ORCID Profile
0000-0002-5712-0113
Current Organisation
University of Melbourne
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Research Topics
In Research Link Australia (RLA), "Research Topics" refer to ANZSRC FOR and SEO codes. These topics are either sourced from ANZSRC FOR and SEO codes listed in researchers' related grants or generated by a large language model (LLM) based on their publications.
Top 5 Research Topics
ANZSRC Field of Research (FoR)
Pure Mathematics | Topology And Manifolds | Numerical and Computational Mathematics | Topology | Algebraic and Differential Geometry | Geometry | Optimisation | Operations Research | Optimisation | Mathematical Sciences Not Elsewhere Classified | Mining Engineering | Mining Engineering | Dynamical Systems | Analysis of Algorithms and Complexity | Applied Mathematics | Mathematical Physics | Calculus of Variations, Systems Theory and Control Theory | Operations Research | Mathematical Aspects of Quantum and Conformal Field Theory, Quantum Gravity and String Theory | Functional Analysis |
ANZSRC Socio-Economic Objective (SEO)
Mathematical sciences | Expanding Knowledge in the Mathematical Sciences | Expanding Knowledge in Engineering | Mining and Extraction of Precious (Noble) Metal Ores | Mining and Extraction of Copper Ores | Education and training not elsewhere classified | Instrumentation not elsewhere classified | Communication Equipment not elsewhere classified | Higher education | Other
Related Links
Publications
Curvature-constrained directional-cost paths in the plane
Publisher: Springer Science and Business Media LLC
Date: 31-05-2012
Note on spun normal surfaces in 1-efficient ideal triangulations
Publisher: Project Euclid
Date: 08-2015
DOI: 10.3792/PJAA.91.118
The Steiner ratio conjecture for six points
Publisher: Elsevier BV
Date: 09-1991
Embedded minimal surfaces in 3-manifolds with positive scalar curvature
Publisher: American Mathematical Society (AMS)
Date: 1985
DOI: 10.1090/S0002-9939-1985-0806087-8
Abstract: Let M M be a closed orientable Riemannian 3 3 -manifold with positive scalar curvature. We prove that any embedded closed minimal surface in M M has a topological description as a generalized Heegaard surface. Also an existence theorem is proved which gives ex les of such minimal surfaces.
Minimum networks for four points in space
Publisher: Springer Science and Business Media LLC
Date: 2002
Stability of asymmetric tetraquarks in the minimal-path linear potential
Publisher: Elsevier BV
Date: 04-2009
Free actions of some finite groups on S3. I
Publisher: Springer Science and Business Media LLC
Date: 06-1979
DOI: 10.1007/BF01364631
Optimising declines in underground mines
Publisher: Informa UK Limited
Date: 12-2003
Shifting: One-inclusion mistake bounds and sample compression
Publisher: Elsevier BV
Date: 2009
Corrigendum to Shifting: One-inclusion mistake bounds and sample compression [J. Comput. System Sci. 75 (1) (2009) 37-59] (DOI:10.1016/j.jcss.2008.07.005)
Publisher: Elsevier BV
Date: 05-2010
Equivariant minimax and minimal surfaces in geometric three-manifolds
Publisher: American Mathematical Society (AMS)
Date: 1988
Graham's problem on shortest networks for points on a circle
Publisher: Springer Science and Business Media LLC
Date: 06-1992
DOI: 10.1007/BF01758758
The Steiner ratio conjecture for cocircular points
Publisher: Springer Science and Business Media LLC
Date: 1992
DOI: 10.1007/BF02187826
The steiner minimal network for convex configurations
Publisher: Springer Science and Business Media LLC
Date: 03-1993
DOI: 10.1007/BF02189325
Approximations and lower bounds for the length of minimal euclidean steiner trees
Publisher: Springer Science and Business Media LLC
Date: 08-2006
Triangulations of hyperbolic 3-manifolds admitting strict angle structures
Publisher: Wiley
Date: 08-10-2012
Cusp structures of alternating links
Publisher: Springer Science and Business Media LLC
Date: 12-1992
DOI: 10.1007/BF01232034
Even triangulations of n–dimensional pseudo-manifolds
Publisher: Mathematical Sciences Publishers
Date: 12-11-2012
Symmetric cut loci in riemannian manifolds
Publisher: American Mathematical Society (AMS)
Date: 1985
DOI: 10.1090/S0002-9939-1985-0784185-5
Abstract: Let M M be a compact Riemannian manifold with H 1 ( M , Z ) = 0 {H_1}(M,Z) = 0 . We show that, for a point p ∈ M p \\in M , the cut locus and conjugate locus of p p must intersect if M M admits a group of isometries which fixes p p and has principal orbits of codimension at most 2. This is a classical theorem of Myers [ 5 ] in the case when M M has dimension 2.
