Event-related potential (ERP) studies are a subset of experimental frameworks within the field of electroencephalography (EEG) that focus on ERPs, the electrical potential outputted by a subject's brain when presented with an implicit task in the form of stimuli. Data comprise an ERP repetition observed for each stimulus across electrodes on the scalp, producing a complex data structure consisting of a functional, longitudinal and spatial dimension. In typical ERP studies, the dimension of data is reduced into a single measure for each subject by cross-sectionally averaging ERP across longitudinal and spatial repetitions. Features are then extracted from the averaged ERP and analyzed using simple statistical methods, ignoring additional information that may be found in the collapsed dimensions. In this dissertation, three types of methodology are proposed for preserving and analyzing the lost dimensions of ERP data. The first method, moving average processed ERP (MAP-ERP), is a two-step approach comprised of a meta-preprocessing step to preserve longitudinal information and a weighted mixed effects regression framework to allow modeling of the resulting meta-preprocessed data. The proposed robust functional clustering (RFC) algorithm identifies substructures in features of the longitudinal ERP processes while accounting for subject-level covariance heterogeneity induced by meta-preprocessing. Finally, the proposed multidimensional functional principal components analysis (MD-FPCA) utilizes a two-stage procedure to summarize important characteristics across all three dimensions of the ERP data structure into an interpretable, low-dimensional form. Proposed methods are applied to a study on neural correlates of visual implicit learning in young children with autism spectrum disorder (ASD). Applications of the proposed methods reveal meaningful trends and substructures in the implicit learning processes of ASD children when compared to typically developing controls. Results indicate proposed methodology effectively preserves important information contained within the multiple dimensions of ERP.

While the native states of proteins usually correspond to their free energy minimum, and can often be found with experimental techniques, predicting the folded native state of

a protein computationally remains a major challenge. This is partly due to the immense conformational space a single protein sequence could potentially fold into, a space that is even larger if the protein sequence is unknown, as in the case of design. In this thesis, I evaluate the performance of current state-of-the-art computational protein structure prediction and design methods (as implemented in the Rosetta macromolecular modeling software suite) on the following commonly encountered modeling problems: estimation of energetic effects of mutations (protein stability (∆∆G) and change in protein-protein interface binding energy post-mutation); (2) protein design predictions (native sequence recovery, evolutionary profile recovery, sequence covariation recovery, and prediction of recognition specificity); and (3)

protein structure prediction (loop modeling). I assemble curated benchmark data for each of these prediction problems that can be used for future evaluation of method performance on a common data set.

As the prior state-of-the-art methods for prediction of change in protein-protein interface binding energy post-mutation were not very effective for predicting mutations to side chains other than alanine, I created a new, more general Rosetta method for prediction of these cases. This “flex ddG” method generates and utilizes ensembles of diverse protein conformational states (generated with “backrub” sampling) to predict interface ∆∆G values. Flex ddG is effective for prediction of change in binding free energy post-mutation for mutations to all amino acids, including mutations to alanine, and is particularly effective (when compared to prior methods) for cases of small side chain to large side chain mutations. I show that the method succeeds in these cases due to increased sampling of diverse conformational states, as performance improves (to a threshold) as more diverse states are sampled.

Mobile technology has become increasingly popular in the past decade through the combination of device portability and advances in network and internet technology. Smart phones, in particular, are at the forefront of these technologies, enabling users to remotely track and further involve themselves in the management of personal health through participatory mobile health applications. Thus far, the majority of participatory applications currently provide users with data visualizations displaying information germane to the user's medical condition, however, there is still a need for in-depth exploratory and inference-based data analysis using advanced statistical methods to maximize the discernment of potential implications carried in these data streams. This paper provides an overview of the structure of participatory data using an asthma management application as an initial platform and discusses several directions for statistical analysis motivated by three usage cases: individuals using the application, creators of the application, and the scientific community. Methods include functional and semi-parametric data analysis, mixed modeling, and clustering methods to model variables representing asthma wellness as a function of subject-specific, population level, and latent spatiotemporal factors. Societal implications are also discussed.

This dissertation describes investigations in the reactivity of mixed carbonyl-isocyanide complexes of molybdenum. A primary challenge in isolating functional surrogates of low-coordinate, zero-valent Group 6 carbonyls, e.g. M(CO)2, M(CO)3, M(CO)4 has been the tendency of these compounds form intramolecular h6-arene interactions with the flanking rings of supporting ligands. In this work, a screening of catalysts for hydrostannation provided insight into stabilization of four-coordinate, zero-valent metal centers. Accordingly, reduction of MoI2(CO)2(CNArDipp2)2 with two equivalents of HSnBu3 in the presence of weakly coordinating Lewis bases (e.g. diisopropyl amine [HNiPr2], Et2O) provided access to masked sources of ML4. The unprecedented reactivity and β-(E)-regioselectivity of MoI2(CO)2(CNArDipp2)2 in hydrostannation of alkynes is discussed in Chapter 2. Chapter 3 describes the use of MoI2(CO)2(CNArDipp2)2 and the CH-agostic complex, Mo(κ2-N,CH)-HNiPr2)(CO)2(CNArDipp2)2 in the activation of elemental phosphorus (P4). The tetravalent product, (h4-P4)MoI2(CO) (CNArDipp2)2 was found to undergo photolytic reductive elimination of white phosphorus. In Chapter 4, the synthesis of two dianionic cyclo-P4 complexes is discussed. Investigations with these compounds revealed cyclo-P4 ligand to be isolobal to benzene in Fischer's classic half-sandwich complex Mo(CO)3(h6-C6H6). Chapter 5 further explores the redox chemistry of cyclo-P4 complexes by cyclic voltammetry. Chapter 6 describes the functionalization of cyclo-P4, including the stoichiometric release of [P-I] by treatment of (h4-P4)Mo(CO)2(CNArDipp2)2 upon treatment with 1 equiv I2.

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