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
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.
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.
Discovery Early Career Researcher Award - Grant ID: DE200101467
Funder
Australian Research Council
Funding Amount
$419,778.00
Summary
The geometric structure of spatial noise. Spatial noise is ubiquitous in nature and science: as interference in medical imaging, in oceanography, in the modelling of telecommunication networks etc. Despite this diversity of sources, spatial noise can be studied in a unified way by considering mathematical models that capture its essential features. This project aims to study spatial noise by analysing its geometric structure, for instance by considering the number of contour lines of the noise, ....The geometric structure of spatial noise. Spatial noise is ubiquitous in nature and science: as interference in medical imaging, in oceanography, in the modelling of telecommunication networks etc. Despite this diversity of sources, spatial noise can be studied in a unified way by considering mathematical models that capture its essential features. This project aims to study spatial noise by analysing its geometric structure, for instance by considering the number of contour lines of the noise, and the way these lines connect different regions of space. The project further aims to apply this analysis to construct statistical tests that can distinguish different classes of spatial noise, with potential applications across all of the disciplines mentioned above.Read moreRead less
Overseeing the internet: new paradigms of network measurement. Like the electricity network, the internet is a core infrastructure, and so must be reliable and efficient. A gap in bandwidth supply is like a blackout in terms of lost business and productivity. This project will provide the measurement breakthroughs to ensure that network behaviour can be accurately and comprehensively monitored.
Australian Laureate Fellowships - Grant ID: FL130100039
Funder
Australian Research Council
Funding Amount
$2,750,000.00
Summary
New stochastic models for Science, Economics, Social Science and Engineering. Stochastic, or random, phenomena abound in society. This project will combine advancement of the theory of stochastic models at a deep level with application to problems arising in science, economics, social science and engineering, and outreach to educate members of the public about random processes of significance in their lives.
ARC Centre of Excellence for Mathematical and Statistical Frontiers of Big Data, Big Models, New Insights. In today's world, massive amounts of data in a variety of forms are collected daily from a multitude of sources. Many of the resulting data sets have the potential to make vital contributions to society, business and government, as well as impact on international developments, but are so large or complex that they are difficult to process and analyse using traditional tools. The aim of this ....ARC Centre of Excellence for Mathematical and Statistical Frontiers of Big Data, Big Models, New Insights. In today's world, massive amounts of data in a variety of forms are collected daily from a multitude of sources. Many of the resulting data sets have the potential to make vital contributions to society, business and government, as well as impact on international developments, but are so large or complex that they are difficult to process and analyse using traditional tools. The aim of this Centre is to create innovative mathematical and statistical models that can uncover the knowledge concealed within the size and complexity of these big data sets, with a focus on using the models to deliver insight into problems vital to the Centre's Collaborative Domains: Healthy People, Sustainable Environments and Prosperous Societies.Read moreRead less
Fundamental investigation of heat and mass transfer in nanofluids: a mechanistic approach. This project aims to develop a mathematical model in order to predict complex boiling in using nanofluids as new coolant for heat removal. Implementation and resultant computer codes thereafter will provide industries with significant benefits and reduce times and costs in their future design of ultra-high efficient heat removal systems.
Discovery Early Career Researcher Award - Grant ID: DE180100463
Funder
Australian Research Council
Funding Amount
$341,248.00
Summary
Understanding randomness in networks. This project aims to bring the latest techniques in modelling phone and wireless networks to Australia by developing new methods and models. Increasing demands of internet data in mobile phone networks has forced researchers to adopt new mathematical approaches. One of these is stochastic geometry, a useful combination of probability and geometry, which in recent years has been used by researchers overseas to model phone and other wireless networks. A key p ....Understanding randomness in networks. This project aims to bring the latest techniques in modelling phone and wireless networks to Australia by developing new methods and models. Increasing demands of internet data in mobile phone networks has forced researchers to adopt new mathematical approaches. One of these is stochastic geometry, a useful combination of probability and geometry, which in recent years has been used by researchers overseas to model phone and other wireless networks. A key point is extending the current, mostly static models, by using methods from queueing theory, resulting in dynamic network models. Another is using theoretical techniques such as large deviations theory that have seen little use in this field, and applying them to network problems. Results from the project will help implement and optimize current network technologies, as well as design future technologies.Read moreRead less
Can green investors drive the transition to a low emissions economy? The project aims to develop a game-theoretical approach to model the impact of climate change on financial markets by studying the interactions between the government, companies and investors. Expected outcomes include novel solution concepts for stochastic games with heterogeneous beliefs, asymmetric information, and model uncertainty, as well as optimal investment and production strategies under climate driven economic transi ....Can green investors drive the transition to a low emissions economy? The project aims to develop a game-theoretical approach to model the impact of climate change on financial markets by studying the interactions between the government, companies and investors. Expected outcomes include novel solution concepts for stochastic games with heterogeneous beliefs, asymmetric information, and model uncertainty, as well as optimal investment and production strategies under climate driven economic transitions. Results will be used to validate and improve the recently launched Australian based climate transition index. The project should yield significant benefits for the financial industry and investors by providing novel insights into financial risks during the transition to a low emissions economy.Read moreRead less