A Unifying Construction for Difference Sets

We present a recursive construction for difference sets which unifies the Hadamard, McFarland, and Spence parameter families and deals with all abelian groups known to contain such difference sets. The construction yields a new family of difference sets with parameters (v, k, λ,n)=(22d+4(22d+2−1)/3, 22d+1(22d+3+1)/3, 22d+1(22d+1+1)/3, 24d+2) for d⩾0. The construction establishes that a McFarland difference set exists in an abelian group of order 22d+3(22d+1+1)/3 if and only if the Sylow 2-subgroup has exponent at most 4. The results depend on a second recursive construction, for semi-regular relative difference sets with an elementary abelian forbidden subgroup of order pr. This second construction deals with all abelian groups known to contain such relative difference sets and significantly improves on previous results, particularly for r\u3e1. We show that the group order need not be a prime power when the forbidden subgroup has order 2. We also show that the group order can grow without bound while its Sylow p-subgroup has fixed rank and that this rank can be as small as 2r. Both of the recursive constructions generalise to nonabelian groups

Constructions of difference sets in nonabelian 2-groups

Difference sets have been studied for more than 80 years. Techniques from algebraic number theory, group theory, finite geometry, and digital communications engineering have been used to establish constructive and nonexistence results. We provide a new theoretical approach which dramatically expands the class of $2$-groups known to contain a difference set, by refining the concept of covering extended building sets introduced by Davis and Jedwab in 1997. We then describe how product constructions and other methods can be used to construct difference sets in some of the remaining $2$-groups. We announce the completion of ten years of collaborative work to determine precisely which of the 56,092 nonisomorphic groups of order 256 contain a difference set. All groups of order 256 not excluded by the two classical nonexistence criteria are found to contain a difference set, in agreement with previous findings for groups of order 4, 16, and 64. We provide suggestions for how the existence question for difference sets in $2$-groups of all orders might be resolved.Comment: 38 page

Game Scoring: Towards a Broader Theory

“Game scoring,” that is, the act of composing music for and through gaming, is distinct from other types of scoring. To begin with, unlike other scoring activities, game scoring depends on — in fact, it arguably is — software programming. The game scorer’s choices are thus first-and-foremost limited by available gaming technology, and the “programmability” of their musical ideas given that technology, at any given historical moment. Moreover, game scores are unique in that they must allow for an unprecedented level of musical flexibility, given the high degree of user interactivity the video game medium enables and encourages. As such, game scoring necessarily constitutes an at least partially aleatoric compositional activity, the final score being determined as much through gameplay as traditional composition. This thesis demonstrates this through case studies of the Nintendo Entertainment System sound hardware configuration, and game scores, including the canonic score for Super Mario Bros. (1985)

Morgan Le Fay and other women : a study of the female phantasm in medieval literature

‘Morgan le Fay and Other Women’ is an interdisciplinary study that seeks to rationalise the various manifestations of a universal Other in medieval culture. Using Theresa Bane’s statement that ‘Morgan le F[a]y is a complicated figure in history and mythology; she has had many names and fulfilled many roles in religion and folklore’ as a focal argument, I present a methodology that identifies these ‘many names’ from what might be described as a primarily medieval perspective. Exploring the medieval notion of ‘character type’, this establishes a series of defining attributes that the culture of the period likely regarded as a ‘standard list’ for Morgan’s underlying identity: the Other Woman. Asserting that Morgan’s role in the medieval tradition is largely an attempt on to manifest this age-old concept in a variety of forms appropriate for different authors’ milieus and genres, this thesis suggests that medieval writers project onto the character a series of attributes recognised as Other from their own contexts. By applying this method, which has a basis in medieval semiotics and philosophy, to a range of characters, I propose that derivatives of the ‘Morganic’ persona might be found in a range of genres including medieval romance, drama, folklore, and, in my final chapter, the tradition of male outlaws

