Institution: The University of Sydney
Dr. J. J. Cannon, The University of Sydney
|
1998 |
1999 |
2000 |
| Funding |
$88,000 |
$90,000 |
$96,000 |
Title: An Integrated Approach to Computation in Arithmetic Fields
Summary:
One of the most ubiquitous structures in mathematics is a field, ie
an algebraic structure in which the four familiar arithmetic operations
(+,-,-,x)are defined. Global fields are finite degree extensions of either
Q or F_p[x], while local fields are completions of some global field with
respect to a valuation. This project is concerned with the discovery of
effective algorithms (based on the global-local principle) for determining
the principal invariants of global and local fields. Its successful completion
will result in the first-ever facility for general computation in arithmetic
fields.
Institution: Macquarie University
Prof. R. Street, Macquarie University
Prof. G. Kelly, The University of Sydney
A/Prof. R. Walters, The University of Sydney
Dr. M. Johnson, Macquarie University
|
1998 |
1999 |
2000 |
| Funding |
$121,000 |
$124,000 |
$127,000 |
Title: Category Theory Arising from Geometry, Algebra, Computer
Science and Physics
Summary:
Category theory is a branch of mathematics concerned with transformation
and composition. It provides an algebra of wide-spread applicability for
the synthesis and analysis of systems and processes in fields as diverse
as geometry, physics and computer science, and also in mathematics itself.
Often it can be used to clarify and simplify the learning, teaching and
development of mathematics. The aim of this project is to develop the general
theory of categories and specifically to investigate those aspects appropriate
to geometry and computer science.
Institution: The University of Sydney
Prof. G. I. Lehrer, The University of Sydney
|
1998 |
1999 |
2000 |
| Funding |
$100,500 |
$102,500 |
$104,500 |
Title: Group Representation Theory and Cohomology of Algebraic
Varieties
Summary:
Group representation theory is at the centre of the mathematical study
of symmetry. New geometic and topological techniques have led recently
to spectacular advances, a feature of which has been the illumination of
new connections between apparently different fields, such as knot theory,
group characters, quantum groups and codes. This project intends to exploit
these connections and establish new ones to make advances in the various
fields. The study of group actions on algebraic varieties and their cohomology
is central to this progress, realising in a concrete fashion thesymmetry
of which groups are abstractions.
Institution: The University of Western Australia
Prof. C. E. Praeger, The University of Western Australia
|
1998 |
1999 |
2000 |
| Funding |
$60,000 |
$57,000 |
$63,000 |
Title: Transitive Graphs and Quasiprimitive Permutation Groups
Summary:
Automorphism groups of graphs provide both a precise measure of symmetry
of a graph and also a powerful tool for analysing the structure of a graph.
This project will develop a framework for describing the structure of an
important family of vertex-transitive graphs. It will also extend the underlying
theory of quasiprimitive permutation groups to make possible a more effective
analysis of these graphs.
Institution: The University of Sydney
Prof. F. N. Dancer, The University of Sydney
|
1998 |
1999 |
2000 |
| Funding |
$68,000 |
$70,000 |
$72,000 |
Title: Population Models and Partial Differential Equations
Summary:
To study a number of nonlinear elliptic and parabolic systems which
arise in models of population growth for interacting species.
Institution: The University of Adelaide
Dr. N. Joshi, The University of Adelaide
Prof. M. D. Kruskal, Rutgers University
Prof. M. J. Ablowitz, University of Colorado, Boulder
Dr. S. Chakravarty, The University of New South Wales
|
1998 |
1999 |
2000 |
| Funding |
$65,000 |
67,000 |
$69,000 |
Title: Complex Asymptotics and Integrability
Summary:
The theory of nonlinear integrable equations, ie those that are solvable
through associated linear problems, has had a strong impact on mathematics
and physics. However, fundamental gaps remain in their complex asymptotic
descriptions and deep questions remain open about their solvability. The
aim of this project is to develop new complex asymptotic methods, from
which both asymptotic and analytic information about solutions of nonlinear
integrable equations can be obtained. Our underlying aim is to apply these
techniques to answer questions about their integrability.
