An optimisation-based framework for non-classical Chebyshev approximation. This project aims to solve open mathematical problems in multivariate and piecewise polynomial approximations, two directions that correspond to fundamental obstacles to extending classical approximation results. Through an innovative combination of optimisation and algebraic technique, the project intends to develop foundations for new results in approximation theory, and new insights into other areas of mathematics, mos ....An optimisation-based framework for non-classical Chebyshev approximation. This project aims to solve open mathematical problems in multivariate and piecewise polynomial approximations, two directions that correspond to fundamental obstacles to extending classical approximation results. Through an innovative combination of optimisation and algebraic technique, the project intends to develop foundations for new results in approximation theory, and new insights into other areas of mathematics, most notably optimisation. The techniques and methods developed should also have significant benefits in the many disciplines where approximation problems appear, such as engineering, physics or data mining. The research outputs resulting from this project will be used in a wide range of fields to help implement programs, policies and improve decision making.Read moreRead less
Expanding and linking random matrix theory. Fundamental to random matrix theory are certain universality laws, holding in scaling limits to infinite matrix size. A basic question is to quantify the rate of convergence to the universal laws. The analysis of data for the Riemann zeros from prime number theory, and of the spectral form factor probe of chaos in black hole physics, are immediate applications. An analysis involving integrable structures holding for finite matrix size and their asympt ....Expanding and linking random matrix theory. Fundamental to random matrix theory are certain universality laws, holding in scaling limits to infinite matrix size. A basic question is to quantify the rate of convergence to the universal laws. The analysis of data for the Riemann zeros from prime number theory, and of the spectral form factor probe of chaos in black hole physics, are immediate applications. An analysis involving integrable structures holding for finite matrix size and their asymptotics is proposed, allowing the rate to be quantified for a large class of model
ensembles, and providing predictions in the various applied settings. The broad project is to be networked with researchers in the Asia-Oceania region, with the aim of establishing leadership status for Australia.Read moreRead less
High-frequency Estimation of Term Structure Models at the Zero Lower Bound. This project aims to quantify monetary policy shocks as shifts of the entire term structure of interest rates, when the central bank’s policy rate is constrained at the near-zero level. The proposed method will use a high-dimensional panel of high frequency government bond data. The term structure and resultant policy shocks estimated at intra-day frequencies for major economies including Australia, will be made publicly ....High-frequency Estimation of Term Structure Models at the Zero Lower Bound. This project aims to quantify monetary policy shocks as shifts of the entire term structure of interest rates, when the central bank’s policy rate is constrained at the near-zero level. The proposed method will use a high-dimensional panel of high frequency government bond data. The term structure and resultant policy shocks estimated at intra-day frequencies for major economies including Australia, will be made publicly available. This project expects to deepen our understanding of how monetary policy decisions affect the macroeconomy in a near-zero interest-rate environment. This should provide significant benefits to policymakers for implementing and monitoring monetary policy in achieving desired economic outcomes.Read moreRead less
Macroeconomic and Financial Modelling in an Era of Extremes. This project aims to develop methods to allow workhorse models in economics and finance to better reflect tail events--low probability extreme events, such as the Global Financial Crisis and the COVID-19 pandemic. It intends to address fundamental technical challenges in the estimation of such models, develop a coherent framework for counterfactual analysis of these models and propose methods to apply these models in a big-data environ ....Macroeconomic and Financial Modelling in an Era of Extremes. This project aims to develop methods to allow workhorse models in economics and finance to better reflect tail events--low probability extreme events, such as the Global Financial Crisis and the COVID-19 pandemic. It intends to address fundamental technical challenges in the estimation of such models, develop a coherent framework for counterfactual analysis of these models and propose methods to apply these models in a big-data environment. Expected outcomes include new insights into the transmission of tail risks in the global economic and financial system. This should provide significant benefits, including guidance to Australian and international policymakers charged with maintaining stability in the face of extreme events.Read moreRead less
