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ContentsForeword 3

Conference Organisation 4

Conference Sponsors 5

Conference Program 6

Plenary Lectures in the Matthew Flinders Theatre 8

Special Sessions1. Groups and Monoids 92. Algebraic Geometry and Representation Theory 103. Applied Mathematics 114. Combinatorics 135. Complex Analysis and Geometry 146. Computational Mathematics 157. DST Group and Industrial Mathematics Session 168. Dynamical Systems 179. Games and Applied Stochastic Processes 19

10. Geometry and Topology 2011. Harmonic Analysis and Partial Differential Equations 2212. Mathematical Biology 2413. Mathematics Education 2614. Mathematical Physics 2815. Mathematics of Medical Imaging 2916. Number Theory 3017. Operator Algebras and Function Analysis 3118. Variational Analysis and Optimisation 3219. Probability 3320. Statistics 34

Conference Timetable 35Mon 28 September 2015 36Tue 29 September 2015 39Wed 30 September 2015 45Thu 1 October 2015 51

List of Registrants 55

Plenary Abstracts 65

Special Session Abstracts1. Groups and Monoids 692. Algebraic Geometry and Representation Theory 723. Applied Mathematics 744. Combinatorics 805. Complex Analysis and Geometry 846. Computational Mathematics 867. DST Group and Industrial Mathematics Session 898. Dynamical Systems 929. Games and Applied Stochastic Processes 96

10. Geometry and Topology 9811. Harmonic Analysis and Partial Differential Equations 10312. Mathematical Biology 10713. Mathematics Education 11214. Mathematical Physics 119

15. Mathematics of Medical Imaging 12116. Number Theory 12317. Operator Algebras and Function Analysis 12518. Variational Analysis and Optimisation 12619. Probability 12920. Statistics 132

Index of Speakers 134

2

Foreword

It is our pleasure to welcome to the 59th Annual Meeting of the Australian Mathematical Society atFlinders University in September, 2015.

The local organising committee, consisting of Raymond Booth, Michael Haythorpe, Gobert Lee andSimon Williams, with support from the School of Computer Science, Engineering and Mathematics,and the VC office, put timeless hours into the preparation of the meeting, keeping traditions andestablishing new features for AustMS conferences.

I hope you’ll enjoy your time at Flinders University!

On behalf of the local organising committee,

Vladimir Ejov

Conference Director

3

Conference Organisation

Program Committee

Jonathan Borwein (University of Newcastle)Jan de Gier (University of Melbourne)Vladimir Ejov (Flinders University)Paul Gaertner (DST Group)Vladimir Gaitsgory (Macquarie University)Catherine Greenhill (University of New South Wales)Andrew Hassell (Australian National University)Phil Pollett (University of Queensland)Stephan Tillman (University of Sydney)Ole Warnaar (University of Queensland)

Local Organising Committee

Vladimir Ejov – Conference DirectorSimon Williams – TreasurerMichael Haythorpe – SecretaryRaymond Booth – AdministrationGobert Lee - Administration

Booklet produced by Michael Haythorpe using the template provided by John David Banks.

4

Conference Sponsors

Conference Booklet template and Register! System provided by John David Banks (University ofMelbourne).

Front cover image: “Hanging Mobius Garden”, Tatiana Bonch-Osmolovskaya, 2011.

5

Conference Program

Overview of the Academic Program

There are 282 talks, including 13 plenary lectures and 20 special sessions.

B Conference Timetable – page 35

Mon 28 September 2015 – page 36Tue 29 September 2015 – page 39Wed 30 September 2015 – page 45Thu 1 October 2015 – page 51

Plenary Lecturers

Martino Bardi (University of Padova)Manjul Bhargava (Princeton University)Aurore Delaigle (University of Melbourne)James Demmel (University of California, Berkeley)Jerzy Filar (Flinders University)Cl lement Hongler (EPFL Switzerland)Frances Kirwan (University of Oxford)Frances Kuo (University of New South Wales)Michael Shelley (New York University)Terence Tao (University of California, Los Angeles)Ruth Williams (University of California, San Diego)Konstantin Zarembo (Nordic Institute for Theoretical Physics)Wadim Zudilin (University of Newcastle)B Timetable of Plenary Lectures – page 8

Special Sessions

1. Groups and Monoids – page 92. Algebraic Geometry and Representation Theory – page 103. Applied Mathematics – page 114. Combinatorics – page 135. Complex Analysis and Geometry – page 146. Computational Mathematics – page 157. DST Group and Industrial Mathematics Session – page 168. Dynamical Systems – page 179. Games and Applied Stochastic Processes – page 19

10. Geometry and Topology – page 2011. Harmonic Analysis and Partial Differential Equations – page 2212. Mathematical Biology – page 2413. Mathematics Education – page 2614. Mathematical Physics – page 2815. Mathematics of Medical Imaging – page 2916. Number Theory – page 3017. Operator Algebras and Function Analysis – page 3118. Variational Analysis and Optimisation – page 3219. Probability – page 3320. Statistics – page 34

6

Conference Program

Early Career Researcher Workshop

I 11:00AM Sunday 27th September, 2015Early Career Researcher WorkshopFlinders University - Tonsley Campus

Social Program

I 6:30PM Sunday 27th September, 2015Women in Mathematics DinnerFlinders University - Tonsley Campus

I 7:00PM - 9:30PM Monday 28th September, 2015Public Lecture (Tao) and Musical RecitalAdelaide Town Hall

I 10:00AM - 4:00PM Tuesday 29th September, 2015Wine Tour - 1847 Chateau Guided TourBarossa Valley

I 6:30PM Tuesday 29th September, 2015Chess CompetitionMatthew Flinders Theatre (foyer)

I 7:00PM Wednesday 30th September, 2015Conference DinnerStamford Grand, Glenelg

Additional Presentations

I 12:30PM - 1:30PM Monday 28th September, 2015Book Launch: Raja R. Huilgol, “Fluid Mechanics of Viscoplasticity”, Springer, 2015Social Sciences North 241

I 12:30 - 12:45PM Tuesday 29th September, 2015Nalini Joshi will speak about the Decadel PlanMatthew Flinders Theatre

I 12:30PM - 1:05PM Wednesday 30th September, 2015Geoff Prince will speak about Choose Maths and the National Research CentreMatthew Flinders Theatre

I 3:00PM - 3:15PM Wednesday 30th September, 2015Jon Borwein will speak about the AMSI Workshop ProgramMatthew Flinders Theatre

Annual General Meeting of the Society

I 5:30PM Tuesday 29th September, 2015Annual General Meeting of the SocietyMatthew Flinders Theatre

Conference Information Desk

The information desk for the conference is located in the foyer of the Matthew Flinders Theatre. Thisdesk will be staffed each day of the conference from 8:00AM to 5:30PM.

Book and Software Display

Throughout the conference, various publishers will be displaying their wares in the foyer of theMatthew Flinders Theatre.

7

Plenary Lectures in Matthew Flinders Theatre

B Mon 28 September 2015

10:00 I James Demmel (University of California Berkeley)

Communication Avoiding Algorithms

11:30 I Frances Kirwan (University of Oxford)

Quotients of algebraic varieties by linear algebraic group

14:00 I Konstantin Zarembo (Nordic Institute for Theoretical Physics)

Random Matrices in Quantum Field Theory

B Tue 29 September 2015

09:00 I Clement Hongler (EPFL)

Random Fields and Curves, Discrete and Continuous Structures

10:00 I Terence Tao (University of California Los Angeles)

Finite time blowup for an averaged Navier-Stokes equation

11:30 I Manjul Bhargava (Princeton University)

What is the Birch and Swinnerton-Dyer Conjecture, and what is known about it?

B Wed 30 September 2015

09:00 I Aurore Delaigle (The University of Melbourne)

Deconvolution when the Error Distribution is Unknown

10:00 I Jerzy Filar (Flinders University)

An Overview of the Flinders Hamiltonian Cycle Project

11:30 I Martino Bardi (University of Padua)

An introduction to Mean Field Games and models of segregation

B Thu 1 October 2015

09:00 I Michael Shelley (New York University)

Mathematical Models and Analysis of Active Suspensions

10:00 I Ruth Williams (UC San Diego)

Resource Sharing in Stochastic Networks

11:30 I Frances Kuo (University of New South Wales)

Liberating the Dimension – Quasi-Monte Carlo Methods for High Dimensional Integration

13:20 I Wadim Zudilin (The University of Newcastle)

The life of 1/Pi

8

Special Session 1: Groups and Monoids

Organisers Murray Elder, Volker Gebhardt

Contributed Talks


15:25 Alexander Fish (University of Sydney)Dynamical methods in additive combinatorics

16:15 John Harrison (The University of Newcastle)Asymptotic behaviour of random walks on certain matrix groups

16:40 Murray Elder (The University of Newcastle)Using random walks to detect amenability in finitely generated groups


13:20 Anne Thomas (University of Sydney)Reflection length in affine Coxeter groups

13:45 Attila Egri-Nagy (Western Sydney University)Independent generating sets of symmetric groups

15:20 Robert McDougall (University of the Sunshine Coast)On substructures which can be carried by homomorphic images

15:45 Lauren Thornton (University of the Sunshine Coast)On base radical and semisimple classes for associative rings

16:10 Nathan Brownlowe (University of Wollongong)Non-embeddings into the Leavitt algebra L2

16:35 Roozbeh Hazrat (University of Western Sydney)Ultramatricial algebras, classification via K-groups

17:00 Colin David Reid (The University of Newcastle)Essentially chief series of locally compact groups


15:20 Marcel Jackson (La Trobe University)From A to B to Z

15:45 James East (University of Western Sydney)Linear sandwich semigroups

16:10 Kathy Horadam (Royal Melbourne Institute of Technology)Coboundary and graph codes and their invariants

16:35 Don Taylor (University of Sydney)Janko’s sporadic simple groups

17:00 Anthony Licata (Australian National University)On the 2-linearity of the free group

9

Special Session 2: Algebraic Geometry andRepresentation Theory

Organisers Anthony Henderson

Contributed Talks


14:10 Shrawan Kumar (University of South Carolina)Positivity in T-equivariant K-theory of flag varieties associated to Kac-Moody groups

15:20 Scott Morrison (Australian National University)A quantum exceptional series

15:45 Slaven Kozic (University of Sydney)

Principal subspaces and vertex operators for quantum affine algebra Uq(sln+1)

16:10 Uri Onn (Australian National University)A variant of Harish-Chandra functors

16:35 Hang Wang (The University of Adelaide)Base change and K-theory

17:00 Jon Xu (The University of Melbourne)Schubert Calculus and Finite Geometry


15:20 Anthony Licata (Australian National University)Geometric representation theory and categorification for braid groups of type ADE

15:45 Jarod Alper (Australian National University)A tale of two polynomials

16:10 Mircea Voineagu (University of New South Wales)An equivariant motivic cohomology

16:35 Arnab Saha (Australian National University)The Frobenius Operator and Descending to Constants

17:00 Anthony Henderson (University of Sydney)Diagram automorphisms revisited

10

Special Session 3: Applied Mathematics

Organisers Robert Scott Anderssen, Yvonne Stokes

Contributed Talks


15:25 Robert Scott Anderssen (CSIRO)Modelling the Dynamics of Vernalization in Plants

15:50 Kylie Foster (University of South Australia)Mathematically modelling the salt stress response of individual plant cells

16:15 Joshua Chopin (University of South Australia)RootAnalyzer: a cross-section image analysis tool for automated characterization ofroot cells and tissues

16:40 Catherine Penington (Queensland University of Technology)Dying in order: how crowding affects particle lifetimes


13:20 Troy Farrell (Queensland University of Technology)Comparing Nernst-Plank and Maxwell-Stefan approaches for modelling electrolytesolutions

14:10 Alise Thomas (University of the Sunshine Coast)The use of the Fast Fourier Transform in the analysis of the fine substructure of3-dimensional spatio-temporal human movement data

14:35 Stanley Joseph Miklavcic (University of South Australia)Mathematical models for competitive ion absorption in a polymer matrix

15:20 Bronwyn Hajek (University of South Australia)Particle transport in asymmetric periodic capillaries

15:45 Raja Ramesh Huilgol (Flinders University)Mesoscopic Models to Bingham Fluids: Mixed Convection Flow in a Cavity

16:10 Tony Miller (Flinders University)Taylor Series and Water Hammer

16:35 Yvonne Stokes (The University of Adelaide)Mathematics in the drawing of microstructured optical fibres.

17:00 Qiang Sun (The University of Melbourne)Why should boundary element methods have to deal with singularities?


13:20 Elizabeth Bradford (University of South Australia)Mathematical techniques to aid the Australian Army in selecting new defence vehicles

13:45 Phil Howlett (University of South Australia)The Key Principles of Optimal Train Control

14:10 Kathy Horadam (Royal Melbourne Institute of Technology)Neighbourhood distinctiveness in complex networks: an initial study

14:35 Ignacio Ortega Piwonka (University of New South Wales)Use of a stochastic model to study the cyclic motion in nanowires trapped by focusedGaussian beams

11

3. Applied Mathematics


14:50 Richard Michael Morris (Durban University of Technology)The algebraic properties of the nonautonomous one- and two-factor problems ofcommodities

15:15 Joel Moitsheki (University of the Witwatersrand)Application of Lie symmetry techniques to reaction-diffusion equations.

15:40 Simon Clarke (Monash University)Complex spatial self-organisation in an extended Daisyworld model

12

Special Session 4: Combinatorics

Organisers Amy Glen, Jamie Simpson

Contributed Talks


15:25 Tony Guttmann (The University of Melbourne)Sorting with two stacks and quarter-plane loops

15:50 Marc Demange (RMIT University)On choosability of graphs with limited number of colours.

16:15 Kieran Clancy (Flinders University)Hamiltonicity-preserving graph reductions

16:40 Nicholas Wormald (Monash University)Proof of Tutte’s 3-flow conjecture in an ”almost all” sense.


15:20 Diana Combe (University of New South Wales)Signed designs

15:45 Asha Rao (Royal Melbourne Institute of Technology)Skolem sequences and Difference covering arrays

16:10 Joanne Hall (Queensland University of Technology)Difference Covering Arrays and Nearly Orthogonal Latin Square

16:35 David G Glynn (Flinders University)Evaluating modular invariants

17:00 Christopher Taylor (La Trobe University)Algebras of incidence structures: representations of regular double p-algebras,

17:25 Stacey Mendan (La Trobe University)Graphic and bipartite graphic sequences


15:20 Murray Neuzerling (La Trobe University)Using algebra to avoid robots

15:45 Tomasz Kowalski (La Trobe University)NP-complete fragments of qualitative calculi

16:10 Lucy Ham (La Trobe University)Definability of SP-classes of uniform hypergraphs

16:35 Jamie Simpson (Curtin university)An introduction to combinatorics of words

17:00 Amy Glen (Murdoch University)On the number of palindromically rich words

13

Special Session 5: Complex Analysis and Geometry

Organisers Grant Cairns, Yuri Nikolayevsky, Gerd Schmalz

Contributed Talks


15:25 Francine Meylan (University of Fribourg)Holomorphicity of Meromorphic Mappings along Real Hypersurfaces

16:15 Sean Curry (The University of Auckland)Constructing Local Invariants for CR Embeddings

16:40 Alessandro ottazzi (University of New South Wales)Conformal maps in nilpotent groups


13:20 Ioannis Tsartsaflis (La Trobe University)Filiform Lie algebras over Z2

13:45 David Bowman (The University of Adelaide)Holomorphic flexibility properties of spaces of elliptic functions

14:10 Timur Sadykov (Plekhanov Russian University)Analytic complexity of binary cluster trees

14:35 Gerd Schmalz (University of New England)A Forelli type theorem for resonant vector fields


14:50 Jorge Lauret (Universidad Nacional de Cordoba)Geometric flows and their solitons on homogeneous spaces

15:15 Martin Kolar (Masaryk University)Normal forms and symmetries in CR geometry

15:40 Tuyen Truong (The University of Adelaide)Two approaches toward the Jacobian conjecture

16:05 Dmitri Alekseevsky (Institute for Information Transmission Problems)Homogeneous locally conformally Kaehler manifolds

16:30 Owen Dearricott (MASCOS / University of Melbourne)An algebraic form for a self-dual Einstein orbifold metric

14

Special Session 6: Computational Mathematics

Organisers Bishnu Lamichhane, Quoc Thong Le Gia

Contributed Talks


13:20 Ian Turner (Queensland University of Technology)Dual-scale Modelling Approaches for Simulating Diffusive Transport in HeterogeneousPorous Media

14:10 Qinian Jin (Australian National University)Landweber iteration of Kaczmarz type for inverse problems in Banach spaces

14:35 Chenxi Fan (University of New South Wales)Effective dimension for weighted ANOVA and anchored spaces


13:20 Markus Hegland (Australian National University)Solving partial differential equations with the sparse grid combination technique

13:45 Gary Froyland (University of New South Wales)Computing Lagrangian coherent structures from Laplace eigenproblems

14:10 Paul Charles Leopardi (School of Mathematical and Physical Sciences The Universityof Newcastle)Equal area partitions of connected Ahlfors regular spaces

14:35 Garry Newsam (The University of Adelaide)Fitting Circular Arcs Through Points in the Plane

15:20 Bishnu Lamichhane (The University of Newcastle)A stabilized mixed finite element method systems for nearly incompressible elasticityand Stokes equations

15:45 Michael Feischl (UNSW)An abstract analysis of optimal goal-oriented adaptivity

16:10 Robert Womersley (University of New South Wales)Efficient spherical designs with good goemetric properties

16:35 Yuguang Wang (University of New South Wales)Fully discrete needlet approximation on the sphere

17:00 Quoc Thong Le Gia (University of New South Wales)Higher order Quasi-Monte Carlo integration for Bayesian Estimation

15

Special Session 7: DST Group and IndustrialMathematics Session

Organisers Paul Gaertner

Contributed Talks


15:25 Richard Taylor (Defence Science and Technology Organisation, Australia)Algorithmic complexity of two defence budget problems

15:50 Darryn Reid (Defence Science and Technology Organisation, Australia)Behavioural Questions in Complexity and Control

16:15 Axel Bender (Defence Science and Technology Organisation, Australia)Design Principle for Adaptable and Robust Complex Systems

16:40 Brandon Pincombe (Defence Science and Technology Organisation, Australia)A case for new models of battle attrition


15:20 Alexander Kalloniatis (Defence Science and Technology Organisation, Australia)A model for distributed decision making: Levy noise and network synchronisation

15:45 Greg Calbert (Defence Science and Technology Organisation, Australia)Military inventory capacity and stock planning with surge and warning time andsupplier constraints

16:10 Minh Tran (Flinders University)Model-Based State Of Charge Estimation Of A Lithium-Ion Battery

16:35 Sangeeta Bhatia (University of Western Sydney)Do I smell gas? Bayesian Inversion for localisation and quantification of fugitiveemissions

16

Special Session 8: Dynamical Systems

Organisers Gary Froyland, Cecilia Gonzalez-Tokman

Contributed Talks


15:25 Vladimir Gaitsgory (Macquarie University)On control of systems with slow variables

15:50 Petrus van Heijster (Queensland University of Technology)Butterfly catastrophe for fronts in a three-component reaction-diffusion system

16:15 Joachim Worthington (University of Sydney)Poisson Structures and Stability for Euler Fluid Equations on a Toroidal Domain

16:40 Yang Shi (University of Sydney)Polytopes, symmetries and discrete integrable systems


13:20 Luchezar Stoyanov (The University Of Western Australia)On Lyapunov regularity for uniformly hyperbolic systems

13:45 Davor Dragicevic (School of mathematics and statistics)Spectral theory under nonuniform hyperbolicity

14:10 Danya Rose (University of Sydney)Finding absolutely and relatively periodic orbits in the equal mass 3-body problemwith vanishing angular momentum

14:35 Andy Hammerlindl (Monash University)Models of chaos in dimensions two and three

15:20 Michael Small (The University Of Western Australia)Random walks on networks built from dynamical systems

15:45 Lewis Mitchell (The University of Adelaide)A shadowing-based inflation scheme for ensemble data assimilation

16:10 Qing Liu (University of Sydney)Elliptic Asymptotic Behaviour of q-Painleve III

16:35 Peter Cudmore (The University of Queensland)Rock and Roll and Quantum Optics.

17:00 Daniel Daners (University of Sydney)Perron-Frobenius theory and eventually positive semigroups of linear operators


13:20 Rua Murray (University of Canterbury)Reliable computation of invariant measures: progress towards Ulam’s conjecture

13:45 Paul Wright (The University Of Western Australia)Dimensional Characteristics of the Non-wandering Sets of Open Billiards

14:10 Eric Kwok (University of New South Wales)Dynamic isoperimetry on weighted manifolds

14:35 Cecilia Gonzalez-Tokman (The University of Queensland)A streamlined approach to the multiplicative ergodic theorem on Banach spaces

17

8. Dynamical Systems


14:50 Bjorn Ruffer (The University of Newcastle)Separable Lyapunov functions for monotone systems

15:15 Tristram Alexander (UNSW)Spontaneous rotation in a resonance-free system

15:40 Nobutaka Nakazono (University of Sydney)A comprehensive method for constructing Lax pairs of discrete Painleve equation:(A2 +A1)(1) case

18

Special Session 9: Games and Applied StochasticProcesses

Organisers Jerzy Filar, Michael Haythorpe

Contributed Talks


15:25 Vladimir Ejov (Flinders University)Kookaburra vs. Concorde: Achilles and Tortoise in TSP race.

16:15 Michael Haythorpe (Flinders University)Applying Continuous Optimisation Techniques to Difficult Discrete OptimisationProblems

16:40 Asghar Moeini (Flinders University)On the Detection of Non-Hamiltonicity via Linear Feasibility Models


13:20 Imma Curiel (Anton de Kom University of Suriname)A combinatorial optimization game arising from a components acquisition situation.

13:45 Ehsan Nekouei (The University of Melbourne)Performance of Gradient-Based Nash Seeking Algorithms Under QuantizedInter-Agent Communications

14:10 Jakub Tomczyk (University of Sydney)A multidimensional correlated square root process

14:35 Jerzy Filar (Flinders University)Ordered Field Property in Discounted Stochastic Games

19

Special Session 10: Geometry and Topology

Organisers Wolfgang Globke, Jonathan Spreer

Contributed Talks


15:25 Artem Pulemotov (The University of Queensland)The prescribed Ricci curvature problem on homogeneous spaces

15:50 Glen Wheeler (University of Wollongong)Curve diffusion flow with free boundary

16:15 Wolfgang Globke (The University of Adelaide)Compact pseudo-Riemannian solvmanifolds

16:40 Andree Lischewski (The University of Adelaide)Globally hyperbolic spacetimes with parallel null vector and related Riemannian flowequations


13:20 Joan Licata (Australian National University)Morse Structures on Open Books

13:45 Craig Hodgson (University of Melbourne)The 3D index and normal surfaces

14:10 Neil Hoffman (The University of Melbourne)Geometry of planar surfaces and exceptional fillings

14:35 Joshua Howie (University of Melbourne)Hyperbolicity For Weakly Generalised Alternating Knots

15:20 Finnur Larusson (The University of Adelaide)Oka theory of affine toric varieties

15:45 Thoan Thi Kim Do (La Trobe University)New progress in the inverse problem in the calculus of variations.

16:10 Jan Slovak (Masaryk University)Subriemannian linearized metrizability

16:35 Geoffrey Prince (Australian Mathematical Sciences Institute)Torsion and the second fundamental form for distributions

17:00 Milena Radnovic (University of Sydney)Geometry of confocal quadrics in pseudo-Euclidean space


13:20 Guillermo Pineda-Villavicencio (Federation University Australia)Lower and upper bound theorems for almost simplicial polytopes

13:45 Ana Dow (University of Melbourne)CAT (0) Semi-Cubings of Adequate links

14:10 Norman Do (Monash University)The combinatorics of tetrahedron index ratios

14:35 Grace Omollo Misereh (La Trobe University)Thrackles

20

10. Geometry and Topology

15:20 Daniel Mathews (Monash University)Counting curves on surfaces

15:45 Benjamin Burton (University of Queensland)The computational hardness of normal surfaces

16:10 Jonathan Spreer (University of Queensland)Collapsibility and 3-sphere recognition

16:35 Yuri Nikolayevsky (La Trobe University)Solvable Lie groups of negative Ricci curvature

17:00 Alexandr Medvedev (University of New England)Differential invariants of ODEs systems of higher order


14:50 Michael Murray (The University of Adelaide)Equivariant bundle gerbes

15:15 Raymond Vozzo (The University of Adelaide)String structures on homogeneous spaces

15:40 David Roberts (The University of Adelaide)Homogeneous String connections

16:05 Zhou Zhang (University of Sydney)Mean curvature flow over almost Fuschian manifold

21

Special Session 11: Harmonic Analysis and PartialDifferential Equations

Organisers Huy The Nguyen, Melissa Tacy

Contributed Talks


15:25 Andrew Hassell (Australian National University)Estimates on boundary values of Neumann eigenfunctions

15:50 Melissa Tacy (The University of Adelaide)Quantised dynamical observables and concentration of eigenfunctions

16:15 Xiaolong Han (Australian National University)Completeness of boundary traces of Dirichlet and Neumann eigenfunctions

16:40 Sean Gomes (Australian National University)Inclusion Bounds and Eigenfunction Localisation


13:20 Glen Wheeler (University of Wollongong)Polyharmonic curvature flow

13:45 Adam Sikora (Macquarie University)Spectral multipliers, Bochner-Riesz means and uniform Sobolev inequalities forelliptic operators

14:10 David Franklin (The University of Newcastle)Hardy Spaces and Paley-Wiener Spaces for Clifford-valued functions

14:35 Ting-Ying Chang (University of Sydney)Singular Solutions to Weighted Divergence Form Equations


13:20 Nirav Arunkumar Shah (The University of Queensland)Regularity of bounded weak solutions to an Euler-Lagrange system in the criticaldimension.

13:45 Kyle Talbot (Monash University)Uniform temporal stability of solutions to doubly degenerate parabolic equations.

14:10 Florica Corina Cirstea (School of Mathematics and Statistics, University of Sydney)Classification of isolated singularities for elliptic equations with Hardy-type potentials

14:35 Xuan Duong (Macquarie University)Factorization for Hardy spaces and characterization for BMO spaces via commutatorsin the Bessel setting.

15:20 Steven Luu (School of Mathematics and Statistics, University of Sydney)Asymptotics of a q-Airy equation

15:45 Michael Twiton (School of Mathematics and Statistics, University of Sydney)On Truncated Solutions of The Fourth Painlev Equation

16:10 James Gregory (University of Sydney)Special Solutions of the Painleve Equations

16:35 Pieter Roffelsen (University of Sydney)Asymptotics of solutions to the discrete Painleve equation q-P (A∗1) which areholomorphic at the origin

22

11. Harmonic Analysis and Partial Differential Equations

17:00 Anh Bui (Macquarie University)Dispersive estimates for the wave equations in R3


14:50 Daniel Hauer (University of Sydney)A simplified approach to the regularising effect of nonlinear semigroups

15:15 Zihua Guo (Monash University)Scattering for the Zakharov system

15:40 Qirui Li (Australian National University)Multiple solutions to the Lp-Minkowski problem

23

Special Session 12: Mathematical Biology

Organisers Edward Green, Joshua Ross

Contributed Talks


15:25 Adelle Coster (University of New South Wales)Modelling at the Limits of Resolution: Single Molecule Fluorescence andProtein-Protein Binding

15:50 Jeremy Sumner (University of Tasmania)A representation-theoretic approach to the calculation of genome rearrangementdistances

16:15 Barbara Johnston (Griffith University)Possible sets of six conductivity values to use in the bidomain model of cardiac tissue

16:40 Jennifer Flegg (Monash University)Wound healing angiogenesis: The clinical implications of a simple mathematicalmodel


13:20 Andrew Black (The University of Adelaide)Modelling the transition from uni- to multi-cellular life

13:45 Mark Flegg (Monash University)Simulation of reaction-diffusion processes in cellular biology

14:10 Benjamin Binder (The University of Adelaide)How do we quantify the filamentous growth in a yeast colony?

14:35 James Ashton Nichols (University of New South Wales)Anomalous dynamics in compartment models, a continuous time random walkapproach


13:20 Deborah Cromer (University of New South Wales)What is the optimal length of HIV Remission?

13:45 Adrianne Jenner (University of Sydney)Mathematical modelling of oncolytic virotherapy and immunotherapy usingdeterministic and stochastic models

14:10 Pouya Baniasadi (Flinders University)Traveling Salesman Problem Approach for Solving DNA Sequencing Problems

14:35 Sangeeta Bhatia (University of Western Sydney)An algebraic approach to determine a minimal weighted inversion distance


14:50 Peter Johnston (Griffith University)A New Model for Aggressive Breeding Amongst Wolbachia Infected Flies

15:15 Owen Jepps (Griffith University)Influence of homeostasis on the long-time-limit behaviour of an autoimmune disease

15:40 Sarthok Sircar (University of Adelaide)Surface deformation and shear flow in ligand mediated cell adhesion

24

12. Mathematical Biology

16:05 Pascal R Buenzli (Monash University)Bulk and surface balance during tissue modelling and remodelling

25

Special Session 13: Mathematics Education

Organisers Amie Albrecht, Joann Cattlin, Deborah King

Contributed Talks


15:25 Sven Trenholm (University of South Australia)Assessment and Feedback in Fully Online Tertiary Mathematics: The InstructorPerspective

15:50 Leigh Wood (Macquarie University)Mathematics and statistics modules for pre-service teachers

16:15 Birgit Loch (Swinburne University of Technology)Making mathematics relevant to first year engineering students

16:40 Aaron Wiegand (University of the Sunshine Coast)To all first-year Calculus students: *pleeease* attend the classes!


13:20 Carolyn Kennett (Macquarie University)Reflections on using vodcasts as an assessment item in first year units

13:45 Donald Shearman (Western Sydney University)Great Expectations: I expect to pass because I already know all this stuff

14:10 Dann Mallet (Queensland University of Technology)Mathematics degree learning outcomes and their assurance

15:20 Jonathan Kress (University of New South Wales)Online tutorials with YouTube and Maple TA: the experience so far

15:45 Caroline Bardini (The University of Melbourne)Symbols: do university students mean what they write and write what they mean?

16:10 Antony Edwards (Swinburne University of Technology)Student reasoning about real-valued sequences: Insights from an example-generationstudy

16:35 Joann Cattlin (University of Melbourne)New Mathematics Special Interest Group for AustMS


13:20 John William Rice (University of Sydney)Galileo and Calculus Unlimited

13:45 Lesley Ward (University of South Australia)Mathematics and Australian Indigenous Culture: Building cultural awareness,competency and literacy in mathematics students at UniSA

14:10 Deborah Jackson (La Trobe University)Development and Implementation of a First Year Statistics Subject for SeniorSecondary Indigenous Students to Encourage Future Engagement in Tertiary Studies

14:35 Diana Quinn (University of South Australia)Learning from experience: developing mathematics courses for an online engineeringdegree

15:20 John Banks (University of Melbourne)Spreadsheet drawings of plant branching from modified Lindenmayer grammars

26

13. Mathematics Education

15:45 Tristram Alexander (UNSW)Assessing for student problem solving ability

16:10 Kevin White (University of South Australia)Mind the Gap: Exploring knowledge decay in online sequential mathematics courses

16:35 Amie Albrecht (University of South Australia)Developing mathematical thinking through puzzles and games


14:50 Jonathan Borwein (The University of Newcastle)A short walk can be beautiful

15:15 Christine Mangelsdorf (University of Melbourne)Understanding and addressing poor student performance in first year universitycalculus

15:40 Katherine Anne Seaton (La Trobe University)Pipelines, ceilings, and acid rain

27

Special Session 14: Mathematical Physics

Organisers Jon Links, David Ridout

Contributed Talks


15:20 David Ridout (Australian National University)Non-rational CFTs and the Verlinde formula

15:45 Christopher Bourne (Australian National University)A noncommutative approach to topological insulators

16:10 Tom Daniels (Flinders University)Singular spectral shift function for Schrodinger operators

16:35 Inna Lukyanenko (The University of Queensland)An integrable case of the p+ ip pairing Hamiltonian interacting with its environment


14:50 Jan De Gier (University of Melbourne)N = 2 supersymmetry on the lattice without fermion conservation

15:15 Guo Chuan Thiang (The University of Adelaide)T-duality and topological phases

15:40 Mathew Zuparic (Defence Science and Technology Group, Australia)Spectra and Greens functions of second order density models

16:05 Jon Links (The University of Queensland)Electron-hole asymmetry of the p+ip pairing model.

