On difunctions

The notion of a difunction was introduced by Jacques Riguet in 1948. Since then it has played a prominent role in database theory, type theory, program specification and process theory. The theory of difunctions is, however, less known in computing than it perhaps should be. The main purpose of the current paper is to give an account of difunction theory in relation algebra, with the aim of making the topic more mainstream. As is common with many important concepts, there are several different but equivalent characterisations of difunctionality, each with its own strength and practical significance. This paper compares different proofs of the equivalence of the characterisations. A well-known property is that a difunction is a set of completely disjoint rectangles. This property suggests the introduction of the (general) notion of the “core” of a relation; we use this notion to give a novel and, we believe, illuminating characterisation of difunctionality as a bijection between the classes of certain partial equivalence relations

Creolisation in Music Traditions: South Connemara, the Scottish Western Isles and Francophone Louisiana

Why do people mix musics? What causes them to break down the boundaries between music genres and produce new genres that are a mix of others, and what does a melody migrating between cultures have to do to conform to a new music culture? Researchers such as Bruno Nettl, John Blacking, George List and Mark Slobin have over the past eighty years or more, attempted to look at the issue of music mixing under the headings of diffusion, acculturation and globalisation. This thesis seeks to further the understanding of this phenomenon, by examining three cases of cultures that are known to have mixed musics and whose particular blending of musics can be demonstrated. The cases in question are the music of French-speaking south Louisiana, Scots Gaelic Protestant psalm singing, and a new type of country music and sean-nós singing mix from south Connemara in Ireland. Examples of the music genres that mixed (the ‘parents’) in each case are analysed to demonstrate characteristics of their genre. Examples of the music mix (‘the child’) are then analysed to demonstrate how the characteristics of the parents can be observed in the child, albeit in a new context. The difference between individual musicians blending musics experimentally and music mixes that have acquired their own names and conventions, are compared to the concepts of pidgin and creole languages. The three case studies take account of the historical, social, linguistic and religious conditions that may have played a part in creating a new music. The study cross-compares the three cases to find common factors, as well as distinguishing differences, between them. The validity of comparisons with sociolinguistics, in particular various modes of code mixing, is assessed in relation to the cases. Finally, the researcher uses the information and music-mixing strategies demonstrated in the three case studies to arrange and compose several newly-recorded pieces. The conclusions point to the importance of individual performers in making the innovations leading to new mixed music genres. They also emphasise how changing social and cultural environments, and the presence of a bi-musical community in the years leading up to the mix, are also an influencing factor. In concluding the study, the researcher finds a deeper affinity with comparisons between creole languages and their creation and the process of creolisation in music