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.

Property investment, construction and economic growth : the case of Malaysia

It is generally accepted that there is a close relationship between property investment and construction activity. The construction sector plays a crucial role in economic development, especially for a developing nation such as Malaysia. However, the volume of new properties added to the property market is only a fraction of the total volume of the property market. Is the conventional assumption of the relationship between property investment and construction supported by empirical data? This paper revisits the tripartite relationships between economic growths, property investment and construction activities with official Malaysian 2000Q1-2010Q4 quarterly time series data. The Granger causality tests are used to establish the causality runs from the GDP to the value of property transactions, and the growth of construction activities to GDP growth. The result is expected to be useful for policymakers and industrial practitioners in formulating industrial policies and corporate strategies.

Assessing the real value in residential property investment

One of the major fall outs from the Global Financial Crisis has been the decline in residential property construction, home lending and residential property prices. This has lead to some extent to a reduction in the number of small investors willing to commit funds to an investment market that is not seen to perform as well as other investment assets, particularly in relation to income return.With a decreasing supply of rental accommodation in the housing markets, less public housing being constructed by both State and Commonwealth Governments, there is the potential for the residential property market to provide more substantial returns than previous years.This paper will analyse the current residential housing market in Brisbane, Australia to determine if there are sectors in this market that are outperforming the average income and total return for residential investment property and the variation in investment performance across the various housing sub-markets. The results show that property investment in residential property provides opportunities to maximize returns based on geographic location and socio-economic economic status, with lower value areas showing the highest income returns and higher value suburbs showing greater capital returns

The Profiling of Property, Plant & Equipment (PPE) Contributions in Australia and Malaysia Public Listed Construction Companies

The purpose of this paper is to study the profiling of property, plant and equipment (PPE) contributions in Australia and Malaysia construction companies. A company’s worth is usually based on the listed share price on the stock exchange. In arriving at the net profit, the contribution of PPE in the company’s assets is somehow being neglected. This paper will investigate the followings; firstly the level of PPE contribution in the construction firms by comparing the PPE contributions to the company’s asset as a whole which includes fixed (non-current) assets and current assets. This will determine the true strength of the companies, rather than relying on the share prices alone. Secondly, the paper will determine the trend of company’s asset ownership to show the company’s performance of the PPE ownership during the period of study. The data is based on the selected construction companies listed on the Australian Stock Exchange (ASX) and Malaysian Stock Exchange, known as Bursa Malaysia. The profiling will help to determine the strength of the construction firms based on the PPE holding, and the level of PPE ownerships in the two countries construction firms during the period of study.

An analysis of NSW rural property market : 1990-2010

Rural property in Australia has seen significant market resurgence over the past 3 years, with improved seasonal conditions in a number of states, improved commodity prices and a greater interest and purchase of rural land by major international corporations and investment institutions. Much of this change in perspective in relation to rural property as an asset class can be linked to the food shortage of 2007 and the subsequent interest by many countries in respect to food security. This paper will address the total and capital return performance of a major agricultural area and compare these returns on the basis of both location of land and land use. The comparison will be used to determine if location or actual land use has a greater influence on rural property capital and income returns. This performance analysis is based on over 40,000 rural sales transactions. These transactions cover all market based rural property transactions in New South Wales, Australia for the period January 1990 to December 2010. Correlation analysis and investment performance analysis has also been carried out to determine the possible relationships between location and land use and subsequent changes in rural land capital values.

Sale of property gifted under a will by an attorney acting under an enduring power of attorney : does the gift adeem and what is the attorney's duty?

The authors examine Moylan v Rickard and how the case illustrates the effectiveness of the Powers of Attorney Act 1998 (Qld) to provide remedies and other possible avenues of redress

Energy efficiency and sustainability in residential property

The issue of a more sustainable environment has been the aim of many governments and institutions for decades. Current research and literature has shown the continuing impact of global development and population increases on the planet as a whole. Issues such as carbon emissions, global warming, resource sustainability, industrial pollution, waste management and the decline in scarce resources, including food, are now realities and are being addressed at various levels. All levels of government, business and the public now equally share responsibility for the continued sustainable environment in general. Although these issues of global warming, climate change and the overuse of scarce resources are well documented, and constantly covered in all media forms, public attitudes to these issues vary significantly. Despite being aware of these issues many individuals consider that the problem is one for governments to tackle and that their individual efforts are not important or necessary. In many cases individuals are concerned with sustainability, but are either not in the position to take action due to economic circumstances or are not prepared to offset sustainability gains with personal interests...

Place and Space: Community in the Internet Economy and What This Will Mean for Property

By 2020 Australia‟s National Digital Economy Strategy aims to increase household online participation and engage 12 per cent of all employees in teleworking arrangements. Achieving these goals is generally perceived as positive due to the reduced impact on the natural environment from less use of transport. However, this also will enable greater flexibility as to where people live and thus will impact upon the maintenance and formation of communities and on property use. This paper commences by clarifying what is Australia‟s internet economy before highlighting the impact of the internet on community formation and maintenance. The paper concludes by identifying what the achievement of these goals will mean for property use in the future.

