Fixed block configuration GDDs with block size 6 and (3, r)-regular graphs

Chapter 1 is used to introduce the basic tools and mechanics used within this thesis. Most of the definitions used in the thesis will be defined, and we provide a basic survey of topics in graph theory and design theory pertinent to the topics studied in this thesis. In Chapter 2, we are concerned with the study of fixed block configuration group divisible designs, GDD(n; m; k; λ1; λ2). We study those GDDs in which each block has configuration (s; t), that is, GDDs in which each block has exactly s points from one of the two groups and t points from the other. Chapter 2 begins with an overview of previous results and constructions for small group size and block sizes 3, 4 and 5. Chapter 2 is largely devoted to presenting constructions and results about GDDs with two groups and block size 6. We show the necessary conditions are sufficient for the existence of GDD(n, 2, 6; λ1, λ2) with fixed block configuration (3; 3). For configuration (1; 5), we give minimal or nearminimal index constructions for all group sizes n ≥ 5 except n = 10, 15, 160, or 190. For configuration (2, 4), we provide constructions for several families ofGDD(n, 2, 6; λ1, λ2)s. Chapter 3 addresses characterizing (3, r)-regular graphs. We begin with providing previous results on the well studied class of (2, r)-regular graphs and some results on the structure of large (t; r)-regular graphs. In Chapter 3, we completely characterize all (3, 1)-regular and (3, 2)-regular graphs, as well has sharpen existing bounds on the order of large (3, r)- regular graphs of a certain form for r ≥ 3. Finally, the appendix gives computational data resulting from Sage and C programs used to generate (3, 3)-regular graphs on less than 10 vertices.

Writing center handbooks and travel guidebooks : redesigning instructional texts for multicultural, multilingual, and multinational contexts

In an increasingly interconnected world characterized by the accelerating interplay of cultural, linguistic, and national difference, the ability to negotiate that difference in an equitable and ethical manner is a crucial skill for both individuals and larger social groups. This dissertation, Writing Center Handbooks and Travel Guidebooks: Redesigning Instructional Texts for Multicultural, Multilingual, and Multinational Contexts, considers how instructional texts that ostensibly support the negotiation of difference (i.e., accepting and learning from difference) actually promote the management of difference (i.e., rejecting, assimilating, and erasing difference). As a corrective to this focus on managing difference, chapter two constructs a theoretical framework that facilitates the redesign of handbooks, guidebooks, and similar instructional texts. This framework centers on reflexive design practices and is informed by literacy theory (Gee; New London Group; Street), social learning theory (Wenger), globalization theory (Nederveen Pieterse), and composition theory (Canagarajah; Horner and Trimbur; Lu; Matsuda; Pratt). By implementing reflexive design practices in the redesign of instructional texts, this dissertation argues that instructional texts can promote the negotiation of difference and a multicultural/multilingual sensibility that accounts for twenty-first century linguistic and cultural realities. Informed by the theoretical framework of chapter two, chapters three and four conduct a rhetorical analysis of two forms of instructional text that are representative of the larger genre: writing center coach handbooks and travel guidebooks to Hong Kong. This rhetorical analysis reveals how both forms of text employ rhetorical strategies that uphold dominant monolingual and monocultural assumptions. Alternative rhetorical strategies are then proposed that can be used to redesign these two forms of instructional texts in a manner that aligns with multicultural and multilingual assumptions. These chapters draw on the work of scholars in Writing Center Studies (Boquet and Lerner; Carino; DiPardo; Grimm; North; Severino) and Technical Communication (Barton and Barton; Dilger; Johnson; Kimball; Slack), respectively. Chapter five explores how the redesign of coach handbooks and travel guidebooks proposed in this dissertation can be conceptualized as a political act. Ultimately, this dissertation argues that instructional texts are powerful heuristic tools that can enact social change if they are redesigned to foster the negotiation of difference and to promote multicultural/multilingual world views.

Place for video games : a theoretical and pedagogical framework for multiliteracies learning in English studies

Students are now involved in a vastly different textual landscape than many English scholars, one that relies on the “reading” and interpretation of multiple channels of simultaneous information. As a response to these new kinds of literate practices, my dissertation adds to the growing body of research on multimodal literacies, narratology in new media, and rhetoric through an examination of the place of video games in English teaching and research. I describe in this dissertation a hybridized theoretical basis for incorporating video games in English classrooms. This framework for textual analysis includes elements from narrative theory in literary study, rhetorical theory, and literacy theory, and when combined to account for the multiple modalities and complexities of gaming, can provide new insights about those theories and practices across all kinds of media, whether in written texts, films, or video games. In creating this framework, I hope to encourage students to view texts from a meta-level perspective, encompassing textual construction, use, and interpretation. In order to foster meta-level learning in an English course, I use specific theoretical frameworks from the fields of literary studies, narratology, film theory, aural theory, reader-response criticism, game studies, and multiliteracies theory to analyze a particular video game: World of Goo. These theoretical frameworks inform pedagogical practices used in the classroom for textual analysis of multiple media. Examining a video game from these perspectives, I use analytical methods from each, including close reading, explication, textual analysis, and individual elements of multiliteracies theory and pedagogy. In undertaking an in-depth analysis of World of Goo, I demonstrate the possibilities for classroom instruction with a complex blend of theories and pedagogies in English courses. This blend of theories and practices is meant to foster literacy learning across media, helping students develop metaknowledge of their own literate practices in multiple modes. Finally, I outline a design for a multiliteracies course that would allow English scholars to use video games along with other texts to interrogate texts as systems of information. In doing so, students can hopefully view and transform systems in their own lives as audiences, citizens, and workers.

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.

Technical communication in the global context : a heuristic approach to disciplinary identity and pedagogical practices

There is nothing new or original in stating that the global economy directly impacts the profession of technical communicators. The globalization of the workplace requires that technical communicators be prepared to work in increasingly linguistically and culturally diverse contexts. These new exigencies have natural repercussions on the research and educational practices of the field In this work, I draw on rhetoric, linguistics, and literacy theory to explore the definition, role and meaning of the global context for the disciplinary construction of professional and technical communication. By adopting an interdisciplinary and diachronic perspective, I assert that the global context is a heuristic means for sophisticating the disciplinary identity of the field and for reinforcing its place within the humanities. Consequently, I contend that the globalization of the workplace is a kairotic moment for underscoring the rhetorical dimension of professional and technical communication.