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
Complex data, model selection and bootstrap inference. The project will provide new statistical methods and associated software for the analysis and modelling of complex data, as well as quality research training. This project will benefit researchers in statistics and users of statistics who encounter the complex data considered in this project and who need to model and make inferences from these data. Since these kinds of data arise in many areas (such as medicine, genetics, chemistry etc), ....Complex data, model selection and bootstrap inference. The project will provide new statistical methods and associated software for the analysis and modelling of complex data, as well as quality research training. This project will benefit researchers in statistics and users of statistics who encounter the complex data considered in this project and who need to model and make inferences from these data. Since these kinds of data arise in many areas (such as medicine, genetics, chemistry etc), Australia and Australian industry will ultimately benefit from the proposed research. The strengthening of international link and the training of highly trained research scientists in an area of national importance will also benefit Australia.Read moreRead less
Use of Interval Arithmetic and GRID Computing in Computational Molecular Science: Bounding Errors and Locating Global Minima. Catastrophic failure of the Ariane 5 rocket in 1996 and the inability of Patriot missile systems to reach their targets during the 1991 Gulf war were both attributed to numerical computing errors. Less dramatic, but in a similar vein, this project aims to study the numerical stability of contemporary computational molecular science applications. The focus will be on linea ....Use of Interval Arithmetic and GRID Computing in Computational Molecular Science: Bounding Errors and Locating Global Minima. Catastrophic failure of the Ariane 5 rocket in 1996 and the inability of Patriot missile systems to reach their targets during the 1991 Gulf war were both attributed to numerical computing errors. Less dramatic, but in a similar vein, this project aims to study the numerical stability of contemporary computational molecular science applications. The focus will be on linear scaling electronic structure codes, methods that are critical to the study of nano- and bio-materials, and are therefore of great importance to our economic future and medical well being. The project will build expertise within Australia in the area of interval arithmetic, an area that is currently poorly represented.Read moreRead less
Parallel and Distributed Machine Learning - Smart Data Analysis in the Multicore Era. In large data centres our research will lead to reduced energy consumption by using graphics cards which have a much better computation to power ratio than traditional processors. On desktop computers, it will make machine learning practical by enabling efficient algorithms for spam filtering and content analysis. On networked systems it will lead to distributed inference, caching and collaborative filtering ap ....Parallel and Distributed Machine Learning - Smart Data Analysis in the Multicore Era. In large data centres our research will lead to reduced energy consumption by using graphics cards which have a much better computation to power ratio than traditional processors. On desktop computers, it will make machine learning practical by enabling efficient algorithms for spam filtering and content analysis. On networked systems it will lead to distributed inference, caching and collaborative filtering applications which will both reduced the bandwidth required and make the internet safer for users. Finally, it will enable rapid deployment of sensor networks for monitoring and detection, such as for environmental monitoring and safeguarding Australia's borders.Read moreRead less
Equations of Monge-Ampere type and applications. Many fundamental problems in geometry, physics and applied sciences are related to equations of Monge-Ampere type. In recent years there have been rapid developments in the study of these equations with major breakthroughs made by the proposers. This project aims at new discoveries and findings in theory and applications by resolving outstanding open problems, and enhance Australian leadership, expertise, and training in key areas of mathematics a ....Equations of Monge-Ampere type and applications. Many fundamental problems in geometry, physics and applied sciences are related to equations of Monge-Ampere type. In recent years there have been rapid developments in the study of these equations with major breakthroughs made by the proposers. This project aims at new discoveries and findings in theory and applications by resolving outstanding open problems, and enhance Australian leadership, expertise, and training in key areas of mathematics and its applications.Read moreRead less
Singularities and surgery in geometric evolution equations. The analysis of geometric evolution equations is a very active area of mathematical research internationally. The applications of such systems to physical problems such as crystal growth and flame propagation are also of great interest in the broader scientific community. The proposed research addresses questions central to the understanding of curvature flows. The project will yield internationally significant results in theoretical ....Singularities and surgery in geometric evolution equations. The analysis of geometric evolution equations is a very active area of mathematical research internationally. The applications of such systems to physical problems such as crystal growth and flame propagation are also of great interest in the broader scientific community. The proposed research addresses questions central to the understanding of curvature flows. The project will yield internationally significant results in theoretical mathematics, with applications in physics, engineering and image processing. These results will enhance Australia's reputation for high quality theoretical mathematical research with real world applications.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
Novel geometric invariants. Quantum theory is the language of fundamental physics, it describes the small scale structure of matter and possibly space-time. Sophisticated models in condensed matter physics and string theory have exposed geometric and topological structure as basic building blocks of the theory. Issues thrown up by quantum theory are very similar to, and have provided techniques to solve, problems in the geometry of three and four dimensional manifolds. Exciting two way exchanges ....Novel geometric invariants. Quantum theory is the language of fundamental physics, it describes the small scale structure of matter and possibly space-time. Sophisticated models in condensed matter physics and string theory have exposed geometric and topological structure as basic building blocks of the theory. Issues thrown up by quantum theory are very similar to, and have provided techniques to solve, problems in the geometry of three and four dimensional manifolds. Exciting two way exchanges of methods, problems and solutions have emerged. This project aims to settle fundamental questions in the interaction between these two fields.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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Modular Index Theory. This project capitilises on Australian advances in mathematics, particularly noncommutative geometry. It will maintain and extend Australia's prominence in this subject, providing excellent opportunities for young researchers via the research networks this project will establish. Being at the interface of ideas in mathematics and physics, there is potential for future technological spin offs for Australia.