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Conformal invariance and stationary states. Universal properties in nonequilibrium processes, such as scaling of space and time, suggest the existence of a fundamental, model independent theory describing such phenomena. An analogous theory for equilibrium phenomena exists, namely conformal field theory, and is extremely important for our understanding. Using recent insights this project aims at formulating such a theory for universal nonequilibrium behaviour.
The fundamental structure of combinatorial configurations. Combinatorial configurations are fundamental mathematical tools used to model physical problems in the information sciences. Combinatorial trades arise from the differences between combinatorial configurations. They uniquely determine the underlying structure of the configuration and are central to the determination of defining sets. With this proposal we shall study the existence, properties and applications of combinatorial trades and ....The fundamental structure of combinatorial configurations. Combinatorial configurations are fundamental mathematical tools used to model physical problems in the information sciences. Combinatorial trades arise from the differences between combinatorial configurations. They uniquely determine the underlying structure of the configuration and are central to the determination of defining sets. With this proposal we shall study the existence, properties and applications of combinatorial trades and the associated defining sets. Our results will have applications in the areas of biotechnology, information systems, information security and experimental design.Read moreRead less
Random matrix theory and high dimensional inference. The topic of high dimensional inference and random matrix theory is one of present international prominence, as evidenced by the number of special programs on this theme of late. This is due both to recent advances in random matrix theory, and the fact that there are applications to areas such as econometrics, meteorology and engineering. With the CI being an expert in random matrix theory, and Professor Bassler an expert in complex systems, a ....Random matrix theory and high dimensional inference. The topic of high dimensional inference and random matrix theory is one of present international prominence, as evidenced by the number of special programs on this theme of late. This is due both to recent advances in random matrix theory, and the fact that there are applications to areas such as econometrics, meteorology and engineering. With the CI being an expert in random matrix theory, and Professor Bassler an expert in complex systems, another line of applications will be emphasized, and a new axis of international linkage formed.Read moreRead less
Extending the scope of modular analysis for the validation of large systems. The increasing complexity of computer systems has severe implications for verification and validation, especially for critical systems (e.g. medical supervision, avionics mission systems). The standard approach is to build a formal model of the system and automatically analyse its behaviour. Such models can be captured in a modular, high-level description, but the number of states is usually so large as to preclude an ....Extending the scope of modular analysis for the validation of large systems. The increasing complexity of computer systems has severe implications for verification and validation, especially for critical systems (e.g. medical supervision, avionics mission systems). The standard approach is to build a formal model of the system and automatically analyse its behaviour. Such models can be captured in a modular, high-level description, but the number of states is usually so large as to preclude analysis. The modular analysis proposed in this project matches the analysis technique to the structure of the model. Preliminary results are promising and motivate the extension of the technique to a larger class of modular descriptions.Read moreRead less
Digital Imagery for Building 3D City Models. The project will investigate the application of digital photogrammetric imagery, and primarily high-resolution satellite imagery for the creation of visually realistic 3D city models. Virtual reality computer models of urban scenes find application in urban planning, facilities management, engineering and even virtual tourism. Building upon recently initiated collaborative research, the project aims to develop improved methods and procedures for autom ....Digital Imagery for Building 3D City Models. The project will investigate the application of digital photogrammetric imagery, and primarily high-resolution satellite imagery for the creation of visually realistic 3D city models. Virtual reality computer models of urban scenes find application in urban planning, facilities management, engineering and even virtual tourism. Building upon recently initiated collaborative research, the project aims to develop improved methods and procedures for automated, image-based object reconstruction to support the generation of metrically accurate 3D computer models of buildings and the built environment.Read moreRead less
Quantum many-body systems with long-range interactions. Integrable many-body systems with long-range interactions are the subject of intense research activity worldwide, because they involve powerful mathematics and have various physical applications ranging from condensed matter physics to high energy physics. This project involves intensive collaboration between leading mathematical physics groups in Japan and Australia on exciting new developments in the theory of such systems and their appli ....Quantum many-body systems with long-range interactions. Integrable many-body systems with long-range interactions are the subject of intense research activity worldwide, because they involve powerful mathematics and have various physical applications ranging from condensed matter physics to high energy physics. This project involves intensive collaboration between leading mathematical physics groups in Japan and Australia on exciting new developments in the theory of such systems and their applications to physics. The expected outcomes are new progress in an area at the cutting edge of mathematical physics and the establishment of strong research links between Japan and Australia.Read moreRead less
Quantized Algebraic (Super) Structures and Applications. Algebraic structures such as quantized superalgebras and affine Lie (super)algebras provide a universal common algebraic framework underlying applications in a wide range of physical systems, leading to a high level of research activity worldwide. The project involves intensive collaborations between leading mathematical physics groups in China and Australia on exciting new developments in the theory of these algebraic structures and their ....Quantized Algebraic (Super) Structures and Applications. Algebraic structures such as quantized superalgebras and affine Lie (super)algebras provide a universal common algebraic framework underlying applications in a wide range of physical systems, leading to a high level of research activity worldwide. The project involves intensive collaborations between leading mathematical physics groups in China and Australia on exciting new developments in the theory of these algebraic structures and their applications to condensed matter physics and quantum field theories. The expected outcomes are significant new progress in an area at the forefront of mathematical physics and the establishment of strong research links between China and Australia.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
Linear programming approach to nonlinear deterministic and stochastic control problems: perturbations methods and numerical analysis. The proposed research will significantly advance knowledge by creating new analytical and numerical methods for tackling complex nonlinear control problems arising in many applications. The study's outputs will lead to a deeper understanding of fundamental issues in mathematical modelling. Collaboration with renowned researchers will further improve Australia's st ....Linear programming approach to nonlinear deterministic and stochastic control problems: perturbations methods and numerical analysis. The proposed research will significantly advance knowledge by creating new analytical and numerical methods for tackling complex nonlinear control problems arising in many applications. The study's outputs will lead to a deeper understanding of fundamental issues in mathematical modelling. Collaboration with renowned researchers will further improve Australia's standing in the international research community. Also their visits may further promote research both within and outside the host institution. In particular, lectures and seminars that they will deliver will be transmitted to Australian universities participating in the Access Grid Room Project.Read moreRead less
Singular and Analytic Perturbations, Slow and Fast Time Scales in Control Theory and Viability Theory and their Applications. We propose an innovative approach to several important classes of mathematical problems, whose data depend analytically on small perturbation parameters. Time scale problems, and, in particular, the interaction of two types of evolution, slow and fast, arise in many scientific domains (biotechnology, physics, engineering, etc).We expect to develop new techniques for analy ....Singular and Analytic Perturbations, Slow and Fast Time Scales in Control Theory and Viability Theory and their Applications. We propose an innovative approach to several important classes of mathematical problems, whose data depend analytically on small perturbation parameters. Time scale problems, and, in particular, the interaction of two types of evolution, slow and fast, arise in many scientific domains (biotechnology, physics, engineering, etc).We expect to develop new techniques for analysis and asymptotic optimisation of singularly perturbed control systems and Markov decision processes. In particular, we plan to establish links between general nonlinear optimal control problems with time average criteria and linear programming problems in the space of limit occupational measures generated by the underlying control system.Read moreRead less