Research new ideas, develop concepts and undertake investigative/feasibility work to develop and prove software navigation algorithms and processing systems for navigation data. Develop and implement sophisticated navigation algorithms (filtering). Develop complex software, post-process and real-time, covering the full software life-cycle.Develop and maintain software libraries.Manage complex projects; plan, track and manage development tasks.Investigate ideas, suggestions and problems related to existing and new software products raised by staff, reps and customers.Identify opportunities, develop proposals and make plans for innovation and improvement in the navigation algorithms and processing of navigation data.

The main goal of this assignment has been to develop a classical, nonrelativistic 2D fluid simulation of the plasma filaments in a dense plasma focus. This simulation is for a 3-component fluid model in which fluid acceleration includes velocity-dependent friction. It is fully fluid dynamic, with no Ohm's Law (but it has been verified that at times, a tensor Ohm's Law emerges). The simulation features a moving mesh; a Delaunay triangulation is employed to create Voronoi cells. In order to handle shock-like conditions, the advective-compressive part of the simulation uses a finite volume shock-capturing approach which provides a qualitatively correct solution using conservation laws. This is performed by using a nonlinear model of density which I created to be an equivalent to minmod in multiple dimensions. The models of heat conduction and viscosity are valid at all levels of magnetization, and considerable innovations have been made in order to simulate these effectively.A numerical instability arises from the inductive response to a changing current, and this is addressed implicitly. There are further instabilities which are created due to the Lap Az term, and an implicit method requiring an ODE solve was found to overcome these. In an earlier version, there was also a method designed that overcame electrostatic oscillations, to allow charge density.Developing efficient reliable solvers that can be used in "production solving" of discretized DEs, has been a large part of my work. I use principles that are based on reflecting on the problem at hand and designing for reliability; I prioritize geometrically meaningful approaches. Sometimes this is multigrid and sometimes there is a physical reason not to expect long-range interactions at all.For this project I have used CUDA, C/C++, and DirectX for visualisation. Earlier versions were written entirely in C++ but the present version is written in CUDA throughout.

I was responsible for creating forecasts of the future performance of the Unsecured Personal Loan portfolio, in different scenarios. I mainly approached this by applying logistic models of consumer default, the reasoning being based on a latent index model. I also performed some time series analysis, modelling the trajectory of mortgage default data series with reference to macroeconomic variables and other factors. I introduced an approach via establishing the absence of unit roots and then proceeding to Vector Autoregression.I performed analysis of large datasets, using SAS and SQL queries and using a geodemographic database.I calibrated some of the binary models by using Markov Chain Monte Carlo, writing an application in C++ using the Windows Graphical User Interface APIs.

I taught a 1st-year undergraduate module in Probability during the last year of my PhD studies. I developed course materials as well as giving lectures.

The main project was to use large datasets to calibrate hierarchical models via Markov Chain Monte Carlo (MCMC). Using a Bayesian approach it is possible to produce a posterior distribution for the coefficients in a model of educational attainment, including dichotomous outcomes. Model specification testing in SPSS.I led the development of a tool to analyse small datasets to produce Management Information ad hoc for users, making use of downloaded coefficients for the national dataset. I was also responsible for making frequent presentations to management and stakeholders.