Statistical Complexity of Heterogeneous Geometric Networks

Heterogeneity and geometry are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical complexity of networks is not well understood. We introduce a parsimonious normalised measure of statistical complexity for networks -- normalised hierarchical complexity. The measure is trivially 0 in regular graphs and we prove that this measure tends to 0 in Erd\"os-R\'enyi random graphs in the thermodynamic limit. We go on to demonstrate that greater complexity arises from the combination of hierarchical and geometric components to the network structure than either on their own. Further, the levels of complexity achieved are similar to those found in many real-world networks. We also find that real world networks establish connections in a way which increases hierarchical complexity and which our null models and a range of attachment mechanisms fail to explain. This underlines the non-trivial nature of statistical complexity in real-world networks and provides foundations for the comparative analysis of network complexity within and across disciplines.Comment: 12 pages, 6 figure

Novel topological and temporal network analyses for EEG functional connectivity with applications to Alzheimer’s disease

This doctoral thesis outlines several methodological advances in network science aimed towards uncovering rapid, complex interdependencies of electromagnetic brain activity recorded from the Electroencephalogram (EEG). This entails both new analyses and modelling of EEG brain network topologies and a novel approach to analyse rapid dynamics of connectivity. Importantly, we implement these advances to provide novel insights into pathological brain function in Alzheimer’s disease. We introduce the concept of hierarchical complexity of network topology, providing both an index to measure it and a model to simulate it. We then show that the topology of functional connectivity estimated from EEG recordings is hierarchically complex, existing in a scale between random and star-like topologies, this is a paradigm shift from the established understanding that complexity arises between random and regular topologies. We go on to consider the density appropriate for binarisation of EEG functional connectivity, a methodological step recommended to produce compact and unbiased networks, in light of its new-found hierarchical complexity. Through simulations and real EEG data, we show the benefit of going beyond often recommended sparse representations to account for a broader range of hierarchy level interactions. After this, we turn our attention to assessing dynamic changes in connectivity. By constructing a unified framework for multivariate signals and graphs, inspired by network science and graph signal processing, we introduce graph-variate signal analysis which allows us to capture rapid fluctuations in connectivity robust to spurious short-term correlations. We define this for three pertinent brain connectivity estimates- Pearson’s correlation coefficient, coherence and phase-lag index- and show its benefit over standard dynamic connectivity measures in a range of simulations and real data. Applying these novel methods to EEG datasets of the performance of visual short-term memory binding tasks by familial and sporadic Alzheimer’s disease patients, we uncover disorganisation of the topological hierarchy of EEG brain function and abnormalities of transient phase-based activity which paves the way for new interpretations of the disease’s affect on brain function. Hierarchical complexity and graph-variate dynamic connectivity are entirely new methods for analysing EEG brain networks. The former provides new interpretations of complexity in static connectivity patterns while the latter enables robust analysis of transient temporal connectivity patterns, both at the frontiers of analysis. Although designed with EEG functional connectivity in mind, we hope these techniques will be picked up in the broader field, having consequences for research into complex networks in general

Exploring the efficacy of a graph classification GNN in learning non-linear graph metrics

Graph-structured data is common in many felds, including social networks, biological networks, and recommendation systems. The complexity of relationships in such data frequently necessitates the use of advanced modeling approaches to derive relevant insights. With the increasingly large network datasets being made available, deep learning is becoming a more relevant methodology for their exploration. Deep learning architectures which have graph inputs are called Graph Neural Networks (GNNs). One area in particular where great efforts have been made to gather population-wide data is in brain connectomics. The UK BioBank, for example has plans for up to 100,000 MRI scans which can be used for processing into brain connectomes. An important example of a graph classifcation GNN model for use on such data is the Brain Network Convolutional Neural Network (BrainNetCNN) model [1]. The BrainNetCNN is a CNN with special “cross-shaped” kernels for dealing with graph adjacency matrices. However, recent studies have repeatedly shown that the BrainNetCNN (among other GNNs) fails to outperform simpler, linear predictive models such as linear ridge regression in predicting population characteristics and clinical variables [2] [3] [4] [5]. This could be because most of the important characteristic/diagnostic information retrievable from brain networks is linear in nature, or there is still not enough data available to train GNNs on brain networks. But it could also be that developing more powerful models which can better identify more interesting relationships in the data with greater effciency will signifcantly improve predictive power. In order to begin analysing this, here we study how well the BrainNetCNN can learn non-linear patterns and structural characteristics– clustering coeffcient, routing effciency, degree variance, diffusion effciency, and assortativity– in three different types of synthetic graph datasets: Erdos-Renyi graphs, Barabasi-Albert graphs, and random geometric graphs. We use linear ridge regression as a baseline for comparison against linear modelling. We provide this baseline frstly to verify that BrainNetCNN can actually outperform linear models on non-linear metric learning, and secondly to enhance insights into model performance across the different graph metrics and graph datasets studied

Access to Drinking-water and Arsenicosis in Bangladesh

The discovery of arsenic contamination in groundwater has challenged efforts to provide safe drinking-water to households in rural Bangladesh. Two nationally-representative surveys in 2000 and 2002 investigated water-usage patterns, water-testing, knowledge of arsenic poisoning, and behavioural responses to arsenic contamination. Knowledge of arsenicosis rose between the two surveys among women from 42% to 64% but awareness of consequences of arsenic remained limited; only 13% knew that it could lead to death. Behavioural responses to arsenic have been limited, probably in part because of the lack of concern but also because households are uncertain of how best to respond and have a strong preference for tubewell water even when wells are known to be contaminated. Further work conducted by the survey team highlighted the difficulties in providing alternative sources of water, with many households switching back to their original sources of water

