ENHANCING COMMUNICATION THROUGH SUCCESSFUL REPAIR: EXAMINING FLUENCY AND MECHANISMS FOR SYNTACTIC PROGRESS IN APHASIC AND NON-APHASIC SPEECH

The fields of Rhetoric and Communication usually assume a competent speaker who is able to speak well with conscious intent; however, what happens when intent and comprehension are intact but communicative facilities are impaired (e.g., by stroke or traumatic brain injury)? What might a focus on communicative success be able to tell us in those instances? This project considers this question in examining communication disorders through identifying and analyzing patterns of (dis) fluent speech between 10 aphasic and 10 non-aphasic adults. The analysis in this report is centered on a collection of data provided by the Aphasia Bank database. The database’s collection protocol guides aphasic and non-aphasic participants through a series of language assessments, and for my re-analysis of the database’s transcripts I consider communicative success is and how it is demonstrated during a re-telling of the Cinderella narrative. I conducted a thorough examination of a set of participant transcripts to understand the contexts in which speech errors occur, and how (dis) fluencies may follow from aphasic and non-aphasic participant’s speech patterns. An inductive mixed-methods approach, informed by grounded theory, qualitative, and linguistic analyses of the transcripts functioned as a means to balance the classification of data, providing a foundation for all sampling decisions. A close examination of the transcripts and the codes of the Aphasia Bank database suggest that while the coding is abundant and detailed, that further levels of coding and analysis may be needed to reveal underlying similarities and differences in aphasic vs. non-aphasic linguistic behavior. Through four successive levels of increasingly detailed analysis, I found that patterns of repair by aphasics and non-aphasics differed primarily in degree rather than kind. This finding may have therapeutic impact, in reassuring aphasics that they are on the right track to achieving communicative fluency.

Applications of finite geometries to designs and codes

This dissertation concerns the intersection of three areas of discrete mathematics: finite geometries, design theory, and coding theory. The central theme is the power of finite geometry designs, which are constructed from the points and t-dimensional subspaces of a projective or affine geometry. We use these designs to construct and analyze combinatorial objects which inherit their best properties from these geometric structures. A central question in the study of finite geometry designs is Hamada’s conjecture, which proposes that finite geometry designs are the unique designs with minimum p-rank among all designs with the same parameters. In this dissertation, we will examine several questions related to Hamada’s conjecture, including the existence of counterexamples. We will also study the applicability of certain decoding methods to known counterexamples. We begin by constructing an infinite family of counterexamples to Hamada’s conjecture. These designs are the first infinite class of counterexamples for the affine case of Hamada’s conjecture. We further demonstrate how these designs, along with the projective polarity designs of Jungnickel and Tonchev, admit majority-logic decoding schemes. The codes obtained from these polarity designs attain error-correcting performance which is, in certain cases, equal to that of the finite geometry designs from which they are derived. This further demonstrates the highly geometric structure maintained by these designs. Finite geometries also help us construct several types of quantum error-correcting codes. We use relatives of finite geometry designs to construct infinite families of q-ary quantum stabilizer codes. We also construct entanglement-assisted quantum error-correcting codes (EAQECCs) which admit a particularly efficient and effective error-correcting scheme, while also providing the first general method for constructing these quantum codes with known parameters and desirable properties. Finite geometry designs are used to give exceptional examples of these codes.