Curvature flows and spectral estimates. Curvature flows are a class of geometrically motivated equations, modelled on the heat equation. Recently, researchers have developed new methods for studying the regularity of solutions to these equations, and applied them to a different problem, that of estimating quantities depending on the smaller eigenvalues of a Schroedinger operator. This project builds on the early success of this research and will produce a new understanding of the behaviour of ei ....Curvature flows and spectral estimates. Curvature flows are a class of geometrically motivated equations, modelled on the heat equation. Recently, researchers have developed new methods for studying the regularity of solutions to these equations, and applied them to a different problem, that of estimating quantities depending on the smaller eigenvalues of a Schroedinger operator. This project builds on the early success of this research and will produce a new understanding of the behaviour of eigenvalues, establish sharp estimates for spectral quantities, particularly on manifolds with curvature bounds, and find optimal conditions under which non-compact solutions to curvature flows are stable.Read moreRead less
Energy, Cosmic Censorship and Black Hole Stability. Human progress is achieved by confronting fundamental questions, at the leading edge of knowledge. This project will lead to better understanding of space-time physics, and of the properties of singular solutions of non-linear hyperbolic equations. Such equations govern a wide range of physical phenomena, including fluid flow, weather and electromagnetic fields.
Global wavefront propagation and non-elliptic Fredholm theory. Many significant phenomena in the natural world are described by partial differential equations that involve evolution in time. This project aims to develop new mathematical methods, involving recently discovered global wavefront set analysis and Fredholm theory, to solve such equations. These methods aim to extend the range of equations that can be solved as well as yield more information about solutions, in particular, their long-t ....Global wavefront propagation and non-elliptic Fredholm theory. Many significant phenomena in the natural world are described by partial differential equations that involve evolution in time. This project aims to develop new mathematical methods, involving recently discovered global wavefront set analysis and Fredholm theory, to solve such equations. These methods aim to extend the range of equations that can be solved as well as yield more information about solutions, in particular, their long-time asymptotics.Read moreRead less
Ocular Motility In Autism And Asperger S Disorder: Dissociation Of Motor Deficits.
Funder
National Health and Medical Research Council
Funding Amount
$131,235.00
Summary
We will use ocular motor technology to investigate motor dysfunction in autism and Asperger's disorder, to advance our understanding of the neurobiological bases of these disorders. This will help clarify whether neural networks are differentially disrupted in these disorders, as our previous clinical research suggests. This dissociation and the subsequent development of an ocular motor clincal screen may improve diagnosis, and potentially treatment, of these devastating conditions.
Motor Functioning In Autism And Asperger's Disorder: Furthering Current Neurobehavioural And Clinical Definitions
Funder
National Health and Medical Research Council
Funding Amount
$354,932.00
Summary
While it is well known that autism and Asperger's disorder are associated with social, communicative, and behavioural symptoms, it is less well known that affected individuals also have considerable movement and coordination difficulties. For example, these children often have problems with hand writing, walking, hopping, skipping, catching, and running. These skills are very important for success at school; for example, if children are unable to participate in school sports they often feel isol ....While it is well known that autism and Asperger's disorder are associated with social, communicative, and behavioural symptoms, it is less well known that affected individuals also have considerable movement and coordination difficulties. For example, these children often have problems with hand writing, walking, hopping, skipping, catching, and running. These skills are very important for success at school; for example, if children are unable to participate in school sports they often feel isolated and rejected from the peer group. Also, hand writing problems have a significant impact on children's academic performance. Our previous research has suggested that there may be particular patterns of motor problems that characterise individuals with autism and Asperger's disorder. Our proposed research aims to use the kinds of 3D motion analysis technology used in the movie industry to capture exactly how people affected by these conditions move and respond to the environment. This study will enable us to highlight particular parts of the brain-motor circuitry that are affected by these disorders and will also enable us to more clearly distinguish how autism is different from Asperger's disorder. Ultimately, it is hoped that our motor investigations will lead to improved assessment and interventions for these disorders.Read moreRead less