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.

Relevance feature discovery for text analysis

It is a big challenge to guarantee the quality of discovered relevance features in text documents for describing user preferences because of the large number of terms, patterns, and noise. Most existing popular text mining and classification methods have adopted term-based approaches. However, they have all suffered from the problems of polysemy and synonymy. Over the years, people have often held the hypothesis that pattern-based methods should perform better than term- based ones in describing user preferences, but many experiments do not support this hypothesis. This research presents a promising method, Relevance Feature Discovery (RFD), for solving this challenging issue. It discovers both positive and negative patterns in text documents as high-level features in order to accurately weight low-level features (terms) based on their specificity and their distributions in the high-level features. The thesis also introduces an adaptive model (called ARFD) to enhance the exibility of using RFD in adaptive environment. ARFD automatically updates the system's knowledge based on a sliding window over new incoming feedback documents. It can efficiently decide which incoming documents can bring in new knowledge into the system. Substantial experiments using the proposed models on Reuters Corpus Volume 1 and TREC topics show that the proposed models significantly outperform both the state-of-the-art term-based methods underpinned by Okapi BM25, Rocchio or Support Vector Machine and other pattern-based methods.

Grotesque gestures or sensuous signs? Rethinking notions of apprenticeship in early childhood education

Education might be conceptualized as a swarm of signs. Deleuze, in Proust and Signs (1964/2000) suggests that “Everything that teaches us something emits signs” (p. 4). Such conceptualizations regard education as fluid, multiple and temporal; a young child can display great skill in decoding some signs but not others. Regarding education as temporal and complex operates at some distance to the sociocultural concepts suggested by Vygotsky (1978) which focus on linear sequences of gaining managed, culturally-loaded knowledge from more experienced others. Despite differing theorizations around apprenticeship, during early years education a child becomes sensitive to signs that collectively prioritize conventionalized knowledge acquisition and communication practices. Drawing for learning and communicating exemplifies apprenticeship as a creative process rather than as sequential or culturally driven, and serves to exemplify Deleuzian concepts around the relationships between time and learning, rather than age or development stage and learning.

A longitudinal assessment of chronic wound fluid to detect biochemical indicators of healing

Chronic venous leg ulcers are a detrimental health issue plaguing our society, resulting in long term pain, immobility and decreased quality of life for a large proportion of sufferers. The frequency of these chronic wounds has led current research to focus on the wound environment to provide important information regarding the prolonged, fluctuated or static healing patterns of these wounds. Disruption to the normal wound healing process results in release of multiple factors in the wound environment that could correlate to wound chronicity. These biochemical factors can often be detected through non-invasively sampling chronic wound fluid (CWF) from the site of injury. Of note, whilst there are numerous studies comparing acute and chronic wound fluids, there have not been any reports in the literature employing a longitudinal study in order to track biochemical changes in wound fluid as patients transition from a non-healing to healed state. Initially the objective of this study was to identify biochemical changes in CWF associated with wound healing using a proteomic approach. The proteomic approach incorporated a multi-dimensional liquid chromatography fractionation technique coupled with mass spectrometry (MS) to enable identification of proteins present in lower concentrations in CWF. Not surprisingly, many of the proteins identified in wound fluid were acute phase proteins normally expressed during the inflammatory phase of healing. However, the number of proteins positively identified by MS was quite low. This was attributed to the diverse range in concentration of protein species in CWF making it challenging to detect the diagnostically relevant low molecular weight proteins. In view of this, SELDI-TOF MS was also explored as a means to target low molecular weight proteins in sequential patient CWF samples during the course of healing. Unfortunately, the results generated did not yield any peaks of interest that were altered as wounds transitioned to a healed state. During the course of proteomic assessment of CWF, it became evident that a fraction of non-proteinaceous compounds strongly absorbed at 280 nm. Subsequent analyses confirmed that most of these compounds were in fact part of the purine catabolic pathway, possessing distinctive aromatic rings and which results in high absorbance at 254 nm. The accumulation of these purinogenic compounds in CWF suggests that the wound bed is poorly oxygenated resulting in a switch to anaerobic metabolism and consequently ATP breakdown. In addition, the presence of the terminal purine catabolite, uric acid (UA), indicates that the enzyme xanthine oxidoreductase (XOR) catalyses the reaction of hypoxanthine to xanthine and finally to UA. More importantly, the studies provide evidence for the first time of the exogenous presence of XOR in CWF. XOR is the only enzyme in humans capable of catalysing the production of UA in conjunction with a burst of the highly reactive superoxide radical and other oxidants like H2O2. Excessive release of these free radicals in the wound environment can cause cellular damage disrupting the normal wound healing process. In view of this, a sensitive and specific assay was established for monitoring low concentrations of these catabolites in CWF. This procedure involved combining high performance liquid chromatography (HPLC) with tandem mass spectrometry and multiple reaction monitoring (MRM). This application was selective, using specific MRM transitions and HPLC separations for each analyte, making it ideal for the detection and quantitation of purine catabolites in CWF. The results demonstrated that elevated levels of UA were detected in wound fluid obtained from patients with clinically worse ulcers. This suggests that XOR is active in the wound site generating significant amounts of reactive oxygen species (ROS). In addition, analysis of the amount of purine precursors in wound fluid revealed elevated levels of purine precursors in wound fluid from patients with less severe ulcers. Taken together, the results generated in this thesis suggest that monitoring changes of purine catabolites in CWF is likely to provide valuable information regarding the healing patterns of chronic venous leg ulcers. XOR catalysis of purine precursors not only provides a method for monitoring the onset, prognosis and progress of chronic venous leg ulcers, but also provides a potential therapeutic target by inhibiting XOR, thus blocking UA and ROS production. Targeting a combination of these purinogenic compounds and XOR could lead to the development of novel point of care diagnostic tests. Therefore, further investigation of these processes during wound healing will be worthwhile and may assist in elucidating the pathogenesis of this disease state, which in turn may lead to the development of new diagnostics and therapies that target these processes.

