The impact of crime on the mental wellbeing of communities. Considering not only the direct impact of crime on the victims but also the indirect consequences of living in a community with a higher crime rate may in fact lead to a more accurate analysis of the size of the consequences of criminal activities on the society. Further, it may also be the case that the negative externality of crime on non-victims is much larger for some crimes than for others. If this were the case, it could have impl ....The impact of crime on the mental wellbeing of communities. Considering not only the direct impact of crime on the victims but also the indirect consequences of living in a community with a higher crime rate may in fact lead to a more accurate analysis of the size of the consequences of criminal activities on the society. Further, it may also be the case that the negative externality of crime on non-victims is much larger for some crimes than for others. If this were the case, it could have implications for the way in which police resources are presently distributed across different crimes. Better understanding the total societal cost of crime - to both victims and non-victims - could therefore help improve public policy. Read moreRead less
What are the determinants and effects of school choice? An international comparison between Australia and the UK. The project will provide a clearer picture of the determinants of school choice, most notably the impact of economic phenomena on that choice. For Australia, this will mean we have a better understanding of the competing explanations of the growth of students at private schools over the past three decades: the role of government subsidies; the role of demographic changes; the effec ....What are the determinants and effects of school choice? An international comparison between Australia and the UK. The project will provide a clearer picture of the determinants of school choice, most notably the impact of economic phenomena on that choice. For Australia, this will mean we have a better understanding of the competing explanations of the growth of students at private schools over the past three decades: the role of government subsidies; the role of demographic changes; the effects of increased income inequality; and the role of changes in preferences towards private schools. This information will provide a better evidence base for future policy development in this area.Read moreRead less
Knowledge and Networks: An Evaluation of Patent Citation Activity and Active Knowledge Networks. Although many methods from many disciplines have been used, somewhat imperfectly, to examine knowledge creation and knowledge networks, the most accepted method in economics and strategy is patent citation analysis. Yet, even users of the methodology recognize that it is an imperfect measure of innovation, innovativeness and network linkages between innovations. The study sets up a methodology to ex ....Knowledge and Networks: An Evaluation of Patent Citation Activity and Active Knowledge Networks. Although many methods from many disciplines have been used, somewhat imperfectly, to examine knowledge creation and knowledge networks, the most accepted method in economics and strategy is patent citation analysis. Yet, even users of the methodology recognize that it is an imperfect measure of innovation, innovativeness and network linkages between innovations. The study sets up a methodology to examine the relationship between citations and network interactions between patent applicants. The value of the research is in providing a better measure of innovation and knowledge and in the normative lessons about establishing better scientific networks.Read moreRead less
Ergodic theory and number theory. Recent advances in the theory of measured dynamical systems investigated by the proponents include new versions of entropy, and the study of spectral theory for non-singular systems. These will be further developed in this joint project with the French CNRS. The results are expected to have interesting applications in physics and number theory.
