Flexible regression models for functional neuroimaging

Current practice for analysing functional neuroimaging data is to average the brain signals recorded at multiple sensors or channels on the scalp over time across hundreds of trials or replicates to eliminate noise and enhance the underlying signal of interest. These studies recording brain signals non-invasively using functional neuroimaging techniques such as electroencephalography (EEG) and magnetoencephalography (MEG) generate complex, high dimensional and noisy data for many subjects at a number of replicates. Single replicate (or single trial) analysis of neuroimaging data have gained focus as they are advantageous to study the features of the signals at each replicate without averaging out important features in the data that the current methods employ. The research here is conducted to systematically develop flexible regression mixed models for single trial analysis of specific brain activities using examples from EEG and MEG to illustrate the models. This thesis follows three specific themes: i) artefact correction to estimate the `brain' signal which is of interest, ii) characterisation of the signals to reduce their dimensions, and iii) model fitting for single trials after accounting for variations between subjects and within subjects (between replicates). The models are developed to establish evidence of two specific neurological phenomena - entrainment of brain signals to an $\alpha$ band of frequencies (8-12Hz) and dipolar brain activation in the same $\alpha$ frequency band in an EEG experiment and a MEG study, respectively.

Ecology, physiology and performance in high-rate anaerobic digestion

The design demands on water and sanitation engineers are rapidly changing. The global population is set to rise from 7 billion to 10 billion by 2083. Urbanisation in developing regions is increasing at such a rate that a predicted 56% of the global population will live in an urban setting by 2025. Compounding these problems, the global water and energy crises are impacting the Global North and South alike. High-rate anaerobic digestion offers a low-cost, low-energy treatment alternative to the energy intensive aerobic technologies used today. Widespread implementation however is hindered by the lack of capacity to engineer high-rate anaerobic digestion for the treatment of complex wastes such as sewage. This thesis utilises the Expanded Granular Sludge Bed bioreactor (EGSB) as a model system in which to study the ecology, physiology and performance of high-rate anaerobic digestion of complex wastes. The impacts of a range of engineered parameters including reactor geometry, wastewater type, operating temperature and organic loading rate are systematically investigated using lab-scale EGSB bioreactors. Next generation sequencing of 16S amplicons is utilised as a means of monitoring microbial ecology. Microbial community physiology is monitored by means of specific methanogenic activity testing and a range of physical and chemical methods are applied to assess reactor performance. Finally, the limit state approach is trialled as a method for testing the EGSB and is proposed as a standard method for biotechnology testing enabling improved process control at full-scale. The arising data is assessed both qualitatively and quantitatively. Lab-scale reactor design is demonstrated to significantly influence the spatial distribution of the underlying ecology and community physiology in lab-scale reactors, a vital finding for both researchers and full-scale plant operators responsible for monitoring EGSB reactors. Recurrent trends in the data indicate that hydrogenotrophic methanogenesis dominates in high-rate anaerobic digestion at both full- and lab-scale when subject to engineered or operational stresses including low-temperature and variable feeding regimes. This is of relevance for those seeking to define new directions in fundamental understanding of syntrophic and competitive relations in methanogenic communities and also to design engineers in determining operating parameters for full-scale digesters. The adoption of the limit state approach enabled identification of biological indicators providing early warning of failure under high-solids loading, a vital insight for those currently working empirically towards the development of new biotechnologies at lab-scale.

Transmission electron tomography: quality assessment and enhancement for three-dimensional imaging of nanostructures

Nanotechnology has revolutionised humanity's capability in building microscopic systems by manipulating materials on a molecular and atomic scale. Nan-osystems are becoming increasingly smaller and more complex from the chemical perspective which increases the demand for microscopic characterisation techniques. Among others, transmission electron microscopy (TEM) is an indispensable tool that is increasingly used to study the structures of nanosystems down to the molecular and atomic scale. However, despite the effectivity of this tool, it can only provide 2-dimensional projection (shadow) images of the 3D structure, leaving the 3-dimensional information hidden which can lead to incomplete or erroneous characterization. One very promising inspection method is Electron Tomography (ET), which is rapidly becoming an important tool to explore the 3D nano-world. ET provides (sub-)nanometer resolution in all three dimensions of the sample under investigation. However, the fidelity of the ET tomogram that is achieved by current ET reconstruction procedures remains a major challenge. This thesis addresses the assessment and advancement of electron tomographic methods to enable high-fidelity three-dimensional investigations. A quality assessment investigation was conducted to provide a quality quantitative analysis of the main established ET reconstruction algorithms and to study the influence of the experimental conditions on the quality of the reconstructed ET tomogram. Regular shaped nanoparticles were used as a ground-truth for this study. It is concluded that the fidelity of the post-reconstruction quantitative analysis and segmentation is limited, mainly by the fidelity of the reconstructed ET tomogram. This motivates the development of an improved tomographic reconstruction process. In this thesis, a novel ET method was proposed, named dictionary learning electron tomography (DLET). DLET is based on the recent mathematical theorem of compressed sensing (CS) which employs the sparsity of ET tomograms to enable accurate reconstruction from undersampled (S)TEM tilt series. DLET learns the sparsifying transform (dictionary) in an adaptive way and reconstructs the tomogram simultaneously from highly undersampled tilt series. In this method, the sparsity is applied on overlapping image patches favouring local structures. Furthermore, the dictionary is adapted to the specific tomogram instance, thereby favouring better sparsity and consequently higher quality reconstructions. The reconstruction algorithm is based on an alternating procedure that learns the sparsifying dictionary and employs it to remove artifacts and noise in one step, and then restores the tomogram data in the other step. Simulation and real ET experiments of several morphologies are performed with a variety of setups. Reconstruction results validate its efficiency in both noiseless and noisy cases and show that it yields an improved reconstruction quality with fast convergence. The proposed method enables the recovery of high-fidelity information without the need to worry about what sparsifying transform to select or whether the images used strictly follow the pre-conditions of a certain transform (e.g. strictly piecewise constant for Total Variation minimisation). This can also avoid artifacts that can be introduced by specific sparsifying transforms (e.g. the staircase artifacts the may result when using Total Variation minimisation). Moreover, this thesis shows how reliable elementally sensitive tomography using EELS is possible with the aid of both appropriate use of Dual electron energy loss spectroscopy (DualEELS) and the DLET compressed sensing algorithm to make the best use of the limited data volume and signal to noise inherent in core-loss electron energy loss spectroscopy (EELS) from nanoparticles of an industrially important material. Taken together, the results presented in this thesis demonstrates how high-fidelity ET reconstructions can be achieved using a compressed sensing approach.