A comparative study of generalised solution concepts for elliptic partial differential equations using nonsmooth analysis techniques. The solution of ellpitic partial differential equations is central to science and engineering. There are a number of solution concepts, such as those of weak solutions and viscosity solutions, but the relations between these are incompletely understood. We shall investigate this major question using recent advances in optimisation theory and nonsmooth analysis. ....A comparative study of generalised solution concepts for elliptic partial differential equations using nonsmooth analysis techniques. The solution of ellpitic partial differential equations is central to science and engineering. There are a number of solution concepts, such as those of weak solutions and viscosity solutions, but the relations between these are incompletely understood. We shall investigate this major question using recent advances in optimisation theory and nonsmooth analysis. Our approach is to use various approximations and their associated second-order subdifferentials, each of which implies a generalised solution concept and associated abstract convexity. Particular attention, including computational details, will be given to equations which have very different solutions of one type from those of another.Read moreRead less
Operator Integrals and Derivatives. The project is a contribution to the study of non-commutative differential and integral calculus. The novelty of the present project lies in the study of smoothness properties of functions whose domains and ranges are spaces of unbounded, non-commuting operators on some Hilbert space. Our general approach will be based on a detailed investigation of properties of double operator integrals, which permit smoothness estimates of operator-functions. It can be expe ....Operator Integrals and Derivatives. The project is a contribution to the study of non-commutative differential and integral calculus. The novelty of the present project lies in the study of smoothness properties of functions whose domains and ranges are spaces of unbounded, non-commuting operators on some Hilbert space. Our general approach will be based on a detailed investigation of properties of double operator integrals, which permit smoothness estimates of operator-functions. It can be expected that the new techniques generated will find further application in areas of mathematical physics and non-commutative geometry related to quantized calculus.
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Non-commutative analysis and differential calculus. This project is in an area of central mathematical importance and will lead to important scientific advances that will keep Australia at the forefront internationally in this field of research. There is an emphasis on international networking and we will collaborate with leading researchers in USA and France.
Option pricing via path integrals: a new perspective. The risk management of derivative securities is a very exciting challenge for financial market researchers. The knowledge base resulting from this proposal will benefit both large financial institutions and Australia's financial system by creating a more competitive and efficient economic environment, which will inevitably lead to more gross domestic product (GDP) gains.Furthermore a large amount of software and numerical analysis work to be ....Option pricing via path integrals: a new perspective. The risk management of derivative securities is a very exciting challenge for financial market researchers. The knowledge base resulting from this proposal will benefit both large financial institutions and Australia's financial system by creating a more competitive and efficient economic environment, which will inevitably lead to more gross domestic product (GDP) gains.Furthermore a large amount of software and numerical analysis work to be developed during the project can be turned into IP for Australia. This will contribute to catalysing development of internationally competitive financial risk management software industry.Read moreRead less
Nonlinear spatial and spatiotemporal econometrics: theory with applications. Modern societies like Australia have major challenges in the forecasting, measuring and managing of risks associated with global economic and environmental/climate changes. These tasks require advanced econometric techniques in modelling and forecasting of complex nonlinear spatiotemporal variability in economic and social systems. This project will develop frontier econometric technologies that enable more accurate eco ....Nonlinear spatial and spatiotemporal econometrics: theory with applications. Modern societies like Australia have major challenges in the forecasting, measuring and managing of risks associated with global economic and environmental/climate changes. These tasks require advanced econometric techniques in modelling and forecasting of complex nonlinear spatiotemporal variability in economic and social systems. This project will develop frontier econometric technologies that enable more accurate economic and climate forecasts. The tools produced will provide Australia's scientists and policy-makers with a greater capacity to manage the risks associated with these challenges. A side-benefit of the research will be high-quality publications that enhance the nation's reputation in this cutting edge research.Read moreRead less
Operator-Analytic Methods in Telecommunication Systems. Many systems in information technology and telecommunications evolve under conditions of uncertainty. In this context, mathematical modelling is an essential component of the design process. We shall provide techniques for analysing a class of mathematical models, called operator-analytic models, which can be used to study many of the above-mentioned systems, such as the Internet. This project will deliver efficient numerical algorithms tha ....Operator-Analytic Methods in Telecommunication Systems. Many systems in information technology and telecommunications evolve under conditions of uncertainty. In this context, mathematical modelling is an essential component of the design process. We shall provide techniques for analysing a class of mathematical models, called operator-analytic models, which can be used to study many of the above-mentioned systems, such as the Internet. This project will deliver efficient numerical algorithms that will make possible practical analysis of operator-analytic models.Read moreRead less
The Male Partner Contribution To Pregnancy Immune Tolerance Deficit In Women
Funder
National Health and Medical Research Council
Funding Amount
$1,462,925.00
Summary
A complication-free pregnancy and birth of a healthy infant depends on adequate preparation of the mother's immune system to tolerate the 'foreign' fetus, Both the mother and the father contribute to establishing optimal immune tolerance. This project will determine the links between specific agents in male seminal fluid and the female immune response, and will make progress towards new diagnostic tests and treatment options for unexplained subfertility and gestational disorders.
Molecular Profiling Of The Immunoglobulin Proteome In Primary Sjögren’s Syndrome
Funder
National Health and Medical Research Council
Funding Amount
$322,460.00
Summary
Primary Sjögren’s syndrome is a common autoimmune disease. The patients have high levels of circulating immunoglobulins (Igs) in their blood-a hallmark of the disorder. The applicant proposes to sequence these Igs and identify their so-called variable region molecular signatures. These signatures can then be used in a mass spectrometric-based diagnostic platform to identify unique clones in patients as early markers of the disease process, and hopefully lead to more relevant diagnostic markers.
Nonlinear Panel Data Econometrics: Theory and Practice. This research addresses the ARC National Research Priorities Goal of 'An Environmentally Sustainable Australia', specifically 'Reducing and capturing emissions in transport and energy generation'. Avoiding, managing, and/or adapting to the climate change impacts is now the most pressing global environmental problem. This project will produce tangible and original insights into policy options for institutional adjustment to future climate ....Nonlinear Panel Data Econometrics: Theory and Practice. This research addresses the ARC National Research Priorities Goal of 'An Environmentally Sustainable Australia', specifically 'Reducing and capturing emissions in transport and energy generation'. Avoiding, managing, and/or adapting to the climate change impacts is now the most pressing global environmental problem. This project will produce tangible and original insights into policy options for institutional adjustment to future climate change in Australia; will provide insight into the scope for positive community behavioural change; and possible transformations in Australian social debate to maximise adaptive capacity. It will also strengthen and produce original conceptual approaches and research methods.Read moreRead less
ARC Financial Integrity Research Network. The integrity of the financial system is constantly under stress because of the development of ever more complex financial instruments, structures and strategies, and the associated research technologies that continues to accelerate worldwide. FIRN's vision is to harness the considerable strengths of Australia's internationally renowned finance, accounting and economics researchers into a research agenda to address issues concerning the integrity of the ....ARC Financial Integrity Research Network. The integrity of the financial system is constantly under stress because of the development of ever more complex financial instruments, structures and strategies, and the associated research technologies that continues to accelerate worldwide. FIRN's vision is to harness the considerable strengths of Australia's internationally renowned finance, accounting and economics researchers into a research agenda to address issues concerning the integrity of the financial system. It will enable Australian research in this area to match the scale and impact of similar research in other major international financial centres, and play an essential role in placing Australia among the world's leaders in financial markets related research.Read moreRead less