A sequence analytic model of entrepreneurial discovery and exploitation process

This study examined the effect that temporal order within the entrepreneurial discovery exploitation process has on the outcomes of venture creation. Consistent with sequential theories of discovery-exploitation, the general flow of venture creation was found to be directed from discovery toward exploitation in a random sample of nascent ventures. However, venture creation attempts which specifically follow this sequence derive poor outcomes. Moreover, simultaneous discovery-exploitation was the most prevalent temporal order observed, and venture attempts that proceed in this manner more likely become operational. These findings suggest that venture creation is a multi-scale phenomenon that is at once directional in time, and simultaneously driven by symbiotically coupled discovery and exploitation.

Overlapping medical alarms are almost indiscriminable

Objective: We explore how accurately and quickly nurses can identify melodic medical equipment alarms when no mnemonics are used, when alarms may overlap, and when concurrent tasks are performed. Background: The international standard IEC 60601-1-8 (International Electrotechnical Commission, 2005) has proposed simple melodies to distinguish seven alarm sources. Previous studies with nonmedical participants reveal poor learning of melodic alarms and persistent confusions between some of them. The effects of domain expertise, concurrent tasks, and alarm overlaps are unknown. Method: Fourteen intensive care and general medical unit nurses learned the melodic alarms without mnemonics in two sessions on separate days. In the second half of Day 2 the nurses identified single alarms or pairs of alarms played in sequential, partially overlapping, or nearly completely overlapping configurations. For half the experimental blocks nurses performed a concurrent mental arithmetic task. Results: Nurses' learning was poor and was no better than the learning of nonnurses in a previous study. Nurses showed the previously noted confusions between alarms. Overlapping alarms were exceptionally difficult to identify. The concurrent task affected response time but not accuracy. Conclusion: Because of a failure of auditory stream segregation, the melodic alarms cannot be discriminated when they overlap. Directives to sequence the sounding of alarms in medical electrical equipment must be strictly adhered to, or the alarms must redesigned to support better auditory streaming. Application: Actual or potential uses of this research include the implementation of IEC 60601-1-8 alarms in medical electrical equipment.

