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A mathematical analysis of the influence of small scale inhomogeneities on the evolution of the universe. A fundamental unresolved problem in modern cosmology is to quantify the influence of small-scale inhomogeneities on the evolution of the universe. This project will develop the mathematical techniques required to resolve this question. In addition, these techniques will have important applications to the analysis of astronomical data.
Discovery Early Career Researcher Award - Grant ID: DE210101581
Funder
Australian Research Council
Funding Amount
$411,000.00
Summary
Stability and Complexity: New insights from Random Matrix Theory. Complexity is a rule of nature: large ecosystems, the human brain, and turbulent fluids are merely a few examples of complex systems. This project aims to study and classify criteria of stability in large complex systems based on universal probabilistic models. This project expects to generate new important understanding of stability using cutting-edge techniques from random matrix theory. Expected outcomes of this project includ ....Stability and Complexity: New insights from Random Matrix Theory. Complexity is a rule of nature: large ecosystems, the human brain, and turbulent fluids are merely a few examples of complex systems. This project aims to study and classify criteria of stability in large complex systems based on universal probabilistic models. This project expects to generate new important understanding of stability using cutting-edge techniques from random matrix theory. Expected outcomes of this project include development and expansion of an innovative mathematical framework and techniques which allow a unified and universal approach to the question of stability in large complex systems. Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE170100186
Funder
Australian Research Council
Funding Amount
$322,054.00
Summary
Statistical mechanics and topology of polymer systems. This project aims to study the behaviour of systems of long polymers in solution, and the effects of temperature, solvent and other environmental properties. Polymer models capture important physical properties of real-world molecules like DNA. This project will study the topology of polymer chains in tightly confined spaces. Knots and links hinder important biological processes like DNA replication, and this project will research how entang ....Statistical mechanics and topology of polymer systems. This project aims to study the behaviour of systems of long polymers in solution, and the effects of temperature, solvent and other environmental properties. Polymer models capture important physical properties of real-world molecules like DNA. This project will study the topology of polymer chains in tightly confined spaces. Knots and links hinder important biological processes like DNA replication, and this project will research how entanglement forms and how the biological mechanisms are used to manage it. The project is expected to have both important biological consequences and to enhance Australia's position as a centre for research in statistical mechanics.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE200100988
Funder
Australian Research Council
Funding Amount
$425,333.00
Summary
From cells to whales: A mathematical framework to understand navigation. This project aims to understand what drives the navigation of small and large organisms. To achieve this, the project seeks to develop a mathematical framework that unifies models of navigation, communication and uncertainty, for the first time. This is significant as navigation underpins fundamental behaviour such as migration. Expected outcomes of this project include novel insights into the mechanisms underlying navigati ....From cells to whales: A mathematical framework to understand navigation. This project aims to understand what drives the navigation of small and large organisms. To achieve this, the project seeks to develop a mathematical framework that unifies models of navigation, communication and uncertainty, for the first time. This is significant as navigation underpins fundamental behaviour such as migration. Expected outcomes of this project include novel insights into the mechanisms underlying navigation, and new mathematical techniques required to construct the framework. The mathematical framework will be employed to explore and explain critical biological phenomena such as the impact of noise pollution on whale migration, and the conditions required for successful cellular navigation.Read moreRead less
New Directions in Bayesian Statistics: formulation, computation and application to exemplar challenges. Bayesian statistics is a fundamental statistical and machine learning approach for density estimation, data analysis and inference. However, there remain open questions regarding the formulation of the model, the likelihood and priors, and efficient computation. This project proposes new approaches that address these issues, and applies them to two exemplar challenges: the impact of climate ch ....New Directions in Bayesian Statistics: formulation, computation and application to exemplar challenges. Bayesian statistics is a fundamental statistical and machine learning approach for density estimation, data analysis and inference. However, there remain open questions regarding the formulation of the model, the likelihood and priors, and efficient computation. This project proposes new approaches that address these issues, and applies them to two exemplar challenges: the impact of climate change on the Great Barrier Reef and better understanding neurological diseases related aging, in particular Parkinson's Disease. Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE200100200
Funder
Australian Research Council
Funding Amount
$418,398.00
Summary
Next generation causal inference methods for biological data. This project aims to develop next generation causal inference methods for analysing biological data especially the single cell sequencing data and their applications in cell biology. Although Artificial Intelligence and Statistical Machine Learning have been applied successfully in many fields, including biological research, there is still a serious lack of methods for interpreting and reasoning about the mechanism of biological syste ....Next generation causal inference methods for biological data. This project aims to develop next generation causal inference methods for analysing biological data especially the single cell sequencing data and their applications in cell biology. Although Artificial Intelligence and Statistical Machine Learning have been applied successfully in many fields, including biological research, there is still a serious lack of methods for interpreting and reasoning about the mechanism of biological systems, the ultimate goal of research in many areas. Efficient data-driven causality discovery approaches developed by the project will be a timely and significant contribution to the knowledge of biology and statistics as well as the battle against health threats.
