ORCID Profile
0000-0001-7118-8491
Current Organisation
Australian National University
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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)
Artificial Intelligence and Image Processing | Applied Mathematics not elsewhere classified | Composite and Hybrid Materials | Topology And Manifolds | Image Processing | Applied Mathematics | Other Physical Sciences | Petroleum And Reservoir Engineering | Pattern Recognition and Data Mining | Instruments And Techniques | Image Processing | Physical Sciences Not Elsewhere Classified
ANZSRC Socio-Economic Objective (SEO)
Oil and gas | Expanding Knowledge in the Physical Sciences | Expanding Knowledge in the Information and Computing Sciences | Expanding Knowledge in Engineering | Medical instrumentation | Reconstituted products (e.g. chipboard, particle board) | Expanding Knowledge in the Mathematical Sciences | Mathematical sciences | Scientific instrumentation |
Related Links
Publications
Morse theory and persistent homology for topological analysis of 3D images of complex materials
Publisher: IEEE
Date: 10-2014
Topology-based signal separation
Publisher: AIP Publishing
Date: 19-05-2004
DOI: 10.1063/1.1705852
Abstract: Traditional noise-filtering techniques are known to significantly alter features of chaotic data. In this paper, we present a noncausal topology-based filtering method for continuous-time dynamical systems that is effective in removing additive, uncorrelated noise from time-series data. Signal-to-noise ratios and Lyapunov exponent estimates are dramatically improved following the removal of the identified noisy points.
Geometrical and topological evolution of a closed-cell aluminium foam subject to drop-weight impact: An X-ray tomography study
Publisher: Elsevier BV
Date: 05-2020
Computing connectedness: disconnectedness and discreteness
Publisher: Elsevier BV
Date: 05-2000
The Impact of Changes in Resolution on the Persistent Homology of Images
Publisher: IEEE
Date: 15-12-2021
2D hyperbolic groups induce three-periodic Euclidean reticulations
Publisher: Springer Science and Business Media LLC
Date: 06-2004
Ideal geometry of periodic entanglements
Publisher: The Royal Society
Date: 09-2015
Abstract: Three-dimensional entanglements, including knots, knotted graphs, periodic arrays of woven filaments and interpenetrating nets, form an integral part of structure analysis because they influence various physical properties. Ideal embeddings of these entanglements give insight into identification and classification of the geometry and physically relevant configurations in vivo . This paper introduces an algorithm for the tightening of finite, periodic and branched entanglements to a least energy form. Our algorithm draws inspiration from the Shrink-On-No-Overlaps (SONO) (Pieranski 1998 In Ideal knots (eds A Stasiak, V Katritch, LH Kauffman), vol. 19, pp. 20–41.) algorithm for the tightening of knots and links: we call it Periodic-Branched Shrink-On-No-Overlaps (PB-SONO). We reproduce published results for ideal configurations of knots using PB-SONO. We then examine ideal geometry for finite entangled graphs, including θ -graphs and entangled tetrahedron- and cube-graphs. Finally, we compute ideal conformations of periodic weavings and entangled nets. The resulting ideal geometry is intriguing: we see spontaneous symmetrisation in some cases, breaking of symmetry in others, as well as configurations reminiscent of biological and chemical structures in nature.
Tile-Transitive Tilings of the Euclidean and Hyperbolic Planes by Ribbons
Publisher: Springer International Publishing
Date: 2022
A note on the two symmetry-preserving covering maps of the gyroid minimal surface
Publisher: Springer Science and Business Media LLC
Date: 11-2005
Granular compaction and the topology of pore deformation
Publisher: EDP Sciences
Date: 2017
Evolution of local motifs and topological proximity in self-assembled quasi-crystalline phases
Publisher: The Royal Society
Date: 09-2020
Abstract: Using methods from the field of topological data analysis, we investigate the self-assembly and emergence of three-dimensional quasi-crystalline structures in a single-component colloidal system. Combining molecular dynamics and persistent homology, we analyse the time evolution of persistence diagrams and particular local structural motifs. Our analysis reveals the formation and dissipation of specific particle constellations in these trajectories, and shows that the persistence diagrams are sensitive to nucleation and convergence to a final structure. Identification of local motifs allows quantification of the similarities between the final structures in a topological sense. This analysis reveals a continuous variation with density between crystalline clathrate, quasi-crystalline, and disordered phases quantified by ‘topological proximity’, a visualization of the Wasserstein distances between persistence diagrams. From a topological perspective, there is a subtle, but direct connection between quasi-crystalline, crystalline and disordered states. Our results demonstrate that topological data analysis provides detailed insights into molecular self-assembly.
