Inference in partially non-stationary time series models. Economic theories typically specify the long-run relationship between economic variables. However, researchers usually examine the long-run features of the data by fitting a restrictive class of models using criteria that have only proven useful for short-term forecasting. In this project we consider alternative models and modelling strategies that are appropriate for the study of the long-run. We also develop computer intensive (bootstra ....Inference in partially non-stationary time series models. Economic theories typically specify the long-run relationship between economic variables. However, researchers usually examine the long-run features of the data by fitting a restrictive class of models using criteria that have only proven useful for short-term forecasting. In this project we consider alternative models and modelling strategies that are appropriate for the study of the long-run. We also develop computer intensive (bootstrap) methods, which will provide a much-needed improvement over the existing (asymptotic) methods for making inference about the long-run. Our research will lead to more reliable models for long-term planning in business, industry and government.Read moreRead less
Vector ARMA Models and Macroeconomic Modelling: Some New Methodology and Algorithms. Economic variables are strongly related to each other, as well as being strongly related to their recent history. As a result, good dynamic multivariate models are crucial for effective policy making and forecasting in areas of vital national importance such as monetary and fiscal policy, environmental policy and tourism. Our project advances the frontiers of knowledge in multivariate time series modelling. The ....Vector ARMA Models and Macroeconomic Modelling: Some New Methodology and Algorithms. Economic variables are strongly related to each other, as well as being strongly related to their recent history. As a result, good dynamic multivariate models are crucial for effective policy making and forecasting in areas of vital national importance such as monetary and fiscal policy, environmental policy and tourism. Our project advances the frontiers of knowledge in multivariate time series modelling. The outcome of this project will be immediately useful for macroeconomic policy makers such as the Reserve Bank of Australia and the Treasury, and for industry bodies such as Tourism Australia. Read moreRead less
Solvable models on regular and random lattices in statistical mechanics and field theory. There are only a few solvable models in statistical mechanics and field theory, but those that are known give deep insights into the cooperative behaviour that characterizes a critical point, as well as
leading to fascinating mathematics. The two chief investigators have been at the forefront of this field for many years. Currently there are many notable exciting challenges they wish to address:
the re ....Solvable models on regular and random lattices in statistical mechanics and field theory. There are only a few solvable models in statistical mechanics and field theory, but those that are known give deep insights into the cooperative behaviour that characterizes a critical point, as well as
leading to fascinating mathematics. The two chief investigators have been at the forefront of this field for many years. Currently there are many notable exciting challenges they wish to address:
the relationship between Tutte's work on dichromatic polynomials and matrix models, the outstanding problem of calculating the order parameters of the chiral Potts model, and the eigenvalue spectra of the transfer matrices that occur in integrable models.
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Algebraic invariants in mathematics and physics. This project is at the leading edge of fundamental mathematics and will result in important scientific advances that will keep Australia at the forefront internationally in this field of research. The topics under investigation are having high impact worldwide so there is an emphasis on international networking and on research training, particularly of research students. Australians would normally need to go to leading international centres such a ....Algebraic invariants in mathematics and physics. This project is at the leading edge of fundamental mathematics and will result in important scientific advances that will keep Australia at the forefront internationally in this field of research. The topics under investigation are having high impact worldwide so there is an emphasis on international networking and on research training, particularly of research students. Australians would normally need to go to leading international centres such as Paris to partake in projects of this nature. That high profile research of this kind can be done in Australia will enhance our capacity to retain scientific talent.Read moreRead less
The mathematics and physics of interacting systems. Much of the world around us involves the networked interaction between a large number of components. For example, such complex networks may be physical, biological, social or technical in nature and represent connections between magnetic spins, species, people or computers. This Project will provide a firm theoretical foundation for such complex interacting systems through an investigation of the fascinating mathematics and physics behind them. ....The mathematics and physics of interacting systems. Much of the world around us involves the networked interaction between a large number of components. For example, such complex networks may be physical, biological, social or technical in nature and represent connections between magnetic spins, species, people or computers. This Project will provide a firm theoretical foundation for such complex interacting systems through an investigation of the fascinating mathematics and physics behind them. This perspective from mathematical physics, in particular using the tools of statistical mechanics, will lead to a better understanding of many real-world complex systems.Read moreRead less
Solvable models and pattern formation: quantum spin ladders, combinatorics and stromatolite morphogenesis. The aim of this project is to develop new applications of exactly solved models in statistical mechanics. These include the study of quantum spin ladders of great interest in condensed matter physics. The physical properties of new and existing models will be derived to provide valuable benchmarks and predictions for future theoretical and experimental work. We will also undertake the study ....Solvable models and pattern formation: quantum spin ladders, combinatorics and stromatolite morphogenesis. The aim of this project is to develop new applications of exactly solved models in statistical mechanics. These include the study of quantum spin ladders of great interest in condensed matter physics. The physical properties of new and existing models will be derived to provide valuable benchmarks and predictions for future theoretical and experimental work. We will also undertake the study and development of a set of remarkable conjectures relating the properties of a solvable model to an established area of combinatorics. Another aspect of this project involves the investigation of the origins, growth and form of ancient stromatolites.
