New techniques and invariants in low-dimensional topology. The aim of this project is to introduce and apply new methods and invariants in the field of low-dimensional topology by developing parametrised and equivariant enhancements of Seiberg-Witten theory and Floer homology. These new refined invariants, made possible by recent advances in gauge theory, will be more powerful than existing ones, enabling the detection of new exotic phenomena. Expected outcomes include effective means for distin ....New techniques and invariants in low-dimensional topology. The aim of this project is to introduce and apply new methods and invariants in the field of low-dimensional topology by developing parametrised and equivariant enhancements of Seiberg-Witten theory and Floer homology. These new refined invariants, made possible by recent advances in gauge theory, will be more powerful than existing ones, enabling the detection of new exotic phenomena. Expected outcomes include effective means for distinguishing families of spaces, measuring their complexity and new obstructions for their existence. The new invariants and techniques will lead to the resolution of some open problems in low-dimensional topology and enhance Australia's reputation as a world leader in this field.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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Coarse Geometry: a novel approach to the Callias index & topological matter. Coarse geometry is the study of the large-scale structure of metric spaces, in terms of operator algebras. This project aims to use coarse geometry to develop novel approaches to Callias index theory and its applications, and to topological phases of matter, where the Nobel Prize in physics in 2016 was awarded. This will yield new techniques in index theory and other areas, and solutions to several important problems. O ....Coarse Geometry: a novel approach to the Callias index & topological matter. Coarse geometry is the study of the large-scale structure of metric spaces, in terms of operator algebras. This project aims to use coarse geometry to develop novel approaches to Callias index theory and its applications, and to topological phases of matter, where the Nobel Prize in physics in 2016 was awarded. This will yield new techniques in index theory and other areas, and solutions to several important problems. Outcomes include a noncompact generalisation of the famous Guillemin-Sternberg conjecture that quantisation commutes with reduction, and new models of topological phases of matter in terms of K-theory of operator algebras. This project will benefit Australia by reinforcing its position in these highly active areas in science.Read moreRead less
Identification Power and Instrument Strength in Discrete Outcome Models. This project aims to develop new econometric and statistical techniques to quantify causal effects in treatment models with discrete outcomes. Expected outcomes include a much-needed weak instrument test, a measure for identification strength in partial identification setting, and an instrument-covariate selection procedure for high dimensional discrete models based identification power. The benefits include advanced knowle ....Identification Power and Instrument Strength in Discrete Outcome Models. This project aims to develop new econometric and statistical techniques to quantify causal effects in treatment models with discrete outcomes. Expected outcomes include a much-needed weak instrument test, a measure for identification strength in partial identification setting, and an instrument-covariate selection procedure for high dimensional discrete models based identification power. The benefits include advanced knowledge in econometrics and statistics, and enhanced tools for program evaluation and policy assessment in empirical causal analysis using observational data. The project falls into the category of smarter information use and is relevant to any national priority areas where policy interventions require assessment.Read moreRead less
Selection of mixed strength moment restrictions and optimal inference . This project aims to develop consistent model selection criteria even if the target model only provides a weak signal about the parameter of interest. This project expects to generate new knowledge on model selection using new and innovative techniques. Expected outcomes include the quantification of the maximum information on parameter from weak-signal models; new entropy-based model selection criteria; and a robust investi ....Selection of mixed strength moment restrictions and optimal inference . This project aims to develop consistent model selection criteria even if the target model only provides a weak signal about the parameter of interest. This project expects to generate new knowledge on model selection using new and innovative techniques. Expected outcomes include the quantification of the maximum information on parameter from weak-signal models; new entropy-based model selection criteria; and a robust investigation of the still debated hypothesis in environmental economics that with open and liberalized trade, developing countries would become pollution havens for dirty industries of advanced countries. Success in this undertaking will dramatically enlarge the pool of applied work involving economic models with weak signals.Read moreRead less