Pediatric traumatic brain injury: Language outcomes and their relationship to the arcuate fasciculus
Publisher: Elsevier BV
Date: 12-2013
The Persistent Homology of Dual Digital Image Constructions
Publisher: Springer International Publishing
Date: 2022
Correspondence of max-flow to the absolute permeability of porous systems
Publisher: American Physical Society (APS)
Date: 14-05-2021
Computational Topology for Point Data: Betti Numbers of α-Shapes
Publisher: Springer Berlin Heidelberg
Date: 2002
Theory and Algorithms for Constructing Discrete Morse Complexes from Grayscale Digital Images
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 08-2011
Algebraic Topology
Publisher: Wiley-VCH Verlag GmbH & Co. KGaA
Date: 12-03-2015
The Impact of Cyclic Injection Cycles on Capillary Trapping: Comparison of Ambient and Reservoir Condition Experiments
Publisher: Elsevier BV
Date: 2019
DOI: 10.2139/SSRN.3366333
A validation study of a ballistocardiograph sleep tracker against polysomnography
Publisher: American Academy of Sleep Medicine (AASM)
Date: 04-2022
DOI: 10.5664/JCSM.9754
Topological Persistence for Relating Microstructure and Capillary Fluid Trapping in Sandstones
Publisher: American Geophysical Union (AGU)
Date: 2019
DOI: 10.1029/2018WR022780
Abstract: Results from a series of two‐phase fluid flow experiments in Leopard, Berea, and Bentheimer sandstones are presented. Fluid configurations are characterized using laboratory‐based and synchrotron based 3‐D X‐ray computed tomography. All flow experiments are conducted under capillary‐dominated conditions. We conduct geometry‐topology analysis via persistent homology and compare this to standard topological and watershed‐partition‐based pore‐network statistics. Metrics identified as predictors of nonwetting fluid trapping are calculated from the different analytical methods and are compared to levels of trapping measured during drainage‐imbibition cycles in the experiments. Metrics calculated from pore networks (i.e., pore body‐throat aspect ratio and coordination number) and topological analysis (Euler characteristic) do not correlate well with trapping in these s les. In contrast, a new metric derived from the persistent homology analysis, which incorporates counts of topological features as well as their length scale and spatial distribution, correlates very well ( R 2 = 0.97) to trapping for all systems. This correlation encompasses a wide range of porous media and initial fluid configurations, and also applies to data sets of different imaging and image processing protocols.
Topology and Intelligent Data Analysis
Publisher: Springer Berlin Heidelberg
Date: 2003
Periodic entanglement I: networks from hyperbolic reticulations
Publisher: International Union of Crystallography (IUCr)
Date: 28-03-2013
Betti number signatures of homogeneous Poisson point processes
Publisher: American Physical Society (APS)
Date: 11-12-2006
The intrinsic group-subgroup structures of the Diamond and Gyroid minimal surfaces in their conventional unit cells
Publisher: International Union of Crystallography (IUCr)
Date: 2022
DOI: 10.1107/S2053273321012936
Abstract: The intrinsic, hyperbolic crystallography of the Diamond and Gyroid minimal surfaces in their conventional unit cells is introduced and analysed. Tables are constructed of symmetry subgroups commensurate with the translational symmetries of the surfaces as well as group–subgroup lattice graphs.
Trading spaces: Building three-dimensional nets from two-dimensional tilings
Publisher: The Royal Society
Date: 25-01-2012
Abstract: We construct some ex les of finite and infinite crystalline three-dimensional nets derived from symmetric reticulations of homogeneous two-dimensional spaces: elliptic ( S 2 ), Euclidean ( E 2 ) and hyperbolic ( H 2 ) space. Those reticulations are edges and vertices of simple spherical, planar and hyperbolic tilings. We show that various projections of the simplest symmetric tilings of those spaces into three-dimensional Euclidean space lead to topologically and geometrically complex patterns, including multiple interwoven nets and tangled nets that are otherwise difficult to generate ab initio in three dimensions.
Skeletonization and Partitioning of Digital Images Using Discrete Morse Theory
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 03-2015
Experimental and theoretical study of the mechanism and rate constants of the sequential 5-
Publisher: Royal Society of Chemistry (RSC)
Date: 2022
DOI: 10.1039/D2OB00387B
Abstract: In this research the sequential generation and cyclization of
Porous Media Characterization Using Minkowski Functionals: Theories, Applications and Future Directions
Publisher: Springer Science and Business Media LLC
Date: 27-11-2018
Meditation on an Engraving of Fricke and Klein (The Modular Group and Geometrical Chemistry)
Publisher: Wiley
Date: 23-12-2003
Finite auxetic deformations of plane tessellations
Publisher: The Royal Society
Date: 08-01-2013
Abstract: We systematically analyse the mechanical deformation behaviour, in particular Poisson's ratio, of floppy bar-and-joint frameworks based on periodic tessellations of the plane. For frameworks with more than one deformation mode, crystallographic symmetry constraints or minimization of an angular vertex energy functional are used to lift this ambiguity. Our analysis allows for systematic searches for auxetic mechanisms in archives of tessellations applied to the class of one- or two-uniform tessellations by regular or star polygons, we find two auxetic structures of hexagonal symmetry and demonstrate that several other tessellations become auxetic when retaining symmetries during the deformation, in some cases with large negative Poisson ratios ν −1 for a specific lattice direction. We often find a transition to negative Poisson ratios at finite deformations for several tessellations, even if the undeformed tessellation is infinitesimally non-auxetic. Our numerical scheme is based on a solution of the quadratic equations enforcing constant edge lengths by a Newton method, with periodicity enforced by boundary conditions.
