The fundamental equations for inversion of operator pencils. This project seeks to deepen understanding of how complex systems may be significantly changed by incremental changes to ambient conditions. Mathematical models of complex systems (climate change processes, optimal driving strategies, efficient distribution policies, effective search routines) often depend on key parameters. If small perturbations to the parameters cause large changes to the solution, then the perturbations are said to ....The fundamental equations for inversion of operator pencils. This project seeks to deepen understanding of how complex systems may be significantly changed by incremental changes to ambient conditions. Mathematical models of complex systems (climate change processes, optimal driving strategies, efficient distribution policies, effective search routines) often depend on key parameters. If small perturbations to the parameters cause large changes to the solution, then the perturbations are said to be singular. This project aims to reveal the underlying mathematical structures and develop new computational algorithms to analyse a general class of perturbed systems both locally near an isolated singularity and globally. It plans to use these algorithms to solve systems of equations, calculate generalised inverse operators, examine perturbed Markov processes, and estimate exit times from meta-stable states in stochastic population dynamics.Read moreRead less
Investigating the Effects of Network-Induced Delays on Networked Control Systems. Networked control is the current trend for industrial automation. The results of this project will be the first in the world to contribute directly to a deeper understanding of both negative and positive effects of network-induced delays on networked control systems. It will firmly place Australia at the forefront of this research by developing cutting edge technology for reliability and efficiency of industrial ne ....Investigating the Effects of Network-Induced Delays on Networked Control Systems. Networked control is the current trend for industrial automation. The results of this project will be the first in the world to contribute directly to a deeper understanding of both negative and positive effects of network-induced delays on networked control systems. It will firmly place Australia at the forefront of this research by developing cutting edge technology for reliability and efficiency of industrial networked-based control systems. This novel frontier technology will result in cost-saving and improved productivity for Australian industries, e.g. manufacturing industries, power stations, processing industries, automotive industries, vehicular networks and locomotives.Read moreRead less
Variable Structure Control Systems in Networked Environments. This project will be the first in the world to lay the foundation for a new theory for understanding and designing new variable structure control systems in the networked environments, which is in great need due to increasing use of shared communication networks in modern industrial systems. It will firmly place Australia at the forefront of this research by developing a cutting edge technology for improving reliability and efficiency ....Variable Structure Control Systems in Networked Environments. This project will be the first in the world to lay the foundation for a new theory for understanding and designing new variable structure control systems in the networked environments, which is in great need due to increasing use of shared communication networks in modern industrial systems. It will firmly place Australia at the forefront of this research by developing a cutting edge technology for improving reliability and efficiency of industrial variable structure control systems in the networked environments, hence resulting in cost-saving and improved productivity for industry. It will provide training for new leading researchers specialised in this new theory and technology.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE210101344
Funder
Australian Research Council
Funding Amount
$364,981.00
Summary
Advancing genomic-driven infectious diseases modelling. Emerging infectious diseases and antimicrobial resistance are among the greatest threats to Australian health and agriculture, and current surveillance tools may fail to detect and mitigate infectious disease outbreaks in real time. This project will develop advanced phylodynamic methods (i.e., mathematical models of infectious disease transmission and pathogen evolution) to enable real-time surveillance of infectious disease outbreaks as t ....Advancing genomic-driven infectious diseases modelling. Emerging infectious diseases and antimicrobial resistance are among the greatest threats to Australian health and agriculture, and current surveillance tools may fail to detect and mitigate infectious disease outbreaks in real time. This project will develop advanced phylodynamic methods (i.e., mathematical models of infectious disease transmission and pathogen evolution) to enable real-time surveillance of infectious disease outbreaks as they emerge and monitor levels of drug resistance.Read moreRead less
Variational methods in partial differential equations. Research in partial differential equations is a very active area of modern mathematics linking nonlinear functional analysis, calculus of variations and differential geometry to applied sciences. This project will enable Australia-based researchers to participate in the forefront of mathematical research with leading international mathematicians by establishing new collaborations, strengthening on-going collaborations and providing internat ....Variational methods in partial differential equations. Research in partial differential equations is a very active area of modern mathematics linking nonlinear functional analysis, calculus of variations and differential geometry to applied sciences. This project will enable Australia-based researchers to participate in the forefront of mathematical research with leading international mathematicians by establishing new collaborations, strengthening on-going collaborations and providing international research experience for early career researchers. As a result, this proposal will enhance Australia's distinguished reputation in analysis and further link the UQ group with a number of mathematical institutes in USA and China.Read moreRead less
