Neurobiological computation using self organization. Despite their phenomenal power and speed there are many simple things that computers still cannot do, that humans, and indeed many animals, are able to perform effortlessly. The research outlined in this proposal aims to develop new, biologically inspired, computational approaches that attempt to bridge this gap. This research will help place Australia, despite its relatively small size, as a leading research community in the development of ....Neurobiological computation using self organization. Despite their phenomenal power and speed there are many simple things that computers still cannot do, that humans, and indeed many animals, are able to perform effortlessly. The research outlined in this proposal aims to develop new, biologically inspired, computational approaches that attempt to bridge this gap. This research will help place Australia, despite its relatively small size, as a leading research community in the development of the next wave of computing devices. The development of new and "more natural" approaches to computing will deliver large dividends to a range of social, economic and environmental problems.Read moreRead less
Modelling with stochastic differential equations. We will develop methodology for modelling and analysis of phenomena subjected to random and uncertain influences, such as behaviour of investors in the market, evolution of economy, values of stocks and ant colonies. This methodology will enable scientists to achieve more accurate description and analysis of their models and provide better understanding of these phenomena. Creating the tools for understanding such complex systems will have far re ....Modelling with stochastic differential equations. We will develop methodology for modelling and analysis of phenomena subjected to random and uncertain influences, such as behaviour of investors in the market, evolution of economy, values of stocks and ant colonies. This methodology will enable scientists to achieve more accurate description and analysis of their models and provide better understanding of these phenomena. Creating the tools for understanding such complex systems will have far reaching benefits both nationally and internationally and will allow Australia to strengthen its position in international research. The project will also provide for postgraduate training and international scientific exchange.Read moreRead less
Stochastic systems with applications to Biology and Finance. This project is concerned with stochastic systems. These mathematical systems, which are controlled by statistical uncertainty and variability, have profound importance in the fields of biology and finance. They are recognised worldwide as being of primary scientific importance. Important questions to be examined are: 1) Branching processes in DNA Polymerase Chain Reaction, 2) long term stationarity in metastable systems, and 3) Sto ....Stochastic systems with applications to Biology and Finance. This project is concerned with stochastic systems. These mathematical systems, which are controlled by statistical uncertainty and variability, have profound importance in the fields of biology and finance. They are recognised worldwide as being of primary scientific importance. Important questions to be examined are: 1) Branching processes in DNA Polymerase Chain Reaction, 2) long term stationarity in metastable systems, and 3) Stochastic Volatility in Finance. The answers to these questions will underpin the statistical theory for potential breakthroughs in the respective areas. This project will contribute to the theory and applications of Stochastic Processes, as well as modelling in biology and finance.Read moreRead less