Geometric combinatorial algebras: cyclohedron and simplex

In this paper we report on results of our investigation into the algebraic structure supported by the combinatorial geometry of the cyclohedron. Our new graded algebra structures lie between two well known Hopf algebras: the Malvenuto-Reutenauer algebra of permutations and the Loday-Ronco algebra of binary trees. Connecting algebra maps arise from a new generalization of the Tonks projection from the permutohedron to the associahedron, which we discover via the viewpoint of the graph associahedra of Carr and Devadoss. At the same time that viewpoint allows exciting geometrical insights into the multiplicative structure of the algebras involved. Extending the Tonks projection also reveals a new graded algebra structure on the simplices. Finally this latter is extended to a new graded Hopf algebra (one-sided) with basis all the faces of the simplices.Comment: 23 figures, new expanded section about Hopf algebra of simplices, with journal correction

Understanding the small object argument

The small object argument is a transfinite construction which, starting from a set of maps in a category, generates a weak factorisation system on that category. As useful as it is, the small object argument has some problematic aspects: it possesses no universal property; it does not converge; and it does not seem to be related to other transfinite constructions occurring in categorical algebra. In this paper, we give an "algebraic" refinement of the small object argument, cast in terms of Grandis and Tholen's natural weak factorisation systems, which rectifies each of these three deficiencies.Comment: 42 pages; supersedes the earlier arXiv preprint math/0702290; v2: final journal version, minor corrections onl

“It's like giving him a piece of me.”: Exploring UK and Israeli women's accounts of motherhood and feeding

Objective The present study explored how Israeli and UK mothers integrate feeding into their conceptualisations of mothering 2–6 months post-partum. Background The nature and importance of motherhood is subject to differential contextual, cultural, political and historical influences. We set out to compare experiences of motherhood and feeding between these two countries using a qualitative approach. Methods Forty one women (mean age 36.4 ± 2.7 years) from Israel and the UK, mostly married or in a committed relationship were interviewed about their experience of pregnancy, motherhood and feeding. Data were analysed thematically. Results The experience of motherhood in the early postnatal period was dominated, for all mothers, by the experience of breastfeeding and clustered around three representations of mothering, namely; 1) a devoted mother who ignores her own needs; 2) a mother who is available for her infant but acknowledges her needs as well; and 3) a struggling mother for whom motherhood is a burden. Such representations existed within both cultural groups and sometimes coexisted within the same mothers. UK women described more struggles within motherhood whereas a tendency towards idealising motherhood was observed for Israeli women. Conclusion There are similarities in the ways that UK and Israeli women experienced motherhood and feeding. Where family life is strongly emphasized, mothers reported extremes of idealism and burden and associated an “ideal” mother with a breastfeeding mother. Where motherhood is represented as just one of many roles women take up, they are more likely to represent a “good enough” approach to mothering. Understanding the experience of motherhood and feeding in different cultural settings is important to provide the context for postnatal care specifically where mothers are reluctant to share problems or difficulties encountered

Islamist groups in the UK and recruitment

Since 2001 and 7/7 the search to find out why and how Muslims born in Europe join political and violence orientated Islamist groups has occupied policy makers and social scientist. The search has produced explanations that suggest social grievance, Islam and physiological problems are the motivations for why some Muslims join and act on behalf of Islamist groups in the UK. However, the approaches tend not to focus the role emotions generated from events that involve Muslim suffering play in some individuals becoming interested in acquiring and acting upon them. These events are often experienced variously by Muslims living in Europe through the media and are used by Islamist groups as resources to recruit. Consequently, this paper is based on interviews carried out with Islamists in the UK and tentatively discusses two process that take into account the emotional effect of events that concern Muslims in order to make sense of how some Muslims become compelled to acquire extreme ideas, act upon extreme ideas (independently or behalf of a group) or join Islamist groups.Publisher PD