Mathematics of Cryptography. The Australian economy and society requires fast, reliable, and secure communication. Current first-generation security solutions are not capable of supporting the efficiency and scalability requirements of mass-market adoption of wireless and embedded consumer applications. New security infrastructures are emerging and must be carefully, but rapidly, defined. Thus developing new mathematically solid tools in this area is an important and urgent tasks. In addition, t ....Mathematics of Cryptography. The Australian economy and society requires fast, reliable, and secure communication. Current first-generation security solutions are not capable of supporting the efficiency and scalability requirements of mass-market adoption of wireless and embedded consumer applications. New security infrastructures are emerging and must be carefully, but rapidly, defined. Thus developing new mathematically solid tools in this area is an important and urgent tasks. In addition, the intended work advances our knowledge of the theory and the quality of our culture. As such, it will promote the Australian science and will also have many practical applications in Cryptography, Computer Security and E-Commerce.Read moreRead less
Algorithms and computation in four-dimensional topology. This project will establish Australia as a world leader in computational topology, particularly in the all-important areas of topology in three and four dimensions. In four dimensions this work will be truly groundbreaking; until now the field has seen little development due to the complexity of the algorithms and computations required, and the applicant is in the unique position of having the necessary tools to make significant progress ....Algorithms and computation in four-dimensional topology. This project will establish Australia as a world leader in computational topology, particularly in the all-important areas of topology in three and four dimensions. In four dimensions this work will be truly groundbreaking; until now the field has seen little development due to the complexity of the algorithms and computations required, and the applicant is in the unique position of having the necessary tools to make significant progress in a feasible time frame. In three dimensions this project will strengthen the distinguished computational topology community in Melbourne, led by pioneers such as Rubinstein, Goodman, Hodgson as well as the applicant himself.Read moreRead less
Dynamics of eigenvalue/eigenspace algorithms with applications to signal processing. Many problems in signal and systems lead naturally to an eigenvalue/eigenspace determination and tracking problem; for example (acoustic) echo-cancellation, crosstalk suppression in ADSL modems, direction of arrival determination with an array of sensors, linear system identification etc. Exploiting methods from global analysis and dynamical systems theory we will study the available algorithms for eigenspace de ....Dynamics of eigenvalue/eigenspace algorithms with applications to signal processing. Many problems in signal and systems lead naturally to an eigenvalue/eigenspace determination and tracking problem; for example (acoustic) echo-cancellation, crosstalk suppression in ADSL modems, direction of arrival determination with an array of sensors, linear system identification etc. Exploiting methods from global analysis and dynamical systems theory we will study the available algorithms for eigenspace determination to characterise their computational efficiency, accuracy and effectiveness in various data scenarios. The analysis will lead to improved designs for eigenvalue/eigenspace algorithms, as well as design tools to engineer algorithms to specific situations.Read moreRead less
Group actions: combinatorics, geometry and computation. Science today relies on digital technologies using quantised and digital information. Because of the discrete nature of digital information, much of the mathematics underpinning these advances comes from the core disciplines of algebra and combinatorics within which this proposal falls. All aspects of the proposal focus on strengthening theoretical understanding of algebraic and combinatorial structures, and increasing computational power f ....Group actions: combinatorics, geometry and computation. Science today relies on digital technologies using quantised and digital information. Because of the discrete nature of digital information, much of the mathematics underpinning these advances comes from the core disciplines of algebra and combinatorics within which this proposal falls. All aspects of the proposal focus on strengthening theoretical understanding of algebraic and combinatorial structures, and increasing computational power for working with them. The fundamental research outcomes, in terms of theorems, algorithms, and the training of young research mathematicians, will thus both enhance the high international standing of Australian mathematics, and strengthen Australia's capabilities in these important areas.Read moreRead less
Number Theoretic Methods in Cryptography. It is well known that Number Theory, besides its intrinsic beauty, provides many powerful tools for modern Cryptography. The aim of the project is to formulate and solve new and important mathematical problems, which lie in the background of modern cryptography. They are also of independent value for pure mathematics because they very often stimulate new approaches to and new surprising points of view on classical results and methods. The main outcome w ....Number Theoretic Methods in Cryptography. It is well known that Number Theory, besides its intrinsic beauty, provides many powerful tools for modern Cryptography. The aim of the project is to formulate and solve new and important mathematical problems, which lie in the background of modern cryptography. They are also of independent value for pure mathematics because they very often stimulate new approaches to and new surprising points of view on classical results and methods. The main outcome will be advancing our theoretical knowledge about several major cryptosystems. The project will extend and enrich the area of applications of mathematics to cryptography and related areas.Read moreRead less
