Credential Systems and Their Applications in Securing Electronic Health Records. The expected result of this project will be frontier technologies that are essential in applications and services, whose acceptance and take-up will depend on users' assurance of their security in the cyber world. In particular, a service such as the EHR system, which is known to be a complex system, requires the use of new and innovative credential-based systems. The result will also contribute to maintaining Austr ....Credential Systems and Their Applications in Securing Electronic Health Records. The expected result of this project will be frontier technologies that are essential in applications and services, whose acceptance and take-up will depend on users' assurance of their security in the cyber world. In particular, a service such as the EHR system, which is known to be a complex system, requires the use of new and innovative credential-based systems. The result will also contribute to maintaining Australia's leading position in the telecommunication and information technology industries, which has been recognised by increased government funding levels. The resulting applications of this project will place Australia as the first country able to design and implement a secure EHR system.Read moreRead less
Reconciliation strategies for continuous variable quantum key distribution. This project aims to advance a novel key distribution method, called quantum key distribution, which distributes secure keys using the quantum state of optical channels. Key distribution is a foundational part of data security, allowing digital keys to be securely exchanged between two or more parties, before they are used to protect and share information. The expected outcome is new rateless error correction codes desi ....Reconciliation strategies for continuous variable quantum key distribution. This project aims to advance a novel key distribution method, called quantum key distribution, which distributes secure keys using the quantum state of optical channels. Key distribution is a foundational part of data security, allowing digital keys to be securely exchanged between two or more parties, before they are used to protect and share information. The expected outcome is new rateless error correction codes designed specifically to implement quantum key distribution over long distances. Quantum key distribution is beneficial for ultra-secure communications as it avoids the vulnerability to weak random numbers and quantum-computing brute force attacks that currently threated the security of data protected by existing methods. Read moreRead less
Practical Automated Deduction. This project will develop, implement and validate improved methods for automated deduction in decidable fragments of first order logic, also incorporating reasoning in special theories such as arithmetic. It will significantly extend previous work on the model evolution calculus and dynamic semantic resolution, and introduce new techniques that combine these reasoning methods. This work has direct application to reasoning about business rules and about industrial o ....Practical Automated Deduction. This project will develop, implement and validate improved methods for automated deduction in decidable fragments of first order logic, also incorporating reasoning in special theories such as arithmetic. It will significantly extend previous work on the model evolution calculus and dynamic semantic resolution, and introduce new techniques that combine these reasoning methods. This work has direct application to reasoning about business rules and about industrial optimisation problems, and it will motivate and test our systems by means of case studies from both of these areas.Read moreRead less
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
A new model for random discrete structures: distributions, counting and sampling. Random discrete structures are used in countless applications across science for modelling complex systems. This project will study a new, very general model of random discrete structures which encapsulates both random networks and random matrices. This project will develop general tools for working with this model, thereby unlocking the model for use by practitioners in areas such as physics, biology, statistics a ....A new model for random discrete structures: distributions, counting and sampling. Random discrete structures are used in countless applications across science for modelling complex systems. This project will study a new, very general model of random discrete structures which encapsulates both random networks and random matrices. This project will develop general tools for working with this model, thereby unlocking the model for use by practitioners in areas such as physics, biology, statistics and cryptography. The questions that will be tackled are fundamental problems in probability, and include as special cases the analysis of subgraph distribution in models of random networks, and the joint distribution of entries of contingency tables, which are important in statistics.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE170101128
Funder
Australian Research Council
Funding Amount
$360,000.00
Summary
Homological methods in combinatorics, algebra and geometry. This project aims to solve problems in graph theory, lattice theory and geometry using algebraic techniques. The techniques and language provided by this algebraic approach will be used to gain fresh insight into classical problems, prove stronger theorems and uncover connections between different areas. This project intends to integrate Australia’s strength in homological algebra and category theory with applications in various differe ....Homological methods in combinatorics, algebra and geometry. This project aims to solve problems in graph theory, lattice theory and geometry using algebraic techniques. The techniques and language provided by this algebraic approach will be used to gain fresh insight into classical problems, prove stronger theorems and uncover connections between different areas. This project intends to integrate Australia’s strength in homological algebra and category theory with applications in various different fields of mathematics. This is expected to provide tools for further investigation of applications in other fields, including computer science and combinatorial optimisation.Read moreRead less
Stabilisation of nonlinear quantum feedback control systems. One of the most exciting technological developments of this century promises to be the development of quantum technology. Quantum feedback systems will play a key part of this technology and this project will develop the underlying fundamental theory which will be crucial to the systematic design of quantum feedback control systems.
Coherent Feedback Synchronisation and Stabilisation of Quantum Systems. The aim of this project is to address a range of fundamental problems of stabilisation and coherent synchronisation in quantum feedback control systems, leading to new systematic methods of designing controllers for the interacting quantum systems arising in emerging areas of quantum technology. Quantum feedback control systems will be at the heart of emerging areas of quantum technology and stability is essential for their ....Coherent Feedback Synchronisation and Stabilisation of Quantum Systems. The aim of this project is to address a range of fundamental problems of stabilisation and coherent synchronisation in quantum feedback control systems, leading to new systematic methods of designing controllers for the interacting quantum systems arising in emerging areas of quantum technology. Quantum feedback control systems will be at the heart of emerging areas of quantum technology and stability is essential for their operation. Standard control system methods do not take into account the special features of quantum systems and there is a need for new control theories that deal with stabilisation and synchronisation as quantum technologies become more advanced. Read moreRead less
Verifying the Riemann hypothesis to large heights: theory and applications. This project aims to verify the Riemann hypothesis to a record height and apply this verification to the distribution of prime numbers. The Riemann hypothesis (an open problem for 150 years) is ubiquitous in analytic number theory and prevalent in many other areas of mathematics. This project plans to use state-of-the-art computational hardware and the mathematical and algorithmic expertise of the investigators to verify ....Verifying the Riemann hypothesis to large heights: theory and applications. This project aims to verify the Riemann hypothesis to a record height and apply this verification to the distribution of prime numbers. The Riemann hypothesis (an open problem for 150 years) is ubiquitous in analytic number theory and prevalent in many other areas of mathematics. This project plans to use state-of-the-art computational hardware and the mathematical and algorithmic expertise of the investigators to verify the Riemann hypothesis several orders of magnitude further than what is currently known. A secondary aim is to apply this new verification to a multitude of results in analytic number theory: this would provide future researchers with vastly superior results.Read moreRead less
Monge-Ampere equations and applications. The Monge-Ampere equation is a premier fully nonlinear partial differential equation with significant applications in geometry, physics and applied science. Building upon breakthroughs made by the proposers in previous grant research, this project aims to resolve challenging problems involving Monge-Ampere type equations and applications. The project goal is to establish new regularity theory and classify singularity profile for solutions to Monge-Ampere ....Monge-Ampere equations and applications. The Monge-Ampere equation is a premier fully nonlinear partial differential equation with significant applications in geometry, physics and applied science. Building upon breakthroughs made by the proposers in previous grant research, this project aims to resolve challenging problems involving Monge-Ampere type equations and applications. The project goal is to establish new regularity theory and classify singularity profile for solutions to Monge-Ampere type equation arising in applied sciences, by introducing new ideas and developing innovative cutting-edge techniques. Expected outcomes include resolution of outstanding open problems and continuing enhancement of Australian leadership and expertise in a major area of mathematics.
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