A multi-scale approach for modelling coupled transport in heterogeneous and anisotropic porous media. Mathematical Sciences foster interdisciplinary collaboration and underpin fundamental understanding of significant national/international research priorities in science and technology. This world-class team will advance knowledge in modelling complex systems ensuring the competitiveness of Australian research in this important field. A key outcome is a multi-scale computational strategy that can ....A multi-scale approach for modelling coupled transport in heterogeneous and anisotropic porous media. Mathematical Sciences foster interdisciplinary collaboration and underpin fundamental understanding of significant national/international research priorities in science and technology. This world-class team will advance knowledge in modelling complex systems ensuring the competitiveness of Australian research in this important field. A key outcome is a multi-scale computational strategy that can be used by engineers in Australia and France to simulate transport phenomena in porous media, which have significant environmental impact. The research will lead to publications in scientific journals and communications at national/international conferences. Research training of postdocs and PhD students is another excellent outcome of the project.Read moreRead less
Advanced Bayesian Inversion Algorithms for Wave Propagation. This project aims to improve algorithms for detecting hidden items by developing new computational mathematical techniques capable of reconstructing the shape and location of objects using electromagnetic waves. This project expects to generate new knowledge in the areas of Bayesian Inversion and computational wave propagation. Expected outcomes of this project are algorithms that can be developed for use in nonintrusive radio wave sec ....Advanced Bayesian Inversion Algorithms for Wave Propagation. This project aims to improve algorithms for detecting hidden items by developing new computational mathematical techniques capable of reconstructing the shape and location of objects using electromagnetic waves. This project expects to generate new knowledge in the areas of Bayesian Inversion and computational wave propagation. Expected outcomes of this project are algorithms that can be developed for use in nonintrusive radio wave security scanners. This should provide benefits such as the capability to scan a crowd without a checkpoint, which will have the potential to improve security in public places.Read moreRead less
Innovative Methods for Very High Dimensional Problems. Real world problems tend to involve an enormous number of variables. This "curse of dimensionality" poses great difficulty in application areas such as statistics, finance, economics, and physics. These high dimensional problems are not confined to Australia, and there is great demand worldwide for effective and efficient methods to tackle these problems. The novel methods developed here will lead to improvements in prevailing computational ....Innovative Methods for Very High Dimensional Problems. Real world problems tend to involve an enormous number of variables. This "curse of dimensionality" poses great difficulty in application areas such as statistics, finance, economics, and physics. These high dimensional problems are not confined to Australia, and there is great demand worldwide for effective and efficient methods to tackle these problems. The novel methods developed here will lead to improvements in prevailing computational technologies, which will help to enhance Australia's reputation as a leading scientific innovator. The international collaborations will increase the research output of the country, build up the knowledge base in the discipline, draw international interest, and initiate linkages.Read moreRead less
Stochastic Modelling of Genetic Regulatory Networks: Subtitle - Genetic Regulation is a Noisy Business. The completion of the human genome marked the culmination of one hundred years of reductionist science in cell biology. Although further bioinformatics analysis will continue, the focus is shifting towards synthesis and understanding how the regulatory genetic components dynamically interact to form functional phenotypes. The key to this is the understanding of the roles of stochasticity in ....Stochastic Modelling of Genetic Regulatory Networks: Subtitle - Genetic Regulation is a Noisy Business. The completion of the human genome marked the culmination of one hundred years of reductionist science in cell biology. Although further bioinformatics analysis will continue, the focus is shifting towards synthesis and understanding how the regulatory genetic components dynamically interact to form functional phenotypes. The key to this is the understanding of the roles of stochasticity in cellular processes. This project will explore these roles and will develop an integrated complex systems modelling, simulation and visualisation framework. This will be used on an exemplar application for lineage commitment in haematopoiesis and for exploring and validating genetic regulatory models in general.Read moreRead less
Multiscale stochastic modelling of genetic regulatory mechanisms. The completion of the human genome marked the culmination of one hundred years of reductionist science in cell biology. Although further bioinformatics analysis will continue, the focus is shifting towards synthesis and understanding how the regulatory genetic components dynamically interact to form functional phenotypes. The key to this is the understanding of the roles of stochasticity in cellular processes. This project will ex ....Multiscale stochastic modelling of genetic regulatory mechanisms. The completion of the human genome marked the culmination of one hundred years of reductionist science in cell biology. Although further bioinformatics analysis will continue, the focus is shifting towards synthesis and understanding how the regulatory genetic components dynamically interact to form functional phenotypes. The key to this is the understanding of the roles of stochasticity in cellular processes. This project will explore these roles and will develop an integrated complex systems modelling, simulation and visualisation framework for exploring and validating genetic regulatory models in general. This will be used on an exemplar application for understanding the induction process in lambda phage.Read moreRead less