Mathematics of Cryptography. The Australian society and economy requires fast, reliable, and secure communication. First-generation security solutions are not capable of supporting the efficiency and scalability requirements of mass-market adoption of wireless and embedded consumer applications. New security infrastructures are emerging and must be carefully, but rapidly, defined. Thus developing new mathematically solid tools in this area is one of the most important and urgent tasks. Besides, ....Mathematics of Cryptography. The Australian society and economy requires fast, reliable, and secure communication. First-generation security solutions are not capable of supporting the efficiency and scalability requirements of mass-market adoption of wireless and embedded consumer applications. New security infrastructures are emerging and must be carefully, but rapidly, defined. Thus developing new mathematically solid tools in this area is one of the most important and urgent tasks. Besides, the intended work advances our knowledge of the theory and the quality of our culture. As such, it will promote the Australian science and will also have many practical applications in Cryptography, Computer Security and E-Commerce.Read moreRead less
Multivariate Algorithmics: Meeting the Challenge of Real World computational complexity. This Project will result in better methods for designing the algorithms that all computer applications depend on. Algorithms are the instruction sets that tell computers how to process information. Some information processing tasks are intrinsically difficult, even for computers working at enormous speeds. This Project will deliver new mathematical approaches to overcome these difficulties. More efficient al ....Multivariate Algorithmics: Meeting the Challenge of Real World computational complexity. This Project will result in better methods for designing the algorithms that all computer applications depend on. Algorithms are the instruction sets that tell computers how to process information. Some information processing tasks are intrinsically difficult, even for computers working at enormous speeds. This Project will deliver new mathematical approaches to overcome these difficulties. More efficient algorithmic approaches for difficult problems enable advances in all areas of computer applications such as medical diagnosis and health prediction, national security, communications efficiency, industrial productivity and all fields of science and engineering.Read moreRead less
Algorithmics for Interactive 2.5D Graph Drawing. Technological advances have provided a data deluge over the past few years, and consequently have led to many large and complex network models in many domains. This includes terrorrist networks and biological networks, software engineering structures, and webgraphs. Visualisation is an effective tool in helping humans to understand such networks. This project aims to provide a new direction in network visualisation, using 2.5 dimensions. The algor ....Algorithmics for Interactive 2.5D Graph Drawing. Technological advances have provided a data deluge over the past few years, and consequently have led to many large and complex network models in many domains. This includes terrorrist networks and biological networks, software engineering structures, and webgraphs. Visualisation is an effective tool in helping humans to understand such networks. This project aims to provide a new direction in network visualisation, using 2.5 dimensions. The algorithms developed in the project will help security analysts to detect abnormal behavious such as money laundering, help biologists understand protein-protein interaction networks, and help engineers to understand large software systems.Read moreRead less
Efficient Pre-Processing of Hard Problems: New Approaches, Basic Theory and Applications. Computers store even larger amounts of data about all aspects of human and industrial activity. However, they have not become significantly better at solving common problems in optimization and search. Traditional complexity theory indicates many of these problems require algorithms that are very unlikely to exist. The Parameterized Complexity approach allows us to obtain very efficient algorithms for a lar ....Efficient Pre-Processing of Hard Problems: New Approaches, Basic Theory and Applications. Computers store even larger amounts of data about all aspects of human and industrial activity. However, they have not become significantly better at solving common problems in optimization and search. Traditional complexity theory indicates many of these problems require algorithms that are very unlikely to exist. The Parameterized Complexity approach allows us to obtain very efficient algorithms for a large variety of problems, but the machinery required was diverse and complicated. This research will organize the machinery into a new approach that systematically finds good algorithms by applying simplifications around a parameter of the domain of the problem. As a result, efficient algorithms are obtained for many diverse areas.Read moreRead less
Foundations of Nonmonotonic Logic Programming for Complex Knowledge Systems. This project will fundamentally provide a new paradigm of nonmonotonic logic programming. As such, it will significantly contribute towards Australia's leading role in the cutting edge research of intelligent systems development. The new nonmonotonic logic programming can be used as an effecive platform by many Australian computer companies for building complex knowledge systems in real world domains. Hence this projec ....Foundations of Nonmonotonic Logic Programming for Complex Knowledge Systems. This project will fundamentally provide a new paradigm of nonmonotonic logic programming. As such, it will significantly contribute towards Australia's leading role in the cutting edge research of intelligent systems development. The new nonmonotonic logic programming can be used as an effecive platform by many Australian computer companies for building complex knowledge systems in real world domains. Hence this project has potential economic and social benefits for Australia. With a very strong research team across different universities and a collaborative research training environment, this project will further enhance Australia's international reputation as a leader in computing & IT research.Read moreRead less