ARC Centre in Bioinformatics. The Australian Centre for Genome-Phenome Bioinformatics will examine how the genome comes to life in the mammalian cell during differentiation and development. We will model, visualise and experimentally validate the complex cellular systems and regulatory networks that control the transformation of genomic information into biological structure and function. We will develop novel approaches and tools to improve health, optimise agricultural production and exploit ne ....ARC Centre in Bioinformatics. The Australian Centre for Genome-Phenome Bioinformatics will examine how the genome comes to life in the mammalian cell during differentiation and development. We will model, visualise and experimentally validate the complex cellular systems and regulatory networks that control the transformation of genomic information into biological structure and function. We will develop novel approaches and tools to improve health, optimise agricultural production and exploit new cell technologies. The Centre will build critical mass and national focus in bioinformatics to generate the human capital and intellectual property that Australia needs to compete in advanced bioscience and biotechnology.Read moreRead less
Statistical methods and tools for integrative microarray analysis. Tools used for biological and medical research have been evolving and there has been an increase in high-throughput technologies such as genome sequencing and DNA microarray. The growing number of entries and the increasing availability of public microarray repositories and other sequence databases have generated the new challenge of developing tools to efficiently integrate data by different research groups. This research provi ....Statistical methods and tools for integrative microarray analysis. Tools used for biological and medical research have been evolving and there has been an increase in high-throughput technologies such as genome sequencing and DNA microarray. The growing number of entries and the increasing availability of public microarray repositories and other sequence databases have generated the new challenge of developing tools to efficiently integrate data by different research groups. This research provides new statistical methods to integrate different data sets. Its application in the biomedical field will allow researchers to effectively interpret the myriad of data generated within the community.Read moreRead less
Classification of Microarray Gene-Expression Data. The broad aim is to provide statistical methodology for the classification of microarray gene-expression data. Microarrays are part of a new biotechnology that allows the monitoring of expression levels for thousands of genes simultaneously. The explosion in microarrays has produced massive quantities of data that require new statistical techniques for analysis in order to exploit their enormous scientific potential. One of the main uses of ....Classification of Microarray Gene-Expression Data. The broad aim is to provide statistical methodology for the classification of microarray gene-expression data. Microarrays are part of a new biotechnology that allows the monitoring of expression levels for thousands of genes simultaneously. The explosion in microarrays has produced massive quantities of data that require new statistical techniques for analysis in order to exploit their enormous scientific potential. One of the main uses of the methodology to be developed is to expedite the discovery of new subclasses of diseases. Another is to provide prediction rules for the diagnosis and treatment of diseases.Read moreRead less
Dynamic Equations on Measure Chains. Boundary value problems (BVPs) on ``measure chains''are new and useful mathematical equations that describe the world around. This project aims to answer some imporotant and fundamental mathematical questions such as
(i) Under what conditions do BVPs on measure chains actually have solutions?
(ii) If solutions do exist, then what are their properties?
The approach is to use modern tools from mathematical analysis, including topological transversality ....Dynamic Equations on Measure Chains. Boundary value problems (BVPs) on ``measure chains''are new and useful mathematical equations that describe the world around. This project aims to answer some imporotant and fundamental mathematical questions such as
(i) Under what conditions do BVPs on measure chains actually have solutions?
(ii) If solutions do exist, then what are their properties?
The approach is to use modern tools from mathematical analysis, including topological transversality and Leray-Schauder degree.
The project outcomes will
(a) significantly advance current mathematical theory for BVPs on measure chains
(b) unify the theory of BVPs for differential and difference equations
(c) potentially apply to many real-world phenomena.Read moreRead less
Singularities And Classifications Of Integrable Systems. What mathematical models of engineering and nature exclude chaos and have globally predictable solutions? What models occur ubquitously in fields as diverse as photonics and quantum gravity? The answers lie in the theory of integrable systems. We aim to develop powerful new algorithms for identifying integrable models and for deducing their remarkable properties. These algorithms are expected to answer fundamental questions of contempora ....Singularities And Classifications Of Integrable Systems. What mathematical models of engineering and nature exclude chaos and have globally predictable solutions? What models occur ubquitously in fields as diverse as photonics and quantum gravity? The answers lie in the theory of integrable systems. We aim to develop powerful new algorithms for identifying integrable models and for deducing their remarkable properties. These algorithms are expected to answer fundamental questions of contemporary importance. Longer term possible outcomes include applications to nonlinear optics and quantum computing.Read moreRead less
Finite Morse index solutions of nonlinear partial differential equations. We aim to produce mathematics which is of not only of interest to mathematicians but is useful in the study of many physical and biological processes. They occur in the study of processes in industry and the study of the environment.
Transitions and singular behaviour in nonlinear partial differential equations. This research produces crucial mathematical methods and results for the understanding of several important nonlinear problems in applied sciences. The mathematical theory itself is of significant value in nonlinear partial differential equations. The project strengthens Australian research in nonlinear science, a critical area of modern international research, and provides high level training for the next generation ....Transitions and singular behaviour in nonlinear partial differential equations. This research produces crucial mathematical methods and results for the understanding of several important nonlinear problems in applied sciences. The mathematical theory itself is of significant value in nonlinear partial differential equations. The project strengthens Australian research in nonlinear science, a critical area of modern international research, and provides high level training for the next generation of Australian mathematicians.Read moreRead less
Integrable Lattice Equations. When mathematical models are simulated on a computer, the result is a system of partial difference equations, whose solutions evolve with discrete steps on a lattice in space and time. While many tools have been developed to study continuous equations, very few mathematical techniques are available for analysing non-linear lattice equations. We aim to develop techniques of solving the initial-value problem for a class of such equations. Our examples include integrab ....Integrable Lattice Equations. When mathematical models are simulated on a computer, the result is a system of partial difference equations, whose solutions evolve with discrete steps on a lattice in space and time. While many tools have been developed to study continuous equations, very few mathematical techniques are available for analysing non-linear lattice equations. We aim to develop techniques of solving the initial-value problem for a class of such equations. Our examples include integrable lattice equations that arise in the simulation of many physical problems ranging from the progression of shallow water waves to signals in an optical fibre.Read moreRead less
Comparing Einstein to Newton: a mathematical foundation for the Newtonian limit and post-Newtonian expansions. This proposal will benefit the nation in the following ways: (i) to make Australia a world leader in post-Newtonian research, (ii) to contribute to Australia's existing commitment to the search for gravitational waves by providing theoretical tools that will aid in the analysis of gravitational wave data, (iii) to train the next generation of Australian gravitational researchers in a fi ....Comparing Einstein to Newton: a mathematical foundation for the Newtonian limit and post-Newtonian expansions. This proposal will benefit the nation in the following ways: (i) to make Australia a world leader in post-Newtonian research, (ii) to contribute to Australia's existing commitment to the search for gravitational waves by providing theoretical tools that will aid in the analysis of gravitational wave data, (iii) to train the next generation of Australian gravitational researchers in a field whose importance will only grow as the field of gravitational wave astronomy matures, and (iv) to facilitate visits by my collaborators to Australia who will bring world class expertise for the benefit of both Australian students and experts in general relativity.Read moreRead less
Abstract methods for nonlinear partial differential equations. To use abstract methods to study nonlinear partial differential equations where nonlinear effects dominate and where the diffusion is possibly small. These equations arise in many applications of mathematics such as population models and catalysis theory.