Percolating length scales from topological persistence analysis of micro-CT images of porous materials
Publisher: American Geophysical Union (AGU)
Date: 2016
DOI: 10.1002/2015WR017937
Towards enumeration of crystalline frameworks: the 2D hyperbolic approach
Publisher: Elsevier BV
Date: 07-2006
Topology-Inspired Method Recovers Obfuscated Term Information From Induced Software Call-Stacks
Publisher: Frontiers Media SA
Date: 28-05-2021
Abstract: Fuzzing is a systematic large-scale search for software vulnerabilities achieved by feeding a sequence of randomly mutated input files to the program of interest with the goal being to induce a crash. The information about inputs, software execution traces, and induced call stacks (crashes) can be used to pinpoint and fix errors in the code or exploited as a means to damage an adversary’s computer software. In black box fuzzing, the primary unit of information is the call stack: a list of nested function calls and line numbers that report what the code was executing at the time it crashed. The source code is not always available in practice, and in some situations even the function names are deliberately obfuscated (i.e., removed or given generic names). We define a topological object called the call-stack topology to capture the relationships between module names, function names and line numbers in a set of call stacks obtained via black-box fuzzing. In a proof-of-concept study, we show that structural properties of this object in combination with two elementary heuristics allow us to build a logistic regression model to predict the locations of distinct function names over a set of call stacks. We show that this model can extract function name locations with around 80% precision in data obtained from fuzzing studies of various linux programs. This has the potential to benefit software vulnerability experts by increasing their ability to read and compare call stacks more efficiently.
Symmetry groups and reticulations of the hexagonal H surface
Publisher: Elsevier BV
Date: 08-2004
The maximally symmetric surfaces in the 3-torus
Publisher: Springer Science and Business Media LLC
Date: 22-02-2017
Meditation on an Engraving of Fricke and Klein (The Modular Group and Geometrical Chemistry)
Publisher: CSIRO Publishing
Date: 2003
DOI: 10.1071/CH03191
Abstract: A non-technical account of the links between two-dimensional (2D) hyperbolic and three-dimensional (3D) euclidean symmetric patterns is presented, with a number of ex les from both spaces. A simple working hypothesis is used throughout the survey: simple, highly symmetric patterns traced in hyperbolic space lead to chemically relevant structures in euclidean space. The prime ex les in the former space are derived from Felix Klein's engraving of the modular group structure within the hyperbolic plane these include various tilings, networks and trees. Disc packings are also derived. The euclidean ex les are relevant to condensed atomic and molecular materials in solid-state chemistry and soft-matter structural science. They include extended nets of relevance to covalent frameworks, simple (lattice) sphere packings, and interpenetrating extended frameworks (related to novel coordination polymers). Limited discussion of the projection process from 2D hyperbolic to 3D euclidean space via mapping onto triply periodic minimal surfaces is presented.
Experimental investigation of the mechanical stiffness of periodic framework-patterned elastomers
Publisher: The Royal Society
Date: 13-02-2014
Abstract: Recent advances in the cataloguing of three-dimensional nets mean a systematic search for framework structures with specific properties is now feasible. Theoretical arguments about the elastic deformation of frameworks suggest characteristics of mechanically isotropic networks. We explore these concepts on both isotropic and anisotropic networks by manufacturing porous elastomers with three different periodic net geometries. The blocks of patterned elastomers are subjected to a range of mechanical tests to determine the dependence of elastic moduli on geometric and topological parameters. We report results from axial compression experiments, three-dimensional X-ray computed tomography imaging and image-based finite-element simulations of elastic properties of framework-patterned elastomers.
