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
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
Modelling cell invasion incorporating the epithelial to mesenchymal transition: Exploring therapies to control wound healing and cancer progression. Cancer and wounds are closely related, commonly lethal, diseases. Both require cell growth and invasion. This project will apply experimental measurements to create new mathematical models of cancer and wounds; models that will inform new targets and strategies for the treatment of these deadly diseases.
Determination of benchmarking parameters for assessing the mechanical robustness of articular cartilage: a joint mathematical and experimental investigation. Osteoarthritis associated with the deterioration of the articular cartilage affects about 12% of Australian adults. This project will use an integrated approach combining novel mathematical modelling and an extensive experimental program to establish critical mechanical parameters, in particular, the fracture toughness of articular cartilag ....Determination of benchmarking parameters for assessing the mechanical robustness of articular cartilage: a joint mathematical and experimental investigation. Osteoarthritis associated with the deterioration of the articular cartilage affects about 12% of Australian adults. This project will use an integrated approach combining novel mathematical modelling and an extensive experimental program to establish critical mechanical parameters, in particular, the fracture toughness of articular cartilage and will incorporate the unique structure of the dissimilar layers in articular cartilage. It will be used to study how these resist the propagation of an initiated crack and will offer significant insight into the desirable fracture properties of any replacement material for articular cartilage and will provide a basis for assessing replacement biomaterials.Read moreRead less
A Mathematical Model of the Roles of Contraction and Oxygen in Human Wound Healing. Slow or impaired wound healing and excessive scarring associated with burns are both painful and costly. Moreover, the debilitating effect of chronic wounds can be expected to increase with the continuing aging of the population and the current rise in incidence of Type 2 diabetes. This project brings together a multidisciplinary team to develop a mathematical model of human wound healing and to drive the modelli ....A Mathematical Model of the Roles of Contraction and Oxygen in Human Wound Healing. Slow or impaired wound healing and excessive scarring associated with burns are both painful and costly. Moreover, the debilitating effect of chronic wounds can be expected to increase with the continuing aging of the population and the current rise in incidence of Type 2 diabetes. This project brings together a multidisciplinary team to develop a mathematical model of human wound healing and to drive the modelling to generate important breakthroughs at the level of basic science with implications for both experimentalists and clinicians.Read moreRead less