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.
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.
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.
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
More information for better utility; less information for better privacy. More information for better utility; less information for better privacy. The contradiction is everywhere in contemporary IT: doctors need accurate information for diagnosis, but insurance companies' access should be limited; on-line retailers use your postcode to present interesting products, but they also deduce from it how much you will pay. One way to manage this contradiction is to tolerate "small" information flows p ....More information for better utility; less information for better privacy. More information for better utility; less information for better privacy. The contradiction is everywhere in contemporary IT: doctors need accurate information for diagnosis, but insurance companies' access should be limited; on-line retailers use your postcode to present interesting products, but they also deduce from it how much you will pay. One way to manage this contradiction is to tolerate "small" information flows providing the risks involved can be accurately gauged. This project will build on recent advances in information measuring to develop new techniques for measuring the extent to which computer systems can defend against threats to privacy. Success in this project will lead to completely novel methods for security analysis of on-line applications where privacy is a critical issue.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.
Security and Privacy of Individual Data Used to Extract Public Information. The project aims to contribute to the development of techniques to allow the harvesting of useful information without compromising personal privacy. Intelligent analysis of personal data can reveal valuable knowledge about a population but at a risk of invading an individual's privacy. This project aims to provide at least partial solutions to some of the problems associated with the protection of private data. In partic ....Security and Privacy of Individual Data Used to Extract Public Information. The project aims to contribute to the development of techniques to allow the harvesting of useful information without compromising personal privacy. Intelligent analysis of personal data can reveal valuable knowledge about a population but at a risk of invading an individual's privacy. This project aims to provide at least partial solutions to some of the problems associated with the protection of private data. In particular, it plans to work on the problem of security of statistical databases and privacy of streaming data. This would be underpinned by a study of anonymisation and homomorphic encryption. The expected outcomes are new theoretical results, new algorithms and protocols applicable to at least some of the current significant problems in information security.Read moreRead less
Efficient structure search over large graphs. The project aims to develop advanced search technology to support large-scale graph applications. The success of the project not only brings a breakthrough in technology development but also provides training for high quality personnel in this important and growing area, and brings considerable economic and social benefits to Australia.