Spectral Frame Analysis and Learning through Graph Structure

This dissertation investigates the connection between spectral analysis and frame theory. When considering the spectral properties of a frame, we present a few novel results relating to the spectral decomposition. We first show that scalable frames have the property that the inner product of the scaling coefficients and the eigenvectors must equal the inverse eigenvalues. From this, we prove a similar result when an approximate scaling is obtained. We then focus on the optimization problems inherent to the scalable frames by first showing that there is an equivalence between scaling a frame and optimization problems with a non-restrictive objective function. Various objective functions are considered, and an analysis of the solution type is presented. For linear objectives, we can encourage sparse scalings, and with barrier objective functions, we force dense solutions. We further consider frames in high dimensions, and derive various solution techniques. From here, we restrict ourselves to various frame classes, to add more specificity to the results. Using frames generated from distributions allows for the placement of probabilistic bounds on scalability. For discrete distributions (Bernoulli and Rademacher), we bound the probability of encountering an ONB, and for continuous symmetric distributions (Uniform and Gaussian), we show that symmetry is retained in the transformed domain. We also prove several hyperplane-separation results. With the theory developed, we discuss graph applications of the scalability framework. We make a connection with graph conditioning, and show the in-feasibility of the problem in the general case. After a modification, we show that any complete graph can be conditioned. We then present a modification of standard PCA (robust PCA) developed by Cand\`es, and give some background into Electron Energy-Loss Spectroscopy (EELS). We design a novel scheme for the processing of EELS through robust PCA and least-squares regression, and test this scheme on biological samples. Finally, we take the idea of robust PCA and apply the technique of kernel PCA to perform robust manifold learning. We derive the problem and present an algorithm for its solution. There is also discussion of the differences with RPCA that make theoretical guarantees difficult.

Playing for Real: Designing Alternate Reality Games in Learning Contexts

Alternate Reality Game (ARG) represent a new genre of transmedia practice where players hunt for scattered clues, make sense of disparate information, and solve puzzles to advance an ever-evolving storyline. Players participate in ARGs using multiple communications technologies, ranging from print materials to mobile devices. However, many interaction design challenges must be addressed to weave these everyday communication tools together into an immersive, participatory experience. Transmedia design is not an everyday process. Designers must create and connect story bits across multiple media (video, audio, text) and multiple platforms (phones, computers, physical spaces). Furthermore, they must engage with players of varying skill levels. Few studies to-date have explored the design process of ARGs in learning contexts. Fewer still have focused on challenges involved in designing for youth (13-17 years old). In this study, I explore the process of designing ARGs as vehicles for promoting information literacy and participatory culture for adolescents (13-17 years old). Two ARG design scenarios, distinguished by target learning environment (formal and informal context) and target audience (adolescents), comprise the two cases that I examine. Through my analysis of these two design cases, I articulate several unique challenges faced by designers who create interactive, transmedia stories for – and with – youth. Drawing from these design challenges, I derive a repertoire of design strategies that future designers and researchers may use to create and implement ARGs for teens in learning contexts. In particular, I propose a narrative design framework that allows for the categorization of ARGs as storytelling constructs that lie along a continuum of participation and interaction. The framework can serve as an analytic tool for researchers and a guide for designers. In addition, I establish a framework of social roles that designers may employ to craft transmedia narratives before live launch and to promote and scaffold player participation after play begins. Overall, the contributions of my study include theoretical insights that may advance our understanding of narrative design and analysis as well as more practical design implications for designers and practitioners seeking to incorporate transmedia features into learning experiences that target youth.

Action and perception: Neural indices of learning in infants

Early human development offers a unique perspective in investigating the potential cognitive and social implications of action and perception. Specifically, during infancy, action production and action perception undergo foundational developments. One essential component to examine developments in action processing is the analysis of others’ actions as meaningful and goal-directed. Little research, however, has examined the underlying neural systems that may be associated with emerging action and perception abilities, and infants’ learning of goal-directed actions. The current study examines the mu rhythm—a brain oscillation found in the electroencephalogram (EEG)—that has been associated with action and perception. Specifically, the present work investigates whether the mu signal is related to 9-month-olds’ learning of a novel goal-directed means-end task. The findings of this study demonstrate a relation between variations in mu rhythm activity and infants’ ability to learn a novel goal-directed means-end action task (compared to a visual pattern learning task used as a comparison task). Additionally, we examined the relations between standardized assessments of early motor competence, infants’ ability to learn a novel goal-directed task, and mu rhythm activity. We found that: 1a) mu rhythm activity during observation of a grasp uniquely predicted infants’ learning on the cane training task, 1b) mu rhythm activity during observation and execution of a grasp did not uniquely predict infants’ learning on the visual pattern learning task (comparison learning task), 2) infants’ motor competence did not predict infants’ learning on the cane training task, 3) mu rhythm activity during observation and execution was not related to infants’ measure of motor competence, and 4) mu rhythm activity did not predict infants’ learning on the cane task above and beyond infants’ motor competence. The results from this study demonstrate that mu rhythm activity is a sensitive measure to detect individual differences in infants’ action and perception abilities, specifically their learning of a novel goal-directed action.