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
Towards the prime power conjecture. This project attacks a famous and long standing conjecture in pure mathematics that has important ramifications in many applied areas. The project aims to determine when it is possible to produce more efficient codes for electronic communication and statistically balanced designs for experiments in areas as diverse as agriculture and psychology.
Australian Laureate Fellowships - Grant ID: FL120100125
Funder
Australian Research Council
Funding Amount
$1,796,966.00
Summary
Advances in the analysis of random structures and their applications. This project will provide new approaches, insights and results for probabilistic combinatorics. This area has contributed in exciting ways elsewhere in mathematics and provides versatile tools of widespread use in algorithmic computer science, with other applications in physics, coding theory for communications, and genetics.
A new approach to compressed sensing. Compressed sensing is an exciting new paradigm promising vastly improved signal sampling and reconstruction in a wide variety of applications including digital cameras, mobile phones and MRI machines. This project will explore a newly discovered approach to compressed sensing which uses mathematical arrays known as hash families.
Expander graphs, isoperimetric numbers, and forwarding indices. Expanders are sparse but well connected networks. With numerous applications to modern technology, they have attracted many world leaders in mathematics and computer science. This project aims at substantial advancement on some important problems on expanders and related areas. It will put Australia at the forefront of this topical field.
Virtual transport networks. This project will develop specialised time-dependent networks for use in algorithmic software testing and development, focussing on public transportation networks, but applicable elsewhere. The virtual transport networks developed in this project will significantly reduce the cost of producing software products that perform network searches.
Discovery Early Career Researcher Award - Grant ID: DE120100049
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
New integer programming based theory, formulations and decomposition techniques with applications to integrated problems. Optimisation problems permeate science and industry. By developing new techniques to solve larger and harder problems than is currently possible, more complex questions can be answered, and more accurate solutions obtained. Industries can use such tools to make better financial, resource management, operational, and/or strategic planning decisions.
Discovery Early Career Researcher Award - Grant ID: DE140100708
Funder
Australian Research Council
Funding Amount
$297,003.00
Summary
Morphing graph drawings. A morphing is a continuous transformation between two drawings of the same topological graph such that at every time instant the drawing has the same topology. Morphings of graph drawings find applications in several areas of computer science, including computer graphics, animation, and modelling. This project will design algorithms for constructing morphings between graph drawings. Unlike any existing method to morph graph drawings, the algorithms designed for this proj ....Morphing graph drawings. A morphing is a continuous transformation between two drawings of the same topological graph such that at every time instant the drawing has the same topology. Morphings of graph drawings find applications in several areas of computer science, including computer graphics, animation, and modelling. This project will design algorithms for constructing morphings between graph drawings. Unlike any existing method to morph graph drawings, the algorithms designed for this project will guarantee bounds on the complexity of the vertex trajectories, guarantee bounds on the resolution of the drawing at every time instant, and deal with topological graphs that are not necessarily planar.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE170100234
Funder
Australian Research Council
Funding Amount
$360,000.00
Summary
Exact and hybrid algorithms for the Aircraft Landing Problem. This project aims to develop algorithms with superior guaranteed performance. Aircraft Landing Problems (ALP) are an important class of decision problems. Optimal solution of an ALP is applicable in transportation and health care delivery, benefitting systems experiencing long delays. This project aims to address several of the Australian Government's Science and Research Priorities, focusing on food supply chains, effective operation ....Exact and hybrid algorithms for the Aircraft Landing Problem. This project aims to develop algorithms with superior guaranteed performance. Aircraft Landing Problems (ALP) are an important class of decision problems. Optimal solution of an ALP is applicable in transportation and health care delivery, benefitting systems experiencing long delays. This project aims to address several of the Australian Government's Science and Research Priorities, focusing on food supply chains, effective operation and resource allocation in transport, and better models of health care delivery and services.Read moreRead less
Novel dissimilarity techniques for characterising noisy spatial networks. This project will invent new and widely applicable ways of summarising fundamental characteristics of noisy spatial networks that change slightly in space or time. The techniques developed will be applied to solve important problems in two diverse applications - predicting disease spread in wildlife and protecting human biometric information.