CAT-SLAM : probabilistic localisation and mapping using a continuous appearance-based trajectory

This paper describes a new system, dubbed Continuous Appearance-based Trajectory Simultaneous Localisation and Mapping (CAT-SLAM), which augments sequential appearance-based place recognition with local metric pose filtering to improve the frequency and reliability of appearance-based loop closure. As in other approaches to appearance-based mapping, loop closure is performed without calculating global feature geometry or performing 3D map construction. Loop-closure filtering uses a probabilistic distribution of possible loop closures along the robot’s previous trajectory, which is represented by a linked list of previously visited locations linked by odometric information. Sequential appearance-based place recognition and local metric pose filtering are evaluated simultaneously using a Rao–Blackwellised particle filter, which weights particles based on appearance matching over sequential frames and the similarity of robot motion along the trajectory. The particle filter explicitly models both the likelihood of revisiting previous locations and exploring new locations. A modified resampling scheme counters particle deprivation and allows loop-closure updates to be performed in constant time for a given environment. We compare the performance of CAT-SLAM with FAB-MAP (a state-of-the-art appearance-only SLAM algorithm) using multiple real-world datasets, demonstrating an increase in the number of correct loop closures detected by CAT-SLAM.

Using approximate Bayesian computation to estimate transmission rates of nosocomial pathogens

In this paper, we apply a simulation based approach for estimating transmission rates of nosocomial pathogens. In particular, the objective is to infer the transmission rate between colonised health-care practitioners and uncolonised patients (and vice versa) solely from routinely collected incidence data. The method, using approximate Bayesian computation, is substantially less computer intensive and easier to implement than likelihood-based approaches we refer to here. We find through replacing the likelihood with a comparison of an efficient summary statistic between observed and simulated data that little is lost in the precision of estimated transmission rates. Furthermore, we investigate the impact of incorporating uncertainty in previously fixed parameters on the precision of the estimated transmission rates.

An analysis of holding cost impact on housing affordability in relation to midsized Greenfield residential property developments in South East Queensland

The position of housing demand and supply is not consistent. The Australian situation counters the experience demonstrated in many other parts of the world in the aftermath of the Global Financial Crisis, with residential housing prices proving particularly resilient. A seemingly inexorable housing demand remains a critical issue affecting the socio-economic landscape. Underpinned by high levels of population growth fuelled by immigration, and further buoyed by sustained historically low interest rates, increasing income levels, and increased government assistance for first home buyers, this strong housing demand level ensures problems related to housing affordability continue almost unabated. A significant, but less visible factor impacting housing affordability relates to holding costs. Although only one contributor in the housing affordability matrix, the nature and extent of holding cost impact requires elucidation: for example, the computation and methodology behind the calculation of holding costs varies widely - and in some instances completely ignored. In addition, ambiguity exists in terms of the inclusion of various elements that comprise holding costs, thereby affecting the assessment of their relative contribution. Such anomalies may be explained by considering that assessment is conducted over time in an ever-changing environment. A strong relationship with opportunity cost - in turn dependant inter alia upon prevailing inflation and / or interest rates - adds further complexity. By extending research in the general area of housing affordability, this thesis seeks to provide a detailed investigation of those elements related to holding costs specifically in the context of midsized (i.e. between 15-200 lots) greenfield residential property developments in South East Queensland. With the dimensions of holding costs and their influence over housing affordability determined, the null hypothesis H0 that holding costs are not passed on can be addressed. Arriving at these conclusions involves the development of robust economic and econometric models which seek to clarify the componentry impacts of holding cost elements. An explanatory sequential design research methodology has been adopted, whereby the compilation and analysis of quantitative data and the development of an economic model is informed by the subsequent collection and analysis of primarily qualitative data derived from surveying development related organisations. Ultimately, there are significant policy implications in relation to the framework used in Australian jurisdictions that promote, retain, or otherwise maximise, the opportunities for affordable housing.

Alternating direction implicit numerical method for the space and time fractional Bloch-Torrey equation in 3-D

Recently, some authors have considered a new diffusion model–space and time fractional Bloch-Torrey equation (ST-FBTE). Magin et al. (2008) have derived analytical solutions with fractional order dynamics in space (i.e., _ = 1, β an arbitrary real number, 1 < β ≤ 2) and time (i.e., 0 < α < 1, and β = 2), respectively. Yu et al. (2011) have derived an analytical solution and an effective implicit numerical method for solving ST-FBTEs, and also discussed the stability and convergence of the implicit numerical method. However, due to the computational overheads necessary to perform the simulations for nuclear magnetic resonance (NMR) in three dimensions, they present a study based on a two-dimensional example to confirm their theoretical analysis. Alternating direction implicit (ADI) schemes have been proposed for the numerical simulations of classic differential equations. The ADI schemes will reduce a multidimensional problem to a series of independent one-dimensional problems and are thus computationally efficient. In this paper, we consider the numerical solution of a ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. A fractional alternating direction implicit scheme (FADIS) for the ST-FBTE in 3-D is proposed. Stability and convergence properties of the FADIS are discussed. Finally, some numerical results for ST-FBTE are given.