28

Special Session 15: Mathematics of Medical Imaging

Organisers Murk Bottema, Gobert Lee, Simon Williams

Contributed Talks


13:20 Michael Ng (Hong Kong Baptist University)Variational Models and Computational Methods in Image Processing

14:10 Gobert Lee (Flinders University)Moment Invariants for Medical image segmentation

14:35 Simon Williams (Flinders University)Estimating an additive gaussian model for projective images

15:20 Murk Bottema (Flinders University)Textons in rat bones and mammograms

15:45 Amelia Gontar (Flinders University)Textons and their applications in medical imaging

16:10 shelda sajeev (Flinders University)An Adaptive CLAHE for Improving Medical Image Segmentation

16:35 Rui-Sheng Lu (Flinders University)Texture Analysis Improves the Estimate of Bone Fracture Risk from DXA Images

29

Special Session 16: Number Theory

Organisers Michael Coons, Timothy Trudgian

Contributed Talks


13:20 Karl Dilcher (Dalhousie University)Generalized Fermat numbers and congruences for Gauss factorials

13:45 Mumtaz Hussain (The University of Newcastle)A metrical problem in Non-linear Diophantine approximation

14:10 Grant Cairns (La Trobe University)Generalisations of Wilson’s Theorem for Double, Hyper, Sub and Superfactorials

14:35 Angus McAndrew (The University of Melbourne)Galois Representations for Siegel Modular Forms

15:20 Jeffrey Lay (Australian National University)Iterated sums of the Mobius function

15:45 Adrian Dudek (Australian National University)On Solving a Curious Inequality of Ramanujan

16:10 Randell Heyman (University of New South Wales)The approximate GCD problem

16:35 Stijn Hanson (Australian National University)Generalisations of Chen’s Theorem and the vector sieve

17:00 Simon Macourt (Macquarie University)Dedekind Sums


14:50 Shaun Cooper (Massey University)Ramanujan’s level 7 theta functions

15:15 Alexandru Ghitza (The University of Melbourne)Analytic evaluation of Hecke eigenvalues

15:40 Min Sha (University of New South Wales)The Arithmetic of Consecutive Polynomial Sequences over Finite Fields

16:05 Timothy Trudgian (Australian National University)Every prime greater than 61 has three consecutive primitive roots

30

Special Session 17: Operator Algebras and FunctionAnalysis

Organisers Aidan Sims

Contributed Talks


15:20 Mathai Varghese (The University of Adelaide)Magnetic spectral gap-labelling conjectures

16:10 Nathan Brownlowe (University of Wollongong)C*-algebras associated to graphs of groups

16:35 Guo Chuan Thiang (The University of Adelaide)Dualities in real K-theory and physical applications

17:00 Aidan Sims (University of Wollongong)Stable finiteness of k-graph algebras

31

Special Session 18: Variational Analysis andOptimisation

Organisers Regina Burachik, Yalcin Kaya

Contributed Talks


15:20 Markus Hegland (Australian National University)Solving some variational problems with iterated function systems

15:45 Yoni Nazarathy (The University of Queensland)Scheduling for a Processor Sharing System with Linear Slowdown

16:10 Qinian Jin (Australian National University)Alternating direction method of multipliers for inverse problems

16:35 Matthew Tam (The University of Newcastle)Reconstruction Algorithms for Blind Ptychographic Imaging

17:00 Soorena Ezzati (Federation University Australia)An Improvement for the Conjugate Gradient Analysis Method


15:20 Jonathan Borwein (The University of Newcastle)Convexity on Groups and Semigroups

16:10 Ohad Giladi (The University of Newcastle)Convexity on topological groups and semigroups, II

16:35 Vera Roshchina (RMIT University)Geometry of solution sets in multivariate Chebyshev polynomial approximationproblem

17:00 Ryan Loxton (Curtin University of Technology)Optimal control of 1,3-propanediol production processes


14:50 Brailey Sims (The University of Newcastle)Spaces of convex sets

15:15 Andrew Eberhard (RMIT University)Orbital Geometry and Eigenvalue optimization

15:40 Mohammed Mustafa Rizvi (University of South Australia)New Algorithms to Generate the Pareto Front of Multiobjective OptimizationProblems

16:05 Regina Burachik (University of South Australia)Proper Efficiency and Proper KarushKuhnTucker Conditions for SmoothMultiobjective Optimization Problems

16:30 Yalcin Kaya (University of South Australia)Duality and Computations for Control-constrained Optimal Control Problems

32

Special Session 19: Probability

Organisers Giang Thu Nguyen, Leonardo Rojas Nandayapa

Contributed Talks


15:20 Philip Keith Pollett (University of Queensland)Population networks with local extinction probabilities that evolve over time

16:10 Jie Yen Fan (Monash University)SPDE limits for the age structure of a population

16:35 Fima Klebaner (Monash University)Approximations of stochastic system near unstable fixed point

17:00 Leonardo Rojas Nandayapa (The University of Queensland)Statistical inference for phase-type scale mixtures


13:20 Andrew David Barbour (Universitaet Zuerich)Discrete multivariate approximation in total variation

13:45 Andriy Olenko (La Trobe University)Whittaker-Kotel’nikov-Shannon approximation of sub-Gaussian random processes

14:10 Giang Nguyen (The University of Adelaide)Slowing time: Markov-modulated Brownian motion with a sticky boundary

14:35 Nigel Bean (The University of Adelaide)Stochastic Two-dimensional Fluid Models: an operator approach

15:20 Kais Hamza (Monash University)Bootstrap Random Walks

15:45 Brendan Patch (The University of Queensland)A Simulation Algorithm for Queueing Network Stability Identification

16:10 Julia Kuhn (The University of Queensland)False Alarm Control for Window-Limited Change Detection

16:35 Daniel Dufresne (The University of Melbourne)Pricing discrete average options

17:00 Peter Gerrard Taylor (The University of Melbourne)Calculating optimal limits for transacting credit card customers

33

Special Session 20: Statistics

Organisers Darfiana Nur

Contributed Talks


13:20 Inge Koch (The University of Adelaide)Analysis of Proteomics Imaging Mass Spectrometry Data

14:10 Heri kuswanto (Institut Teknologi Sepuluh Nopember)Simple Method to Define Extreme Events for multiple dataset

14:35 Muhammad Shuaib Khan (The University of Newcastle)Mixture of two Transmuted Weibull distributions


14:50 Richard Boys (The University of Newcastle UK)Inference for population dynamics in the Neolithic period

15:40 Irhamah Irhamah (Institut Teknologi Sepuluh Nopember)Hybrid Fractionally Integrated STAR and Genetic Algorithm for ModelingForeign-Exchange Rates

16:05 Darfiana Nur (Flinders University)Bayesian inference for Vector Smooth Transition Autoregressive model

16:30 Elizabeth Stojanovski (The University of Newcastle)Heterogeneity in meta-analysis

34

Conference Timetable Summary

Sunday Monday Tuesday Wednesday Thursday

9:00

9:30

10:00

10:30

11:00

11:30

12:00

12:30

13:00

13:30

14:00

14:30

15:00

15:30

16:00

16:30

17:00

17:30

18:00

18:30

19:00

19:30

20:00

20:30

21:00

21:30

22:00

Early CareerResearcherWorkshop

WIMSIGGeneral Meeting

Women inMathematics

Dinner

Opening Addressand AustMSPresentation

Plenary 1James Demmel

Morning Tea

Plenary 2Frances Kirwan

Lunch.Book Launch

(SSN 241)

Plenary 3Konstantin

Zarembo

Afternoon Tea

Special SessionsBlock 1

3:25PM – 5:05PM

Public LectureTerence Tao

Musical RecitalRaymond Booth

Jan Slovak

Plenary 4Clement Hongler

Plenary 5Terence Tao

Morning Tea

Plenary 6Manjul Bhargava

Lunch


1:20PM – 3:00PM

Afternoon Tea


3:20PM – 5:25PM

AustMS2015 AGM

Chess Competition

Plenary 7Aurore Delaigle

Plenary 8Jerzy Filar

Morning Tea

Plenary 9Martino Bardi

Lunch


1:20PM – 3:00PM

Afternoon Tea


3:20PM – 5:25PM

Conference DinnerStanford Grand

Plenary 10Michael Shelley

Plenary 11Ruth Williams

Morning Tea

Plenary 12Frances Kuo

Lunch

Plenary 13Wadim Zudilin

Afternoon Tea


2:50PM – 4:55PM

35

Mon 28 September 2015

Opening – Matthew Flinders Theatre 09:00 – 09:30

AustMS presentation – Matthew Flinders Theatre 09:30 – 10:00

Book Launch – Social Sciences North 241 12:30 – 13:30

Plenary Lecture – Matthew Flinders Theatre

10:00 I James Demmel (University of California Berkeley)

Communication Avoiding Algorithms


11:30 I Frances Kirwan (University of Oxford)

Quotients of algebraic varieties by linear algebraic group


14:00 I Konstantin Zarembo (Nordic Institute for Theoretical Physics)

Random Matrices in Quantum Field Theory

Afternoon Special Sessions

1. Groups and Monoids

SSN223

15:25 Alexander Fish (University of Sydney)Dynamical methods in additive combinatorics

16:15 John Harrison (The University of Newcastle)Asymptotic behaviour of random walks on certain matrix groups

16:40 Murray Elder (The University of Newcastle)Using random walks to detect amenability in finitely generated groups


MFT

15:25 Robert Scott Anderssen (CSIRO)Modelling the Dynamics of Vernalization in Plants

15:50 Kylie Foster (University of South Australia)Mathematically modelling the salt stress response of individual plant cells

16:15 Joshua Chopin (University of South Australia)RootAnalyzer: a cross-section image analysis tool for automated characterization ofroot cells and tissues

16:40 Catherine Penington (Queensland University of Technology)Dying in order: how crowding affects particle lifetimes

36


4. Combinatorics

HUM115

15:25 Tony Guttmann (The University of Melbourne)Sorting with two stacks and quarter-plane loops

15:50 Marc Demange (RMIT University)On choosability of graphs with limited number of colours.

16:15 Kieran Clancy (Flinders University)Hamiltonicity-preserving graph reductions

16:40 Nicholas Wormald (Monash University)Proof of Tutte’s 3-flow conjecture in an ”almost all” sense.

5. Complex Analysis and Geometry

SSN235

15:25 Francine Meylan (University of Fribourg)Holomorphicity of Meromorphic Mappings along Real Hypersurfaces

16:15 Sean Curry (The University of Auckland)Constructing Local Invariants for CR Embeddings

16:40 Alessandro ottazzi (University of New South Wales)Conformal maps in nilpotent groups

7. DST Group and Industrial Mathematics Session

SSN013

15:25 Richard Taylor (Defence Science and Technology Organisation, Australia)Algorithmic complexity of two defence budget problems

15:50 Darryn Reid (Defence Science and Technology Organisation, Australia)Behavioural Questions in Complexity and Control

16:15 Axel Bender (Defence Science and Technology Organisation, Australia)Design Principle for Adaptable and Robust Complex Systems

16:40 Brandon Pincombe (Defence Science and Technology Organisation, Australia)A case for new models of battle attrition


SSN008

15:25 Vladimir Gaitsgory (Macquarie University)On control of systems with slow variables

15:50 Petrus van Heijster (Queensland University of Technology)Butterfly catastrophe for fronts in a three-component reaction-diffusion system

16:15 Joachim Worthington (University of Sydney)Poisson Structures and Stability for Euler Fluid Equations on a Toroidal Domain

16:40 Yang Shi (University of Sydney)Polytopes, symmetries and discrete integrable systems

9. Games and Applied Stochastic Processes

SSN015

15:25 Vladimir Ejov (Flinders University)Kookaburra vs. Concorde: Achilles and Tortoise in TSP race.

16:15 Michael Haythorpe (Flinders University)Applying Continuous Optimisation Techniques to Difficult Discrete OptimisationProblems

16:40 Asghar Moeini (Flinders University)On the Detection of Non-Hamiltonicity via Linear Feasibility Models

37



NTH1

15:25 Artem Pulemotov (The University of Queensland)The prescribed Ricci curvature problem on homogeneous spaces

15:50 Glen Wheeler (University of Wollongong)Curve diffusion flow with free boundary

16:15 Wolfgang Globke (The University of Adelaide)Compact pseudo-Riemannian solvmanifolds

16:40 Andree Lischewski (The University of Adelaide)Globally hyperbolic spacetimes with parallel null vector and related Riemannian flowequations


SSN102

15:25 Andrew Hassell (Australian National University)Estimates on boundary values of Neumann eigenfunctions

15:50 Melissa Tacy (The University of Adelaide)Quantised dynamical observables and concentration of eigenfunctions

16:15 Xiaolong Han (Australian National University)Completeness of boundary traces of Dirichlet and Neumann eigenfunctions

16:40 Sean Gomes (Australian National University)Inclusion Bounds and Eigenfunction Localisation


HUM133

15:25 Adelle Coster (University of New South Wales)Modelling at the Limits of Resolution: Single Molecule Fluorescence andProtein-Protein Binding

15:50 Jeremy Sumner (University of Tasmania)A representation-theoretic approach to the calculation of genome rearrangementdistances

16:15 Barbara Johnston (Griffith University)Possible sets of six conductivity values to use in the bidomain model of cardiac tissue

16:40 Jennifer Flegg (Monash University)Wound healing angiogenesis: The clinical implications of a simple mathematicalmodel


NTH2

15:25 Sven Trenholm (University of South Australia)Assessment and Feedback in Fully Online Tertiary Mathematics: The InstructorPerspective

15:50 Leigh Wood (Macquarie University)Mathematics and statistics modules for pre-service teachers

16:15 Birgit Loch (Swinburne University of Technology)Making mathematics relevant to first year engineering students

16:40 Aaron Wiegand (University of the Sunshine Coast)To all first-year Calculus students: *pleeease* attend the classes!

38

Tue 29 September 2015

Nalini Joshi - Decadel Plan – Matthew Flinders Theatre 12:30 – 12:45


09:00 I Clement Hongler (EPFL)

Random Fields and Curves, Discrete and Continuous Structures


10:00 I Terence Tao (University of California Los Angeles)

Finite time blowup for an averaged Navier-Stokes equation


11:30 I Manjul Bhargava (Princeton University)

What is the Birch and Swinnerton-Dyer Conjecture, and what is known about it?

AGM – Matthew Flinders Theatre 17:30 – 18:30



SSN235

13:20 Anne Thomas (University of Sydney)Reflection length in affine Coxeter groups

13:45 Attila Egri-Nagy (Western Sydney University)Independent generating sets of symmetric groups

SSN102

15:20 Robert McDougall (University of the Sunshine Coast)On substructures which can be carried by homomorphic images

15:45 Lauren Thornton (University of the Sunshine Coast)On base radical and semisimple classes for associative rings

16:10 Nathan Brownlowe (University of Wollongong)Non-embeddings into the Leavitt algebra L2

16:35 Roozbeh Hazrat (University of Western Sydney)Ultramatricial algebras, classification via K-groups

17:00 Colin David Reid (The University of Newcastle)Essentially chief series of locally compact groups

39


2. Algebraic Geometry and Representation Theory

SSN235

14:10 Shrawan Kumar (University of South Carolina)Positivity in T-equivariant K-theory of flag varieties associated to Kac-Moody groups

15:20 Scott Morrison (Australian National University)A quantum exceptional series

15:45 Slaven Kozic (University of Sydney)

Principal subspaces and vertex operators for quantum affine algebra Uq(sln+1)

16:10 Uri Onn (Australian National University)A variant of Harish-Chandra functors

16:35 Hang Wang (The University of Adelaide)Base change and K-theory

17:00 Jon Xu (The University of Melbourne)Schubert Calculus and Finite Geometry


NTH1

13:20 Troy Farrell (Queensland University of Technology)Comparing Nernst-Plank and Maxwell-Stefan approaches for modelling electrolytesolutions

14:10 Alise Thomas (University of the Sunshine Coast)The use of the Fast Fourier Transform in the analysis of the fine substructure of3-dimensional spatio-temporal human movement data

14:35 Stanley Joseph Miklavcic (University of South Australia)Mathematical models for competitive ion absorption in a polymer matrix

15:20 Bronwyn Hajek (University of South Australia)Particle transport in asymmetric periodic capillaries

15:45 Raja Ramesh Huilgol (Flinders University)Mesoscopic Models to Bingham Fluids: Mixed Convection Flow in a Cavity

16:10 Tony Miller (Flinders University)Taylor Series and Water Hammer

16:35 Yvonne Stokes (The University of Adelaide)Mathematics in the drawing of microstructured optical fibres.

17:00 Qiang Sun (The University of Melbourne)Why should boundary element methods have to deal with singularities?

4. Combinatorics

SSN015

15:20 Diana Combe (University of New South Wales)Signed designs

15:45 Asha Rao (Royal Melbourne Institute of Technology)Skolem sequences and Difference covering arrays

16:10 Joanne Hall (Queensland University of Technology)Difference Covering Arrays and Nearly Orthogonal Latin Square

16:35 David G Glynn (Flinders University)Evaluating modular invariants

17:00 Christopher Taylor (La Trobe University)Algebras of incidence structures: representations of regular double p-algebras,

17:25 Stacey Mendan (La Trobe University)Graphic and bipartite graphic sequences

40


6. Computational Mathematics

13:20 Ian Turner (Queensland University of Technology)Dual-scale Modelling Approaches for Simulating Diffusive Transport in HeterogeneousPorous Media

14:10 Qinian Jin (Australian National University)Landweber iteration of Kaczmarz type for inverse problems in Banach spaces

14:35 Chenxi Fan (University of New South Wales)Effective dimension for weighted ANOVA and anchored spaces


HUM115

15:20 Alexander Kalloniatis (Defence Science and Technology Organisation, Australia)A model for distributed decision making: Levy noise and network synchronisation

15:45 Greg Calbert (Defence Science and Technology Organisation, Australia)Military inventory capacity and stock planning with surge and warning time andsupplier constraints

16:10 Minh Tran (Flinders University)Model-Based State Of Charge Estimation Of A Lithium-Ion Battery

16:35 Sangeeta Bhatia (University of Western Sydney)Do I smell gas? Bayesian Inversion for localisation and quantification of fugitiveemissions

17:00 ()


MFT

13:20 Luchezar Stoyanov (The University Of Western Australia)On Lyapunov regularity for uniformly hyperbolic systems

13:45 Davor Dragicevic (School of mathematics and statistics)Spectral theory under nonuniform hyperbolicity

14:10 Danya Rose (University of Sydney)Finding absolutely and relatively periodic orbits in the equal mass 3-body problemwith vanishing angular momentum

14:35 Andy Hammerlindl (Monash University)Models of chaos in dimensions two and three

15:20 Michael Small (The University Of Western Australia)Random walks on networks built from dynamical systems

15:45 Lewis Mitchell (The University of Adelaide)A shadowing-based inflation scheme for ensemble data assimilation

16:10 Qing Liu (University of Sydney)Elliptic Asymptotic Behaviour of q-Painleve III

16:35 Peter Cudmore (The University of Queensland)Rock and Roll and Quantum Optics.

17:00 Daniel Daners (University of Sydney)Perron-Frobenius theory and eventually positive semigroups of linear operators


SSN013

13:20 Imma Curiel (Anton de Kom University of Suriname)A combinatorial optimization game arising from a components acquisition situation.

13:45 Ehsan Nekouei (The University of Melbourne)Performance of Gradient-Based Nash Seeking Algorithms Under QuantizedInter-Agent Communications

14:10 Jakub Tomczyk (University of Sydney)A multidimensional correlated square root process

41


14:35 Jerzy Filar (Flinders University)Ordered Field Property in Discounted Stochastic Games


NTH2

13:20 Joan Licata (Australian National University)Morse Structures on Open Books

13:45 Craig Hodgson (University of Melbourne)The 3D index and normal surfaces

14:10 Neil Hoffman (The University of Melbourne)Geometry of planar surfaces and exceptional fillings

14:35 Joshua Howie (University of Melbourne)Hyperbolicity For Weakly Generalised Alternating Knots

15:20 Finnur Larusson (The University of Adelaide)Oka theory of affine toric varieties

15:45 Thoan Thi Kim Do (La Trobe University)New progress in the inverse problem in the calculus of variations.

16:10 Jan Slovak (Masaryk University)Subriemannian linearized metrizability

16:35 Geoffrey Prince (Australian Mathematical Sciences Institute)Torsion and the second fundamental form for distributions

17:00 Milena Radnovic (University of Sydney)Geometry of confocal quadrics in pseudo-Euclidean space


SSN008

13:20 Glen Wheeler (University of Wollongong)Polyharmonic curvature flow

13:45 Adam Sikora (Macquarie University)Spectral multipliers, Bochner-Riesz means and uniform Sobolev inequalities forelliptic operators

14:10 David Franklin (The University of Newcastle)Hardy Spaces and Paley-Wiener Spaces for Clifford-valued functions

14:35 Ting-Ying Chang (University of Sydney)Singular Solutions to Weighted Divergence Form Equations


SSN102

13:20 Andrew Black (The University of Adelaide)Modelling the transition from uni- to multi-cellular life

13:45 Mark Flegg (Monash University)Simulation of reaction-diffusion processes in cellular biology

14:10 Benjamin Binder (The University of Adelaide)How do we quantify the filamentous growth in a yeast colony?

14:35 James Ashton Nichols (University of New South Wales)Anomalous dynamics in compartment models, a continuous time random walkapproach


HUM133

13:20 Carolyn Kennett (Macquarie University)Reflections on using vodcasts as an assessment item in first year units

13:45 Donald Shearman (Western Sydney University)Great Expectations: I expect to pass because I already know all this stuff

42


14:10 Dann Mallet (Queensland University of Technology)Mathematics degree learning outcomes and their assurance

15:20 Jonathan Kress (University of New South Wales)Online tutorials with YouTube and Maple TA: the experience so far

15:45 Caroline Bardini (The University of Melbourne)Symbols: do university students mean what they write and write what they mean?

16:10 Antony Edwards (Swinburne University of Technology)Student reasoning about real-valued sequences: Insights from an example-generationstudy

16:35 Joann Cattlin (University of Melbourne)New Mathematics Special Interest Group for AustMS

16. Number Theory

HUM115

13:20 Karl Dilcher (Dalhousie University)Generalized Fermat numbers and congruences for Gauss factorials

13:45 Mumtaz Hussain (The University of Newcastle)A metrical problem in Non-linear Diophantine approximation

14:10 Grant Cairns (La Trobe University)Generalisations of Wilson’s Theorem for Double, Hyper, Sub and Superfactorials

14:35 Angus McAndrew (The University of Melbourne)Galois Representations for Siegel Modular Forms

SSN013

15:20 Jeffrey Lay (Australian National University)Iterated sums of the Mobius function

15:45 Adrian Dudek (Australian National University)On Solving a Curious Inequality of Ramanujan

16:10 Randell Heyman (University of New South Wales)The approximate GCD problem

16:35 Stijn Hanson (Australian National University)Generalisations of Chen’s Theorem and the vector sieve

17:00 Simon Macourt (Macquarie University)Dedekind Sums

18. Variational Analysis and Optimisation

SSN008

15:20 Markus Hegland (Australian National University)Solving some variational problems with iterated function systems

15:45 Yoni Nazarathy (The University of Queensland)Scheduling for a Processor Sharing System with Linear Slowdown

16:10 Qinian Jin (Australian National University)Alternating direction method of multipliers for inverse problems

16:35 Matthew Tam (The University of Newcastle)Reconstruction Algorithms for Blind Ptychographic Imaging

17:00 Soorena Ezzati (Federation University Australia)An Improvement for the Conjugate Gradient Analysis Method

19. Probability

SSN223

15:20 Philip Keith Pollett (University of Queensland)Population networks with local extinction probabilities that evolve over time

16:10 Jie Yen Fan (Monash University)SPDE limits for the age structure of a population

43


16:35 Fima Klebaner (Monash University)Approximations of stochastic system near unstable fixed point

17:00 Leonardo Rojas Nandayapa (The University of Queensland)Statistical inference for phase-type scale mixtures

44

Wed 30 September 2015

Geoff Prince - Choose Maths and the National Research Centre – Matthew Flinders Theatre12:30 – 13:05


09:00 I Aurore Delaigle (The University of Melbourne)

Deconvolution when the Error Distribution is Unknown


10:00 I Jerzy Filar (Flinders University)

An Overview of the Flinders Hamiltonian Cycle Project


11:30 I Martino Bardi (University of Padua)

An introduction to Mean Field Games and models of segregation

Jon Borwein - AMSI Workshop Program – Matthew Flinders Theatre 15:00 – 15:15



SSN008

15:20 Marcel Jackson (La Trobe University)From A to B to Z

15:45 James East (University of Western Sydney)Linear sandwich semigroups

16:10 Kathy Horadam (Royal Melbourne Institute of Technology)Coboundary and graph codes and their invariants

16:35 Don Taylor (University of Sydney)Janko’s sporadic simple groups

17:00 Anthony Licata (Australian National University)On the 2-linearity of the free group

45



SSN013

15:20 Anthony Licata (Australian National University)Geometric representation theory and categorification for braid groups of type ADE

15:45 Jarod Alper (Australian National University)A tale of two polynomials

16:10 Mircea Voineagu (University of New South Wales)An equivariant motivic cohomology

16:35 Arnab Saha (Australian National University)The Frobenius Operator and Descending to Constants

17:00 Anthony Henderson (University of Sydney)Diagram automorphisms revisited


SSN102

13:20 Elizabeth Bradford (University of South Australia)Mathematical techniques to aid the Australian Army in selecting new defence vehicles

13:45 Phil Howlett (University of South Australia)The Key Principles of Optimal Train Control

14:10 Kathy Horadam (Royal Melbourne Institute of Technology)Neighbourhood distinctiveness in complex networks: an initial study

14:35 Ignacio Ortega Piwonka (University of New South Wales)Use of a stochastic model to study the cyclic motion in nanowires trapped by focusedGaussian beams

4. Combinatorics

15:20 Murray Neuzerling (La Trobe University)Using algebra to avoid robots

15:45 Tomasz Kowalski (La Trobe University)NP-complete fragments of qualitative calculi

16:10 Lucy Ham (La Trobe University)Definability of SP-classes of uniform hypergraphs

16:35 Jamie Simpson (Curtin university)An introduction to combinatorics of words

17:00 Amy Glen (Murdoch University)On the number of palindromically rich words


SSN015

13:20 Ioannis Tsartsaflis (La Trobe University)Filiform Lie algebras over Z2

13:45 David Bowman (The University of Adelaide)Holomorphic flexibility properties of spaces of elliptic functions

14:10 Timur Sadykov (Plekhanov Russian University)Analytic complexity of binary cluster trees

14:35 Gerd Schmalz (University of New England)A Forelli type theorem for resonant vector fields


HUM115

13:20 Markus Hegland (Australian National University)Solving partial differential equations with the sparse grid combination technique

13:45 Gary Froyland (University of New South Wales)Computing Lagrangian coherent structures from Laplace eigenproblems

46


14:10 Paul Charles Leopardi (School of Mathematical and Physical Sciences The Universityof Newcastle)Equal area partitions of connected Ahlfors regular spaces

14:35 Garry Newsam (The University of Adelaide)Fitting Circular Arcs Through Points in the Plane

15:20 Bishnu Lamichhane (The University of Newcastle)A stabilized mixed finite element method systems for nearly incompressible elasticityand Stokes equations

15:45 Michael Feischl (UNSW)An abstract analysis of optimal goal-oriented adaptivity

16:10 Robert Womersley (University of New South Wales)Efficient spherical designs with good goemetric properties

16:35 Yuguang Wang (University of New South Wales)Fully discrete needlet approximation on the sphere

17:00 Quoc Thong Le Gia (University of New South Wales)Higher order Quasi-Monte Carlo integration for Bayesian Estimation


NTH1

13:20 Rua Murray (University of Canterbury)Reliable computation of invariant measures: progress towards Ulam’s conjecture

13:45 Paul Wright (The University Of Western Australia)Dimensional Characteristics of the Non-wandering Sets of Open Billiards

14:10 Eric Kwok (University of New South Wales)Dynamic isoperimetry on weighted manifolds

14:35 Cecilia Gonzalez-Tokman (The University of Queensland)A streamlined approach to the multiplicative ergodic theorem on Banach spaces


MFT

13:20 Guillermo Pineda-Villavicencio (Federation University Australia)Lower and upper bound theorems for almost simplicial polytopes

13:45 Ana Dow (University of Melbourne)CAT (0) Semi-Cubings of Adequate links

14:10 Norman Do (Monash University)The combinatorics of tetrahedron index ratios

14:35 Grace Omollo Misereh (La Trobe University)Thrackles

15:20 Daniel Mathews (Monash University)Counting curves on surfaces

15:45 Benjamin Burton (University of Queensland)The computational hardness of normal surfaces

16:10 Jonathan Spreer (University of Queensland)Collapsibility and 3-sphere recognition

16:35 Yuri Nikolayevsky (La Trobe University)Solvable Lie groups of negative Ricci curvature

17:00 Alexandr Medvedev (University of New England)Differential invariants of ODEs systems of higher order


SSN008

13:20 Nirav Arunkumar Shah (The University of Queensland)Regularity of bounded weak solutions to an Euler-Lagrange system in the criticaldimension.

47


13:45 Kyle Talbot (Monash University)Uniform temporal stability of solutions to doubly degenerate parabolic equations.

14:10 Florica Corina Cirstea (School of Mathematics and Statistics, University of Sydney)Classification of isolated singularities for elliptic equations with Hardy-type potentials

14:35 Xuan Duong (Macquarie University)Factorization for Hardy spaces and characterization for BMO spaces via commutatorsin the Bessel setting.

NTH1

15:20 Steven Luu (School of Mathematics and Statistics, University of Sydney)Asymptotics of a q-Airy equation

15:45 Michael Twiton (School of Mathematics and Statistics, University of Sydney)On Truncated Solutions of The Fourth Painlev Equation

16:10 James Gregory (University of Sydney)Special Solutions of the Painleve Equations

16:35 Pieter Roffelsen (University of Sydney)Asymptotics of solutions to the discrete Painleve equation q-P (A∗1) which areholomorphic at the origin

17:00 Anh Bui (Macquarie University)Dispersive estimates for the wave equations in R3


HUM133

13:20 Deborah Cromer (University of New South Wales)What is the optimal length of HIV Remission?

13:45 Adrianne Jenner (University of Sydney)Mathematical modelling of oncolytic virotherapy and immunotherapy usingdeterministic and stochastic models

14:10 Pouya Baniasadi (Flinders University)Traveling Salesman Problem Approach for Solving DNA Sequencing Problems

14:35 Sangeeta Bhatia (University of Western Sydney)An algebraic approach to determine a minimal weighted inversion distance


NTH2

13:20 John William Rice (University of Sydney)Galileo and Calculus Unlimited

13:45 Lesley Ward (University of South Australia)Mathematics and Australian Indigenous Culture: Building cultural awareness,competency and literacy in mathematics students at UniSA

14:10 Deborah Jackson (La Trobe University)Development and Implementation of a First Year Statistics Subject for SeniorSecondary Indigenous Students to Encourage Future Engagement in Tertiary Studies

14:35 Diana Quinn (University of South Australia)Learning from experience: developing mathematics courses for an online engineeringdegree

15:20 John Banks (University of Melbourne)Spreadsheet drawings of plant branching from modified Lindenmayer grammars

15:45 Tristram Alexander (UNSW)Assessing for student problem solving ability

16:10 Kevin White (University of South Australia)Mind the Gap: Exploring knowledge decay in online sequential mathematics courses

16:35 Amie Albrecht (University of South Australia)Developing mathematical thinking through puzzles and games

17:00 ()

48


14. Mathematical Physics

SSN235

15:20 David Ridout (Australian National University)Non-rational CFTs and the Verlinde formula

15:45 Christopher Bourne (Australian National University)A noncommutative approach to topological insulators

16:10 Tom Daniels (Flinders University)Singular spectral shift function for Schrodinger operators

16:35 Inna Lukyanenko (The University of Queensland)An integrable case of the p+ ip pairing Hamiltonian interacting with its environment

17:00 ()

15. Mathematics of Medical Imaging

SSN013

13:20 Michael Ng (Hong Kong Baptist University)Variational Models and Computational Methods in Image Processing

14:10 Gobert Lee (Flinders University)Moment Invariants for Medical image segmentation

14:35 Simon Williams (Flinders University)Estimating an additive gaussian model for projective images

HUM120

15:20 Murk Bottema (Flinders University)Textons in rat bones and mammograms

15:45 Amelia Gontar (Flinders University)Textons and their applications in medical imaging

16:10 shelda sajeev (Flinders University)An Adaptive CLAHE for Improving Medical Image Segmentation

16:35 Rui-Sheng Lu (Flinders University)Texture Analysis Improves the Estimate of Bone Fracture Risk from DXA Images

17:00 ()

17. Operator Algebras and Function Analysis

SSN015

15:20 Mathai Varghese (The University of Adelaide)Magnetic spectral gap-labelling conjectures

16:10 Nathan Brownlowe (University of Wollongong)C*-algebras associated to graphs of groups

16:35 Guo Chuan Thiang (The University of Adelaide)Dualities in real K-theory and physical applications

17:00 Aidan Sims (University of Wollongong)Stable finiteness of k-graph algebras


HUM133

15:20 Jonathan Borwein (The University of Newcastle)Convexity on Groups and Semigroups

16:10 Ohad Giladi (The University of Newcastle)Convexity on topological groups and semigroups, II

16:35 Vera Roshchina (RMIT University)Geometry of solution sets in multivariate Chebyshev polynomial approximationproblem

17:00 Ryan Loxton (Curtin University of Technology)Optimal control of 1,3-propanediol production processes

49


19. Probability

SSN223

13:20 Andrew David Barbour (Universitaet Zuerich)Discrete multivariate approximation in total variation

13:45 Andriy Olenko (La Trobe University)Whittaker-Kotel’nikov-Shannon approximation of sub-Gaussian random processes

14:10 Giang Nguyen (The University of Adelaide)Slowing time: Markov-modulated Brownian motion with a sticky boundary

14:35 Nigel Bean (The University of Adelaide)Stochastic Two-dimensional Fluid Models: an operator approach

15:20 Kais Hamza (Monash University)Bootstrap Random Walks

15:45 Brendan Patch (The University of Queensland)A Simulation Algorithm for Queueing Network Stability Identification

16:10 Julia Kuhn (The University of Queensland)False Alarm Control for Window-Limited Change Detection

16:35 Daniel Dufresne (The University of Melbourne)Pricing discrete average options

17:00 Peter Gerrard Taylor (The University of Melbourne)Calculating optimal limits for transacting credit card customers

20. Statistics

SSN235

13:20 Inge Koch (The University of Adelaide)Analysis of Proteomics Imaging Mass Spectrometry Data

14:10 Heri kuswanto (Institut Teknologi Sepuluh Nopember)Simple Method to Define Extreme Events for multiple dataset

14:35 Muhammad Shuaib Khan (The University of Newcastle)Mixture of two Transmuted Weibull distributions

50

Thu 1 October 2015


09:00 I Michael Shelley (New York University)

Mathematical Models and Analysis of Active Suspensions


10:00 I Ruth Williams (UC San Diego)

Resource Sharing in Stochastic Networks


11:30 I Frances Kuo (University of New South Wales)

Liberating the Dimension – Quasi-Monte Carlo Methods for High Dimensional Integration


13:20 I Wadim Zudilin (The University of Newcastle)

The life of 1/Pi



MFT

14:50 Richard Michael Morris (Durban University of Technology)The algebraic properties of the nonautonomous one- and two-factor problems ofcommodities

15:15 Joel Moitsheki (University of the Witwatersrand)Application of Lie symmetry techniques to reaction-diffusion equations.

15:40 Simon Clarke (Monash University)Complex spatial self-organisation in an extended Daisyworld model

16:05 ()

16:30 ()

51

Thu 1 October 2015


SSN015

14:50 Jorge Lauret (Universidad Nacional de Cordoba)Geometric flows and their solitons on homogeneous spaces

15:15 Martin Kolar (Masaryk University)Normal forms and symmetries in CR geometry

15:40 Tuyen Truong (The University of Adelaide)Two approaches toward the Jacobian conjecture

16:05 Dmitri Alekseevsky (Institute for Information Transmission Problems)Homogeneous locally conformally Kaehler manifolds

16:30 Owen Dearricott (MASCOS / University of Melbourne)An algebraic form for a self-dual Einstein orbifold metric


NTH1

14:50 Bjorn Ruffer (The University of Newcastle)Separable Lyapunov functions for monotone systems

15:15 Tristram Alexander (UNSW)Spontaneous rotation in a resonance-free system

15:40 Nobutaka Nakazono (University of Sydney)A comprehensive method for constructing Lax pairs of discrete Painleve equation:(A2 +A1)(1) case

16:05 ()

16:30 ()


NTH2

14:50 Michael Murray (The University of Adelaide)Equivariant bundle gerbes

15:15 Raymond Vozzo (The University of Adelaide)String structures on homogeneous spaces

15:40 David Roberts (The University of Adelaide)Homogeneous String connections

16:05 Zhou Zhang (University of Sydney)Mean curvature flow over almost Fuschian manifold

16:30 ()


SSN008

14:50 Daniel Hauer (University of Sydney)A simplified approach to the regularising effect of nonlinear semigroups

15:15 Zihua Guo (Monash University)Scattering for the Zakharov system

15:40 Qirui Li (Australian National University)Multiple solutions to the Lp-Minkowski problem

16:05 ()

16:30 ()


SSN102

14:50 Peter Johnston (Griffith University)A New Model for Aggressive Breeding Amongst Wolbachia Infected Flies

52

Thu 1 October 2015

15:15 Owen Jepps (Griffith University)Influence of homeostasis on the long-time-limit behaviour of an autoimmune disease

15:40 Sarthok Sircar (University of Adelaide)Surface deformation and shear flow in ligand mediated cell adhesion

16:05 Pascal R Buenzli (Monash University)Bulk and surface balance during tissue modelling and remodelling

16:30 ()


HUM133

14:50 Jonathan Borwein (The University of Newcastle)A short walk can be beautiful

15:15 Christine Mangelsdorf (University of Melbourne)Understanding and addressing poor student performance in first year universitycalculus

15:40 Katherine Anne Seaton (La Trobe University)Pipelines, ceilings, and acid rain

16:05 ()

16:30 ()


SSN013

14:50 Jan De Gier (University of Melbourne)N = 2 supersymmetry on the lattice without fermion conservation

15:15 Guo Chuan Thiang (The University of Adelaide)T-duality and topological phases

15:40 Mathew Zuparic (Defence Science and Technology Group, Australia)Spectra and Greens functions of second order density models

16:05 Jon Links (The University of Queensland)Electron-hole asymmetry of the p+ip pairing model.

