Generating finite integral relation algebras

Relation algebras and categories of relations in particular have proven to be extremely useful as a fundamental tool in mathematics and computer science. Since relation algebras are Boolean algebras with some well-behaved operations, every such algebra provides an atom structure, i.e., a relational structure on its set of atoms. In the case of complete and atomic structure (e.g. finite algebras), the original algebra can be recovered from its atom structure by using the complex algebra construction. This gives a representation of relation algebras as the complex algebra of a certain relational structure. This property is of particular interest because storing the atom structure requires less space than the entire algebra. In this thesis I want to introduce and implement three structures representing atom structures of integral heterogeneous relation algebras, i.e., categorical versions of relation algebras. The first structure will simply embed a homogeneous atom structure of a relation algebra into the heterogeneous context. The second structure is obtained by splitting all symmetric idempotent relations. This new algebra is in almost all cases an heterogeneous structure having more objects than the original one. Finally, I will define two different union operations to combine two algebras into a single one.

Exploring multiracial/cultural identities through mothers' voices /

This study explored the experiences of mothers of multiracial/cultural children within the context of family, school, and community. Three categories of mothers of multiracial/cultural children were interviewed privately and then invited to meet as a group to explore some of their reflections and experiences. The categories consisted of 4 mothers with multiracial/cultural children presently attending elementary school, 2 mothers of multiracial/cultural children who are now adults and 3 mothers from my own multiracial/cultural family. The study explored the researcher's personal quest for a multiracial/cultural identity and combined interviews with her daughter, her sister, and her mother to reveal the multiracial/cultural experience from a personal perspective. Content analysis of the narratives revealed that multiracial/cultural children produce their own culture and establish new and personally relevant priorities as they develop their self-identities. Findings further indicated that present-day, mainstream mothers from the dominant majority group of Canadians, tell a different story than similar mothers of previous cohorts, and that although sociopolitical and economic changes have influenced the experiences ofthese women, their stories remain remarkably similar across racial and cultural lines. The findings from this study may promote the development of multicultural programs in Canada as they offer both prospects and challenges to multiracial/cultural children and multicultural educators. It is hoped that this study will provide a better understanding of multiculturalism and encourage educators to heighten their racial and cultural awareness as they strive to critically examine their own cultural stories and realign their praxis within the evolving Canadian mosaic.

Marginal/minority popular music : the concept of the "third space" and the case for "hybridities" of cultures/identities /

The topic of this thesis is marginaVminority popular music and the question of identity; the term "marginaVminority" specifically refers to members of racial and cultural minorities who are socially and politically marginalized. The thesis argument is that popular music produced by members of cultural and racial minorities establishes cultural identity and resists racist discourse. Three marginaVminority popular music artists and their songs have been chosen for analysis in support of the argument: Gil Scott-Heron's "Gun," Tracy Chapman's "Fast Car" and Robbie Robertson's "Sacrifice." The thesis will draw from two fields of study; popular music and postcolonialism. Within the area of popular music, Theodor Adorno's "Standardization" theory is the focus. Within the area of postcolonialism, this thesis concentrates on two specific topics; 1) Stuart Hall's and Homi Bhabha's overlapping perspectives that identity is a process of cultural signification, and 2) Homi Bhabha's concept of the "Third Space." For Bhabha (1995a), the Third Space defines cultures in the moment of their use, at the moment of their exchange. The idea of identities arising out of cultural struggle suggests that identity is a process as opposed to a fixed center, an enclosed totality. Cultures arise from historical memory and memory has no center. Historical memory is de-centered and thus cultures are also de-centered, they are not enclosed totalities. This is what Bhabha means by "hybridity" of culture - that cultures are not unitary totalities, they are ways of knowing and speaking about a reality that is in constant flux. In this regard, the language of "Otherness" depends on suppressing or marginalizing the productive capacity of culture in the act of enunciation. The Third Space represents a strategy of enunciation that disrupts, interrupts and dislocates the dominant discursive construction of US and THEM, (a construction explained by Hall's concept of binary oppositions, detailed in Chapter 2). Bhabha uses the term "enunciation" as a linguistic metaphor for how cultural differences are articulated through discourse and thus how differences are discursively produced. Like Hall, Bhabha views culture as a process of understanding and of signification because Bhabha sees traditional cultures' struggle against colonizing cultures as transforming them. Adorno's theory of Standardization will be understood as a theoretical position of Western authority. The thesis will argue that Adorno's theory rests on the assumption that there is an "essence" to music, an essence that Adorno rationalizes as structure/form. The thesis will demonstrate that constructing music as possessing an essence is connected to ideology and power and in this regard, Adorno's Standardization theory is a discourse of White Western power. It will be argued that "essentialism" is at the root of Western "rationalization" of music, and that the definition of what constitutes music is an extension of Western racist "discourses" of the Other. The methodological framework of the thesis entails a) applying semiotics to each of the three songs examined and b) also applying Bhabha's model of the Third Space to each of the songs. In this thesis, semiotics specifically refers to Stuart Hall's retheorized semiotics, which recognizes the dual function of semiotics in the analysis of marginal racial/cultural identities, i.e., simultaneously represent embedded racial/cultural stereotypes, and the marginal raciaVcultural first person voice that disavows and thus reinscribes stereotyped identities. (Here, and throughout this thesis, "first person voice" is used not to denote the voice of the songwriter, but rather the collective voice of a marginal racial/cultural group). This dual function fits with Hall's and Bhabha's idea that cultural identity emerges out of cultural antagonism, cultural struggle. Bhabha's Third Space is also applied to each of the songs to show that cultural "struggle" between colonizers and colonized produces cultural hybridities, musically expressed as fusions of styles/sounds. The purpose of combining semiotics and postcolonialism in the three songs to be analyzed is to show that marginal popular music, produced by members of cultural and racial minorities, establishes cultural identity and resists racist discourse by overwriting identities of racial/cultural stereotypes with identities shaped by the first person voice enunciated in the Third Space, to produce identities of cultural hybridities. Semiotic codes of embedded "Black" and "Indian" stereotypes in each song's musical and lyrical text will be read and shown to be overwritten by the semiotic codes of the first person voice, which are decoded with the aid of postcolonial concepts such as "ambivalence," "hybridity" and "enunciation."