Three-dimensional Euclidean nets from two-dimensional hyperbolic tilings: Kaleidoscopic examples
Publisher: International Union of Crystallography (IUCr)
Date: 28-01-2009
Principal component analysis of persistent homology rank functions with case studies of spatial point patterns, sphere packing and colloids
Publisher: Elsevier BV
Date: 11-2016
Effect of network topology on relative permeability
Publisher: Springer Science and Business Media LLC
Date: 04-2004
Periodic entanglement II: weavings from hyperbolic line patterns
Publisher: International Union of Crystallography (IUCr)
Date: 28-03-2013
Finding auxetic frameworks in periodic tessellations
Publisher: Wiley
Date: 21-04-2011
Abstract: It appears that most models for micro‐structured materials with auxetic deformations were found by clever intuition, possibly combined with optimization tools, rather than by systematic searches of existing structure archives. Here we review our recent approach of finding micro‐structured materials with auxetic mechanisms within the vast repositories of planar tessellations. This approach has produced two previously unknown auxetic mechanisms, which have Poisson's ratio ν ss = ‐1 when realized as a skeletal structure of stiff incompressible struts pivoting freely at common vertices. One of these, baptized Triangle‐Square Wheels , has been produced as a linear‐elastic cellular structure from Ti‐6Al‐4V alloy by selective electron beam melting. Its linear‐elastic properties were measured by tensile experiments and yield an effective Poisson's ratio ν LE ≈ ‐0.75, also in agreement with finite element modeling. The similarity between the Poisson's ratios ν SS of the skeletal structure and ν LE of the linear‐elastic cellular structure emphasizes the fundamental role of geometry for deformation behavior, regardless of the mechanical details of the system. The approach of exploiting structure archives as candidate geometries for auxetic materials also applies to spatial networks and tessellations and can aid the quest for inherently three‐dimensional auxetic mechanisms.
Structural and mechanical features of the order-disorder transition in experimental hard-sphere packings
Publisher: American Physical Society (APS)
Date: 05-06-2015
Computing connectedness: An exercise in computational topology
Publisher: IOP Publishing
Date: 07-1998
Pore configuration landscape of granular crystallization
Publisher: Springer Science and Business Media LLC
Date: 12-05-2017
DOI: 10.1038/NCOMMS15082
Abstract: Uncovering grain-scale mechanisms that underlie the disorder–order transition in assemblies of dissipative, athermal particles is a fundamental problem with technological relevance. To date, the study of granular crystallization has mainly focussed on the symmetry of crystalline patterns while their emergence and growth from irregular clusters of grains remains largely unexplored. Here crystallization of three-dimensional packings of frictional spheres is studied at the grain-scale using X-ray tomography and persistent homology. The latter produces a map of the topological configurations of grains within static partially crystallized packings. Using numerical simulations, we show that similar maps are measured dynamically during the melting of a perfect crystal. This map encodes new information on the formation process of tetrahedral and octahedral pores, the building blocks of perfect crystals. Four key formation mechanisms of these pores reproduce the main changes of the map during crystallization and provide continuous deformation pathways representative of the crystallization dynamics.
Unification and classification of two-dimensional crystalline patterns using orbifolds
Publisher: International Union of Crystallography (IUCr)
Date: 28-05-2014
DOI: 10.1107/S205327331400549X
Abstract: The concept of an orbifold is particularly suited to classification and enumeration of crystalline groups in the euclidean (flat) plane and its elliptic and hyperbolic counterparts. Using Conway's orbifold naming scheme, this article explicates conventional point, frieze and plane groups, and describes the advantages of the orbifold approach, which relies on simple rules for calculating the orbifold topology. The article proposes a simple taxonomy of orbifolds into seven classes, distinguished by their underlying topological connectedness, boundedness and orientability. Simpler `crystallographic hyperbolic groups' are listed, namely groups that result from hyperbolic sponge-like sections through three-dimensional euclidean space related to all known genus-three triply periodic minimal surfaces ( i.e. the P , D , Gyroid , CLP and H surfaces) as well as the genus-four I-WP surface.
Related Organisations
Related Funding Activities
Topological Data Analysis For Enhanced Modelling Of The Physical Properties Of Complex Micro-structured Materials
Start Date: 2015
End Date: 2018
Funder: Australian Research Council
View Funded Activity3D Shape Segmentation And Shape Characterisation Driven By Topological Persistence
Start Date: 2006
End Date: 2008
Funder: Australian Research Council
View Funded ActivityDiscovery Projects - Grant ID: DP0666442
Start Date: 2006
End Date: 12-2009
Amount: $310,000.00
Funder: Australian Research Council
View Funded ActivityDiscovery Projects - Grant ID: DP110102888
Start Date: 2011
End Date: 12-2016
Amount: $255,000.00
Funder: Australian Research Council
View Funded ActivityARC Future Fellowships - Grant ID: FT140100604
Start Date: 02-2015
End Date: 09-2021
Amount: $672,384.00
Funder: Australian Research Council
View Funded ActivityLinkage Infrastructure, Equipment And Facilities - Grant ID: LE0668019
Start Date: 2006
End Date: 12-2007
Amount: $240,000.00
Funder: Australian Research Council
View Funded Activity