Irreducible triangulations of surfaces with boundary

A triangulation of a surface is irreducible if no edge can be contracted to produce a triangulation of the same surface. In this paper, we investigate irreducible triangulations of surfaces with boundary. We prove that the number of vertices of an irreducible triangulation of a (possibly non-orientable) surface of genus g>=0 with b>=0 boundaries is O(g+b). So far, the result was known only for surfaces without boundary (b=0). While our technique yields a worse constant in the O(.) notation, the present proof is elementary, and simpler than the previous ones in the case of surfaces without boundary

A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography

We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy's foundational work associated with the work of Boyer and Grabiner; and to Bishop's constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography, teaching, and research.Comment: 57 pages; 3 figures. Corrected misprint

Spin Foams and Noncommutative Geometry

We extend the formalism of embedded spin networks and spin foams to include topological data that encode the underlying three-manifold or four-manifold as a branched cover. These data are expressed as monodromies, in a way similar to the encoding of the gravitational field via holonomies. We then describe convolution algebras of spin networks and spin foams, based on the different ways in which the same topology can be realized as a branched covering via covering moves, and on possible composition operations on spin foams. We illustrate the case of the groupoid algebra of the equivalence relation determined by covering moves and a 2-semigroupoid algebra arising from a 2-category of spin foams with composition operations corresponding to a fibered product of the branched coverings and the gluing of cobordisms. The spin foam amplitudes then give rise to dynamical flows on these algebras, and the existence of low temperature equilibrium states of Gibbs form is related to questions on the existence of topological invariants of embedded graphs and embedded two-complexes with given properties. We end by sketching a possible approach to combining the spin network and spin foam formalism with matter within the framework of spectral triples in noncommutative geometry.Comment: 48 pages LaTeX, 30 PDF figure

Fertility, Living Arrangements, Care and Mobility

There are four main interconnecting themes around which the contributions in this book are based. This introductory chapter aims to establish the broad context for the chapters that follow by discussing each of the themes. It does so by setting these themes within the overarching demographic challenge of the twenty-first century – demographic ageing. Each chapter is introduced in the context of the specific theme to which it primarily relates and there is a summary of the data sets used by the contributors to illustrate the wide range of cross-sectional and longitudinal data analysed

Sex-biased parental care and sexual size dimorphism in a provisioning arthropod

The diverse selection pressures driving the evolution of sexual size dimorphism (SSD) have long been debated. While the balance between fecundity selection and sexual selection has received much attention, explanations based on sex-specific ecology have proven harder to test. In ectotherms, females are typically larger than males, and this is frequently thought to be because size constrains female fecundity more than it constrains male mating success. However, SSD could additionally reflect maternal care strategies. Under this hypothesis, females are relatively larger where reproduction requires greater maximum maternal effort – for example where mothers transport heavy provisions to nests. To test this hypothesis we focussed on digger wasps (Hymenoptera: Ammophilini), a relatively homogeneous group in which only females provision offspring. In some species, a single large prey item, up to 10 times the mother’s weight, must be carried to each burrow on foot; other species provide many small prey, each flown individually to the nest. We found more pronounced female-biased SSD in species where females carry single, heavy prey. More generally, SSD was negatively correlated with numbers of prey provided per offspring. Females provisioning multiple small items had longer wings and thoraxes, probably because smaller prey are carried in flight. Despite much theorising, few empirical studies have tested how sex-biased parental care can affect SSD. Our study reveals that such costs can be associated with the evolution of dimorphism, and this should be investigated in other clades where parental care costs differ between sexes and species

Anticancer properties of propofol-docosahexaenoate and propofol-eicosapentaenoate on breast cancer cells

INTRODUCTION: Epidemiological evidence strongly links fish oil, which is rich in docosahexaenoic acid (DHA) and eicosapentaenoic acid (EPA), with low incidences of several types of cancer. The inhibitory effects of omega-3 polyunsaturated fatty acids on cancer development and progression are supported by studies with cultured cells and animal models. Propofol (2,6-diisopropylphenol) is the most extensively used general anesthetic–sedative agent employed today and is nontoxic to humans at high levels (50 μg/ml). Clinically relevant concentrations of propofol (3 to 8 μg/ml; 20 to 50 μM) have also been reported to have anticancer activities. The present study describes the synthesis, purification, characterization and evaluation of two novel anticancer conjugates, propofol-docosahexaenoate (propofol-DHA) and propofol-eicosapentaenoate (propofol-EPA). METHODS: The conjugates linking an omega-3 fatty acid, either DHA or EPA, with propofol were synthesized and tested for their effects on migration, adhesion and apoptosis on MDA-MB-231 breast cancer cells. RESULTS: At low concentrations (25 μM), DHA, EPA or propofol alone or in combination had minimal effect on cell adhesion to vitronectin, cell migration against serum and the induction of apoptosis (only 5 to 15% of the cells became apoptotic). In contrast, the propofol-DHA or propofol-EPA conjugates significantly inhibited cell adhesion (15 to 30%) and migration (about 50%) and induced apoptosis (about 40%) in breast cancer cells. CONCLUSION: These results suggest that the novel propofol-DHA and propofol-EPA conjugates reported here may be useful for the treatment of breast cancer

Whiteness and diasporic Irishness: nation, gender and class

Whiteness is often detached from the notion of diaspora in the recent flurry of interest in the phenomenon, yet it is a key feature of some of the largest and oldest displacements. This paper explores the specific contexts of white racial belonging and status over two centuries in two main destinations of the Irish diaspora, the USA and Britain. Its major contribution is a tracing of the untold story of ‘How the Irish became white in Britain’ to parallel and contrast with the much more fully developed narrative in the USA. It argues that, contrary to popular belief, the racialisation of the Irish in England did not fade away at the end of the nineteenth century but became transmuted in new forms which have continued to place the ‘white’ Irish outside the boundaries of the English nation. These have been strangely ignored by social scientists, who conflate Irishness and working-class identities in England without acknowledging the distinctive contribution of Irish backgrounds to constructions of class difference. Gender locates Irish women and men differently in relation to these class positions, for example allowing mothers to be blamed for the perpetuation of the underclass. Class and gender are also largely unrecognised dimensions of Irish ethnicity in the USA, where the presence of ‘poor white’ neighbourhoods continues to challenge the iconic story of Irish upward mobility. Irishness thus remains central to the construction of mainstream ‘white’ identities in both the USA and Britain into the twenty-first century