Parameterized Algorithm Design and Complexity Analysis: New Methods and Strategic Applications in the FPT Algorithmic Server Project. A fundamental discovery of the first decades of computer science is that completely efficient (polynomial time) algorithms probably do not exist for thousands of natural computational problems. The project will result in new methods for designing and analyzing algorithms for hard problems with natural parameters, and in improved
algorithms for these problems.
Evolutionary algorithms for problems in functional genomics data analysis. Skin cancer has a high incidence in the Australian population. Schizophrenia is a psychiatric disorder that affects a significant proportion of the population worldwide. Both illnesses have genetic roots and can be triggered by environmental factors. We will uncover genetic relationship to disease and their responses to environmental conditions using computational methods and mathematical algorithms that can aid in the de ....Evolutionary algorithms for problems in functional genomics data analysis. Skin cancer has a high incidence in the Australian population. Schizophrenia is a psychiatric disorder that affects a significant proportion of the population worldwide. Both illnesses have genetic roots and can be triggered by environmental factors. We will uncover genetic relationship to disease and their responses to environmental conditions using computational methods and mathematical algorithms that can aid in the determination of function, especially in disease states. Understanding the complex genetic interactions that trigger these illnesses would give great benefits in preventive health care, skin cancer and schizophrenia genetic basis, and may lay the ground for building new methods for "personalized medicine".
Read moreRead less
Group orbits in garmonic analysis and ergodic theory. Researchers from many areas need a type of mathematical analysis which involves the behaviour of a system - which may be a set of data points - under repeated application of some operation or group of operations. The structures arising from this kind of process are known as group orbits. The project gives information about their nature. Two major types of orbits are considered, coming from actions of discrete groups on measure spaces, and fro ....Group orbits in garmonic analysis and ergodic theory. Researchers from many areas need a type of mathematical analysis which involves the behaviour of a system - which may be a set of data points - under repeated application of some operation or group of operations. The structures arising from this kind of process are known as group orbits. The project gives information about their nature. Two major types of orbits are considered, coming from actions of discrete groups on measure spaces, and from smooth actions of Lie groups on manifolds, where powerful geometric methods are available. The project will yield new understandings of entropy, and new approaches to Fourier analysis.Read moreRead less
Symmetries in analysis. Technical research is like an iceberg. The 10% you see in applications is supported by 90% hidden, long-term, sometimes abstruse or theoretical-sounding work. The area of mathematical analysis has, for over 200 years, proved its worth as part of the unseen 90%, giving us such important tools as Fourier analysis, statistical mechanics and quantum mechanics. Australia is known as a world leader in mathematical analysis, and it is important for the country to maintain that e ....Symmetries in analysis. Technical research is like an iceberg. The 10% you see in applications is supported by 90% hidden, long-term, sometimes abstruse or theoretical-sounding work. The area of mathematical analysis has, for over 200 years, proved its worth as part of the unseen 90%, giving us such important tools as Fourier analysis, statistical mechanics and quantum mechanics. Australia is known as a world leader in mathematical analysis, and it is important for the country to maintain that edge in a number of key disciplines, so we can continue to participate in global technological advance. The project has an international focus which will enable that to happen. It will also provide training for the next generation of mathematicians. Read moreRead less
Dynamical systems: theory and practice. Mathematical science has proven a crucial platform for science and technology: it may have a long lead-time to application but its impacts are more profound than glamorous technical developments. Australia has an economic imperative to maintain investment in fundamental mathematics. Dynamical systems underpin a wide range of applications in physics, engineering, information science, finance and economics. This project will improve our capacity to model sy ....Dynamical systems: theory and practice. Mathematical science has proven a crucial platform for science and technology: it may have a long lead-time to application but its impacts are more profound than glamorous technical developments. Australia has an economic imperative to maintain investment in fundamental mathematics. Dynamical systems underpin a wide range of applications in physics, engineering, information science, finance and economics. This project will improve our capacity to model systems and to study their evolution, giving us better predictive power. It will keep Australia in the forefront of international research, providing a basis of expertise not otherwise available to Australian researchers and industry. Read moreRead less
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.