16:30 ()

16. Number Theory

SSN223

14:50 Shaun Cooper (Massey University)Ramanujan’s level 7 theta functions

15:15 Alexandru Ghitza (The University of Melbourne)Analytic evaluation of Hecke eigenvalues

15:40 Min Sha (University of New South Wales)The Arithmetic of Consecutive Polynomial Sequences over Finite Fields

16:05 Timothy Trudgian (Australian National University)Every prime greater than 61 has three consecutive primitive roots

16:30 ()


HUM115

14:50 Brailey Sims (The University of Newcastle)Spaces of convex sets

15:15 Andrew Eberhard (RMIT University)Orbital Geometry and Eigenvalue optimization

15:40 Mohammed Mustafa Rizvi (University of South Australia)New Algorithms to Generate the Pareto Front of Multiobjective OptimizationProblems

53

Thu 1 October 2015

16:05 Regina Burachik (University of South Australia)Proper Efficiency and Proper KarushKuhnTucker Conditions for SmoothMultiobjective Optimization Problems

16:30 Yalcin Kaya (University of South Australia)Duality and Computations for Control-constrained Optimal Control Problems

20. Statistics

SSN235

14:50 Richard Boys (The University of Newcastle UK)Inference for population dynamics in the Neolithic period

15:40 Irhamah Irhamah (Institut Teknologi Sepuluh Nopember)Hybrid Fractionally Integrated STAR and Genetic Algorithm for ModelingForeign-Exchange Rates

16:05 Darfiana Nur (Flinders University)Bayesian inference for Vector Smooth Transition Autoregressive model

16:30 Elizabeth Stojanovski (The University of Newcastle)Heterogeneity in meta-analysis

54

List of Registrants

As of 19 September 2007

Dr Amie Albrecht University of South AustraliaProf Dmitri Alekseevsky Institute for Information Transmission ProblemsDr Tristram Alexander UNSWDr Jarod Alper Australian National UniversityDr Robert Scott Anderssen CSIRODr Robyn Patrice Araujo Queensland University of TechnologyMr Pouya Baniasadi Flinders UniversityDr John Banks University of MelbourneProf Andrew David Barbour Universitaet ZuerichProf Martino Bardi University of PaduaDr Caroline Bardini The University of MelbourneDr Frank Barrington The University of MelbourneProf Nigel Bean The University of AdelaideDr Andrea Bedini The University of MelbourneDr Axel Bender Defence Science and Technology Organisation, AustraliaMr Dmitry Berdinsky The University of AucklandProf Manjul Bhargava Princeton UniversityMs Sangeeta Bhatia University of Western SydneyDr Benjamin Binder The University of AdelaideDr Andrew Black The University of AdelaideDr Raymond Booth Flinders UniversityDr Jonathan Borwein The University of NewcastleDr Murk Bottema Flinders UniversityMr Christopher Bourne Australian National UniversityMr David Bowman The University of AdelaideProf Richard Boys The University of Newcastle UKMs Elizabeth Bradford University of South AustraliaDr Jill Brown Australian Catholic UniversityDr Nathan Brownlowe University of WollongongDr Pascal R Buenzli Monash UniversityDr Anh Bui Macquarie UniversityAssoc Regina Burachik University of South AustraliaDr Benjamin Burton University of QueenslandMr Timothy Peter Bywaters University of WollongongMr Edie Cain Australian National UniversityDr Grant Cairns La Trobe UniversityDr Greg Calbert Defence Science and Technology Organisation, AustraliaMr Richard McLaurin Campbell The University of MelbourneMs Joann Cattlin University of MelbourneProf Derek Chan The University of MelbourneMiss Ting-Ying Chang University of SydneyMr Yi Chen Federation University AustraliaMr Brett Simon Chenoweth The University of AdelaideMr Joshua Chopin University of South AustraliaDr Florica Corina Cirstea University of SydneyMr Kieran Clancy Flinders UniversityDr Simon Clarke Monash UniversityDr Diana Combe University of New South WalesMr Brendan Cooney Royal Melbourne Institute of Technology

55

List of Registrants

Dr Michael Coons The University of NewcastleDr Shaun Cooper Massey UniversityDr Adelle Coster University of New South WalesDr Brendan Creutz University of CanterburyDr Deborah Cromer University of New South WalesDr Lito Cruz Monash UniversityMr Peter Cudmore The University of QueenslandDr Imma Curiel Anton de Kom University of SurinameMr Sean Curry The University of AucklandDr Daniel Daners University of SydneyMr Tom Daniels Flinders UniversityProf Jan De Gier University of MelbourneMiss Marike de Waard University of QueenslandDr Owen Dearricott MASCOS / University of MelbourneProf Aurore Delaigle The University of MelbourneAssoc Marc Demange RMIT UniversityProf James Demmel University of California BerkeleyDr Karl Dilcher Dalhousie UniversityDr Norman Do Monash UniversityMrs Thoan Thi Kim Do La Trobe UniversityMs Ana Dow University of MelbourneDr Davor Dragicevic University of New South WalesMr Adrian Dudek Australian National UniversityProf Daniel Dufresne The University of MelbourneProf Xuan Duong Macquarie UniversityDr James East University of Western SydneyProf Andrew Eberhard RMIT UniversityProf Andrew Craig Eberhard Royal Melbourne Institute of TechnologyMr Cain James Edie-Michell Australian National UniversityMr Cain James Edie-Michell Australian National UniversityDr Antony Edwards Swinburne University of TechnologyDr Attila Egri-Nagy Western Sydney UniversityDr Vladimir Ejov Flinders UniversityDr Murray Elder The University of NewcastleDr Ali Sayed Elfard The University of MelbourneMr Andrew Elvey Price The University of MelbourneMr Soorena Ezzati Federation University AustraliaMiss Chenxi Fan University of New South WalesMiss Jie Yen Fan Monash UniversityAssoc Troy Farrell Queensland University of TechnologyDr Michael Feischl UNSWProf Jerzy Filar Flinders UniversityDr Alexander Fish University of SydneyDr Jennifer Flegg Monash UniversityDr Mark Flegg Monash UniversityMrs Kylie Foster University of South AustraliaMr David Franklin The University of NewcastleProf Gary Froyland University of New South WalesDr Paul Gaertner Defence Science and Technology Organisation, AustraliaProf Vladimir Gaitsgory Macquarie UniversityDr Volker Gebhardt University of Western SydneyDr Alexandru Ghitza The University of MelbourneDr Ohad Giladi The University of NewcastleDr Amy Glen Murdoch UniversityDr Wolfgang Globke The University of AdelaideDr David G Glynn Flinders UniversityMr Sean Gomes Australian National UniversityMiss Amelia Gontar Flinders UniversityDr Cecilia Gonzalez-Tokman The University of Queensland

56

List of Registrants

Ms Lindy Grahn Fintona Girls’ SchoolDr Edward Green The University of AdelaideMr James Gregory University of SydneyMr Zihua Guo Monash UniversityProf Tony Guttmann The University of MelbourneDr Bronwyn Hajek University of South AustraliaDr Joanne Hall Queensland University of TechnologyMs Lucy Ham La Trobe UniversityDr Andy Hammerlindl Monash UniversityDr Kais Hamza Monash UniversityDr Xiaolong Han Australian National UniversityMr Stijn Hanson Australian National UniversityMr John Harrison The University of NewcastleProf Andrew Hassell Australian National UniversityDr Daniel Hauer University of SydneyMr Mitchell Hawkins University of WollongongDr Michael Haythorpe Flinders UniversityDr Roozbeh Hazrat University of Western SydneyProf Markus Hegland Australian National UniversityDr Anthony Henderson University of SydneyMr Randell Heyman University of New South WalesDr Craig Hodgson University of MelbourneDr Neil Hoffman The University of MelbourneDr Clement Hongler EPFLProf Kathy Horadam Royal Melbourne Institute of TechnologyDr Ecaterina Howard Macquarie UniversityDr Algy Howe Australian National UniversityMr Joshua Howie University of MelbourneProf Phil Howlett University of South AustraliaDr Peter Howley The University of NewcastleProf Raja Ramesh Huilgol Flinders UniversityDr Mumtaz Hussain The University of NewcastleDr Irhamah Irhamah Institut Teknologi Sepuluh NopemberDr Deborah Jackson La Trobe UniversityDr Marcel Jackson La Trobe UniversityDr Tamiru Jarso Department of DefenceDr Brian Jefferies University of New South WalesMs Adrianne Jenner University of SydneyDr Owen Jepps Griffith UniversityDr Qinian Jin Australian National UniversityDr Barbara Johnston Griffith UniversityAssoc Peter Johnston Griffith UniversityProf Nalini Joshi University of SydneyMr Ching Joshua University of SydneyDr Alexander Kalloniatis Defence Science and Technology Organisation, AustraliaDr Khurram Kamran Texas A and M UniversityDr Yalcin Kaya University of South AustraliaMr Luke Keating Hughes University of AdelaideMs Carolyn Kennett Macquarie UniversityMr Muhammad Shuaib Khan The University of NewcastleDr Tran Vu Khanh University of WollongongProf Frances Kirwan University of OxfordProf Fima Klebaner Monash UniversityAssoc Inge Koch The University of AdelaideAssoc Martin Kolar Masaryk UniversityDr Tomasz Kowalski La Trobe UniversityDr Slaven Kozic University of SydneyDr Jonathan Kress University of New South WalesDr Alexander Kruger Federation University Australia

57

List of Registrants

Ms Julia Kuhn The University of QueenslandDr Sanjeev Kumar Dr. B.R. Ambedkar University, AgraProf Shrawan Kumar University of South CarolinaAssoc Frances Kuo University of New South WalesDr Heri Kuswanto Institut Teknologi Sepuluh NopemberMr Eric Kwok University of New South WalesDr Bishnu Lamichhane The University of NewcastleDr Finnur Larusson The University of AdelaideProf Jorge Lauret Universidad Nacional de CordobaMr Jeffrey Lay Australian National UniversityDr Quoc Thong Le Gia University of New South WalesDr Gobert Lee Flinders UniversityMs Melissa Lee The University Of Western AustraliaDr Thomas Leistner The University of AdelaideDr Paul Charles Leopardi The University of NewcastleDr Ji Li Macquarie UniversityDr Qirui Li Australian National UniversityDr Anthony Licata Australian National UniversityDr Joan Licata Australian National UniversityMr Khey Jenq Lim Queensland University of TechnologyDr Jon Links The University of QueenslandDr Andree Lischewski The University of AdelaideMiss Qing Liu University of SydneyAssoc Birgit Loch Swinburne University of TechnologyDr Heather Lonsdale Curtin UniversityProf John Loxton University of Western SydneyAssoc Ryan Loxton Curtin University of TechnologyMr Rui-Sheng Lu Flinders UniversityMiss Inna Lukyanenko The University of QueenslandMr Steven Luu University of SydneyMr Simon Macourt Macquarie UniversityDr Robert Maillardet The University of MelbourneProf Dann Mallet Queensland University of TechnologyDr Christine Mangelsdorf University of MelbourneProf Timothy Marchant University of WollongongMr Dean Marchiori NoneDr Daniel Mathews Monash UniversityMr Angus McAndrew The University of MelbourneDr Nick McConnell Defence Science and Technology Organisation, AustraliaDr James McCoy University of WollongongDr Robert McDougall University of the Sunshine CoastDr Peter McNamara The University of QueenslandDr Alexandr Medvedev University of New EnglandDr Vincent Mellor The University of QueenslandMs Stacey Mendan La Trobe UniversityDr Francine Meylan University of FribourgMs Andrea Michaels NDA LawProf Stanley Joseph Miklavcic University of South AustraliaDr Tony Miller Flinders UniversityMs Stephanie Mills University of South AustraliaMs Grace Omollo Misereh La Trobe UniversityDr Lewis Mitchell The University of AdelaideMr Asghar Moeini Flinders UniversityProf Joel Moitsheki University of the WitwatersrandDr Richard Michael Morris Durban University of TechnologyDr Scott Morrison Australian National UniversityProf Michael Murray The University of AdelaideDr Rua Murray University of CanterburyDr Nobutaka Nakazono University of Sydney

58

List of Registrants

Dr Yoni Nazarathy The University of QueenslandDr Ehsan Nekouei The University of MelbourneMr Murray Neuzerling La Trobe UniversityDr Garry Newsam The University of AdelaideProf Michael Ng Hong Kong Baptist UniversityDr Giang Nguyen The University of AdelaideDr Huy The Nguyen University of QueenslandMs Trang Thi Thien Nguyen University of South AustraliaDr James Ashton Nichols University of New South WalesDr Yuri Nikolayevsky La Trobe UniversityMr Matthew Nolan University of SydneyDr Darfiana Nur Flinders UniversityDr Andriy Olenko La Trobe UniversityAssoc Uri Onn Australian National UniversityMr Ignacio Ortega Piwonka University of New South WalesDr Alessandro Ottazzi University of New South WalesDr Lukasz Pa˜kowski Nagoya UniversityMr Brendan Patch The University of QueenslandDr Tracy Payne Idaho State UniversityDr Catherine Penington Queensland University of TechnologyDr William Erik Pettersson The University of QueenslandDr Julia Piantadosi University of South AustraliaDr Brandon Pincombe Defence Science and Technology Organisation, AustraliaDr Guillermo Pineda-Villavicencio Federation University AustraliaProf Philip Keith Pollett University of QueenslandProf Geoffrey Prince Australian Mathematical Sciences InstituteDr Artem Pulemotov The University of QueenslandDr Diana Quinn University of South AustraliaDr Milena Radnovic University of SydneyDr Asha Rao Royal Melbourne Institute of TechnologyDr Charl Ras The University of MelbourneDr Colin David Reid The University of NewcastleDr Darryn Reid Defence Science and Technology Organisation, AustraliaProf John William Rice University of SydneyDr David Ridout Australian National UniversityDr Mohammed Mustafa Rizvi University of South AustraliaDr David Roberts The University of AdelaideMr David Roberts The University of AdelaideMr Pieter Roffelsen University of SydneyDr Leonardo Rojas Nandayapa The University of QueenslandMr Danya Rose University of SydneyDr Vera Roshchina RMIT UniversityDr Joshua Ross The University of AdelaideDr Joachim Hyam Rubinstein The University of MelbourneDr Bjorn Ruffer The University of NewcastleProf Timur Sadykov Plekhanov Russian UniversityDr Arnab Saha Australian National UniversityMrs Shelda Sajeev Flinders UniversityMiss Tian Sang University of MelbourneDr Gerd Schmalz University of New EnglandDr Katherine Anne Seaton La Trobe UniversityMs Emilia Seto The University of AdelaideDr Min Sha University of New South WalesMr Nirav Arunkumar Shah The University of QueenslandMr Donald Shearman Western Sydney UniversityProf Michael Shelley New York UniversityMs Yang Shi University of SydneyMuhammad Shuaib Khan The University of Newcastle

Dr Adam Sikora Macquarie University

59

List of Registrants

Dr Jamie Simpson Curtin universityDr Aidan Sims University of WollongongDr Brailey Sims The University of NewcastleDr Sarthok Sircar University of AdelaideMr Matthw Paul Skerritt The University of NewcastleProf Jan Slovak Masaryk UniversityProf Michael Small The University Of Western AustraliaMrs Andrea Smith Flinders UniversityMr Godfrey Smith The University of QueenslandProf Paul Smith Macquarie UniversityProf Kate Smith-Miles Monash UniversityDr Jonathan Spreer University of QueenslandDr Peter Stacey La Trobe UniversityDr Elizabeth Stojanovski The University of NewcastleDr Yvonne Stokes The University of AdelaideProf Luchezar Stoyanov The University Of Western AustraliaDr Jeremy Sumner University of TasmaniaDr Qiang Sun The University of MelbourneDr Melissa Tacy The University of AdelaideMr Kyle Talbot Monash UniversityMr Matthew Tam The University of NewcastleProf Terence Tao University of California Los AngelesMr Christopher Taylor La Trobe UniversityDr Don Taylor University of SydneyProf Peter Gerrard Taylor The University of MelbourneDr Richard Taylor Defence Science and Technology Organisation, AustraliaDr Testing Testing Flinders UniversityDr Guo Chuan Thiang The University of AdelaideMiss Alise Thomas University of the Sunshine CoastDr Anne Thomas University of SydneyProf Doreen Thomas The University of MelbourneMiss Lauren Thornton University of the Sunshine CoastMr Jakub Tomczyk University of SydneyMr James Totterdell University of SydneyMr Minh Tran Flinders UniversityProf Thanh Tran University of New South WalesDr Sven Trenholm University of South AustraliaDr Timothy Trudgian Australian National UniversityDr Tuyen Truong The University of AdelaideMr Ioannis Tsartsaflis La Trobe UniversityDr Ilknur Tulunay University of Technology, SydneyProf Ian Turner Queensland University of TechnologyMr Michael Twiton University of SydneyProf John Urbas Australian National UniversityDr Petrus van Heijster Queensland University of TechnologyProf Mathai Varghese The University of AdelaideDr Mircea Voineagu University of New South WalesDr Raymond Vozzo The University of AdelaideDr Paul Vrbik The University of NewcastleDr Hang Wang The University of AdelaideDr Yuguang Wang University of New South WalesAssoc Lesley Ward University of South AustraliaProf Ole Warnaar The University of QueenslandDr Glen Wheeler University of WollongongDr Michael Wheeler The University of MelbourneDr Kevin White University of South AustraliaDr Aaron Wiegand University of the Sunshine CoastMr Roy Williams Flinders UniversityProf Ruth Williams UC San Diego

60

List of Registrants

Dr Simon Williams Flinders UniversityDr George Willis The University of NewcastleMr Sean Wilson The University of QueenslandDr Robert Womersley University of New South WalesAssoc David Wood Monash UniversityProf Leigh Wood Macquarie UniversityDr Nicholas Wormald Monash UniversityMr Joachim Worthington University of SydneyMr Kyle Wright Australian National UniversityDr Paul Wright The University Of Western AustraliaMr Jon Xu The University of MelbourneProf Konstantin Zarembo Nordic Institute for Theoretical PhysicsDr Yinan Zhang University of SydneyDr Zhou Zhang University of SydneyProf Song-Ping Zhu University of WollongongProf Wadim Zudilin The University of NewcastleDr Mathew Zuparic Defence Science and Technology Group, Australia

61

Abstracts

Plenaries 65

Special Sessions1. Groups and Monoids 692. Algebraic Geometry and Representation Theory 723. Applied Mathematics 744. Combinatorics 805. Complex Analysis and Geometry 846. Computational Mathematics 867. DST Group and Industrial Mathematics Session 898. Dynamical Systems 929. Games and Applied Stochastic Processes 96

10. Geometry and Topology 9811. Harmonic Analysis and Partial Differential Equations 10312. Mathematical Biology 10713. Mathematics Education 11214. Mathematical Physics 11915. Mathematics of Medical Imaging 12116. Number Theory 12317. Operator Algebras and Function Analysis 12518. Variational Analysis and Optimisation 12619. Probability 12920. Statistics 132

63

0. Plenary

0.1. An introduction to Mean Field Games andmodels of segregation

Martino Bardi (University of Padua)

11:30 Wed 30 September 2015 – MFT

Prof Martino Bardi

The first part of this talk will be a soft introduc-tion to the recent theory of Mean Field Games fol-lowing the approach of J.-M. Lasry and P.-L. Li-ons. The theory aims at describing the collectivebehaviour of a continuum of rational agents com-peting to minimise their individual expected costor maximising a payoff. The states of the agentsevolve in time according to differential equationsinvolving a control and affected by noise, and theplayers seek Nash equilibria. I will present somemotivating examples and the basic partial differ-ential equations arising in the simplest models.The second part of the talk stems from the workof the Nobel Laureate T. Schelling, who studiedthe segregation of different ethnic groups in ameri-can cities in the 60s. We propose some Mean FieldGames models of such phenomena, involving twopopulations of agents. Some results on the exis-tence of equilibria will be presented, with exam-ples of non-uniqueness, as well as numerical simu-lations. This part is joint work with Marco Cirant(Universit di Milano) and Yves Achdou (UniversitParis-Diderot).

0.2. What is the Birch and Swinnerton-DyerConjecture, and what is known about it?

Manjul Bhargava (Princeton University)

11:30 Tue 29 September 2015 – MFT

Prof Manjul Bhargava

Over the past half-century, the Birch and Swinnerton-Dyer Conjecture has become one of the most noto-riously difficult unsolved problems in mathemat-ics, and has been listed as one of the seven million-dollar ”Millennium Prize Problems” of the ClayMathematics Institute. In this talk, we describethe problem in elementary terms, and the surpris-ing and beautiful ways in which it is related toseveral well-known open problems in number the-ory. Despite the difficulties in solving it, there isactually quite a bit known now towards the con-jecture. We will give a survey of what is known in-cluding several recent advances and, finally, whatremains to be done!

0.3. Deconvolution when the Error Distribution isUnknown

Aurore Delaigle (The University of Melbourne)


Prof Aurore Delaigle

In nonparametric deconvolution problems, in or-der to estimate consistently a density or distribu-tion from a sample of data contaminated by ad-ditive random noise it is often assumed that thenoise distribution is completely known or that anadditional sample of replicated or validation datais available. Methods have also been suggestedfor estimating the scale of the error distribution,but they require somewhat restrictive smoothnessassumptions on the signal distribution, which canbe hard to verify in practice. Taking a completelynew approach to the problem, we argue that datararely come from a simple, regular distribution,and that this can be exploited to estimate the sig-nal distributions using a simple procedure, oftengiving very good performance. Our method canbe extended to other problems involving errors-in-variables, such as nonparametric regression esti-mation. Its performance in practice is remarkablygood, often equalling (even unexpectedly) the per-formance of techniques that use additional data toestimate the unknown error distribution.

This is joint work with Peter Hall.

0.4. Communication Avoiding Algorithms

James Demmel (University of California Berkeley)

10:00 Mon 28 September 2015 – MFT

Prof James Demmel

Algorithms have two costs: arithmetic and com-munication, i.e. moving data between levels of amemory hierarchy or processors over a network.Communication costs (measured in time or en-ergy per operation) already greatly exceed arith-metic costs, and the gap is growing over timefollowing technological trends. Thus our goal isto design algorithms that minimize communica-tion. We present algorithms that attain provablelower bounds on communication, and show largespeedups compared to their conventional counter-parts. These algorithms are for direct and itera-tive linear algebra, for dense and sparse matrices,as well as direct n-body simulations. Several ofthese algorithms exhibit perfect strong scaling, inboth time and energy: run time (resp. energy)for a fixed problem size drops proportionally tothe number of processors p (resp. is independentof p). Finally, building on recent work of Ben-nett, Carbery, Christ and Tao extending boundsof Holder, Brascamp and Lieb, we describe exten-sions to very general algorithms involving arbi-trary loop nests and array accesses, in a way thatmay be incorporated into compilers.

65

0. Plenary

0.5. An Overview of the Flinders HamiltonianCycle Project

Jerzy Filar (Flinders University)


Prof Jerzy Filar

We consider the famous Hamiltonian cycle prob-lem (HCP) from the perspective of approachesstudied by members of the Flinders Hamilton-ian Cycle Project. In particular, we shall brieflyoutline results from three, somewhat overlapping,lines of investigations.

The first of these stems from an embedding of theHCP in a Markov decision process (MDP). Morespecifically, we consider the HCP as an optimiza-tion problem over the space of occupational mea-sures induced by the MDP’s stationary policies.The shape and volume of that space will dependon a small parameter that induces a number ofinteresting phenomena as it approaches zero.

The second line of research describes the devel-opment of a very successful “Snakes-and-LaddersHeuristic” (SLH) for finding a Hamiltonian cy-cle in an undirected graph. Despite the fact thatHCP is known to be NP-complete, this polyno-mial complexity heuristic has proved itself to beextremely reliable in solving Hamiltonian graphseven in cases where the number of Hamiltoniancycles is extremely small relative to the numberof potential candidate solutions.

The third line, aims to correctly identify non-Hamiltonian cubic graphs via polynomial com-plexity heuristics. The latter leads to a suitablyconstructed parametrized polytope of discountedoccupational measures that can be used as a do-main where Hamiltonian solutions are sought. Itis known that whenever a given graph possessesHamiltonian cycles, these correspond to certainextreme points of that polytope. In addition, weconsider the limiting - parameter free - polyhedralregion that can serve as a basis for determiningnon-Hamiltonicity of cubic graphs. Numerical re-sults indicate that determining non-Hamiltonicityof a great majority of non-Hamiltonian cubicgraphs is likely to be a problem of polynomialcomplexity despite the fact that HCP is knownto be NP-complete already for cubic graphs.

0.6. Random Fields and Curves, Discrete andContinuous Structures

Clement Hongler (EPFL)


Dr Clement Hongler

The planar Ising model is one of the most fun-damental models of statistical mechanics. It ex-hibits remarkable integrability structures, whichallow one to study it at an unparalleled level ofresolution, and to gain mathematical insight intothe nature of deep physical processes.

A particularly fascinating connection between themodel and conformal quantum field theories wasconjectured about forty years ago, allowing oneto reveal beautiful algebraic and geometric struc-tures describing the phase transition of the model.

We are now very close to understanding rigorouslythis connection. I will explain what the connec-tion is, how it can be understood in terms of com-binatorics, complex analysis, stochastic processesand representation theory, and what are the newobjects that we come up with.

Based on joint works with S. Benoist, D. Chelkak,H. Duminil-Copin, K. Izyurov, K. Kytola and S.Smirnov

0.7. Quotients of algebraic varieties by linearalgebraic group

Frances Kirwan (University of Oxford)


Prof Frances Kirwan

Many moduli spaces in algebraic geometry arisenaturally as quotients of linear algebraic groupactions on quasi-projective varieties. Mumford’sgeometric invariant theory (GIT), developed inthe 1960s, provides a method for constructing(projective completions of) quotient varieties forlinear actions of reductive groups on projectivevarieties. This talk will review some of the mainideas of GIT and discuss possible ways to extendthem to actions of linear algebraic groups whichare not necessarily reductive.

Applications include the construction known assymplectic implosion (due to Guillemin, Jeffreyand Sjamaar) and more recently an analogous con-struction in hyperkahler geometry.

0.8. Liberating the Dimension – Quasi-MonteCarlo Methods for High Dimensional Integration

Frances Kuo (University of New South Wales)

11:30 Thu 1 October 2015 – MFT

Assoc Prof Frances Kuo

High dimensional problems are coming to playan ever more important role in applications, in-cluding, for example, option pricing problems inmathematical finance, maximum likelihood prob-lems in statistics, and porous flow problems incomputational physics and uncertainty quantifi-cation. High dimensional problems pose immensechallenges for practical computation, because of anearly inevitable tendency for the cost of compu-tation to increase exponentially with dimension.Effective and efficient methods that do not sufferfrom this “curse of dimensionality” are in greatdemand, especially since some practical problemsare in fact infinite dimensional.

In this talk I will start with an introduction to“quasi-Monte Carlo methods”, focusing on the

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0. Plenary

theory and construction of “lattice rules” (or-der one) and “interlaced polynomial lattice rules”(higher order) developed in the past decade. ThenI will showcase our very latest work on how thismodern theory can be “tuned” for a given appli-cation. The motivating example will involve anelliptic PDE with a random coefficient, which isbased on a simplified porous flow problem wherethe permeability is modeled as a random field.

0.9. Mathematical Models and Analysis of ActiveSuspensions

Michael Shelley (New York University)


Prof Michael Shelley

Suspensions that have a ”bio-active” microstruc-ture – like swimming bacteria or the active con-stituents inside of cells – are examples of so-calledactive matter. These internally driven fluids canexhibit strange mechanical properties, and showpersistent activity-driven flows and elements ofself-organization. I will discuss first-principlesPDE models that capture the two-way couplingbetween ”active stresses” generated by collectivemicroscopic activity and the macroscopic flow.These PDEs have interesting analytical structuresand dynamics that agree qualitatively with exper-imental observations. I’ll discuss how these mod-els are being used to study even more complexbiophysical systems.

0.10. Finite time blowup for an averagedNavier-Stokes equation

Terence Tao (University of California Los Angeles)


Prof Terence Tao

The Navier-Stokes equation in three dimensionscan be expressed in the form ut = ∆u + B(u, u)for a certain bilinear operator B. It is a notoriousopen question whether finite time blowup solu-tions exist for this equation. We do not addressthis question directly, but instead study an aver-aged Navier-Stokes equation ut = ∆u + B(u, u),

where B is a certain average of B (where the av-erage involves rotations and Fourier multipliers oforder 0). This averaged Navier-Stokes equationobeys the same energy identity as the originalNavier-Stokes equation, and the nonlinear termB(u, u) obeys essentially the same function spaceestimates as the original nonlinearity B(u, u). Byusing a modification of a dyadic Navier-Stokesmodel of Katz and Pavlovic, which is “engineered”to generate “self-replicating machine” or “vonNeumann machine” type solutions, we can con-struct an example of an averaged Navier-Stokesequation which exhibits finite time blowup. Thisdemonstrates a “barrier” to establishing globalregularity for the true Navier-Stokes equations, in

that one cannot hope to prove global regularity byrelying purely on function space estimates on thenonlinearity B, combined with the energy iden-tity.

0.11. Resource Sharing in Stochastic Networks

Ruth Williams (UC San Diego)


Prof Ruth Williams

Stochastic models of processing networks arise ina wide variety of applications in science and en-gineering, e.g., in high-tech manufacturing, trans-portation, telecommunications, computer systems,customer service systems, and biochemical reac-tion networks. Such networks are often hetero-geneous in that different entities share (i.e., com-pete for) common network resources. Frequentlythe processing capacity of resources is limited andthere are bottlenecks, resulting in congestion anddelay due to entities waiting for processing. Thecontrol and analysis of such networks present chal-lenging mathematical problems.

This talk will explore the effects of resource shar-ing in stochastic networks and describe associatedmathematical analysis based on elegant fluid anddiffusion approximations. Illustrative exampleswill be drawn from biology and telecommunica-tions.

0.12. Random Matrices in Quantum Field Theory

Konstantin Zarembo (Nordic Institute for

Theoretical Physics)


Prof Konstantin Zarembo

Random matrices, or Matrix models, make ubiq-uitous appearance in many areas of physics, inparticular in Quantum Field Theory. Exact, non-perturbative results in Quantum Field Theory arevery rare, and one often has to rely on various ap-proximation schemes, such as Feynman perturba-tion theory.

In some cases, however, the problem reduces tocorrelation function of random matrices and canthen be solved exactly without making any ap-proximations. Results of this type have been usedto put conjectured relationship between QuantumFields and String Theory to rigorous tests.

I will review how random matrices arise in Quan-tum Field Theory, going from simple examplesbased on the Gaussian matrix model to more com-plicated, but still solvable matrix models arisingin supersymmetric field theories via localization ofpath integrals.

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0. Plenary

0.13. The life of 1/Pi

Wadim Zudilin (The University of Newcastle)


Prof Wadim Zudilin

The number π = 3.1415926 . . . is recognised asthe bestselling mathematical constant of all thetime. One hundred years ago, well before the eraof the computer, the Indian prodigy Srinivasa Ra-manujan found a remarkable list of formulae for1/π, which can be used to compute the quantityto several thousand places. Today, Ramanujan’sequations are still in use. The last few decadeshave witnessed an exploding development of newmethods and generalisations of these formulae,bringing together topics from analysis, combina-torics, algebraic geometry, differential equationsand number theory. In my talk, I will surf on thewaves of the story of 1/π.

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1.1. Non-embeddings into the Leavitt algebra L2

Nathan Brownlowe (University of Wollongong)

16:10 Tue 29 September 2015 – SSN102

Dr Nathan Brownlowe

Leavitt path algebras are algebraic analogues ofgraph C*-algebras. We will focus on the algebraL2, which is the algebraic analogue of the Cuntzalgebra O2. The C*-algebra O2 has many spe-cial properties; in particular, the tensor productO2 ⊗ O2 is isomorphic to O2. While it is knownthat L2⊗L2 is not isomorphic to L2, it is an openproblem in the subject whether L2 ⊗ L2 embedsinto L2. In this talk we report on some progressmade on this problem. We show that the tensorproduct does not embed when the ring of coef-ficients is the integers. We also make some re-marks about the more general cases of rings andfields as coefficients. This is joint work with AdamSorensen of the University of Oslo.

1.2. Linear sandwich semigroups

James East (University of Western Sydney)

15:45 Wed 30 September 2015 – SSN008

Dr James East (with Prof Igor Dolinka, University of

Novi Sad)

LetMmn denote the set of allm×nmatrices over afield F , and fix some n×m matrix A ∈Mnm. Anassociative operation ? may be defined on Mmn

by X ? Y = XAY for all X,Y ∈ Mmn, andthe resulting “sandwich semigroup” is denotedMAmn. It seems these linear sandwich semigroups

were introduced by Lyapin in his 1960 monograph,and they are related to the so-called generalizedmatrix algebras of Brown (1955), but they havenot received a great deal of attention since someearly papers by Magill and Subbiah in the 60sand 70s. In this talk, I will report on joint workwith Igor Dolinka (Novi Sad) in which we inves-tigate certain combinatorial questions regardingthe linear sandwich semigroups, including: regu-larity, Green’s relations, ideals, rank and idempo-tent rank. We also outline a general frameworkfor studying more general sandwich semigroups:the context is a kind of partial semigroup relatedto Ehresmann-style arrows-only categories.

1.3. Independent generating sets of symmetricgroups

Attila Egri-Nagy (Western Sydney University)


Dr Attila Egri-Nagy

We summarize recent enumeration results of in-dependent generating sets of symmetric groups(n ∈ 1, . . . , 7), and discuss how the analysis of

these low degree cases can get us closer to a fullclassification.

1.4. Using random walks to detect amenability infinitely generated groups

Murray Elder (The University of Newcastle)

16:40 Mon 28 September 2015 – SSN223

Dr Murray Elder, Mr Cameron Rogers

We use random walks to experimentally computethe first few terms of the cogrowth series for afinitely presented group.

We propose candidates for the amenable radi-cal of any non-amenable group, and a Følner se-quence for any amenable group, based on conveg-ence properties of random walks.

1.5. Dynamical methods in additive combinatorics

Alexander Fish (University of Sydney)


Dr Alexander Fish

Ergodic theory can be used in studying variousadditive problems in infinite countable groups.We will concentrate on applications to additivecombinatorics of measure rigidity of algebraic ac-tions on homogeneous spaces, and of Kroneckerfactor of Furstenberg’s system corresponding tothe product-set in an amenable group. Thetalk is based on joint works with M. Bjorklund(Chalmers)

1.6. Asymptotic behaviour of random walks oncertain matrix groups

John Harrison (The University of Newcastle)


Mr John Harrison

Random walks have been used to model stochas-tic processes in many scientific fields. I will in-troduce invariant random walks on groups, wherethe transition probabilities are given by a prob-ability measure. The Poisson boundary will alsobe discussed. It is a space associated with ev-ery group random walk that encapsulates the be-haviour of the walks at infinity and gives a descrip-tion of certain harmonic functions on the groupin terms of the essentially bounded functions onthe boundary. I will then discuss my attemptsto describe the boundary for a certain family ofupper-triangular matrix groups.

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1.7. Ultramatricial algebras, classification viaK-groups

Roozbeh Hazrat (University of Western Sydney)


Dr Roozbeh Hazrat

For the class of ultramatricial algebras (i.e., a di-rect limit of matricial algebras), the theorem ofBrattelli-Elliott shows that the monoid of equiva-lent idempotents is a complete invariant for suchrings. If a ring is equipped with an extra struc-ture, it is natural to expect that this structureshould be reflected in its associated monoid. Weinvestigate this idea, when the ring has involutionand/or graded.

1.8. Coboundary and graph codes and theirinvariants

Kathy Horadam (Royal Melbourne Institute of

Technology)


Prof Kathy Horadam

Functions f : mathbbZmp → mathbbZmp are im-portant for many applications in cryptographyand coding.

We investigate two new codes derived from suchf , the graph code and the coboundary code. Inparticular we prove the dimension of the kernel ofeach code determines a new invariant of the CCZequivalence class and of the EA equivalence classof f , respectively.

We present computational results for p = 2 andsmall m, and some open questions.

This is joint work with Merc‘e Villanueva, Univer-sitat Aut‘onoma de Barcelona, Spain

1.9. From A to B to Z

Marcel Jackson (La Trobe University)


Dr Marcel Jackson

The infinite Zimin word Z∞ is the limit of thesequence Z0 := x0, Zn+1 := Znxn+1Zn; it is thecritical pattern for recording unavoidability of fi-nite patterns. Any word w gives rise to a monoidM(w) whose elements are 0 along with all possi-bly empty subwords of w, with concatenation asthe operation. The monoid M(Z∞) is infinite, butplays a critical role in the equational theory of fi-nite semigroups. The 6-element monoids A1

2 andB1

2 play similarly pivotal roles.

The variety (that is, equational class) generatedby of A1

2 contains that of B12, which in turn con-

tains that of M(Z∞). Edmond Lee has askedwhether the variety defined by B1

2 is definablewithin the variety of A1

2 by the addition of thesingle law xxyy = yyxx, and whether the varietydefined by M(Z∞) is definable within the varietyof B1

2 by the single law xxy = yxx. We show

these are false, and moreover that there is a con-tinuum of distinct counterexamples in both cases.The proof employs a hypergraph-theoretic resultdue to Erdos and Hajnal.

1.10. On the 2-linearity of the free group

Anthony Licata (Australian National University)


Dr Anthony Licata

The free group Fn arises in Coxeter theory as theuniversal Coxeter group. This perspective leadsto a categorical action of the Free group on thederived category of modules over an explicit finite-dimensional algebraBn. We prove that this actionis faithful, and relate gradings on the algebra Bnto metrics on Fn and to the dual positive braidmonoid of Bessis.

1.11. On substructures which can be carried byhomomorphic images

Robert McDougall (University of the Sunshine

Coast)


Dr Robert McDougall

The genesis of radical theory for associative ringswas to describe a process for using ideals to re-move a particular property from a ring through ahomomorphic mapping to a ring where the idealcontaining this property was now zero. Since thenthe places where radicals have meaning and themeaning of radicals has evolved and in this presen-tation we discuss the notion of robust to describerings which can be carried by all of the homo-morphic images of a ring. Easy examples includesimple rings which are robust as subrings and ac-cessible subrings, while the integers are robust asa subring but not as an accessible subring.

