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.

Patterns of correlation between vehicle occupant seat pressure and anthropometry

Seat pressure is known as a major factor of seat comfort in vehicles. In passenger vehicles, there is lacking research into the seat comfort of rear seat occupants. As accurate seat pressure measurement requires significant effort, simulation of seat pressure is evolving as a preferred method. However, analytic methods are based on complex finite element modeling and therefore are time consuming and involve high investment. Based on accurate anthropometric measurements of 64 male subjects and outboard rear seat pressure measurements in three different passenger vehicles, this study investigates if a set of parameters derived from seat pressure mapping are sensitive enough to differentiate between different seats and whether they correlate with anthropometry in linear models. In addition to the pressure map analysis, H-Points were measured with a coordinate measurement system based on palpated body landmarks and the range of H-Point locations in the three seats is provided. It was found that for the cushion, cushion contact area and cushion front area/force could be modeled by subject anthropometry,while only seatback contact area could be modeled based on anthropometry for all three vehicles. Major differences were found between the vehicles for other parameters.

Severity of driver injury and vehicle damage in traffic crashes at intersections: A Bayesian hierarchical analysis

Most crash severity studies ignored severity correlations between driver-vehicle units involved in the same crashes. Models without accounting for these within-crash correlations will result in biased estimates in the factor effects. This study developed a Bayesian hierarchical binomial logistic model to identify the significant factors affecting the severity level of driver injury and vehicle damage in traffic crashes at signalized intersections. Crash data in Singapore were employed to calibrate the model. Model fitness assessment and comparison using Intra-class Correlation Coefficient (ICC) and Deviance Information Criterion (DIC) ensured the suitability of introducing the crash-level random effects. Crashes occurring in peak time, in good street lighting condition, involving pedestrian injuries are associated with a lower severity, while those in night time, at T/Y type intersections, on right-most lane, and installed with red light camera have larger odds of being severe. Moreover, heavy vehicles have a better resistance on severe crash, while crashes involving two-wheel vehicles, young or aged drivers, and the involvement of offending party are more likely to result in severe injuries.

Anisotropy of articular cartilage reflects the ECM gradient architecture : Hough-Radon Transform Analysis

Tissue-specific extracellular matrix (ECM) is known to be an ideal bioscaffold to inspire the future of regenerative medicine. It holds the secret of how nature has developed such an organization of molecules into a unique functional complexity. This work exploited an innovative image processing algorithm and high resolution microscopy associated with mechanical analysis to establish a correlation between the gradient organization of cartiligous ECM and its anisotropic biomechanical response. This was hypothesized to be a reliable determinant that can elucidate how microarchitecture interrelates with biomechanical properties. Hough-Radon transform of the ECM cross-section images revealed its conformational variation from tangential interface down to subchondral region. As the orientation varied layer by layer, the anisotropic mechanical response deviated relatively. Although, results were in good agreement (Kendall's tau-b > 90%), there were evidences proposing that alignment of the fibrous network, specifically in middle zone, is not as random as it was previously thought.

Computational fluid dynamic analysis of intracranial aneurysm bleb Formation (NS26P)

Purpose: The management of unruptured aneurysms remains controversial as treatment infers potential significant risk to the currently well patient. The decision to treat is based upon aneurysm location, size and abnormal morphology (e.g. bleb formation). A method to predict bleb formation would thus help stratify patient treatment. Our study aims to investigate possible associations between intra-aneurysmal flow dynamics and bleb formation within intracranial aneurysms. Competing theories on aetiology appear in the literature. Our purpose is to further clarify this issue. Methodology: We recruited data from 3D rotational angiograms (3DRA) of 30 patients with cerebral aneurysms and bleb formation. Models representing aneurysms pre-bleb formation were reconstructed by digitally removing the bleb, then computational fluid dynamics simulations were run on both pre and post bleb models. Pulsatile flow conditions and standard boundary conditions were imposed. Results: Aneurysmal flow structure, impingement regions, wall shear stress magnitude and gradients were produced for all models. Correlation of these parameters with bleb formation was sought. Certain CFD parameters show significant inter patient variability, making statistically significant correlation difficult on the partial data subset obtained currently. Conclusion: CFD models are readily producible from 3DRA data. Preliminary results indicate bleb formation appears to be related to regions of high wall shear stress and direct impingement regions of the aneurysm wall.