Functional alignments in brain connectivity networks

Alzheimer’s disease (AD) is a brain disconnection syndrome, where functional connectivity analysis can detect changes in neural activity in pre-dementia stages [8]. Functional connectivity networks from functional magnetic resonance imaging (fMRI) and electroencephalogram (EEG) are susceptible to signal noise from biologic artefacts (e.g. cardiac artefacts) and environmental sources (e.g. electrical interference). A particular challenge for EEG is volume conduction, whereby a signal from a single source propagates through biological tissue to be detected simultaneously by multiple sensors (channels). The imaginary part of coherency (iCOH) provides a measure for connectivity that avoids this signal contamination, by ignoring correlation between signals with zero or π-phase lag. This removes false instantaneous activity with connectivity denoting synchronised signals at a given time lag, but it does come at the cost of erasing true instantaneous activity. We propose eigenvector alignment (EA) as a method for evaluating pairwise relationships from network eigenvectors; revealing noise robust, structural, insights from functional connectivity networks

Accuracy of high b-value diffusion-weighted MRI for prostate cancer detection: a meta-analysis

Background: The diagnostic accuracy of diffusion-weighted imaging (DWI) to detect prostate cancer is well-established. DWI provides visual and also quantitative means of detecting tumor, the Apparent Diffusion Coefficient (ADC). Recently higher b-values have been used to improve DWI’s diagnostic performance. Purpose: To determine the diagnostic performance of high b-value DWI at detecting prostate cancer and whether quantifying ADC improves accuracy. Material and Methods: A comprehensive literature search of published and unpublished databases was performed. Eligible studies had histopathologically proven prostate cancer, DWI sequences using b-values ≥ 1000 s/mm2, > 10 patients, and data for creating a 2x2 table. Study quality was assessed with QUADAS-2 (Quality Assessment of diagnostic Accuracy Studies). Sensitivity and specificity were calculated and tests for statistical heterogeneity and threshold effect performed. Results were plotted on a summary receiver operating characteristic curve (sROC) and the area under the curve (AUC) determined the diagnostic performance of high b-value DWI. Results: Ten studies met eligibility criteria with 13 subsets of data available for analysis, including 522 patients. Pooled sensitivity and specificity were 0.59 (95% CI 0.57–0.61) and 0.92 (95% CI 0.91–0.92) respectively and the sROC AUC was 0.92. Subgroup analysis showed a statistically significant (p=0.03) improvement in accuracy when using tumor visual assessment rather than ADC. Conclusion: High b-value DWI gives good diagnostic performance for prostate cancer detection and visual assessment of tumor diffusion is significantly more accurate than ROI measurements of ADC

Fire regimes and carbon in Australian vegetation

Fires regularly affect many of the world\u27s terrestrial ecosystems, and, as a result, fires mediate the exchange of greenhouse gases (GHG) between the land and the atmosphere at a global scale and affect the capacity of terrestrial ecosystems to store carbon (Bowman et al. 2009). Variations in fire -regimes can therefore potentially affect the global, regional and local carbon balance and, potentially, climate change itself (Bonan 2008). Here we examine how variation in fire regimes (Gill 1975; Bradstock et al. 2002) will potentially affect carbon in fire-prone Australian ecosystems via interactions with the stocks and transfers of carbon that are inherent to all terrestrial ecosystems. There are two key reasons why an appreciation of fire regimes is needed to comprehend the fate of terrestrial carbon. First, the status of terrestrial carbon over time will be a function of the balance between losses (emissions) from individual fires (of differing type, season and intensity), which occur as a result of immediate combustion as well as mortality and longerterm decomposition of dead biomass, and carbon that accumulates during regeneration in the intervals between fires. The length of the interval between fires will determine the amount of biomass that accumulates. Second, fire regimes influence the composition and structure of ecosystems and key processes such as plant mortality and recruitment. Hence, alternative trajectories of vegetation composition and structure that result from differing fire regimes will affect carbon dynamics. We explore these themes and summarise the dynamic aspects of carbon stocks and transfers in relation to fire, present conceptual models of carbon dynamics and fire regimes, and review how variation in fire regimes may affect overall storage potential as a function of fireinduced losses and post-fire uptake in two widespread Australian vegetation types. We then appraise future trends under global change and the likely potential for managing fire regimes for carbon \u27benefits\u27, especially with respect to emissions

Access to Drinking-water and Arsenicosis in Bangladesh

The discovery of arsenic contamination in groundwater has challenged efforts to provide safe drinking-water to households in rural Bangladesh. Two nationally-representative surveys in 2000 and 2002 investigated water-usage patterns, water-testing, knowledge of arsenic poisoning, and behaviouralresponses to arsenic contamination. Knowledge of arsenicosis rose between the two surveys among women from 42% to 64% but awareness of consequences of arsenic remained limited; only 13% knew that it could lead to death. Behavioural responses to arsenic have been limited, probably in part because of the lack of concern but also because households are uncertain of how best to respond and have a strong preference for tubewell water even when wells are known to be contaminated. Further work conducted by the survey team highlighted the difficulties in providing alternative sources of water, with many households switching back to their original sources of water