Mathematical Methods for Next Generation Sequencing. The emergence of a new generation of high throughput genomic sequencing technologies is providing unprecedented opportunities for biological research. Hidden within the huge amounts of data generated by this technology is information about the expression and regulation of genes, and the complex functional purpose of non-coding, so called 'junk', DNA. Development of mathematical and statistical tools is essential to interpreting these data. The ....Mathematical Methods for Next Generation Sequencing. The emergence of a new generation of high throughput genomic sequencing technologies is providing unprecedented opportunities for biological research. Hidden within the huge amounts of data generated by this technology is information about the expression and regulation of genes, and the complex functional purpose of non-coding, so called 'junk', DNA. Development of mathematical and statistical tools is essential to interpreting these data. The proposed research will enhance Australia's reputation for developing novel quantitative techniques at the cutting edge of modern biology. The proposed project has a broad range of potential applications in biotechnology, particularly in the medical and agricultural industries.Read moreRead less
A New Approach to Sampled-Data Control Design for Nonlinear Systems. This project aims to exploit new sampling and sampled-data modelling insights to bridge the continuous/sampled-data gap in the control of nonlinear systems. The goal is to investigate the impact of these insights on the control design problem and provide a new class of digital control laws for continuous time non-linear systems.
New Frontiers and Advances in Discrete Integrable Systems. Integrable systems boast a long and venerable history, and have such famous members as the Kepler system, the Korteweg-de Vries equation, and the sine-Gordon equation. More recently, interest in integrable systems has expanded to include systems with discrete time, that is, ordinary difference equations (or maps) and integrable partial difference equations. These discrete integrable systems are arguably more fundamental than the continuo ....New Frontiers and Advances in Discrete Integrable Systems. Integrable systems boast a long and venerable history, and have such famous members as the Kepler system, the Korteweg-de Vries equation, and the sine-Gordon equation. More recently, interest in integrable systems has expanded to include systems with discrete time, that is, ordinary difference equations (or maps) and integrable partial difference equations. These discrete integrable systems are arguably more fundamental than the continuous-time ones. Based upon recent breakthroughs this study will combine analysis, geometry, and computer algebra to expand and systematise this new interdisciplinary field of discrete integrable systems.Read moreRead less
Energy efficient sensing, computing and communication. This research will study trade-offs in resource use: bandwidth, power, and computational capacity of systems of sensors such as cameras, radars, and distributed sensor networks based on a statistical mechanical theory of information processing, leading to practical algorithms to optimize resource use in the design of such systems.
Suspension flows and particle focusing in curved geometries. The project aims to develop fast predictive tools to investigate suspension flows in curved channels and thin ducts and the effect of channel geometry on the focusing of particles by weight to different regions of the channel. Interaction between particles and fluid in suspension flows is a fundamental problem that is little understood but which is important in a wide range of problems in nature and industry (eg for design of microscal ....Suspension flows and particle focusing in curved geometries. The project aims to develop fast predictive tools to investigate suspension flows in curved channels and thin ducts and the effect of channel geometry on the focusing of particles by weight to different regions of the channel. Interaction between particles and fluid in suspension flows is a fundamental problem that is little understood but which is important in a wide range of problems in nature and industry (eg for design of microscale segregation devices for separation of different cells in a blood sample, and of macroscale devices for separation of mineral particles from crushed ore). At present, the description of these processes is qualitative, with quantitative understanding seen as a challenge without intensive computation. The project plans to develop, solve and validate mathematical models to give a quantitative understanding of these processes.Read moreRead less
Mathematical models of cell migration in three-dimensional living tissues. This project aims to develop mathematical models of cell migration in crowded, living tissues. Existing models rely solely on stochastic simulations, and therefore provide no general mathematical insight into how properties of the crowding environment (obstacle shape, size, density) affect the migration of cells through that environment. This project will produce mathematical analysis, mathematical calculations and exact ....Mathematical models of cell migration in three-dimensional living tissues. This project aims to develop mathematical models of cell migration in crowded, living tissues. Existing models rely solely on stochastic simulations, and therefore provide no general mathematical insight into how properties of the crowding environment (obstacle shape, size, density) affect the migration of cells through that environment. This project will produce mathematical analysis, mathematical calculations and exact analytical tools that quantify how the crowding environment in three-dimensional living tissues affects the migration of cells within these tissues. Long term effects will be the translation of this new mathematical knowledge into decision support tools for researchers from the life sciences.Read moreRead less
