THE RELATIVE SIGNIFICANCE OF SYNTACTIC KNOWLEDGE AND VOCABULARY KNOWLEDGE IN SECOND LANGUAGE LISTENING COMPREHENSION

The main purpose of the current study was to examine the role of vocabulary knowledge (VK) and syntactic knowledge (SK) in L2 listening comprehension, as well as their relative significance. Unlike previous studies, the current project employed assessment tasks to measure aural and proceduralized VK and SK. In terms of VK, to avoid under-representing the construct, measures of both breadth (VB) and depth (VD) were included. Additionally, the current study examined the role of VK and SK by accounting for individual differences in two important cognitive factors in L2 listening: metacognitive knowledge (MK) and working memory (WM). Also, to explore the role of VK and SK more fully, the current study accounted for the negative impact of anxiety on WM and L2 listening. The study was carried out in an English as a Foreign Language (EFL) context, and participants were 263 Iranian learners at a wide range of English proficiency from lower-intermediate to advanced. Participants took a battery of ten linguistic, cognitive and affective measures. Then, the collected data were subjected to several preliminary analyses, but structural equation modeling (SEM) was then used as the primary analysis method to answer the study research questions. Results of the preliminary analyses revealed that MK and WM were significant predictors of L2 listening ability; thus, they were kept in the main SEM analyses. The significant role of WM was only observed when the negative effect of anxiety on WM was accounted for. Preliminary analyses also showed that VB and VD were not distinct measures of VK. However, the results also showed that if VB and VD were considered separate, VD was a better predictor of L2 listening success. The main analyses of the current study revealed a significant role for both VK and SK in explaining success in L2 listening comprehension, which differs from findings from previous empirical studies. However, SEM analysis did not reveal a statistically significant difference in terms of the predictive power of the two linguistic factors. Descriptive results of the SEM analysis, along with results from regression analysis, indicated to a more significant role for VK.

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.