Ladies of the lodge : a history of Scottish Orangewomen, c. 1909-2013

This thesis focuses upon the under-researched history of the Ladies’ Orange Association of Scotland from 1909-2013. Challenging prevalent assumptions that Orangewomen are overwhelmingly working-class, it demonstrates a small - yet significant - core of female luminaries to be occupationally middle-class. The desire to articulate dual Scottish and British patriotic - rather than diasporic Irish Protestant - identities is also acknowledged as an emergent subjective shift in women’s motivations for joining. The sisters' apparent complicity with their unequal institutional standing is accounted for chiefly in terms of their desire to promote a unified public image of Orangeism as a ‘family’ institution. Orangewomen however, also actively resisted gendered ‘equal but different’ organisational discourses by using familial networks to sway male voting, appropriation of charitable work to showcase their abilities, subversive contributions to organisational literature and mobilisation of national press to lobby for the reversal of their subordinate status. This thesis represents a rare academic exploration of gendered Orange ritual symbolism, interpreting female rites as both spiritual legitimation of patriarchal subordination and, conversely, as a celebration of sisterly love. Additionally, this study exposes the one-dimensionality of media representations of Orangewomen which obscure, rather than divulge, individual subjectivities. It is argued that Orangewomen adaptively prioritised their class, gender, and ethno-religious identities, according to the differing contexts in which they operated, to support a disparate profile of benevolent causes and political campaigns. Appropriating oral history testimony and archival sources, this work not only updates findings of existing research, but also engages unexplored aspects of female Orangeism to illustrate Orangewomen’s considerable diversity

Gendering Fiction: A Mixed Methods Examination Of The Influence Of The boy Book/ girl Book Phenomenon On The Willingness To Read Of Young Adolescents

Well-meaning educators often recommend more boy books to increase reading motivation amongst boys. This experimental mixed-methods study investigated the influence of the boy book/ girl book phenomenon on willingness to read using a researcher-designed instrument called the Textual Features Sort (TFS). The TFS measured two attitudinal constructs—gendered beliefs about texts and willingness to read—in relation to individual textual features of selected young adult novels. Data came from 50 sixth and seventh grade students at a mid-sized public school in a rural New England state. Mean scores, frequencies, and percentages were analyzed using independent samples t-tests, paired t-tests, and Fisher\u27s exact test. Qualitative data was used to explain quantitative results. Findings indicate that boys were not more willing to read boy books than other books, nor less willing to read books with female protagonists. Boys were significantly less willing to read girl books, though individual textual features of a single novel elicited different gendered beliefs along with varying degrees of willingness to read. Girls were significantly less willing to read a novel if it was first sorted as a boy book. Research revealed a widespread belief in social consequences for a boy carrying a girl book down the hallway, that did not hold for girls. Findings suggest that sociocultural constructions of gender inhibit both boys and girls as readers, though to varying degrees, and challenge the notion that highly gendered and heteronormative assumptions about books and reading practices will increase willingness to read among young adolescent boys

Heterosexual Parents' Gender Role Attitudes, Religious Orientation, Heterosexist Beliefs, Support Group Experiences, and Relationship Functioning with their Lesbian or Gay Children

The purpose of this study was to explore how support group experiences are related to parents' attitudes and relationships with their lesbian, gay, or bisexual children in an effort to understand the development of positive attitudes and relationships and what experiences might facilitate this process. This study assessed the interrelationships among parental attitudes (including gender role attitudes, religious orientation, and heterosexist beliefs), parent-child and family relationships (including current family and parent-child relationship functioning, and changes in relationship functioning following disclosure or participation in a support group), and parents' experiences with psychoeducation and social support (including overall involvement in a support group as well as involvement in support, education, and advocacy activities). Participants were contacted through chapters of Parents and Friends of Lesbians and Gays (PFLAG). The final sample consisted of 167 individuals, 110 females and 52 males, who identified as heterosexual parents of one or more same-sex oriented children. Some key findings suggested that greater parental endorsement of heterosexist attitudes was associated with less positive views of their current parent-child relationship functioning and fewer reports of positive changes in their relationships with their children since their child's disclosure of her/his same-sex orientation. Results further indicated that the more participants were involved in PFLAG overall as well as in its support, education, and advocacy activities, the less they endorsed heterosexist attitudes. Regression results indicated that parents with higher levels of PFLAG involvement, especially involvement in advocacy, were least likely to endorse heterosexist attitudes. Also, the more parents were involved overall, and the more they were involved in support, education, and especially advocacy, the more they perceived positive changes in their relationships with their children since disclosure. The results of this study confirm previous research that explored some of the steps that parents may take as they attempt to understand, accept, and integrate their lesbian, gay, or bisexual child. It appears that accessing resources in the community, participating in supportive or self-help groups, and engaging in social advocacy are some of these important steps for parents. Additional findings and implications for future research, practice, and advocacy are discussed