Geometric Flows of Diffeomorphisms

The idea of this thesis is to apply the methodology of geometric heat flows to the study of spaces of diffeomorphisms. We start by describing the general form that a geometrically natural flow must take and the implications this has for the evolution equations of associated geometric quantities. We discuss the difficulties involved in finding appropriate flows for the general case, and quickly restrict ourselves to the case of surfaces. In particular the main result is a global existence, regularity and convergence result for a geometrically defined quasilinear flow of maps u between flat surfaces, producing a strong deformation retract of the space of diffeomorphisms onto a finite-dimensional submanifold. Partial extensions of this result are then presented in several directions. For general Riemannian surfaces we obtain a full local regularity estimate under the hypothesis of bounds above and below on the singular values of the first derivative. We achieve these gradient bounds in the flat case using a tensor maximum principle, but in general the terms contributed by curvature are not easy to control. We also study an initial-boundary-value problem for which we can attain the necessary gradient bounds using barriers, but the delicate nature of the higher regularity estimate is not well-adapted for obtaining uniform estimates up to the boundary. To conclude, we show how appropriate use of the maximum principle can provide a proof of well-posedness in the smooth category under the assumption of estimates for all derivatives

Prospective surveillance of invasive group a streptococcal disease, Fiji, 2005-2007.

We undertook a prospective active surveillance study of invasive group A streptococcal (GAS) disease in Fiji over a 23-month period, 2005-2007. We identified 64 cases of invasive GAS disease, which represents an average annualized all-ages incidence of 9.9 cases/100,000 population per year (95% confidence interval [CI] 7.6-12.6). Rates were highest in those >65 years of age and in those <5 years, particularly in infants, for whom the incidence was 44.9/100,000 (95% CI 18.1-92.5). The case-fatality rate was 32% and was associated with increasing age and underlying coexisting disease, including diabetes and renal disease. Fifty-five of the GAS isolates underwent emm sequence typing; the types were highly diverse, with 38 different emm subtypes and no particular dominant type. Our data support the view that invasive GAS disease is common in developing countries and deserves increased public health attention

Recreational Fishing-Related Injuries to Australian Pelicans (Pelecanus Conspicillatus ) and Other Seabirds in a South Australian Estuarine and River Area

113 seabirds treated over 5.5 years had 132 fishing-related injuries that included entanglement with line only (N=35/132; 26.5%), entanglement with line and an associated hook (N=47/132; 35.6%), embedded hooks only (N=34/132; 25.7%) and foreign body ingestion (N=16/132; 12.1%). The percentage of fishing-related injuries ranged from 0.9% for banded stilts (Cladorhynchus leucocephalus), pacific gulls (Larus pacificus) and masked lapwing plovers (Vanellus miles), to 59.3% for Australian pelicans (Pelecanus conspicillatus). Entanglement and/or embedded hooks were present more often than injuries from ingestion; i.e. 97% (70/72) of pelicans had entanglement and/or embedded hook injuries; of these 35/72 [48.6%] were entangled with line and hooks, 24/72 [33.3%] had embedded hooks alone and 11/72 [15.3%] were entangled with lines only, with only 3% (2/72) having injuries from ingestion. A count of sea and river birds in close proximity to fishers revealed that the majority were pelicans (33.9%), compared to pied cormorants (28.6%), silver gulls (21.4%) and black swans (16.1%). Regular removal of discarded fishing material along local shores resulted in no reduction in the numbers of entangled or hooked seabirds. It appears likely, therefore, that such injuries may result from seabird proximity to active recreational fishing, rather than from entanglement in discarded material