Ring constructions and algorithms for enhancing performance of BCH codes. BCH codes form a major class of codes used in modern communication systems. The aim of this project is to enhance the efficiency of this class of codes by combining them in constructions enabling correction of deletion and insertion errors, and develop efficient implementations of encoding and decoding algorithms incorporating soft decision methods for enhanced error correction. Significance of the project is explained by ....Ring constructions and algorithms for enhancing performance of BCH codes. BCH codes form a major class of codes used in modern communication systems. The aim of this project is to enhance the efficiency of this class of codes by combining them in constructions enabling correction of deletion and insertion errors, and develop efficient implementations of encoding and decoding algorithms incorporating soft decision methods for enhanced error correction. Significance of the project is explained by the role of fast, secure and reliable communications in modern information and communication technology. Expected outcomes include new efficient algorithms and commercial modules available for symbolic computation systems with applications in telecommunications industry.
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Markov invariants and phylogenetic tree reconstruction. The project will assist Australia to progress as an innovator in the production phylogenetic tree reconstruction techniques.
Identifying species is a difficult task with environmental, social and economic benefits to Australia. DNA evidence and phylogenetic methods clearly achieve this task. Conservation of rare species depends upon identification and hence robust phylogenetic analysis. Phylogenetically identifying fish species has econom ....Markov invariants and phylogenetic tree reconstruction. The project will assist Australia to progress as an innovator in the production phylogenetic tree reconstruction techniques.
Identifying species is a difficult task with environmental, social and economic benefits to Australia. DNA evidence and phylogenetic methods clearly achieve this task. Conservation of rare species depends upon identification and hence robust phylogenetic analysis. Phylogenetically identifying fish species has economic importance as different fish species are all managed separately, having different catch limits, catch areas and market values. Using effective phylogenetic methods, epidemiologists can track the spread of a disease through a population. Read moreRead less
Algebraically informed models of biological sequence evolution. To make sense of the patterns they see in the natural world, biologists across fields as diverse as genetics, epidemiology and biogeography need an accurate picture of evolutionary history. DNA sequences provide an exciting means to establish this picture of the past, but to decode it successfully requires mathematical models of how DNA evolves. Mathematical inconsistencies have been identified with current approaches. In particular ....Algebraically informed models of biological sequence evolution. To make sense of the patterns they see in the natural world, biologists across fields as diverse as genetics, epidemiology and biogeography need an accurate picture of evolutionary history. DNA sequences provide an exciting means to establish this picture of the past, but to decode it successfully requires mathematical models of how DNA evolves. Mathematical inconsistencies have been identified with current approaches. In particular, understanding the effect of natural selection in different parts of the tree of life requires models that behave robustly in the face of shifting evolutionary processes. This project aims to use insights from algebraic methods to construct mathematically consistent models of wide biological utility.Read moreRead less
An efficient approach to the computation of bacterial evolutionary distance. This project aims to apply advanced mathematical tools to improve our understanding of bacterial evolution. Bacteria account for as much total Earth biomass as all plant species put together, and have an unparalleled ability to evolve quickly and adapt to changing environments. Unfortunately, the existing mathematical models used to model bacterial evolution are generally computationally intractable. This project will r ....An efficient approach to the computation of bacterial evolutionary distance. This project aims to apply advanced mathematical tools to improve our understanding of bacterial evolution. Bacteria account for as much total Earth biomass as all plant species put together, and have an unparalleled ability to evolve quickly and adapt to changing environments. Unfortunately, the existing mathematical models used to model bacterial evolution are generally computationally intractable. This project will rectify this situation by using representation theory to transform combinatorial group theory into linear algebra, allowing for the application of advanced methods of numeric approximation. This will provide a better understanding of how bacteria evolve and improve our ability to manage their impact.Read moreRead less
Statistical Literacy for the Twenty-first Century: A Consolidated Model of Understanding for Application to Learning in Context. The overall aim of this project is to achieve a complete developmental model of school students? understanding of the concepts required to participate as statistically literate members of society. Australia is now an information- and data-driven society and to achieve its goals economically, scientifically, and socially, it requires citizens who can make decisions base ....Statistical Literacy for the Twenty-first Century: A Consolidated Model of Understanding for Application to Learning in Context. The overall aim of this project is to achieve a complete developmental model of school students? understanding of the concepts required to participate as statistically literate members of society. Australia is now an information- and data-driven society and to achieve its goals economically, scientifically, and socially, it requires citizens who can make decisions based on appropriate quantitative understanding. A major component of this is statistical literacy. The outcomes of this project based on the theoretical model will include assessment instruments, recommendations for the school curriculum, and trialed learning materials and technologies shown to contribute to understanding, for classroom use.Read moreRead less