Conversations with EFL teachers: toward an understanding of whiteness in the classroom /

Few teachers would question that teaching is a contextual and situational process, yet as Gay (2000) reminds us, too few teachers have sufficient knowledge of how teaching practices reflect dominant cultural values. This qualitative study explored whiteness in the EFL classroom and the relation between teacher identity and pedagogy. This research was shaped by the overarching research questions: How does being white influence teachers' educational practices? How can teachers successfully negotiate crosscultural teaching? Data included open-ended interviews, a content analysis of EFL training materials, and my research and personal journals. The experiences of five EFL teachers form the central focus of this study. My personal story, as a white EFL teacher, is also included throughout this thesis. This study offers a detailed description of the complex and dynamic ways in which these five teachers understood their racial identities, and the classroom decisions they made in response to their understandings. Included in the discussion are the strategies that my participants and I used to subtly resist the notion and exploration of racial privilege. Implications for teacher education programs and possible directions for further study are offered.

South Asian Women's Identities: A Media and Personal Narrative Analysis

This study examines issues of racism and sexism through the lens of Critical Race Theory and the interaction of personal and composite narratives. Specifically, the study explores how mainstream media’s hegemonic portrayal of South Asian culture and the 2007 socalled honour killing of Aqsa Parvez contribute to post-9/11 Islamophobia. The researcher presents a personal narrative that draws upon her experiences growing up in Dubai, U.A.E., and in Ontario, Canada and critically analyzes majoritarian stories related to Parvez as well as “counter-perspectives” that challenge such views. Study findings highlight the impact of 9/11 and Parvez’s murder on the researcher’s identity formation, and how media portray Muslim women as oppressed beings who live under the yoke of patriarchy. Results also indicate that although certain articles offer a counter-perspective that challenge dominant narratives, most recent media representations of the Parvez story equate Islam with honour killings and thus foster continued Islamophobia.

Unveiling Shi’i Religious Identities: Case Studies of Hijab in Culturally Homogeneous Canadian Schools

