Stein's method for probability approximation. Data of counts in time, such as incoming calls in telecommunications and the clusters of palindromes in a family of herpes-virus genomes, arise in an extraordinarily diverse range of fields from science to business. These problems can be modelled by sums of random variables taking values 0 and 1 in probability theory, thus permitting approximate calculations which are often good enough in practice. This project will obtain such approximate solutions ....Stein's method for probability approximation. Data of counts in time, such as incoming calls in telecommunications and the clusters of palindromes in a family of herpes-virus genomes, arise in an extraordinarily diverse range of fields from science to business. These problems can be modelled by sums of random variables taking values 0 and 1 in probability theory, thus permitting approximate calculations which are often good enough in practice. This project will obtain such approximate solutions and estimate the errors involved. Applications include analysis of data in insurance, finance, flood prediction in hydrology.Read moreRead less
Quantum decoherence: A game-theoretic perspective. Algorithms based on quantum computation have the ability to significantly speed up information processing compared to standard computers. The increase in computational power can have enormous impact on humankind and this project will help maintain Australia's position in the global forefront of this effort.This project focuses on the thoeretical foundations of quantum computation and complements the efforts of several groups in Australia collabo ....Quantum decoherence: A game-theoretic perspective. Algorithms based on quantum computation have the ability to significantly speed up information processing compared to standard computers. The increase in computational power can have enormous impact on humankind and this project will help maintain Australia's position in the global forefront of this effort.This project focuses on the thoeretical foundations of quantum computation and complements the efforts of several groups in Australia collaborating on the experimental design of quantum computers. The project will increase the fundamental understanding of how quantum information is processed in the presence of noise, which is necessary for the successful operation of quantum computers. Read moreRead less
Random Structures and Asymptotics. Discrete random structures have many uses in algorithms in computer science (for instance, random networks modelling computer link-ups), biology (for instance, random sequences modelling DNA) and engineering. New techniques for studying these structures will lead to powerful new results on their properties. The emphasis will be on the behaviour of the random structures when their size becomes large. With the advent of
more powerful computing techniques, it is ....Random Structures and Asymptotics. Discrete random structures have many uses in algorithms in computer science (for instance, random networks modelling computer link-ups), biology (for instance, random sequences modelling DNA) and engineering. New techniques for studying these structures will lead to powerful new results on their properties. The emphasis will be on the behaviour of the random structures when their size becomes large. With the advent of
more powerful computing techniques, it is often the large-scale behaviour which has relevance to the more diffucult computations being undertaken. The results are also of potential application to other areas of mathematics.Read moreRead less