Institution: Macquarie University
Prof. A. Mcintosh, Macquarie University
|
1998 |
1999 |
2000 |
| Funding |
$79,000 |
$81,000 |
$83,000 |
Title: Harmonic Analysis, Boundary Value Problems, and Maxwell's
Equations in Lipschitz Domains
Summary:
Boundary value problems for partial differential equations arise naturally
when physical problems are expressed in mathematical terms. This project
concerns the systematic development of the harmonic analysis of partial
differential operators, and of the corresponding boundary integrals, in
order to solve such problems on irregular regions. Particular emphasis
is given to studying the propagation of electromagnetic waves through irregularly
shaped objects, approximating physical devises which generate, transmit
and receive radio waves.
Institution: The University of New South Wales
A/Prof. E. S. Noussair, The University of New South Wales
Prof. E. N. Dancer, The University of Sydney
|
1998 |
1999 |
2000 |
| Funding |
$58,500 |
$60,500 |
$66,500 |
Title: The effects of the domain geometry and topology in nonlinear
elliptic equations
Summary:
To study the effect of the domain geometry and topology on the existence,
multiplicity, and profile of spike layer solutions of nonlinear elliptic
equations. Such problems arise from diverse branches of mathematical, physical
and biological sciences, ranging from differential geometry, movements
of cells in chemotaxis, pattern formations, phase transition in superconductors,
genetic models, to the condensation of virus in certain populations.
Institution: The University of Adelaide
Prof. A. Carey, The University of Adelaide
|
1998 |
1999 |
2000 |
| Funding |
$36,000 |
$36,000 |
$36,000 |
Title: Type II spectral flow and applications to mathematical
physics
Summary:
Spectral flow is an invariant of a family of differential operators
depending on a parameter and has played a key technical role over the last
20 years in topology and geometry. Until recently its application has been
restricted: the operators must have discrete spectrum (physically this
means working only with bound states). This spectrum condition is violated
for example in the Atiyah-Singer L^2 theory. I will study the case where
the operators commute with a finite von Neumann algebra and apply it to
problems in mathematical physics thus handling the novel situation where
there may be continuous spectrum.
Institution: The University of Newcastle
Prof. I. Raeburn, The University of Newcastle
|
1998 |
1999 |
2000 |
| Funding |
$78,000 |
$80,000 |
$82,000 |
Title: Toeplitz algebras, semigroup crossed products, and number
theory
Summary:
Dynamical systems are mathematical structures designed to model time
evolution in physics. In quantum physics, an appropriate dynamical system
might consist of a C*-algebra representing the observables and an action
of the real line on the C*-algebra representing time evolution. Using ideas
from number theory, Bost and Connes have recently constructed such a dynamical
system which exhibits a phase transition like those arising in statistical
mechanics. Here we propose to develop methods previously used for studying
Toeplitz algebras, and apply them to a variety of dynamical systems, including
number-theoretic ones like that of Bost and Connes.
Institution: Monash University
Prof. K. Ecker, Monash University
|
1998 |
1999 |
2000 |
| Funding |
$53,000 |
$55,000 |
$57,000 |
Title: Mean Curvature Flow of Noncompact Spacelike Hypersurfaces
in Asymptotically Flat Spacetimes with Applications in General Relativity
Summary:
We study a geometric heat flow of spacelike hypersurfaces in asymptotically
flat spacetimes. This flow propagates a given hypersurfaces at every point
in the direction of its unit normal with speed given by its mean curvature.
We will focus in particular on long-term behaviour of this flow and also
study selfsimilar solutions. Apart from providing new insights into the
theory of geometric evolution equations, this process has applications
in General Relativity. Applications of such geometric evolution equations
in physics and material sciences range from crystal growth and the motion
of grain boundaries to flame propagation.
Institution: Queensland University of Technology
Dr. V. V. Anh, Queensland University of Technology
Prof. C. C. Heyde, The Australian National University
Prof. M. Farge, Ecole Normale Superieure, Paris
|
1998 |
1999 |
2000 |
| Funding |
$60,000 |
$62,000 |
$64,000 |
Title: Structural Study of Long-Range Dependence, Infinite Variance
and Coherent Structures.
