A Novel Geometric Approach to Shocks in Reaction-Nonlinear Diffusion Models. Reaction-nonlinear diffusion models play a vital role in the study of cell migration and population dynamics. However, the presence of aggregation, or backward diffusion, leads to the formation of shock waves - distinct, sharp interfaces between different populations of densities of cells - and the breakdown of the model. This project will develop new geometric methods to explain the formation and temporal evolution of ....A Novel Geometric Approach to Shocks in Reaction-Nonlinear Diffusion Models. Reaction-nonlinear diffusion models play a vital role in the study of cell migration and population dynamics. However, the presence of aggregation, or backward diffusion, leads to the formation of shock waves - distinct, sharp interfaces between different populations of densities of cells - and the breakdown of the model. This project will develop new geometric methods to explain the formation and temporal evolution of these shock waves, while simultaneously unifying existing regularisation techniques under a single, geometric banner. It will devise innovative tools in singular perturbation theory and stability analysis that will identify key parameters in the creation of shock waves, as well as their dynamic behaviour.Read moreRead less
ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. The ARC Centre for the Mathematical Analysis of Cellular Systems aims to deliver the mathematics required to compute life. The Centre will deliver innovation in computational and mathematical biology and establish in silico biology alongside in vivo and in vitro biology. These models will allow us to understand the complexity of life at the cellu ....ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. The ARC Centre for the Mathematical Analysis of Cellular Systems aims to deliver the mathematics required to compute life. The Centre will deliver innovation in computational and mathematical biology and establish in silico biology alongside in vivo and in vitro biology. These models will allow us to understand the complexity of life at the cellular level and enable new ways of combining diverse and heterogenous data. This will allow us to understand the mechanisms underlying cellular behaviour, and to apply rational design engineering methods in order to control the dynamics of biological systems. Read moreRead less
The fundamental equations for inversion of operator pencils. This project seeks to deepen understanding of how complex systems may be significantly changed by incremental changes to ambient conditions. Mathematical models of complex systems (climate change processes, optimal driving strategies, efficient distribution policies, effective search routines) often depend on key parameters. If small perturbations to the parameters cause large changes to the solution, then the perturbations are said to ....The fundamental equations for inversion of operator pencils. This project seeks to deepen understanding of how complex systems may be significantly changed by incremental changes to ambient conditions. Mathematical models of complex systems (climate change processes, optimal driving strategies, efficient distribution policies, effective search routines) often depend on key parameters. If small perturbations to the parameters cause large changes to the solution, then the perturbations are said to be singular. This project aims to reveal the underlying mathematical structures and develop new computational algorithms to analyse a general class of perturbed systems both locally near an isolated singularity and globally. It plans to use these algorithms to solve systems of equations, calculate generalised inverse operators, examine perturbed Markov processes, and estimate exit times from meta-stable states in stochastic population dynamics.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE160100213
Funder
Australian Research Council
Funding Amount
$335,000.00
Summary
Optimising the National Benefits From Restoring Environmental Water Flows. The project plans to evaluate strategies that may maximise the national benefits from restoring environmental flows in Australia’s Murray–Darling Basin (MDB). MDB water supply is characterised by prolonged droughts and flood events, and future climatic projections anticipate that these water supply events will intensify. As the uncertainty of future water supply increases, it is important that the volume of water provided ....Optimising the National Benefits From Restoring Environmental Water Flows. The project plans to evaluate strategies that may maximise the national benefits from restoring environmental flows in Australia’s Murray–Darling Basin (MDB). MDB water supply is characterised by prolonged droughts and flood events, and future climatic projections anticipate that these water supply events will intensify. As the uncertainty of future water supply increases, it is important that the volume of water provided by the portfolio of water rights is known. By examining how decision-makers adapt to water supply uncertainty, optimal management strategies could be determined for watering key ecological assets, trading water between irrigators and the government; and private and public investments.Read moreRead less
Classification methods for providing personalised and class decisions. This project provides a novel approach to the clustering of multivariate samples on entities in a class that automatically matches the sample clusters across the entities, allowing for inter-sample variation between the samples in a class. The project aims to develop a widely applicable, mixture-model-based framework for the simultaneous clustering of multivariate samples with inter-sample variation in a class and for the mat ....Classification methods for providing personalised and class decisions. This project provides a novel approach to the clustering of multivariate samples on entities in a class that automatically matches the sample clusters across the entities, allowing for inter-sample variation between the samples in a class. The project aims to develop a widely applicable, mixture-model-based framework for the simultaneous clustering of multivariate samples with inter-sample variation in a class and for the matching of the clusters across the entities in the class. The project will use a statistical approach to automatically match the clusters, since the overall mixture model provides a template for the class. It will provide a basis for discriminating between different classes in addition to the identification of atypical data points within a sample and of anomalous samples within a class. Key applications include biological image analysis and the analysis of data in flow cytometry which is one of the fundamental research tools for the life scientist.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE160101565