A new implicit numerical method for the space and time fractional Bloch-Torrey equation

In recent years, it has been found that many phenomena in engineering, physics, chemistry and other sciences can be described very successfully by models using mathematical tools from fractional calculus. Recently, noted a new space and time fractional Bloch-Torrey equation (ST-FBTE) has been proposed (see Magin et al. (2008)), and successfully applied to analyse diffusion images of human brain tissues to provide new insights for further investigations of tissue structures. In this paper, we consider the ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we propose a new effective implicit numerical method (INM) for the STFBTE whereby we discretize the Riesz fractional derivative using a fractional centered difference. Secondly, we prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent, and the order of convergence of the implicit numerical method is ( T2 - α + h2 x + h2 y + h2 z ). Finally, some numerical results are presented to support our theoretical analysis.

Effort-release public-key encryption from cryptographic puzzles

Timed-release cryptography addresses the problem of “sending messages into the future”: information is encrypted so that it can only be decrypted after a certain amount of time, either (a) with the help of a trusted third party time server, or (b) after a party performs the required number of sequential operations. We generalise the latter case to what we call effort-release public key encryption (ER-PKE), where only the party holding the private key corresponding to the public key can decrypt, and only after performing a certain amount of computation which may or may not be parallelisable. Effort-release PKE generalises both the sequential-operation-based timed-release encryption of Rivest, Shamir, and Wagner, and also the encapsulated key escrow techniques of Bellare and Goldwasser. We give a generic construction for ER-PKE based on the use of moderately hard computational problems called puzzles. Our approach extends the KEM/DEM framework for public key encryption by introducing a difficulty notion for KEMs which results in effort-release PKE. When the puzzle used in our generic construction is non-parallelisable, we recover timed-release cryptography, with the addition that only the designated receiver (in the public key setting) can decrypt.

Analytical and numerical solutions of the space and time fractional bloch-torrey equation

Fractional order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brown-ian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As MRI is applied with increasing temporal and spatial resolution, the spin dynamics are being examined more closely; such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments where processes are often anisotropic. Anomalous diffusion in the human brain using fractional order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (see R.L. Magin et al., J. Magnetic Resonance, 190 (2008) 255-270). However effective numerical methods and supporting error analyses for the fractional Bloch-Torrey equation are still limited. In this paper, the space and time fractional Bloch-Torrey equation (ST-FBTE) is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE, and the stability and convergence of the INM are investigated. We prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.

Measuring reef complexity and rugosity from monocular video bathymetric reconstruction

Topographic structural complexity of a reef is highly correlated to coral growth rates, coral cover and overall levels of biodiversity, and is therefore integral in determining ecological processes. Modeling these processes commonly includes measures of rugosity obtained from a wide range of different survey techniques that often fail to capture rugosity at different spatial scales. Here we show that accurate estimates of rugosity can be obtained from video footage captured using underwater video cameras (i.e., monocular video). To demonstrate the accuracy of our method, we compared the results to in situ measurements of a 2m x 20m area of forereef from Glovers Reef atoll in Belize. Sequential pairs of images were used to compute fine scale bathymetric reconstructions of the reef substrate from which precise measurements of rugosity and reef topographic structural complexity can be derived across multiple spatial scales. To achieve accurate bathymetric reconstructions from uncalibrated monocular video, the position of the camera for each image in the video sequence and the intrinsic parameters (e.g., focal length) must be computed simultaneously. We show that these parameters can be often determined when the data exhibits parallax-type motion, and that rugosity and reef complexity can be accurately computed from existing video sequences taken from any type of underwater camera from any reef habitat or location. This technique provides an infinite array of possibilities for future coral reef research by providing a cost-effective and automated method of determining structural complexity and rugosity in both new and historical video surveys of coral reefs.