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.

Using injection and production data, we can evaluate the connectivity between injector and producer well pairs to characterize their interwell regions and provide a tool for waterflood management. The capacitance model (CM) has been suggested as a phenomenological method to analyze the injection and production data for these purposes. Early studies involving reservoir simulation have shown CM to be a valuable tool but also have revealed several shortcomings. Many of these deficiencies have become more transparent in analyzing field data. This work consists of two parts: in the first part, we investigate some of the shortcomings of the CM and attempt to overcome them by modifying the algorithms. In the second part, we relate the problem of interwell connectivity to the rigorous concept of Multiwell Productivity Index (MPI) and provide a semi analytical approach. We have developed two modifications on the CM: the segmented CM that can be used where bottomhole pressures (BHP) are unknown and may change during the analysis interval, and the compensated CM that overcomes the requirement to rerun the model after adding a new producer or shutting in an existing producer. If both BHP changes and shut-in periods occur, the segmented and compensated CMs can be used simultaneously to construct a single model for a period of data. We show several hypothetical cases and a field case where these modifications generate a more reliable evaluation of interwell connectivity and increase the R2 of the model up to 15%. On the other hand, the MPI-based approach can predict the reservoir performance analytically for homogeneous cases under specific conditions. In the heterogeneous cases, this approach provides a robust connectivity parameter, which solely represents the reservoir heterogeneity and possible anisotropy and hence allows improved information exchange with the geologist. In addition, this connectivity parameter is insensitive to possible variations of skin factor and changes in number of wells. A further advantage of the new method is the flexibility to incorporate additional information, such as injector BHP, into the analysis process. We applied this approach on several hypothetical cases and observed excellent evaluation of both reservoir performance and connectivity.

Intrinsic connectivity networks (ICNs) refer to brain functional networks that are consistently found under various conditions, during tasks or at rest. Some studies demonstrated that while some stimuli do not impact intrinsic connectivity, other stimuli actually activate intrinsic connectivity through suppression, excitation, moderation or modi cation. Most analyses of functional magnetic resonance imaging (fMRI) data use ad-hoc methods to estimate the latent structure of ICNs. Modeling the effects on ICNs has also not been fully investigated. Bayesian Intrinsic Connectivity Network (BICNet) captures the ICN structure with We propose a BICNet model, an extended Bayesian dynamic sparse latent factor model, to identify the ICNs and quantify task-related effects on the ICNs. BICNet has the following advantages: (1) It simultaneously identifies the individual and group-level ICNs; (2) It robustly identifies ICNs by jointly modeling resting-state fMRI (rfMRI) and task-related fMRI (tfMRI); (3) Compared to independent component analysis (ICA)-based methods, it can quantify the difference of ICNs amplitudes across different states; (4) The sparsity of ICNs automatically performs feature selection, instead of ad-hoc thresholding. We apply BICNet to the rfMRI and language tfMRI data from the Human Connectome Project (HCP) and identify several ICNs related to distinct language processing functions.