Knowledge for teaching primary mathematics: How teachers' pedagogical content knowledge develops and affects classroom practices and students' mathematics achievement. The study will investigate mathematics teaching in upper primary school, to identify the influence of teachers? mathematics-specific pedagogical knowledge, first on teaching practice and subsequently on students? learning outcomes. Case study evidence shows this influence is strong, but statistical evidence shows it is weak. This ....Knowledge for teaching primary mathematics: How teachers' pedagogical content knowledge develops and affects classroom practices and students' mathematics achievement. The study will investigate mathematics teaching in upper primary school, to identify the influence of teachers? mathematics-specific pedagogical knowledge, first on teaching practice and subsequently on students? learning outcomes. Case study evidence shows this influence is strong, but statistical evidence shows it is weak. This study aims to resolve this paradox by employing quality data that probes the heart of teaching and learning mathematics within a statistical study. The growth of knowledge and classroom practices of teachers graduating from two contrasting pre-service programs will also be tracked, to inform recommendations on the nature of discipline-specific pedagogical knowledge in teacher training.Read moreRead less
Statistical literacy in the primary school: beginning inference. Australia is committed to building a stronger foundation for school mathematics and science. This project will introduce primary school students to beginning inference, a core component of statistical literacy and an increasingly important life skill. Foundations for secondary mathematics study and productive societal participation will be laid.
Viscous Effects in Free-Surface Flows. Australia has a proud record of achievement in the field of free-surface fluid mechanics. This project will build and extend these research achievements. It will provide new information about how fluid layers overturn and mix, which is an important process in oceanography. It will examine the sloshing behaviour of fluid in moving storage tanks, which is important in fuel transport and building design. The project will develop new mathematical methods fo ....Viscous Effects in Free-Surface Flows. Australia has a proud record of achievement in the field of free-surface fluid mechanics. This project will build and extend these research achievements. It will provide new information about how fluid layers overturn and mix, which is an important process in oceanography. It will examine the sloshing behaviour of fluid in moving storage tanks, which is important in fuel transport and building design. The project will develop new mathematical methods for solving these problems accurately, and will contribute to the next generation of research mathematicians in Australia. Read moreRead less
Structure and informatics of the genetic code. Recent advances in biotechnology have seen its emergence as a highly
quantitative, numerically-based discipline. To exploit the available
data to the full will require, alongside computing power, new
analytical techniques. This project aims to develop such techniques,
by handling the systematics of the genetic code with methods derived
from theoretical physics and chemistry. Expected outcomes include a
dynamical (quantum field theory) model ....Structure and informatics of the genetic code. Recent advances in biotechnology have seen its emergence as a highly
quantitative, numerically-based discipline. To exploit the available
data to the full will require, alongside computing power, new
analytical techniques. This project aims to develop such techniques,
by handling the systematics of the genetic code with methods derived
from theoretical physics and chemistry. Expected outcomes include a
dynamical (quantum field theory) model of phylogenetic branching,
analyses of nucleic acid structure and content (spin chain models of
RNA binding and of DNA open reading frames), and insights into the
origin of the code itself (via numerical codon similarity measures).
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Managing infectious disease through partial wildlife social networks. This project aims to investigate the dynamics of the spread of infectious disease in wildlife, derived from incomplete information about contact networks. Infectious diseases in wildlife are difficult to track and control, because it is not feasible to monitor each individual in a population and know the contact network for a population. The project will create ways to best utilise incomplete observational data of contact netw ....Managing infectious disease through partial wildlife social networks. This project aims to investigate the dynamics of the spread of infectious disease in wildlife, derived from incomplete information about contact networks. Infectious diseases in wildlife are difficult to track and control, because it is not feasible to monitor each individual in a population and know the contact network for a population. The project will create ways to best utilise incomplete observational data of contact networks to develop robust predictions of disease spread and population fate, and to reliably predict the outcomes of management interventions. These robust prediction methods will provide better insights for conservation of Australian wildlife.Read moreRead less