The mathematics and language of engineering uncertainty, preference and utility. Australian engineering firms are principals in many high-profile projects. To defend their position, they must demonstrate both sound engineering and quality processes, which by international standards includes the traceability of decisions. Yet, there are few tools to vet the multitude of decisions that go into large-scale engineering works. This project aims to form mathematical models of decision-making based on ....The mathematics and language of engineering uncertainty, preference and utility. Australian engineering firms are principals in many high-profile projects. To defend their position, they must demonstrate both sound engineering and quality processes, which by international standards includes the traceability of decisions. Yet, there are few tools to vet the multitude of decisions that go into large-scale engineering works. This project aims to form mathematical models of decision-making based on the language modelling of what is written in engineering documentation about the bases of decisions. The new methods will help decision makers to pinpoint irrationalities in decisions and notify them of possible errors. The research can therefore be applied to important problems in the engineering sector such as risk management.Read moreRead less
Algorithmic approaches to braids and their generalisations. This project combines theoretical methods from pure mathematics with computational experiments in order to gain new knowledge. The objects of interest, so-called braid groups and generalisations, are important for many fields of mathematics, but also have applications for data security. Both the theoretical outcomes of this project and the algorithms developed will strengthen Australia as a centre of cutting-edge research in computatio ....Algorithmic approaches to braids and their generalisations. This project combines theoretical methods from pure mathematics with computational experiments in order to gain new knowledge. The objects of interest, so-called braid groups and generalisations, are important for many fields of mathematics, but also have applications for data security. Both the theoretical outcomes of this project and the algorithms developed will strengthen Australia as a centre of cutting-edge research in computational algebra. Moreover, the results can lead to new technologies for protecting confidential data, which are more efficient and hence cheaper to implement than existing alternatives. Secure identification of legitimate users in the context of online banking is one possible field of application.Read moreRead less
Totally disconnected groups and their algebras. Groups are algebraic objects which convey symmetry much as
numbers convey size. For example, the symmetries of a
crystal form a crystallographic group and the classification of
crystallographic groups describes all possible crystal
structures. Totally disconnected groups arise as
symmetries of network structures having nodes and a `neighbour'
relation, as models of crystals do, but which are not rigid like
crystals. Powerful techniques for a ....Totally disconnected groups and their algebras. Groups are algebraic objects which convey symmetry much as
numbers convey size. For example, the symmetries of a
crystal form a crystallographic group and the classification of
crystallographic groups describes all possible crystal
structures. Totally disconnected groups arise as
symmetries of network structures having nodes and a `neighbour'
relation, as models of crystals do, but which are not rigid like
crystals. Powerful techniques for analysing totally
disconnected groups have recently been discovered and this
project aims to develop those techniques. The resulting
significant advances in the understanding of symmetry will
extend the range of applications of
group theory.
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Multiparameter Harmonic Analysis: Weighted Estimates for Singular Integrals. This project aims to study advanced harmonic analysis concerning multiparameter theory and related topics. Harmonic analysis lies at the intersection of the frontiers of many branches of mathematics. It is fundamental to the study of operator theory and partial differential equations which has wide applications in many fields such as mathematical modelling, probability and number theory. This project aims to solve a num ....Multiparameter Harmonic Analysis: Weighted Estimates for Singular Integrals. This project aims to study advanced harmonic analysis concerning multiparameter theory and related topics. Harmonic analysis lies at the intersection of the frontiers of many branches of mathematics. It is fundamental to the study of operator theory and partial differential equations which has wide applications in many fields such as mathematical modelling, probability and number theory. This project aims to solve a number of open problems at the frontier of research in modern harmonic analysis including estimates on multilinear operators with nonsmooth kernels and advanced multiparameter theory on product spaces.Read moreRead less
Totally disconnected groups in algebra and geometry. Mathematics research creates and develops new concepts for understanding the world. Group theory is a branch of mathematics based on our innate sense of symmetry. It was invented 200 hundred years ago and has grown into a language for analysing and classifying things ranging from wallpaper patterns to crystals, the fundamental particles of physics and Rubik's cube. The chief investigators have made significant breakthroughs in the study of sym ....Totally disconnected groups in algebra and geometry. Mathematics research creates and develops new concepts for understanding the world. Group theory is a branch of mathematics based on our innate sense of symmetry. It was invented 200 hundred years ago and has grown into a language for analysing and classifying things ranging from wallpaper patterns to crystals, the fundamental particles of physics and Rubik's cube. The chief investigators have made significant breakthroughs in the study of symmetry groups of networks, giving Australia an international lead in this research area. The project will develop the insights gained to make Australia a centre of expertise on these symmetry groups, which have applications to many areas including information and communication technology.Read moreRead less
Harmonic analysis: function spaces and singular integral operators. This project advances knowledge in harmonic analysis to new settings such as dyadic and multiparameter theories, Laplacian-like operators, and rough singular integrals. Outcomes will be solutions to long-standing problems, training of researchers, strong links with international researchers and enhancement of Australia's reputation in mathematics.