1.12. Essentially chief series of locally compactgroups

Colin David Reid (The University of Newcastle)


Colin Reid and Phillip Wesolek

The theory of locally compact groups includesas special cases compact groups, which are rela-tively well-understood, and discrete groups, wheretopology plays no role in the structure. In un-derstanding the structure of a locally compactgroup, it is useful to be able to decompose thegroup into finitely many factors that are eithercompact, discrete, or ’irreducible’ in some sense.Such a decomposition has long been known forLie groups. For general locally compact groups,complications arise due to the totally disconnectedcase, and to obtain any finiteness results it is nec-essary to specialise to the compactly generatedcase. Even in this case, the normal subgroup

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structure of such groups was not well-understooduntil recently. The first significant progress wasmade in a 2011 paper of P-E. Caprace and N.Monod, which gave some sufficient conditions forthe existence of minimal and maximal closed nor-mal subgroups.

We build on ideas of Caprace–Monod to prove thefollowing: Any compactly generated locally com-pact group has a finite normal series in which thefactors are compact, discrete or chief (a chief fac-tor of G being a closed normal factor K/L suchthat no closed normal subgroup of G lies strictlybetween K and L). Moreover, the ’large’ chieffactors in such a series are unique up to a suitablenotion of equivalence, and the decomposition iswell-behaved with respect to P. Wesolek’s theoryof elementary groups (which is an alternative ap-proach to building locally compact groups out ofcompact and discrete pieces).

1.13. Janko’s sporadic simple groups

Don Taylor (University of Sydney)


Don Taylor and Terry Gagen

Fifty years ago, to quote George Szekeres, “Aus-tralian mathematics produced something whichsurprised the whole world”: Zvonimir Janko,working at the ANU, discovered and constructeda new simple group which was neither an alternat-ing group nor a group of Lie type. A decade laterthe number of new sporadic simple groups hadrisen to 21 and Janko had found four of them, in-cluding the first and the last. This talk recountssome of the history of those exciting times.

1.14. Reflection length in affine Coxeter groups

Anne Thomas (University of Sydney)


Dr Elizabeth Milicevic, Dr Petra Schwer and Dr

Anne Thomas

Let W be an affine Coxeter group, meaning thatW is a discrete group of isometries of Euclideanspace generated by the finite set S of reflections inthe faces of a compact Euclidean polytope. Thereflections in W are defined to be the set R ofall W-conjugates of elements of S. The reflectionsform an infinite generating set for W, and theword length with respect to R is called reflec-tion length. We obtain new bounds on reflectionlength for all elements of W, and the precise re-flection length for certain elements. This is anapplication of new techniques we have developedfor studying affine Deligne-Lusztig varieties; noknowledge of these varieties will be assumed inthis talk.

1.15. On base radical and semisimple classes forassociative rings

Lauren Thornton (University of the Sunshine

Coast)


Miss Lauren Thornton

A recent publication by McConnell, McDougalland Stokes extended the known properties of baseradical and semisimple classes in a quite generalsetting framed by Puczylowski. In this presenta-tion, we use the universal class of associative ringsto revisit the work to determine which of the re-sults hold in this more restricted setting and ex-tend the investigation of the semigroup of classoperators described there with further examples.

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2.1. A tale of two polynomials

Jarod Alper (Australian National University)


Dr Jarod Alper

We will begin by studying the history and signifi-cance of the determinant versus permanent ques-tion: for a given integer n, what is the smallest in-teger m such that the permanent of an arbitraryn × n matrix can be computed by the determi-nant of an m×m matrix, where each entry is anaffine linear combination of the original entries?We will provide a historical summary of the mainresults and techniques relating to this question.The main goal is to then prove that when n = 3,the smallest integer is m = 7. This is joint workwith Mauricio Velasco and Tristram Bogart.

2.2. Diagram automorphisms revisited

Anthony Henderson (University of Sydney)


Dr Anthony Henderson

The automorphisms of the finite and affine Dynkindiagrams of types A, D and E lie behind manyphenomena in Lie theory. Any structure (root sys-tem, Lie algebra, quiver variety, etc.) that can bedefined purely in terms of the Dynkin diagramwill automatically inherit these ”diagram auto-morphisms”. In previous papers with PramodAchar (”Geometric Satake, Springer correspon-dence, and small representations”) and AnthonyLicata (”Diagram automorphisms of quiver vari-eties”), I studied special situations where such di-agram automorphisms had surprisingly nice for-mulas. In this talk I will attempt to make theseresults less surprising by adopting a new view-point, inspired by gauge theory and the work ofNakajima.

2.3. Principal subspaces and vertex operators for

quantum affine algebra Uq(sln+1)

Slaven Kozic (University of Sydney)


Dr Slaven Kozic

In this talk, we consider principal subspaces of

the integrable highest weight Uq(sln+1)-modules.We construct combinatorial bases of the principalsubspaces, consisting of quasi-particle monomialsacting on the highest weight vector, and discuss,for n = 1, related constructions in terms of vertexoperator monomials.

2.4. Positivity in T-equivariant K-theory of flagvarieties associated to Kac-Moody groups

Shrawan Kumar (University of South Carolina)


Prof Shrawan Kumar

Let X=G/B be the full flag variety associated toa symmetrizable Kac-Moody group G. Let T bethe maximal torus of G. The T-equivariant K-theory of X has a certain natural basis definedas the dual of the structure sheaves of the op-posite finite codimension Schubert varieties. Weshow that under this basis, the structure con-stants are polynomials with nonnegative coeffi-cients. This result in the finite case was obtainedby Anderson-Griffeth-Miller (following a conjec-ture by Graham-Kumar).

2.5. Geometric representation theory andcategorification for braid groups of type ADE

Anthony Licata (Australian National University)


Dr Anthony Licata

The braid groups of type ADE have two ”Garsidestructures” on them. Each of these Garside struc-tures determines a positive submonoid of the braidgroup, and a metric on the braid group. The goalof this talk will be to explain how both of theseGarside structures. submonioids, and metrics ap-pear naturally when one considers actions of thebraid group on the derived category of modulesover the zigzag algebra of the associated quiver.(This is joint work with Hoel Queffelec.)

2.6. A quantum exceptional series

Scott Morrison (Australian National University)


Dr Scott Morrison

Deligne has proposed a one-parameter family oftensor categories, which at special points recoversthe representation categories of the exceptionalsimple Lie algebras. It’s still unknown if thesecategories are well defined at other points, how-ever. In joint work with Noah Snyder and DylanThurston, I’ve recently been studying a potentialtwo-parameter family of tensor categories, recov-ering the quantum representation categories of theexceptional Lie algebras along certain curves. Westill can’t resolve the central problem: are thesecategories well-defined. Nevertheless there’s someinteresting new evidence, including candidate two-variable knot invariants.

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2.7. A variant of Harish-Chandra functors

Uri Onn (Australian National University)


Assoc Prof Uri Onn

A prominent role in the representation theory ofreductive groups over finite fields is played by theHarish-Chandra functors, or parabolic inductionand restriction functors, which are used to passbetween the representations of a group and thoseof its Levi subgroups. In this talk I will describe ageneralisation of these functors that is more suit-able for reductive groups over compact discretevaluation rings. This is a joint work with TyroneCrisp and Ehud Meir.

2.8. The Frobenius Operator and Descending toConstants

Arnab Saha (Australian National University)


Dr Arnab Saha

We show that if a formal scheme over functionfields of positive characteristic admits a lift ofFrobenius on its structure sheaf, then it descendsto the ring of constants of the Frobenius operator.This is in parallel to what happens in the case ofdifferential algebra as we view the Frobenius op-erator as an analogue for the derivative operator.We also prove a related result in the mixed char-acteristic case.

2.9. An equivariant motivic cohomology

Mircea Voineagu (University of New South Wales)


Dr Mircea Voineagu

The groundbreaking conjecture of Beilinson andLichtenbaum connecting motivic cohomology withfinite coefficients and etale cohomology with finitecoefficients was recently proved by Voevodsky andRost. We construct an equivariant motivic coho-mology and prove that, with finite coefficients andapplied to a complex variety with Z/2-action, it isidentified in a range of indexes with Bredon coho-mology of the equivariant space of complex pointsof the complex variety. This is a joint work withJ.Heller and P.A.Ostvaer.

2.10. Base change and K-theory

Hang Wang (The University of Adelaide)


Dr Hang Wang

Tempered representations of an algebraic groupcan be classified by the K-theory of the corre-sponding group C∗-algebra. We use Archimedeanbase change between Langlands parameters ofreal and complex algebraic groups to compare K-theory of the corresponding C∗-algebras of groups

over different number fields. This is work inprogress with K.F. Chao.

2.11. Schubert Calculus and Finite Geometry

Jon Xu (The University of Melbourne)


Mr Jon Xu

Ovoids in projective space were first defined byJacques Tits in 1962 after the realisation thatthe Suzuki groups have a natural action on setsof points which share many geometric propertieswith elliptic quadrics. In 1972, Jef Thas gave adefinition of ovoids for polar spaces. The study ofovoids is an active field of research in finite geom-etry, and there are many open problems.

Schubert calculus involves translating geometricproperties to a Schubert variety and studying itscohomology. Schubert varieties are one of themost well-studied complex projective varieties inthe literature.

It is known that some non-degenerate hyperplanesections of Schubert varieties are ovoids. There-fore, it is natural to ask: what are the necessaryand sufficient conditions for hyperplane sections ofSchubert varieties to be ovoids? I will talk aboutthe current progress on this problem.

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3.1. Modelling the Dynamics of Vernalization inPlants

Robert Scott Anderssen (CSIRO)


Dr Robert Scott Anderssen

For a plant to flower, its development must switchfrom the vegetative to the flowering state in orderto make the seeds for the next generation. For ce-reals and the model plant Arabidopsis, the switch-ing occurs in response to a cold event, signalling tothe plant that it is winter with spring and summersoon to follow. Much is understood about the na-ture of this switching process genetically in termsof how the expression of the FLC gene, orchestrat-ing the vegetative development, is repressed. Onlyrecently has a mechanism been proposed that ex-plains how the cold initiates the repression processthat switches off the expression of FLC. This talkwill explain how the mathematics of rubber elas-ticity has been the conceptualization step to theformulation of a model for the initiation of therepression.

3.2. Mathematical techniques to aid the AustralianArmy in selecting new defence vehicles

Elizabeth Bradford (University of South Australia)


Amie R. Albrecht, Erika Belchamber, Elizabeth

Bradford, Ajini Galapitage, Stephanie Mills, Trang

Thi Thien Nguyen, Andrew Sargent, Kathryn Ward,

Lesley A. Ward and Peter Williams

When the Australian Army requires new landcombat vehicles to replace their old fleet, it isnot simply a matter of swapping each old ve-hicle with a new one. Many competing factorsplay a role in determining which and how manyvehicles to purchase. In this talk we describeresearch undertaken by the University of SouthAustralia (UniSA) Mathematics Clinic team forproject sponsor the Defence Science and Technol-ogy Organisation (DSTO). The outcomes of ourresearch form part of the Australian Armys Land400 projectthe largest Army project ever.

In this talk we examine two situations requiringvehicles. In each situation we determine both theoptimal number of vehicles and how best to usethem. These two situations are the Cavalry Screenvignette and the Area Search vignette.

In the Cavalry Screen vignette, an object (forexample a battalion or a building) is screenedby a number of vehicles. The vehicles in thescreen provide surveillance and gather informa-tion on any approaching enemy troops that may

pass through the screen, while remaining unde-tected themselves. Our aim was to determineboth the optimal number and placement of ve-hicles within the screen. We used simulation toinvestigate different arrangements of the screen-ing vehicles. To determine the optimal arrange-ment, we used a probabilistic search techniquecalled Cross-Entropy Optimisation.

In the Area Search vignette, vehicles are taskedwith finding a specific target in an area in theshortest possible time. We used Markov Chainsto simulate different search patterns and variedthe number of vehicles and size of the area. Wealso considered the effects of the targets initial po-sition, the vehicles initial positions, and whetherthe target is moving or stationary. We analysedthe trade-off between the number of vehicles de-ployed in the search and the time taken to findthe target.

Our findings, recommendations and prototypesoftware will be used by DSTO in formulatingtheir technical advice to Army about the numbersand types of new vehicles to purchase.

The Mathematics Clinic is a year-long team-basedsponsored research project undertaken by final-year mathematics undergraduates at the Univer-sity of South Australia. The Mathematics Clinicoffers a rigorous research experience in tacklingreal-world mathematics problems sourced from in-dustry and with support from academic advisors.

3.3. RootAnalyzer: a cross-section image analysistool for automated characterization of root cellsand tissues

Joshua Chopin (University of South Australia)


Mr Joshua Chopin

The morphology of plant root anatomical featuresis a key factor in effective water and nutrient up-take. Existing techniques for phenotyping rootanatomical traits are often based on manual orsemi-automatic segmentation and annotation ofmicroscopic images of root cross sections. In thisarticle, we propose a fully automated tool, re-ferred to as RootAnalyzer, for efficiently extract-ing and analyzing anatomical traits from root-cross section images. Using a range of mathe-matical and image processing techniques such aslocal thresholding and nearest neighbor identifica-tion, RootAnalyzer segments the plant root fromthe image’s background, classifies and character-izes the different tissue regions and subsequentlyproduces statistics about the morphological prop-erties of the root cells and tissues. We use Root-Analyzer to analyze 15 images of wheat plants

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and evaluate its performance against manually-obtained ground truth data. The comparisonshows that RootAnalyzer can fully characterizemost root tissue regions with over 90

3.4. Complex spatial self-organisation in anextended Daisyworld model

Simon Clarke (Monash University)


Benjamin Price, Simon Clarke

We consider a two-dimensional variant of the orig-inal non-spatial Daisyworld model, developed byWatson and Lovelock. We examine how the envi-ronmental regulation which emerges in the orig-inal Daisyworld model translates in a spatiallytwo-dimensional context. To achieve this, we in-troduce the capacity for migration of the system’sbiota via diffusion, and diffusion of the tempera-ture, to the original equations. It is demonstratedmathematically two distinct modes of spatial equi-librium, consistent with the preservation of spa-tially averaged optimal environmental regulation,are possible under this scenario. Firstly, the Tur-ing mode of diffusion-driven instability, resultingfrom the combined diffusive motions over spaceof the system’s biota and temperature, drives theformation of static spatial patterns, in the formof spots and stripes, over the Daisyworld sur-face. Secondly, we identify a spatiotemporal Hopfmode, arising from a Hopf bifurcation in the non-spatial dynamics, and show, via canonical reduc-tion to the complex Ginzburg-Landau equation,the existence of travelling plane and rotating spi-ral wave solutions. Finally, this new behaviour isexamined on a one-dimensional spherical domain,in order to compare the current results with pre-viously published.

3.5. Comparing Nernst-Plank and Maxwell-Stefanapproaches for modelling electrolyte solutions

Troy Farrell (Queensland University of Technology)

13:20 Tue 29 September 2015 – NTH1

Assoc Prof Troy Farrell

The applicability of the Nernst-Planck equationsfor modelling charge transport in electrolyte solu-tions is widely recognised. Although derived frominfinitely dilute solution assumptions, they havebeen successfully used to model a range of elec-trochemical problems. An alternative approach isthe use of Maxwell-Stefan equations. By includ-ing the effect of interactions between each species,the Maxwell-Stefan equations attempt to accountfor the multicomponent nature of electrolyte so-lutions.

The main disadvantage in using the Maxwell-Stefan equations is the characterisation of the re-quired transport parameters. These are difficultto obtain experimentally, and to this end we have

explored the use of molecular dynamics simula-tions in an attempt to calculate these parametersin a ternary electrolyte. The simulated trans-port parameters have then been included in ourMaxwell-Stefan charge transport model.

In this work we present a comparison between theNernst-Planck and Maxwell-Stefan equations, formodelling charge transport in the Li+/I−/I−3 /ACNelectrolyte originally used in dye-sensitised solarcells.

3.6. Mathematically modelling the salt stressresponse of individual plant cells

Kylie Foster (University of South Australia)


Mrs Kylie Foster

High salinity affects one-fifth of the world’s ir-rigated land and two-thirds of Australian cerealcrops. Modelling the uptake of water and ionsby plants will improve our understanding of thebiophysical mechanisms responsible for a plant’ssalinity tolerance. Important salinity tolerancemechanisms occur at the cell level. In partic-ular, plant cells maintain a low level of salt inthe cytoplasm (the living material in the cell) byactively transporting salt into storage compart-ments within the cell (the vacuoles) and out of thecell into the external medium (the apoplast). Inthis presentation I will outline a model of ion andwater transport across the membranes of a sin-gle, isolated plant cell, and demonstrate how thismodel can be used to increase our understandingof how plant cells respond to salt stress. I willpresent some results from this model, includingcomparisons of the model simulations with exper-imentally observed cell behaviour.

3.7. Particle transport in asymmetric periodiccapillaries

Bronwyn Hajek (University of South Australia)


Dr Bronwyn Hajek, Mr Nazmul Islam, Prof Stan

Milkavcic, Prof Lee White

There has been renewed interest in the flow struc-ture within tubes of periodically varying cross-section with the recognition that they can be usedas particle separation devices. We use the bound-ary element method to solve for the flow in anasymmetric periodic tube in the absence of parti-cles, and determine the influence of the capillaryshape and geometry on the flow structure. Infor-mation about the flow is then used in a diffusion-convection model which solves for the behaviourof the particles within the tube. When an oscilla-tory pressure difference is applied to the ends ofan asymmetric periodic tube, for some tube ge-ometries there is found to be a net transport ofparticles, whilst is there is no net fluid flow.

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3.8. Neighbourhood distinctiveness in complexnetworks: an initial study

Kathy Horadam (Royal Melbourne Institute of

Technology)


Prof Kathy Horadam

We investigate the potential for using neigh-bourhood attributes to match unidentified nodesacross complex networks, and to classify themwithin such networks. The motivation is to iden-tify individuals across the dark social networksthat underlie communications networks.

We test an Enron email database and show theout-neighbourhoods of email addresses are highlydistinctive. Then, using citation databases asproxies, we show that a paper in CiteSeer whichis also in DBLP, is highly likely to be matchedsuccessfully, based on its in-neighbours alone. Apaper in SPIRES can be classified with 80% ac-curacy, based on classification ratios in its in-neighbourhood alone.

This is joint work with Adrian Hecker and Jaco-bien Carstens.

3.9. The Key Principles of Optimal Train Control

Phil Howlett (University of South Australia)


Prof Phil Howlett, Dr Amie Albrecht, Dr Peter

Pudney

The key principles of optimal train control havebeen developed over the past 30 years. In thistalk I will concentrate on some of the importantideas that relate the mathematical model to thereal physical world. I explain why a train with dis-tributed mass can be treated as a point mass train;describe the five optimal control modes; show thatthe structure of an optimal journey is like a con-certina with two ends of essentially fixed lengthand a middle of arbitrary length; discuss the localenergy minimization principle that allows glob-ally optimal switching points to be found by solv-ing a local optimization problem; outline the wayin which perturbation analysis has been used toprove uniqueness of an optimal strategy; present asurprising new result about cost-time curves andtalk about a difficult and largely unsolved problemof train separation.

3.10. Mesoscopic Models to Bingham Fluids:Mixed Convection Flow in a Cavity

Raja Ramesh Huilgol (Flinders University)


Prof Raja R. Huilgol and Gholamreza H. R. Kefayati

The equations of evolution for the particle distri-bution functions in a D2Q9 lattice are shown to

lead to the equations of motion for an incompress-ible fluid. Using the lattice model, the mixed con-vection flow of a Bingham fluid in a square cavityis examined when the upper plate is given a con-stant velocity, and the two vertical walls are set attwo different temperatures. The resulting stream-lines along with the yielded/unyielded zones in thefluid are exhibited for a wide range of Bingham,Prandtl and Reynolds numbers.

3.11. Mathematical models for competitive ionabsorption in a polymer matrix

Stanley Joseph Miklavcic (University of South

Australia)


Prof Stanley Joseph Miklavcic

Materials with extreme efficiency and selectivityfor adsorbing specific ions open up possibilitiesfor large scale liquid purification technologies andfor new materials for the prevention of biologi-cal growth. On the molecular scale, the mate-rial’s efficiency and selectivity depends on com-petitive metal ion diffusion into a nanometer thinpolymer film and on competitive binding of metalions to specific ligand sites. We present and ex-plore two reaction-diffusion models describing thedetailed transport and competitive absorption ofmetal ions in the polymer matrix. The diffusivetransport of the ions into an interactive, porouspolymer layer of finite thickness, supported by animpermeable substrate and in contact with an infi-nite electrolyte reservoir, is governed by forced dif-fusion equations, while metal ion binding is mod-elled by a set of coupled reaction equations. Thebehaviour observed in actual experiments can bereproduced and explained in terms of a combina-tion of (a) differing ion diffusive rates and, effec-tively, (b) an ion exchange process that is super-imposed on independent binding processes. Thelatter’s origin is due to conformational changestaking place in the polymer structure in responseto the binding of one of the species. In the talkwe present results of simulations under differentconditions. These are discussed in relation to ex-perimental observations.

3.12. Taylor Series and Water Hammer

Tony Miller (Flinders University)


Dr Tony Miller

At the recent Mathematics in Industry StudyGroup (MISG 2015) one of the industry problemsrelated to simple methods of analysis that couldbe applied at the preliminary scoping stage of thedesign of surge protection systems for long dis-tance water supply pipelines. In particular, oneaim was to clarify the role and applicability of theclassical Joukowsky result for the pressure surge

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arising from an instantaneous stoppage of flow.Although a numerical method of characteristicssolution of the water hammer equations is rela-tively straightforward, what is ideally required atthe scoping and costing phase of a design projectis a semi-analytical approach that clearly presentsthe dependence and sensitivity of the water ham-mer response to the various design and physicalparameters, some of which will only be known ap-proximately. To this end, an analytical solutionwas obtained. In the course of doing this, theauthor gained a new appreciation of some of theclassical theory of Taylor series. This will be de-scribed in this talk.

3.13. Application of Lie symmetry techniques toreaction-diffusion equations.

Joel Moitsheki (University of the Witwatersrand)


Joel Moitsheki*, Bronwyn Bradshaw-Hajek, Kirsten

Louw and Marcio Lorenco

We consider reaction-diffusion equations arising inpopulation dynamics and heat transfer problems.We apply both the classical and non-classical sym-metry methods to analyse these problems. Itturns out that some equations representing thesteady state admits eight classical Lie point sym-metries; such equations are linearisable and ex-actly solvable. On the other hand, the unsteadystate models with spatial dependent diffusivity ad-mit the genuine non-classical symmetries. We in-troduce the modified Hopf-Cole transformation tosimplify some reduced equation. Group-invariantsolutions are constructed.

3.14. The algebraic properties of thenonautonomous one- and two-factor problems ofcommodities

Richard Michael Morris (Durban University of

Technology)


A Paliathanasis, RM Morris and PGL Leach

Over the years there has been less emphasis put onthe application of symmetry analysis in the areaof Financial Mathematics. ES Schwartz [1] pro-posed three models in the late 90s which study thestochastic behaviour of the prices of commoditiesthat take into account several aspects of possibleinfluences on the prices. Sophocleous, Leach andAndriopoulos illustrated an analysis of the sym-metry and algebraic properties for the one-, two-and three-factor models, where the parameterswere assumed to be constant [2]. However, in real-life problems they may vary with time if the time-span of the model is taken to be sufficiently long.We perform symmetry analysis and study the al-gebraic structures of the nonautonomous one- andtwo-factor models, where the coefficients are taken

to be time-dependent. We compare the results tothe autonomous cases.

References

[1] ES Schwartz, The stochastic behaviour of com-modity prices: implications for valuation andhedging, The Journal of Finance, Volume 52, Pagenumbers 923-973, (1997)

[2] C Sophocleuous, PGL Leach and K Andriopou-los, Algebraic properties of evolution partial dif-ferential equations modelling prices of commodi-ties, Mathematical Methods in the Applied Sci-ences, Volume 31, Page numbers 679-694, (2008)

3.15. Use of a stochastic model to study the cyclicmotion in nanowires trapped by focused Gaussianbeams

Ignacio Ortega Piwonka (University of New South

Wales)


Mr Ignacio Ortega Piwonka

A simple two-dimensional, stochastic model isproposed to study the dynamics of high aspectratio nanowires axially trapped in linearly polar-ized, Gaussian optical beams. A parameter reduc-tion is rendered in order to simplify this study andprovide a full description of the system responsein terms of the probability distribution, the powerspectral density and its critical frequencies; also asto characterize the persistent bias to cyclic motionaround the equilibrium trapping position, whichhas direct relation with the non-conservative na-ture of the optical force.

This model is in good agreement with simula-tions of nanowires modeled as arrays of particles,and it is in partially good agreement with resultsfrom experiments conducted with indium phos-phide nanowires: While the former can be mod-eled by means of a set of two-dimensional uncou-pled systems, the latter requires coupling terms tobe added in the equations.

3.16. Dying in order: how crowding affects particlelifetimes

Catherine Penington (Queensland University of

Technology)


Dr Catherine Penington, Prof Matthew Simpson

Suppose we have several agents on a line. Theymove around randomly, but once they reach anend they disappear permanently. How long willthey survive? Without crowding effects, particlesnear the edges tend to leave sooner than those atthe centre, but there is a lot of variation. Whencrowding is included, and agents cannot occupythe same position at the same time, both the meantime to disappear and its variance changes dra-matically. In this presentation, we use simulation

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and analysis to discuss the effects of crowding onagent lifetimes.

3.17. Mathematics in the drawing ofmicrostructured optical fibres.

Yvonne Stokes (The University of Adelaide)


Dr Yvonne Stokes

A microstructured optical fibre (MOF) has a pat-tern of air channels aligned with the fibre axis thatmodify the refractive index of the fibre material toform a waveguide for transmission of light alongthe core. In principle any pattern of air channelsis possible so that MOFs promise to revolutionizeoptical fibre technology. In practice fabrication ofa MOF of a desired geometry, by drawing a macro-scopic preform having the desired geometry at alarge scale, down to a long slender fibre, is diffi-cult due to deformation of the air channels in thedrawing process. Mathematics is needed to solvethe inverse problem of determining the preformgeometry and draw parameters that will yield adesired fibre.

Perturbation methods exploiting the slendernessof the fibre, to obtain a 1D axial stretching modelcoupled with a 2D model of the surface-tension-driven flow in the cross section, have been usedto model fibre drawing for some years. But theneed to handle the inverse problem for a wideclass of complex geometries in an efficient man-ner has led to a novel formulation of the problemand other mathematical developments. In turn,the mathematical model has given valuable newinsight into the drawing of optical fibres. In thistalk I will review the interaction between the ap-plication and the mathematics and the knowledgethis has yielded.

3.18. Why should boundary element methods haveto deal with singularities?

Qiang Sun (The University of Melbourne)


Dr Qiang Sun

The boundary integral method (BIM) is an ef-ficient approach for solving elliptic differentialequations that arise in many physical problems.By using the fundamental solution and the Gaussdivergence theorem, the domain differential equa-tions are converted into integral equations on theboundaries. The advantage of the BIM is that thenumber of dimensions of the problems is reducedby one and N logN methods have been developedto deal with the full matrices that arise from thediscretization of the integral equations. However,

a well-known drawback of the traditional formu-lation of the BIM is that singularities in the inte-grands arise from the fundamental solution. Al-though such singularities are integrable, in prac-tice, the complexity of dealing with such singulari-ties in numerical implementation means that onlysimple surface elements such as planar elementsare used together with the assumption that theunknown function is a constant within such simplesurface elements. This places a limit on the nu-merical precision that can be achieved. Further-more, large numerical errors seem unavoidable incases where parts of the boundary of the bound-ary are nearly in contact such as in multi-scaleproblems.

Here we address the question of whether singularintegrands must be a mathematical consequenceof the formulation of the boundary integral equa-tion when the physical problem itself being mod-elled is generally well-behaved on the boundaries?

In this paper, an analytical formulation of theboundary integral equation is developed wherebyall the singularities in the integrands of the tradi-tional BIM for solving the Helmholtz type equa-tion ∇2φ + k2φ = 0 are completely eliminatedby subtracting the solution of a related prob-lem. With this boundary regularised integralequation formulation (BRIEF) [1], numerically ro-bust quadrature methods can use to evaluate thenon-singular surface integrals that result in con-siderable savings in coding efforts. Furthermore,higher order surface elements and shape functionscan be readily applied, which results in a signifi-cant reduction in problem size with improved ac-curacy. Also, multi-scale problems with extremegeometric aspect ratio can be handled without los-ing precision.

More generally, the results for the Helmholtzequation also apply to the Laplace equation (k =0) [2] and the Debye-Huckel model (k is imagi-nary) and a similar desingularisation formulationcan be developed for the equations of Stokes flow[3, 4] and linear elasticity [5].

[1] Q. Sun, E. Klaseboer, B. C. Khoo and D. Y.C. Chan, Boundary regularised integral equationformulation of the Helmholtz equation in acous-tics, Roy. Soc. Open Sci. 2 pp. 140520-140529(2015).

[2] Q. Sun, E. Klaseboer, B. C. Khoo and D. Y.C. Chan, A robust and non-singular formulationof the boundary integral method for the potentialproblem, Engin. Anal. Bound. Elements 43 pp.117-123 (2014).

[3] Q. Sun, E. Klaseboer, B. C. Khoo and D. Y.C. Chan, Boundary regularized integral equationformulation of Stokes flow, Phys. Fluids 27 pp.23102:1-19 (2015).

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[4] Q. Sun, E. Klaseboer, B. C. Khoo and D. Y.C. Chan, Stokesian dynamics of pill-shaped Janusparticles with stick and slip boundary conditions,Phys. Rev. E. 87 pp. 043009: 1-5 (2013).

[5] E. Klaseboer, Q. Sun and D. Y. C. Chan, Non-singular boundary integral methods for fluid me-chanics applications, J. Fluid Mech. 696 pp. 468-478 (2012).

3.19. The use of the Fast Fourier Transform in theanalysis of the fine substructure of 3-dimensionalspatio-temporal human movement data

Alise Thomas (University of the Sunshine Coast)


Miss Alise Thomas

The contemporary approach to the analysis ofrepetitive, biomechanical, time-series data pro-vides limited quantitative detail on the fine sub-structure of human motion. Information on thissubstructure would allow biomechanists to iden-tify patterns or inconsistencies in this type of mo-tion, so that it can be improved, injury avoided, orfor the development of motion-assisting devices.

While many previous studies focused on the useof general descriptive statistics to quantify thismovement, the periodic waveform nature of suchdata lends itself to analysis by the fast Fouriertransform (FFT), to identify the sinusoidal sub-components from which each waveform is com-posed. While the FFT has been applied to biome-chanical data prior to this study, it has not beenused to compare spatially (across body) and tem-porally separated movement data. In order to fillthis gap, a MATLAB program (KAFT) has beenwritten that performs the FFT on raw biomechan-ical time-series data.

KAFT enables biomechanists to explore the mo-tion of subjects in fine detail, by identifying peri-odic motion subcomponents with magnitudes assmall as 1 mm. The program also quantifiesmovement variability by identifying the substruc-ture of the motion that is not periodic. The effi-cacy of KAFT was assessed using kinematic datafrom a cyclist comparing KAFTs numerical out-put against an independent, contemporary analy-sis. It was concluded that application of the fastFourier transform to this type of data can pro-vide additional detail on its substructure, and thatKAFT shows promise to be a powerful tool for thequantification of periodic biomechanical data.

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4. Combinatorics

4.1. Hamiltonicity-preserving graph reductions

Kieran Clancy (Flinders University)

16:15 Mon 28 September 2015 – HUM115

Mr Kieran Clancy

The famous Hamiltonian cycle problem (HCP) todetermine whether a graph possesses a simple cy-cle that passes through all vertices is known to beNP-complete even for the relatively simple class ofcubic graphs. A graph is said to be Hamiltonianif it contains a Hamiltonian cycle. In this pre-sentation, we will consider a collection of efficientand practical Hamiltonicity-preserving graph re-ductions. The motivation is that a graph whoseHamiltonicity is difficult to determine may permita reduction to a smaller graph whose Hamiltonic-ity can then be determined more easily. Thesereductions are primarily based on the symmetriesin the underlying graph structure. It is shown thatcertain non-Hamiltonian graphs that were partic-ularly hard to identify by some of the previouslypublished approaches lend themselves to these re-duction methods.

4.2. Signed designs

Diana Combe (University of New South Wales)


Dr Diana Combe

The blocks of a balanced block design can besigned over a group G by signing each of the el-ements of the block by an element of G. Subjectto satisfying suitable balancing conditions with re-gard to G, the design is a generalized Bhaskar Raoblock design and the corresponding group signedincidence matrices are generalised Bhaskar Raodesigns. Constructing such designs, and provingresults about their existence for certain sets of pa-rameters and large families of groups involves ex-ploring the relationship between group structureand the balancing conditions of balanced blockdesigns.

In this talk we present results and constructionsfor generalised Bhaskar Rao designs which haveunderlying block designs which are triples - thatis, have block size 3.

This is joint work with Julian Abel (UNSW) ,Adrian Nelson and William Palmer (USyD).

4.3. On choosability of graphs with limited numberof colours.

Marc Demange (RMIT University)

15:50 Mon 28 September 2015 – HUM115Marc Demange, RMIT University, Melbourne, Vic.,Australia ([email protected])

Dominique de Werra, EPFL, Lausanne, Switzerland

([email protected])

Graph colouring is among the most studied prob-lems in graph optimisation. Given a non-directedsimple graph and an integer k, a k-colouring isa function assigning to every vertex a colour in1, . . . , k such that adjacent vertices are not ofthe same colour. In the list-colouring problem, ev-ery vertex of the instance graph is assigned a listof available colours and the question is whether itis possible to find a k-colouring satisfying all listconstraints. Finally, given a graph and a functionf assigning to every vertex a list size, the graph iscalled f -choosable if a list colouring exists for anysystem of f -lists. This notion has been extensivelystudied during the last years.

In this talk, I will discuss the concept of choosabil-ity with a particular focus on the case where onlya limited number of colours may be used in total.I will discuss some complexity results in restric-tive classes of planar graphs with 3, 4 or 5 avail-able colours. I will also discuss how choosabilitymay be affected in a given graph if the number ofcolours is increased by one.

4.4. On the number of palindromically rich words

Amy Glen (Murdoch University)


Dr Amy Glen

Rich words (also known as full words) are a specialfamily of finite and infinite words characterised bycontaining the maximal number of distinct palin-dromes. We prove that the number of rich wordsof length n over a finite alphabet A (consisting of3 or more letters) grows at least polynomially withthe size of A. We also show asymptotic exponen-tial growth for the number of rich words of length2n over a 2-letter alphabet. Moreover, we discusspossible factor complexity functions of rich wordsand consider the difficult (open) problem of enu-merating the finite rich words over a fixed finitealphabet.

4.5. Evaluating modular invariants

David G Glynn (Flinders University)


Dr David G Glynn

In 1894, A.B. Kempe (of 4-colour theorem andlinkages fame) showed how to express any prod-uct of n differences of roots of polynomials of de-gree 2n as sums of products of ”disjoint” differ-ences, where ”disjoint” is based on having n non-intersecting chords of a circle having 2n points on

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4. Combinatorics

it. He used some fundamental Grassmann iden-tities of small products of determinants. This isactually important in the invariant theory of poly-nomials. For the ”modular” theory i.e. modulo aprime p, for q = ph, a corresponding (Glynn) in-variant isXq of any 2 by 2(q−1) matrix over a fieldof characteristic p. What we can do is use eitherKempe’s idea, or another idea with completely ho-mogeneous sets of permutations, to evaluate Xq

in an optimal way, using a minimal number ofterms. This leads to many connections betweenvarious areas of mathematics, e.g. Grassmann co-ordinates in line-geometry, elementary symmetricpolynomials, “authentication” perpendicular ar-rays, coset leaders in coding theory, the manycombinatorial meanings of the Catalan numbers.

4.6. Sorting with two stacks and quarter-planeloops

Tony Guttmann (The University of Melbourne)


Prof Tony Guttmann

There are three classic problems in theoreticalcomputer science, posed by Knuth in the 1960s.Knuth asked for the number of permutations oflength n that could be sorted by (a) two stacks inparallel,(b) two stacks in series and (c) a double-ended queue, or deque. These have resisted attackuntil now. Recently Albert and Bousquet-Mlousolved the first problem by relating the generat-ing function to that of quarter-plane loops.