Property, planning and purpose : legal concerns facing broadband rollout in Australia

The Australian government, and opposition, are committed to facilitating high-speed broadband provision. In April 2009 the (then) Labor government announced a proposal to facilitate provision by mandating “…the use of fibre optic infrastructure … in greenfield estates ….” Separately, the installation of (usually overhead) cables commenced in select brownfield areas throughout Australia. In the lead up to the 2010 federal election, the broadband policy focus of the (then) federal opposition was to enabling private investment rather than direct investment by government itself. High-speed broadband is essential for Australia’s economic future. Whether implementation is undertaken by government, government owned corporations or private investors, will impact on the processes to be followed. Who does what, also will determine the rights available to land owners. The next stage, of necessity, will involve the establishment of procedures to require the retrofitting of existing urban environments. This clearly will have major property, property rights and valuation impacts. As Horan (2000) observed “…preserving... unique characteristics … of…regions requires a compromise between economic ambitions and social, cultural, and environmental values”. The uncertainty following the federal election, and the influence of independants with individual agendas; presents unique challenges for broadband implementation. This paper seeks to identify the processes to be followed by various potential broadband investors as they work to establish a ubiquitous network. It overviews current legislative regimes and examines concerns raised by stakeholders in various government reviews. It concludes by plotting a clear way forward to the future, with particular regard to property rights and usage.

Enabling sustainable property practices by ensuring security of tenure

Sustainable property practices will be essential for Australia’s future. The various levels of government offer incentives aimed at encouraging residents to participate in sustainable practices. Many of these programmes however are only accessible by owner occupiers, or landlords and tenants with long term tenancies. Improving security of tenure for tenants, to enable longer term tenancies, would positively impact upon property practices. This article explains what security of tenure is and identifies how a lack of security of tenure adversely impacts property practices. By comparison with Genevan property practices, it concludes by making suggestions as to how security of tenure can be reinforced.

Its place in property education : where does property law fit into property programs?

Property law is one of the key elements in any property-based degree program. In particular, an understanding of 'property law' is one of the required knowledge fields for inclusion in property programs accredited by professional institutes such as the Royal Institution of Chartered Surveyors, the Appraisal Institute and the Australian Property Institute. Despite the importance of property law as a cornerstone element of all property programs this aspect of the program is often approached from a more generic legal perspective with teaching resources used and pedagogical approach more aligned to the study of law that property. The specificity of this type of program is rarely adequately acknowledged. The question arises as to what the study of 'property law' entails and what the composition of a 'property law' subject should be. Replicating the methodology used by Placid and Weeks (2009) in their examination of the current composition of real estate law courses in the United States, this paper examines the current composition and pedagogical approach adopted by Australian universities based on the study of three Queensland property programs. In particular the curriculum, teaching resources used, assessment and engagement strategies are considered with a view to making improvements to the way these property law courses can be more effectively tailored to property students. It is anticipated that the outcomes of this paper will be of interest to all academics who are responsible for developing and delivering property law subjects and those who manage property programs in Australia and internationally.

Reviewing the impact of the 2008/2009 global financial crisis (GFC) on international property markets and property professions

The global financial crisis that impacted on all world economies throughout 2008 and 2009. This impact has not been confined to the finance industries but has had a direct and indirect impact on the property industry worldwide from both an ownership and investment perspective. Property markets have experienced various levels of impact from this event, but universally the greatest impact has been on the traditional commercial and industrial property sectors from the investor perspective, with investment and superannuation funds reporting significant declines in the reported value of these investments. Despite the very direct impact of these declining property markets, the GFC has also had a very significant indirect impact on the various property professions and how these professions are now operating in this declining property market. Of particular interest is the comparison of the property market forecasts in late 2007 to the actual results in 2008/2009.

Models of collective cell behaviour with crowding effects : comparing lattice-based and lattice-free approaches

Individual-based models describing the migration and proliferation of a population of cells frequently restrict the cells to a predefined lattice. An implicit assumption of this type of lattice based model is that a proliferative population will always eventually fill the lattice. Here we develop a new lattice-free individual-based model that incorporates cell-to-cell crowding effects. We also derive approximate mean-field descriptions for the lattice-free model in two special cases motivated by commonly used experimental setups. Lattice-free simulation results are compared to these mean-field descriptions and to a corresponding lattice-based model. Data from a proliferation experiment is used to estimate the parameters for the new model, including the cell proliferation rate, showing that the model fits the data well. An important aspect of the lattice-free model is that the confluent cell density is not predefined, as with lattice-based models, but an emergent model property. As a consequence of the more realistic, irregular configuration of cells in the lattice-free model, the population growth rate is much slower at high cell densities and the population cannot reach the same confluent density as an equivalent lattice-based model.