Root-to-shoot: modeling the salt stress response of a plant vascular system. Salt and drought are the two major abiotic stresses affecting crop plant health, growth and development. We aim to understand salt and water transport in plants and the physiological effects of soil salinity. Using biophysical models, we will quantify the movement of salt through plant organs, tissues and cells, from root to leaf. We aim to answer the question of how salt moves across the different tissues and major org ....Root-to-shoot: modeling the salt stress response of a plant vascular system. Salt and drought are the two major abiotic stresses affecting crop plant health, growth and development. We aim to understand salt and water transport in plants and the physiological effects of soil salinity. Using biophysical models, we will quantify the movement of salt through plant organs, tissues and cells, from root to leaf. We aim to answer the question of how salt moves across the different tissues and major organs, how salt accumulates in root, leaf and shoot cells, and how movement and accumulation is controlled by the diversity of transport mechanisms operating in plants. We aim to quantify tissue tolerance, osmotic tolerance and ionic tolerance and discover new mechanisms by which plants can stave off the effect of salt stress.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE240100097
Funder
Australian Research Council
Funding Amount
$389,670.00
Summary
Mathematical models for actin scavenging and biofilm removal. The project aims to develop mathematical models for actin scavenging and biofilm removal, processes that combine to alleviate tissue damage and inflammation. Actin scavenging eliminates the protein F-actin which is released during cell death, but this process is not fully-understood. Biofilms are colonies of micro-organisms, for example bacteria, that are highly resistant to antimicrobial treatment. This project expects to generate ne ....Mathematical models for actin scavenging and biofilm removal. The project aims to develop mathematical models for actin scavenging and biofilm removal, processes that combine to alleviate tissue damage and inflammation. Actin scavenging eliminates the protein F-actin which is released during cell death, but this process is not fully-understood. Biofilms are colonies of micro-organisms, for example bacteria, that are highly resistant to antimicrobial treatment. This project expects to generate new knowledge, using an innovative combination of mathematical modelling and cell biology experiments. Expected outcomes include new theory and software, yielding the benefits of increased understanding of cell biology, and potential to enhance development of smart materials that eliminate biofilms.Read moreRead less
New mathematics for lipids and cells: structured models for atherosclerosis. The project aims to create new mathematical theory for immune cell behaviour which leads to heart attacks and strokes. This includes formulation and analysis of new types of mathematical models for atherosclerotic plaque development, leading to the creation of new mathematical tools to investigate cell fate in plaques and to generate new hypotheses for experimental research. Expected outcomes of this project include po ....New mathematics for lipids and cells: structured models for atherosclerosis. The project aims to create new mathematical theory for immune cell behaviour which leads to heart attacks and strokes. This includes formulation and analysis of new types of mathematical models for atherosclerotic plaque development, leading to the creation of new mathematical tools to investigate cell fate in plaques and to generate new hypotheses for experimental research. Expected outcomes of this project include powerful and reliable mathematical models ready for application, and national and international collaborations with scientists and mathematicians. This should provide significant benefits including increased capacity to use mathematical models in vascular biology and training young researchers in interdisciplinary methods.Read moreRead less
Advanced mathematical models and methods for a randomly-varying world. This project aims to develop advanced stochastic models and novel techniques, to analytically obtain performance measures and to efficiently simulate the time evolution. This project also plans to apply new models and methods to address important problems in ecology and epidemiology. The outputs of this project will advance knowledge in mathematics as well as in the intended application areas, including ultimately in improved ....Advanced mathematical models and methods for a randomly-varying world. This project aims to develop advanced stochastic models and novel techniques, to analytically obtain performance measures and to efficiently simulate the time evolution. This project also plans to apply new models and methods to address important problems in ecology and epidemiology. The outputs of this project will advance knowledge in mathematics as well as in the intended application areas, including ultimately in improved understanding, modelling, and tracking of the spread of diseases.Read moreRead less
Symmetry and geometric partial differential equations. This project aims to develop tools to assist the study of partial differential equations, which are fundamental to our understanding of the physical world. Symmetries of the Laplace equation are fundamental in both finding and interpreting its solutions and can be traced to the conformal symmetries of the underlying space. Only for the most symmetric of spaces, Euclidean space and the sphere, is this correspondence well understood. Using pow ....Symmetry and geometric partial differential equations. This project aims to develop tools to assist the study of partial differential equations, which are fundamental to our understanding of the physical world. Symmetries of the Laplace equation are fundamental in both finding and interpreting its solutions and can be traced to the conformal symmetries of the underlying space. Only for the most symmetric of spaces, Euclidean space and the sphere, is this correspondence well understood. Using powerful geometric tools from conformal geometry, the project will extend this to less symmetric spaces. The knowledge generated from this project will extend to more general geometric contexts providing a concrete setting for the study of the associated natural equations in curved spaces.Read moreRead less