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ARC Complex Open Systems Research Network. Complexity is the common frontier in the physical, biological and social sciences. This Network will link specialists in all three sciences through five generic conceptual and mathematical theme activities. It will promote research into how subsystems self-organise into new emergent structures when assembled into an open, non-equilibrium system. Outcomes will include new technologies and software tools and deeper understanding of fundamental questions i ....ARC Complex Open Systems Research Network. Complexity is the common frontier in the physical, biological and social sciences. This Network will link specialists in all three sciences through five generic conceptual and mathematical theme activities. It will promote research into how subsystems self-organise into new emergent structures when assembled into an open, non-equilibrium system. Outcomes will include new technologies and software tools and deeper understanding of fundamental questions in science. An essential function of the network will be introducing researchers end users to new tools and broadening the horizons of graduate students.Read moreRead less
Statistical Mechanics of Classical Glasses. Glasses and ceramics can possess a combination of properties not available in other materials and thus they are of technological importance with rapidly developing applications. However a fundamental theoretical basis for describing these systems has been missing. The reason for this is that glasses are not in thermodynamic equilibrium, so the standard tools of equilibrium statistical mechanics cannot be rigorously applied . This project will make an i ....Statistical Mechanics of Classical Glasses. Glasses and ceramics can possess a combination of properties not available in other materials and thus they are of technological importance with rapidly developing applications. However a fundamental theoretical basis for describing these systems has been missing. The reason for this is that glasses are not in thermodynamic equilibrium, so the standard tools of equilibrium statistical mechanics cannot be rigorously applied . This project will make an important contribution towards building a strong local knowledge base by addressing the problem of understanding the glassy state. The knowledge base can then serve as a springboard for possible high tech applications in materials science and engineering.Read moreRead less
Low-dimensional quantum systems. The theory of integrable systems of statistical mechanics and quantum field theory is currently one of most rapidly developing and fascinating subjects in theoretical physics and mathematics.
It allows to obtain an exact description of strongly-interacting quantum systems in one or two space dimensions and provides fundamental tools for understanding of critical phenomena and physics of small systems like quantum wires, carbon nanotubes and Josephson junctions ....Low-dimensional quantum systems. The theory of integrable systems of statistical mechanics and quantum field theory is currently one of most rapidly developing and fascinating subjects in theoretical physics and mathematics.
It allows to obtain an exact description of strongly-interacting quantum systems in one or two space dimensions and provides fundamental tools for understanding of critical phenomena and physics of small systems like quantum wires, carbon nanotubes and Josephson junctions. The project addresses two particular problems in this field: the three-dimensional lattice model with continuous spins and calculation of form factors in a two-dimensional massive field theory with a supersymmetry.
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Practical and theoretical aspects of structure enumeration. Many areas of study involve processing of large numbers of
objects in some class. These are countless examples in
chemistry, physics, mathematics, and other disciplines.
Structure Enumeration is the study of methods for efficient
generation and analysis of such objects. The project will
involve exploitation and extension of recent advances, many
due to the CI, which have added orders of magnitude to what
was possible only a few ....Practical and theoretical aspects of structure enumeration. Many areas of study involve processing of large numbers of
objects in some class. These are countless examples in
chemistry, physics, mathematics, and other disciplines.
Structure Enumeration is the study of methods for efficient
generation and analysis of such objects. The project will
involve exploitation and extension of recent advances, many
due to the CI, which have added orders of magnitude to what
was possible only a few years ago. The outcome will be a
combination of theoretical results and practical achievements,
whose usefulness will be demonstrated with some serious
applications in physics and mathematics.
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