Innovative damage assessment of steel truss bridges using modal strain energy correlation

As a part of vital infrastructure and transportation network, bridge structures must function safely at all times. Bridges are designed to have a long life span. At any point in time, however, some bridges are aged. The ageing of bridge structures, given the rapidly growing demand of heavy and fast inter-city passages and continuous increase of freight transportation, would require diligence on bridge owners to ensure that the infrastructure is healthy at reasonable cost. In recent decades, a new technique, structural health monitoring (SHM), has emerged to meet this challenge. In this new engineering discipline, structural modal identification and damage detection have formed a vital component. Witnessed by an increasing number of publications is that the change in vibration characteristics is widely and deeply investigated to assess structural damage. Although a number of publications have addressed the feasibility of various methods through experimental verifications, few of them have focused on steel truss bridges. Finding a feasible vibration-based damage indicator for steel truss bridges and solving the difficulties in practical modal identification to support damage detection motivated this research project. This research was to derive an innovative method to assess structural damage in steel truss bridges. First, it proposed a new damage indicator that relies on optimising the correlation between theoretical and measured modal strain energy. The optimisation is powered by a newly proposed multilayer genetic algorithm. In addition, a selection criterion for damage-sensitive modes has been studied to achieve more efficient and accurate damage detection results. Second, in order to support the proposed damage indicator, the research studied the applications of two state-of-the-art modal identification techniques by considering some practical difficulties: the limited instrumentation, the influence of environmental noise, the difficulties in finite element model updating, and the data selection problem in the output-only modal identification methods. The numerical (by a planer truss model) and experimental (by a laboratory through truss bridge) verifications have proved the effectiveness and feasibility of the proposed damage detection scheme. The modal strain energy-based indicator was found to be sensitive to the damage in steel truss bridges with incomplete measurement. It has shown the damage indicator's potential in practical applications of steel truss bridges. Lastly, the achievement and limitation of this study, and lessons learnt from the modal analysis have been summarised.

Analysis of acoustic emission data for accurate damage assessment for structural health monitoring applications

Structural health monitoring (SHM) refers to the procedure used to assess the condition of structures so that their performance can be monitored and any damage can be detected early. Early detection of damage and appropriate retrofitting will aid in preventing failure of the structure and save money spent on maintenance or replacement and ensure the structure operates safely and efficiently during its whole intended life. Though visual inspection and other techniques such as vibration based ones are available for SHM of structures such as bridges, the use of acoustic emission (AE) technique is an attractive option and is increasing in use. AE waves are high frequency stress waves generated by rapid release of energy from localised sources within a material, such as crack initiation and growth. AE technique involves recording these waves by means of sensors attached on the surface and then analysing the signals to extract information about the nature of the source. High sensitivity to crack growth, ability to locate source, passive nature (no need to supply energy from outside, but energy from damage source itself is utilised) and possibility to perform real time monitoring (detecting crack as it occurs or grows) are some of the attractive features of AE technique. In spite of these advantages, challenges still exist in using AE technique for monitoring applications, especially in the area of analysis of recorded AE data, as large volumes of data are usually generated during monitoring. The need for effective data analysis can be linked with three main aims of monitoring: (a) accurately locating the source of damage; (b) identifying and discriminating signals from different sources of acoustic emission and (c) quantifying the level of damage of AE source for severity assessment. In AE technique, the location of the emission source is usually calculated using the times of arrival and velocities of the AE signals recorded by a number of sensors. But complications arise as AE waves can travel in a structure in a number of different modes that have different velocities and frequencies. Hence, to accurately locate a source it is necessary to identify the modes recorded by the sensors. This study has proposed and tested the use of time-frequency analysis tools such as short time Fourier transform to identify the modes and the use of the velocities of these modes to achieve very accurate results. Further, this study has explored the possibility of reducing the number of sensors needed for data capture by using the velocities of modes captured by a single sensor for source localization. A major problem in practical use of AE technique is the presence of sources of AE other than crack related, such as rubbing and impacts between different components of a structure. These spurious AE signals often mask the signals from the crack activity; hence discrimination of signals to identify the sources is very important. This work developed a model that uses different signal processing tools such as cross-correlation, magnitude squared coherence and energy distribution in different frequency bands as well as modal analysis (comparing amplitudes of identified modes) for accurately differentiating signals from different simulated AE sources. Quantification tools to assess the severity of the damage sources are highly desirable in practical applications. Though different damage quantification methods have been proposed in AE technique, not all have achieved universal approval or have been approved as suitable for all situations. The b-value analysis, which involves the study of distribution of amplitudes of AE signals, and its modified form (known as improved b-value analysis), was investigated for suitability for damage quantification purposes in ductile materials such as steel. This was found to give encouraging results for analysis of data from laboratory, thereby extending the possibility of its use for real life structures. By addressing these primary issues, it is believed that this thesis has helped improve the effectiveness of AE technique for structural health monitoring of civil infrastructures such as bridges.

