The estimation of genotype-phenotype relationships from family data and of animal abundance from capture-recapture data with frequent capture occasions: A semiparametric approach. Semiparametric statistical methods allow researchers to only model those features of their data that are of interest, but still allow standard statistical inferences to be made about these features. The aim here is to develop non standard applications of semiparametric statistical methods in the estimation of genotype ....The estimation of genotype-phenotype relationships from family data and of animal abundance from capture-recapture data with frequent capture occasions: A semiparametric approach. Semiparametric statistical methods allow researchers to only model those features of their data that are of interest, but still allow standard statistical inferences to be made about these features. The aim here is to develop non standard applications of semiparametric statistical methods in the estimation of genotype-phenotype relationships from family data and the estimation of animal abundance from capture-recapture data. The methods will be applied to real data and their theoretical properties developed. The practical significance of the project is the flexible new statistical methods that will become available to researchers. The theoretical significance will be the insights into semiparametric methods gained by developing these nonstandard applications. The expected outcomes are the new statistical procedures and the resulting theoretical insights into semiparametric statistics.Read moreRead less
Patient-specific Computational Tools for Diagnosing and Treating Gait Disorders in Children with Cerebral Palsy. This proposal addresses one of the most fundamental and difficult questions related to the treatment of children with cerebral palsy: Why do these children walk in a crouched position, with excessively bent hips and knees? High-fidelity, patient-specific computer simulations of walking can help to answer this question and, in so doing, can improve the outcomes of orthopaedic surgeries ....Patient-specific Computational Tools for Diagnosing and Treating Gait Disorders in Children with Cerebral Palsy. This proposal addresses one of the most fundamental and difficult questions related to the treatment of children with cerebral palsy: Why do these children walk in a crouched position, with excessively bent hips and knees? High-fidelity, patient-specific computer simulations of walking can help to answer this question and, in so doing, can improve the outcomes of orthopaedic surgeries designed to correct movement abnormalities in these patients. Realistic computer simulations of human movement can play a pivotal role in healthcare through patient rehabilitation; in sports, through the development of personalized training programs for elite athletes; and in entertainment, through the creation of video games and animated films.Read moreRead less
Advanced matrix-analytic methods with applications. Over the last twenty-five years, matrix-analytic methods have proved to be very successful in formulating and analysing certain classes of stochastic models. Motivated by applications, this project will investigate more advanced matrix-analytic methods than have hitherto been studied.
Large-scale three dimensional deformation of the lithosphere by subduction and mantle flow. We will be modelling of the dynamics of the Earth's crust and shallow lithosphere in response to the huge stresses created by plate motions. For Australia these stresses are transmitted from the distant plate boundaries, but they have a direct controlling influence on the evolution of the petroleum rich basins of Australia. These basins have reached maturity; further exploration will be in deep water wher ....Large-scale three dimensional deformation of the lithosphere by subduction and mantle flow. We will be modelling of the dynamics of the Earth's crust and shallow lithosphere in response to the huge stresses created by plate motions. For Australia these stresses are transmitted from the distant plate boundaries, but they have a direct controlling influence on the evolution of the petroleum rich basins of Australia. These basins have reached maturity; further exploration will be in deep water where geophysical prospecting methods are unreliable. Model-driven "exploration geodynamics" methods such as those we are developing will be needed to support traditional exploration techniques in these areas.Read moreRead less
Stein's method for probability approximation. Data of counts in time, such as incoming calls in telecommunications and the clusters of palindromes in a family of herpes-virus genomes, arise in an extraordinarily diverse range of fields from science to business. These problems can be modelled by sums of random variables taking values 0 and 1 in probability theory, thus permitting approximate calculations which are often good enough in practice. This project will obtain such approximate solutions ....Stein's method for probability approximation. Data of counts in time, such as incoming calls in telecommunications and the clusters of palindromes in a family of herpes-virus genomes, arise in an extraordinarily diverse range of fields from science to business. These problems can be modelled by sums of random variables taking values 0 and 1 in probability theory, thus permitting approximate calculations which are often good enough in practice. This project will obtain such approximate solutions and estimate the errors involved. Applications include analysis of data in insurance, finance, flood prediction in hydrology.Read moreRead less
Random walks with long memory. This project aims to study novel random walk models with long memory, including systems of multiple random walkers that interact through their environment. This would provide a mathematical understanding of phenomena such as aggregation in colonies of bacteria, and ant colony optimisation algorithms. The project aims to produce highly cited publications, and to train future researchers.
Multifractal models in finance via the crossing tree. High level mathematical modelling is an established part of the modern finance industry, in particular the Black-Scholes option pricing formula is now an indispensable financial tool.
To remain competitive the Australian financial sector needs to keep up with developments in mathematical finance, which is only possible if the Australian academic community remains active in the field.
The work on multifractal modelling proposed here is innov ....Multifractal models in finance via the crossing tree. High level mathematical modelling is an established part of the modern finance industry, in particular the Black-Scholes option pricing formula is now an indispensable financial tool.
To remain competitive the Australian financial sector needs to keep up with developments in mathematical finance, which is only possible if the Australian academic community remains active in the field.
The work on multifractal modelling proposed here is innovative both in its theoretical aspects and its applied methodology, and will ensure that Australian research remains at the cutting edge of this highly competitive and fast moving field.Read moreRead less
Non-invasive assessment of hip fracture risk in elderly people. No falls, no fractures - this will be the main benefit of the proposed research. The most significant outcome will be new computational tools to improve current understanding of the biomechanics of falls and bone fragility in elderly people, which, in turn, will help to reduce healthcare costs associated with the treatment and management of hip fractures. Realistic models and computer simulations of human movement can play a pivota ....Non-invasive assessment of hip fracture risk in elderly people. No falls, no fractures - this will be the main benefit of the proposed research. The most significant outcome will be new computational tools to improve current understanding of the biomechanics of falls and bone fragility in elderly people, which, in turn, will help to reduce healthcare costs associated with the treatment and management of hip fractures. Realistic models and computer simulations of human movement can play a pivotal role in three of Australia's largest industries: healthcare, through the diagnosis and treatment of movement disorders; sports, through the development of personalized training programs for elite athletes; and entertainment, through the development of video/digital games and animated films.Read moreRead less
A Control Systems Approach for Understanding Human Locomotion. This proposal addresses fundamental, difficult questions in the context of human movement: How do muscles move our limbs during walking? How do the nervous system and muscles work together to control movement? Realistic computer simulations of human movement can help answer these questions and, in so doing, can play a pivotal role in three of Australia's largest industries: healthcare, through clinical gait analysis and gait rehabili ....A Control Systems Approach for Understanding Human Locomotion. This proposal addresses fundamental, difficult questions in the context of human movement: How do muscles move our limbs during walking? How do the nervous system and muscles work together to control movement? Realistic computer simulations of human movement can help answer these questions and, in so doing, can play a pivotal role in three of Australia's largest industries: healthcare, through clinical gait analysis and gait rehabilitation (diagnosis and treatment of movement disorders); sports, through the development of personalized training programs for elite athletes; and entertainment, through the development of video/digital games and animated films (creation of virtual life-like actors).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