The canonical stratification of jet spaces. Singularities occur everywhere in nature, from the formation and collapse of stars to the morphology of living embryos. They appear whenever the geometry of surfaces or spaces undergoes a process of twisting, folding, or collapsing on itself. Singularity Theory is the study of such phenomena, an important branch of modern mathematics which has close connections with many other branches of mathematics and applied sciences. Singularity Theory lies at the ....The canonical stratification of jet spaces. Singularities occur everywhere in nature, from the formation and collapse of stars to the morphology of living embryos. They appear whenever the geometry of surfaces or spaces undergoes a process of twisting, folding, or collapsing on itself. Singularity Theory is the study of such phenomena, an important branch of modern mathematics which has close connections with many other branches of mathematics and applied sciences. Singularity Theory lies at the crossroads of the paths connecting the most important areas of applications of mathematics with its most abstract parts. Analytic Singularity Theory is a central part of Singularity Theory. This project would lead to substantially new advancements in Analytic Singularity Theory.Read moreRead less
ANATOMICAL ORGAN MODELLING AND SURGICAL PROCEDURE SIMULATION FOR THORACOSCOPIC SURGERY. We aim to establish novel virtual reality-based surgical procedure simulation methodologies, geometric and physical models of human organs, and surgical tools and interaction modules for thoracoscopic surgery or for minimally invasive surgical procedures. This is needed to optimize surgical strategy and to anticipate possible problems that may arise during the procedure, and to train medical staff as the tren ....ANATOMICAL ORGAN MODELLING AND SURGICAL PROCEDURE SIMULATION FOR THORACOSCOPIC SURGERY. We aim to establish novel virtual reality-based surgical procedure simulation methodologies, geometric and physical models of human organs, and surgical tools and interaction modules for thoracoscopic surgery or for minimally invasive surgical procedures. This is needed to optimize surgical strategy and to anticipate possible problems that may arise during the procedure, and to train medical staff as the trend towards robotic-assisted minimally invasive surgery continues. What makes this project novel is the anatomical organ modeling approach based on virtual springs and dampers traversing between the top and bottom surfaces of the organs and tissues, contrary to previous approaches.Read moreRead less
Mathematical Modelling For Improved Planning Of Infectious Diseases Control Policy
Funder
National Health and Medical Research Council
Funding Amount
$2,750,000.00
Summary
We will develop high-level technical capacity in mathematical modeling of infectious disease transmission and control in Australia, with a focus on research that informs health policy. The aim is to assist Australia to have efficient and effective control strategies and help to prepare us against the threat of emerging infections. Priority areas are vaccination programs, HIV-AIDS, emerging infections and bio-terrorism. Six talented young researchers will be trained by the lead applicant team. To ....We will develop high-level technical capacity in mathematical modeling of infectious disease transmission and control in Australia, with a focus on research that informs health policy. The aim is to assist Australia to have efficient and effective control strategies and help to prepare us against the threat of emerging infections. Priority areas are vaccination programs, HIV-AIDS, emerging infections and bio-terrorism. Six talented young researchers will be trained by the lead applicant team. Together, we will develop a prominent and experienced research team capable of sustaining international quality research into the future. Their work will meet immediate, existing policy needs at state, national and global levels. The program includes the establishment of a Network of Infectious Diseases Modellers of Australia (NIDMA) as a research resource of national expertise, peer support and a means of ongoing communication and collaboration in infectious diseases control. The critical mass of modeling expertise that we create will be sustainable long-term, and will expand to support research concerned with chronic and other non-infectious diseases after the lifetime of the grant.Read moreRead less
The efficacy of models for educational service delivery for students with autism spectrum disorders. This project will evaluate the effectiveness of two models of support (Satellite Class and Consultative model) for children with autism spectrum disorders (ASD) in regular schools. This research has significant potential to provide insight into the best ways of supporting children with ASD and improving their educational outcomes.
