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.

ABLE-BODIED WOMANHOOD: DISABILITY AND CORPOREALLY EXCLUSIONARY NARRATIVES IN BLACK AND WHITE WOMEN’S RIGHTS DISCOURSES, 1832-1932

This project is a feminist disability rhetorical analysis of US black and white women’s rights movements from 1832-1932. Guided by Disability and Feminist Theory, it works to identify the presence and use of patterns of disability tropes in women’s rights discourses. From Lucretia Coffin Mott to Sojourner Truth, Elizabeth Cady Stanton to Mary Church Terrell, and Charlotte Perkins Gilman to Addie Hunton, this project interrogates the rhetorical work of dominant narratives and lesser known voices in women’s rights discourses. I argue that early black and white women’s rights advocates often utilized and repeated a disability rhetoric that relied on disability metaphor, narrative prosthesis, and corporeally exclusionary narratives in order to construct definitions of womanhood. Their insistence on cognitive ability as a marker of “fitness” and “ability” provided the foundation for rights arguments based on ableist assumptions of autonomy and citizenship. I also argue that this use of disability rhetoric relied on and furthered a pervasive ableist ideology present not only in many of these movements, but in US society. In the process, US black and white women’s rights discourses have continually elided women with disabilities from women’s rights discourses because their bodies (physically, cognitively, and/or psychologically) did not meet the ableist prerequisites set for claiming women’s rights during this time period.

Parsing, Generation and Grammar

Humans use their grammatical knowledge in more than one way. On one hand, they use it to understand what others say. On the other hand, they use it to say what they want to convey to others (or to themselves). In either case, they need to assemble the structure of sentences in a systematic fashion, in accordance with the grammar of their language. Despite the fact that the structures that comprehenders and speakers assemble are systematic in an identical fashion (i.e., obey the same grammatical constraints), the two ‘modes’ of assembling sentence structures might or might not be performed by the same cognitive mechanisms. Currently, the field of psycholinguistics implicitly adopts the position that they are supported by different cognitive mechanisms, as evident from the fact that most psycholinguistic models seek to explain either comprehension or production phenomena. The potential existence of two independent cognitive systems underlying linguistic performance doubles the problem of linking the theory of linguistic knowledge and the theory of linguistic performance, making the integration of linguistics and psycholinguistic harder. This thesis thus aims to unify the structure building system in comprehension, i.e., parser, and the structure building system in production, i.e., generator, into one, so that the linking theory between knowledge and performance can also be unified into one. I will discuss and unify both existing and new data pertaining to how structures are assembled in understanding and speaking, and attempt to show that the unification between parsing and generation is at least a plausible research enterprise. In Chapter 1, I will discuss the previous and current views on how parsing and generation are related to each other. I will outline the challenges for the current view that the parser and the generator are the same cognitive mechanism. This single system view is discussed and evaluated in the rest of the chapters. In Chapter 2, I will present new experimental evidence suggesting that the grain size of the pre-compiled structural units (henceforth simply structural units) is rather small, contrary to some models of sentence production. In particular, I will show that the internal structure of the verb phrase in a ditransitive sentence (e.g., The chef is donating the book to the monk) is not specified at the onset of speech, but is specified before the first internal argument (the book) needs to be uttered. I will also show that this timing of structural processes with respect to the verb phrase structure is earlier than the lexical processes of verb internal arguments. These two results in concert show that the size of structure building units in sentence production is rather small, contrary to some models of sentence production, yet structural processes still precede lexical processes. I argue that this view of generation resembles the widely accepted model of parsing that utilizes both top-down and bottom-up structure building procedures. In Chapter 3, I will present new experimental evidence suggesting that the structural representation strongly constrains the subsequent lexical processes. In particular, I will show that conceptually similar lexical items interfere with each other only when they share the same syntactic category in sentence production. The mechanism that I call syntactic gating, will be proposed, and this mechanism characterizes how the structural and lexical processes interact in generation. I will present two Event Related Potential (ERP) experiments that show that the lexical retrieval in (predictive) comprehension is also constrained by syntactic categories. I will argue that the syntactic gating mechanism is operative both in parsing and generation, and that the interaction between structural and lexical processes in both parsing and generation can be characterized in the same fashion. In Chapter 4, I will present a series of experiments examining the timing at which verbs’ lexical representations are planned in sentence production. It will be shown that verbs are planned before the articulation of their internal arguments, regardless of the target language (Japanese or English) and regardless of the sentence type (active object-initial sentence in Japanese, passive sentences in English, and unaccusative sentences in English). I will discuss how this result sheds light on the notion of incrementality in generation. In Chapter 5, I will synthesize the experimental findings presented in this thesis and in previous research to address the challenges to the single system view I outlined in Chapter 1. I will then conclude by presenting a preliminary single system model that can potentially capture both the key sentence comprehension and sentence production data without assuming distinct mechanisms for each.

