Navigating tipping points in complex dynamical systems. This project aims to use applied mathematics to investigate the onset of tipping points in dynamical systems. Working with clinicians and practicing engineers, the project aims to contribute to the development of new treatment regimes for dynamical diseases and develop improved management strategies for resource focussed engineering industries. This should provide significant benefit to many areas, including the personalised treatment of di ....Navigating tipping points in complex dynamical systems. This project aims to use applied mathematics to investigate the onset of tipping points in dynamical systems. Working with clinicians and practicing engineers, the project aims to contribute to the development of new treatment regimes for dynamical diseases and develop improved management strategies for resource focussed engineering industries. This should provide significant benefit to many areas, including the personalised treatment of disease.Read moreRead less
TSuNAMi: Time Series Network Animal Modelling. Our proposal is motivated by and based upon the successful representation of time series as a network (or graph). We construct an abstract representation of a system from measurements of its changing behaviour over time. Properties of that structure (the network) then allow us to infer diagnostic information of the system. Specifically, we propose to apply this to livestock welfare during transport. By measuring the biological and environment condi ....TSuNAMi: Time Series Network Animal Modelling. Our proposal is motivated by and based upon the successful representation of time series as a network (or graph). We construct an abstract representation of a system from measurements of its changing behaviour over time. Properties of that structure (the network) then allow us to infer diagnostic information of the system. Specifically, we propose to apply this to livestock welfare during transport. By measuring the biological and environment condition of the animal we construct a network representation of that system. Geometric features of that network can then be used to infer health or duress of the subject. This proposal will develop the generic mathematical machinery to connect geometric features of the network with system behaviour. Read moreRead less
Complex dynamical systems: inferring form and function of interacting biological systems. Often in biology a large number of simple parts interacting according to simple rules can result in behaviour that is rich and varied. This project aims to develop the mathematics of complex systems theory to describe how such collections of simple interacting parts can form large complicated structures, and to deduce what dynamical behaviour can result.
Quantifying complexity and measuring structure within complex systems. Most interesting systems are complex. The complex systems of interest in this project are characterised by a simple dynamical behaviour on each individual part; and a complicated web of interaction between the many distinct parts. The project will focus on the massive system of interacting neurones in the brain, and transmission of influenza via interpersonal contacts. This project will provide a better model of that web of i ....Quantifying complexity and measuring structure within complex systems. Most interesting systems are complex. The complex systems of interest in this project are characterised by a simple dynamical behaviour on each individual part; and a complicated web of interaction between the many distinct parts. The project will focus on the massive system of interacting neurones in the brain, and transmission of influenza via interpersonal contacts. This project will provide a better model of that web of interactions; and new methods for statistically validating this model against data. Existing models of complex networks are statistically biased so, by employing robust statistical methodologies, this problem will be rectified and provide a method for randomly choosing representative complex systems. Read moreRead less
Mathematical model reduction for complex networks. This project aims to develop new mathematical methodology to describe the collective behaviour of large networks of oscillators with parameters called collective coordinates. This will allow for the quantitative description of finite-size networks as well as chaotic dynamics, which are both out of reach for current model reduction methods. The project will apply methodology to understand the causes of, and ways to prevent, glitches and failure i ....Mathematical model reduction for complex networks. This project aims to develop new mathematical methodology to describe the collective behaviour of large networks of oscillators with parameters called collective coordinates. This will allow for the quantitative description of finite-size networks as well as chaotic dynamics, which are both out of reach for current model reduction methods. The project will apply methodology to understand the causes of, and ways to prevent, glitches and failure in the emerging modern decentralised power grids. This will develop a framework to address this question, tailored to deal with the hitherto uncharted case of finite-size networks.Read moreRead less
Engineering evolving complex network systems through structure intervention. This project aims to create a theory and technology for engineering complex network systems (CSS) through structural intervention. Complex network systems with evolving components are ubiquitous in nature and society. The science of biological networks, the Internet and large-scale power networks demand tools to understand and influence their evolving dynamics. This project could result in a breakthrough theory in netwo ....Engineering evolving complex network systems through structure intervention. This project aims to create a theory and technology for engineering complex network systems (CSS) through structural intervention. Complex network systems with evolving components are ubiquitous in nature and society. The science of biological networks, the Internet and large-scale power networks demand tools to understand and influence their evolving dynamics. This project could result in a breakthrough theory in network science and technology to augment biological systems and power grids. Expected benefits include cost-effective augmentation of power networks injected with renewable energy sources, and advancing basic biology research.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE140100620
Funder
Australian Research Council
Funding Amount
$395,220.00
Summary
Inference, control and protection of interdependent spatial networked structures. Networked structures are everywhere and modern societies largely depend on their proper functioning. Some of these networks are spatial with each node having a geographical tag. Examples include power grids, the internet and transportation networks. These networks are often interdependent where their functioning depends on each other. This project will establish a mathematical framework to efficiently observe and c ....Inference, control and protection of interdependent spatial networked structures. Networked structures are everywhere and modern societies largely depend on their proper functioning. Some of these networks are spatial with each node having a geographical tag. Examples include power grids, the internet and transportation networks. These networks are often interdependent where their functioning depends on each other. This project will establish a mathematical framework to efficiently observe and control interdependent spatial networks and develop design strategies in order to maximise residency of spatial networks against catastrophic failures in their components. The outcomes of the project will protect the Australian power grid and transportation networks against random and intentional failures. Read moreRead less