Graphs of relations and Hilbert series

We are discussing certain combinatorial and counting problems related to quadratic algebras. First we give examples which confirm the Anick conjecture on the minimal Hilbert series for algebras given by $n$ generators and $\frac {n(n-1)}{2}$ relations for $n \leq 7$. Then we investigate combinatorial structure of colored graph associated to relations of RIT algebra. Precise descriptions of graphs (maps) corresponding to algebras with maximal Hilbert series are given in certain cases. As a consequence it turns out, for example, that RIT algebra may have a maximal Hilbert series only if components of the graph associated to each color are pairwise 2-isomorphic.

Explaining voting behaviour on free votes: Solely a matter of preference?

While studies examining free votes find MPs’ preferences influence their voting behaviour, most studies also show MPs tend to divide along party lines even after the whips have been withdrawn. Recent work offers a possible alternative explanation for this finding: this sustained party cohesion represents the impact of MPs’ party identification similar to party identification effects in the electorate. This argument is tested using a series of free votes on same-sex relations. Even after controlling for preferences using several direct measures, party continues to shape voting behaviour. Although indirect, this provides evidence in favour of the party-asidentification argument. 

Attitudes to community relations in Northern Ireland: signs of optimisim in the post-cease fire period?

This article uses attitudinal data to explore Catholic and Protestant perspectives on community relations and equality since the paramilitary cease fires in 1994. Although attitudes tend to fluctuate with the‘headline grabbing'events of the day, the article argues that there are signs that some fundamental changes have taken place in the post cease fire period. Of particular importance in this regard is the positive response recorded by the Catholic community towards government measures to tackle disadvantage and inequality. Equally significant is the protestant response to many of these measures which is often one of ambivalence rather than derision. In so far as the data appear to challenge the‘zero-sum'game that traditionally underpins relations between the two communities in Northern Ireland, they provide some grounds for optimism. Yet such optimism is tempered somewhat by the seeds of discontent which are manifest within the protestant community, particularly around issues of equality in employment and cultural traditions. Despite the more positive assessment of community relations and equality in 2002, it is argued that further monitoring will be required to determine the long-term effects of policy reform on relationships between the two communit

Professional Educational Psychology and Community Relations Education in Northern Ireland.

This article provides an account of practice-based research of, at least, one-star quality in terms of its contribution to both theory and practice. Aimed at practitioner (as opposed to academic) psychologists, the article addresses a dimension of the practitioner role that has remained silent in the literature. The article makes creative and original connections between school effectiveness, school improvement and education in a divided society. Post 11th September, the article was described as being highly original, significant and relevant to all practising educational psychologists. Concrete evidence for this is gained from, eg: hits on the online electronic version (2002-2003 Annual Report of the Association of Educational Psychologists), citations in reviews of research, and author invitations to present his work at UK and international practitioner psychology conferences. The article is published in the premier journal reporting on quality applied educational research and practice within the United Kingdom and beyond.