Localising Dehn's lemma and the loop theorem in 3-manifolds
Publisher: Cambridge University Press (CUP)
Date: 09-2004
Inflations of ideal triangulations
Publisher: Elsevier BV
Date: 12-2014
Maximizing the net present value of a Steiner tree
Publisher: Springer Science and Business Media LLC
Date: 22-10-2014
Solving the prize‐collecting Euclidean Steiner tree problem
Publisher: Wiley
Date: 05-08-2020
DOI: 10.1111/ITOR.12853
Abstract: The prize‐collecting Euclidean Steiner tree (PCEST) problem is a generalization of the well‐known Euclidean Steiner tree (EST) problem. All points given in an EST problem instance are connected by the shortest possible network in a solution. A solution can include additional points called Steiner points. A PCEST problem instance differs from an EST problem instance by the addition of weights for each given point. A PCEST solution connects a subset of the given points in order to maximize the net value of the network (the sum of the selected point weights, less than the length of the network). We present an algorithmic framework for solving the PCEST problem. Included in the framework are efficient methods to determine subsets of points that must be in every solution, and subsets of points that cannot be in any solution. Also included are methods to generate and concatenate full Steiner trees.
Gradient-Constrained Minimum Networks. III. Fixed Topology
Publisher: Springer Science and Business Media LLC
Date: 29-03-2012
ℤ2 -Thurston norm and complexity of 3-manifolds
Publisher: Springer Science and Business Media LLC
Date: 21-06-2013
Cost optimisation for underground mining networks
Publisher: Springer Science and Business Media LLC
Date: 06-2005
Improving underground mine access layouts using software tools
Publisher: Institute for Operations Research and the Management Sciences (INFORMS)
Date: 04-2014
Abstract: The authors have developed two software tools, PUNO and DOT, for optimally designing the layout of the system of tunnels in an underground mine, known as the access network for the mine. We recently applied these tools, which use principles from geometric optimization, to ore deposits at the Prominent Hill mine in South Australia and the Leeville gold mine in Nevada. When we compared the designs that the tools generated with the designs prepared by mining engineers, we found that our tools generated designs more quickly, were at least as cost efficient, and often revealed new design options by which the engineers’ original designs could be improved.
Bounding embeddings of VC classes into maximum classes
Publisher: Springer International Publishing
Date: 2015
Knots and k-width
Publisher: Springer Science and Business Media LLC
Date: 23-04-2009
Minimum Steiner trees on a set of concyclic points and their center
Publisher: Wiley
Date: 13-09-2021
DOI: 10.1111/ITOR.13055
Abstract: Consider a configuration of points comprising a point q and a set of concyclic points R that are all a given distance r from q in the Euclidean plane. In this paper, we investigate the relationship between the length of a minimum Steiner tree (MStT) on and a minimum spanning tree on R . We show that if the degree of q in the MStT is 1, then the difference between these two lengths is at least , and that this lower bound is tight. This bound can be applied as part of an efficient algorithm to find the solution to the prize‐collecting Euclidean Steiner tree problem, as outlined in an earlier paper.
Gradient-constrained discounted Steiner trees I: optimal tree configurations
Publisher: Springer Science and Business Media LLC
Date: 20-06-2016
Nonorientable surfaces in some non-haken 3-manifolds
Publisher: American Mathematical Society (AMS)
Date: 1982
DOI: 10.1090/S0002-9947-1982-0645327-7
Abstract: If a closed, irreducible, orientable 3 3 -manifold M M does not possess any 2 2 -sided incompressible surfaces, then it can be very useful to investigate embedded one-sided surfaces in M M of minimal genus. In this paper such 3 3 -manifolds M M are studied which admit embeddings of the nonorientable surface K K of genus 3 3 . We prove that a 3 3 -manifold M M of the above type has at most 3 3 different isotopy classes of embeddings of K K representing a fixed element of H 2 ( M , Z 2 ) {H_2}(M,\\,{Z_2}) . If M M is either a binary octahedral space, an appropriate lens space or Seifert manifold, or if M M has a particular type of fibered knot, then it is shown that the embedding of K K in M M realizing a specific homology class is unique up to isotopy.
