Mathematical Methods for Next Generation Sequencing. The emergence of a new generation of high throughput genomic sequencing technologies is providing unprecedented opportunities for biological research. Hidden within the huge amounts of data generated by this technology is information about the expression and regulation of genes, and the complex functional purpose of non-coding, so called 'junk', DNA. Development of mathematical and statistical tools is essential to interpreting these data. The ....Mathematical Methods for Next Generation Sequencing. The emergence of a new generation of high throughput genomic sequencing technologies is providing unprecedented opportunities for biological research. Hidden within the huge amounts of data generated by this technology is information about the expression and regulation of genes, and the complex functional purpose of non-coding, so called 'junk', DNA. Development of mathematical and statistical tools is essential to interpreting these data. The proposed research will enhance Australia's reputation for developing novel quantitative techniques at the cutting edge of modern biology. The proposed project has a broad range of potential applications in biotechnology, particularly in the medical and agricultural industries.Read moreRead less
Statistical and Mathematical Analyses of Sequence and Array Data. Development of mathematical and statistical methods and tools in bioinformation science will ensure that Australia is at the cutting-edge of modern biology. This will enhance Australia's reputation for dealing with the exponentially growing body of genomic data emerging from life sciences laboratories throughout the world. The proposed project has a broad range of potential applications in biotechnology, particularly in the medic ....Statistical and Mathematical Analyses of Sequence and Array Data. Development of mathematical and statistical methods and tools in bioinformation science will ensure that Australia is at the cutting-edge of modern biology. This will enhance Australia's reputation for dealing with the exponentially growing body of genomic data emerging from life sciences laboratories throughout the world. The proposed project has a broad range of potential applications in biotechnology, particularly in the medical and agricultural industries. Examples include improvements to livestock, in plant breeding such as drought resistance, and better genetic disease diagnosis, including earlier cancer diagnosis, and personalised treatment.Read moreRead less
New mathematical and statistical methods that inform the control of infectious disease outbreaks. Emerging infectious diseases are an ever-present threat to our community, as highlighted by the recent SARS epidemic and current fears concerning avian influenza. The research proposed by this project will help policy makers implement effective border control and outbreak control against a variety of emerging and re-emerging infectious diseases, including SARS, influenza and the deliberate release o ....New mathematical and statistical methods that inform the control of infectious disease outbreaks. Emerging infectious diseases are an ever-present threat to our community, as highlighted by the recent SARS epidemic and current fears concerning avian influenza. The research proposed by this project will help policy makers implement effective border control and outbreak control against a variety of emerging and re-emerging infectious diseases, including SARS, influenza and the deliberate release of an infectious disease such as smallpox. The project will enhance preparedness through a better understanding of the relative merits of different control strategies, and provide new methodology that can dynamically guide border and outbreak control in the midst of an outbreak by making effective use of data. Read moreRead less
Fundamental mathematical structures in statistical and quantum systems. Mathematics is playing a key role in modern science and technology. This project will bring together world leading experts from Australia and the USA to unravel the most fundamental mathematical structures in of statistical and quantum systems arising in settings ranging from physics of tiny quantum dots to string theory in high energy physics. This research will ensure Australia's involvement in cutting-edge international d ....Fundamental mathematical structures in statistical and quantum systems. Mathematics is playing a key role in modern science and technology. This project will bring together world leading experts from Australia and the USA to unravel the most fundamental mathematical structures in of statistical and quantum systems arising in settings ranging from physics of tiny quantum dots to string theory in high energy physics. This research will ensure Australia's involvement in cutting-edge international developments in mathematical sciences poised to deliver new significant results in the fundamental quantum theory of matter. The project will also contribute to training young researchers to maintain Australia's international standing in fundamental science.Read moreRead less
Quantization of polyhedral surfaces. Recent developments in the theory of discrete surfaces have revealed their fascinating links to many other areas of mathematics including integrable systems and quantum geometry. Rapid progress in this field is motivated by applications in pure mathematics, mathematical physics, computer graphics and engineering. Australian researchers are world recognized experts in integrable systems and this project will link them together with German experts in discrete d ....Quantization of polyhedral surfaces. Recent developments in the theory of discrete surfaces have revealed their fascinating links to many other areas of mathematics including integrable systems and quantum geometry. Rapid progress in this field is motivated by applications in pure mathematics, mathematical physics, computer graphics and engineering. Australian researchers are world recognized experts in integrable systems and this project will link them together with German experts in discrete differential geometry. The project will advance our knowledge base in fundamental and applied sciences and offer a unique research training opportunity for students in contemporary areas of pure and applied mathematics.Read moreRead less