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New mathematical approaches to learn the equations of life from noisy data. New mathematical models and mathematical modelling methods must be continually developed to interpret emerging biotechnology experiments. Contemporary research in tissue engineering involves growing tissues on 3d-printed scaffolds to mimic constrained in vivo geometries. Previous mathematical models of tissue growth focus on computationally expensive discrete mathematical models that are poorly suited for parameter infe ....New mathematical approaches to learn the equations of life from noisy data. New mathematical models and mathematical modelling methods must be continually developed to interpret emerging biotechnology experiments. Contemporary research in tissue engineering involves growing tissues on 3d-printed scaffolds to mimic constrained in vivo geometries. Previous mathematical models of tissue growth focus on computationally expensive discrete mathematical models that are poorly suited for parameter inference and experimental design. This project will deliver and deploy high-fidelity, computationally efficient moving boundary continuum mathematical models that will: (i) predict/interpret new experiments, (ii) provide quantitative insight into biological mechanisms, and (iii) enable reproducible experimental design.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE240100650
Funder
Australian Research Council
Funding Amount
$443,237.00
Summary
Behind the barrier: using mathematics to understand the neuro-immune system. This project aims to develop new mathematical methods to study healthy immune cell regulation in the brain and movement across the Blood Brain Barrier. The project expects to develop novel deterministic and stochastic mathematics that captures the stochasticity of immune cells in the Central Nervous System (brain and spine) and form the foundation of a new field of mathematical research: mathematical neuroimmunology. Ex ....Behind the barrier: using mathematics to understand the neuro-immune system. This project aims to develop new mathematical methods to study healthy immune cell regulation in the brain and movement across the Blood Brain Barrier. The project expects to develop novel deterministic and stochastic mathematics that captures the stochasticity of immune cells in the Central Nervous System (brain and spine) and form the foundation of a new field of mathematical research: mathematical neuroimmunology. Expected benefits of this project include new mathematical tools, biological insight, and strong interdisciplinary collaborations. From this project, Australia will be placed at the forefront of mathematical research in neuroimmunology, and there will be a complete understanding of homeostasis of the neuro-immune system. Read moreRead less
Building macroscale models from microscale probabilistic models. Spatial patterns arise in biological and physical processes. Understanding how local individual-based functions, such as movement and interactions between individuals, give rise to global spatial distributions and patterns in populations of individuals is generating much interest. Probabilistic agent-based models provide information about the movement of individuals, whereas continuum models provide information about the global pro ....Building macroscale models from microscale probabilistic models. Spatial patterns arise in biological and physical processes. Understanding how local individual-based functions, such as movement and interactions between individuals, give rise to global spatial distributions and patterns in populations of individuals is generating much interest. Probabilistic agent-based models provide information about the movement of individuals, whereas continuum models provide information about the global properties, such as spread of populations. This project will provide tools for determining the connection between the two types of models, thereby linking the behaviour on microscopic and macroscopic scales.Read moreRead less
From trip to tail: tracking the origins, development and evolution of coherent structures in turbulent boundary layers. This project will investigate the lifespan of large-scale repeating patterns within turbulent boundary layers (the thin layer of chaotic fluid that envelopes a body as it moves through a fluid). These recurrent patterns play an important role in our lives, dictating the drag of aircraft and dominating environmental processes in the lower atmosphere.