Entropy and maximal entropy in Markov systems. Entropy is a measure of how well-ordered a system is: chaotic systems have high entropy. Two approaches to entropy are available, via the limiting behaviour of the orbits of points, which yields topological entropy, and via the behaviour of the distributions of measures of partitions, yielding measure-theoretic entropy. The topological entropy is the least upper bound of entropies of all possible measures. We study when there is a measure which real ....Entropy and maximal entropy in Markov systems. Entropy is a measure of how well-ordered a system is: chaotic systems have high entropy. Two approaches to entropy are available, via the limiting behaviour of the orbits of points, which yields topological entropy, and via the behaviour of the distributions of measures of partitions, yielding measure-theoretic entropy. The topological entropy is the least upper bound of entropies of all possible measures. We study when there is a measure which realises this bound, describing the structure of such systems via Markov and Bratteli diagrams. Our methods will be applied to new versions of entropy for non-singular systems. This will assist in the description of chaotic behaviour.Read moreRead less
Design of Secure Electronic Voting Systems. It is inevitable that electronic voting will eventually replace current paper based voting schemes. The main outcome of the research will be the fundamental knowledge required to develop secure electronic voting schemes. The security aspects of the design will be thoroughly analysed to ensure that the integrity of the ballot is maintained without compromising user privacy. The practical aspects of implementing such a system will also be investigated ....Design of Secure Electronic Voting Systems. It is inevitable that electronic voting will eventually replace current paper based voting schemes. The main outcome of the research will be the fundamental knowledge required to develop secure electronic voting schemes. The security aspects of the design will be thoroughly analysed to ensure that the integrity of the ballot is maintained without compromising user privacy. The practical aspects of implementing such a system will also be investigated and a prototype implementation provided. The project will combine the expertise in electronic voting schemes at QUT with that of Dr Lee.Read moreRead less
A new erasure resilient technique for encoding internet packets. Efficient internet communication tolerates losing some packets sent across the web by sending a bit more information than is required. Any holes in the transmission can be repaired using the redundant data. We propose a new transmission protocol that is much simpler to encode and repairs broken messages faster. This new approach, based on sending data plus summed versions of itself, has generic applicability across all packet switc ....A new erasure resilient technique for encoding internet packets. Efficient internet communication tolerates losing some packets sent across the web by sending a bit more information than is required. Any holes in the transmission can be repaired using the redundant data. We propose a new transmission protocol that is much simpler to encode and repairs broken messages faster. This new approach, based on sending data plus summed versions of itself, has generic applicability across all packet switched information networks.Read moreRead less
Propagation of singularities for the Schrodinger equation. The time-dependent Schrodinger equation governs the evolution of quantum particles. In this project we aim to use new techniques from mathematical scattering theory to analyse solutions of the Schrodinger equation and obtain sharp bounds on their singularities. Controlling such singularities will allow us to deduce quantitative bounds on the number of eigenvalues in certain situations, and provide new techniques for studying nonlinear Sc ....Propagation of singularities for the Schrodinger equation. The time-dependent Schrodinger equation governs the evolution of quantum particles. In this project we aim to use new techniques from mathematical scattering theory to analyse solutions of the Schrodinger equation and obtain sharp bounds on their singularities. Controlling such singularities will allow us to deduce quantitative bounds on the number of eigenvalues in certain situations, and provide new techniques for studying nonlinear Schrodinger equations. Read moreRead less
Dynamics of eigenvalue/eigenspace algorithms with applications to signal processing. Many problems in signal and systems lead naturally to an eigenvalue/eigenspace determination and tracking problem; for example (acoustic) echo-cancellation, crosstalk suppression in ADSL modems, direction of arrival determination with an array of sensors, linear system identification etc. Exploiting methods from global analysis and dynamical systems theory we will study the available algorithms for eigenspace de ....Dynamics of eigenvalue/eigenspace algorithms with applications to signal processing. Many problems in signal and systems lead naturally to an eigenvalue/eigenspace determination and tracking problem; for example (acoustic) echo-cancellation, crosstalk suppression in ADSL modems, direction of arrival determination with an array of sensors, linear system identification etc. Exploiting methods from global analysis and dynamical systems theory we will study the available algorithms for eigenspace determination to characterise their computational efficiency, accuracy and effectiveness in various data scenarios. The analysis will lead to improved designs for eigenvalue/eigenspace algorithms, as well as design tools to engineer algorithms to specific situations.Read moreRead less
Representations of dynamical systems, amenability, and proper actions. Mathematicians study abstract objects by representing them in terms of well-understood concrete models, and need to know when a representation is faithful, in the sense that the model contains complete information. Dynamical systems are an abstraction of physical systems suitable for studying time evolution and symmetries. The project aims to determine when important representations of dynamical systems are faithful, or, in ....Representations of dynamical systems, amenability, and proper actions. Mathematicians study abstract objects by representing them in terms of well-understood concrete models, and need to know when a representation is faithful, in the sense that the model contains complete information. Dynamical systems are an abstraction of physical systems suitable for studying time evolution and symmetries. The project aims to determine when important representations of dynamical systems are faithful, or, in mathematical language, when the dynamical system is amenable. The proposed strategy involves extending Rieffel's notion of proper actions; the construction should be of wide applicability apart from the intended applications to amenability.Read moreRead less