Funder
Australian Research Council
Funding Amount
$330,000.00
Summary
Flexible data modelling via skew mixture models:challenges and applications. This project seeks to explore new models for handling data with non-normal features. Parametric distributions are fundamental to statistical modelling and inference. For centuries, the ‘normal’ distribution has been the dominant model for continuous data. However, real data rarely satisfy the assumption of normality. There is thus a strong demand for more flexible distributions. This project aims to develop new methodol ....Flexible data modelling via skew mixture models:challenges and applications. This project seeks to explore new models for handling data with non-normal features. Parametric distributions are fundamental to statistical modelling and inference. For centuries, the ‘normal’ distribution has been the dominant model for continuous data. However, real data rarely satisfy the assumption of normality. There is thus a strong demand for more flexible distributions. This project aims to develop new methodologies in finite mixture modelling using skew component distributions to provide better models for handling data with non-normal features (such as skewness, heavy/light tails, and multimodality). Applications may include security intrusion detection, clinical diagnosis and prognosis, and flow and mass cytometry.Read moreRead less
Extreme soil acidification and metal release risks from increasing drought. The project aims to study the effects of drought on pH and metal speciation in soils, and develop tools to assess current and future risks. Social and economic well-being depends on good soil and water quality. Climate change makes droughts more frequent and severe, which could cause soil acidification (pH<4) and metal release in many regions. The project will integrate experimental data on the effects of drought on soil ....Extreme soil acidification and metal release risks from increasing drought. The project aims to study the effects of drought on pH and metal speciation in soils, and develop tools to assess current and future risks. Social and economic well-being depends on good soil and water quality. Climate change makes droughts more frequent and severe, which could cause soil acidification (pH<4) and metal release in many regions. The project will integrate experimental data on the effects of drought on soil geochemistry with hydro-geochemical models, and apply these to national-scale predictions. The intended outcomes are improved management and preparedness for droughts and new research directions for geochemistry.Read moreRead less
Economic complexity as a driver of innovation and smart specialisation. This project aims to determine how economic complexity can drive innovation and smart specialisation and how industry can be supported to transition to a more competitive economy. With the downturn of traditional manufacturing, innovation is crucial to create new industries and the jobs of the future. The expected outcomes of this project include high-value industry intelligence in support of product diversification. This sh ....Economic complexity as a driver of innovation and smart specialisation. This project aims to determine how economic complexity can drive innovation and smart specialisation and how industry can be supported to transition to a more competitive economy. With the downturn of traditional manufacturing, innovation is crucial to create new industries and the jobs of the future. The expected outcomes of this project include high-value industry intelligence in support of product diversification. This should provide significant benefits, such as increased international competitiveness, exports, revenue, and economic growth.
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Special Research Initiatives - Grant ID: SR0354716
Funder
Australian Research Council
Funding Amount
$10,000.00
Summary
Energetically Open Systems Research Network Study. Conceptual frameworks arising in the physical sciences, such as non-equilibrium statistical mechanics and thermodynamics, synergetics, chaos and dynamical systems theory, are seminal in the emerging science of complexity. This study will lay the groundwork for a network to link Australian and overseas research on these fundamental concepts, and their application within the context of entropy-producing systems vital to the long-term sustainabilit ....Energetically Open Systems Research Network Study. Conceptual frameworks arising in the physical sciences, such as non-equilibrium statistical mechanics and thermodynamics, synergetics, chaos and dynamical systems theory, are seminal in the emerging science of complexity. This study will lay the groundwork for a network to link Australian and overseas research on these fundamental concepts, and their application within the context of entropy-producing systems vital to the long-term sustainability of the earth - oceans, atmosphere, biosphere, CO2-free energy production, space and solar environment. The network would facilitate the development of young investigators and be linked into wider complex systems networks such as the CSIRO Centre for Complex Systems Science.Read moreRead less
Redesigning Landcare policy to better coordinate across landholders. This project aims to study how landscape-sensitive economic incentives and social norms can be leveraged to enhance the short- and long-term effectiveness of conservation programs. It will yield new knowledge for innovative designs in conservation contracting that is urgently needed to address worsening environmental threats in Australia and worldwide. In collaboration with Nobel laureate Vernon Smith’s team, new methods and pr ....Redesigning Landcare policy to better coordinate across landholders. This project aims to study how landscape-sensitive economic incentives and social norms can be leveraged to enhance the short- and long-term effectiveness of conservation programs. It will yield new knowledge for innovative designs in conservation contracting that is urgently needed to address worsening environmental threats in Australia and worldwide. In collaboration with Nobel laureate Vernon Smith’s team, new methods and protocols will improve our ability to generate better data and better understand how social and incentive mechanisms can constructively interact to facilitate collaborative environmental action. Results will help make the achievement of environmental targets and the use of public funds more cost-effective. Read moreRead less