More recently still, in joint work with AndrewElvey-Price we have done the same for deques,and established the (unusual) asymptotics (nu-merically) for both problems. For two stacks inseries, we give numerical estimates of the asymp-totics, but are unable to give a complete solution.

4.7. Difference Covering Arrays and NearlyOrthogonal Latin Square

Joanne Hall (Queensland University of Technology)


Fatih Demirkale, Diane Donovan, Joanne Hall,

Abdollah Khodkar, Asha Rao

Difference arrays are used in applications such assoftware testing, authentication codes and datacompression. Pseudo-orthogonal Latin squaresare used in experimental designs particularly forexperiments involving animals. A special classof pseudo-orthogonal Latin squares are the mu-tually nearly orthogonal Latin squares (MNOLS).We exploit a connection between difference cover-ing arrays and MNOLS to construct some sets ofMNOLS.

4.8. Definability of SP-classes of uniformhypergraphs

Lucy Ham (La Trobe University)


Lucy Ham

An SP-class of k-uniform hypergraphs is a classof k-uniform hypergraphs closed under taking in-duced substructures and direct products. The 2-uniform hypergraphs are just the simple graphs.

Using results of Erdos and Hajnal, we show thatfor k > 2, no SP-class of k-uniform hypergraphswith bounded chromatic number is definable bya single first-order sentence, except in two trivialcases. This result is analogous to one proved byCaicedo for simple graphs (after Erdos, Nesetriland Pultr), where there are four exceptional cases.We also show that both our result and Caicedo’scontinue to hold when we restrict to the class of fi-nite uniform hypergraphs, verifying the finite levelSP-preservation theorem in this case. The finitelevel SP-preservation theorem remains open forarbitrary relational structures.

4.9. NP-complete fragments of qualitative calculi

Tomasz Kowalski (La Trobe University)


Dr Tomasz Kowalski

A qualitative calculus is (from one point of view)an algebra of the type of Tarski’s relation alge-bras, which is representable as a certain structureof binary relations over a set. Typical examplesinclude Allen’s Interval Algebra (IA) and RegionConnection Calculus (RCC8). Qualitative calculihave been quite widely studied - and applied - incomputer science. One of the most commonly in-vestigated theoretical problems in qualitative cal-culi is computational complexity of constraint sat-isfaction over them, or, as it is commonly known inthe area, the Network Satisfaction Problem. Ex-isting results, however, focus on complexity of net-work satisfaction over some particular qualitativecalculus: for example, tractable and NP-completefragments of IA and RCC8 have been completelyclassified.

I will present a rather simple sufficient conditionfor a fragment of any qualitative calculus to haveNP-complete network satisfaction problem.

4.10. Graphic and bipartite graphic sequences

Stacey Mendan (La Trobe University)


Ms Stacey Mendan

This talk will present some definitions and con-cepts relevant to understanding when a sequenceis graphic and a pair of sequences is bipartitegraphic. We will meet the fundamental results:the Erdos-Gallai Theorem and the Gale-Ryser

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4. Combinatorics

Theorem. Our focus will be an exploration ofsufficient conditions for graphicsness and bipar-tite graphicsness and the central role played bysequences consisting of two elements in these con-ditions.

4.11. Using algebra to avoid robots

Murray Neuzerling (La Trobe University)


Mr Murray Neuzerling

Qualitative calculi are algebraic models of reason-ing that have found application in robotics, plane-tary rovers, ship navigation and bird flocking. Wediscuss methods of determining if reasoning withconstraints over a qualitative calculus is tractable,and offer some small examples.

4.12. Skolem sequences and Difference coveringarrays

Asha Rao (Royal Melbourne Institute of

Technology)


Dr Asha Rao

A Skolem sequence S = (s1, s2, . . . , s2n) of ordern is a sequence of length 2n, such that for everyk ∈ 1, 2, . . . , n, there are exactly two elementssi, sj ∈ S such that si = sj = k and if si = sj = k,with i < j, then j − i = k.

A difference covering array DCA(κ, η, n) over anabelian group G of order n is a κ× η matrix Q =[q(i, j)] with entries from G such that, for all pairsof rows 0 ≤ i, i′ ≤ κ − 1, i 6= i′, the difference setδi,i′ = q(i, j) − q(i′, j)|0 ≤ j ≤ η − 1 containsevery element of G at least once.

In this talk, I will explore the connections betweenSkolem sequences and difference covering arrays,and discuss how these connections may be used toestablish a lower bound on the number of differ-ence covering arrays of even order.

This is joint work with Joanne Hall, Fatih Demirkaleand Diane Donovan.

4.13. An introduction to combinatorics of words

Jamie Simpson (Curtin university)


Dr Jamie Simpson

A word is a sequence of symbols taken from a(usually finite) alphabet. The study of the com-binatorics of words lies on the border of mathe-matics and computer science, with applications incomputer science including searching, data com-pression, cryptography and error correction, ap-plied to words such as computer files and DNAsequences. For mathematicians there are many in-teresting problems, particularly to do with whatpatters can be avoided in words, how few timesand how many times a pattern can occur in a

word of given length. I’ll talk about what is knownand what isn’t known about some of these prob-lems. This interesting talk will be followed byAmy Glen’s even more fascinating one on the samearea.

4.14. Algebras of incidence structures:representations of regular double p-algebras,

Christopher Taylor (La Trobe University)


Mr Christopher Taylor

The extensive study of boolean algebras has led tonumerous generalisations. In particular, comple-mentation has been weakened in many ways. Onesuch weakening is the focus of this talk: pseu-docomplementation. In a lattice mathbfL, thepseudocomplement of x ∈ L, when it exists, isthe largest element z such that xwedgez = 0.The dual pseudocomplement is defined similarly.A double p-algebra is an algebra with a latticereduct that has both the pseudocomplement anddual pseudocomplement defined.

An algebra is called regular if, whenever two con-gruences share a congruence class, they are in factthe same congruence. Varlet proved that regulardouble p-algebras can be characterised by a singlequasi-equation. We prove that the lattice of point-preserving substructures of an incidence structurenaturally forms a regular double p-algebra. Anincidence structure is a standard geometric ob-ject consisting of a set of points, a set of lines, anan incidence relation specifying which points lieon which lines. This concept generalises, for ex-ample, both graphs and projective planes. Thus,in particular, the lattice of subgraphs of a graphforms a regular double p-algebra.

The result given in this talk is a characterisationof the regular double p-algebras which are isomor-phic to a lattice of point-preserving substructuresof an incidence structure. In addition to the corol-lary that every finite regular double p-algebra isisomorphic to a lattice of point-preserving sub-structures, a special case of the result is a standardtheorem for boolean algebras: a boolean algebrais isomorphic to a powerset lattice if and only if itis complete and atomic.

4.15. Proof of Tutte’s 3-flow conjecture in an”almost all” sense.

Nicholas Wormald (Monash University)


Dr Nicholas Wormald

Tutte’s 3-flow conjecture, from 1972, is that every4-edge connected graph has a nowhere-zero 3-flow,or equivalently, that 5-regular 4-edge-connectedgraph has an edge orientation in which every out-degree is either 1 or 4. We have shown recently

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4. Combinatorics

that the equivalent formulation holds asymptoti-cally almost surely for random 4-edge connected5-regular graphs.

This is joint work with Pawe l Pra lat.

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5.1. Homogeneous locally conformally Kaehlermanifolds

Dmitri Alekseevsky (Institute for Information

Transmission Problems)

16:05 Thu 1 October 2015 – SSN015

Prof Dmitri Alekseevsky

A Hermitian manifold (M,J, g) is called a locallyconformally Kahler if the Kahler form ω = g Jis conformal to a closed form. It is called a Vais-man manifold if the universal cover (M, g) is aRiemannian product of a real line and a sim-ply connected Sasaki manifold. We prove that aa homogeneous locally conformally Kahler man-ifold M = G/H of a reductive group G is Vais-man if the normalizer N(H) of the stability sub-group H is compact. The proof is based on a cor-respondence between (quantizable) Kahler mani-folds, regular Sasaki manifolds and Kahler conesand on classification of homogeneous left-invariantlocally conformally Kahler structures on reduc-tive Lie groups. They are not necessary Vaismanmanidolds.

This is a joint work with V. Cortes, K. Hasegawaand Y. Kamishima (Int. J. Math., 2015).

5.2. Holomorphic flexibility properties of spaces ofelliptic functions

David Bowman (The University of Adelaide)


Mr David Bowman

The set of meromorphic functions on an ellip-tic curve naturally possesses the structure of acomplex manifold. The component of degree 3functions is 6-dimensional and enjoys several in-teresting complex-analytic properties that makeit, loosely speaking, the opposite of a hyperbolicmanifold. Our main result is that this componenthas a 54-sheeted branched covering space that isan Oka manifold. This implies that the compo-nent is both dominable and C-connected.

5.3. Constructing Local Invariants for CREmbeddings

Sean Curry (The University of Auckland)


Mr Sean Curry

CR geometry and CR embeddings arise naturallyin the study of proper holomorphic mappings be-tween smoothly bounded domains in several com-plex variables. CR invariants of the boundaries ofdomains are used to tell whether two domains arebiholomorphically equivalent. Local invariants ofCR embeddings are basic objects of interest and

can be applied for instance to distinguishing Mil-nor links of singularities of complex analytic va-rieties up to biholomorphic equivalence. We givean invariant theory for CR embeddings using CRtractor calculus which parallels the Ricci calculusbased invariant theory for Riemannian submani-folds.

5.4. An algebraic form for a self-dual Einsteinorbifold metric

Owen Dearricott (MASCOS / University of

Melbourne)

16:30 Thu 1 October 2015 – SSN015

Dr Owen Dearricott

In the 90s Hitchin found a number of algebraicsolutions to the Painleve VI equation through thestudy of triaxial Bianchi IX self-dual Einstein met-rics via the theory of isomonodromic deforma-tions. In this talk we discuss a new algebraic so-lution of Painleve VI and how it gives rise to analgebraic parametrisation of an SDE metric on acertain space with a locus of conical singularities.

5.5. Normal forms and symmetries in CR geometry

Martin Kolar (Masaryk University)

15:15 Thu 1 October 2015 – SSN015

Assoc Prof Martin Kolar

We will discuss recent results on the local equiv-alence problem for Levi degenerate hypersurfacesin Cn.

5.6. Geometric flows and their solitons onhomogeneous spaces

Jorge Lauret (Universidad Nacional de Cordoba)

14:50 Thu 1 October 2015 – SSN015

Prof Jorge Lauret

We develop a general approach to study geomet-ric flows on homogeneous spaces. Our main toolwill be a dynamical system defined on the vari-ety of Lie algebras called the bracket flow, whichcoincides with the original geometric flow after anatural change of variables. The advantage of us-ing this method relies on the fact that the pos-sible pointed (or Cheeger-Gromov) limits of so-lutions, as well as self-similar solutions or soli-ton structures, can be much better visualized.The approach has already been worked out in theRicci flow case and for general curvature flows ofalmost-hermitian structures on Lie groups. Thispaper is intended as an attempt to motivate theuse of the method on homogeneous spaces for anyflow of geometric structures under minimal natu-ral assumptions. As a novel application, we finda closed G2-structure on a nilpotent Lie group

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which is an expanding soliton for the Laplacianflow and is not an eigenvector.

5.7. Holomorphicity of Meromorphic Mappingsalong Real Hypersurfaces

Francine Meylan (University of Fribourg)


Dr Francine Meylan

We construct an example of a rational map Ffrom C2 to P2 that has indeterminacies on theunit sphere S3 ⊂ C2 such that F |S3 is continuous,the image K := F (S3) is contained in the affinepart C2 of P2, and K does not contain any germof a nonconstant complex curve.

5.8. Conformal maps in nilpotent groups

Alessandro Ottazzi (University of New South

Wales)


Dr Alessandro Ottazzi

We consider nilpotent and stratified Lie groupswith their associated left-invariant control dis-tance. We study conformal maps and prove that,with few exceptions, these are only affine transfor-mation. Namely, compositions of translations andconformal group isomorphisms. The exceptionsoccur when a conformal inversion can be defined.This only happens when the group is the nilpotentpart of the Iwasawa decomposition of a simple Liegroup of rank one. This work is in collaborationwith M. Cowling (UNSW).

5.9. Analytic complexity of binary cluster trees

Timur Sadykov (Plekhanov Russian University)


Prof Timur Sadykov

The Kolmogorov-Arnold theorem yields a repre-sentaion of a multivariate continuous function interms of a composition of functions which dependon at most two variables. In the analytic case,understanding the complexity of such a represen-tation naturally leads to the notion of the analyticcomplexity of (a germ of) a bivariate multi-valuedanalytic function. According to Beloshapka’s lo-cal definition, the order of complexity of any uni-variate function is equal to zero while the n-thcomplexity class is defined recursively to consistof functions of the form a(b(x, y) + c(x, y)), wherea is a univariate analytic function and b and cbelong to the (n − 1)-th complexity class. Sucha represenation is meant to be valid for suitablegerms of multi-valued holomorphic functions.

A randomly chosen bivariate analytic functionswill most likely have infinite analytic complex-ity. However, for a number of important familiesof special functions of mathematical physics their

complexity is finite and can be computed or esti-mated. Using this, we introduce the notion of theanalytic complexity of a binary tree, in particular,a cluster tree, and investigate its properties.

5.10. A Forelli type theorem for resonant vectorfields

Gerd Schmalz (University of New England)


Dr Gerd Schmalz

The classical Forelli theorem can be stated asfollows: If a complex-valued C∞ function on aneighbourhood of 0 in Cn (n > 1) is annihi-lated by the antiholomorphic Euler vector fieldX = z1

∂∂z1

+ · · · + zn∂∂zn

then it is holomor-phic. A generalisation of this result for diagonal-isable vector fields was proved by Kim, Poletskyand Schmalz, but left the case of resonant (non-diagonalisable) vector fields open. I will present aresult dealing with the resonant case. This is jointwork with Joo and Kim.

5.11. Two approaches toward the Jacobianconjecture

Tuyen Truong (The University of Adelaide)

15:40 Thu 1 October 2015 – SSN015

Dr Tuyen Truong

We discuss two possible approaches toward theJacobian conjecture, based on the reductions toDruzkowski maps and to maps with integer coef-ficients, and the fact that the set of Keller maps(of a given degree and dimension) which satisfythe Jacobian conjecture is Zariski closed. The ap-proaches are to study some conditions on squarematrices, and we show that for a given rank rthese conditions are satisfied for a generic matrixof rank r. The Jacobian conjecture is true if theseconditions are satisfied either for all Druzkowskimatrices with integer coefficients or for a genericDruzkowski matrix. We illustrate the effectivenessof using these conditions to indirectly check thatsome examples of Druzkowski maps, previouslyconsidered by other authors, satisfy the Jacobianconjecture.

5.12. Filiform Lie algebras over Z2

Ioannis Tsartsaflis (La Trobe University)


Mr Ioannis Tsartsaflis

We recently discovered a Lie algebra over Z2

which has maximal nilpotency but no elementsof maximal rank. In this talk we will give someexamples of this kind and present related results.

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6.1. Effective dimension for weighted ANOVA andanchored spaces

Chenxi Fan (University of New South Wales)


Chenxi Fan

Effective dimension, an indicator of the difficultyof high dimensional integration, describes whethera function can be well approximated by low di-mensional terms or a sum of low dimensionalterms. This talk considers weighted ANOVA andanchored spaces of functions. The main focus is tostudy how the variance is related to the norms andwhy this connection is useful in the context of ef-fective dimension, using relations between the cor-responding multivariate decompositions and theembedding between these two spaces.

6.2. An abstract analysis of optimal goal-orientedadaptivity

Michael Feischl (UNSW)

15:45 Wed 30 September 2015 – HUM115

Michael Feischl, Dirk Praetorius, Kris van der Zee

We provide an abstract framework for optimalgoal-oriented adaptivity for finite element meth-ods and boundary element methods in the spiritof [Carstensen et al., Comput. Math. Appl. 67(2014)]. We prove that this framework coversstandard discretizations of general second-orderlinear elliptic PDEs and hence generalizes avail-able results [Mommer et al., SIAM J. Numer.Anal. 47 (2009); Becker et al., SIAM J. Numer.Anal. 49 (2011)] beyond the Poisson equation.

6.3. Computing Lagrangian coherent structuresfrom Laplace eigenproblems

Gary Froyland (University of New South Wales)


Gary Froyland, Oliver Junge

The eigenspectrum and eigenfunctions of the Laplace-Beltrami operator have a long history in differen-tial geometry, where many connections have beenmade with properties of Riemannian manifolds.In this talk, I will adapt these ideas to a prob-lem in nonlinear dynamics, namely the determina-tion of so-called Lagrangian coherent structures,which have application in aerodynamics, physicaloceanography, and meteorology. I will describenew theoretical results and illustrate these withidealised models of fluid flow. Initial numericalwork to solve the Laplace eigenproblems usingfinite-difference methods and radial basis functioncollocation will be reported.

6.4. Solving partial differential equations with thesparse grid combination technique

Markus Hegland (Australian National University)


Prof Markus Hegland

The sparse grid combination technique is used tosolve high (larger than four) dimensional partialdifferential equations. I will provide an introduc-tion to this technique, a review of some applica-tions and some recent results we obtained at theANU and the Technical Unversity of Munich. Theresults covered mainly relate to the accuracy ofthe method.

This is joint work with Matthias Wong, BrendanHarding, Christoph Kowitz and others.

6.5. Landweber iteration of Kaczmarz type forinverse problems in Banach spaces

Qinian Jin (Australian National University)


Dr Qinian Jin

The determination of solutions of many inverseproblems usually requires a set of measurementswhich leads to solving systems of ill-posed equa-tions. In this talk we propose the Landweber it-eration of Kaczmarz type with general uniformlyconvex penalty functional. The method is formu-lated by using tools from convex analysis. Thepenalty term is allowed to be non-smooth to in-clude the L1 and total variation (TV) like penaltyfunctions, which are significant in reconstruct-ing special features of solutions such as spar-sity and piece-wise constancy in practical applica-tions. Under reasonable conditions, we establishthe convergence of the method. Finally we presentnumerical simulations on tomography problemsand parameter identification in partial differentialequations to indicate the performance. This is ajoint work with Wei Wang.

6.6. A stabilized mixed finite element methodsystems for nearly incompressible elasticity andStokes equations

Bishnu Lamichhane (The University of Newcastle)


Dr Bishnu Lamichhane

We present a finite element method for nearly in-compressible elasticity using a mixed formulationof linear elasticity in the displacement-pressureform. We combine the idea of stabilization ofan equal order interpolation for the Stokes equa-tions with the idea of biorthogonality to get ridof the bubble functions used in an earlier pub-lication with a biorthogonal system. We work

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with a Petrov-Galerkin formulation for the pres-sure equation, where the trial and test spaces aredifferent and form a g-biorthogonal system. Thisnovel approach leads to a displacement-based loworder finite element method for nearly incompress-ible elasticity for simplicial, quadrilateral and hex-ahedral meshes. Numerical results are provided todemonstrate the efficiency of the approach.

6.7. Higher order Quasi-Monte Carlo integrationfor Bayesian Estimation

Quoc Thong Le Gia (University of New South

Wales)


Dr Quoc Thong Le Gia

We analyze higher order Quasi-Monte Carlo nu-merical integration methods in Bayesian estima-tion of solutions to parametric operator equa-tions with holomorphic dependence on the pa-rameters. Such problems arise in numerical un-certainty quantification and in Bayesian inversionof operator equations with distributed uncertaininputs, such as uncertain coefficients, uncertaindomains or uncertain source terms and boundarydata.

We establish error bounds for higher order, Quasi-Monte Carlo quadrature for the Bayesian estima-tion. This implies that the Quasi-Monte Carloquadrature methods are applicable to these prob-lem classes, with dimension-independent conver-gence ratesO(N−1/p) ofN -point HoQMC approx-imated Bayesian estimates where 0 < p < 1 de-pends only on the sparsity class of the uncertaininput in the Bayesian estimation.

This is a joint work with Josef Dick (UNSW Aus-tralia), Christoph Schwab and Robert Gantner(ETH, Switzerland).

6.8. Equal area partitions of connected Ahlforsregular spaces

Paul Charles Leopardi (School of Mathematical

and Physical Sciences The University of Newcastle)


Dr Paul Charles Leopardi

For N sufficiently large, any connected Ahlforsregular space of Hausdorff dimension d can bepartitioned into N regions of equal measure andbounded diameter, where the bound is of orderN−1/d. The construction is a generalization ofa construction of Feige and Schechtman usingdyadic cubes in place of Voronoi cells. This isjoint work with Giacomo Gigante of the Univer-sity of Bergamo.

6.9. Fitting Circular Arcs Through Points in thePlane

Garry Newsam (The University of Adelaide)


Dr Garry Newsam

Many computer vision tasks include fitting conicsections through collections of points in the planeextracted by image processing primitives such asedge detection. Unfortunately at present mostof the standard algorithms for fitting such sec-tions, such as orthogonal distance regression, arenot consistent with respect to errors in the data:the fitted conic converges to the true conic if thenoise level goes to zero, but if the noise level is keptfixed while the number of points goes to infinitythen the fit does not converge. Inconsistency isa consequence of an incomplete statistical modelfor the data: for example orthogonal distance re-gression assumes that the data are observationsof true points lying on the true curve that havebeen perturbed by i.i.d. Gaussian errors, but itmakes no assumption about the distribution ofthe unknown true points. The paper will presenta complete model for the problem of fitting a cir-cular arc though data based on i.i.d. Gaussianerrors and a von Mises prior on the circle for theunknown true points and derive a closed form ex-pression for the resulting distribution of points inthe plane. This appears to be perhaps the onlynon-trivial conic, or indeed nonlinear curve, forwhich a closed form for this distribution exists:the expression’s utility lies in its ability to provideproofs of the inconsistency of orthogonal distanceregression, Cramer-Rao bounds on parameter esti-mates, and similar results. The paper will presentsome of these derivations along with numerical re-sults on the performance of fitting routines for thismodel that use maximum likelihood and method-of-moments estimators, and briefly consider theimplications of the analysis for more general conicfitting problems.

6.10. Dual-scale Modelling Approaches forSimulating Diffusive Transport in HeterogeneousPorous Media

Ian Turner (Queensland University of Technology)


Ian Turner, Elliot Carr and Patrick Perre

Recent developments in the dual-scale compu-tational modelling of diffusion in heterogenousporous media are presented. The model cou-ples the scale of the porous medium (macroscale)with the pore scale (microscale) by imposingmacroscopic gradients of the appropriate variableson the microscopic field using suitably definedboundary conditions. An important contributionof the work is the use of a microcell for the fluxestimation derived directly from the morphology

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of the porous medium, which avoids the need fordetermining the effective diffusivity in the macro-scopic model. An overview is also given of thefinite volume and Krylov subspace methods usedto ensure computationally efficient and accuratesimulations.

6.11. Fully discrete needlet approximation on thesphere

Yuguang Wang (University of New South Wales)


Dr Yuguang Wang

Spherical needlets have applications in signal pro-cessing and astrophysics. The original semidis-crete spherical needlet approximation is not com-putable, in that the needlet coefficients dependon inner product integrals. In this work with QThong Le Gia, Ian Sloan and Robert Womersley,we approximate these integrals by a second quad-rature rule with an appropriate degree of preci-sion, to construct a fully discrete needlet approx-imation. We prove that the resulting approxima-tion is equivalent to filtered hyperinterpolation,that is to a filtered Fourier-Laplace series partialsum with inner products replaced by appropri-ate cubature sums. It follows that the Lp-error,1 ≤ p ≤ ∞, of discrete needlet approximationachieves the optimal rate of convergence in thesense of optimal recovery. A numerical experi-ment uses needlets over the whole sphere for thelower levels together with high-level needlets withcenters restricted to a local region. The resultingerrors are reduced in the local region away fromthe boundary, indicating that local refinement inspecial regions is a promising strategy.

6.12. Efficient spherical designs with goodgoemetric properties

Robert Womersley (University of New South

Wales)


Dr Robert Womersley

This talk considers the calculation and propertiesof spherical t-designs on Sd, and in particular forS2 where most applications reside.

Bondarenko, Radchenko and Viazovska (2013)proved that there exists a cd such that spherical t-designs withN points exist for allN ≥ cdtd, whichis the optimal order. Moreover they showed thatthere exist such spherical designs that are well-separated (2014). The interest here is in efficientspherical designs with N < td.

The geometric properties of point sets on Sd canbe characterised by their separation (twice thepacking radius), their mesh norm (covering ra-dius) and mesh ratio (covering radius / packingradius), amongst many other criteria. A com-mon assumption arising in application is that the

the sequence of point sets is quasi-uniform, that istheir mesh ratios are uniformly bounded. The in-terest here is in sets of efficient spherical t-designswith small mesh ratios.

Examples of spherical t-designs on S2 with N =t2/2 + O(t) points and mesh ratio < 1.8 fort = 1, . . . , 301 are given. These provide excellentsets of points for both numerical integration andapproximation, for example by needlets.

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7.1. Design Principle for Adaptable and RobustComplex Systems

Axel Bender (Defence Science and Technology

Organisation, Australia)


Dr Axel Bender

Understanding how systems can be designed tobe both robust and adaptable is fundamental toresearch in optimisation, evolution, and complexsystems science. A recent theory on the origins ofsystemic flexibility in biological systems has pro-posed that degeneracy the realisation of multi-ple, functionally versatile components with con-textually overlapping functional redundancy is aprimary determinant of the robustness and adapt-ability found in living systems. While degeneracyscontribution to biological flexibility is well doc-umented, it is somehow underrepresented in op-erations research and systems engineering. Thistalk presents the principles of degeneracy-baseddesign and illustrates its effect on robustness andadaptability in the context of a strategic resourceplanning problem. A simple model will be pre-sented that captures the most important dynam-ics of a vehicle fleet resource planning problem,namely: changes in the assignment of vehicles totasks, changes in the composition of vehicles thatmake up a fleet, changes in the tasks that mustbe executed during fleet operations, and changesin the composition of tasks at a timescale compa-rable to the timescale for changes in fleet compo-sition. Simulating this model in an evolutionarycomputation environment demonstrates that de-generacy improves the robustness and adaptabil-ity of a vehicle fleet towards unpredicted changesin task requirements without incurring costs tofleet efficiency.

The generic characteristics of the presented modelallows for the generalisation of some of the find-ings. The talk thus will identify and elaborateon operations research and engineering exampleswhere degeneracy-based design may improve theadaptability and robustness of complex systems.

7.2. Do I smell gas? Bayesian Inversion forlocalisation and quantification of fugitive emissions

Sangeeta Bhatia (University of Western Sydney)

16:35 Tue 29 September 2015 – HUM115

Ms Sangeeta Bhatia

Accurate measurement of fugitive methane emis-sions is a topical issue of global importance. Inthis talk, I will present a Bayesian inversion modelfor localizing and quantifying the emission rate ofa point source of emission. This is an extension of

an earlier technique called atmospheric tomogra-phy. The atmospheric tomography technique wasextended to use open path methane laser measure-ments. This research will have a direct applicationfor coal seam gas wells, oil and gas wells, methaneseeps, agricultural emissions and many others.

7.3. Military inventory capacity and stock planningwith surge and warning time and supplierconstraints

Greg Calbert (Defence Science and Technology



Dr Greg Calbert

Linear programming has since its inception, al-ways been strongly linked to inventory manage-ment. Linear programming has also been usedextensively in many military stockage problems.In a military context, two general events test andshape the supply chain. The first is the develop-ment of inventory control, stockholding and ca-pacity policies to meet demands associated withraise train and sustain operations. This firstproblem has very similar characteristics to stock-holding in a commercial supply chain, where de-mands are forecasted and corresponding procure-ment takes place.

The second event is the occurrence of a contin-gency demand, often termed a surge demand. Inthe second case, a contingency will have a planneddemand, sustainment period and correspondingwarning time. While the demand and sustainmentperiod are critical to stockholding decisions, it isthe warning time, which in conjunction with thevendors constraints on supplying at surge ratesthat is critical to developing inventory holdings,capacity and reserve stocks, often called war re-serve materiel in the United States Departmentof Defence. One can often summarise the vendorsconstraints in supplying at a surge rate throughthe Contingency Provisioning Lead Time (CPLT),which is defined as that time the vendor can sup-ply at the required contingency throughput rate.The CPLT may be greater than the combinedwarning time and the sustainment period, indi-cating the vendor cannot supply at the requiredrate throughput the term of the contingency.

With the basic input parameters of raise, trainand sustain demands, contingency demands, warn-ing time, CPLT and maximum order quantities,we form a linear program that optimises the ca-pacity, reserve stocks and nominal inventory hold-ings at a Defence Logistics Installation. This lin-ear program is extended to include an anytimecontingency; where the inventory constraints are

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formed assuming surge demand can occur at anytime during the raise train and sustain cycle.

The linear program is solved and sensitivity anal-ysis is conducted over demand variation and varia-tion in warning times. A further extension of thelinear program is developed which includes con-straints on bulk delivery lead times.

Finally, we discuss stochasticity in demand, sup-ply and warning times. Inevitability, there is un-certainty in each of the aforementioned parame-ters. We form a two-stage stochastic linear pro-gram. In this construct, the first stage deci-sions are the optimal capacity, raise train and sus-tain and reserve stock inventory holdings. Thesecond stage variables are the procurement deci-sions required to ensure sustainability under dif-ferent demand, supply and warning time scenar-ios. Approaches to solving the stochastic linearprogramming exactly or approximately throughthe Monte-Carlo based stochastic average approx-imation algorithm are also discussed.

7.4. A model for distributed decision making: Levynoise and network synchronisation

Alexander Kalloniatis (Defence Science and

Technology Organisation, Australia)


Dr Alexander Kalloniatis

Recently a model for phase oscillators synchronis-ing through interactions on a network has beenadapted to represent a group of agents sharing in-formation in order to reach coherent decision mak-ing. A number of mathematical developments arerequired to advance such a model to achieve bet-ter fidelity. One of these is to model the humanpropensity to ”jump ahead” based on intuition orpattern recognition. In recent years significantprogress has been made in clarifying the math-ematical properties of random walk processes in-volving ”jumps”; these are non-Gaussian with dis-tributions exhibiting ”fat” power-law tails. Inthis talk I will report on work with Dr DaleRoberts (ANU) in incorporating tempered stableLevy noise into the well-known Kuramoto modelfor network synchronisation.

7.5. A case for new models of battle attrition

Brandon Pincombe (Defence Science and

Technology Organisation, Australia)


Dr Brandon Pincombe

We describe the three most commonly used massaction models of combat and demonstrate thatnone of them match the available combat datasets. The three models each represent differentbattle processes; however they do not include ex-plicit representations of these processes. Unfor-tunately none of the models are useful to force

planners because they do not include the variablesnecessary to answer the questions about combinedarms teams that those planners ask. After empha-sising the importance of the mathematical char-acteristics of the datasets and models and thepotential applicability of models of battle attri-tion in other areas, we briefly introduce a numberof other battle processes and suggest how thesecan be explicitly included in models and so makemathematical modelling useful to force designers.We conclude with suggestions for the qualitativeand quantitative investigations needed to developmore accurate and useful combat models.

7.6. Behavioural Questions in Complexity andControl

Darryn Reid (Defence Science and Technology



Dr Darryn Reid

I propose to shift the problem choice for math-ematical modelling away from trying to charac-terise a system and towards defining models forcontrollers that are able to successfully operatetogether in unpredictable environments. Interest-ingly, this also means that they be able to con-tribute towards generating uncertainty. Standardorder parameters from Nonlinear Dynamics, suchas Lyapunov Exponents and entropy, and fromAlgorithmic Information Theory, might then beapplied to investigate and categorise the proper-ties of such a system; this suggests that we have anew kind of test, analogous to the famous TuringTest, for controllers in complex dynamical envi-ronments.

Like Artificial Intelligence, mathematical mod-elling usually assumes a strong separation betweenthe problem and the controllers that are supposedto solve it. The complexity of the problem is in-herently limited by this structure. In effect, mod-elling and simulation problems are typically ori-ented around a high-fidelity environment that istightly defined to try to eliminate the unexpected.I maintain instead that significant advances willcome from the development of models for con-trollers that capable of dealing with a genuinelycomplex problem comprising unpredictable futurestates of an environment, within some limitations.In other words, fidelity should be traded for un-predictability, rather than the other way around.

Chaos and unpredictability is generated by thecomplex interactions between things in an envi-ronment. My main conclusion here is that mathe-matical modelling should tackle problems of con-trol in which the interactions between the con-trollers that solve the problem, within their oper-ational setting, are what actually create the prob-lem the controllers themselves are there to solve.

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The controllers are thus at least indirectly, if notalso directly, self-referential. This implies defin-ing the problem on top of a base world of an en-vironment and resources, with the interactions ofcontrollers creating the complexity that producesunpredictable future states of the system whilethey are in the process of solving the problem ofjust surviving in the very environment they col-lectively create.

This approach also raises the intriguing possibil-ity of a new kind of simulation environment thatpermits scenarios to be discovered. This contrastsstarkly to extant approaches in which the scenar-ios are modelled; in this traditional approach, thepreconceptions of the modeller are built into thesimulation from the outset. Any time we have acomplex dynamical system one that is not sta-tionary or not regular, so a K-system or Bernoullisystem suffices as an example we have a sys-tem in which more data does not necessarily givemore information about the generating function,and which manifests unique transient states. Suchunique transient states are scenarios, and may bemuch more useful for testing the sensitivities tofailure of our agents than preconceived scenariosthat are limited by the scope of our preconcep-tions.

7.7. Algorithmic complexity of two defence budgetproblems

Richard Taylor (Defence Science and Technology



Dr Richard Taylor

A fundamental challenge in the development ofdefence capability is to decide on a collection ofprojects that represent the best value within agiven budget constraint. A complicating factorin doing this is taking account of the interrela-tionships between projects when assessing value.We investigate two such models. The first assignsvalue based on subsets of projects that come to-gether to provide effects, the second assigns valuethrough the intermediary of scenarios. In terms ofrecognised combinatorial optimisation problemsthe first is a form of the Set Union Knapsack prob-lem while the second appears to be a new problemwe call the Budget Scenario problem. We analysethe known results about the algorithmic complex-ity of these problems by showing their relation-ships with existing problems and known approxi-mation and inapproximation results. We also dis-cuss new approximation results for both problems.

7.8. Model-Based State Of Charge Estimation OfA Lithium-Ion Battery

Minh Tran (Flinders University)


Mr Minh Tran

The battery’s state of charge (SoC) is analogousto the level of fuel remaining displayed on a fuelgauge. An accurate estimation of the SoC willimprove the effectiveness of a battery manage-ment (BMS) to manage a rechargeable battery (eglithium ion battery). In this presentation a newapproach for estimating the battery’s SoC will bepresented. The method uses the measurement ofcurrent and voltage to directly calculate SoC ofthe battery. In addition, the method to calculatethe parameters of the model will also be discussed.

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8.1. Spontaneous rotation in a resonance-freesystem

Tristram Alexander (UNSW)

15:15 Thu 1 October 2015 – NTH1

Dr Tristram Alexander

We consider a driven-damped continuous timesystem with no natural frequency, realised by amass free to rotate in the horizontal plane aboutan oscillating pivot point. For harmonic rectilin-ear forcing we find a complex bifurcation picture,proceeding from a parametric resonance betweendriving and damping, through a series of perioddoubling and symmetry breaking bifurcations tochaotic motion, which beyond a critical drivingstrength collapses to rotations synchronised to thepivot oscillations. We find that changing the sym-metry of the driving qualitatively changes the bi-furcation picture, with strongly anharmonic driv-ing able to mimic the kicked rotor, and circulardriving constraining the dynamics to a fixed rota-tion. We extend our analysis to the significantlymore complex case of two impacting masses andsee that the spontaneous rotation persists at largeforcing.

8.2. Rock and Roll and Quantum Optics.

Peter Cudmore (The University of Queensland)


Mr Peter Cudmore

Room temperature quantum optics is tricky busi-ness. As soon as an experiment is performed outof the ’fridge’ noise resulting from thermal excita-tions is drastically increased. In this talk we willdiscuss a means to improve the signal-to-noise ra-tio in a broad class of quantum optomechanicalsystems. This is achieved by driving the systemonto a limit cycle much in the same way that aguitarist uses distortion to produce musical feed-back. We will also discuss how we can ’hear’ dif-ferent states by observing the spectral propertiesof the system, which could allow the measurementof quantum tunnelling.