Application of novel exact combinatorial optimisation techniques and metaheuristic methods for problems in cancer research. Novel biotechnologies are offering an unprecedented opportunity to understand the genetic basis of cancer development and progression. However, they present us with a challenge; new computational methods and improved mathematical models and algorithms need to be introduced to complement these technologies in the determination of the function of our individual genetic makeup ....Application of novel exact combinatorial optimisation techniques and metaheuristic methods for problems in cancer research. Novel biotechnologies are offering an unprecedented opportunity to understand the genetic basis of cancer development and progression. However, they present us with a challenge; new computational methods and improved mathematical models and algorithms need to be introduced to complement these technologies in the determination of the function of our individual genetic makeup, especially in connection with disease states. The project will deal with research questions and datasets related to some of the highest incidence cancers in Australia. This project will contribute towards the development of new powerful algorithms for pattern recognition for future "personalized" molecular diagnostics methods.Read moreRead less
Constrained and Stable Solutions of Nonlinear and Semismooth Equations. In this project, comprehensive models for designing safe power system parameters will be proposed, efficient algorthms for solving these models will be constructed. The new models and algorithms in this project will provide efficient tools to prevent catastrophic events in power systems, which is related with national security. This project will also strengthen collaboration of Australian applied
mathematians with inter ....Constrained and Stable Solutions of Nonlinear and Semismooth Equations. In this project, comprehensive models for designing safe power system parameters will be proposed, efficient algorthms for solving these models will be constructed. The new models and algorithms in this project will provide efficient tools to prevent catastrophic events in power systems, which is related with national security. This project will also strengthen collaboration of Australian applied
mathematians with international researchers and engineering scientists. This is important for the advance of science and technology in
Australia.Read moreRead less
Monotreme immune system provides insights into their evolutionary relationships. Genes of immunological importance will be cloned and characterised from the short-beaked echidna with the purpose of investigating the immune system in monotremes, gaining insights into the timing and order of evolutionary separation of the three extant mammalian groups:- the Prototherians (monotremes), the Metatherians (marsupials) and Eutherians (placentals), increasing understanding of the evolution of the verteb ....Monotreme immune system provides insights into their evolutionary relationships. Genes of immunological importance will be cloned and characterised from the short-beaked echidna with the purpose of investigating the immune system in monotremes, gaining insights into the timing and order of evolutionary separation of the three extant mammalian groups:- the Prototherians (monotremes), the Metatherians (marsupials) and Eutherians (placentals), increasing understanding of the evolution of the vertebrate immune system and providing the basis for making immunological reagents which are necessary for studying monotreme diseases (as a precautionary conservation strategy).Read moreRead less
Functional and harmonic analysis of function spaces: synthesis, development and applications. Recent advances in mathematics are on the borderlines of its branches. This interdisciplinary project develops and binds the research areas attracting growing interest of prominent mathematicians during the last 30 years because of not only its theoretical value, but also its ties with the key equations describing a multitude of physical phenomena and the theoretical foundation of numerical methods. Th ....Functional and harmonic analysis of function spaces: synthesis, development and applications. Recent advances in mathematics are on the borderlines of its branches. This interdisciplinary project develops and binds the research areas attracting growing interest of prominent mathematicians during the last 30 years because of not only its theoretical value, but also its ties with the key equations describing a multitude of physical phenomena and the theoretical foundation of numerical methods. The Euler, Helmholtz, Lamb, Navier-Stokes and acoustic equations, studied in terms of function spaces, govern incompressible viscous fluid flows and wave propagations. Contributing to both pure mathematics and, particularly, Short-Term Tsunami Prediction, the project will enhance Australia's research reputation.Read moreRead less