This dissertation introduces a novel approach at gauging patterns of informa- tion flow using brain connectivity analysis and partial directed coherence (PDC) in epilepsy. The main objective of this dissertation is to assess the key characteristics that delineate neural activities obtained from patients with epilepsy, considering both focal and generalized seizures. The use of PDC analysis is noteworthy as it es- timates the intensity and direction of propagation from neural activities generated in the cerebral cortex, and it ascertains the coefficients as weighted measures in formulating the multivariate autoregressive model (MVAR). The PDC is used here as a feature extraction method for recorded scalp electroencephalograms (EEG) as means to examine the interictal epileptiform discharges (IEDs) and reflect the phys- iological changes of brain activity during interictal periods. Two experiments were set up to investigate the epileptic data by using the PDC concept. For the investigation of IEDs data (interictal spike (IS), spike and slow wave com- plex (SSC), and repetitive spikes and slow wave complex (RSS)), the PDC analysis estimates the intensity and direction of propagation from neural activities gener- ated in the cerebral cortex, and analyzes the coefficients obtained from employing MVAR. Features extracted by using PDC were transformed into adjacency matrices using surrogate data analysis and were classified by using the multilayer Perceptron (MLP) neural network. The classification results yielded a high accuracy and pre- cision number. The second experiment introduces the investigation of intensity (or strength) of information flow. The inflow activity deemed significant and flowing from other regions into a specific region together with the outflow activity emanating from one region and spreading into other regions were calculated based on the PDC results and were quantified by the defined regions of interest. Three groups were considered for this study, the control population, patients with focal epilepsy, and patients with generalized epilepsy. A significant difference in inflow and outflow validated by the nonparametric Kruskal-Wallis test was observed for these groups. By taking advantage of directionality of brain connectivity and by extracting the intensity of information flow, specific patterns in different brain regions of interest between each data group can be revealed. This is rather important as researchers could then associate such patterns in context to the 3D source localization where seizures are thought to emanate in focal epilepsy. This research endeavor, given its generalized construct, can extend for the study of other neurological and neurode- generative disorders such as Parkinson, depression, Alzheimers disease, and mental illness.

The brain connectivity of resting-state fMRI (rs-fMRI) represents an intrinsic state of brain architecture, and it has been used as a useful neural marker for detecting psychiatric conditions such as autism spectrum disorder, as well as for predicting psychosocial characteristics such as age. However, most studies using brain connectivity have focused more on the strength of functional connectivity over time (static-FC) than temporal features of connectivity changes (connectome variability). The primary goal of the current study was to investigate the effectiveness of using the connectome variability in classifying an individual’s pathological characteristics from others and predicting psychosocial characteristics. In addition, the current study aimed to prove that benefits of the connectome variability are reliable across various analysis procedures. To this end, three open public large rs-fMRI datasets including ABIDE, COBRE, and NKI were used. The static-FC and the connectome variability metrics were calculated with various brain parcellations and parameters and then utilized for subsequent machine learning (ML) classification and prediction. The results demonstrated that including the connectome variability increased the ML performances significantly in most cases of analytical variations. In addition, including the connectome variability prevented ML performance deterioration when excessive components were used. In conclusion, the current finding proved the usefulness of the connectome variability and its reliability. / M.S. / Functional magnetic resonance imaging (fMRI) with functional connectivity (FC) analysis has been widely used to understand the human brain’s system and cognitive processes. Especially, the resting-state fMRI (rs-fMRI) has been regarded as a comprehensive map of the brain’s large-scale functional architecture. Previous seminal findings demonstrated that brain regions show synchronized patterns even without any external stimulus or task (Biswal et al., 1995; Power et al., 2011), and recent studies also demonstrated that functional network architecture during tasks can be formed based on resting-state network architecture primarily suggesting that the resting-state is an intrinsic and fundamental of brain organization functionally. At the early stage of fMRI FC studies, researchers commonly adopted static measure of connectivity (static-FC) such as Pearson correlation. However, the brain has a dynamic nature, thus the static approach does not capture temporal information of the brain. In this context, time-varying or dynamic-FC has been suggested as a promising substitute. The derived dynamic-FC usually has been used to distinguish several dynamic states by identifying repeated spatial dynamic-FC profiles. Another utilization is quantifying moment-to-moment changes of dynamic-FC (connectome variability) which can represent how much dynamic-FC is stable. Interestingly, although its importance of dynamic-FC temporal features, few studies have utilized connectome variability. In addition, only a few studies compared static-FC and connectome variability (Fong et al., 2019; Wang et al., 2018). Therefore, it is necessary to demonstrate the benefits of connectome variability and its reliability across various cognitive domains and analytic procedures. To this aim, this study used three large open fMRI datasets: ABIDE comprised of autism spectrum disorder and typical development, COBRE comprised of schizophrenia and control group, and NKI which is a developmental dataset across the lifespan. In individuals’ resting-state fMRI, brain signal time series was extracted using various parcellation methods including AAL2 atlas (Rolls et al., 2015), bilateralized AAL2 atlas, and LAIRD network atlas (Laird et al., 2011). To calculate static-FC, pairwise Pearson correlation was used. For the dynamic-FC, sliding-window correlation was used with 60 second window size. Additional 90 second and 120 second sliding window sizes were also used to test the reliability of the current study. The additional sliding window sizes showed almost identical results to that of the main sliding window size (60s). The derived dynamic-FC was used to calculate ‘connectome variability’ using mean square successive difference (MSSD). The calculated static-FC and the connectome variability were inputted to support vector machine (SVM) for group classifications or support vector regression (SVR) for predicting individuals’ characteristics. Before machine learning analysis (SVM, SVR), lasso regression was adopted as a feature selection method. The SVM results showed that including connectome variability increased group classification performances in ABIDE and COBRE datasets. Interestingly, including connectome variability improved the robustness of SVM classification when the number of components was controlled. Similarly, the SVR results also demonstrated that including connectome variability increased prediction performances for autism symptom severity score (ADOS), social responsiveness score (SRS), and individuals’ age. These benefits were consistent across three parcellation schemes. In conclusion, the current study demonstrated that the connectome variability is useful to classify different groups and to predict individuals’ characteristics. Such benefits were reliable across multiple cognitive domains and robust to several analytic procedures. These results emphasized that the connectome variability which has been usually overlooked reflects some aspects of functional brain architecture, and future fMRI studies should more attend connectome variability between brain regions.