8.3. Perron-Frobenius theory and eventuallypositive semigroups of linear operators

Daniel Daners (University of Sydney)


Daniel Daners, Jochen Glueck, James B. Kennedy

There is a well established theory of positive semi-groups (etA)tgeq0 of linear operators with gen-erator A on Banach lattices. An importantpart in the theory of positive semigroups is thePerron-Frobenius theorem (or Krein-Rutman the-orem). It provides important information on

the spectrum of the generator of positive semi-group. The main aim of the talk is to considera converse to the Perron-Frobenius theorem: Weshow that Perron-Frobenius type spectral condi-tions are characterised by empheventually positivesemigroups, that is, semigroups having the prop-erty that for every initial condition u0 > 0 thereexists t0 > 0 such that etAu0 > 0 for all t > t0.In general etAu0 is not positive for t > 0 small.We illustrate the theory by a variety of examples,artificial and simple applications.

8.4. Spectral theory under nonuniformhyperbolicity

Davor Dragicevic (School of mathematics and

statistics)


Dr Davor Dragicevic

For a linear nonautonomous dynamics, we con-sider the notion of nonuniform spectrum. This isdefined in terms of the existence of nonuniformexponential dichotomies with an arbitrarily smallnonuniform part and can be seen as a nonuniformversion of the spectrum introduced by Sacker andSell in the case of a single trajectory. We will de-scribe the structure of the nonuniform spectrumand discuss its connection with the theory of Lya-punov exponents. Furthermore, we will considerboth the discrete and continuous as well as finiteand infinite-dimensional dynamics. This is a jointwork with Luis Barreira and Claudia Valls.

8.5. On control of systems with slow variables

Vladimir Gaitsgory (Macquarie University)


Prof Vladimir Gaitsgory

Dynamical systems with slow observables havebeen studied by a number of researchers. Howeverproblems of control of such systems have neverbeen discussed in the literature (to the best ofour knowledge).

In this talk, we will present results of a pilot studyof the way how a problem of optimal control of asystem with slow observables can be approached.We will discuss a possibility of approximating thisproblem with a problem of optimal control of theaveraged system, the construction of the latter be-ing a key element of our research. We will illus-trate our discussion with a numerical example.

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8.6. A streamlined approach to the multiplicativeergodic theorem on Banach spaces

Cecilia Gonzalez-Tokman (The University of

Queensland)

14:35 Wed 30 September 2015 – NTH1

Dr Cecilia Gonzalez Tokman

Multiplicative ergodic theorems (METs) provide apowerful tool for the study of non-autonomous dy-namical systems. Recent advances in the field in-clude so-called semi-invertible and infinite-dimensionalresults, which have important consequences in ap-plications to the detection of coherent structures.In this talk, we present a streamlined and con-structive approach to infinite-dimensional METson Banach spaces, based on singular-value typedecompositions. We also discuss how this point ofview clarifies some connections between theoreti-cal and numerical aspects of the subject. This isjoint work with Anthony Quas.

8.7. Models of chaos in dimensions two and three

Andy Hammerlindl (Monash University)


Dr Andy Hammerlindl

I will talk about known models of chaotic dynam-ical systems in dimensions two and three and myown recent work related to the discovery of a newform of a chaotic three-dimensional system.

This is joint work with C. Bonatti, A. Gogolev,and R. Potrie.

8.8. Dynamic isoperimetry on weighted manifolds

Eric Kwok (University of New South Wales)


Mr Eric Kwok

Transport and mixing in dynamical systems areimportant mechanisms for many physical pro-cesses. We consider the detection of transportbarriers using a recently developed geometrictechnique [1]: the dynamic isoperimetric problem.Solutions to the dynamic isoperimetric problemare sets with persistently small boundary size rel-ative to interior volume, as the sets are evolvedby the dynamics. In the presence of small diffu-sion these sets have very low dispersion over finite-times because of their lasting small boundary size,and thus are natural candidates for coherent sets,bounded by transport barriers.

We construct a weighted dynamic Laplacian op-erator, and show corresponding results for a dy-namic Cheeger inequality and dynamic Federer-Fleming theorem.We can handle general nonlin-ear dynamics, and weighted versions of area andvolume. Finally, we formulate the connection be-tween the present geometrical approach to recentprobabilistic approaches to determining coherentsets using transfer operators.

[1] G. Froyland, ”Dynamic isoperimetry and thegeometry of Lagrangian coherent structures.”

8.9. Elliptic Asymptotic Behaviour of q-Painleve III

Qing Liu (University of Sydney)


Miss Elynor Liu

We examine the asymptotic behaviour of q-PainleveIII as q tends to 1, and show that to leading or-der, solutions can be expressed as Jacobi ellipticfunctions. As a step toward using this informationto gain insight to the corresponding q-Painleve IIILax pair, we perform a similar analysis for a sim-pler case, the continuous Painleve II Lax pair.

8.10. A shadowing-based inflation scheme forensemble data assimilation

Lewis Mitchell (The University of Adelaide)


Dr Lewis Mitchell

Data assimilation is the process by which informa-tion from observational data is used to improveinitial conditions for ensemble forecasts. Artifi-cial inflation of ensemble covariances is a commontechnique to prevent ensemble divergence and un-derestimation of forecast errors. This talk willdiscuss ensemble shadowing and a new applica-tion of shadowing techniques as a method of co-variance inflation in ensemble data assimilation.We will present results comparing the proposedshadowing inflation scheme with traditional co-variance inflation techniques in the context of alow-order nonlinear system exhibiting chaotic dy-namics analogous to the atmosphere.

8.11. Reliable computation of invariant measures:progress towards Ulam’s conjecture

Rua Murray (University of Canterbury)


Dr Rua Murray

Ulam’s conjecture is that physically relevant in-variant measures for a discrete time dynamicalsystem can be approximated by a (now familiar)Galerkin-type approximation scheme. Ulam sug-gested the scheme 1960, and it underpins the spec-tacular success (since the 1990s) of set-orientednumerical methods for determining interestingglobal structures in dynamical systems. However,proofs of convergence of the method are limitedto settings with very strong a priori control ofhyperbolicity. This talk will report some recentprogress by Chris Bose and myself on ”provingUlam’s method”. By casting as an L2 approxi-mation problem, we are able to identify Ulam’sscheme as a limit of a family regularised prob-lems, obtaining some convergence results withoutstrong assumptions on the underlying dynamics.

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8.12. A comprehensive method for constructingLax pairs of discrete Painleve equation:(A2 +A1)(1) case

Nobutaka Nakazono (University of Sydney)


Dr Nobutaka Nakazono

Construction of the Lax pairs of the ordinary dif-ference equations called discrete Painleve equa-tions from those of the partial difference equationscalled ABS equations via the periodic type reduc-tion are well investigated. In this talk we will shownew method to obtain the Lax pairs of discretePainleve equations from the integer lattice asso-ciated with ABS equation. This work has beendone in collaboration with Prof. Nalini Joshi.

8.13. Finding absolutely and relatively periodicorbits in the equal mass 3-body problem withvanishing angular momentum

Danya Rose (University of Sydney)


Mr Danya Rose

The equal-mass, zero-angular momentum casepresents the greatest number of discrete symme-tries and reversing symmetries of the 3-body prob-lem. These symmetries involve permutations ofindices, reflection in space, and reflection in time.We present a result that allows us to choose sym-metries in such a way as that imposing these sym-metries upon periodic trajectories in coordinatesthat reduce by translations and rotations, withsimultaneous regularisation of binary collisions,forces the trajectory to be either absolutely or rel-atively periodic when transformed back to phys-ical coordinates. The theorem is illustrated withmany periodic orbits found numerically, some ofwhich we believe are new.

8.14. Separable Lyapunov functions for monotonesystems

Bjorn Ruffer (The University of Newcastle)


Bjorn Ruffer

For monotone systems evolving on the positive or-thant of Rn+ two types of Lyapunov functions areconsidered: Sum- and max-separable Lyapunovfunctions. One can be written as a sum, theother as a maximum of functions of scalar argu-ments. Several constructive existence results forboth types are given. Notably, one constructionprovides a max-separable Lyapunov function thatis defined at least on an arbitrarily large compactset, based on little more than the knowledge aboutone trajectory. Another construction for a classof planar systems yields a global sum-separableLyapunov function, provided the right hand sidesatisfies a small-gain type condition. A number

of examples demonstrate these methods and shedlight on the relation between the shape of sublevelsets and the right hand side of the system equa-tion. Negative examples show that there are in-deed globally asymptotically stable systems thatdo not admit either type of Lyapunov function.

8.15. Polytopes, symmetries and discreteintegrable systems

Yang Shi (University of Sydney)


Dr Yang Shi

Symmetry plays a central role in the study of in-tegrable systems. In this work, we uncover therelations between different nonlinear discrete in-tegrable systems by exploiting the geometric andcombinatorial properties of the finite and affineWeyl groups.

The objects of fundamental interest here are thepolytopes (higher dimensional generalization ofpolygons in 2-dimension) associated with the sym-metry groups. We gave examples of relating somewell-known classes of discrete integrable systemssuch as the lattice modified KdV and discretePainleve equations.

8.16. Random walks on networks built fromdynamical systems

Michael Small (The University Of Western

Australia)


Prof Michael Small

We have previously described techniques to con-struct graphs from time series recorded from adeterministic dynamical system. Takes theoremensures that the time series can be reconstructedin a way that preserves the “interesting bit” ofthe dynamics of the dynamical system. By rep-resenting this as a network we provide a furtherabstraction and a useful way of characterising im-portant features of the dynamical system. We nowgo in the revers direction - by treating the graphas a model of a dynamical system we generate in-dependent realisations of that system.

8.17. On Lyapunov regularity for uniformlyhyperbolic systems

Luchezar Stoyanov (The University Of Western

Australia)


Prof Luchezar Stoyanov

A certain approach will be discussed for estimat-ing the sizes of Lyapunov regular neighbourhoodsof regular points for Anosov or Axiom A flows (ordiffeomorphisms). As a consequence one shouldget a better control over the distribution of theregular neighbourhoods.

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8.18. Butterfly catastrophe for fronts in athree-component reaction-diffusion system

Petrus van Heijster (Queensland University of

Technology)


Dr Petrus van Heijster

A paradigm for the occurrence of fronts are phaseseparation phenomena and Allen-Cahn type equa-tions provide the simplest model class. The cou-pling to further equations with scale-separationleads to a surprisingly rich class of singularly per-turbed problems that is amenable to analysis.

In this talk we showcase an analysis of a three-component model with two linear equations cou-pled to an Allen-Cahn equation with scale sepa-ration. Via a combination of geometric singularperturbation theory, Evans function analysis, andcenter manifold reduction, we show that the frontdynamics is organized by a butterfly catastrophethat leads to accelerating and direction reversingslow fronts. In addition, a more general resultconcerning the imbedding of arbitrary singulari-ties in such front bifurcations is shown.

This is joint work with Martina Chirilus-Bruckner,Arjen Doelman and Jens Rademacher.

8.19. Poisson Structures and Stability for EulerFluid Equations on a Toroidal Domain

Joachim Worthington (University of Sydney)


Mr Joachim Worthington

The 2D Euler Equations can be written on atoroidal domain as an infinite dimensional Hamil-tonian system. Zeitlin (1991) introduced a structure-preserving truncation for this problem in FourierSpace. In this setting, we study stationary solu-tions of the form α cos(mx+ny)+β sin(mx+ny).We begin by replicating the results of Li (2000)in this new setting, namely the splitting of thelinearised problem into classes, infinitely many ofwhich are stable. We also show that nearly all thestationary solutions described are unstable. Theusefulness of numerical and analytical usefullnessof Zeitlin’s truncation is also demonstrated. I willalso present the extension to the 3D case and thestability results in 3D.

8.20. Dimensional Characteristics of theNon-wandering Sets of Open Billiards

Paul Wright (The University Of Western Australia)


Dr Paul Wright

An open billiard is a dynamical system in whicha pointlike particle moves at constant speed in an

unbounded domain, reflecting off a boundary ac-cording to the classical laws of optics. The non-wandering set of an open billiard is the set ofbilliard trajectories that never escape to infinity.For three or more convex obstacles satisfying cer-tain conditions, this set has an interesting fractalstructure, being homeomorphic to a Cantor set.

In this talk we use Bowen’s equation and the vari-ational principle for topological pressure to in-vestigate the fractal structure of these systems,particularly the Hausdorff dimension of the non-wandering set. We show that, for billiards in theplane, the Hausdorff dimension depends smoothlyon smooth perturbations to the boundary of theobstacles. In higher dimensions, we show that thedimension satisfies some estimates.

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9.1. A combinatorial optimization game arisingfrom a components acquisition situation.

Imma Curiel (Anton de Kom University of

Suriname)


Dr Imma Curiel

We consider a situation in which several compa-nies can cooperate to reduce the costs of acquisi-tion of a particular component which is necessaryfor the operation of the companies. The use of thecomponent is time, space, and type dependent. Acomponent can be used by several companies aslong as their is no overlap in the time-intervals ofusage by different companies and there is enoughtime to move the component from where a com-pany has stopped using it to the where the nextcompany needs it. Examples are: Railway com-panies which need locomotives to pull trains, air-line companies which need crew teams to oper-ate flights, transportation companies which need afleet to meet transportation demands. By settingstarting point and ending point for all companiesto be one point this model also covers situations inwhich the component does not move like in the ex-ample of educational institutes which need class-rooms for teaching purposes. We model this situ-ation as a cooperative cost game < N, c >) whereN is the set of companies. The set of possiblestart and end points of usage of is denoted by V .The operations of the companies are periodic sowe consider the problem during one period. A pe-riod can be a day, a week, a month, or any otherduration of time. At the beginning of a periodtime starts at zero. The end time of a period isdenoted by T . There are L different types of thecomponent. The different types of the componentare denoted by 1, 2, . . . , L. With each type l of thecomponent a cost cl is associated. Each companyhas a schedule that indicates its need for the com-ponent during a period. By cooperating the com-panies can reduce the costs involved in fulfillingthe requirements of their schedule. The scheduleof a coalition S is the union of the schedule of allthe members of S. The cost c(S) of coalition Sis defined as the minimum cost required to satisfythe schedule of S. We show under what conditionsthis game is balanced and how to find a core el-ement. We discuss the computational complexityof finding a core element

9.2. Kookaburra vs. Concorde: Achilles andTortoise in TSP race.

Vladimir Ejov (Flinders University)


Dr Vladimir Ejov, Serguei Rossomakhine

Concorde and LKH programs deserve the reputa-tion as the best known TSP solvers. However, forsparse TSP problems, when finding any Hamiltoncycle (HC) is relatively difficult, they are not soeffective. It becomes important to generate many”unbiased” (in terms of the weight) Hamiltoniancycles and use those as initial tours for LKH orConcorde. Kookaburra is a new TSP heuristicthat initially constructs ”unbiased” HC and thenuses parallel LKH (or Concorde) as tour improve-ment algorithms. We demonstrate effect of thisapproach not only on TSP arising from difficultHCP instances, but also on well known Eucledian2d TSP from TSPLIB.

9.3. Ordered Field Property in DiscountedStochastic Games

Jerzy Filar (Flinders University)


Prof Jerzy Filar

Modern Game Theory dates back to von Neu-mann’s 1928 proof of the minimax theorem formatrix games and the 1944 seminal treatise “The-ory of Games and Economic Behavior” by vonNeumann and Morgenstern. Despite many ad-vances in Game Theory resulting from its subse-quent popularity, perturbation theory for dynamicand stochastic games is still in its infancy.

A fundamental issue pertinent to the developmentof such perturbation theory is the ordered fieldproperty (OFP) originally raised by Weyl whoproved that for matrix games the game value andextreme optimal strategies lie in the same closedordered field as data defining the game. Shapley’sremark in his seminal 1953 paper on StochasticGames pointing out that they lack that propertystimulated a line of research aimed at characteris-ing the largest subclass of these games possessingOFP.

In this presentation, without any assumptions onthe structure of the game, we show that the or-dered field property holds for Shapley’s stochasticgames over the field of algebraic real numbers.

9.4. Applying Continuous Optimisation Techniquesto Difficult Discrete Optimisation Problems

Michael Haythorpe (Flinders University)


Dr Michael Haythorpe

A wide variety of important, difficult problemscan be cast as discrete optimisation problems withlinear constraints. It has long been recognisedthat such problems can be further cast as (noncon-vex) continuous optimisation problems with linear

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constraints, by first relaxing the discrete require-ments, and then ensuring the global solution hasnot been altered through the use of appropriatepenalty functions or other such techniques. How-ever, in practice, standard continuous optimisa-tion algorithms usually perform quite poorly onproblems posed in this way.

In this talk, I consider one such relaxed formula-tion based on the Hamiltonian cycle problem, adiscrete NP-complete problem. I describe an al-gorithm which was specifically designed to takeadvantage of the features present in the formula-tion. I discuss some interesting features that arisewhich are likely to be present in all continuousformulations arising from relaxations of discreteoptimisation problems.

9.5. On the Detection of Non-Hamiltonicity viaLinear Feasibility Models

Asghar Moeini (Flinders University)


Mr Asghar Moeini

We analyse a polyhedron which contains the min-imal polyhedron that is the convex hull of allHamiltonian cycles of a given undirected con-nected cubic graph. Our constructed polyhedronis de

ned by polynomially-many linear constraints inpolynomially-many continuous variables. Clearly,the emptiness of the constructed polyhedron im-plies that the graph is non- Hamiltonian. How-ever, whenever a constructed polyhedron is non-empty, the result is inconclusive. Hence, the fol-lowing natural question arises: if we assume that anon-empty polyhedron implies Hamiltonicity, howfre- quently is this diagnosis incorrect? We com-pare our set of constraints to a set of constraintsde

ning previously published Base polytope. In par-ticular, for cubic graphs containing up to 18vertices, There exist 223 non- Hamiltonian non-bridge graphs that Base polytope failed to detecttheir non-Hamiltonicity. All these graphes aredetected by the our proposed set of constraints.These empirical results suggest that polynomialalgorithms based on our constructed polyhedronmay be able to correct identify Hamil- tonicity ofa cubic graphs.

9.6. Performance of Gradient-Based Nash SeekingAlgorithms Under Quantized Inter-AgentCommunications

Ehsan Nekouei (The University of Melbourne)


Dr Ehsan Nekouei

Nash equilibrium (NE) is one of the most impor-tant solution concepts in non-cooperative game

theory, in which multiple agents aim to maximizetheir individual utility functions. Gradient-basedequilibrium-seeking algorithms have been widelyused for finding the NE of games with continuousaction spaces and differentiable utility functions.In this talk, we focus on the impact of quantizedinter-agent communications on the asymptoticand transient behaviour of gradient-based Nashseeking algorithms in non-cooperative games. Us-ing the information-theoretic notion of entropypower, we establish a universal lower bound onthe asymptotic rate of exponential mean-squareconvergence, for all quantizers able to achieve NE.Next, we study transient performance and derivean upper bound on the average time required tosettle inside a specified ball around the NE underuniform quantization. We also establish an upperbound on the probability that agents actions lieoutside this ball, and show that this bound de-cays double-exponentially with time. Finally, wepropose an adaptive quantization scheme that en-ables agents to converge to the NE.

9.7. A multidimensional correlated square rootprocess

Jakub Tomczyk (University of Sydney)


Mr Jakub Tomczyk

The one-dimensional square root process was in-troduced by William Feller. It was proved to besuccessful in modelling stochastic interest ratesand stochastic volatility (CIR model and Hestonmodel) and is deeply connected to the norm ofmultidimensional Brownian motion. The multidi-mensional square root process with correlation in-troduced in the diffusion is a natural extension ofthe one-dimensional model. In this talk, we willpresent results involving basic properties of themultidimensional square root process, such as ex-istence and uniqueness of solution and of station-ary measure, and regularity of transition density.We will also address the special subclass which isanalytically tractable and describe possible simu-lation techniques.

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10.1. The computational hardness of normalsurfaces

Benjamin Burton (University of Queensland)


Dr Benjamin Burton

In knot theory and 3-manifold topology, normalsurface theory is a powerful toolkit that is usedin many algorithms as well as complexity results.An appealing variant is immersed normal surfacetheory, which offers the potential to reduce com-plex topological problems to simple linear pro-gramming problems. Here we show that this ap-proach has inherent limitations: it is NP-hard todecide whether a given set of coordinates (as foundthrough linear programming, for example) repre-sents an immersed normal surface or not.

This is joint work with ric Colin de Verdire andArnaud de Mesmay.

10.2. The combinatorics of tetrahedron indexratios

Norman Do (Monash University)


Dr Norman Do

The tetrahedron index assigns a q-series to a pairof integers and is the building block for the physi-cally motivated 3-manifold invariant known as the3D index. Garoufalidis observed empirically thata particular ratio of tetrahedron indices yields a q-series whose coefficients are positive integers. Wewill prove this statement by showing that theseintegers enumerate combinatorial objects.

10.3. New progress in the inverse problem in thecalculus of variations.

Thoan Thi Kim Do (La Trobe University)


Mrs Thoan Thi Kim Do, Prof. Geoff Prince

We present a new class of solutions for the inverseproblem in the calculus of variations in arbitrarydimension n. This is the problem of determiningthe existence and uniqueness of Lagrangians forsystems of n second order differential equations.We also provide a number of new theorems con-cerning the inverse problem using exterior differ-ential systems theory. Our new techniques pro-vide a significant advance in the understanding ofthe inverse problem in arbitrary dimension and,in particular, how to generalise Jesse Douglas’sfamous solution for n = 2. We give some non-trivial examples in dimensions 2,3 and 4. We givea new classification scheme for the inverse prob-lem in arbitrary dimension.

10.4. CAT (0) Semi-Cubings of Adequate links

Ana Dow (University of Melbourne)


Ms Ana Dow

In the special case of reduced adequate link dia-grams, the projection of the diagram onto its Tu-raev surface is alternating and the checker-boardspanning surfaces are essential. The subset ofthese link diagrams with zero genus Turaev sur-face have a canonical CAT(0) cubicle decomposi-tion. In this talk an algorithm generalising thisconstruction is presented and the implications forhow the pair of spanning surfaces are situated rel-ative to one another are considered.

10.5. Compact pseudo-Riemannian solvmanifolds

Wolfgang Globke (The University of Adelaide)

16:15 Mon 28 September 2015 – NTH1

Oliver Baues, Wolfgang Globke

A pseudo-Riemannian solvmanifold is a homoge-neous space M on which a connected solvable Liegroup G of isometries acts transitively and almosteffectively. We show that G acts almost freely onM and that the metric on M is induced by a bi-invariant pseudo-Riemannian metric on G. Fur-thermore, we show that the identity component ofthe isometry group of M coincides with G. Thisis joint work with Oliver Baues.

10.6. The 3D index and normal surfaces

Craig Hodgson (University of Melbourne)


Dr Craig Hodgson

The 3D index of an ideal triangulation T of anorientable cusped 3-manifold M is a collection ofq-series with integer coefficients introduced by thephysicists Dimofte, Gaiotto and Gukov. We showhow to write the 3D index as a sum over certainnormal surfaces, and deduce that the summationconverges if and only if the triangulation T is 1-efficient. We also discuss the behaviour of theindex under 2-3 and 0-2 moves on a triangulation,and conclude that the 3D index gives a topologicalinvariant if the manifold M is hyperbolic. (Thistalk includes joint work with Garoulfalidis, Hoff-man, Rubinstein and Segerman.)

10.7. Geometry of planar surfaces and exceptionalfillings

Neil Hoffman (The University of Melbourne)


Dr Neil Hoffman

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If a hyperbolic 3-manifold admits an exceptionalDehn filling, then the length of the slope of thatDehn filling is known to be at most six. However,the bound of six appears to be sharp only in thetoroidal case. This talk will discuss bounds forthe other types of exceptional fillings, including aconstruction hyperbolic 3-manifolds that have thelongest known slopes for reducible fillings. This isjoint work with Jessica Purcell.

10.8. Hyperbolicity For Weakly GeneralisedAlternating Knots

Joshua Howie (University of Melbourne)


Mr Joshua Howie

Thurston showed that non-trivial knots can bepartitioned into three classes: hyperbolic, satelliteor torus. From an alternating planar diagram, itis easy to decide when such a diagram representsa hyperbolic knot. Partial results are also knownfor toroidally alternating knots.

We define weakly generalised alternating knots,which are a class of knots with alternating pro-jections onto closed orientable surfaces, and showthat in many cases it is possible to decide whensuch a diagram represents a hyperbolic knot.

10.9. Oka theory of affine toric varieties

Finnur Larusson (The University of Adelaide)


Dr Finnur Larusson

A complex manifold Y is said to have the interpo-lation property if a holomorphic map to Y froma subvariety S of a reduced Stein space X has aholomorphic extension to X if it has a continuousextension. Taking S to be a contractible subman-ifold of X = Cn gives an ostensibly much weakerproperty called the convex interpolation property.By a deep theorem of Forstneric, the two prop-erties are equivalent. They (and about a dozenother nontrivially equivalent properties) define theclass of Oka manifolds.

In recent joint work, Richard Larkang and I makethe first attempt to develop Oka theory for singu-lar targets. The targets that we study are affinetoric varieties, not necessarily normal. We provethat every affine toric variety satisfies a weak-ening of the interpolation property that is muchstronger than the convex interpolation property,but the full interpolation property fails for mostaffine toric varieties, even for a source as simpleas the product of two annuli embedded in C4.

10.10. Morse Structures on Open Books

Joan Licata (Australian National University)


Dr Joan Licata

Open book decompositions of three-manifolds areboth a classical object in low-dimensional topol-ogy and an important contemporary tool in con-tact geometry. I’ll describe joint work with DaveGay introducing the notion of a Morse structureon an open book, a combinatorial description ofany (contact) three-manifold as a compactifica-tion of a collection of open solid tori. This newstructure allows us to define front projectionsfor Legendrian knots in arbitrary closed contactthree-manifolds.

10.11. Globally hyperbolic spacetimes with parallelnull vector and related Riemannian flow equations

Andree Lischewski (The University of Adelaide)


Andree Lischewski

The existence of a parallel null vector field on aLorentzian manifold imposes constraints on anyspacelike hypersurface. Starting with these con-straint equations, we derive suitable hyperbolicevolution equations whose solutions yield globallyhyperbolic Lorentzian manifolds with parallel nullvector field. We then show how further propertiesof the holonomy group of Lorentzian manifoldsconstructed in this way are equivalently encodedin terms of flow equations for Riemannian metricswith special holonomy on the initial hypersurface.

10.12. Counting curves on surfaces

Daniel Mathews (Monash University)


Dr Daniel Mathews

The counting of curves is an important part ofcontemporary mathematics. Often such countingrefers to moduli spaces of curves, leading to con-nections with mathematical physics through tech-nology such as topological recursion. It turns outthat if we simply count curves — in the everydaysense of embedded arcs — on surfaces, much of thesame structure appears. Results on the combina-torics of curves give concrete topological exam-ples of structures at the frontiers of mathematicalphysics. Many of these results have statementsand proofs which could have been found over acentury ago, but so far as we know, they are new.

10.13. Differential invariants of ODEs systems ofhigher order

Alexandr Medvedev (University of New England)


Dr Alexandr Medvedev

We study Cartan geometries associated with sys-tems of ordinary differential equations of order≥ 4 under the group of point transformations.Our main object of interest is relative differentialinvariants of these ODEs systems. We found a

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minimal generating set (via operation of invariantdifferentiation) of relative differential invariants,which we call fundamental invariants.

It turns out that starting from systems of order(k + 1) ≥ 4, the complete set of fundamental in-variants is formed by k generalized Wilczynski in-variants coming from the linearized system and anadditional invariant of degree 2.

10.14. Thrackles

Grace Omollo Misereh (La Trobe University)


Ms Grace Omollo Misereh

Conway’s Thrackle Conjecture is the most famousopen problem in graph drawing. This problemwas posed by John H. Conway (Princeton) in thelate sixties. Surprising little progress has beenmade on this problem, but there has been a seriesof recent papers on the problem by two groups:Janos Pach (EPFL Lausanne) and his coworkerson one hand, and Cairns and Nikolayevsky (LaTrobe) on the other. If proved to be true, Con-way’s thrackle conjecture could shed more lightin other areas of graph drawings. In this talk wepresent necessary and sufficient conditions for afinite simple graph to have a thrackle representa-tion on the plane using the ideas given by D.R.Woodall on his paper ’Thrackles and deadlock’.

10.15. Equivariant bundle gerbes

Michael Murray (The University of Adelaide)


Prof Michael Murray

I will present the definitions of strong and weakgroup actions on a bundle gerbe and calculatethe strongly equivariant class of the basic bundlegerbe on a unitary group. This is joint work withDavid Roberts, Danny Stevenson and RaymondVozzo and forms part of arXiv:1506.07931.

10.16. Solvable Lie groups of negative Riccicurvature

Yuri Nikolayevsky (La Trobe University)


Dr Yuri Nikolayevsky

The question of which homogeneous manifolds ad-mit a left-invariant metric with the given sign ofthe curvature is well understood for the sectionalcurvature and also for the positive and zero Riccicurvature. The case of negative Ricci curvatureis wide open (semisimple examples constructed inthe 80’s). Our main question is the characteri-sation of (nonunimodular) solvable Lie groups ad-mitting a left-invariant metric with Ric ¡ 0. We an-swer this question for solvable Lie algebras whosenilradical is either abelian, or Heisenberg, or fili-form. All the answers have the same flavour: there

exists a vector Y such that real parts of the restric-tion of ad(Y) to the nilradical satisfy certain linearinequalities (which depend on the particular nil-radical). Whether or not this can be generalisedto all nilradicals is an open question.

This is a joint ongoing project with Yurii Nikonorov.

10.17. Lower and upper bound theorems foralmost simplicial polytopes

Guillermo Pineda-Villavicencio (Federation

University Australia)


Dr Guillermo Pineda-Villavicencio

What is the largest number of facets, ridges,...,edgesof a simplicial d-polytope with a given num-ber of vertices? A simplicial d-polytope is apolytope in which every facet is a (d-1)-simplex.In 1970 McMullen answered the aforementionedquestion. The result is known as the Upper Boundtheorem for simplicial polytopes. Equally, wecan ask: what is the smallest number of facets,ridges,...,edges of such a polytope with a given thenumber of vertices. Between 1971 and 1973 Bar-nette answered the latter question, proving theLower Bound theorem for simplicial polytopes.Both results are considered major achievementsin the combinatorial theory of polytopes. BothMcMullen and Barnette also characterised the ex-treme polytopes.

In this talk we consider almost simplicial poly-topes, that is, polytopes in which every facet, withat most one exception, is a simplex. This notiongeneralises the notion of simplicial polytopes. Weprove lower and upper bounds theorems and char-acterise the extreme cases.

This is a joint work with Eran Nevo (HebrewUniversity of Jerusalem), Julien Ugon (FederationUniversity Australia) and David Yost (FederationUniversity Australia).

10.18. Torsion and the second fundamental formfor distributions

Geoffrey Prince (Australian Mathematical Sciences

Institute)


Prof Geoffrey Prince

While the torsion of a linear connection is intrin-sically defined it is natural to ask if it is the skewpart of some intrinsic bilinear form.

In this talk the second fundamental form of Rie-mannian geometry is generalised to the case ofa manifold with a linear connection and an inte-grable distribution. This bilinear form is generallynot symmetric and its skew part is the torsion ofthe connection. The bilinear form itself is closelyrelated to the shape map of the connection. Therelationship to principal curvatures is explored.

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10.19. The prescribed Ricci curvature problem onhomogeneous spaces

Artem Pulemotov (The University of Queensland)


Dr Artem Pulemotov

We will discuss the problem of recovering the Rie-mannian metric on a compact homogeneous spacefrom its Ricci curvature.

10.20. Geometry of confocal quadrics inpseudo-Euclidean space

Milena Radnovic (University of Sydney)


Dr Milena Radnovic

We study confocal families of quadrics in pseudo-Euclidean spaces of arbitrary dimension and anysignature. A new discrete combinatorial-geometricstructure associated to a confocal pencil of quadricsis introduced, by which we decompose quadrics ofd+1 geometric types of a pencil into new relativis-tic quadrics of d relativistic types. Deep insightof related geometry and combinatorics comes fromdiscriminant sets of tropical lines and their singu-larities.

10.21. Homogeneous String connections

David Roberts (The University of Adelaide)


Dr David Roberts

Higher gauge theory has inspired the theory ofString bundles, or more generally 2-bundles, whichfor suitable choices of manifold and 2-group shouldform the background geometry for heterotic stringtheories. Examples with enough detail for geomet-ric or even analytic calculations have been hard tocome by, but in the case of homogeneous geometryone can give explicit Lie groupoids that give thehigher bundle structure. The next step is clearlyto find String connections on such higher bun-dles. This talk will present the theory of homo-geneous 2-connections and give examples of geo-metric String structures on homogeneous spaces.These are one of several equivalent ways to presentthe data of String connections. This is joint workwith Raymond Vozzo.

10.22. Subriemannian linearized metrizability

Jan Slovak (Masaryk University)


Prof Jan Slovak

Recently, the classical linearized metrizability hasbeen understood for a large class of parabolic ge-ometries. This leads to the quest for subrieman-nian metric partial connections within the class ofthe Weyl structures on a given parabolic geome-try. I will explain the general setup and illustratethe procedure on some explicit example. The talk

will reflect work in progress, joint with David M.J.Calderbank and Vladimir Soucek.

10.23. Collapsibility and 3-sphere recognition

Jonathan Spreer (University of Queensland)


Dr Jonathan Spreer

The problem of recognising the 3-sphere is be-lieved to be solvable in polynomial time. In con-trast to that most approaches to solve this prob-lem seem to be computationally difficult. One ofthese is the framework of collapsibility which facesnot one, but two fundamental difficulties. On theone hand, deciding whether a triangulation is col-lapsible (a certificate for being a 3-ball) is believedto be computationally hard. On the other handthere are 3-ball triangulations which are not col-lapsible at all. However, collapsibility is extremelyefficient in recognising 3-balls (and thus 3-spheres)heuristically. In this talk I will present a num-ber of experiments targeted at understanding thiscounter-intuitive nature of collapsibility. In par-ticular I will a) present a method to estimate howdifficult it is to collapse a given 3-ball triangula-tion, b) construct “difficult” 3-ball triangulations,and c) investigate how common such “difficult”triangulations are using the census of all 3-spheretriangulations of up to ten vertices.

10.24. String structures on homogeneous spaces

Raymond Vozzo (The University of Adelaide)


Dr Raymond Vozzo

In many areas of geometry and physics we requirethat the spaces we work with carry a spin struc-ture, that is a lift of the structure group of the tan-gent bundle from SO(n) to its simply connectedcover Spin(n). In string theory and in higher ge-ometry the analogue is to ask for a string struc-ture; this is a further lift of the structure groupto the 3-connected group String(n). These struc-tures can be described in terms of bundle gerbes(which are the abelian objects in higher geometryasort of categorification of a line bundle). Unfortu-nately, explicit examples are lacking. In this talkI will explain how all this works and give some ex-amples of such structures. This is joint work withDavid Roberts.

10.25. Curve diffusion flow with free boundary

Glen Wheeler (University of Wollongong)


Dr Glen Wheeler

In this talk we discuss some new results for thecurve diffusion flow with free boundary supportedon lines.

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10.26. Mean curvature flow over almost Fuschianmanifold

Zhou Zhang (University of Sydney)


Dr Zhou Zhang

We study mean curvature flow in the non-Euclideansetting. More specifically, the ambient mani-fold is almost Fuschian, which is one kind ofwarped geometry with great interest in both low-dimensional topology and differential geometry.The surface of evolution under consideration isa graph. General discussion is provided at thebeginning, and then we restrict ourselves to thecase of Fuschian manifold where the understand-ing is more complete with fairly satisfying nec-essary condition for smooth convergence to theminimal surface. The result might be useful toconstruct intriguing example of finite time singu-larity for mean curvature flow. This is an ongo-ing joint work with Zheng Huang (CUNY) andLongzhi Lin(UCSC).

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11.1. Dispersive estimates for the wave equationsin R3

Anh Bui (Macquarie University)


Dr Anh Bui

Let L = −∆ + V be a Schrodinger operator inR3 with a potential V belonging to certain Katoclasses. The main aim of this paper is to provedispersive L∞ decay estimates for a 3-dimensionalwave equation related to L. This is joint workwith X. Duong and Y. Hong.

