Equivariant BRST quantization and reducible symmetries

Working from first principles, quantization of a class of Hamiltonian systems with reducible symmetry is carried out by constructing first the appropriate reduced phase space and then the BRST cohomology. The constraints of this system correspond to a first class set for a group G and a second class set for a subgroup H. The BRST operator constructed is equivariant with respect to H. Using algebraic techniques analogous to those of equivariant de Rham theory, the BRST operator is shown to correspond to that obtained by BV quantization of a class of systems with reducible symmetry. The 'ghosts for ghosts' correspond to the even degree two generators in the Cartan model of equivariant cohomology. As an example of the methods developed, a topological model is described whose BRST quantization relates to the equivariant cohomology of a manifold under a circle action.Comment: 23 pages LaTeX. Some refrences added and some clarification made to tex

Recovery dynamics of the Caribbean long-spined sea urchin, Diadema antillarum

The sea urchin Diadema antillarum is a keystone herbivore in the Caribbean and its functional extinction due to an epidemic in 1983 had a marked effect on coral reef health. Recovery of D. antillarum has been associated with improvements in reef health but has been unexpectedly slow and patchy with many populations persisting at low abundance on the reefs. This thesis investigates possible reasons for low and variable recovery of D. antillarum on the reef using combined techniques of population dynamic modelling, meta-analysis and field experimentation. Population dynamic modelling was used to explore the implications of alternative process hypotheses for recovery dynamics. Depensatory density dependence (Allee effects) or cultivation effects are predicted to lead to complex dynamics characterized by switching between alternative, high and low abundance states. Density independent variation in vital rates, e.g. due to environmental change, are predicted to affect recovery abundance and rates without leading to complex dynamics. Time series data explored through meta-analysis, and local recovery patterns examined in Curacao, exhibit recovery dynamics and spatial distributions which indicate that variation in density independent factors, rather than depensatory density dependent processes are the key drivers of population dynamics. Recovering populations and patches of high D. antillarum abundance are both associated with locations which exhibit high resource availability, high macroalgal abundance, few herbivorous fish competitors, reduced predation risk and local larval retention. Specifically, I find evidence to suggest that rates of recovery are determined by resource availability and population sizes are controlled by predation pressure and larval retention. Interestingly, the environmental characteristics which appear favourable to D. antillarum are also characteristics which tend to result from high levels of human threat. My results demonstrate that D. antillarum populations favour specific habitat characteristics which occur in a variety of habitat types and indicate that coral reefs, upon which most attention has been focused, actually represent relatively poor habitat for the species. In light of this, I predict that the widespread reappearance of D. antillarum on coral reefs will only occur once population densities in preferred, sheltered, shallow, nutrient enriched, often humanimpacted habitats become high enough to depress habitat quality in these locations, such that forereefs become suitable as alternative habitats

Anticommuting Variables, Fermionic Path Integrals and Supersymmetry

(Replacement because mailer changed `hat' for supercript into something weird. The macro `\sp' has been used in place of the `hat' character in this revised version.) Fermionic Brownian paths are defined as paths in a space para\-metr\-ised by anticommuting variables. Stochastic calculus for these paths, in conjunction with classical Brownian paths, is described; Brownian paths on supermanifolds are developed and applied to establish a Feynman-Kac formula for the twisted Laplace-Beltrami operator on differential forms taking values in a vector bundle. This formula is used to give a proof of the Atiyah-Singer index theorem which is rigorous while being closely modelled on the supersymmetric proofs in the physics literature.Comment: 18 pages, KCL-TH-92-

Does Slow and Variable Recovery of Diadema antillarum on Caribbean Fore-Reefs Reflect Density-Dependent Habitat Selection?

Recovery of the Caribbean long-spined sea urchin Diadema antillarum from the pathogen-induced mass mortality event of 1983 has been slow and variable. Multiple studies indicate that post-mortality population densities are greatest in sheltered lagoon and back reef habitats, and that recovery is limited on forereefs where pre-mortality densities were also high (Miller R. J. et al., 2003; Van der Hal, 2005; Debrot and Nagelkerken, 2006; Steiner and Williams, 2006; Vermeij et al., 2010). We carried out detailed surveys of a recovering population of D. antillarum in Curacao to document an ongoing influence of habitat type on population density, and to explore what ecosystem characteristics might drive observed recovery patterns. We quantified D. antillarum population density, larval settlement rates, herbivorous fish biomass, algal turfs, macroalgae, and predatory fish biomass in sites with and without structural complexity on reefs in sheltered lagoon and backreef locations, and on the forereef, using an orthogonal survey design. D. antillarum densities were greatest in sheltered lagoon and backreef locations, with high structural complexity. However, densities were significantly lower than those reported prior to the mass mortality event. Larval settlement rates were greater in sheltered lagoon and backreef locations but did not fully account for observed patterns in urchin density. Sheltered lagoon and backreef habitats had more turf algae and fewer herbivorous fish than forereef habitats. Predator abundance was generally low and did not differ significantly among habitat types. In light of our results, we hypothesize that patterns of D. antillarum recovery in Curacao are consistent with dynamics expected in the presence of density-dependent habitat selection. More algal resources and fewer herbivorous fish provide a mechanism for increased fitness and habitat suitability in sheltered, lagoon, and backreef habitats. Forereefs, by contrast, offer reduced habitat suitability and, we hypothesize, will only be re-colonized once the carrying capacity of more favorable habitats is exceeded. We propose a number of testable predictions to explore this theory further, and advocate for including sheltered lagoon and backreef habitats in D. antillarum population surveys to monitor recovery, as well as protecting populations found in these habitats where necessary. We predict that when current populations return to pre-mortality densities, range expansion may allow for a return of D. antillarum to Caribbean forereefs

Gauge fixing and equivariant cohomology

The supersymmetric model developed by Witten to study the equivariant cohomology of a manifold with an isometric circle action is derived from the BRST quantization of a simple classical model. The gauge-fixing process is carefully analysed, and demonstrates that different choices of gauge-fixing fermion can lead to different quantum theories.Comment: 18 pages LaTe

Diagnostic waste:Whose responsibility?

Waste management is notably absent from current discussions about efforts to improve access to diagnostics in low-and middle-income Countries (LMICs). Yet an increase in testing will inevitably lead to an increase in diagnostic waste, especially since many of the diagnostic tests designed for use in LMICs are single-use point-of-care tests. Diagnostic waste poses a threat to both human and environmental health. In this commentary we draw on our experience of diagnostic waste management in Sierra Leone and review current evidence on: the volume and impact of diagnostic waste in LMICs, existing health-care waste management capacity in LMICs, established national and international policies for improving health-care waste management, and opportunities for strengthening policy in this area. We argue that questions of safe disposal for diagnostics should not be an afterthought, only posed once questions of access have already been addressed. Moreover, responsibility for safe disposal of diagnostic waste should not fall solely on national health systems by default. Instead, consideration of the end-life of diagnostic products must be fully integrated into the diagnostic access agenda and greater pressure should be placed on manufacturers to take responsibility for the full life-cycle of their products