Optimal curvature-constrained paths for general directional-cost functions
Publisher: Springer Science and Business Media LLC
Date: 17-12-2013
A variational approach to the Steiner network problem
Publisher: Springer Science and Business Media LLC
Date: 06-1991
DOI: 10.1007/BF02071984
Diffeomorphisms of Elliptic 3-Manifolds
Publisher: Springer Berlin Heidelberg
Date: 2012
Minimal steiner trees for 2k × 2k square lattices
Publisher: Elsevier BV
Date: 1996
OPTIMAL LOCATION OF AN UNDERGROUND CONNECTOR USING DISCOUNTED STEINER TREE THEORY
Publisher: Cambridge University Press (CUP)
Date: 07-2020
DOI: 10.1017/S1446181120000231
Abstract: The objective of this paper is to demonstrate that the gradient-constrained discounted Steiner point algorithm (GCDSPA) described in an earlier paper by the authors is applicable to a class of real mine planning problems, by using the algorithm to design a part of the underground access in the Rubicon gold mine near Kalgoorlie in Western Australia. The algorithm is used to design a decline connecting two ore bodies so as to maximize the net present value (NPV) associated with the connector. The connector is to break out from the access infrastructure of one ore body and extend to the other ore body. There is a junction on the connector where it splits in two near the second ore body. The GCDSPA is used to obtain the optimal location of the junction and the corresponding NPV. The result demonstrates that the GCDSPA can be used to solve certain problems in mine planning for which currently available methods cannot provide optimal solutions.
Coverings and minimal triangulations of 3-manifolds
Publisher: Mathematical Sciences Publishers
Date: 04-05-2011
One-sided heegaard splittings and homeotopy groups of some 3-manifolds
Publisher: Wiley
Date: 11-1984
Closed geodesics on incomplete surfaces
Publisher: Springer Science and Business Media LLC
Date: 23-11-2005
Incompressible surfaces and the topology of 3-dimensional manifolds
Publisher: Cambridge University Press (CUP)
Date: 08-1993
DOI: 10.1017/S144678870003189X
Abstract: Existence and properties of incompressible surfaces in 3-dimensional manifolds are surveyed. Some conjectures of Waldhausen and Thurston concerning such surfaces are stated. An outline is given of the proof that such surfaces can be pulled back by non-zero degree maps between 3-manifolds. The effect of surgery on immersed, incompressible surfaces and on hierarchies is discussed. A characterisation is given of the immersed, incompressible surfaces previously studied by Hass and Scott, which arise naturally with cubings of non-positive curvature.
PL equivariant surgery and invariant decompositions of 3-manifolds
Publisher: Elsevier BV
Date: 02-1989
A polynomial algorithm for a constrained traveling salesman problem
Publisher: Wiley
Date: 14-08-2001
DOI: 10.1002/NET.1025
Decline design in underground mines using constrained path optimisation
Publisher: Informa UK Limited
Date: 06-2008
On 3-manifolds that have finite fundamental group and contain klein bottles
Publisher: American Mathematical Society (AMS)
Date: 1979
DOI: 10.1090/S0002-9947-1979-0531972-6
Abstract: The closed irreducible 3-manifolds with finite fundamental group and containing an embedded Klein bottle can be identified with certain Seifert fibre spaces. We calculate the isotopy classes of homeomorphisms of such 3-manifolds. Also we prove that a free involution acting on a manifold of this type, gives as quotient either a lens space or a manifold in this class. As a corollary it follows that a free action of Z 8 {Z_8} or a generalized quaternionic group on S 3 {S^3} is equivalent to an orthogonal action.
Minimal curvature-constrained paths in the plane with a constraint on arcs with opposite orientations
Publisher: World Scientific Pub Co Pte Lt
Date: 06-2013
DOI: 10.1142/S0218195913500064
Abstract: The declines that provide vehicle access in an underground mine are typically designed as paths formed by concatenating line segments and circular arcs. In order to reduce wear on the ore trucks and the road surfaces and to enhance driver safety, such paths may be subject to a further constraint: each pair of consecutive arcs with opposite orientations must be separated by a straight line segment of at least a certain specified length. In order to reduce the construction and operational costs of the mine, it is desirable to minimize the lengths of such paths between any given pair of directed points. Some necessary and sufficient conditions are obtained for paths of this form to be locally or globally minimal with respect to length. In particular, it is shown that there is always a globally minimal path that contains at most four circular arcs.
