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.

High-resolution DNA melt curve analysis of the clustered, regularly interspaced short-palindromic-repeat locus of Campylobacter jejuni

A novel method for genotyping the clustered, regularly interspaced short-palindromic-repeat (CRISPR) locus of Campylobacter jejuni is described. Following real-time PCR, CRISPR products were subjected to high-resolution melt (HRM) analysis, a new technology that allows precise melt profile determination of amplicons. This investigation shows that the CRISPR HRM assay provides a powerful addition to existing C. jejuni genotyping methods and emphasizes the potential of HRM for genotyping short sequence repeats in other species

Photocatalytic disinfection of bacterial pollutants using suspended and immobilized TiO(2) powders

The photocatalytic disinfection of Enterobacter cloacae and Enterobacter coli using microwave (MW), convection hydrothermal (HT) and Degussa P25 titania was investigated in suspension and immobilized reactors. In suspension reactors, MW-treated TiO(2) was the most efficient catalyst (per unit weight of catalyst) for the disinfection of E. cloacae. However, HT-treated TiO(2) was approximately 10 times more efficient than MW or P25 titania for the disinfection of E. coli suspensions in surface water using the immobilized reactor. In immobilized experiments, using surface water a significant amount of photolysis was observed using the MW- and HT-treated films; however, disinfection on P25 films was primarily attributed to photocatalysis. Competitive action of inorganic ions and humic substances for hydroxyl radicals during photocatalytic experiments, as well as humic substances physically screening the cells from UV and hydroxyl radical attack resulted in low rates of disinfection. A decrease in colony size (from 1.5 to 0.3 mm) was noted during photocatalytic experiments. The smaller than average colonies were thought to occur during sublethal (•) OH and O(2) (•-) attack. Catalyst fouling was observed following experiments in surface water and the ability to regenerate the surface was demonstrated using photocatalytic degradation of oxalic acid as a model test system

Geologically ancient DNA: fact or artefact?

Studies continue to report ancient DNA sequences and viable microbial cells that are many millions of years old. In this paper we evaluate some of the most extravagant claims of geologically ancient DNA. We conclude that although exciting, the reports suffer from inadequate experimental setup and insufficient authentication of results. Consequently, it remains doubtful whether amplifiable DNA sequences and viable bacteria can survive over geological timescales. To enhance the credibility of future studies and assist in discarding false-positive results, we propose a rigorous set of authentication criteria for work with geologically ancient DNA.

Combined mitochondrial and nuclear DNA sequences resolve the interrelations of the major Australasian marsupial radiations

Australasian marsupials include three major radiations, the insectivorous/carnivorous Dasyuromorphia, the omnivorous bandicoots (Peramelemorphia), and the largely herbivorous diprotodontians. Morphologists have generally considered the bandicoots and diprotodontians to be closely related, most prominently because they are both syndactylous (with the 2nd and 3rd pedal digits being fused). Molecular studies have been unable to confirm or reject this Syndactyla hypothesis. Here we present new mitochondrial (mt) genomes from a spiny bandicoot (Echymipera rufescens) and two dasyurids, a fat-tailed dunnart (Sminthopsis crassicaudata) and a northern quoll (Dasyurus hallucatus). By comparing trees derived from pairwise base-frequency differences between taxa with standard (absolute, uncorrected) distance trees, we infer that composition bias among mt protein-coding and RNA sequences is sufficient to mislead tree reconstruction. This can explain incongruence between trees obtained from mt and nuclear data sets. However, after excluding major sources of compositional heterogeneity, both the “reduced-bias” mt and nuclear data sets clearly favor a bandicoot plus dasyuromorphian association, as well as a grouping of kangaroos and possums (Phalangeriformes) among diprotodontians. Notably, alternatives to these groupings could only be confidently rejected by combining the mt and nuclear data. Elsewhere on the tree, Dromiciops appears to be sister to the monophyletic Australasian marsupials, whereas the placement of the marsupial mole (Notoryctes) remains problematic. More generally, we contend that it is desirable to combine mt genome and nuclear sequences for inferring vertebrate phylogeny, but as separately modeled process partitions. This strategy depends on detecting and excluding (or accounting for) major sources of nonhistorical signal, such as from compositional nonstationarity.

Isolation and characterisation of novel microsatellite and mitochondrial DNA markers for the Eastern Water Dragon (Physignathus lesueurii)

Habitat fragmentation as a result of urbanisation is a growing problem for native lizard species. The Eastern Water Dragon (Physignathus lesueurii) is a social arboreal agamid lizard, native to Australia. This species represents an ideal model species to investigate the effect of urbanisation because of their prominent abundance in the urban landscape. Here we describe the isolation and characterisation of a novel set of 74 di-, tri-, and tetramicrosatellites from which 18 were selected and optimised into two multiplexes. The 18 microsatellites generated a total 148 alleles across the two populations. The number of alleles per locus varied from 2 to 18 alleles and measures of Ho and He varied from 0.395 to 0.877 and from 0.441 to 0.880, respectively. We also present primers for four novel mitochondrial DNA (mtDNA) markers. The combined length of the four mtDNA marker pairs was 2,528 bp which included 15 nucleotides changes. In comparison to threatened species, which are generally characterised by small population sizes, the Eastern Water Dragon represents an ideal model species to investigate the effect of urbanisation on their behavioural ecology and connectivity patterns among populations.

Identification of bifunctional GA and AG intrastrand crosslinks formed between cisplatin and DNA

A combination of enzymatic digestion and electrospray ionisation mass spectrometry (ESI-MS) was used to characterise bifunctional adducts in which cisplatin is bound to GA base sequences in 8mer and 16mer oligonucleotides that do not contain other, higher affinity binding sites. The extent of formation of bifunctional adducts with GA base sequences was significant, but less than that seen with similar oligonucleotides containing either AG or GG sequences.