Stochastic Geometry for Multi-sensor Data Fusion System. The aim of this project is to develop efficient algorithms for tracking and sensor management in a multi-sensor multi-target environment. Finite random set theory provides a natural way of representing a random number of (random) object states, an issue that has been largely ignored in the tracking literature until recently. Although a satisfactory foundation for multiple object filtering has been provided by random set theory, in this ear ....Stochastic Geometry for Multi-sensor Data Fusion System. The aim of this project is to develop efficient algorithms for tracking and sensor management in a multi-sensor multi-target environment. Finite random set theory provides a natural way of representing a random number of (random) object states, an issue that has been largely ignored in the tracking literature until recently. Although a satisfactory foundation for multiple object filtering has been provided by random set theory, in this early stage no algorithm capable of tracking many targets has emerged from this framework. We are confident that efficient algorithms can be developed by exploiting the insights and mathematical tools of stochastic geometryRead moreRead less
Discovery Early Career Researcher Award - Grant ID: DE230100579
Funder
Australian Research Council
Funding Amount
$445,754.00
Summary
The existence and abundance of small bases of permutation groups. This project aims to study bases for permutation groups, which are the mathematical formalisation of symmetry. Bases are crucial to encoding and computing with groups in diverse areas of science. Small bases are desirable for efficiency, but can be hard to find. This project expects to combine techniques from areas of algebra and probability to determine the existence and abundance of bases. Expected outcomes of this project inclu ....The existence and abundance of small bases of permutation groups. This project aims to study bases for permutation groups, which are the mathematical formalisation of symmetry. Bases are crucial to encoding and computing with groups in diverse areas of science. Small bases are desirable for efficiency, but can be hard to find. This project expects to combine techniques from areas of algebra and probability to determine the existence and abundance of bases. Expected outcomes of this project include new methods to address enduring open problems in the study of bases, as well as novel applications of existing techniques. This should provide significant benefits, such as creating and strengthening international collaborations, and building on Australia’s reputation as a powerhouse of finite group theory.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE180100957
Funder
Australian Research Council
Funding Amount
$339,328.00
Summary
Partial differential equations, free boundaries and applications. This project aims to investigate fundamental problems in the analysis of partial differential equations and free boundary theory, to develop advanced mathematical theories with the possibility of important applications. The expected outcome is the establishment of a regularity and classification theory for nonlocal equations and for free boundary problems in linear and nonlinear settings. The benefit of the project lies in a concr ....Partial differential equations, free boundaries and applications. This project aims to investigate fundamental problems in the analysis of partial differential equations and free boundary theory, to develop advanced mathematical theories with the possibility of important applications. The expected outcome is the establishment of a regularity and classification theory for nonlocal equations and for free boundary problems in linear and nonlinear settings. The benefit of the project lies in a concrete advancement of the mathematical research with advantages for a deeper understanding of complex phenomena in physics and biology. Some of the problems also provide results useful for industrial applications.Read moreRead less
Non-local equations at work. This project aims to study non-local fractional equations. These problems arise naturally in many fields of pure and applied mathematics. This project will consider symmetry and rigidity results; problems from atom dislocation theory; nonlocal minimal surfaces; symbolic dynamics for nonlocal equations; and free boundary problems. This project aims to obtain substantial progress in this field, both from the point of view of the mathematical theory and in view of concr ....Non-local equations at work. This project aims to study non-local fractional equations. These problems arise naturally in many fields of pure and applied mathematics. This project will consider symmetry and rigidity results; problems from atom dislocation theory; nonlocal minimal surfaces; symbolic dynamics for nonlocal equations; and free boundary problems. This project aims to obtain substantial progress in this field, both from the point of view of the mathematical theory and in view of concrete applications. This project should contribute to the development of the mathematical theory and give insight for concrete applications in physics and biology.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE130101191
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
Formation of the osteocyte network in bone matrix. The formation of new bone, which occurs throughout life for bone renewal and acutely after fractures, entraps a network of cells that can detect micro-damage and direct repair mechanisms. Mathematical and computational methods will be used to understand how this network can lead to a self-detecting and self-repairing biomaterial.
