SES-RELATED DIFFERENCES IN WORD LEARNING: EFFECTS OF COGNITIVE INHIBITION AND WORD LEARNING

Socioeconomic status (SES) influences language and cognitive development, with discrepancies particularly noticeable in vocabulary development. This study examines how SES-related differences impact the development of syntactic processing, cognitive inhibition, and word learning. 38 4-5-year-olds from higher- and lower-SES backgrounds completed a word-learning task, in which novel words were embedded in active and passive sentences. Critically, unlike the active sentences, all passive sentences required a syntactic revision. Measures of cognitive inhibition were obtained through a modified Stroop task. Results indicate that lower-SES participants had more difficulty using inhibitory functions to resolve conflict compared to their higher-SES counterparts. However, SES did not impact language processing, as the language outcomes were similar across SES background. Additionally, stronger inhibitory processes were related to better language outcomes in the passive sentence condition. These results suggest that cognitive inhibition impact language processing, but this function may vary across children from different SES backgrounds

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.