Efficient Computational Methods for Constrained Path Problems. We consider a class of path design problems which arise when an object needs to traverse between two points through a specified region. The region may be a continuous space or the path may be restricted to the edges of a network. The path must optimise a prescribed criterion such
as risk, reliability or cost and satisfy a number of constraints.
Problems of this type readily arise in the defence, transport and
communication i ....Efficient Computational Methods for Constrained Path Problems. We consider a class of path design problems which arise when an object needs to traverse between two points through a specified region. The region may be a continuous space or the path may be restricted to the edges of a network. The path must optimise a prescribed criterion such
as risk, reliability or cost and satisfy a number of constraints.
Problems of this type readily arise in the defence, transport and
communication industries. In addition to efficient solution methods
for these problems the project will produce computational tools for
a wide range of related network routing problems.Read moreRead less
Automated Determination of the Pose of a Human from Visual Information - Markerless 3D Pose Recovery of Humans from Videos. The development of 3D human pose recovery has been sought by computer vision researchers for many years. Our results will, firstly, have benefit for Australia's standing in the international computer vision community. Over time, the research outcomes will be developed into a software product for rehabilitation analysis by recognizing discrepancies between the walking pat ....Automated Determination of the Pose of a Human from Visual Information - Markerless 3D Pose Recovery of Humans from Videos. The development of 3D human pose recovery has been sought by computer vision researchers for many years. Our results will, firstly, have benefit for Australia's standing in the international computer vision community. Over time, the research outcomes will be developed into a software product for rehabilitation analysis by recognizing discrepancies between the walking patterns of healthy individuals and those with abnormalities as a result of accidents or diseases. The Australian economy will benefit by the reduction in the lifetime cost of injuries. This software will also provide benefits to the movie animation, computer games industry, and the training of athletes.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
The stability of unsteady fluid flows in channels and pipes. The main benefit from this project will be a better theoretical understanding of the stability properties of unsteady fluid flows. The theoretical results obtained would help guide future experimental
investigations into the paths to turbulence in unsteady flows and would be a basis for future research in the increasingly important area of flow stability control. The project will also provide advanced training and skills transfer in a ....The stability of unsteady fluid flows in channels and pipes. The main benefit from this project will be a better theoretical understanding of the stability properties of unsteady fluid flows. The theoretical results obtained would help guide future experimental
investigations into the paths to turbulence in unsteady flows and would be a basis for future research in the increasingly important area of flow stability control. The project will also provide advanced training and skills transfer in an important area of fluid mechanics research.
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Special Research Initiatives - Grant ID: SR0354727
Funder
Australian Research Council
Funding Amount
$20,000.00
Summary
Mathematics for Government, Industry and Community -- The *Magic* Network. The *Magic* network will promote the use of mathematics by government, industry and community to analyse real problems and implement practical solutions. It will connect the most promising young Australian mathematicians to experienced researchers with strong research teams linked directly to the broader community. Our program will demand research excellence, emphasise a sustainable society, support outstanding young mat ....Mathematics for Government, Industry and Community -- The *Magic* Network. The *Magic* network will promote the use of mathematics by government, industry and community to analyse real problems and implement practical solutions. It will connect the most promising young Australian mathematicians to experienced researchers with strong research teams linked directly to the broader community. Our program will demand research excellence, emphasise a sustainable society, support outstanding young mathematicians and create opportunities for promising postgraduate students. We will offer scholarships for professional development and fund research visits and exchanges. *Magic* will provide tangible incentives for young Australian mathematicians and a new generation of researchers and research leaders.Read moreRead less
ARC Complex Open Systems Research Network. Complexity is the common frontier in the physical, biological and social sciences. This Network will link specialists in all three sciences through five generic conceptual and mathematical theme activities. It will promote research into how subsystems self-organise into new emergent structures when assembled into an open, non-equilibrium system. Outcomes will include new technologies and software tools and deeper understanding of fundamental questions i ....ARC Complex Open Systems Research Network. Complexity is the common frontier in the physical, biological and social sciences. This Network will link specialists in all three sciences through five generic conceptual and mathematical theme activities. It will promote research into how subsystems self-organise into new emergent structures when assembled into an open, non-equilibrium system. Outcomes will include new technologies and software tools and deeper understanding of fundamental questions in science. An essential function of the network will be introducing researchers end users to new tools and broadening the horizons of graduate students.Read moreRead less
Robust Reformulation Methods. Many decision problems in engineering, business and economics are modeled as nonlinear continuous optimization problems. Often these are made difficult by the existence of constraints. In this project, we reformulate such problems as constrained nonsmooth equations, rather than optimization problems, and develop generalized Newton and quasi-Newton methods for solving them. The expected outcomes of this project include a systematic theory of reformulation methods, ....Robust Reformulation Methods. Many decision problems in engineering, business and economics are modeled as nonlinear continuous optimization problems. Often these are made difficult by the existence of constraints. In this project, we reformulate such problems as constrained nonsmooth equations, rather than optimization problems, and develop generalized Newton and quasi-Newton methods for solving them. The expected outcomes of this project include a systematic theory of reformulation methods, and robust and efficient algorithms for solving some important nonlinear continuous optimization problems. There is high potential for applications in engineering, business and finance.Read moreRead less
Groups: statistics, structure, and algorithms. 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 workin ....Groups: statistics, structure, and algorithms. 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
Factorisation of Finite Groups and Graphs. The combinatorial structure of a graph is strongly influenced by its
symmetry, and the symmetry is described precisely by its group of
automorphisms. Interplay between actions of the automorphism group on
vertices, edges, and other configurations, reveals important graph
structure, especially the existence of graph factorisations. In turn, a group factorisation arises whenever a group has two
independent transitive actions, and these arise in parti ....Factorisation of Finite Groups and Graphs. The combinatorial structure of a graph is strongly influenced by its
symmetry, and the symmetry is described precisely by its group of
automorphisms. Interplay between actions of the automorphism group on
vertices, edges, and other configurations, reveals important graph
structure, especially the existence of graph factorisations. In turn, a group factorisation arises whenever a group has two
independent transitive actions, and these arise in particular while
determining graph automorphism groups, and graph factorisations. We will classify families of group factorisations, especially for simple groups, and apply this to establish a theory of symmetrical graph
factorisations, and to study Cayley graphs and 2-closures of permutation groups.
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Efficient computation in finite groups with applications in algebra and graph theory. The cutting-edge research of the project will further strengthen Australia's prominent role in computational group theory and algebraic graph theory. Besides the theoretical advances, the project includes the implementation and wide distribution of matrix group algorithms, benefiting immediately the algebraic research community and undergraduate mathematical education.