A comparison theorem for simplicial resolutions

It is well known that Barr and Beck's definition of comonadic homology makes sense also with a functor of coefficients taking values in a semi-abelian category instead of an abelian one. The question arises whether such a homology theory has the same convenient properties as in the abelian case. Here we focus on independence of the chosen comonad: conditions for homology to depend on the induced class of projectives only.Comment: 16 page

The fundamental group functor as a Kan extension

We prove that the fundamental group functor from categorical Galois theory may be computed as a Kan extension.Comment: Final published version. 26 pages. Dedicated to Rene Guitart on the occasion of his sixty-fifth birthda

Three viewpoints on semi-abelian homology

The main theme of the thesis is to present and compare three different viewpoints on semi-abelian homology, resulting in three ways of defining and calculating homology objects. Any two of these three homology theories coincide whenever they are both defined, but having these different approaches available makes it possible to choose the most appropriate one in any given situation, and their respective strengths complement each other to give powerful homological tools. The oldest viewpoint, which is borrowed from the abelian context where it was introduced by Barr and Beck, is comonadic homology, generating projective simplicial resolutions in a functorial way. This concept only works in monadic semi-abelian categories, such as semi-abelian varieties, including the categories of groups and Lie algebras. Comonadic homology can be viewed not only as a functor in the first entry, giving homology of objects for a particular choice of coefficients, but also as a functor in the second variable, varying the coefficients themselves. As such it has certain universality properties which single it out amongst theories of a similar kind. This is well-known in the setting of abelian categories, but here we extend this result to our semi-abelian context. Fixing the choice of coefficients again, the question naturally arises of how the homology theory depends on the chosen comonad. Again it is well-known in the abelian case that the theory only depends on the projective class which the comonad generates. We extend this to the semi-abelian setting by proving a comparison theorem for simplicial resolutions. This leads to the result that any two projective simplicial resolutions, the definition of which requires slightly more care in the semi-abelian setting, give rise to the same homology. Thus again the homology theory only depends on the projective class. The second viewpoint uses Hopf formulae to define homology, and works in a non-monadic setting; it only requires a semi-abelian category with enough projectives. Even this slightly weaker setting leads to strong results such as a long exact homology sequence, the Everaert sequence, which is a generalised and extended version of the Stallings-Stammbach sequence known for groups. Hopf formulae use projective presentations of objects, and this is closer to the abelian philosophy of using any projective resolution, rather than a special functorial one generated by a comonad. To define higher Hopf formulae for the higher homology objects the use of categorical Galois theory is crucial. This theory allows a choice of Birkhoff subcategory to generate a class of central extensions, which play a big role not only in the definition via Hopf formulae but also in our third viewpoint. This final and new viewpoint we consider is homology via satellites or pointwise Kan extensions. This makes the universal properties of the homology objects apparent, giving a useful new tool in dealing with statements about homology. The driving motivation behind this point of view is the Everaert sequence mentioned above. Janelidze's theory of generalised satellites enables us to use the universal properties of the Everaert sequence to interpret homology as a pointwise Kan extension, or limit. In the first instance, this allows us to calculate homology step by step, and it removes the need for projective objects from the definition. Furthermore, we show that homology is the limit of the diagram consisting of the kernels of all central extensions of a given object, which forges a strong connection between homology and cohomology. When enough projectives are available, we can interpret homology as calculating fixed points of endomorphisms of a given projective presentation

Policy Response to Pandemic Influenza: The Value of Collective Action

This paper examines positive externalities and complementarities between countries in the use of antiviral pharmaceuticals to mitigate pandemic influenza. It demonstrates the presence of treatment externalities in simple SIR (susceptible-infectious-recovered) models and simulations of a Global Epidemiological Model. In these simulations, the pandemic spreads from city to city through the international airline network and from cities to rural areas through ground transport. While most treatment benefits are private, spillovers suggest that it is in the self-interest of high-income countries to pay for some antiviral treatment in low-income countries. The most cost-effective policy is to donate doses to the country where the outbreak originates; however, donating doses to low-income countries in proportion to their populations may also be cost-effective. These results depend on the transmissibility of the flu strain, its start date, the efficacy of antivirals in reducing transmissibility, and the proportion of infectious people who can be identified and treated.pandemic influenza, disease control externalities