Invariants of singular spaces from noncommutative geometry. The project addresses questions of significance at the international forefront in the mathematical sciences and the ARC funds will enable research training of students and postdoctoral fellows at this very high level. International collaboration and networking is a key feature that will enhance Australia's scientific standing and provide opportunities for early career researchers to engage internationally with world leaders. The mainten ....Invariants of singular spaces from noncommutative geometry. The project addresses questions of significance at the international forefront in the mathematical sciences and the ARC funds will enable research training of students and postdoctoral fellows at this very high level. International collaboration and networking is a key feature that will enhance Australia's scientific standing and provide opportunities for early career researchers to engage internationally with world leaders. The maintenance of a high quality research program at ANU enhances Australia's ability to attract international students and places the ANU in the top league of world universities. It brings with it recognition of Australia as a culturally advanced nation.Read moreRead less
Quantum many-body systems with higher mathematical symmetries. Ongoing developments in the experimental realisation of ultracold quantum systems play a leading role in the international effort towards the eventual realisation of quantum technology. This project brings together Australian and US researchers with complementary strengths to develop the mathematical study of fundamental systems of interacting quantum particles of relevance to experiments. The project will ensure that Australian rese ....Quantum many-body systems with higher mathematical symmetries. Ongoing developments in the experimental realisation of ultracold quantum systems play a leading role in the international effort towards the eventual realisation of quantum technology. This project brings together Australian and US researchers with complementary strengths to develop the mathematical study of fundamental systems of interacting quantum particles of relevance to experiments. The project will ensure that Australian researchers participate in and benefit from international developments in a leading edge area of fundamental research. It will also contribute to training students in rapidly advancing areas with the capacity to contribute to a wide range of problems, including the emerging technology of quantum devices.Read moreRead less
The mathematical analysis of ultracold quantum gases. Ongoing developments in the experimental realisation of ultracold quantum
gases play a leading role in the international effort towards the
eventual realisation of quantum technology. This project brings together Australian
researchers with complementary strengths to develop a sophisticated range of innovative
mathematical tools for understanding these fundamental quantum systems. The expected
outcomes will thus include potentially far r ....The mathematical analysis of ultracold quantum gases. Ongoing developments in the experimental realisation of ultracold quantum
gases play a leading role in the international effort towards the
eventual realisation of quantum technology. This project brings together Australian
researchers with complementary strengths to develop a sophisticated range of innovative
mathematical tools for understanding these fundamental quantum systems. The expected
outcomes will thus include potentially far reaching impacts on downstream quantum technology.
The project will contribute to training mathematically talented students and thus take essential
steps to establish the long term future of mathematical physics in Australia. It will also establish enduring key international research links.Read moreRead less
A new generation of fractals: theory, computation, and applications particularly to digital imaging. The project develops the mathematical and algorithmic foundations of superfractals and applies these results to a number of different areas, including in particular, digital imaging. For example, the ``third generation'' of mobile communications (3G), combines wireless mobile technology with high data transmission capacities. Currently the requirement for extensive bandwidth is a problem for e ....A new generation of fractals: theory, computation, and applications particularly to digital imaging. The project develops the mathematical and algorithmic foundations of superfractals and applies these results to a number of different areas, including in particular, digital imaging. For example, the ``third generation'' of mobile communications (3G), combines wireless mobile technology with high data transmission capacities. Currently the requirement for extensive bandwidth is a problem for efficient use. Superfractals and the associated colouring algorithm could be used to develop a new system to produce synthetic content for wireless devices that would require only low bandwidth.Read moreRead less
Geometric methods in quantum theory. Quantum theory is the fundamental language of physics, it describes the small scale structure of matter and possibly space-time. The advent of sophisticated models, particularly of quarks has emphasised geometric structure as a basic component of the theory. The issues thrown up by quantum theory are similar to problems encountered in the geometry of manifolds so that tools from the latter have been successfully employed in the former and vice-versa. ....Geometric methods in quantum theory. Quantum theory is the fundamental language of physics, it describes the small scale structure of matter and possibly space-time. The advent of sophisticated models, particularly of quarks has emphasised geometric structure as a basic component of the theory. The issues thrown up by quantum theory are similar to problems encountered in the geometry of manifolds so that tools from the latter have been successfully employed in the former and vice-versa. Previous work of the Chief Investigators has shown the importance of geometric structures known as gerbes which this Project will extend and apply in novel ways.Read moreRead less