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
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
New Approaches to Modelling and Analysing Long-Memory Random Processes. The project aims to develop new approaches using infinite-dimensional Markov processes to solving important long-standing problems from the theory of long memory random processes and their applications. It aims to: construct a class of new representations of random processes; derive inequalities for the key numerical characteristics; and, devise and investigate numerical methods for computing the characteristics and for perf ....New Approaches to Modelling and Analysing Long-Memory Random Processes. The project aims to develop new approaches using infinite-dimensional Markov processes to solving important long-standing problems from the theory of long memory random processes and their applications. It aims to: construct a class of new representations of random processes; derive inequalities for the key numerical characteristics; and, devise and investigate numerical methods for computing the characteristics and for performing statistical inference on the long memory models. The accuracy of numerical approximations will be analysed using simulations on supercomputers. Expected outcomes include models and results of practical importance with applications such as intrusion detection problems, cell motility for biological data and telecommunication.Read moreRead less
New universality in stochastic systems. This project aims to uncover new analyses and effects in the complex behaviour of non-linear systems with random noise. Many systems originate near an unstable equilibrium. This project will develop a new mathematical theory that establishes a universality in the way the long term effect of noise expresses itself as random initial conditions in the dynamics. It will fill gaps in Mathematics and make refinements to existing fundamental scientific laws by in ....New universality in stochastic systems. This project aims to uncover new analyses and effects in the complex behaviour of non-linear systems with random noise. Many systems originate near an unstable equilibrium. This project will develop a new mathematical theory that establishes a universality in the way the long term effect of noise expresses itself as random initial conditions in the dynamics. It will fill gaps in Mathematics and make refinements to existing fundamental scientific laws by including random initial conditions as predicted by our theory. This will advance our understanding of complex systems subjected to noise and will provide significant benefits in the scientific discoveries in Biology, Ecology, Physics and other Sciences where such systems are frequently met.Read moreRead less
Advances in data integration modelling for infectious disease response. This project aims to develop powerful mathematical frameworks that integrate data from multiple sources to facilitate informed decisions in response to the threat of present, and future, infectious diseases. The project expects to generate new knowledge in mathematics by advancing the tools for incorporating multiple data sources into models of infectious diseases. The expected outcomes include enhanced capacity to predict s ....Advances in data integration modelling for infectious disease response. This project aims to develop powerful mathematical frameworks that integrate data from multiple sources to facilitate informed decisions in response to the threat of present, and future, infectious diseases. The project expects to generate new knowledge in mathematics by advancing the tools for incorporating multiple data sources into models of infectious diseases. The expected outcomes include enhanced capacity to predict spatiotemporal changes in transmission of infectious diseases. This project should provide significant benefits in the advancement of modelling techniques broadly applicable to infectious disease settings, which will be demonstrated for antimalarial drug resistance – a major threat to malaria elimination.
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