Uncertainty on spheres and shells: mathematics and methods for applications. This project aims to develop new mathematics and mathematically rigorous approximation methods for physical problems on spherical geometries in the presence of uncertainty. Many physical phenomena are modelled on either a sphere or a spherical shell. Such models typically have large uncertainty in the input data, through uncertainty in model coefficients, forcing terms, geometry or boundary conditions. Yet their stochas ....Uncertainty on spheres and shells: mathematics and methods for applications. This project aims to develop new mathematics and mathematically rigorous approximation methods for physical problems on spherical geometries in the presence of uncertainty. Many physical phenomena are modelled on either a sphere or a spherical shell. Such models typically have large uncertainty in the input data, through uncertainty in model coefficients, forcing terms, geometry or boundary conditions. Yet their stochastic modelling and subsequent numerical analysis in the presence of uncertainty are still in their infancy. This project will conduct numerical analysis, stochastic analysis and approximation to address such problems.Read moreRead less
Advanced computational algorithms for three-dimensional systems. This project deals with the development, analysis and implementation of efficient computer algorithms for a range of complex three dimensional systems. Major areas of focus are forward and inverse acoustic and electromagnetic scattering; dynamical and evolution processes in water waves and tumour growth; and the solution of mathematical models on spheres (earth). Potential application areas of the project include defence science ....Advanced computational algorithms for three-dimensional systems. This project deals with the development, analysis and implementation of efficient computer algorithms for a range of complex three dimensional systems. Major areas of focus are forward and inverse acoustic and electromagnetic scattering; dynamical and evolution processes in water waves and tumour growth; and the solution of mathematical models on spheres (earth). Potential application areas of the project include defence science; ocean engineering; medical research; meteorology and global environmental sciences.Read moreRead less
Lifting the curse of dimensionality - bringing together the quasi Monte Carlo and sparse grid methods. This project is expected to lead to improved methods for handling high-dimensional problems (i.e. problems with many variables) that arise in finance, statistics, commerce, physics, and many other fields. In turn this could lead to significant economic benefit, especially to high-value service industries such as the finance industry. By strengthening international collaboration, it will also ....Lifting the curse of dimensionality - bringing together the quasi Monte Carlo and sparse grid methods. This project is expected to lead to improved methods for handling high-dimensional problems (i.e. problems with many variables) that arise in finance, statistics, commerce, physics, and many other fields. In turn this could lead to significant economic benefit, especially to high-value service industries such as the finance industry. By strengthening international collaboration, it will also help to maintain Australia's strong position in international research in the mathematical sciences.Read moreRead less
Novel Mathematical Technologies for Financial Valuation and Risk. The finance industry is a key industry sector in Australia, with a highly qualified and well-paid work force. The profitability and stability of financial institutions rests in part on their ability to accurately and rapidly value innovative financial products and to quantify risk, yet many contemporary financial products are difficult to value quickly and accurately. This project will bring innovative mathematical technologies ....Novel Mathematical Technologies for Financial Valuation and Risk. The finance industry is a key industry sector in Australia, with a highly qualified and well-paid work force. The profitability and stability of financial institutions rests in part on their ability to accurately and rapidly value innovative financial products and to quantify risk, yet many contemporary financial products are difficult to value quickly and accurately. This project will bring innovative mathematical technologies to bear on complex financial problems. It has the potential to improve both the profitability and stability of Australian financial institutions, and to enhance their role regionally and internationally.Read moreRead less
Constrained and Stable Solutions of Nonlinear and Semismooth Equations. In this project, comprehensive models for designing safe power system parameters will be proposed, efficient algorthms for solving these models will be constructed. The new models and algorithms in this project will provide efficient tools to prevent catastrophic events in power systems, which is related with national security. This project will also strengthen collaboration of Australian applied
mathematians with inter ....Constrained and Stable Solutions of Nonlinear and Semismooth Equations. In this project, comprehensive models for designing safe power system parameters will be proposed, efficient algorthms for solving these models will be constructed. The new models and algorithms in this project will provide efficient tools to prevent catastrophic events in power systems, which is related with national security. This project will also strengthen collaboration of Australian applied
mathematians with international researchers and engineering scientists. This is important for the advance of science and technology in
Australia.Read moreRead less