Statistical Analysis of State-Dependent Government Spending Multipliers. This project aims to provide a new statistical analysis of the government spending multiplier by acknowledging that government spending is the sum of sectoral spending which has heterogeneous effects on the economy. An added complication is that the multiplier can also be state-dependent, meaning that its magnitude can differ across recessions and expansions. Expected outcomes of this project include a better understanding ....Statistical Analysis of State-Dependent Government Spending Multipliers. This project aims to provide a new statistical analysis of the government spending multiplier by acknowledging that government spending is the sum of sectoral spending which has heterogeneous effects on the economy. An added complication is that the multiplier can also be state-dependent, meaning that its magnitude can differ across recessions and expansions. Expected outcomes of this project include a better understanding of the components of the multiplier by novel decomposition and the development of a new statistical test for the state-dependency of the multiplier. This should provide significant benefits to researchers by bringing in new tools and insights and to policymakers by providing timely guidance on fiscal policies.Read moreRead less
Industrial Transformation Training Centres - Grant ID: IC220100035
Funder
Australian Research Council
Funding Amount
$4,958,927.00
Summary
ARC Training Centre for Hyphenated Analytical Separation Technologies . The toughest analytical science challenges typically require advanced analytical technologies to acquire the desired solutions. In the field of separation science this inevitably involves hyphenated separation technologies, specifically the combination of chromatography and mass spectrometry. Advancing this technology to its full capability requires the collaborative strength of academic, industry and end-user partnerships, ....ARC Training Centre for Hyphenated Analytical Separation Technologies . The toughest analytical science challenges typically require advanced analytical technologies to acquire the desired solutions. In the field of separation science this inevitably involves hyphenated separation technologies, specifically the combination of chromatography and mass spectrometry. Advancing this technology to its full capability requires the collaborative strength of academic, industry and end-user partnerships, providing the materials and inspiration for young researchers to apply novel hyphenated methods to complex environmental and industrial systems. This Centre will deliver fundamental developments in hyphenated technologies, new analytical capability, and applied outcomes across multiple end-user groups and interests. Read moreRead less
Prior sensitivity analysis for Bayesian Markov chain Monte Carlo output. This project aims to develop the first set of techniques to implement an automated output sensitivity analysis for Markov Chain Monte Carlo (MCMC) estimation methods. Computationally intense Bayesian MCMC provide a powerful alternative to classical methods for the estimation of economic models. An obstacle to their wider application is that researchers need to specify prior beliefs about model parameters that will affect t ....Prior sensitivity analysis for Bayesian Markov chain Monte Carlo output. This project aims to develop the first set of techniques to implement an automated output sensitivity analysis for Markov Chain Monte Carlo (MCMC) estimation methods. Computationally intense Bayesian MCMC provide a powerful alternative to classical methods for the estimation of economic models. An obstacle to their wider application is that researchers need to specify prior beliefs about model parameters that will affect the results. The expected outcomes will enable researchers to undertake a routine assessment of the sensitivity of the results to prior inputs.Read moreRead less
The RGG/RG motif as an RNA chaperone: advancing CRISPR-Cas RNA technology. This project investigates the way in which protein molecules interact effectively with RNA molecules and also aims to enhance the CRISPR-Cas13a system for RNA detection. Innovative approaches will be used to test the role of a particular protein motif, called the RGG/RG motif, in remodelling RNA structure and enhancing the Cas13a protein. This knowledge is expected to shift our understanding of protein-RNA interactions th ....The RGG/RG motif as an RNA chaperone: advancing CRISPR-Cas RNA technology. This project investigates the way in which protein molecules interact effectively with RNA molecules and also aims to enhance the CRISPR-Cas13a system for RNA detection. Innovative approaches will be used to test the role of a particular protein motif, called the RGG/RG motif, in remodelling RNA structure and enhancing the Cas13a protein. This knowledge is expected to shift our understanding of protein-RNA interactions that are fundamental to almost every aspect of cell biology. The project is intended to benefit Australia through contributing to fundamental knowledge in the field, facilitating the development of new CRISPR-Cas biotechnologies for RNA detection and through the training of young researchers in frontier technologies. Read moreRead less
Integral transforms and moduli theory. This project is in algebraic geometry, a branch of pure
mathematics. An overarching goal is a better understanding of the
algebra underlying the sophisticated geometries that arise in the
classification problems that are pervasive in mathematics and its
applications to physics. This new knowledge will then be applied to
further elucidate the geometry of these spaces.
Expected outcomes of this project include major progress in our
understanding of derived ....Integral transforms and moduli theory. This project is in algebraic geometry, a branch of pure
mathematics. An overarching goal is a better understanding of the
algebra underlying the sophisticated geometries that arise in the
classification problems that are pervasive in mathematics and its
applications to physics. This new knowledge will then be applied to
further elucidate the geometry of these spaces.
Expected outcomes of this project include major progress in our
understanding of derived categories of algebraic stacks via the
Fourier-Mukai transform.
The benefit will be to enhance the international stature of Australian
science.Read moreRead less