Stochastic modelling of spatiotemporal nonlinear diffusion processes with multifractal characteristics. This research is relevant to solute transport and plume evolution in heterogeneous media. Detailed modelling of these processes is computer-intensive, while the diffusion models of this project offer a more economical alternative. Our study will also benefit the research on the salinity problem. Excessive demand for irrigation water to support agricultural production has stretched freshwater a ....Stochastic modelling of spatiotemporal nonlinear diffusion processes with multifractal characteristics. This research is relevant to solute transport and plume evolution in heterogeneous media. Detailed modelling of these processes is computer-intensive, while the diffusion models of this project offer a more economical alternative. Our study will also benefit the research on the salinity problem. Excessive demand for irrigation water to support agricultural production has stretched freshwater aquifers beyond their long-term yield. Large areas of land have been lost to saltwater intrusion. This proposal will provide suitable tools to predict the level and movement of saltwater in the aquifers. Application to the development of management strategies would bring direct benefit to coastal areas where salinity is a sustainability issue.Read moreRead less
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
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
The improvement of climate change investigations by developing and applying innovative evolutionary subset time series modelling using semi-parametric sparse-patterned approaches. With an estimated US$6.98 trillion loss indicated in the Stern review, severe climate change will make world climate conditions harsher and more likely include large natural climate disasters. The health of the Australian economy is critically dependent on decisions of environmental managers. However, most problems of ....The improvement of climate change investigations by developing and applying innovative evolutionary subset time series modelling using semi-parametric sparse-patterned approaches. With an estimated US$6.98 trillion loss indicated in the Stern review, severe climate change will make world climate conditions harsher and more likely include large natural climate disasters. The health of the Australian economy is critically dependent on decisions of environmental managers. However, most problems of complexity arising in climate change involve issues on which we do not possess a deep understanding. This project draws upon a set of inter-disciplinary concepts and models centred in neural networks that enable us to advance our understanding of complexity, leading to superior quantitative tools and models to allow for improved environmental decision-making.
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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
Statistical estimation and approximation of anomalous diffusion. This project investigates diffusion processes with long memory, heavy-tailed distributions and higher-order information. Each of these characteristics has been a subject of extensive current research. These processes arise in important applications with significant social/economic benefits such as heat conduction and fluid flow in porous media, propagation of seismic waves, transport of drug molecules in living tissues. Built on ou ....Statistical estimation and approximation of anomalous diffusion. This project investigates diffusion processes with long memory, heavy-tailed distributions and higher-order information. Each of these characteristics has been a subject of extensive current research. These processes arise in important applications with significant social/economic benefits such as heat conduction and fluid flow in porous media, propagation of seismic waves, transport of drug molecules in living tissues. Built on our recent fundamental developments of fractional generalised random fields and fractional diffusion equations, this project tackles the key problems of statistical estimation, approximation and prediction of diffusion processes with all the above characteristics in a unified framework not provided by other approaches.Read moreRead less
Bayesian Statistical Inference for Implicitly defined Probability Models. Bayesian statistics has recently been used to provide solutions for a large number of hitherto intractable problems in science and technology. The success of Bayesian statistics has mainly been due to the application of so-called Markov chain Monte Carlo computational techniques. We aim to improve these algorithms, by providing fast, simple and efficient computational implementations. We will use the results to give ins ....Bayesian Statistical Inference for Implicitly defined Probability Models. Bayesian statistics has recently been used to provide solutions for a large number of hitherto intractable problems in science and technology. The success of Bayesian statistics has mainly been due to the application of so-called Markov chain Monte Carlo computational techniques. We aim to improve these algorithms, by providing fast, simple and efficient computational implementations. We will use the results to give insight by carefully quantifying and modelling uncertainty for such topics as the transmission rate of infectious diseases, the spatial distribution of plant and animal species, investigating biological theory for the genome of a virus, and changes in human fertility.Read moreRead less
Effective and accurate model dynamics, deterministic and stochastic, across multiple space and time scales. A persistent feature of complex systems in engineering and science is the emergence of macroscopic, coarse grained, coherent behaviour from the interactions of microscopic agents (molecules, cells, grains) and with their environment. In current modeling, ranging from ecology to materials science, the underlying microscopic mechanisms are often known, but the closures to translate microscal ....Effective and accurate model dynamics, deterministic and stochastic, across multiple space and time scales. A persistent feature of complex systems in engineering and science is the emergence of macroscopic, coarse grained, coherent behaviour from the interactions of microscopic agents (molecules, cells, grains) and with their environment. In current modeling, ranging from ecology to materials science, the underlying microscopic mechanisms are often known, but the closures to translate microscale knowledge to a system level macroscopic description are rarely available in closed form. Our novel methodology will explore this stumbling block, and promises to radically change the modeling, exploration and understanding of multiscale complex system behaviour.Read moreRead less
Motor Unit Numbers Estimation (MUNE) using Bayesian statistical methodology for monitoring of progression of neuromuscular diseases. A means of objectively measuring the pathology of a neuromuscular disease involving motor unit loss, such as motor neuron disease, is much needed. This will be achieved by using newly developed electrophysiological techniques and developing new Bayesian statistical methodology to determine the number of motor units that supply a muscle. Our innovations will reliabl ....Motor Unit Numbers Estimation (MUNE) using Bayesian statistical methodology for monitoring of progression of neuromuscular diseases. A means of objectively measuring the pathology of a neuromuscular disease involving motor unit loss, such as motor neuron disease, is much needed. This will be achieved by using newly developed electrophysiological techniques and developing new Bayesian statistical methodology to determine the number of motor units that supply a muscle. Our innovations will reliably determine the number of motor units that supply a muscle in both normal subjects and in diseased patients with loss of motor nerves. This will enable the monitoring of disease progression. An outcome will be a software package that can be used with standard electrophysiology machines.Read moreRead less
Principles of Quantum Information Science. The use of quantum mechanical systems to carry and process information is enabling a revolution in information technology through innovations such as quantum computation and quantum teleportation. This project investigates the fundamental theory of quantum information science. The project aims to formulate general principles governing the power and behaviour of quantum information. These principles will, in turn, enable the development of powerful new ....Principles of Quantum Information Science. The use of quantum mechanical systems to carry and process information is enabling a revolution in information technology through innovations such as quantum computation and quantum teleportation. This project investigates the fundamental theory of quantum information science. The project aims to formulate general principles governing the power and behaviour of quantum information. These principles will, in turn, enable the development of powerful new applications of quantum information. Principal areas to be addressed include: general conditions for a physical system to be usable for quantum computation, the development of new algorithms for quantum computers, the development of new quantum communication protocols, and the theory of quantum entanglement.Read moreRead less