Optimising disease surveillance to support decision-making. COVID-19 has demonstrated the critical role of epidemic data and analytics in guiding government response to pandemic threats, reducing disease and saving lives. The demand for epidemic analytics for response to threats of national significance will only grow. The goals of this project are to 1) determine the combination(s) of surveillance methods that provide the most useful data for epidemic analysis and 2) translate these findings in ....Optimising disease surveillance to support decision-making. COVID-19 has demonstrated the critical role of epidemic data and analytics in guiding government response to pandemic threats, reducing disease and saving lives. The demand for epidemic analytics for response to threats of national significance will only grow. The goals of this project are to 1) determine the combination(s) of surveillance methods that provide the most useful data for epidemic analysis and 2) translate these findings into the blueprint for a next-generation infectious disease surveillance system for Australia. We will use a simulation-evaluation approach, coupling methods from infectious disease modelling with those from information theory optimal design. Outcomes will enable more tailored and effective pandemic response.Read moreRead less
Modelling and estimation methods for discrete multi-dimensional systems. Multi-dimensional signal processing plays a role in a variety of application areas, ranging from remote sensing for environmental monitoring and geological mapping, to medical imaging and the automatic control of industrial processes. The success of the project will provide mathematical tools for the advancement of the state-of-the-art in these broad areas.
Providing the Mathematical Foundation for an Innovative Australia within Reform Based Learning Environments. The focus of this project is the pedagogical change that The Review of Teaching and Teacher Education indicates must take place in order to lay the quantitative foundations for advancing innovation, science, technology, and mathematics, while satisfying the requirements of a reform-based learning environment. Professional learning directed at teachers' pedagogical content knowledge and be ....Providing the Mathematical Foundation for an Innovative Australia within Reform Based Learning Environments. The focus of this project is the pedagogical change that The Review of Teaching and Teacher Education indicates must take place in order to lay the quantitative foundations for advancing innovation, science, technology, and mathematics, while satisfying the requirements of a reform-based learning environment. Professional learning directed at teachers' pedagogical content knowledge and belief structures with respect to mathematics within an environment of curricular change, will be evaluated in evidence-based terms related to teacher change and student outcomes. Significance includes the context, the middle school years in rural district schools, and the influence of technology on pedagogy.Read moreRead less
Scalable Robust Video Surveillance over Constrained Networks. Real-time monitoring of large numbers of people is becoming increasingly important for applications such as efficient service delivery and security against both common crime and terrorism. The use of human operators for such tasks is infeasible due to the large amount of data collected. Existing autonomous video surveillance systems are prone to high numbers of false alarms and often require expensive hardware. This proposal seeks ....Scalable Robust Video Surveillance over Constrained Networks. Real-time monitoring of large numbers of people is becoming increasingly important for applications such as efficient service delivery and security against both common crime and terrorism. The use of human operators for such tasks is infeasible due to the large amount of data collected. Existing autonomous video surveillance systems are prone to high numbers of false alarms and often require expensive hardware. This proposal seeks to address both difficulties by using rigorous statistical signal processing methods to optimally fuse information from a network of low-cost cameras.Read moreRead less
Performance evaluation and characterisation for filtering in multi-object system. The project falls within the National Research Priority of 'Safeguarding Australia' and associated research priority goal of 'Transforming Defence Technology'. The project outcomes will provide cutting edge technology in surveillance, and monitoring of potential threat in our air, sea, and land space. Fast, reliable information enable our personnel to make timely, intelligent judgements, and appropriate responses i ....Performance evaluation and characterisation for filtering in multi-object system. The project falls within the National Research Priority of 'Safeguarding Australia' and associated research priority goal of 'Transforming Defence Technology'. The project outcomes will provide cutting edge technology in surveillance, and monitoring of potential threat in our air, sea, and land space. Fast, reliable information enable our personnel to make timely, intelligent judgements, and appropriate responses in the event of a threat, thereby maintaining Australia's operational advantage. Other application areas that benefits from our research include radar, sonar, guidance, navigation, air traffic control, image processing, oceanography, autonomous vehicles and robotics, remote sensing, and biomedical research.
Read moreRead less