11.2. Singular Solutions to Weighted DivergenceForm Equations

Ting-Ying Chang (University of Sydney)


Ting-Ying Chang

We study problems associated with the weighteddivergence operator

div(A(|x|)|∇u(x)|p−2∇u(x))

and fully classify solutions u(x) with isolated sin-gularities in the punctured unit ball. We showhow the usual trichotomous classification changeswith respect to what the operator is equal to. Wediscuss ongoing research related to the problemand how the weight A affects the results of thep-Laplacian operator (when A = 1) which has al-ready been studied extensively in the literature.

11.3. Classification of isolated singularities forelliptic equations with Hardy-type potentials

Florica Corina Cirstea (School of Mathematics and

Statistics, University of Sydney)


Florica Corina Cirstea and Mihai Mihailescu

In this talk, we consider a class of elliptic equa-tions in the unit ball of RN punctured at zero.We establish the existence and asymptotic profilenear zero of all positive solutions with a suitableDirichlet boundary condition on the unit sphere.In this classification, we reveal the critical roleplayed by the operator, which may contain moregeneral potentials than the Hardy-type ones. Thisis joint work with Mihai Mihailescu (University ofCraiova).

11.4. Factorization for Hardy spaces andcharacterization for BMO spaces via commutatorsin the Bessel setting.

Xuan Duong (Macquarie University)


Prof Xuan Duong

Fix λ > 0. Consider the Bessel operators

4λ := − d2

dx2 − 2λx

ddx .Also consider the Hardy

space H1(R+, dmλ) in the sense of Coifman andWeiss, where dmλ := x2λdx with dx the Lebesguemeasure. The Hardy space H1

∆λassociated with

∆λ is defined via the Riesz transform R∆λ:=

∂x(∆λ)−1/2. It is known thatH1∆λ

andH1(R+, dmλ)coincide. We will prove a weak factorization ofH1(R+, dmλ) by using a bilinear form of the Riesztransform R∆λ and the characterization of theBMO space associated to ∆λ via the commuta-tors related to R∆λ

. This is joint work with Ji Li,Brett Wick and Dongyong Yang.

11.5. Hardy Spaces and Paley-Wiener Spaces forClifford-valued functions

David Franklin (The University of Newcastle)


Mr David Franklin

The Hardy and Paley-Wiener Spaces are defineddue to important structural theorems relating thesupport of a function’s Fourier transform to thegrowth rate of the analytic extension of a function.In this talk we show that analogues of these spacesexist for Clifford-valued functions in n dimensions,using the Clifford-Fourier Transform of Brackx etal and the monogenic (n+1 dimensional) exten-sion of these functions.

11.6. Inclusion Bounds and EigenfunctionLocalisation

Sean Gomes (Australian National University)


Mr Sean Gomes

Suppose D is a sufficiently smooth compact do-main in Rn.

It is intuitive that if (u,E) is an eigenpair of theLaplacian on D with small Dirichlet boundarydata, then E should be close to a Dirichlet eigen-value. Moreover, we expect that u should be closeto a corresponding Dirichlet eigenmode.

11.7. Special Solutions of the Painleve Equations

James Gregory (University of Sydney)


Mr James Gregory

The Painleve equations have been a constantsource of wonder and intrigue since their discoveryin the early 20th century. Despite their transcen-dental solutions, mathematicians have uncovereda wealth of information regarding these solutions’nature. We will introduce the Painleve equations,as well as the phenomena of rational special so-lutions, using the continuous Painleve II equation

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and the q-discrete Painleve III equation as exam-ples.

11.8. Scattering for the Zakharov system

Zihua Guo (Monash University)

15:15 Thu 1 October 2015 – SSN008

Zihua Guo, I. Bejenaru, S. Herr, S. Lee, K.

Nakanishi. C. Wang, S. Wang

I will talk about our recent results on the scat-tering problem for the Zakharov system in threeand four dimensions. The Zakharov system is animportant model in mathematical physics and hasbeen extensively studied, e.g. on the low regular-ity well-posedness. In 3D, global well-posednesswith small data in the energy space was proved byBourgain and Colliander in 1996, however, little isknown about the asymptotic behavior of the solu-tion due to the quadratic interactions. Recently,we obtain various results towards this problem. In4D, we prove global well-posedness and scatteringfor small data in the energy space.

11.9. Completeness of boundary traces of Dirichletand Neumann eigenfunctions

Xiaolong Han (Australian National University)


Dr Xiaolong Han

It is well-known that there exists an orthonormalbasis of Laplacian eigenfunctions in a smooth do-main, we show that the boundary traces (definedas the normal derivatives of Dirichlet eigenfunc-tions and boundary values of Neumann eigenfunc-tions) are aymptotically complete on the bound-ary. Then we give a microlocal interpretationand semiclassical generalization of such phenom-ena. This is a joint work with Hassell, Hezari, andZelditch.

11.10. Estimates on boundary values of Neumanneigenfunctions

Andrew Hassell (Australian National University)


Prof Andrew Hassell

This is joint work with Alex Barnett and MelissaTacy. We show how to obtain comparable up-per and lower bounds on the L2 norms of bound-ary values of Neumann eigenfunctions on a Eu-clidean domain with smooth boundary. This isless straightforward than the corresponding prob-lem for Dirichlet eigenfunctions, because in theNeumann case, one needs to apply an appropriate‘spectral weight’ to the boundary value in order toattain comparability between the upper and lowerbounds.

11.11. A simplified approach to the regularisingeffect of nonlinear semigroups

Daniel Hauer (University of Sydney)

14:50 Thu 1 October 2015 – SSN008

Dr Daniel Hauer

Since the beginning of the 21st century, there ap-peared a huge flow of papers written on the regu-larising effect of nonlinear semigroups. Most au-thors of these papers follow the same approach:As a first step, a one parameter family of Log-Sobolev inequalities is derived from a knownSobolev inequality. Then by using this familyof Log-Sobolev inequalities, one shows that thefunction t 7→ ||Tt||r(t) satisfies a differential in-equality which is strong enough to conclude anLp-Lq-regularisation of the trajectories t 7→ Ttϕof the given semigroup Tt. In this talk, wepresent a simplified approach to this regularity ef-fect without constructing a one-parameter familyof Sobolev-type inequalities. Instead, our methodis based on a new nonlinear interpolation theoremwhich is of independed interest. We illustrate thestrength of new method on varous examples as,for instance, the semigroup generated by the totalvariational flow or Dirichlet-to-Neumann operatroassociated with the p-Laplace operator.

11.12. Multiple solutions to the Lp-Minkowskiproblem

Qirui Li (Australian National University)

15:40 Thu 1 October 2015 – SSN008

Yan He, Qirui Li, Xujia Wang

In this talk I will present a multiplicity resultfor the Lp-Minkowski problem when p < −n. Iwill show that for any integer N > 0 there ex-ists a smooth positive function f on Sn such thatthe Lp-Minkowski problem admits at least N dif-ferent smooth solutions. I will also construct anonsmooth, positive function f for which the Lp-Minkowski problem has infinitely many C1,1 so-lutions. This is a joint work with Yan He andXu-Jia Wang.

11.13. Asymptotics of a q-Airy equation

Steven Luu (School of Mathematics and Statistics,

University of Sydney)


Mr Steven Luu

We will investigate how we can study the be-haviour of linear q-difference equations when theindependent variable is large (or small). In par-ticular, we will show how this method works ona q-Airy equation and compare the results we ob-tain to the literature.

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11.14. Asymptotics of solutions to the discretePainleve equation q-P (A∗1) which are holomorphicat the origin

Pieter Roffelsen (University of Sydney)


Mr Pieter Roffelsen

All meromorphic solutions to the continuous Painleveequations which are of Briot-Bouquet type at oneof the fixed singularities of the equation have beenclassified by Kaneko and Ohyama. Similarly onecan classify all the solutions to the q-P (A∗1) equa-tion, meromorphic at the origin, using a q-discreteanalogue of the celebrated Briot-Bouquet Theo-rem. We discuss these special Painleve transcen-dents in detail, with a special interest in theirasymptotics. As it turns out, these asymptoticsare part of a large family of true solutions to theq-P (A∗1) equation, both around the origin and in-finity. We discuss the corresponding connectionproblem, as explicit connection formulae for con-tinuous Painleve equations have proven to be verypowerful in physical applications.

11.15. Regularity of bounded weak solutions to anEuler-Lagrange system in the critical dimension.

Nirav Arunkumar Shah (The University of

Queensland)


Nirav Shah

In this talk we will consider bounded weak solu-tions to the following vector-valued Euler-Lagrangesystem:

(1) − div(A(x, u)Du

)= g in Ω

for Ω a bounded open domain in R2. Underquite mild assumptions on the principal part,A(x, u)Du, and inhomogeneous part, g, we willshow that every bounded weak solution of (1) isHolder continuous. Since the dimension of Ω is2 we are in the critical setting, and hence, can-not use the Sobolev embedding theorem to deduceHolder continuity. This result resolves a conjec-ture by Beck and Frehse (2013).

11.16. Spectral multipliers, Bochner-Riesz meansand uniform Sobolev inequalities for ellipticoperators

Adam Sikora (Macquarie University)


Dr Adam Sikora

I will discuss Lp to Lq bounds for spectral multi-pliers, the uniform Sobolev estimates and Bochner-Riesz means with negative index in the generalsetting of abstract self-adjoint operators.

11.17. Quantised dynamical observables andconcentration of eigenfunctions

Melissa Tacy (The University of Adelaide)


Dr Melissa Tacy

The quantum-classical correspondence principleleads us to expect that high energy stationarystates (eigenfunctions of the Hamiltonian) shoulddisplay echoes of classical behaviour. One wayto understand this is to view the problem withinthe semiclassical framework and study quantisedversions of dynamical observables such as veloc-ity, acceleration and jerk. In this talk I will dis-cuss some concentration (and non-concentration)results and link them to the dynamics of analo-gous classical systems.

11.18. Uniform temporal stability of solutions todoubly degenerate parabolic equations.

Kyle Talbot (Monash University)


Jerome Droniou, Robert Eymard and Kyle Talbot

Consider the doubly nonlinear parabolic initial-boundary value problem(P)∂tβ(u)− div(a(x, ν(u),∇ζ(u))) = f in Ω× (0, T ),

β(u)(x, 0) = β(uini)(x) in Ω,

ζ(u) = 0 on ∂Ω× (0, T )

on a bounded open set Ω ⊂ Rd. The func-tions β and ζ are Lipschitz continuous, nonde-creasing and ν satisfies ν′ = β′ζ ′. The Leray-Lions operator −div(a(x, s, ·)) acts on W 1,p

0 (Ω),and uini ∈ L2(Ω). Instances of (P) arise in ground-water flow modelling, phase transitions and non-Newtonian filtration. I will sketch a proof thatthe quantity ν(u) — which depending upon thecontext may represent a saturation, temperatureor velocity — exhibits uniform temporal stabil-ity to perturbations of the data (β, ζ, ν, a, f, uini).This is particularly relevant in applications, whereone may have only approximate knowledge of thedata and one is interested in the value of ν(u) at aparticular instant in time. The proof relies uponmonotonicity arguments, compensated compact-ness, and the connection between ν(u) and an un-derlying convex structure that emerges naturallyfrom energy estimates on the solution.

This is joint work with my advisor Jerome Dro-niou (Monash University) and Robert Eymard(Universite Paris-Est Marne-la-Vallee).

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11.19. On Truncated Solutions of The FourthPainlev Equation

Michael Twiton (School of Mathematics and

Statistics, University of Sydney)


Mr Michael Twiton

In Boutroux’s 1913 paper, solutions of the firstPainlev equation are specified with the propertythat they have no poles of large modulus exceptthose located in a sector of angle 2π/5. The rea-son for the pole-freeness is the leading asymptotic

behaviour(x6

)1/2for these solutions. In a paper

by N. Joshi and A. V. Kitaev this asymptotic be-haviour of the solutions is pulled back to the finitedomain, which allows one to determine, say, thelocations of the zero and pole of the solutions,which are closest to the origin.

In this talk, we will discuss similar results for thefourth Painlev equation.

11.20. Polyharmonic curvature flow

Glen Wheeler (University of Wollongong)


Dr Glen Wheeler

In this talk we discuss progress on curvature flowof arbitrary order of surfaces.

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12.1. Traveling Salesman Problem Approach forSolving DNA Sequencing Problems

Pouya Baniasadi (Flinders University)


Mr Pouya Baniasadi

The ground-breaking discovery of DNA structurein the 1950s opened up an unparalleled oppor-tunity for multidisciplinary efforts, such as themulti-billion dollar Human Genome Project, tocome together in a quest for understanding ”life”.Mathematics has proved to be vital in many suchefforts, specifically the DNA Sequencing Problem;aligning and merging fragments of DNA to con-struct the original sequence.

The importance and mathematical beauty in theDNA-Sequencing Problem stem from its close tiesto fundamental problems in Combinatorial Opti-mization and Complexity Theory. In particular,the basic idealized DNA-sequencing Problem canbe easily embedded in a Traveling Salesman Prob-lem (TSP) which, arguably, is the most widelystudied problem in combinatorial optimizationthanks to its theoretical importance and its widerange of applications. While the close relation-ship between the two problems is under-exploiteddue to the computational difficulty of TSP, re-cent advances in the quality of TSP heuristic al-gorithms provide a compelling opportunity for anew approach to DNA-Sequencing Problem. Ourproject is aimed at exploring this opportunity fordeveloping TSP-based models and algorithms toadvance our mathematical understanding of theDNA-Sequencing Problem as well as offering prac-tical solutions to the DNA-sequencing Problem.

12.2. An algebraic approach to determine aminimal weighted inversion distance

Sangeeta Bhatia (University of Western Sydney)


Ms Sangeeta Bhatia

Inversion is an important chromosomal rearrange-ment event and inversion distance is a popularmetric for constructing phylogenies. A standardapproach to this problem is to place no constrainton the set of inversions that can be used to ”sort”an arrangement of genes. That is, any inversionthat can happen, will happen and will be used byalgorithms.

The biological evidence on the other hand suggeststhat the frequency of the inversion of a chromo-somal segment may depend on its length. Shorterinversions are observed to happen more frequentlythan longer ones.

In this context, a lot of work is being done on find-ing weighted inversion distances. In this talk, I’llshare a new approach of determining a weighteddistance, which in algebraic terms translates sim-ply to finding a path on weighted Cayley graph.

12.3. How do we quantify the filamentous growthin a yeast colony?

Benjamin Binder (The University of Adelaide)


Dr Benjamin Binder

In nutrient-depleted environments, it is commonlyobserved that strains of the yeast Saccharomycescerevisiae forage by the mechanism of filamentousgrowth. How do we quantify this spatial pattern-ing of outward growth from a yeast colony? Pre-vious studies have primarily relied on measuringthe amount of filamentous growth, but do not takeinto account the spatial distribution of this highlynon-uniform process. In this talk, we fill this voidby providing a statistical approach that enablesthe quantification of this important spatial infor-mation, enabling a more detailed mathematicalanalysis of the filamentous growth process.

12.4. Modelling the transition from uni- tomulti-cellular life

Andrew Black (The University of Adelaide)


Dr Andrew Black

The transition from uni-cellular life to multi-cellular is one of the best known examples of theemergence of a new level of biological organisa-tion. To understand how this transition proceededwe need to know how early groups of cells cameto have the properties needed for Darwinian evo-lution, i.e. groups must possess some form of re-production with heritable variations in fitness. Inthis talk I will present some recent work towardsmodelling the very early stages of this transitionand the emergence of crude forms of group levelreproduction in a system in which groups can formwhen individual cells remain attached to their par-ents after reproduction.

12.5. Bulk and surface balance during tissuemodelling and remodelling

Pascal R Buenzli (Monash University)

16:05 Thu 1 October 2015 – SSN102

Dr Pascal R Buenzli

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Several biological tissues undergo changes both intheir geometry and in their bulk material prop-erties due to modelling processes (tissue genera-tion/destruction) and remodelling processes (tis-sue renewal). These processes may suddenly andlocally erase slowly maturing properties of the tis-sue and overwrite them with immature content(newly formed tissue). This is particularly ap-parent in bone tissues, which as a result, havean evolving microarchitecture and exhibit mineral”patches”, i.e., adjacent regions containing vari-ous concentrations of minerals and various degreesof maturity of embedded cells.

In this contribution, generalised equations govern-ing the evolution of such tissues are developed.These equations take into account nonconserva-tive, discontinuous surface mass balance due tocreation and destruction of material at moving in-terfaces, and bulk balance due to tissue matura-tion. Numerical simulations exemplify how theseequations make it possible to model patchy tis-sue states and their evolution without explicitlymaintaining a record of when/where resorptionand formation processes occurred. This formalismalso enables the systematic derivation of equationsgoverning the temporal evolution of spatial aver-ages of tissue properties. Such spatially-averagedequations cannot be written in closed form as theyretain traces that tissue creation and destructionis localised at the tissue interface.

12.6. Modelling at the Limits of Resolution: SingleMolecule Fluorescence and Protein-Protein Binding

Adelle Coster (University of New South Wales)


Dr Adelle Coster

The actin cytoskeleton plays a critical role inmost cellular processes including determination ofcell shape, cell adhesion and migration, cytoki-nesis, membrane function and intracellular trans-port. This functional specialisation is associatedwith differences in intracellular localisation, fila-ment organisation, dynamics and interaction withactin-binding proteins.

Microfluidic devices for rapid solution exchangehave been integrated with imaging systems ofhigh temporal and spatial resolution to take re-constituted systems from the single-filament tothe single-molecule level. However, this also re-quires the development of automated image anal-ysis methods to identify different behaviours, ex-tract kinetic parameters and determine associa-tion constants in an unbiased fashion, and informthe mathematical models for the function of theactin cytoskeleton.

Here a model of the interaction of tropomyosinand actin is developed, considering the bindingprocesses along two independent one-dimensional

lattices. Simulation studies of the ideal systemare compared with experimental results, and theimplications for the theories of actin decorationdiscussed.

12.7. What is the optimal length of HIVRemission?

Deborah Cromer (University of New South Wales)


Dr Deborah Cromer, Prof Miles P. Davenport

Advances in HIV therapies mean that by tak-ing combination antiretroviral drugs patients cannow control their viral load to below detectablelevels and reduce viral transmission. Howevertheir virus is by no means cured, since as soonas treatment is halted the virus rebounds to pre-treatment levels. Recent work has focused on re-moving of the latent pool of HIV, which is thoughtto be the cause of viral re-activation. These newdrugs, termed latency reversing agents (LRAs)are both highly toxic and not completely effec-tive. Though curing HIV using this method doesnot yet seem a possibility, the current target isto reduce the latent reservoir to a sufficient levelso that patients can be put into HIV remission.We have modeled the number of treatments thatwould be required for each patient to achieve dif-ferent lengths of HIV remission and determinedthe optimal length of viral remission to minimizethe overall number of treatments a patient wouldhave to endure. We assume that patients re-awaken from latency at an exponential rate that isdependent on the size of their latent pool. We alsoincorporate a natural decay in the latent reservoirwhich occurs over a much longer time scale thanreactivation. The results of our modelling willhave implications for designing optimal latency re-versing agents.

12.8. Wound healing angiogenesis: The clinicalimplications of a simple mathematical model

Jennifer Flegg (Monash University)


Dr Jennifer Flegg

Nonhealing wounds are a major burden for healthcare systems worldwide. In addition, a patientwho suffers from this type of wound usually has areduced quality of life. While the wound healingprocess is undoubtedly complex, in this talk, Illdiscuss a deterministic mathematical model, for-mulated as a system of partial differential equa-tions, that focuses on an important aspect of suc-cessful healing: oxygen supply to the wound bedby a combination of diffusion from the surround-ing unwounded tissue and delivery from newlyformed blood vessels. The model equations aresolved numerically, and asymptotic methods usedto establish conditions under which new blood

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vessel growth can be initiated and wound-bedangiogenesis can progress. These conditions aregiven in terms of key model parameters includingthe rate of oxygen supply and its rate of consump-tion in the wound. The implications of the modelon chronic wound treatments such as hyperbaricoxygen therapy and revascularisation therapy arediscussed.

12.9. Simulation of reaction-diffusion processes incellular biology

Mark Flegg (Monash University)


Dr Mark Flegg

One of the ‘Grand challenges’ in computational bi-ology for the 21st century is to develop a computa-tional model of a human cell. This is such a monu-mental challenge because the stochastic nature ofcellular behaviour forces any whole cell simulationto consider discrete/noisy molecular populationsthat may have an impact from anywhere on themolecular scale to the cellular scale. I will be talk-ing about a variety of thought provoking mathe-matical techniques that have been developed inpursuit of this grand challenge.

12.10. Mathematical modelling of oncolyticvirotherapy and immunotherapy using deterministicand stochastic models

Adrianne Jenner (University of Sydney)


Ms Adrianne Lena Jenner

Finding effective cancer treatments is an ongo-ing challenge in our society, and combined on-colytic virotherapy and immunotherapy are fieldsinvestigating possible solutions. Two mathemat-ical models using ordinary differential equationsare developed for both of these areas and opti-mised to current experimental data. In addition,a stochastic simulation based on the Gillespie al-gorithm is created based on the previous optimi-sations to simulate the effects of randomness andinvestigate what changes could be made to thetreatment to possibly improve its effectiveness.Modifications to the lysis rate and infectivity ofthe virus are shown through the stochastic simu-lations to provide improvements to the effective-ness of the treatment. The models are used tofurther understand the complex dynamics of theimmune-tumour interaction and simulate possibletreatment improvements.

12.11. Influence of homeostasis on thelong-time-limit behaviour of an autoimmune disease

Owen Jepps (Griffith University)

15:15 Thu 1 October 2015 – SSN102

Dr Owen Jepps, Dr Lindsay Nicholson, Prof David

Nicholson

We have recently developed ODE models for ex-perimental autoimmune uveitis (EAU), a diseasecharacterised by T-cell-mediated inflammation ofthe retina and choroid. Uveitis is the second com-monest cause of blindness in the working popu-lation in the developed world. EAU serves notonly as an important biological model for uveitisin humans, but more generally in developing ourunderstanding of autoimmunity and disease inimmune-privileged environments, where immune-cell species are compartmentalised inside and out-side the relevant organ (in our case the eye) dur-ing autoimmune disease. To our knowledge, wehave produced the first mathematical model ofimmune disease in an immune-privileged environ-ment. Our mathematical models of EAU bear im-portant similarities with epidemiological modelsof mosquito-borne diseases such as malaria anddengue fever, due to the analogous nature of in-teractions among the key populations.

Despite their complexity, the long-time-limit be-haviour of our EAU models always leads to eithera globally asymptotically stable (GAS) disease-free equilibrium (DFE), or an endemic equilib-rium (EE) which is either GAS or admits glob-ally attracting limit cycles. In this talk I willdiscuss recent work in which we have used Lya-punov functions to establish the global stabilityof the DFE and EE, under appropriate conditionson the parameters. Interestingly, and perhapssurprisingly, the homeostasis terms describing thedisease-free cell-population dynamics (and usuallyapproximated using quite simple expressions) playa critical role in determining certain aspects of theendemic dynamics.

12.12. Possible sets of six conductivity values touse in the bidomain model of cardiac tissue

Barbara Johnston (Griffith University)


Dr Barbara Johnston

When modelling electric potential in cardiac tis-sue, the most commonly used model is the bido-main model, which considers the tissue as con-sisting of two interpenetrating domains (intracel-lular and extracellular), each allowing conductionin three directions (along, across and normal tothe cardiac fibres). This results in six bidomainconductivity values in these models. No experi-mentally determined sets of these values exist andthe three measured sets of four conductivity val-ues, which assume conductivities across and nor-mal to the fibres are equal, are from more than 30years ago and are inconsistent.

In his 1997 paper, Roth used realistic values forexperimentally deteremined parameters combinedwith mathematical formulae to produce a set offour “nominal” conductivity values that could be

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used to compare simulations. Recent experimen-tal work in 2007 by Hooks et al. and in 2009by Caldwell et al. has found that monodomainconductivities and conduction velocities each splitapproximately in the ratio 4:2:1 in the directionsmentioned above. The current study considers theeffect of these results on sets of four bidomain con-ductivities and compares these with the previoussets of values. It then extends the process to pro-duce sets of six bidomain conductivities and mod-els their effect on epicardial potential distributionsassociated with regions of ischaemic tissue.

12.13. A New Model for Aggressive BreedingAmongst Wolbachia Infected Flies

Peter Johnston (Griffith University)

14:50 Thu 1 October 2015 – SSN102

Dr Peter Johnston and Dr Jeremy Brownlie

Wolbachia is a mosquito bacteria used to controldengue fever and malaria. The effect of Wolbachiaon the mosquitoes is to shorten their lifespan andchange their reproduction patterns. It is alsothought that the bacteria changes the way maleand female insects interact with one another. Herewe will develop a new model for male and femalefruit flies (because they are used for laboratoryexperiments) both with and without Wolbachia

Consider a population of male and female flies,some of which are infected with Wolbachia. Thebasic breeding model is as follows:

• Mating two normal flies produces 100%normal flies.• Mating an infected male with an unin-

fected female produces no flies.• Mating two infected flies produces 95%

infected flies and 5% uninfected flies.• Mating an uninfected male with an in-

fected female produces 95% infected fliesand 5% uninfected flies.

We will derive a system of four ordinary differen-tial equations that takes into account the abovebreeding rules and includes an “aggression” fac-tor for mating relationships. Based on observa-tions from numerical solutions to the system ofdifferential equations and analysis of the steadystates of the full system, we can make some ap-proximations and reduce the system to a studyof one differential equation for the infected femalepopulation. We will examine the steady statesand study the stability of this equation to explainsome experimental observations.

12.14. Anomalous dynamics in compartmentmodels, a continuous time random walk approach

James Ashton Nichols (University of New South

Wales)


Dr James Ashton Nichols

Anomalous dynamics are reactions, transitions,and movement that follows power-law expecta-tions in time. These sorts of dynamics are typ-ically represented with fractional derivatives inODEs or PDEs. Diseases that exhibit chronicinfection, or particles that cross mucousal tissueslowly are examples of systems that are modelledwell with anomalous dynamics.

Continuous time random walks (CTRWs) are sto-chastic processes from which we can derive gen-eralised master equations that can correspond toa wide variety of ODEs and PDEs, and can beused to derive physically correct anomalous sys-tems. We derive a general framework for com-partment models with anomalous dynamics, showthe resulting fractional systems of coupled ODEs,discuss the numerical methods that arise from thisapproach, and present real-world application sys-tems.

12.15. Surface deformation and shear flow inligand mediated cell adhesion

Sarthok Sircar (University of Adelaide)

15:40 Thu 1 October 2015 – SSN102

Dr Sarthok Sircar

We present a single, unified, multi-scale modelto study the attachment/detachment dynamics oftwo deforming, near spherical cells, coated withbinding ligands and subject to a slow, homoge-neous shear flow in a viscous fluid medium. Thebinding ligands on the surface of the cells expe-rience attractive and repulsive forces in an ionicmedium and exhibit finite resistance to rotationvia bond tilting. The macroscale drag forcesand couples describing the fluid flow inside thesmall separation gap between the cells, are cal-culated using a combination of methods in lubri-cation theory and previously published numericalresults. For a select range of material and fluidparameters, a hysteretic transition of the stick-ing probability curves between the adhesion andfragmentation domain is attributed to a nonlin-ear relation between the total microscale bindingforces and the separation gap between the cells.We show that adhesion is favored in highly ionicfluids, increased deformability of the cells, elas-tic binders and a higher fluid shear rate (until acritical value). Continuation of the limit pointspredict a bistable region, indicating an abruptswitching between the adhesion and fragmenta-tion regimes at critical shear rates, and suggesting

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that adhesion of two deformable surfaces in shear-ing fluids may play a significant dynamical role inmany cell adhesion applications.

12.16. A representation-theoretic approach to thecalculation of genome rearrangement distances

Jeremy Sumner (University of Tasmania)


Dr Jeremy Sumner

A simple model of circular genome rearrange-ments is obtained by taking a restricted set of genepermutations S and considering the distance be-tween two genomes to be related to the numberof permutations required to convert one genomeinto the other. Stochastically, we consider genomeevolution as a Poisson process where each permu-tation in S is applied with uniform rate, with thedistance between two genomes defined as the max-imum likelihood time passed. Algebraically, theset of permutations S generates a group G and weneed to compute the number of ways of express-ing a given element of G as a word of length k in”letters” S. Unfortunately, this algebraic task iscombinatorially intensive (factorial in the numberof genes/regions) but must be solved in order forthe stochastic analysis to proceed. I will presentsome recent ponderings taking a representation-theoretic approach which converts the combina-torial problem into linear algebra and the compu-tation of certain eigenvalues. This improves thecomplexity of the problem a little (by a squareroot), but is by no means a silver bullet (squareroot of factorial complexity is still terrible).

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13.1. Developing mathematical thinking throughpuzzles and games

Amie Albrecht (University of South Australia)


Dr Amie Albrecht

Problem solving—the exploratory and creativeprocess of devising a solution—is at the heart ofworking mathematically. But how can we mean-ingfully develop our students’ skills in problemsolving?

In this talk I’ll discuss a new course ’Develop-ing Mathematical Thinking’ which is an electivefor primary and middle education students atthe University of South Australia. The courseaims to build student confidence in tackling un-familiar problems, encourage exploration of mul-tiple solution strategies, promote flexible thinkingthrough use of different representations, help stu-dents develop mathematical communication skills,and stimulate mathematical curiosity. Through-out the course we seek to reproduce the collabo-rative, active and enjoyable environment in whichmathematicians work.

The course explicitly articulates the mathemati-cal processes that underpin effective problem solv-ing, such as specialising and generalising, workingsystematically, making conjectures, and provingstatements. It also focuses on phases of work:understanding the problem (the Entry phase),trying to solve the problem (the Attack phase),and checking and extending work (the Reviewphase). In class, students work mostly in groupsand at their own pace on carefully-chosen prob-lems that require a range of mathematical tech-niques but are purposefully selected to reinforcethe weekly focus on a particular mathematicalprocess. Of particular interest are ’low-threshold,high-ceiling’ activities that everyone can begin butwhich have potential for more challenging mathe-matical exploration. The major assessment pieceis an in-depth student-selected investigation thatdraws together concepts and skills from the entirecourse.

I will give examples of a typical class, assessmentitems, and scaffolded activities designed to buildskills and confidence. I’ll also share student reflec-tions from the first offering of the course, whichsuggest that it has helped these prospective math-ematics teachers develop into enthusiastic, confi-dent and capable problem solvers.

13.2. Assessing for student problem solving ability

Tristram Alexander (UNSW)


Dr Tristram Alexander

Assessment typically drives student learning, how-ever it is a challenge to assess learning of problemsolving skills as these skills are complex, hiddenand context dependent. Tasks which require deepengagement on a student’s part, and which exposethe underlying thinking of a student, typically re-quire significant teaching resources, such as indi-vidual monitoring of a reflective journal or reg-ular one-on-one discussion between student andteacher. As part of a problem solving course run-ning at UNSW Canberra we are using a mixtureof online, peer- and self-assessment techniques toencourage and test the development of problemsolving skills in a less resource intensive manner.I will discuss our preliminary results and our ex-periences with the problem solving course moregenerally.

13.3. Spreadsheet drawings of plant branchingfrom modified Lindenmayer grammars

John Banks (University of Melbourne)


Dr John Banks

Lindenmayer Grammars can be used to model arange of geometric phenomena. The motivatingapplication is that of branching structures in an-nual plants. This very visual instance of a math-ematical model describing how a complicated bi-ological structure can be generated by a simplesystem of growth rules afforded the author an ex-cellent illustrative example when designing a firstyear subject introducing mathematical models inbiology. In this approach, a Lindenmayer Gram-mar specifies the branching rules and a deriva-tion from this grammar is used to generate anabstract instruction string describing the branch-ing structure at a particular stage of growth. Aturtle graphics approach is then used to turn theinstruction string into a diagram. This processis somewhat computationally intensive, making itprohibitive for students to compute realistic ex-amples by hand. On the other hand, spreadsheetsenable students to calculate and plot very sat-isfying diagrams of branching structures. How-ever, the implementation of Turtle graphics inthis setting conventionally requires the use of astack, which is rather delicate and difficult to im-plement in a spreadsheet. The author will showhow this difficulty can be sidestepped by convert-ing the Lindenmayer Grammar into a modifiedform that generates instruction strings that maybe processed without the need for a stack. How-ever, this raises an interesting mathematical prob-lem of equivalence with the stack based method ofprocessing.

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13.4. Symbols: do university students mean whatthey write and write what they mean?

Caroline Bardini (The University of Melbourne)


Dr Caroline Bardini

Analysis of mathematical notations must considerboth syntactical aspects of symbols and the under-pinning mathematical concept(s) conveyed. Weargue that the construct of syntax template pro-vides a theoretical framework for analysing under-graduate mathematics students written solutions,where we have identified several types of symbol-related errors and lack of attention to symbolicstructure. A focus on syntax templates may ad-dress this issue of an under-developed symbolsense of many tertiary mathematics students.

13.5. A short walk can be beautiful

Jonathan Borwein (The University of Newcastle)

14:50 Thu 1 October 2015 – HUM133

Dr Jonathan Borwein

The story I tell is of research undertaken, with stu-dents and colleagues, in the last six or so years onshort uniform random walks. As the research pro-gressed, my criteria for beauty changed. Thingsseemingly remarkable became simple and otherseemingly simple things became more remarkableas our analytic and computational tools were re-fined, and understanding improved.

13.6. New Mathematics Special Interest Group forAustMS

Joann Cattlin (University of Melbourne)


Ms Joann Cattlin

Inaugural Meeting of the Special Interest Groupin Mathematics Education (SIGME). There willbe a brief presentation outlining the aims of thisnew SIG followed by a meeting of the group. Allinterested members are welcome to attend.

SIGME - A new special interest group of theAustMS has been established to ensure that AustMSmembers can contribute to, and be informed of,the current national discussions in tertiary math-ematics education on issues including, Reten-tion and progression of tertiary mathematics stu-dents Online learning and eLearning Declininglecture attendance and lecture recording Assess-ment in mathematics The challenges of teachingunderprepared students and addressing high fail-ure rates Transition from tertiary to secondarymathematics The declining number of studentsstudying intermediate and advanced level mathe-matics in upper secondary school Increased teach-ing performance expectations Connections withthe secondary education sector and the AustralianCurriculum

13.7. Student reasoning about real-valuedsequences: Insights from an example-generationstudy

Antony Edwards (Swinburne University of

Technology)


Dr Antony Edwards

Reasoning accurately with examples is a key skillfor expert mathematicians. Fluency in choosingand working with appropriate examples is fun-damental to mathematical understanding (Mitch-ner, 1978), and research has shown that expe-rienced mathematicians use examples in variousdeliberate ways: as illustrations, as prototypes toguide proof construction, as counterexamples, asa means of clarifying conceptual boundaries, andso on (Alcock, 2004; Mills, 2012).

Recently, there has been a move towards usingexample generation as a learning tool (e.g. Wat-son and Mason, 2005), not least because activi-ties in which students generate their own exam-ples of newly-met concepts are are a natural fitfor “flipped” learning environments in which thefocus is shifted from a teacher-centred ‘definition-theorem-proof’ pedagogy to one in which studentsengage actively with mathematical processes andobjects.

In this talk we discuss factors that should be con-sidered when designing such tasks, basing our ar-guments on an example-generation activity usedin task-based interviews with 15 undergraduatemathematics majors at a large research-intensiveUK university. In this activity, students wereasked to give examples of real-valued sequencessatisfying combinations of properties (for exam-ple, a sequence that tends to infinity that is not in-creasing). In analysing student responses, we wit-nessed two different types of misconception. Thefirst is well known in the literature: ‘everyday’meanings of key terms can override their math-ematical counterparts—for example, limit mightbe interpreted to mean an impassible boundary.The second was more unexpected: in some casesstudents interpreted property terms meaningfullybut, in attempting to construct objects that sat-isfied these, they failed to keep the base objectinvariant—their examples were not, in fact, se-quences.

We conclude that when designing such tasks for aflipped classroom environment, instructors shouldbe aware of a wide range of possible responses,including some that effectively alter the task pa-rameters; example generation can promote deepdiscussion of issues in conceptual understanding,

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but students will require guidance to ensure thatsuch activities address the learning outcomes theyare designed to meet.

References

Alcock, L. (2004). Uses of example objects inproving. In Proceedings of the 28th Conferenceof the International Group for the Psychology ofMathematics Education (Vol. 2, pp. 17-24).