A Feminist Affective Turn for Public Relations: Mothers, Passionate Publics, and the Childhood Vaccine Debate

This project proposes a feminist intervention in how affect and publics are theorized in public relations research. Drawing from extant literature, I argue that public relations theories of affect and publics have been apolitical and lack depth and context (Leitch & Motion, 2010a). Using the context of the online childhood vaccine debate, I illustrate several theories and concepts of the new feminist affective turn, as well as postmodern theories of affect, relevant to public relations research: (a) Public Feelings, “ugly” feelings, agency, and community (Cvetkovich, 2012; Ngai, 2007); (b) passionate politics (Mouffe, 2014); (c) postmodern assemblages, biopower, and body politics (Deleuze & Guattari, 1988; Foucault, 1984); (d) affective facts and logics of future threats (Massumi, 2010); and (e) affective ethics (Bertleson & Murphie, 2010). Scholarship in the areas of public relations, risk, feminist and postmodern affect theory, and the vaccine debate provided theoretical grounding for this project. My research questions asked: How is feminist affect theory embodied by mothers in the vaccine debate? How do mothers understand risks as affective facts in the vaccine debate (if at all)? What affective logics are used by mothers in the vaccine debate (if any)? And, What are sources of knowledge for mothers in the vaccine debate? Multi-sited online ethnographic methods were used to explore how feminist affect theory contributes to public relations research, including 29 one-on-one in-depth interviews with mothers of young children and participant observation of 15 online discussions about vaccines on parenting websites BabyCenter.com, TheBump.com, and WhatToExpect.com. I used snowball sampling to recruit interview participants and grounded theory (Glaser & Strauss, 1967) to analyze interview and online data. Results show that feminist affect theory contributes to theoretical and practical knowledge in public relations by politicizing and contextualizing understandings of publics and elucidating how affective facts and logics inform publics’ knowledge and choices, specifically in the context of risk. I also found evidence of suppression of dissent (Martin, 2015) and academic bias in vaccine debate research, which resulted in cultures of silence. Further areas of study included how specific contexts such as motherhood and issues of privilege and access affect publics’ experiences, knowledges, and choices.

Jiao Tong: A Grounded Theory of Chinese International Students' Transition to American Tertiary Education

University students are more globally mobile than ever before, increasingly receiving education outside of their home countries. One significant student exchange pattern is between China and the United States; Chinese students are the largest population of international students in the U.S. (Institute of International Education, 2014). Differences between Chinese and American culture in turn influence higher education praxis in both countries, and students are enculturated into the expectations and practices of their home countries. This implies significant changes for students who must navigate cultural differences, academic expectations, and social norms during the process of transition to a system of higher education outside their home country. Despite the trends in students’ global mobility and implications for international students’ transitions, scholarship about international students does not examine students’ experiences with the transition process to a new country and system of higher education. Related models were developed with American organizations and individuals, making it unlikely that they would be culturally transferable to Chinese international students’ transitions. This study used qualitative methods to deepen the understanding of Chinese international students’ transition processes. Grounded theory methods were used to invite the narratives of 18 Chinese international students at a large public American university, analyze the data, and build a theory that reflects Chinese international students’ experiences transitioning to American university life. Findings of the study show that Chinese international students experience a complex process of transition to study in the United States. Students’ pre-departure experiences, including previous exposure to American culture, family expectations, and language preparation, informed their transition. Upon arrival, students navigate resource seeking to fulfill their practical, emotional, social, intellectual, and ideological needs. As students experienced various positive and discouraging events, they developed responses to the pivotal moments. These behaviors formed patterns in which students sought familiarity or challenge subsequent to certain events. The findings and resulting theory provide a framework through which to better understand the experiences of Chinese international students in the context of American higher education.