Summary:
Data in a large number of fields commonly display long-range dependance
and infinite variance. These characteristics of turbulent flows may be
induced by their coherent structures. Traditional models of turbulence
diffusion, such as stochastic differential equations with Brownian motion
input and Markov random fields, are not capable of capturing these coherent
structures. This project will develop some new classes of models and tools
to represent and analyse the long-range dependence, infinite variance and
coherent structures of turbulent random fields. These include stochastic
differential equations driven by modified fractional Brownian fields and
higher-order wavelet spectra. Application to financial modelling and two-dimensional
turbulence will be undertaken.
Institution: The University of Western Australia
Dr. R. K. Milne, The University of Western Australia
Dr. G. F. Yeo, Murdoch University
A/Prof. B. W. Madsen, The University of Western Australia
|
1998 |
1999 |
2000 |
| Funding |
$53,000 |
$55,000 |
$57,000 |
Title: Ion Channel Interactions: Stochastic Modelling and Inference
Summary:
We propose models of and methods for the analysis of a system of interacting
ion channels. Ion channels are fundamentally important in the regulation
of cellular physiology. The project will develop probabilistic, statistical
and computational methods for the study of these systems, emphasising interactive
and spatial aspects about which little is presently known. Some of these
methods will also be applied to multiprocessors comprising processors and
buffers with application to system reliability.
Institution: The Australian National University
Prof. P. Hall, The Australian National University
|
1998 |
1999 |
2000 |
| Funding |
$180,000 |
$186,000 |
$204,000 |
Title: Theory and Applications of Computer-Intensive Statistical
Methods
Summary:
Four inter-related projects are proposed, addressing (1) estimating
the intensity of a point process with infinite poles, (II) testing hypotheses
about the number of modes of a population, (III) estimating a boundary
from digitised data, and (IV) implementing the bootstrap with spatial data.
The projects are motivated by problems arising in, respectively, (I) geophysics,
(II) population mixtures, (III) image analysis, and (IV) biological science.
Institution: Murdoch University
Prof. I. R. James, Murdoch University
A/Prof. R. A. Maller, The University of Western Australia
|
1998 |
1999 |
2000 |
| Funding |
$50,000 |
$52,000 |
$54,000 |
Title: Multivariate Failure Time Analysis
Summary:
Multivariate failure times arise in a wide variety of practical situations,
such as when repeated episodes of the same event occur on an individual,
when times to different events are recorded on the same individual, or
when single events occur for each case, but where cases may be associated
by environmental, genetic or other factors. Resulting correlations between
the failure times plus the added complication of potential incompleteness
in the data (censoring) mandates development of statistical methods which
accommodate general correlation structures and are robust to censoring
assumptions. This project aims to develop a suite of methods to achieve
this.
Institution: The University of New South Wales
Prof. R. Kohn, The University of New South Wales
A/Prof. S. J. Sheather, The University of New South Wales
|
1998 |
1999 |
2000 |
| Funding |
$60,000 |
$55,000 |
$57,000 |
Title: Flexible methods for estimating regression models
Summary:
Regression analysis tries to predict the value of one variable from
the values of one or more predictor variables. It is proposed to develop
methods for estimating the regression function without assuming that its
form is known. The methods will be comprehensive and widely applicable.
In particular, we will apply the methodology to detect trends in ozone
data and to determine the drives of customers satisfaction. The methods
will cover a range of settings including discrete and continuous data for
cases in which the variance may not be constant. The approach involves
both Bayesian and non Bayesian methods.
Institution: Queensland University of Technology
Dr. R. C. Wolff, Queensland University of Technology
Dr. K. L. Mengersen, Queensland University of Technology
|
1998 |
1999 |
2000 |
| Funding |
$25,000 |
$24,906 |
$50,000 |
Title: Convergence Diagnostics for Markov Chain Monte Carlo: A
Non-Parametric and Non-Linear Dynamical Systems Approach
Summary:
Markov chain Monte Carlo (MCMC) methods are employed to conduct numerically
complex statistical inference especially where a theoretical approach is
unavailable. It is almost always required to verify that MCMC output is
regularly behaved (stationary): many present methods involve dated classical
techniques which are restricted in their scope. This project takes a novel
approach by proposing a suite of new techniques to assess stationarity
which draw on methods from non-linear dynamical systems theory which have
enjoyed recent statistical development in their own right. The research
will contribute new methodology and software for this specific and more
general applications.
