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
Solving inverse problems with Iterative regularisation and convex penalties. This project aims to develop and investigate new computational procedures for the solution of inverse problems which do not have the usual smoothness properties (or source conditions) required for the traditional regularisation methods. Examples of such inverse problems are very common and include image restoration, photo-acoustic tomography and spectroscopy. It is anticipated that this project will substantially extend ....Solving inverse problems with Iterative regularisation and convex penalties. This project aims to develop and investigate new computational procedures for the solution of inverse problems which do not have the usual smoothness properties (or source conditions) required for the traditional regularisation methods. Examples of such inverse problems are very common and include image restoration, photo-acoustic tomography and spectroscopy. It is anticipated that this project will substantially extend the toolbox of methods for such problems utilising ideas from Banach spaces, convex analysis, parallel computing and optimisation. This project is expected to make a substantial contribution to a better understanding of inverse problems and their solution procedures.Read moreRead less
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
Hypergraph models for complex discrete systems. This project aims to better understand the structure and properties of very large hypergraphs of various kinds. Hypergraphs are very general mathematical objects which can be used to model complex discrete systems. They arise naturally in many areas such as ecology, chemistry and computer science. Despite this, our theoretical understanding of very large, or random, hypergraphs lags far behind the intensely-studied special case of graphs. This proj ....Hypergraph models for complex discrete systems. This project aims to better understand the structure and properties of very large hypergraphs of various kinds. Hypergraphs are very general mathematical objects which can be used to model complex discrete systems. They arise naturally in many areas such as ecology, chemistry and computer science. Despite this, our theoretical understanding of very large, or random, hypergraphs lags far behind the intensely-studied special case of graphs. This project will answer many fundamental questions about large, random hypergraphs. The expected outcomes of the project also include new tools for working with hypergraphs, such as efficient algorithms for sampling hypergraphs. These outcomes will benefit researchers who use hypergraphs in their work and will enhance Australia's reputation for research in this area.Read moreRead less
A new model for random discrete structures: distributions, counting and sampling. Random discrete structures are used in countless applications across science for modelling complex systems. This project will study a new, very general model of random discrete structures which encapsulates both random networks and random matrices. This project will develop general tools for working with this model, thereby unlocking the model for use by practitioners in areas such as physics, biology, statistics a ....A new model for random discrete structures: distributions, counting and sampling. Random discrete structures are used in countless applications across science for modelling complex systems. This project will study a new, very general model of random discrete structures which encapsulates both random networks and random matrices. This project will develop general tools for working with this model, thereby unlocking the model for use by practitioners in areas such as physics, biology, statistics and cryptography. The questions that will be tackled are fundamental problems in probability, and include as special cases the analysis of subgraph distribution in models of random networks, and the joint distribution of entries of contingency tables, which are important in statistics.Read moreRead less
Dynamic Analysis and Control for Hybrid Systems and Networks. Hybrid systems are now accepted as the best way to model many high-tech situations in transport, energy management, networking, household and industrial automation. This project will develop the theoretical tools needed to ensure such systems operate stably and efficiently despite imperfections and outside disturbances.
Guiding principles and guardrails for genetic association studies. This project aims to investigate deep connections between genetic structure (population genetic processes, linkage disequilibrium and population structure) and the ability to statistically detect genetic variants responsible for variation in traits. The project expects to generate new knowledge in the areas of statistics, mathematics and biology through an innovative, multidisciplinary approach that synthesises and extends founda ....Guiding principles and guardrails for genetic association studies. This project aims to investigate deep connections between genetic structure (population genetic processes, linkage disequilibrium and population structure) and the ability to statistically detect genetic variants responsible for variation in traits. The project expects to generate new knowledge in the areas of statistics, mathematics and biology through an innovative, multidisciplinary approach that synthesises and extends foundational disciplinary results. Expected outcomes of this project include principles and methodology that underpin future genetic association studies by supplying a framework for interpreting results. This should provide significant benefits by reducing false conclusions and their associated costs.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
Linear Dynamical Quantum Networks: Synthesis and Control. Australia is recognized as a leader in the international race to develop quantum technologies of the future. This project will strengthen Australia's profile in quantum technology engineering by developing a new theory for building arbitrary complex linear quantum mechanical control systems for control tasks in quantum technology, and presenting new control system design tools to support high performance quantum communication systems. The ....Linear Dynamical Quantum Networks: Synthesis and Control. Australia is recognized as a leader in the international race to develop quantum technologies of the future. This project will strengthen Australia's profile in quantum technology engineering by developing a new theory for building arbitrary complex linear quantum mechanical control systems for control tasks in quantum technology, and presenting new control system design tools to support high performance quantum communication systems. The project outcomes together with advances in experimental physics are anticipated to play an important role in the long term as enablers of viable quantum technologies that can provide new commercial opportunities for Australian hi-tech industries to benefit Australia's economy in the future.Read moreRead less