The manufacturing industry is continuously evolving as new practices and technology are adopted to improve productivity and remain competitive. There have been three well established manufacturing revolutions in recent history and some say that the fourth is occurring currently by the name of Smart Manufacturing, Indusrie 4.0, and others. This latest manufacturing revolution is highly dependent on industrial connectivity. This research aims to gage the ability of Industrial Innovation Platforms (IIPs) to reduce complexity of implementing base-line industrial connectivity for small and medium-sized enterprises (SMEs). The results of this study would be especially relevant to decision makers in industrial SMEs who are considering implementing industrial connectivity as well as providing insights into approaches for establishing base-line industrial connectivity. The research methodology consists of three main steps: 1) creation of IIP and non-IIP connectivity solutions that enable connectivity of the vast amount of industrial equipment, 2) Gathering measures from solutions in accordance with metrics identified for complexity evaluation, 3) discussion and interpretation of data To have a more complete analysis, quantitative and qualitative data was used and evaluated to address the varying elements of the broad task of establishing industrial connectivity. The research showed that IIPs can reduce complexity for select industrial equipment. Some industrial equipment have robust and streamlined connectivity solutions provided by the IIP. In these cases, the IIP almost certainly will reduce the complexity of establishing connectivity. Other industrial equipment have a solution provided by the IIP which requires piecing together and some component modifications. In these cases, the IIPs reduce complexity of establishing connectivity dependent on circumstances. Lastly, when no form of solution is available through the IIP for the industrial equipment, the IIP's has no ability to reduce complexity other than hosting the server used in connectivity. These findings open additional avenues of research which could improve the understanding of benefits IIPs may provide to SMEs.

Sustainable Built Environments Senior Capstone Project / Sidewalk fragmentation in Tucson is the result of City Code Ordinance 25-12 that places the responsibility of sidewalk installation and maintenance on property owner. However, with an average household income 27% below the national average and 25% of Tucson residents living below poverty level sidewalk fragmentation has become a pedestrian safety concern. By using Google Earth to measure the percentage of paved, unpaved and not present sidewalks in four historic communities in central Tucson; this study found a directly proportional relationship between the length of time the neighborhood has been listed as a historic community and the percentage of paved sidewalks within the neighborhood.