Institution: The University of New South Wales
Prof. I. H. Sloan, The University of New South Wales
|
1998 |
1999 |
2000 |
| Funding |
$68,000 |
$70,000 |
$76,000 |
Title: Numerical integration and approximation in high
dimensions
Summary:
Multiple integrals play a key role in atomic and molecular chemistry
and physics, solid-state and nuclear physics, statistics and statistical
mechanics, and other areas of science. When there are many variables (ie
when the dimension is high) such integrals are hard to evaluate accurately
and reliably. Computer evaluations are typically both expensive and of
uncertain accuracy. This project aims to develop and analyse new and existing
computational methods of multiple integration and related approximation
problems, and improve the theoretical knowledge of what is achievable if
the integration rules are as good as possible.
Institution: The University of New South Wales
A/Prof. D. W. Kelly, The University of New South Wales
Prof. I. H. Sloan, The University of New South Wales
|
1998 |
1999 |
2000 |
| Funding |
$62,500 |
$61,000 |
$65,500 |
Title: Improved pointwise error bounds for the
finite element method in engineering
Summary:
Practical engineering applications of the finite element method
would be enhanced if reliable bounds on the errors in
computed stresses and other quantities were available.
In an earlier project rigorous error bounds for certain model problems,
both linear and (in a restricted sense) nonlinear, were developed.
This project aims to refine the procedure to the point where the
computed error bounds are reliably within a factor of two of the true error,
to develop a measure of the quality of the bound, and to broaden
the range of engineering applications to which the procedure can be applied.
Institution: The University of New South Wales
A/Prof. L. Qi, The University of New South Wales
Dr. R. S. Womersley, The University of New South Wales
|
1998 |
1999 |
2000 |
| Funding |
$55,000 |
$57,000 |
$59,000 |
Title: SQP and QP-free algorithms for nonlinear programming
Summary:
Nonlinear programming (NLP) is widely used to model decision problems
in engineering, business and economics. Sequential quadratical programming
(SQP) is one of the most successful computational methods for solving NLP.
Later improvements of SQP methods include feasible SQP and QP-free methods.
This project is to analyse weaker convergence conditions for these methods,
to construct new versions of these methods which are effective even in
degenerate cases, and thus to develop more efficient and robust algorithms
for solving NLP.
Institution: The University of Adelaide
A/Prof. C. E. Pearce, The University of Adelaide
|
1998 |
1999 |
2000 |
| Funding |
$53,000 |
$55,000 |
$57,000 |
Title: Tight bounds for some performance measures in loss systems
occurring in telecommunications networks
Summary:
In the analysis of telecommunication networks, full details of system
parameters are often unavailable. In such situations it is useful to have
tight upper and lower bounds for performance measures over the family of
parameter values prescribed by the information available on the parameter
values. These provide practical tools useful for performance analysis and
dimensioning in the realistic context of incomplete knowledge. This project
aims to obtain new results which can be used in this way.
Institution: The University of Queensland
A/Prof. G. Havas, The University of Queensland
|
1998 |
1999 |
2000 |
| Funding |
$48,000 |
$50,000 |
$52,000 |
Title: Algorithms and Applications in Finite Fields
Summary:
We will develop new, efficient algorithms for specificproblems in finite
field theory where current computing techniques areinadequate. These algorithms
will then be used to obtain new results.Computational group theory plays
a prominent role in mathematical research.Much of the work in this area
is related to group theory, combinatorics, graphtheory, projective geometry,
coding theory and cryptography, so that advancesmade by this project will
also benefit these areas. The results obtained willprovide insight into
a wide range of related problems, enabling furtheradvances in specific
problems.
Institution: The University of Queensland
A/Prof. G. Havas, The University of Queensland
|
1998 |
1999 |
2000 |
| Funding |
$54,000 |
$56,000 |
$58,000 |
Title: Computing with Finitely Presented Groups
Summary:
Group theory is a fundamental part of pure mathematicsand computational
group theory addresses many of its problems. We will design,implement,
test, analyase and apply improved basic algorithms for finitelypresented
groups on high performance computers. This means designing newalgorithms,
redesigning old ones, and using such algorithms to solve problemswhere
current techniques are in adequate. We will provide training for advancedstudents,
and collaborate both nationally and internationally.