This qualitative case study explored 10 young female Shi’i Muslim Arabic-Canadian students’ experiences associated with wearing the Hijab (headscarf) within their home, community, and predominantly White Canadian public elementary school environments. The study integrated several bodies of scholarly theories in order to examine the data under a set of comprehensive lenses that more fully articulates and theorizes on the diversity of female Shi’i Muslim Canadian students’ experiences. These theories are: identity theories with a focus on religious identity and negative stereotypes associated with Muslims; feminism and the Hijab discourses; research pertaining to Muslims in school settings; and critical race theory. In order to readdress the dearth of information about Shi’is’ experiences in schools, this study provides an in-depth case study analysis in which the methodology strategies included 10 semi-structured in-depth interviews, 2 focus-group meetings, and the incorporation of the researcher’s fieldnotes. Data analysis revealed the following themes corresponding to participants’ experiences and values in their social worlds of home, community, and schools: (a) martyrdom and self-sacrifice as a means for social justice; (b) transformational meaning of the Hijab; (c) intersectionality between culture, religion, and gender; and (d) effects of visits “back home” on participants’ religious identities. Additional themes related to participants’ school experiences included: (a) “us versus them” mentality; (b) religious and complex secular dialogues; (c) absence of Muslim representations in monocultural schools; (d) discrimination; (e) remaining silent versus speaking out; and (f) participants’ strategies for preserving their identities. Recommendations are made to integrate Shi’i Muslim females’ identity within the context of Islam and the West, most notably in relation to: (a) the role of Muslim community in nondiverse settings as a space that advances and nurtures Shi’i Muslim identity; and (b) holistic and culturally responsive teaching that fosters respect of others’ religiosity and spirituality. This study makes new inroads into feminist theorizing by drawing conceptual links between these previously unknown connections such as the impact of the historical female exemplary role model and the ritual stories on the experiences of Muslim females wearing the Hijab.

Mental Health and Becoming a Teacher: A Narrative on the Experiences and Identities of Teacher Candidates

This study used narrative inquiry to shed light on the identity development of teacher candidates who experienced mental health issues during teacher education programs. The study sought to examine (a) stories that teacher candidates tell about being in a teacher education program while experiencing mental health issues; (b) identity development of teachers who have experienced mental health issues; and (c) how narratives of teacher candidates and beginning teachers challenge stereotyping and stigmatization. Through discussion and letter correspondence, the participants and I shared stories that represented our lived experiences. The study explored our stories using the 3 commonplaces of temporality, sociality, and place from a theoretical framework of narrative inquiry. Four themes emerged from the data analysis: the stigmatization of mental health issues; dealing with conflict; the need for a safe and supportive environment; and the complexity of mental health issues. This study contributes to the literature by exploring the lived experiences of teacher candidates and beginning teachers with mental health issues. The narratives inform teacher education programs, the teaching profession, and the mental health field.

Developing an Understanding of Cultural Diversity: How an Experience Living in a Multicultural Nation and an Experience Teaching Abroad Contribute to Southern Ontario Teachers' Identities

This is a narrative design study focusing on the understandings that a group of 6 Southern Ontario teachers have of cultural diversity and how these understandings integrated into their development of teacher identity. Given the high culturally diverse population of Canada and its national multicultural values, conducting this study on Canadian pre-service and in-service teachers offers an interesting contribution to the field. In efforts to explore the participants’ understandings, the research examined a teaching abroad experience. The aim was to investigate how these participants gained insight from their experiences with cultural diversity and whether these insights stimulated a greater culturally conscious teacher identity. Narratives provided a description of the lived experiences of these 6 teachers and identified meanings made from these experiences. Participants included 2 pre-service teachers who were in a teacher education program at the time of the interview, and 4 certified teachers who graduated from a teacher education program within the past 5 years. One on one interviews focused on lived experiences within a participant’s home, school community, and teaching abroad. The researcher used grounded theory during the data analysis to assist in identifying themes, and then compared these themes among participants. Overall, this study suggests that even though these participants live in a multicultural nation, experiences varied greatly based on contributing factors such as heritage and exposure to cultural diversity through their home and school life. Despite their varying level of cultural competence, all participants gained insight from their teaching abroad experience, contributing to a teacher identity that considered inclusive practices. This study suggests that there are some important factors to consider when preparing teachers to teach in a multicultural society.

Socio-demographic factors, smoking, symptoms, morbidities and pulmonary function and quality of life in individuals with a heavy smoking history

Objective: To determine which socio-demographic, exposure, morbidity and symptom variables are associated with health-related quality of life among former and current heavy smokers. Methods: Cross sectional data from 2537 participants were studied. All participants were at ≥2% risk of developing lung cancer within 6 years. Linear and logistic regression models utilizing a multivariable fractional polynomial selection process identified variables associated with health-related quality of life, measured by the EQ-5D. Results: Upstream and downstream associations between smoking cessation and higher health-related quality of life were evident. Significant upstream associations, such as education level and current working status and were explained by the addition of morbidities and symptoms to regression models. Having arthritis, decreased forced expiratory volume in one second, fatigue, poor appetite or dyspnea were most highly and commonly associated with decreased HRQoL. Discussion: Upstream factors such as educational attainment, employment status and smoking cessation should be targeted to prevent decreased health-related quality of life. Practitioners should focus treatment on downstream factors, especially symptoms, to improve health-related quality of life.