Abstract:
South Africa is a society characterised by deep inequalities structured along racial, geographical and socio-economic lines. Since 1994 the new democratic government has instituted a number of large-scale policies and programmes with explicit pro-equity objectives. Although these have improved access to health care and other social resources for the poor, their equity impact has been constrained by a macro-economic policy context that has dictated fiscal restraint, and by an accompanying orientation that has privileged technical over developmental considerations. This article briefly analyses the above factors and policies and proposes an approach that focuses on equity in allocation of health resources in relation to need. It suggests that while measurement of such inequities is fundamental to pro-equity policies, the implementation of such policies requires, in addition to technically efficacious interventions, both advocacy initiatives, and communication with and involvement of affected communities in promotion of health equity.

Abstract:
The exact mean time between encounters of a given particle in a system consisting of many particles undergoing random walks in discrete time is calculated, on both regular and complex networks. Analytical results are obtained both for independent walkers, where any number of walkers can occupy the same site, and for walkers with an exclusion interaction, when no site can contain more than one walker. These analytical results are then compared with numerical simulations, showing very good agreement.

Abstract:
We investigate statistical properties of several classes of periodic billiard models which are diffusive. An introductory chapter gives motivation, and then a review of statistical properties of dynamical systems is given in chapter 2. In chapter 3, we study the geometry dependence of diffusion coefficients in a two-parameter 2D periodic Lorentz gas model, including a discussion of how to estimate them from data. In chapter 4, we study the shape of position and displacement distributions, which occur in the central limit theorem. We show that there is an oscillatory fine structure and what its origin is. This allows us to conjecture a refinement of the central limit theorem in these systems. A non-Maxwellian velocity distribution is shown to lead to a non-Gaussian limit distribution. Chapter 5 treats polygonal billiard channels, developing a picture of when normal and anomalous diffusion occur, the latter being due to parallel scatterers in the billiard causing a channelling effect. We also characterize the crossover from normal to anomalous diffusion. In chapter 6, we extend our methods to a 3D periodic Lorentz gas model, showing that normal diffusion occurs under certain conditions. In particular, we construct an explicit finite-horizon model, and we discuss the effect that holes in configuration space have on the diffusive properties of the system. We finish with conclusions and directions for future research.

Abstract:
We show, both heuristically and numerically, that three-dimensional periodic Lorentz gases -- clouds of particles scattering off crystalline arrays of hard spheres -- often exhibit normal diffusion, even when there are gaps through which particles can travel without ever colliding, i.e., when the system has an infinite horizon. This is the case provided that these gaps are not "too big", as measured by their dimension. The results are illustrated with simulations of a simple three-dimensional model having different types of diffusive regime, and are then extended to higher-dimensional billiard models, which include hard-sphere fluids.

Abstract:
We summarize the results of two recent searches for flavor-changing neutral current, lepton-flavor violating, and lepton-number violating decays of D+, Ds, and D0 mesons (and their antiparticles) into modes containing muons and electrons. Using data from Fermilab charm hadroproduction experiment E791, we examined D+ and Ds pi,l,l and K,l,l decay modes and the D0 dilepton decay modes containing either l+,l-, a rho0, K*0, or phi vector meson, or a non-resonant pi,pi, K,pi, or K,K pair of pseudoscalar mesons. No evidence for any of these decays was found. Therefore, we presented branching-fraction upper limits at 90% confidence level for the 51 decay modes examined. Twenty-six of these modes had no previously reported limits, and eighteen of the remainder were reported with significant improvements over previously published results.

Abstract:
We investigate deterministic diffusion in periodic billiard models, in terms of the convergence of rescaled distributions to the limiting normal distribution required by the central limit theorem; this is stronger than the usual requirement that the mean square displacement grow asymptotically linearly in time. The main model studied is a chaotic Lorentz gas where the central limit theorem has been rigorously proved. We study one-dimensional position and displacement densities describing the time evolution of statistical ensembles in a channel geometry, using a more refined method than histograms. We find a pronounced oscillatory fine structure, and show that this has its origin in the geometry of the billiard domain. This fine structure prevents the rescaled densities from converging pointwise to gaussian densities; however, demodulating them by the fine structure gives new densities which seem to converge uniformly. We give an analytical estimate of the rate of convergence of the original distributions to the limiting normal distribution, based on the analysis of the fine structure, which agrees well with simulation results. We show that using a Maxwellian (gaussian) distribution of velocities in place of unit speed velocities does not affect the growth of the mean square displacement, but changes the limiting shape of the distributions to a non-gaussian one. Using the same methods, we give numerical evidence that a non-chaotic polygonal channel model also obeys the central limit theorem, but with a slower convergence rate.

Abstract:
I briefly review the results of recent searches for flavor-changing neutral current and lepton-flavor and lepton-number violating decays of D+, Ds, and D0 mesons (and their antiparticles) into modes containing muons and electrons. The primary focus is the results from Fermilab charm hadroproduction experiment E791. E791 examined 24 pi,l,l and K,l,l decay modes of D+ and Ds and l+l- decay modes of D0. Limits presented by E791 for 22 rare and forbidden dilepton decays of D mesons were more stringent than those obtained from previous searches, or else were the first reported.

Abstract:
We report the results of some recent E791 charm analyses. They include: 1) a search for rare and forbidden decays, 2) measurements of form factors for D+ --> K*,l,nu and Ds --> phi,l,nu, and 3) Ds and D0 lifetime measurements including the lifetime difference between D0-->Kpi and D0-->KK. The latter is the first direct search for a possible lifetime difference that could contribute to D0-D0bar mixing.