Differences in the association between childhood trauma and BMI in black and white South African women

Objective: Childhood trauma has previously been associated with adult obesity. The aim of this study was to determine if ethnicity altered the relationship between childhood trauma and obesity in South African women. Methods: Forty-four normalweight (BMI<25kg/m2) and obese (BMI>30kg/m2), black and white premenopausal women completed the Childhood Trauma Questionnaire (CTQ), which retrospectively assessed emotional and physical neglect, and emotional, physical and sexual abuse in childhood. Results: Body composition did not differ by ethnicity in the normal-weight and obese groups. However,independent of BMI group, there were significant differences in socioeconomic status (SES) between black and white women (P<0.01). Total CTQ score, as well as the sub-scales, physical and emotional neglect, and physical and sexual abuse were higher in black than white women (all P<0.05), but these scores did not differ between BMI groups. Apart from the sexual abuse score, the differences in physical and emotional neglect and physical abusescores were no longer significant after adjusting for ethnic differences in age and SES. For sexual abuse, there was a significant interaction between ethnicity and BMI group(P=0.04), with scores in normal weight women being higher in black than white women, but scores in obese women not differing by ethnicity. Conclusion: Ethnicity alters the association between childhood sexual abuse and BMI status. Larger studies are required to verify this finding, including measures of body image and body size satisfaction that may explain these findings.Keywords: Childhood trauma questionnaire; Body fat; Body image; Sexual abuse; Ethnicity, Socioeconomic statu

Accuracy of reporting food energy intake: influence of ethnicity and body weight status in South African women

The current study sought to identify characteristics that may be associated with the misreporting of food energy intake (EI) in urban South African women. A total of 198 women (61 black, 76 of mixed ancestry, 61 white) completed a quantified food frequency questionnaire, from which daily energy and macronutrient intake were calculated. Body composition (body mass index [BMI], percentage of body fat), body image (Feel-Ideal Difference index and Body Shape questions) and socio-economic status (SES) (household density and asset index) were also measured. Food EI in relation to estimated basal metabolic rate ratio that was less than 1.05 represented under-reporting, whereas a ratio greater than 2.28 represented over-reporting. Results suggested that 26% of the participants under-reported, 64% adequately reported and 10% over-reported. Participants who under-reported had a higher BMI (p < 0.01) and higher percentage of body fat (p < 0.05) than those who adequately and over-reported. The majority of under-reporters were black (38%) versus 21% under-reporters of mixed ancestry and 20% white under-reporters (p < 0.01). Eighty-three per cent of black under-reporters were obese. On the other hand, a majority (63%) of overweight women of mixed ancestry and a majority (50%) of white normal-weight women under-reported their food EI. Under-reporters reported a lower intake of dietary fat (p < 0.01) and a higher intake of dietary protein (p < 0.01) than adequate or over-reporters. Food EI reporting was not influenced by SES or body image. In conclusion, results suggest that food EI reporting is influenced by body size, and may be ethnic-specific in South African women.Keywords: South African women; misreporting; energy intake; body image; socioeconomic statu

Books

LOCALISATION OF BRAIN LESIONS AND DEVELOPMENTAL FUNCTIONS*Mariani Foundation Paediatric Neurology: 9. Edited by D Riva and A Benton. Pp. vi + 165. Illustrated. £39. John Libbey &amp; Co Ltd. 2000. ISBN 0-86196-599x.SPORTS ENDOCRINOLOGY Contemporary Endocrinology. Edited by Michelle P Warren and Naama W Constantini. Pp. x + 486. US$ 135. The Humana Press. 2000. ISBN 0-89603-586-7.SPORTS MEDICINE HANDBOOK* Edited by Roger Hackney and Angus Wallace. Pp. x + 495. Illustrated. £75. 1999. BMJ. ISBN 0-7279-1031-0