Institution: The University of Queensland
Prof. A. P. Street, The University of Queensland
Prof. J. R. Seberry, University of Wollongong
Dr. T. Hardjono, University of Western Sydney
|
1998 |
1999 |
2000 |
| Funding |
$50,000 |
$52,000 |
$54,000 |
Title: Access Schemes amd Data Protection Schemes for Computer
Security and Electronic Strongboxes from Combinatorial Structures.
Summary:
Combinatorics is the study of configurations, which arise whenever
objects are distributed according to certain pre-determined constraints.
Block designs and Latin squares are two such configurations, long studied
for their mathematical elegance; since 1935, they have also been studied
for their applications, most recently in the construction of access (secret-sharing)
schemes for computer security and of electronic strongboxes. This project
builds on results of earlier ARC-funded projects to produce combinatorial
structures for more efficient access schemes and for application in electronic
commerce, making particular use of bent functions associated with Hadamard
designs and of minimal substructures defining designs and squares.
Institution: Curtin University of Technology
Prof. K. Teo, Curtin University of Technology
Prof. L. Caccetta, Curtin University of Technology
Dr. V. Rehbock, Curtin University of Technology
Dr. S. Wang, Curtin University of Technology
|
1998 |
1999 |
2000 |
| Funding |
$54,000 |
$56,000 |
$58,000 |
Title: Static and Dynamic Optimisation Problems InvolvingVariable
Switching Times and Mixed Discrete Decision Variables
Summary:
The aim of the project is to develop efficientcomputational algorithms
to solve a range of optimisation problems, includingboth static and dynamic
problems, where some or all of the decision variablesare restricted to
a discrete set of values. The techniques developed fordynamic optimisation
problems will also be used in developing solution methodsfor dynamic optimisation
problems with switching and impulsive controls.Finally the project also
aims to find new and more efficient methods forsolving semi-infinite programming
problems in order to greatly extend the classof problems that can be dealt
with by the earlier methods.
Institution: The University of Queensland
Dr. P. M. Diamond, The University of Queensland
Dr. X. Z. Yuan, The University of Queensland
Dr. H. B. Thompson, The University of Queensland
|
1998 |
1999 |
2000 |
| Funding |
$50,000 |
$50,000 |
$52,000 |
Title: Set-Valued Methods in Robust Control
Summary:
Control of systems or industrial processes must deal with plant variability
and uncertainty, possibly with extremely strict performance specifications.
The central problem of feedback control is to design controllers which
both tolerate and reduce effects of variability and imprecision attaining
robust control over a family of processes. This is typically accomplished
by studying how plant perturbations affect output. This project examines
robust control from a different perspective, considering a class of systems
as a whole rather than perturbing a single, nominal plant. Set-valued methods
and processes will be used to control sets of plant encompassing all variations
and uncertainties.
Institution: Queensland University of Technology
Prof. D. L. McElwain, Queensland University of Technology
Dr. S. A. Domanti, James Cook University of North Queensland
|
1998 |
1999 |
2000 |
| Funding |
$51,200 |
$50,000 |
$53,000 |
Title: Modelling the Tinplate Temper Rolling Process
Summary:
Tinplate temper rolling, which often represents the final stage of
processing, involves product of high added value and is of prime importance
in determining the final product quality. Despite this, the current models
used to control these mills do not have a good predictive capability. This
project employs a novel approach using high-level applied mathematical
and numerical analysis to develop a model of temper rolling with the aim
of providing a better understanding of the underlying processes. This will
lead to improved on-line algorithms for temper mill control and advances
in the selection of suitable roll surface finishes.
Institution: The University of Melbourne
Prof. J. H. Rubinstein, The University of Melbourne
A/Prof. N. Wormald, The University of Melbourne
Dr. D. Thomas, The University of Melbourne
|
1998 |
1999 |
2000 |
| Funding |
$60,200 |
$56,000 |
$62,000 |
Title: Optimal Transport Networks
Summary:
The network design problem has extensive applications in industry and
communications. We will investigate the problem of designing networks which
are as short as possible and which satisfy a constraint on the steepness
of edges. This situation arises, for example, in underground mining where
gradients of tunnels connecting discrete nodular ore deposits are constrained
by haulage costs. Other applications are road, track or pipeline systems.
The purpose of this work is to develop a complete theory of gradient constrained
minimal networks and apply it to finding fast algorithms for constructing
these networks.