An knowledge-based approach to multi-document text summarisation for automated meta-analysis of the scientific literature. The biomedical sciences produce literature at an exponential rate, and the size of this knowledge base far exceeds the capacity of humans to keep up with the growth in new knowledge. This project will develop computational text summarisation methods to abstract the content of scientific journal articles reporting clinical trials, and develop multi-document summarisation meth ....An knowledge-based approach to multi-document text summarisation for automated meta-analysis of the scientific literature. The biomedical sciences produce literature at an exponential rate, and the size of this knowledge base far exceeds the capacity of humans to keep up with the growth in new knowledge. This project will develop computational text summarisation methods to abstract the content of scientific journal articles reporting clinical trials, and develop multi-document summarisation methods to synthesise these abstracts using automated statistical meta-analysis methods. These methods have broad potential to improve text-summarisation technologies in general, to profoundly enhance our ability to integrate published knowledge, and to make a highly significant and specific contribution to improving the quality of evidence used in health decision-making. Read moreRead less
Defence and Security Risk Assessment using Agent Based Distillations. Today's society continues to be occupied with the idea of risk. The recent events of September 11th, the Bali bombing, SARS, the bush fires in Canberra, and the Tsunami are examples of human-made and natural disasters. These events had dramatic consequences on the social, economic, and political environment and numerous industries. This project offers an innovative methodological paradigm for assessing risk through the transfe ....Defence and Security Risk Assessment using Agent Based Distillations. Today's society continues to be occupied with the idea of risk. The recent events of September 11th, the Bali bombing, SARS, the bush fires in Canberra, and the Tsunami are examples of human-made and natural disasters. These events had dramatic consequences on the social, economic, and political environment and numerous industries. This project offers an innovative methodological paradigm for assessing risk through the transfer of technologies drawn from defence simulations to the safety and security areas. The success of this project will mark a paradigm shift in the area of risk assessment and management.Read moreRead less
Computational Methods for the Social Accounting of Teamwork. The cornerstone of the knowledge industries underlying the Australian economy is not just mechanical efficiency but also teamwork productivity. The increasing trend toward placing Australian employees nearer to their customers means that Australian companies face an even greater challenge in managing effective teamwork. This research examines the pragmatics and theoretical issues of developing computer-based systems that enable real-ti ....Computational Methods for the Social Accounting of Teamwork. The cornerstone of the knowledge industries underlying the Australian economy is not just mechanical efficiency but also teamwork productivity. The increasing trend toward placing Australian employees nearer to their customers means that Australian companies face an even greater challenge in managing effective teamwork. This research examines the pragmatics and theoretical issues of developing computer-based systems that enable real-time assessments of teamwork productivity. Automated assessments of how well relationships are progressing in teams will enable them to realise the same levels of productivity gains that automated workflow management has facilitated.Read moreRead less
Constructive Representation Theory and its Applications. The algorithms developed will make it possible to determine the different ways (representations) in which a group of symmetries may be realised as transformations of some space. Such knowledge is required in many areas including differential equations, digital signal processing, engineering ('strut-and-cable' constructions), the design of telephone networks, crystallography and quantum information processing. The high-performance tools fo ....Constructive Representation Theory and its Applications. The algorithms developed will make it possible to determine the different ways (representations) in which a group of symmetries may be realised as transformations of some space. Such knowledge is required in many areas including differential equations, digital signal processing, engineering ('strut-and-cable' constructions), the design of telephone networks, crystallography and quantum information processing. The high-performance tools for linear algebra developed will also find application in cryptography and coding theory. This work represents the latest stage in a long-term project to discover practical algorithms for elucidating the properties of complex algebraic structures - an area where Australia is a world-leader.Read moreRead less