Mathematical Sciences: Statistical Methods of Scientific Interest Requiring Heavy Computer Usage

This research addresses a series of problems arising in industry, in geophysics and in statistics; all require intensive computational efforts and most have a strong geometric aspect. Whether the topic is geometric work associated with the design of molecules, the timing of folding and magnetization of the earth or dynamical systems of fractals, the emphasis and the novelty will be found in the formulation of the problems. The methods of attack will draw on computational mathematics, as in the computation of fractal dimensions and the fractal pursuit index. Access to affordable computing means that 'solutions' for practical problems can be found. More than ever before, the important step is that of expressing the problem precisely and correctly in mathematical terms in order to execute correct computations. This means capturing the scientific essence of the problem, which is not always what it at first appears to be. Then, with careful selection of mathematical and computational methods, simulation and other procedures can yield good working solutions or even exact ones.