Stochastic modelling of genetic regulatory networks with burst process. This project will develop the next generation of stochastic modelling to study the fundamental principles of genetic regulation. Simulations will yield deeper insight into the origin of bistability and oscillation in gene networks.
Computational methods for population-size-dependent branching processes. Branching processes are the primary mathematical tool used to model populations that evolve randomly in time. Most key results in the theory are derived under the simplifying assumption that individuals reproduce and die independently of each other. However, this assumption fails in most real-life situations, in particular when the environment has limited resources or when the habitat has a restricted capacity. This project ....Computational methods for population-size-dependent branching processes. Branching processes are the primary mathematical tool used to model populations that evolve randomly in time. Most key results in the theory are derived under the simplifying assumption that individuals reproduce and die independently of each other. However, this assumption fails in most real-life situations, in particular when the environment has limited resources or when the habitat has a restricted capacity. This project aims to develop novel and effective algorithmic techniques and statistical methods for a class of branching processes with dependences. We will use these results to study significant problems in the conservation of endangered island bird populations in Oceania, and to help inform their conservation management.Read moreRead less
Statistical methods for detection of non-coding RNAs in eukaryote genomes. Understanding how eukaryotic cells work is a major goal of 21st century biology. A crucial step will be to catalogue the functional components of eukaryotic genomes. Australian researchers must be involved in this process at an early stage, in order to maximise commercial opportunities, attract quality researchers and position ourselves for further advances. This project will make major contributions to international effo ....Statistical methods for detection of non-coding RNAs in eukaryote genomes. Understanding how eukaryotic cells work is a major goal of 21st century biology. A crucial step will be to catalogue the functional components of eukaryotic genomes. Australian researchers must be involved in this process at an early stage, in order to maximise commercial opportunities, attract quality researchers and position ourselves for further advances. This project will make major contributions to international efforts in this area, via the development of statistical methods for segmenting genomes, classification of those segments, and study of the resulting classes. In the long term, enhanced understanding of eukaryotic cells will lead to breakthroughs in biology, and to medical, pharmaceutical, agricultural and scientific advances.Read moreRead less
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
Statistical Methods for Discovering Ribonucleic acids (RNAs) contributing to human diseases and phenotypes. Identifying the causative genetic factors involved in quantitative phenotypes and diseases is a major goal of biology in the 21st century and beyond. A crucial step towards this goal is identifying and classifying the functional non-protein-coding Ribonucleic acids (RNAs) encoded in the human genome. This project will make major contributions to international efforts in this area by identi ....Statistical Methods for Discovering Ribonucleic acids (RNAs) contributing to human diseases and phenotypes. Identifying the causative genetic factors involved in quantitative phenotypes and diseases is a major goal of biology in the 21st century and beyond. A crucial step towards this goal is identifying and classifying the functional non-protein-coding Ribonucleic acids (RNAs) encoded in the human genome. This project will make major contributions to international efforts in this area by identifying RNA molecules that contribute to quantitative phenotypes including susceptibility to disease. As such, it will directly benefit fundamental science via the discovery and classification of new molecules. Indirectly, it will lead to breakthroughs in biology, and consequently to major medical and pharmaceutical advances in the diagnosis and treatment of genetic disease.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
Discovery Early Career Researcher Award - Grant ID: DE160100227
Funder
Australian Research Council
Funding Amount
$355,481.00
Summary
Experimentally validated multiphase mathematical models of leg ulcers. The project is designed to develop mathematical models of the complex biological processes of leg ulcer formation and healing. The project intends to combine mathematical techniques from fluid dynamics, mathematical biology, numerical analysis and statistical inference to develop novel, multiphase, validated mathematical models that capture the complex spatiotemporal evolution of cellular and chemical species during the forma ....Experimentally validated multiphase mathematical models of leg ulcers. The project is designed to develop mathematical models of the complex biological processes of leg ulcer formation and healing. The project intends to combine mathematical techniques from fluid dynamics, mathematical biology, numerical analysis and statistical inference to develop novel, multiphase, validated mathematical models that capture the complex spatiotemporal evolution of cellular and chemical species during the formation and healing of a leg ulcer – biological processes which are currently poorly understood. The mathematical models are expected to provide new insight into the underlying biological mechanisms of leg ulcers and may ultimately improve management of chronic wounds.Read moreRead less
Can an anti-HIV gene in blood stem cells protect from immune depletion by HIV? Approximately 15,000 individuals in Australia are currently HIV infected. Gene therapy has the capacity to remove antiretroviral treatment related issues, dramatically decrease treatment costs and simplify treatment of HIV.
In this study we will model a new approach to treat HIV in which the patient's own cells are used as the therapy by incorporating an anti-HIV gene. These cells are then re-introduced into the p ....Can an anti-HIV gene in blood stem cells protect from immune depletion by HIV? Approximately 15,000 individuals in Australia are currently HIV infected. Gene therapy has the capacity to remove antiretroviral treatment related issues, dramatically decrease treatment costs and simplify treatment of HIV.
In this study we will model a new approach to treat HIV in which the patient's own cells are used as the therapy by incorporating an anti-HIV gene. These cells are then re-introduced into the patient.
The strong mathematical focus of this project, and its application to a promising approach against HIV, will place Australia at the forefront of the mathematics of gene research and contribute to the National Priority Area of Promoting and Maintaining Good Health and the Priority Goal of Preventative Healthcare.
Read moreRead less
Measure-valued analysis of stochastic populations. The project aims to develop new mathematical models and tools for the rigorous analysis of very general stochastic populations that are subject to internal competition and feedback. The proposed mathematical framework is that of measure-valued processes, a setting needed to encompass the complexity and random structure inherent in such systems. Models of this kind have real-world applications in evolutionary biology, cell kinetics and cancer res ....Measure-valued analysis of stochastic populations. The project aims to develop new mathematical models and tools for the rigorous analysis of very general stochastic populations that are subject to internal competition and feedback. The proposed mathematical framework is that of measure-valued processes, a setting needed to encompass the complexity and random structure inherent in such systems. Models of this kind have real-world applications in evolutionary biology, cell kinetics and cancer research, and are essential to our understanding of the persistence of endemic disease and of the preservation of endangered species. The results of this project are expected to provide insight into the behaviour and (in-)stabilities of complex stochastic populations, and offer guidance for their management.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE150101044
Funder
Australian Research Council
Funding Amount
$315,000.00
Summary
New computational approaches for branching processes in population biology. Branching processes are powerful modelling tools in population biology. They describe how individuals live and reproduce according to specific probability laws, and can be used to answer a wide range of population-related questions. This project aims to develop new algorithmic methods for a tractable class of branching processes called Markovian binary trees. Following a matrix analytic approach, it will deliver new resu ....New computational approaches for branching processes in population biology. Branching processes are powerful modelling tools in population biology. They describe how individuals live and reproduce according to specific probability laws, and can be used to answer a wide range of population-related questions. This project aims to develop new algorithmic methods for a tractable class of branching processes called Markovian binary trees. Following a matrix analytic approach, it will deliver new results on the efficient estimation of model parameters, and on the effects of random environments on population dynamics. These results will be used to study significant problems in evolutionary and conservation biology, thereby establishing the relevance of the developed techniques.Read moreRead less