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Algorithms for hard graph problems based on auxiliary data. When solving computational problems, algorithms usually access only the data that is absolutely necessary to define the problem. However, much more data is often readily available. Especially for important or slowly evolving data, such as road networks, social graphs, company rankings, or molecules, more and more auxiliary data becomes available through computational processes, sensors, and simple user entries. This auxiliary data can g ....Algorithms for hard graph problems based on auxiliary data. When solving computational problems, algorithms usually access only the data that is absolutely necessary to define the problem. However, much more data is often readily available. Especially for important or slowly evolving data, such as road networks, social graphs, company rankings, or molecules, more and more auxiliary data becomes available through computational processes, sensors, and simple user entries. This auxiliary data can greatly speed up an algorithm and improve its accuracy. This project aims to design improved algorithms that harness auxiliary data to solve selected high-impact NP-hard graph problems, and will build a new empowering theory to discern when auxiliary data can be used to improve algorithms.Read moreRead less
A mathematical analysis of the influence of small scale inhomogeneities on the evolution of the universe. A fundamental unresolved problem in modern cosmology is to quantify the influence of small-scale inhomogeneities on the evolution of the universe. This project will develop the mathematical techniques required to resolve this question. In addition, these techniques will have important applications to the analysis of astronomical data.
Representation theory of diagram algebras and logarithmic conformal field theory. Generalized models of polymers and percolation are notoriously difficult to handle mathematically, but can be described and solved using diagram algebras and logarithmic conformal field theory. Potential applications include polymer-like materials, filtering of drinking water, spatial spread of epidemics and bushfires, and tertiary recovery of oil.
Design, analysis and application of Monte Carlo methods in statistical mechanics. Statistical mechanics is a general framework for studying complex systems and Monte Carlo methods are an important computational tool in such studies. This project will develop new, vastly more efficient, Monte Carlo methods for problems in statistical mechanics, and will apply these methods to real-world problems such as urban traffic flow.
Computational studies of soft matter. Soft matter systems such as colloidal suspensions and polymers are ubiquitous in nature, and industrially important. For colloidal systems, specifically hard spheres, this project will utilise new algorithms to attack long standing questions about the nature of the virial series. For self-avoiding walks and related models of polymers, research studies have recently developed radically improved Monte Carlo simulation algorithms. These algorithms will enable t ....Computational studies of soft matter. Soft matter systems such as colloidal suspensions and polymers are ubiquitous in nature, and industrially important. For colloidal systems, specifically hard spheres, this project will utilise new algorithms to attack long standing questions about the nature of the virial series. For self-avoiding walks and related models of polymers, research studies have recently developed radically improved Monte Carlo simulation algorithms. These algorithms will enable this project to simulate polymers which may be as long as DNA, and to calculate physical properties with unprecedented precision. The software developed for studying polymers will be released as an open source software library which will revolutionise the field of polymer simulation.Read moreRead less
Quasi-subtractive varieties: a unified framework for substructural, modal and quantum logic. An algebraic theory is proposed that provides a common umbrella for a plethora of non-classical logics. At the same time, it identifies a core that these logics share with classical algebras.
Understanding somatic mutation in plants: new methods, new software, new data. Somatic mutations accumulate as plants grow, affecting everything from short-term ecological interactions to long-term evolutionary dynamics. These mutations have important consequences for plant industry and conservation, but because they are so hard to measure almost nothing is known about them. This project aims to develop new methods and software to detect, analyse, and compare the genome-wide history of somatic m ....Understanding somatic mutation in plants: new methods, new software, new data. Somatic mutations accumulate as plants grow, affecting everything from short-term ecological interactions to long-term evolutionary dynamics. These mutations have important consequences for plant industry and conservation, but because they are so hard to measure almost nothing is known about them. This project aims to develop new methods and software to detect, analyse, and compare the genome-wide history of somatic mutation in individual plants, providing an unprecedented level of detail into an important but understudied source of biological variation. By applying these methods to an iconic experimental population, This project aims to provide the first insights into the genome-wide causes and consequences of somatic mutation in plants.Read moreRead less
Smart comparison and assessment of prediction models for better health using next generation data mining. Prediction models can be used to provide early warning of events, such as adverse medical outcomes. This project will develop principles for the smart management of large collections of prediction models using data mining, enabling more timely medical interventions for Australians to live healthier and longer.
How the gut nervous system interacts with bacteria. This project aims to reveal how the enteric nervous system of the gastrointestinal (GI) tract interacts with the gut microbiota. Gut function has largely been studied without considering microbiota. The project will use genetically modified animal models, image analysis of gut motility and sequencing of gut microbes, and develop neurophysiological methods to understand gut function. Expected benefits include better understanding of mechanisms u ....How the gut nervous system interacts with bacteria. This project aims to reveal how the enteric nervous system of the gastrointestinal (GI) tract interacts with the gut microbiota. Gut function has largely been studied without considering microbiota. The project will use genetically modified animal models, image analysis of gut motility and sequencing of gut microbes, and develop neurophysiological methods to understand gut function. Expected benefits include better understanding of mechanisms underlying antibiotic resistance, risks associated with discretionary caesarean sections and the benefits of breastfeeding.Read moreRead less
Algebraic categories and categorical algebra. Algebra is the study of operations, such as addition and multiplication, and the relationships between these operations. This project will study two exciting new branches of algebra, quantum algebra and postmodern algebra, which will lead to important advances in physics, geometry, and computing.