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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
Emergence of robust, stable structures via computation within natural networks. An ever-increasing challenge for modern society is the sheer complexity of vast infrastructures. Unexpected, and sometimes catastrophic, behaviour often emerges from interactions between elements of large systems. As a result, highly complex systems such as the Internet, international finance markets, and power grids are highly susceptible to costly problems such as cascading failures, inefficiency, and critical sens ....Emergence of robust, stable structures via computation within natural networks. An ever-increasing challenge for modern society is the sheer complexity of vast infrastructures. Unexpected, and sometimes catastrophic, behaviour often emerges from interactions between elements of large systems. As a result, highly complex systems such as the Internet, international finance markets, and power grids are highly susceptible to costly problems such as cascading failures, inefficiency, and critical sensitivity. High-tech industries, such as biotechnology and information networking, also face problems in coordinating swarms of interacting agents. This project will contribute to solving such problems by identifying and adapting solutions from nature.Read moreRead less
Dual phase evolution in networks. A grand challenge for modern society is the sheer complexity of vast networks arising from organizations and infrastructures. Unexpected, sometimes catastrophic, behaviour often emerges from interactions within such systems. As a result, the Internet, financial markets, power grids and other vital infrastructures are susceptible to costly problems such as cascading failures, inefficiency, and unpredictability. High-tech industries, such as biotechnology and info ....Dual phase evolution in networks. A grand challenge for modern society is the sheer complexity of vast networks arising from organizations and infrastructures. Unexpected, sometimes catastrophic, behaviour often emerges from interactions within such systems. As a result, the Internet, financial markets, power grids and other vital infrastructures are susceptible to costly problems such as cascading failures, inefficiency, and unpredictability. High-tech industries, such as biotechnology and information networking, face problems in coordinating networks of interacting agents. This project will expand the horizon of complex systems by deriving the design principles underpinning stable and resilient network structures and validate these principles on real world networks.Read moreRead less
Efficient Estimation of Statistical Models with Many Parameters. Statistical models are used extensively in business, engineering and the sciences to describe the behavior of systems subject to uncertainty. There are often many unknowns in such models and relatively little data to estimate them. The object of the research is to develop methods that make these statistical models practical to use. The research team will apply the methodology to solve problems in economics, finance, marketing and t ....Efficient Estimation of Statistical Models with Many Parameters. Statistical models are used extensively in business, engineering and the sciences to describe the behavior of systems subject to uncertainty. There are often many unknowns in such models and relatively little data to estimate them. The object of the research is to develop methods that make these statistical models practical to use. The research team will apply the methodology to solve problems in economics, finance, marketing and the analysis of gene expression data. The project will also train doctoral and postdoctoral students and enhance Australia's reputation for research excellence in the Statistical and Mathematical Sciences. Read moreRead less
Saddlepoint approximation, likelihood analysis and ancestral graphs for strong and weak natural selection, genetic drift and population subdivision. Building new research strength in theoretical population genetics and related statistical techniques will enhance Australia's capability in harnessing the power of post-genomic information. Sophisticated statistical techniques that make smart use of genetic data are being developed in this project. The extent to which natural selection and migrati ....Saddlepoint approximation, likelihood analysis and ancestral graphs for strong and weak natural selection, genetic drift and population subdivision. Building new research strength in theoretical population genetics and related statistical techniques will enhance Australia's capability in harnessing the power of post-genomic information. Sophisticated statistical techniques that make smart use of genetic data are being developed in this project. The extent to which natural selection and migration affect current genetic polymorphism on a population level can be quantified using these new methods. New modeling provides a rigorous foundation with which to construct inference techniques currently beyond computational approaches to the data. Assessing selective effects on genetic mutations associated with human disease will be a consequence of this new statistical methodology.Read moreRead less
Linkage Infrastructure, Equipment And Facilities - Grant ID: LE0882357
Funder
Australian Research Council
Funding Amount
$500,000.00
Summary
A Computational Facility for Multi-scale Modelling in Bio and Nanotechnology. Bio- and nanotechnology have the potential to transform Australian industry and research, and to bring significant benefits for consumers. The scope will include materials for energy storage, medical diagnostics and cellular imaging, bioengineering, drug and gene delivery, improved foods by molecular design, novel materials for electronics, improved techniques for particle processing, and molecular sieves for filtering ....A Computational Facility for Multi-scale Modelling in Bio and Nanotechnology. Bio- and nanotechnology have the potential to transform Australian industry and research, and to bring significant benefits for consumers. The scope will include materials for energy storage, medical diagnostics and cellular imaging, bioengineering, drug and gene delivery, improved foods by molecular design, novel materials for electronics, improved techniques for particle processing, and molecular sieves for filtering/purifying water and gases. The dedicated computing facility will enable a fast interactive cycle between simulation and experiment in these areas, accelerating the pace of research and applications.Read moreRead less
To flee or not to flee: surviving on incomplete information. Even lowly animals, like the Australian fiddler crabs we will be investigating, are surprisingly competent in making the right decisions in complex situations. They actively acquire information and make good use of it to assure their immediate safety and their long term gains. Animals are exquisitely honed by evolution and we would benefit greatly by understanding what makes them so competent: on a theoretical level, we may learn about ....To flee or not to flee: surviving on incomplete information. Even lowly animals, like the Australian fiddler crabs we will be investigating, are surprisingly competent in making the right decisions in complex situations. They actively acquire information and make good use of it to assure their immediate safety and their long term gains. Animals are exquisitely honed by evolution and we would benefit greatly by understanding what makes them so competent: on a theoretical level, we may learn about efficient rules of good decision making and on a practical level, we may be able to design more flexible, robust and clever machines. Besides being useful in this wider context, the results of our research will thus also contribute to a new and 'sophisticated' appreciation of the cognitive design of animal.Read moreRead less
Theory and Applications of Computer-Intensive Statistical Methods. The availability of powerful computing equipment has had a dramatic impact on statistical methods and thinking. It has motivated development of novel approaches to data analysis, whose conception
and appreciation, even their application, often demand sophisticated and complex theoretical methods. In this context, the project will develop new approaches to solving non-standard statistical problems. These techniques will eithe ....Theory and Applications of Computer-Intensive Statistical Methods. The availability of powerful computing equipment has had a dramatic impact on statistical methods and thinking. It has motivated development of novel approaches to data analysis, whose conception
and appreciation, even their application, often demand sophisticated and complex theoretical methods. In this context, the project will develop new approaches to solving non-standard statistical problems. These techniques will either have direct application to solving practical problems of national or community concern, or provide a better understanding of the nature of such problems.Read moreRead less
Nonlinear Dynamics of Pulse Coupled Oscillators. A mathematical model of the heart pacemaker system will be created, based on simple interacting units. These units have been shown to be good models of physiological information e.g. the discrimination of different influences on heart rate. We will firstly look at the interaction of the units in simple combinations and then tune the model to mimic the behaviour of the cardiac pacemaker.
Potential benefits may arise from elucidating the mechanis ....Nonlinear Dynamics of Pulse Coupled Oscillators. A mathematical model of the heart pacemaker system will be created, based on simple interacting units. These units have been shown to be good models of physiological information e.g. the discrimination of different influences on heart rate. We will firstly look at the interaction of the units in simple combinations and then tune the model to mimic the behaviour of the cardiac pacemaker.
Potential benefits may arise from elucidating the mechanisms underlying arrhythmias which contribute to ?sudden cardiac death? in young men, and suggesting strategies for artificial pacemakers to effectively arrest abnormal rhythms before they convert to potentially fatal fibrillation.Read moreRead less