most important at a given scale of interest and the related problem of how to translate this understanding into models that are computationally feasible, retain a sound physical basis and demonstrate useful predictive skill. In particular, we explore the limitations of a primary scale approach and the extent to which these can be resolved with reference to the concept of the coastal tract and application of systems theory. Thirdly, we consider the importance of different styles of landform change and the need to resolve not only incremental evolution of morphology but also changes in the qualitative dynamics of a system and/or its gross morphological configuration. The extreme complexity and spatially distributed nature of landform systems means that quantitative prediction of future changes must necessarily be approached through mechanistic modelling of some form or another. Geomorphology has increasingly embraced so-called ‘reduced complexity’ models as a means of moving from an essentially reductionist focus on the mechanics of sediment transport towards a more synthesist view of landform evolution. However, there is little consensus on exactly what constitutes a reduced complexity model and the term itself is both misleading and, arguably, unhelpful. Accordingly, we synthesise a set of requirements for what might be termed ‘appropriate complexity modelling’ of quantitative coastal morphological change at scales commensurate with contemporary management and policy-making requirements: 1) The system being studied must be bounded with reference to the time and space scales at which behaviours of interest emerge and/or scientific or management problems arise; 2) model complexity and comprehensiveness must be appropriate to the problem at hand; 3) modellers should seek a priori insights into what kind of behaviours are likely to be evident at the scale of interest and the extent to which the behavioural validity of a model may be constrained by its underlying assumptions and its comprehensiveness; 4) informed by qualitative insights into likely dynamic behaviour, models should then be formulated with a view to resolving critical state changes; and 5) meso-scale modelling of coastal morphological change should reflect critically on the role of modelling and its relation to the observable world.

Object transportation by multiple mobile robots controlled by attractor dynamics: theory and implementation

Dynamical systems theory is used as a theoretical language and tool to design a distributed control architecture for teams of mobile robots, that must transport a large object and simultaneously avoid collisions with (either static or dynamic) obstacles. Here we demonstrate in simulations and implementations in real robots that it is possible to simplify the architectures presented in previous work and to extend the approach to teams of n robots. The robots have no prior knowledge of the environment. The motion of each robot is controlled by a time series of asymptotical stable states. The attractor dynamics permits the integration of information from various sources in a graded manner. As a result, the robots show a strikingly smooth an stable team behaviour.