Finding planar surfaces in knot- and link-manifolds
Publisher: World Scientific Pub Co Pte Lt
Date: 03-2009
DOI: 10.1142/S0218216509006987
Abstract: It is shown that given any link-manifold, there is an algorithm to decide if the manifold contains an embedded, essential planar surface if it does, the algorithm will construct one. Two similar results are obtained with added boundary conditions. Namely, given a link-manifold M, a component B of ∂M, and a slope γ on B, there is an algorithm to decide if there is an embedded punctured-disk in M with boundary γ and punctures in ∂M\\B and given a link-manifold M, a component B of ∂M, and a meridian slope μ on B, there is an algorithm to decide if there is an embedded punctured-disk with boundary a longitude on B and punctures in ∂M\\B. In both cases, if there is one, the algorithm will construct one. The proofs introduce a number of new methods and differ from the classical proofs, using normal surfaces, as solutions may not be found among the fundamental solutions.
Gradient-constrained discounted Steiner trees II: optimally locating a discounted Steiner point
Publisher: Springer Science and Business Media LLC
Date: 24-06-2016
Gradient-constrained minimum networks. I. Fundamentals
Publisher: Springer Science and Business Media LLC
Date: 2001
Finiteness of 3-manifolds associated with non-zero degree mappings
Publisher: European Mathematical Society - EMS - Publishing House GmbH
Date: 2014
DOI: 10.4171/CMH/312
Optimal curvature and gradient-constrained directional cost paths in 3-space
Publisher: Springer Science and Business Media LLC
Date: 15-10-2015
Related Organisations
University Of California, Berkeley
Location: United States of America
Related Funding Activities
Discovery Projects - Grant ID: DP0664276
Start Date: 2006
End Date: 12-2009
Amount: $246,000.00
Funder: Australian Research Council
View Funded ActivityDiscovery Projects - Grant ID: DP140103163
Start Date: 2014
End Date: 09-2017
Amount: $368,000.00
Funder: Australian Research Council
View Funded ActivityDiscovery Projects - Grant ID: DP0772708
Start Date: 2008
End Date: 12-2012
Amount: $400,000.00
Funder: Australian Research Council
View Funded ActivityDiscovery Projects - Grant ID: DP190102259
Start Date: 07-2019
End Date: 12-2024
Amount: $375,000.00
Funder: Australian Research Council
View Funded ActivityDiscovery Projects - Grant ID: DP130103694
Start Date: 2013
End Date: 03-2017
Amount: $360,000.00
Funder: Australian Research Council
View Funded ActivityDiscovery Projects - Grant ID: DP160104502
Start Date: 03-2016
End Date: 06-2019
Amount: $334,000.00
Funder: Australian Research Council
View Funded ActivityLinkage Projects - Grant ID: LP0882627
Start Date: 2008
End Date: 12-2010
Amount: $179,786.00
Funder: Australian Research Council
View Funded ActivityLinkage Projects - Grant ID: LP0453632
Start Date: 12-2004
End Date: 12-2007
Amount: $248,259.00
Funder: Australian Research Council
View Funded ActivityLinkage Projects - Grant ID: LP100200112
Start Date: 11-2010
End Date: 12-2013
Amount: $195,000.00
Funder: Australian Research Council
View Funded ActivityDiscovery Projects - Grant ID: DP1095760
Start Date: 01-2010
End Date: 12-2013
Amount: $345,000.00
Funder: Australian Research Council
View Funded ActivityDiscovery Projects - Grant ID: DP0208490
Start Date: 2002
End Date: 12-2007
Amount: $466,000.00
Funder: Australian Research Council
View Funded ActivityDiscovery Projects - Grant ID: DP190102363
Start Date: 06-2019
End Date: 12-2024
Amount: $300,000.00
Funder: Australian Research Council
View Funded ActivityLinkage Projects - Grant ID: LP140100124
Start Date: 07-2014
End Date: 07-2017
Amount: $322,975.00
Funder: Australian Research Council
View Funded ActivitySpecial Research Initiatives - Grant ID: SR0354727
Start Date: 2003
End Date: 12-2003
Amount: $20,000.00
Funder: Australian Research Council
View Funded ActivityDiscovery Projects - Grant ID: DP0344091
Start Date: 2003
End Date: 12-2007
Amount: $185,000.00
Funder: Australian Research Council
View Funded ActivitySpecial Research Initiatives - Grant ID: SR0354466
Start Date: 2004
End Date: 12-2004
Amount: $20,000.00
Funder: Australian Research Council
View Funded Activity