Analysis of a negatively buoyant jet

The behavior of plane fountains, resulting from the injection of dense fluid (water) upwards into a large container of homogeneous fluid of lower density (air),was investigated. In this study the behavior of fountains was examined numerically and experimentally for different Froude and Reynolds numbers. The flow rate and nozzle diameter of the inlet of the fountain was varied to cover a wide range of Reynolds and Froude numbers. The effect of inclination angle of the inlet for different nozzle diameter and flow rate on fountain behavior was observed. It was found that the height of the fountain greatly depends on Froude number. An empirical correlation was developed for non-dimensional fountain height with Froude number. However the non-dimensional fountain height can more accurately be represented when regressed with both Reynolds and Froude number by the following relationship H/r=exp(5.94)*Re^-0.72*Fr^2.26. The result are compared with previous numerical and experimental results and found to be consistent.

Underground power cable environment on-line monitoring and analysis

Knowledge of cable parameters has been well established but a better knowledge of the environment in which the cables are buried lags behind. Research in Queensland University of Technology has been aimed at obtaining and analysing actual daily field values of thermal resistivity and diffusivity of the soil around power cables. On-line monitoring systems have been developed and installed with a data logger system and buried spheres that use an improved technique to measure thermal resistivity and diffusivity over a short period. Results based on long term continuous field data are given. A probabilistic approach is developed to establish the correlation between the measured field thermal resistivity values and rainfall data from weather bureau records. This data from field studies can reduce the risk in cable rating decisions and provide a basis for reliable prediction of “hot spot” of an existing cable circuit

Years lived with disability (YLDs) for 1160 sequelae of 289 diseases and injuries 1990–2010 : a systematic analysis for the Global Burden of Disease Study 2010