Mathematical models of 4D multicellular spheroids. Mathematical models have a long, successful history of providing biological insight, and new mathematical models must be developed to keep pace with emerging technologies. Modern experimental procedures involve studying 3D multicellular spheroids with fluorescent labels to show both the location of cells and the cell cycle progression. This 4D data (3D spatial information + cell cycle time) provides vast information. No mathematical models ha ....Mathematical models of 4D multicellular spheroids. Mathematical models have a long, successful history of providing biological insight, and new mathematical models must be developed to keep pace with emerging technologies. Modern experimental procedures involve studying 3D multicellular spheroids with fluorescent labels to show both the location of cells and the cell cycle progression. This 4D data (3D spatial information + cell cycle time) provides vast information. No mathematical models have been specifically developed to interpret/predict 4D spheroids. This project will deliver the first high-fidelity mathematical models to interpret/predict 4D spheroid experiments in real time, providing quantitative insight into innate mechanisms and responses to various intervention treatments. Read moreRead less
Fractional dynamic models for MRI to probe tissue microstructure. This project aims to develop new mathematical tools for mapping tissue microstructural properties via the use of space-time fractional calculus methods. In magnetic resonance imaging, mathematical models and their parameters play a key role in associating information between images and biology, with the overall aim of producing spatially resolved maps of tissue property variations. However, models which can inform on changes in mi ....Fractional dynamic models for MRI to probe tissue microstructure. This project aims to develop new mathematical tools for mapping tissue microstructural properties via the use of space-time fractional calculus methods. In magnetic resonance imaging, mathematical models and their parameters play a key role in associating information between images and biology, with the overall aim of producing spatially resolved maps of tissue property variations. However, models which can inform on changes in microscale tissue properties are lacking. The tools developed by this project will be used to generate new magnetic resonance image based maps to convey information on tissue microstructure changes in the human brain. Additionally, the mathematical tools developed will be transferable to other applications where diffusion and transport in heterogeneous porous media play a role.Read moreRead less
Human skin equivalent constructs: enhanced culturing and application of laboratory-grown skin through mathematical modelling and in silico experimentation. Laboratory-grown human skin equivalent constructs, given social and legislative imperatives, will be critical for advances in novel treatment protocol definitions for wound repair, dermatogical screening of pharmacueticals and fundamental studies of skin diseases.
In silico studies undertaken in this project will make a significant contrib ....Human skin equivalent constructs: enhanced culturing and application of laboratory-grown skin through mathematical modelling and in silico experimentation. Laboratory-grown human skin equivalent constructs, given social and legislative imperatives, will be critical for advances in novel treatment protocol definitions for wound repair, dermatogical screening of pharmacueticals and fundamental studies of skin diseases.
In silico studies undertaken in this project will make a significant contribution to the effectiveness of the application of human skin constructs, by delivering new and deeper insights into the interplay between dependent processes that regulate the behaviour of skin, in vivo or ex vivo. The models and the researchers associated with this project will drive innovative studies in medical science over the next decade.Read moreRead less
New mathematics for understanding complex patterns in the natural sciences. This project aims to examine the interaction of fundamental two-dimensional patterns such as spots and stripes in reaction-diffusion equations, by developing and extending mathematical techniques. These fundamental planar structures form the backbone of more complex patterns and are, for example, observed in models that describe the propagation of impulses in nerve axons and the formation of vegetation patterns. The futu ....New mathematics for understanding complex patterns in the natural sciences. This project aims to examine the interaction of fundamental two-dimensional patterns such as spots and stripes in reaction-diffusion equations, by developing and extending mathematical techniques. These fundamental planar structures form the backbone of more complex patterns and are, for example, observed in models that describe the propagation of impulses in nerve axons and the formation of vegetation patterns. The future impact of this research will have economic and environmental benefits. For example, the project will develop a deeper understanding of interacting patterns that will provide insights into the role of vegetation in ecosystems that are undergoing desertification.Read moreRead less