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Grants
Algebraic algorithms for investigating the space of bacterial genomes - ARC Discovery Grant 2013-2015
Andrew Francis and Volker Gebhardt
The aim of this project is to develop algorithmic approaches to algebraic problems associated with bacterial evolution. Building realistic group-theoretic models of bacterial evolution based on the inversion process, this project will establish methods for determining the evolutionary distance between two genomes. It will also address the central problem of constructing a phylogeny relating several bacterial genomes from the point of view of geometric group theory and walks on the Cayley graph. The outcomes will be new methods for evolutionary biology, and new results and algorithms in computational, combinatorial and geometric group theory.
Quantized identification of feedback control systems - ARC Discovery Grant 2012-2014
The theory of system identification with quantified data underpins frontier technologies that enable more efficient and sustainable telecommunications, automotive and biomedical industry. This project extends the fundamental framework of quantified system identification. The work will enhance Australia's international standing in the control field.
Algebraic evolution and evolutionary algebra - ARC Future Fellowships 2010-2014
Mathematics has made numerous significant contributions to our understanding of biological systems. This project brings a new approach to mathematical biology by modelling evolutionary processes in bacteria using algebraic ideas. This will not only provide the answers to questions in bacterial evolution that are otherwise unsolved and provide new mathematical and computational tools for biologists, but identify important new areas of research for algebraists.
Algorithmic approaches to braids and their generalisations - ARC Discovery Grant 2010-2012
Volker Gebhardt, Patrick Dehornoy, Juan Gonzalez-Meneses
This project combines theoretical methods from pure mathematics with computational experiments in order to gain new knowledge. The objects of interest, so-called braid groups and generalisations, are important for many fields of mathematics, but also have applications for data security.
Both the theoretical outcomes of this project and the algorithms developed will strengthen Australia as a centre of cutting-edge research in computational algebra. Moreover, the results can lead to new technologies for protecting confidential data, which are more efficient and hence cheaper to implement than existing alternatives. Secure identification of legitimate users in the context of online banking is one possible field of application.
Mathematical models and bioinformatic analyses of bacterial genome evolution - ARC Discovery Grant 2009-2013
Mark Tanaka, Andrew Francis and Ruiting Lan
This project aims to understand the evolution of bacterial genome organisation. It seeks to explain: why genes of a common pathway are often clustered along chromosomes, how mobile genes can survive despite their damaging effects, and why there is wide genomic variation within some bacterial species. We will construct biologically grounded mathematical models describing the relevant processes, using them to analyse the abundant genome data. This will allow discrimination among hypotheses concerning the observed genome structures. This research will make progress towards a coherent theory of bacterial genome evolution, and hence a better understanding of bacterial pathogens.
Development of Identification Methods for Nonlinear Dynamical Systems - ARC Discovery Grant 2007-2009
Wei Zheng, E.-W. Bai and Y. Zheng
It is widely recognized that nonlinear systems theory will mark a new era of control science in the coming decade, and will be used in various types of applications. Driven by such immense opportunities and needs, identification of nonlinear systems is emerging as a vital, active area of research. The success of this project will enhance Australia's leading role in the international control community. The training of the postdoctoral research associates will generate the expertise needed to maintain the involvement of the coming generation in cutting-edge technological advancement. The project will strengthen research activities in Australia through strong international collaborations.