Background Non-fatal health outcomes from diseases and injuries are a crucial consideration in the promotion and monitoring of individual and population health. The Global Burden of Disease (GBD) studies done in 1990 and 2000 have been the only studies to quantify non-fatal health outcomes across an exhaustive set of disorders at the global and regional level. Neither effort quantified uncertainty in prevalence or years lived with disability (YLDs). Methods Of the 291 diseases and injuries in the GBD cause list, 289 cause disability. For 1160 sequelae of the 289 diseases and injuries, we undertook a systematic analysis of prevalence, incidence, remission, duration, and excess mortality. Sources included published studies, case notification, population-based cancer registries, other disease registries, antenatal clinic serosurveillance, hospital discharge data, ambulatory care data, household surveys, other surveys, and cohort studies. For most sequelae, we used a Bayesian meta-regression method, DisMod-MR, designed to address key limitations in descriptive epidemiological data, including missing data, inconsistency, and large methodological variation between data sources. For some disorders, we used natural history models, geospatial models, back-calculation models (models calculating incidence from population mortality rates and case fatality), or registration completeness models (models adjusting for incomplete registration with health-system access and other covariates). Disability weights for 220 unique health states were used to capture the severity of health loss. YLDs by cause at age, sex, country, and year levels were adjusted for comorbidity with simulation methods. We included uncertainty estimates at all stages of the analysis. Findings Global prevalence for all ages combined in 2010 across the 1160 sequelae ranged from fewer than one case per 1 million people to 350 000 cases per 1 million people. Prevalence and severity of health loss were weakly correlated (correlation coefficient −0·37). In 2010, there were 777 million YLDs from all causes, up from 583 million in 1990. The main contributors to global YLDs were mental and behavioural disorders, musculoskeletal disorders, and diabetes or endocrine diseases. The leading specific causes of YLDs were much the same in 2010 as they were in 1990: low back pain, major depressive disorder, iron-deficiency anaemia, neck pain, chronic obstructive pulmonary disease, anxiety disorders, migraine, diabetes, and falls. Age-specific prevalence of YLDs increased with age in all regions and has decreased slightly from 1990 to 2010. Regional patterns of the leading causes of YLDs were more similar compared with years of life lost due to premature mortality. Neglected tropical diseases, HIV/AIDS, tuberculosis, malaria, and anaemia were important causes of YLDs in sub-Saharan Africa. Interpretation Rates of YLDs per 100 000 people have remained largely constant over time but rise steadily with age. Population growth and ageing have increased YLD numbers and crude rates over the past two decades. Prevalences of the most common causes of YLDs, such as mental and behavioural disorders and musculoskeletal disorders, have not decreased. Health systems will need to address the needs of the rising numbers of individuals with a range of disorders that largely cause disability but not mortality. Quantification of the burden of non-fatal health outcomes will be crucial to understand how well health systems are responding to these challenges. Effective and affordable strategies to deal with this rising burden are an urgent priority for health systems in most parts of the world. Funding Bill & Melinda Gates Foundation.

Characterization of tight gas reservoir pore structure using USANS/SANS and gas adsorption analysis

Small-angle and ultra-small-angle neutron scattering (SANS and USANS) measurements were performed on samples from the Triassic Montney tight gas reservoir in Western Canada in order to determine the applicability of these techniques for characterizing the full pore size spectrum and to gain insight into the nature of the pore structure and its control on permeability. The subject tight gas reservoir consists of a finely laminated siltstone sequence; extensive cementation and moderate clay content are the primary causes of low permeability. SANS/USANS experiments run at ambient pressure and temperature conditions on lithologically-diverse sub-samples of three core plugs demonstrated that a broad pore size distribution could be interpreted from the data. Two interpretation methods were used to evaluate total porosity, pore size distribution and surface area and the results were compared to independent estimates derived from helium porosimetry (connected porosity) and low-pressure N2 and CO2 adsorption (accessible surface area and pore size distribution). The pore structure of the three samples as interpreted from SANS/USANS is fairly uniform, with small differences in the small-pore range (<2000 Å), possibly related to differences in degree of cementation, and mineralogy, in particular clay content. Total porosity interpreted from USANS/SANS is similar to (but systematically higher than) helium porosities measured on the whole core plug. Both methods were used to estimate the percentage of open porosity expressed here as a ratio of connected porosity, as established from helium adsorption, to the total porosity, as estimated from SANS/USANS techniques. Open porosity appears to control permeability (determined using pressure and pulse-decay techniques), with the highest permeability sample also having the highest percentage of open porosity. Surface area, as calculated from low-pressure N2 and CO2 adsorption, is significantly less than surface area estimates from SANS/USANS, which is due in part to limited accessibility of the gases to all pores. The similarity between N2 and CO2-accessible surface area suggests an absence of microporosity in these samples, which is in agreement with SANS analysis. A core gamma ray profile run on the same core from which the core plug samples were taken correlates to profile permeability measurements run on the slabbed core. This correlation is related to clay content, which possibly controls the percentage of open porosity. Continued study of these effects will prove useful in log-core calibration efforts for tight gas.

