Stochastic modelling and analysis of spatio-temporal processes with fractal characteristics. Interest has grown in recent years on the derivation of fractal models to represent certain physical phenomena such as diffusion and transport in porous media, oceanic and atmospheric turbulence, climatology, etc. This project focuses on the phenomenon of diffusion on domains with multifractal geometry. Recent advances in harmonic analysis on fractals and our own development of fractional generalized ran ....Stochastic modelling and analysis of spatio-temporal processes with fractal characteristics. Interest has grown in recent years on the derivation of fractal models to represent certain physical phenomena such as diffusion and transport in porous media, oceanic and atmospheric turbulence, climatology, etc. This project focuses on the phenomenon of diffusion on domains with multifractal geometry. Recent advances in harmonic analysis on fractals and our own development of fractional generalized random fields allow us to formulate a comprehensive program to tackle some key problems including modeling, processing and statistical estimation of fractional diffusion. Advances made in this program will in turn benefit the developments in related scientific fields.Read moreRead less
Computational methods for precise reconstruction of white-matter fibre tracts in the human brain using diffusion tensor imaging. One in five Australians will experience a mental illness. This project will facilitate a new method for: (1) brain researchers to advance the fundamental understanding of mental illnesses and brain disorders; (2) medical clinicians to diagnose and assess the growing incidence of mental illness confronting Australia's ageing population, thereby addressing the ageing wel ....Computational methods for precise reconstruction of white-matter fibre tracts in the human brain using diffusion tensor imaging. One in five Australians will experience a mental illness. This project will facilitate a new method for: (1) brain researchers to advance the fundamental understanding of mental illnesses and brain disorders; (2) medical clinicians to diagnose and assess the growing incidence of mental illness confronting Australia's ageing population, thereby addressing the ageing well and ageing productively national research priority; and, (3) neurosurgeons to guide surgery via localisation of major neural tracts. In addition to contributing to the understanding, diagnosis and treatment of Australia's endemic mental health burden, this project will advance Australia's skill-base and international standing in basic scientific research.Read moreRead less
Increasing the effectiveness of quantitative verification. The ability to analyse the performance of complex systems and protocols is a vital part of the development of large-scale computer applications. Methods that improve the effectiveness of the analysis task would increase the competitiveness of the software industry, and would attract future development work (in complex systems) to Australia. The results of this project will have a direct influence on currently available design tools; the ....Increasing the effectiveness of quantitative verification. The ability to analyse the performance of complex systems and protocols is a vital part of the development of large-scale computer applications. Methods that improve the effectiveness of the analysis task would increase the competitiveness of the software industry, and would attract future development work (in complex systems) to Australia. The results of this project will have a direct influence on currently available design tools; the fact that Australian institutions will be (in part) responsible for key theoretical results in this growing field will strengthen Australia's position worldwide as an international centre for computer science.Read moreRead less