Canals have created grooves through the landscape of England and Wales for over 250 years, but they were dismissed by modernity, and narratives of disenchantment linger. Whilst visitor numbers grow as canals experience a ‘Second Golden Age’ and attempts are made to promote these waterways as ecological resources, they remain overlooked within conservation and their futures are precarious. The linearity of canals generates ecological connection and safe passage, whilst these environments also enable expressive territories and tranquil atmospheres. This research highlights the capacity for canals to enchant and support liveliness, and situates discussions of socio-ecological management within growing national concerns for connectivity as an effective response to climatic change and habitat fragmentation. The twin aims of this research were explored empirically through a case study of the Basingstoke Canal and sought to consider the position of such waterways within conservation and address a neglect of water within human geography. In accompanying practitioners and experimenting with creative methodologies this research begins by demonstrating the possibilities for wonder, surprise, and attachment after the ontological loss of Nature. Subsequent chapters draw upon fieldwork encounters, interdisciplinarity alliances, and a reworking of concepts within ecology and multinatural geography to exercise recombination as the central mode of address of this research. In inflecting the term’s ecological salience with a materialist regard for multiplicity, repetition, and emergence this research challenges the position of canals and the presentation of corridors within conservation. The beguiling simplicity of connectivity has enabled its ready incorporation within conservation discourse, despite a paucity of empirical attention; whilst contributing to work addressing this lacuna this research also introduces a more nuanced notion of complexity into discussions of connectivity and interrogates the apparent separation of corridors and sites. Encounters with the ecologies and publics assembling and disassembling through the Basingstoke Canal demonstrate that linearity does not preclude interested gatherings or absolve management of the obligation to respond, and highlights the need for biosecurity practices which are more articulate and attuned to difference. Recombinant ecologies invite and demand response, but conservation remains spatially cautious and this is further foregrounded as the challenges of incorporating the watery, connective, environments of canals are traced.

The human brain is composed of distributed networks that connect a disproportionately large neocortex to the brainstem, cerebellum and other subcortical structures. New methods for analyzing non-invasive imaging data have begun to reveal new insights into human brain organization. These methods permit characterization of functional interactions within and across brain networks, and allow us to appreciate points of departure between the human brain and non-human primates. / Psychology

This thesis is concerned with one important question in artificial neural networks, that is, how biologically inspired connectivity of a network affects its associative memory performance. In recent years, research on the mammalian cerebral cortex, which has the main responsibility for the associative memory function in the brains, suggests that the connectivity of this cortical network is far from fully connected, which is commonly assumed in traditional associative memory models. It is found to be a sparse network with interesting connectivity characteristics such as the “small world network” characteristics, represented by short Mean Path Length, high Clustering Coefficient, and high Global and Local Efficiency. Most of the networks in this thesis are therefore sparsely connected. There is, however, no conclusive evidence of how these different connectivity characteristics affect the associative memory performance of a network. This thesis addresses this question using networks with different types of connectivity, which are inspired from biological evidences. The findings of this programme are unexpected and important. Results show that the performance of a non-spiking associative memory model is found to be predicted by its linear correlation with the Clustering Coefficient of the network, regardless of the detailed connectivity patterns. This is particularly important because the Clustering Coefficient is a static measure of one aspect of connectivity, whilst the associative memory performance reflects the result of a complex dynamic process. On the other hand, this research reveals that improvements in the performance of a network do not necessarily directly rely on an increase in the network’s wiring cost. Therefore it is possible to construct networks with high associative memory performance but relatively low wiring cost. Particularly, Gaussian distributed connectivity in a network is found to achieve the best performance with the lowest wiring cost, in all examined connectivity models. Our results from this programme also suggest that a modular network with an appropriate configuration of Gaussian distributed connectivity, both internal to each module and across modules, can perform nearly as well as the Gaussian distributed non-modular network. Finally, a comparison between non-spiking and spiking associative memory models suggests that in terms of associative memory performance, the implication of connectivity seems to transcend the details of the actual neural models, that is, whether they are spiking or non-spiking neurons.