Managing memory and reducing I/O cost for correlation matrix calculation in bioinformatics

The generation of a correlation matrix from a large set of long gene sequences is a common requirement in many bioinformatics problems such as phylogenetic analysis. The generation is not only computationally intensive but also requires significant memory resources as, typically, few gene sequences can be simultaneously stored in primary memory. The standard practice in such computation is to use frequent input/output (I/O) operations. Therefore, minimizing the number of these operations will yield much faster run-times. This paper develops an approach for the faster and scalable computing of large-size correlation matrices through the full use of available memory and a reduced number of I/O operations. The approach is scalable in the sense that the same algorithms can be executed on different computing platforms with different amounts of memory and can be applied to different problems with different correlation matrix sizes. The significant performance improvement of the approach over the existing approaches is demonstrated through benchmark examples.

Quantifying spatial structure in experimental observations and agent-based simulations using pair-correlation functions

We define a pair-correlation function that can be used to characterize spatiotemporal patterning in experimental images and snapshots from discrete simulations. Unlike previous pair-correlation functions, the pair-correlation functions developed here depend on the location and size of objects. The pair-correlation function can be used to indicate complete spatial randomness, aggregation or segregation over a range of length scales, and quantifies spatial structures such as the shape, size and distribution of clusters. Comparing pair-correlation data for various experimental and simulation images illustrates their potential use as a summary statistic for calibrating discrete models of various physical processes.

Metabolomic analysis characterizes tissue specific indomethacin-induced metabolic perturbations of rats

In this study, the promising metabolomic approach integrating with ingenuity pathway analysis (IPA) was applied to characterize the tissue specific metabolic perturbation of rats that was induced by indomethacin. The selective pattern recognition analyses were applied to analyze global metabolic profiling of urine of rats treated by indomethacin at an acute dosage of reference that has been proven to induce tissue disorders in rats, evaluated throughout the time-course of -24-72 h. The results preliminarily revealed that modifications of amino acid metabolism, fatty acid metabolism and energetically associated metabolic pathways accounted for metabolic perturbation of the rats that was induced by indomethacin. Furthermore, IPA was applied to deeply analyze the biomarkers and their relations with the metabolic perturbations evidenced by pattern recognition analyses. Specific biochemical functions affected by indomethacin suggested that there is an important correlation of its effects in kidney and liver metabolism, based on the determined metabolites and their pathway-based analysis. The IPA correlation of the three major biomarkers, identified as creatinine, prostaglandin E2 and guanosine, suggested that the administration of indomethacin induced certain levels of toxicity in the kidneys and liver. The changes in the levels of biomarker metabolites allowed the phenotypical determination of the metabolic perturbations induced by indomethacin in a time-dependent manner.

Analysis of chromosome 1 microsatellite markers and the FHM2-ATP1A2 gene mutations in migraine pedigrees

OBJECTIVES: The aims of the study were: (i) to extend our linkage analysis of chromosome 1q microsatellite markers in predominantly migraine with aura pedigrees and (ii) to test the novel FHM-2 ATP1A2 gene for involvement in these migraine affected pedigrees and a previous pedigree (MF14) showing evidence of linkage of markers to C1q31. METHODS: A chromosome 1 scan (31 markers) was performed in 21 multiplex pedigrees affected predominantly with migraine with aura (MA). The known FHM-2 ATP1A2 gene mutations were tested, by sequencing, for the involvement in MA and migraine without aura (MO) in these pedigrees. Sequencing was performed in the coding areas of the ATP1A2 gene through three MA individuals from MF14. RESULTS: Evidence for linkage was obtained at C1q23 to markers spanning the ATP1A2 gene. However, testing of the known ATP1A2 gene mutations (for FHM) in common migraine probands of pedigrees showing excess allele sharing was negative. Sequencing of the entire coding areas of the gene through all the three MA affected from MF14 was also negative for mutations. DISCUSSION: Microsatellite markers on chromosome 1q23 show evidence of excess allele sharing in MA and some MO pedigrees, suggesting linkage to the common forms of migraine and the presence of a susceptibility gene in this region. The FHM-2 (ATP1A2 gene) does not seem to be involved in the common types of migraine. Despite certain clinical characteristics, the genetic correlation between FHM and familial typical migraine remains unclear. Several candidate genes lie within the C1q23 and C1q31 cytogenetic regions; therefore, further studies are needed.