Development of a multivariate physiologic state space analysis framework for characterising functional properties of the cardiovascular system. Pathologies of the cardiovascular system arising from heart diseases make a major contribution to morbidity and mortality in the Australian community. This project will provide new diagnostic modalities based on advanced noninvasive bioinstrumentation, signal processing and model-based analytical methods to identify early signs of developing disease or t ....Development of a multivariate physiologic state space analysis framework for characterising functional properties of the cardiovascular system. Pathologies of the cardiovascular system arising from heart diseases make a major contribution to morbidity and mortality in the Australian community. This project will provide new diagnostic modalities based on advanced noninvasive bioinstrumentation, signal processing and model-based analytical methods to identify early signs of developing disease or the acute exacerbation of existing disease. The impact of these new technologies on the early diagnosis and improved triaging of patients in emergency departments is potentially profound and could result in improved healthcare outcomes for the patients and reduced admissions to hospital as well as the development of a substantial international market.Read moreRead less
Multi-scale modelling of cell migration in developmental biology. Interpretative and predictive tools are needed for the comprehensive understanding of directed cell migration in the medical sciences. Mathematical models and modelling methodologies developed in this project will make a significant contribution to the investigation of cell migration and the testing and generation of hypotheses. Such models are needed to understand observed cellular patterns. This project will contribute to knowle ....Multi-scale modelling of cell migration in developmental biology. Interpretative and predictive tools are needed for the comprehensive understanding of directed cell migration in the medical sciences. Mathematical models and modelling methodologies developed in this project will make a significant contribution to the investigation of cell migration and the testing and generation of hypotheses. Such models are needed to understand observed cellular patterns. This project will contribute to knowledge of normal and abnormal developmental processes, especially in embryonic growth. Understanding these processes should lead to prediction and treatment of congenital disorders and contribute to a healthy start to life.Read moreRead less
Optimisation of piezoelectric metamaterials: Towards robotic stress sensors. This project aims to design new piezoelectric material microstructures that can enhance the measurement of complex local stress states within robotic limbs. The project expects to generate new knowledge of the achievable properties of multi-poled piezoelectric materials and develop computational tools for the analysis and structural optimisation of such materials. The designed microstructures may revolutionise piezoelec ....Optimisation of piezoelectric metamaterials: Towards robotic stress sensors. This project aims to design new piezoelectric material microstructures that can enhance the measurement of complex local stress states within robotic limbs. The project expects to generate new knowledge of the achievable properties of multi-poled piezoelectric materials and develop computational tools for the analysis and structural optimisation of such materials. The designed microstructures may revolutionise piezoelectric sensor technology. Expected outcomes include manufactured proof-of-concept sensors that enable measurement of local stress fields. This should provide significant benefits, such as improved future robot capability and reliability, and research training for next-generation Australian computational mathematicians. Read moreRead less
Fractional dynamic models for MRI to probe tissue microstructure. This project aims to develop new mathematical tools for mapping tissue microstructural properties via the use of space-time fractional calculus methods. In magnetic resonance imaging, mathematical models and their parameters play a key role in associating information between images and biology, with the overall aim of producing spatially resolved maps of tissue property variations. However, models which can inform on changes in mi ....Fractional dynamic models for MRI to probe tissue microstructure. This project aims to develop new mathematical tools for mapping tissue microstructural properties via the use of space-time fractional calculus methods. In magnetic resonance imaging, mathematical models and their parameters play a key role in associating information between images and biology, with the overall aim of producing spatially resolved maps of tissue property variations. However, models which can inform on changes in microscale tissue properties are lacking. The tools developed by this project will be used to generate new magnetic resonance image based maps to convey information on tissue microstructure changes in the human brain. Additionally, the mathematical tools developed will be transferable to other applications where diffusion and transport in heterogeneous porous media play a role.Read moreRead less
Bodies in space. By investigating how a change in shape of the human body can produce a change in spatial orientation, the project will bring a fundamental advance of knowledge in the intersection of applied mathematics, sports science and mechanical engineering. These knowledge advances will lead to a novel theory regarding the control of the aerial dynamics of athletes, specifically springboard and platform divers. When applied in collaboration with world class Australian athletes, this theory ....Bodies in space. By investigating how a change in shape of the human body can produce a change in spatial orientation, the project will bring a fundamental advance of knowledge in the intersection of applied mathematics, sports science and mechanical engineering. These knowledge advances will lead to a novel theory regarding the control of the aerial dynamics of athletes, specifically springboard and platform divers. When applied in collaboration with world class Australian athletes, this theory will result in innovative platform and springboard diving techniques and improved performance. The reach of new insights generated by this work extends to many other fields, including robotics, spacecraft dynamics and nano technology.Read moreRead less