How schools make decisions about supporting students with disability. How schools make decisions about supporting students with disability. This project aims to examine how schools decide about adjustments for students with disability. More students with disability are enrolled in mainstream schools, and schools take decisions about resourcing to support them. Little is known about how schools make these decisions and data suggest an over-reliance on teacher assistants. This project will develop ....How schools make decisions about supporting students with disability. How schools make decisions about supporting students with disability. This project aims to examine how schools decide about adjustments for students with disability. More students with disability are enrolled in mainstream schools, and schools take decisions about resourcing to support them. Little is known about how schools make these decisions and data suggest an over-reliance on teacher assistants. This project will develop and evaluate a pilot professional learning package to support schools to make better decisions will be developed and evaluated. A better understanding of decision-making processes is expected to help schools make optimal, cost-effective decisions that personalise learning and support.Read moreRead less
Profiling developmental standards of learning for students with intellectual disabilities. This project addresses an area of educational assessment that has been traditionally neglected as 'too hard'. It offers hope to students with intellectual disabilities. If developmental progress can be mapped and identified in competency terms and linked to successful teaching and learning strategies, the students can be expected to make more rapid progress towards achieving their potential. Teachers in ma ....Profiling developmental standards of learning for students with intellectual disabilities. This project addresses an area of educational assessment that has been traditionally neglected as 'too hard'. It offers hope to students with intellectual disabilities. If developmental progress can be mapped and identified in competency terms and linked to successful teaching and learning strategies, the students can be expected to make more rapid progress towards achieving their potential. Teachers in mainstream schools can also expect to be helped in recognising development and given advice for intervention. The materials will be made available world wide to help all students in this challenging area.Read moreRead less
Partner training and communication outcomes for students with multiple and severe disabilities. This research has the potential to benefit one of the most disadvantaged groups in the community: students with multiple and severe disabilities. These students typically spend more than 70% of the school day with no communication with teachers, teacher aides or other students. The proposed research will investigate whether it is possible to improve levels of communication and engagement through train ....Partner training and communication outcomes for students with multiple and severe disabilities. This research has the potential to benefit one of the most disadvantaged groups in the community: students with multiple and severe disabilities. These students typically spend more than 70% of the school day with no communication with teachers, teacher aides or other students. The proposed research will investigate whether it is possible to improve levels of communication and engagement through training teachers and teacher aides as effective communication partners. Higher levels of communication at school will improve Quality of Life for these students. This research will inform the development of training programs for school staff working with students with multiple and severe disabilities.Read moreRead less
Harmonic analysis of Laplacians in curved spaces. Harmonic Analysis is a branch of mathematics which is interrelated to other fields of mathematics like complex analysis, number theory and partial differential equations (pdes) with many applications in engineering and technology. This project aims to solve a number of difficult fundamental problems at the frontier of harmonic analysis in understanding Laplacians in curved spaces. Such Laplacians control the propagation of heat and waves on manif ....Harmonic analysis of Laplacians in curved spaces. Harmonic Analysis is a branch of mathematics which is interrelated to other fields of mathematics like complex analysis, number theory and partial differential equations (pdes) with many applications in engineering and technology. This project aims to solve a number of difficult fundamental problems at the frontier of harmonic analysis in understanding Laplacians in curved spaces. Such Laplacians control the propagation of heat and waves on manifolds and Lie groups, arising in mathematical physics and quantum mechanics. Expected outcomes are the solutions of dispersive equations and the framework of singular integrals in curved spaces; new ideas and techniques in harmonic analysis developed; and training of Australian future mathematicians.Read moreRead less
Generalised conformal mappings. A conformal mapping preserves shape, at least at very small scale, circles are mapped to circles. The more recently introduced quasi-conformal mappings nearly preserves shape, at least at a very small scale, circles are mapped to regions which are similar to circles. This project will allow different directions to be scaled differently, and will consider mappings that send circles to ellipses of arbitrary eccentricity. The theory to be developed is mathematical an ....Generalised conformal mappings. A conformal mapping preserves shape, at least at very small scale, circles are mapped to circles. The more recently introduced quasi-conformal mappings nearly preserves shape, at least at a very small scale, circles are mapped to regions which are similar to circles. This project will allow different directions to be scaled differently, and will consider mappings that send circles to ellipses of arbitrary eccentricity. The theory to be developed is mathematical and it will provide a unified approach to important results in several areas, including Lie groups and functions of several complex variables. Read moreRead less
Symmetries in real and complex geometry. This project concerns an important area of abstract modern geometry. The results and techniques of the project will lead to significant progress in this area. It will benefit the national scientific reputation, strengthen the research profile of the home institutions, and provide training to young researchers.