Mills, M. (2014). A framework for example usagein proof presentations. The Journal of Mathemat-ical Behavior, 33, 106-118.

Michener, E. R. (1978). Understanding under-standing mathematics. Cognitive science, 2(4),361-383.

Watson, A., & Mason, J. (2005). Mathematics asa constructive activity: The role of learner gener-ated examples.

13.8. Development and Implementation of a FirstYear Statistics Subject for Senior SecondaryIndigenous Students to Encourage FutureEngagement in Tertiary Studies

Deborah Jackson (La Trobe University)


Dr Deborah Jackson and Tania Blanksby

La Trobe University’s Office of Indigenous Strat-egy and Education, and the College of Science,Health and Engineering, in collaboration with theKoorie Academy of Excellence, have developed astrategy to encourage Indigenous senior secondarystudents to continue with mathematics and con-sider tertiary studies in the future. A first yearstatistics subject (STA1DCT), which also devel-ops numeracy and critical thinking skills, has beenredeveloped and delivered to students from theAcademy. This presentation explains some keyfeatures of this project, including how the contenthas been culturally contextualized to increase en-gagement, how the current curriculum has beendelivered in three separate three-day modules, andhow weekly help sessions provide feedback andan extra resource between module delivery. It ishoped that the program will help students see therelevance of mathematics and statistics to theirlives, and encourage them to consider a future inscience, statistics or mathematics.

13.9. Reflections on using vodcasts as anassessment item in first year units

Carolyn Kennett (Macquarie University)


Mr Chris Gordon, Ms Carolyn Kennett

Over the past several years there has been increas-ing emphasis on graduate outcomes and thresh-old learning outcomes for mathematics programs

at universities. The nationally developed Math-ematical Sciences Threshold Learning Outcomesinclude the statement that graduates (of math-ematics and statistics programs) will be able todemonstrate, amongst other things, appropriatepresentation of information, reasoning and conclu-sions in a variety of modes, to diverse audiences(expert and non-expert) and the ability to workeffectively, responsibly and safely in an individualor team context.

Traditional assessment items in mathematics unitsare usually closed book exams and tests or individ-ual written assignments, particularly in first yearunits. Written communication is a very impor-tant component of communicating mathematicalideas, however using only written assignments andclosed book exams does not assess the outcomesset out in the TLOs referencing communicatingusing a variety of modes or demonstrating an abil-ity to work effectively in a group. Where programsdo include assessment of oral presentations, thesetend to occur in later years of study.

A group assessment task was included in the as-sessment mix for several of our first year units.The task required students to create a vodcastpresenting any aspect of the unit or any applica-tion of the material covered in the unit. In thistalk we will discuss our evaluation of this assess-ment task and the changes that have made overthe course of several iterations of setting this task.We will also discuss reflections by the teachingstaff, the markers and the students on the useful-ness of the vodcast as a learning and assessmenttool.

Note: I am attending the ACSME conference aswell so would appreciate an earlier time slot if ourabstract is accepted.

13.10. Online tutorials with YouTube and MapleTA: the experience so far

Jonathan Kress (University of New South Wales)


Dr Jonathan Kress

This year at UNSW we have replaced half of our‘higher’ level first year classroom tutorials withonline tutorials consisting of short videos andhomework exercises presented using Maple TA.Our primary motivation has been to increase stu-dent engagement by providing a richer environ-ment, encouragement to work on problems outsideof class and a greater level of feedback. This hasalso reduced the time tutors spend at the black-board freeing up a resource that can be redirectedelsewhere. This talk will give an overview of thismodel and report on our experiences with it sofar.

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13.11. Making mathematics relevant to first yearengineering students

Birgit Loch (Swinburne University of Technology)


Birgit Loch, Julia Lamborn and Michelle Dunn

We have observed that first-year mathematicsstudy is often seen as irrelevant and distractingby engineering students who are more interestedin applied engineering subjects. Many disengagefor this reason, perform in mathematics at lev-els below their capabilities, and struggle later onwhen the first year material becomes prerequisiteto further studies.

In this talk I will introduce the ”MathematicsRelevance Project”, a research project to inves-tigate how to make engineering students under-stand the relevance of their first year mathemat-ics topics. This project takes a novel angle by in-volving higher year students in the production ofre-usable resources for first year students. Thesehigher year students are recruited from engineer-ing degrees, but also from multi-media degreesto ensure a quality outcome. Two iterations ofthis project have been completed now, resulting insix animations describing a range of mathematicaltopics needed to construct a high-rise building orto improve the aerodynamics of a car, or focusingon individual topics needed for cruise-control of acar, ECGs, breaking down of alcohol in the body,and moving a robot.

I will describe how the students collaborated, theirthinking when selecting topics and applications,but also how the resulting animations were per-ceived by first year students. The third iterationhas just received funding, and I plan to report onfirst outcomes of this round in this talk.

The six existing, and all future animations, maybe accessed by going to http://commons.swin.edu.au,proceeding as guest, and searching for ”rele-vance”.

13.12. Mathematics degree learning outcomes andtheir assurance

Dann Mallet (Queensland University of Technology)


Prof Dann Mallet

In this session, the Threshold Learning Outcomesfor mathematics degrees will be revisited. Discus-sion will then centre on the nature of assessmentin mathematics degrees as well as the strengthsand weaknesses of such assessment in assuring stu-dents’ learning outcomes.

13.13. Understanding and addressing poor studentperformance in first year university calculus

Christine Mangelsdorf (University of Melbourne)

15:15 Thu 1 October 2015 – HUM133

Dr Christine Mangelsdorf, Dr Robert Maillardet

MAST10006 Calculus 2 accounts for 2100 of 6000first year enrolments at the University of Mel-bourne and so is a major contributor to Depart-mental teaching outcomes and income generation.Despite excellent and consistent feedback fromstudents on lecture and tutorial quality, scaledfailure rates have averaged an unacceptably high29.4

We present data on the areas of poor performance.Many of these areas relate to basic weaknesses instudent’s secondary preparation.

We consider realistic options for detecting theseweaknesses and potential ways to help remedythem in the hope we can improve student perfor-mance without watering down content and stan-dards.

13.14. Learning from experience: developingmathematics courses for an online engineeringdegree

Diana Quinn (University of South Australia)


Dr Amie Albrecht, Dr Diana Quinn, Dr Brian

Webby, Dr Kevin White

Many universities are seeking to improve effi-ciency, competitiveness and broaden their poten-tial audience by expanding into online education.In 2010 the University of South Australia part-nered with Open Universities Australia (OUA) toprogressively move the Associate Degree in En-gineering, including five engineering mathematicsunits, into a fully online offering.

The conversion of a face-to-face unit for online de-livery is not simply a matter of uploading videos,notes and problem sets, but requires considera-tion of student needs, instructional design, andthe best use of online tools to support learning.It is also an opportunity to rethink the content ofthe unit and how learners engage with it.

In this talk we will review ten development cy-cles of Essential Mathematics 1: Algebra andTrigonometry (EM1), the first unit in the mathe-matics sequence of the Associate Degree in Engi-neering. EM1 is part of the OUA’s suite of openaccess units which means there are no academicprerequisites for enrolment. The 13-week unit isdelivered up to four times per year, allowing forintense and sustained evaluation, reflection andplanning of sequential interventions.

We will discuss specific actions in several devel-opment categories concerning the technical andpedagogical demands of an online mathematics

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course on students, teachers and infrastructure.We used a ’learning from experience’ approach tohelp prioritise our interventions within the limitsof available time and resources. For example, theorganisation and layout of the website has beencontinually refined to improve navigability, speedup access and help students keep track of theirprogress in learning activities.

Our actions led to unit-specific improvements, abetter understanding of our student cohort, andan increase in staff skills for online teaching. Themost dramatic shift in informal and formal met-rics of student satisfaction and success was dueto curriculum-focused actions in which unit topicswere streamlined, and activities and assessmentsrefined.

The spiral of development also led to improve-ments for both the corresponding on-campus ver-sion of EM1 as well as other mathematics units,enhancing the flexibility and effectiveness of learn-ing for many more students.

13.15. Galileo and Calculus Unlimited

John William Rice (University of Sydney)


Prof John William Rice

At school and university the concepts of calculusand how they develop are very much set in stone,so much so that we might think that they couldnot be developed any other way. However, it is ispossible that calculus might have developed quitedifferently, and more transparently, in a paralleluniverse, starting with the work of Galileo. Re-markably, a re-envisioning of the concept of in-definite integrals, inspired by the work of Galileo,makes them as basic and intuitive as graphs forthe representation of varying quantities. The con-cept of rate of change and derivation of the rulesof calculus take on a different, and arguably moretransparent character from this perspective. Thisapproach avoids necessity for ideas like infinitesi-mal changes or limits.

Flexibility of approach helps us to meet the needsof a wider variety of students, many of whommight find in this approach, or elements of it, afar more transparent and meaningful introductionto calculus than the standard one.

find in this approach, or elements of it, a far moretransparent and meaningful introduction to cal-culus than the standard one.

13.16. Pipelines, ceilings, and acid rain

Katherine Anne Seaton (La Trobe University)

15:40 Thu 1 October 2015 – HUM133

Dr Katherine Anne Seaton

Last September, in his President’s Column in theGazette [1], Peter Forrester raised some questions

regarding the retention of female students at ter-tiary level and the representation of women inteaching-research positions, going so far as to saythat “There is no doubt the problem is extreme”.Since then, I have been working on a responseand an elaboration of the matters he raised, andin this talk I will present from my reading, a mix-ture of what has been published, what has beenmeasured, and some (to me) startling images fromthe last year.

[1] Gazette of the Australian Mathematical Soci-ety, 41 (4), 212-213 (2014)

13.17. Great Expectations: I expect to passbecause I already know all this stuff

Donald Shearman (Western Sydney University)


Donald Shearman and Leanne Rylands

There is a substantial body of evidence to sug-gest that students are arriving at university sig-nificantly under-prepared to study mathematics,however little appears to have been done to iden-tify students’ evaluation of their own abilities inthis area, or of their attitudes towards mathemat-ics. We conducted a study recently in three firstyear mathematics subjects to probe students’ per-ceived ability in several areas of mathematics aswell as their expectations and attitudes. Studentswere also asked about their mathematics back-ground. Surveys were conducted at both the startand end of semester to identify changes in theseareas during the semester. Here we report on theresults of the survey run in the first lecture at thestart of semester to predominantly first semester,first year students. The three first year subjectsare all low level mathematics subjects. Most stu-dents were enrolled in an industrial design, engi-neering or science degree.

Forty-eight percent of students enrolled in theunits responded to the survey. Many of thesewere mathematically poorly prepared for univer-sity study. Despite this, almost all students hadtotally unrealistic expectations about their per-formance in their mathematics subject, includingthose who reported that their algebra, statistics,trigonometry and calculus skills were weak or non-existent. Almost all students expected to pass thesubject, yet the failure rates in the three subjectswere all over 30%. A majority of students ex-pected to gain a distinction or high distinction atthe commencement of the semester.

We report on several other interesting observa-tions from this survey, including the fact thatabout 45% of students reported “Okay” to “Excel-lent” calculus skills, despite the fact that almost60% of the students had not done any calculusat school or, one assumes, elsewhere. This brings

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into question how much of the terminology thatwe take for granted is understood by students.

Overall, students’ attitudes to mathematics werevery positive; “enjoy”, “understand” and “like”were the three most commonly used words (thesewere rarely preceded by don’t or not). Studentsalso expected to gain knowledge and understand-ing from their mathematics subject.

Whilst interesting in themselves, these resultshave important implications for the provision ofmathematical support at university. Support ser-vices are usually designed for students in subjectssimilar to those surveyed, yet it appears that veryfew of these students feel that they will have needof such services.

13.18. Assessment and Feedback in Fully OnlineTertiary Mathematics: The Instructor Perspective

Sven Trenholm (University of South Australia)


Sven Trenholm (University of South Australia), Lara

Alcock and Carol Robinson (Loughborough

University)

As part of a dramatic recent shift in tertiary ed-ucation, many undergraduate students now learnmathematics via fully online (FO) courses. Atpresent the mathematics education research com-munity knows very little about this shift, and inthis report we consider implications of a mixed-methods investigation into the instructor experi-ence of assessment and feedback in FO undergrad-uate mathematics courses. The investigation ex-plored assessment schemes, feedback practices andapproaches to teaching, and used semi-structuredinterviews to ask participants to compare their ex-periences of FO and face-to-face assessment andfeedback. The main emergent theme was concernabout the loss of short-cycle face-to-face humaninteraction, and we argue that this concern is se-rious but should be seen as an opportunity for ed-ucation researchers to leverage knowledge abouteffective mathematics teaching to simultaneouslyalleviate instructors difficulties and promote ped-agogical development.

13.19. Mathematics and Australian IndigenousCulture: Building cultural awareness, competencyand literacy in mathematics students at UniSA

Lesley Ward (University of South Australia)


Ms Andrea Duff and Dr Lesley Ward

This talk will be given by Andrea Duff (UniSA)and Lesley Ward (UniSA). Australian Indigenouscontent has been taught in the sciences at theUniversity of South Australia (UniSA) since 2009,

under the umbrella of UniSA’s Indigenous Con-tent in Undergraduate Programs (ICUP) initia-tive. As in many other science disciplines, math-ematics teaching in universities is not an areatraditionally associated with Indigenous curricu-lum. It is in this environment that Indigenous andnon-Indigenous staff at UniSA have been develop-ing and embedding curriculum which recognisesWestern and Indigenous views of mathematics.Universities and professional bodies are increas-ingly looking to ways of developing the culturalawareness, competency and literacy of their stu-dents. A practical model is given by the ICUPapproach we take in the course MathematicalCommunication, where we embed cultural skillscurriculum within the framework of developingour students’ professional skills. A recognitionof the learning preferences of our students, alongwith demonstrating respect for Indigenous world-views, goes some way toward showing respect fordualities and commonalities across cultures. Wewill outline the nuts and bolts of how ICUP worksin Mathematical Communication, along with ob-stacles we have overcome and some encouragingoutcomes.

13.20. Mind the Gap: Exploring knowledge decayin online sequential mathematics courses

Kevin White (University of South Australia)


Brian Webby, Diana Quinn, Amie Albrecht, Kevin

White

Open access, digitally-enabled learning can pro-vide freedom and choice for new learners - not onlyin how and what they study, but when. With thisfreedom comes risk. One potential risk lies in thetiming of enrolment in courses, particularly wherefundamental knowledge is built across a year andwhere extended gaps between sequential coursesmight cause knowledge decay. Mathematics maybe susceptible here. Our concerns were allayed;an examination of data suggested that new stu-dents preferentially minimise gaps and found nosignificant evidence for knowledge decay over pe-riods of up to 15 months. Nevertheless, to supportstudent learning in open online learning environ-ments, it could be important to provide resourcesfor student self-assessment of knowledge deficien-cies, and the facility to refresh and regain under-standing.

13.21. To all first-year Calculus students:*pleeease* attend the classes!

Aaron Wiegand (University of the Sunshine Coast)


Dr Aaron Wiegand

Although the ideas and content in first year Calcu-lus courses are new to many students, attendance

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at classes (lectures and tutes) is typically less than60%. This lack of guided, repeated exposure of-ten translates to poor learning outcomes in indi-viduals and, subsequently, fail rates that manage-ment regard as obstructing student progression,contributing to attrition and thus limiting univer-sity growth. Interestingly, in spite of the wealthof published evidence that suggests that atten-dance is a key predictor for success, attendancein itself is not seen to be an issue by manage-ment and is not considered to be a contributingfactor to poor learning outcomes. Instead, aca-demics are encouraged to cater for modern-agestudents for whom traditional modes of contentdelivery (lectures and tutorials) are unsuitable, os-tensibly because students now have different ex-pectations about what university study should in-volve, or simply because they are time poor. A fo-cus on Student Centred Learning means that con-siderable effort is thus expended into providingadditional pathways for exposure to course ma-terial, via opportunities provided by recorded lec-tures, blended learning and a variety of assessmenttypes. This approach may be extremely success-ful for students who take responsibility for theirown learning, but for many young students whohave not yet learned to learn, direct instruction,repeated exposure and guided practice are key tolearning new mathematics. Although they them-selves are unaware of it, many first-year studentsfall into this category. So what is a course co-ordinator to do to provide motivation for attend-ing classes, repeated exposure and regular prac-tice? Linking assessment tasks to physical pres-ence at classes? Directed homework? Blendedlearning? Interventions? Peer-supported Q& Asessions? Begging? In a single semester of afirst-year Calculus course, all of these were imple-mented at various stages. Ultimately, the singlegreatest predictor of student performance was, un-surprisingly, physical attendance at tutorials andat lectures. In this presentation, I will discussbriefly the strategies employed during the courseand their respective impacts on attendance andstudent learning, within the context of the con-temporary literature.

13.22. Mathematics and statistics modules forpre-service teachers

Leigh Wood (Macquarie University)


Prof Leigh Wood

Leigh Wood, Carmel Coady, Dorian Stoilescu,Ayse Bilgin, Carolyn Kennett, Vince Geiger, MichaelCavanagh, Peter Petocz, Joanne Mulligan, LizDate-Huxtable, Scarlet An

In a project that brings mathematicians, statis-ticians, scientists and education specialists to-gether, Opening Real Science has developed eight

online mathematics modules for pre-service teach-ers (enrolled in BEd, DipEd). These cover numer-acy, financial literacy, statistical literacy, mathe-matical modelling and the concept of infinity. Themodules use an engaging approach to learningabout primary and secondary school mathemat-ics. The delivery of the materials using a MoodleLearning Management System (LMS) interfacemeans flexible delivery and opportunity for so-cial networks to form, enabling peer-learning andlearning through discourse and reflection. Thereare also 16 modules covering aspects of astronomy,physics, biology, earth and environmental scienceand chemistry, for which the mathematics mod-ules provide support with respect to quantificationstrategies.

The philosophy of the project emphasises the useof authentic examples and engaging tasks demon-strating links across the disciplines. Each modulerepresents four weeks of student work (approxi-mately 40 hours) and so can be slotted into exist-ing subjects. The numeracy module is designed toincrease students confidence with numbers, sta-tistical literacy modules help students to makeevidence based decisions in their teaching and intheir lives, financial literacy modules explore per-sonal, community and government levels of finan-cial management and secondary students explorethe concept of infinitely large and small numbersby investigating the dimensions of fractals and theuniverse. Mathematical modelling brings togetherthe numerical skills required to explore scientificphenomena and test their application and rele-vance to the world.

This presentation will show examples from theproject and explore how the modules can be usedin other contexts through creative commons.

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14.1. A noncommutative approach to topologicalinsulators

Christopher Bourne (Australian National

University)


Mr Christopher Bourne

We study topological insulators, regarded as phys-ical systems giving rise to topological invari-ants determined by symmetries both linear andanti-linear. Our perspective is that of non-commutative index theory of operator algebras.In particular, we show that the periodic table oftopological insulators and superconductors can berealised as a real or complex index pairing of aKasparov module capturing internal symmetriesof the Hamiltonian with a spectral triple encod-ing the geometry of the sample’s (possibly non-commutative) Brillouin zone. Time permitting wewill also discuss the K-theoretic bulk-edge corre-spondence of such materials. This is joint workwith Alan Carey and Adam Rennie.

14.2. Singular spectral shift function forSchrodinger operators

Tom Daniels (Flinders University)


N. Azamov, T. Daniels

I will talk briefly about the following theoremand its proof. Let H0 = −∆ + V0(x) be a 3-dimensional Schrodinger operator, where V0(x) isa bounded measurable real-valued function on R3

and let V be an operator of multiplication by areal-valued measurable function V (x) such that|V (x)| ≤ const.(1 + |x|2)−3/2−ε for some ε > 0and let Hr = H0 + rV. Let

ξ(s)(φ) =

∫ 1

0

Tr(V φ(H(s)r )) dr, φ ∈ Cc(R),

where H(s)r is the singular part of Hr. Then ξ(s)

is a correctly defined absolutely continuous mea-sure and its density ξ(s)(λ) (denoted by the samesymbol) is integer-valued for a.e. λ. The proof ofthis theorem relies on a constructive approach tostationary scattering theory.

14.3. N = 2 supersymmetry on the lattice withoutfermion conservation

Jan De Gier (University of Melbourne)

14:50 Thu 1 October 2015 – SSN013

Prof Jan De Gier

I will discuss a solvable lattice model that hasmanifest N = 2 supersymmetry and lacks fermionnumber conservation. The eigenstates of theHamiltonian are exponentially degenerated. The

spectrum can be calculated using the nested Betheansatz which illuminates a mechanism that ex-plains the high degeneracy in terms of zero energyCooper pairs.

14.4. Electron-hole asymmetry of the p+ip pairingmodel.

Jon Links (The University of Queensland)

16:05 Thu 1 October 2015 – SSN013

Jon Links, Ian Marquette, Amir Moghaddam

The p+ip pairing model arises in studies of su-perconductivity. I will examine the electron-holeasymmetry of the model from the perspective ofthe Bethe Ansatz solution. A main result of thestudy is that for the attractive system there is aregion in parameter space whereby all states occuras partial condensates of hole-pairs.

14.5. An integrable case of the p+ ip pairingHamiltonian interacting with its environment

Inna Lukyanenko (The University of Queensland)


Miss Inna Lukyanenko

We consider a generalisation of the p + ip pair-ing Hamiltonian with external interaction terms.These terms allow for the exchange of particlesbetween the system and its environment. As aresult the u(1) symmetry associated with conser-vation of particle number, present in the p + ipHamiltonian, is broken. Nonetheless the gener-alised model is integrable. We establish integra-bility using the Boundary Quantum Inverse Scat-tering Method, with one of the reflection matriceschosen to be non-diagonal. We also present thecorresponding Bethe Ansatz Equations, the rootsof which parametrise the exact solution for theenergy spectrum.

14.6. Non-rational CFTs and the Verlinde formula

David Ridout (Australian National University)


Dr David Ridout

While logarithmic rational CFTs have receiveda lot of attention over the last ten years, thereis strong physical motivation to also study non-rational CFTs. Recently, it has been shown thatthe most tractable examples admit a formalismthat seems to generalise the paradigm of modu-larity and the Verlinde formula, familiar from ra-tional CFT. This talk will introduce and reviewthis formalism, with the aid of an example, andexplain how it may resolve the contentious issueof a Verlinde formula for the known examples oflog-rational CFTs, the triplet models.

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14.7. T-duality and topological phases

Guo Chuan Thiang (The University of Adelaide)

15:15 Thu 1 October 2015 – SSN013

Dr Guo Chuan Thiang

K-theory groups are known to classify D-branecharges in string theory as well as symmetry pro-tected topological phases in condensed matterphysics. I will explain how ideas from T-dualitycan be used in the latter, providing a notion ofdual phases. As a further application, topologicalboundary maps such as the bulk-boundary corre-spondence, are simplified.

The talk is based on recent joint work with V.Mathai, arXiv:1503.01206, arXiv:1505.05250, andarXiv:1506.04492.

14.8. Spectra and Greens functions of secondorder density models

Mathew Zuparic (Defence Science and Technology

Group, Australia)

15:40 Thu 1 October 2015 – SSN013

Mathew Zuparic

Many processes in the quantitative sciences canbe expressed as 2nd order density models (aka.hyperbolic/Fokker-Planck equations). From theirapplication in quantitative finance, Brownian mo-tion and quantum mechanics, they provide the im-portant macroscopic view of inherently stochasticphenomena. From a purely mathematical view-point 2nd order density models are a beautiful fu-sion of Hilbert spaces, spectral theory, orthogonalpolynomials and hypergeometric series.

In this talk we seek to construct the Greensfunction of the so-called Whittaker-Ince limits ofthe Confluent Heun equation and the Double-Confluent Heun equation. To accomplish this weapply the results of Figueiredo et al. who give thenecessary solutions to the above equations, com-bined with Linetskys spectral classification result,to ultimately perform a MacRoberts proof for theGreens functions. If time permits, we shall dis-cuss the applications of this result regarding C-integrable equations.

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15.1. Textons in rat bones and mammograms

Murk Bottema (Flinders University)


Dr Murk Bottema

Local and global texture properties in images playan important role in such tasks as image segmen-tation, object detection, classification and imageunderstanding. Texture plays a larger role in med-ical image analysis than in in general imagery. Of-ten the nature of important texture patterns is un-known and the problem of characterising textureis exacerbated by not knowing what to look for.The method of textons includes a clustering stepthat automatically identifies recurrent patterns inan image or image set.

In this talk, basic textons will be introduced alongwith some variants that have proven useful inanalysis of screening mammograms and charac-terising the structure of cancellous bone.

15.2. Textons and their applications in medicalimaging

Amelia Gontar (Flinders University)


Miss Amelia Gontar, Murk Bottema

The method of textons is a relatively recent de-vice for characterising texture in images. Briefly,a pixel, p, in an image X is assigned a fea-ture vector vp based on local image characteris-tics. The ith component of vp may be the fil-ter output hi ∗ X(p) where hi is filter i in a fil-ter bank. Alternatively, vp may simply be thelist of pixel intensities in a neighbourhood of p.Whatever the method for assigning feature vec-tors, textures in X are viewed as clusters in thefeature space F = vp : p ∈ X. Thus a clus-tering method is chosen to identify dense regionsin F and the resulting clusters are called textons.The image of texton labels obtained by replacingeach p ∈ X by the label of the cluster (texton)closest to vp in F is called the texton map. Thenormalised histogram of texton occurrences in thetexton map is the distribution of textons and isviewed as a representation of the texture contentof X.

Here, a study is presented on the ability of textonsto recognise texture in the presence of noise. Ap-plications include characterising texture in screen-ing mammograms to facilitate early detection ofbreast cancer and characterising the trabecularstructure in cancellous bone to quantify changesdue ageing or disease.

15.3. Moment Invariants for Medical imagesegmentation

Gobert Lee (Flinders University)


Dr Gobert Lee and Dr Mariusz Bajger

The invariant properties of moments and theircombinations have been well-studied. Many stud-ies have been focused on creating functions of mo-ments with invariant properties. The invariantfunctions of moments first introduced by Hu werebased on the theory of algebraic invariants. Inthis paper, the potential of complex moment in-variants with respect to translation, rotation andscaling for shape retrieval was investigated. Itshows that complex moment invariants of orderup to three possess sufficient discrimination powerfor retrieval of organ shapes from segmented CTimages. The performance of the method was eval-uated by the Dice coefficient as a measure of mu-tual agreement between the retrieved shape andthe expert segmented organ. The Dice values forliver, spleen and kidney were 0.96, 0.96 and 0.92,respectively.

15.4. Texture Analysis Improves the Estimate ofBone Fracture Risk from DXA Images

Rui-Sheng Lu (Flinders University)


Rui-Sheng Lu, Mark Taylor, and Murk Bottema

Elderly people, particularly women, are at a sig-nificantly higher risk of suffering a bone fractureas a result of a fall. Traditionally dual energy x-ray absorptiometry (DXA) is used to assess frac-ture risk, a technique which calculates area bonemineral density (aBMD), T-score and geometricparameters. However, these measures may notfully exploit the information content available inDXA images regarding risk of fracture as thereare still several limitations with DXA technologyand the way currently to analyse DXA imagesincluding: it is not an accurate measurement oftrue bone mineral density because DXA calculatesBMD using area; bone density is averaged overRegions of Interests (ROIs) and ignore the restinformation; only discrete geometric measures aretaken, and again the rest is ignored; and finallythe density and geometric information are anal-ysed individually.

In this study, Active shape model (ASM) and ac-tive appearance model (AAM) were used to al-low a quantitative characterization of the shapeand gross structure of the proximal femur. Thesemodels provide a level of risk assessment compa-rable to conventional risk measures such as BMDand T-score. In order to improve risk assessment,

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these methods were augmented by image textureanalysis methods, including calculating Gabor fil-ters and textons applied to various ROIs. Texturemethods allow quantification of structure patternsthat have not been considered previously in as-sessing risk of bone fracture. To evaluate thesemethods, we analysed hip DXA scans from the Os-teoporosis Centre of Southampton General Hos-pital, and consisted of 29 older adults with a his-tory of fragility fracture and 90 non-fractured con-trols. Feature selection was used to determinewhich method, or combination of methods wasbest to discriminate between the fracture and con-trol groups.

Test results show that texture features derivedfrom Gabor filters in combination with total T-score provided better estimates of risk than thestandard measures of aBMD or total T-scorealone. Moreover, estimates of risk were more ac-curate when the texture were measured on thewhole femoral neck than other regions.

15.5. Variational Models and ComputationalMethods in Image Processing

Michael Ng (Hong Kong Baptist University)


Prof Michael Ng

In this talk, I discuss several image processingtasks such as histogram equalization, colorization,decolorization, even transfer learning and imageclassification. Both theoretical results and exper-imental results are reported to demosntrate theusefulness of the models and algorithms.

15.6. An Adaptive CLAHE for Improving MedicalImage Segmentation

Shelda Sajeev (Flinders University)


Shelda Sajeev, Mariusz Bajger and Gobert Lee

Mass segmentation in mammograms is a challeng-ing task if the mass is located in a local densebackground. It can be due to the similarity ofintensities between the overlapped normal densebreast tissue and mass. In this paper, a self-adjusted mammogram contrast enhancement so-lution called Adaptive Clip Limit CLAHE (ACL-CLAHE) is developed, aiming to improve masssegmentation in dense regions of mammograms.An optimization algorithm based on entropy isused to optimize the clip limit and window sizeof standard CLAHE. The proposed method istested on 89 mammogram images with 41 masseslocalized in dense background and 48 masses innon-dense background. The results are comparedwith other standard enhancement techniques suchas Adjustable Histogram Equalization, UnsharpMasking, Neutrosophy based enhancement, stan-dard CLAHE and an Adaptive Clip Limit CLAHE

based on standard deviation. With the proposedmethod, 95

15.7. Estimating an additive gaussian model forprojective images

Simon Williams (Flinders University)


Dr Simon Williams

Visual images are derived from measurements ofsurface reflectance in the scene. Conversely, X-ray images are projective in nature being formedfrom the sum of the absorbances of the materi-als between the source and the detector. Highintensities in the image, which can be indicativeof breast cancer in mammograms, can arise fromthe overlap of two low absorbance non-cancerousstructures which could cause an unnecessary call-back for a patient. One approach to this problemis to build a model, P , of the image that takesaccount of its projective nature, we use bivariateGaussians as our building blocks and write:

P =

∞∑n=0

πn(v)g(γn)

where∑∞n=0 πn = 1 and γn are the parameters of

the gaussian g. We show how to estimate all ofthese parameters for a projective image I.

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16. Number Theory

16.1. Generalisations of Wilson’s Theorem forDouble, Hyper, Sub and Superfactorials

Grant Cairns (La Trobe University)


Dr Grant Cairns

As the title suggests, this is a talk in elementarynumber theory, suitable to a general audience.

This is joint work with Christian Aebi (CollegeCalvin, Geneva), published in the Amer. Math.Monthly, 2015.

16.2. Ramanujan’s level 7 theta functions

Shaun Cooper (Massey University)

14:50 Thu 1 October 2015 – SSN223

Dr Shaun Cooper

Many of the results in Ramanujan’s notebooks aretips of proverbial icebergs and can be made intolarger and more general theories. We will developsuch a theory for the theta function

∞∑j=−∞

∞∑k=−∞

qj2+jk+2k2

that is analogous to Jacobi’s theta functions andthe cubic theta functions of the Borweins. Modu-lar forms, hypergeometric functions and sporadicsequences all play a role in the analysis. We shalldescribe both how the results were obtained andhow they fit in a wider setting.

16.3. Generalized Fermat numbers andcongruences for Gauss factorials

Karl Dilcher (Dalhousie University)


Dr Karl Dilcher

We define a Gauss factorial Nn! to be the productof all positive integers up to N that are relativelyprime to n ∈ N. We consider the Gauss factorialsbn−1M cn! for M = 3 and 6, where the case of n

having exactly one prime factor of the form p ≡ 1(mod 6) is of particular interest. A fundamentalrole is played by primes with the property that theorder of p−1

3 ! modulo p is a power of 2 or 3 timesa power of 2; we call them Jacobi primes. Ourmain results are characterizations of those n ≡ ±1(mod M) of the above form that satisfy bn−1

M cn! ≡1 (mod n), M = 3 or 6, in terms of Jacobi primesand certain prime factors of generalized Fermatnumbers. (Joint work with John Cosgrave).

16.4. On Solving a Curious Inequality ofRamanujan

Adrian Dudek (Australian National University)


Mr Adrian Dudek

In one of his notebooks, Ramanujan penned a cu-rious inequality regarding the distribution of theprime numbers. Moreover, he stated that the in-equality will hold for all sufficiently large numbers.In this talk, the speaker will introduce and provethis inequality, before discussing his recent jointwork with Dave Platt (University of Bristol) onthis problem.

16.5. Analytic evaluation of Hecke eigenvalues

Alexandru Ghitza (The University of Melbourne)

15:15 Thu 1 October 2015 – SSN223

Alexandru Ghitza and Nathan Ryan

Existing methods for computing the eigenvaluesof Hecke operators on modular forms tend to ab-stract away the complex-analytic nature of mod-ular forms and simply perform linear algebra overrings of formal power series. I will describe an ap-proach that uses direct evaluation of the Fourierseries of the modular form at an appropriate pointin the complex plane.

16.6. Generalisations of Chen’s Theorem and thevector sieve

Stijn Hanson (Australian National University)


Mr Stijn Hanson

One of Chen’s famous theorems asserts that thereare infinitely many primes p such that p + 2 hasno more than two prime factors. Earlier in theyear this result got generalised by Heath-Brownand Li to a result asserting that there are infin-itely many primes p such that p + 2 has no morethan two prime factors and p + 6 has no morethan 98 prime factors. In this talk we generalisethe methods behind this new work and discusspotential applications to more general tuples.

16.7. The approximate GCD problem

Randell Heyman (University of New South Wales)


Mr Randell Heyman

The approximate GCD problem seeks to effi-ciently determine the GCD of a set of numbers.We do not know most or all of the numbers; ratherwe are given numbers that lie close by. As wellas discussing some methods to solve the problemI will explore two applications of the problem;

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16. Number Theory

namely attacks on RSA and fully homomorphicencryption. I will finish with a dual problem andsome related problems from joint work with IgorShparlinski.

16.8. A metrical problem in Non-linearDiophantine approximation

Mumtaz Hussain (The University of Newcastle)


Dr Mumtaz Hussain

In this talk, I will present some of my recentLebesgue and Hausdorff measure results for theset of vectors satisfying infinitely many fully non-linear Diophantine inequalities. The set is alsoassociated with a class of linear inhomogeneouspartial differential equations whose solubility is re-lated to a certain Diophantine condition. The fail-ure of the Diophantine condition guarantees theexistence of a smooth solution.

16.9. Iterated sums of the Mobius function

Jeffrey Lay (Australian National University)


Mr Jeffrey Lay

We discuss some results regarding iterated sums ofthe Mobius function. In particular, we show thatoscillatory behaviour of the sum of the Mobiusfunction extends naturally to iterated sums. Wealso investigate the true order of these iteratedsums. The methods used to derive our results canbe readily applied to the study of iterated sumsof the Liouville function.

16.10. Dedekind Sums

Simon Macourt (Macquarie University)


Mr Simon Macourt

We define the Dedekind sum for integers h, k by

(2) s(h, k) =

k∑µ=1

((hµ

k

))((µk

)).

The symbol ((x)) is the sawtooth function, whichis defined by(3)

((x)) =

x− [x]− 1/2 if x is not an integer,

0 if x is an integer,

where [x] is the integer part of x.

Myerson and Phillips raised the following problemin their study of fixed points of the Dedekind sum.

For 11ab ≡ 1 (mod c)

(4) s(a, c) + s(b, c)− a

c− b

cis an integer.

We provide a solution to this problem and alsoprove a more general result than the one men-tioned.

We also extend Myerson and Phillips proof of den-sity of fixed points of the Dedekind sum to showthat solutions to s(x) = x/6 and s(x) = x/4 arealso dense in the reals.

16.11. Galois Representations for Siegel ModularForms

Angus McAndrew (The University of Melbourne)


Mr Angus McAndrew

The representation theory of Gal(Q/Q) has at-tracted much attention over recent decades. Itis a powerful tool in understanding the mysteri-ous structure of the algebraic numbers. Today itforms part of the Langlands philosophy, connect-ing objects from Number Theory, Algebra, Geom-etry, and Analysis in a universal theory.

The work of Deligne, Serre and others provided apowerful link between Galois representations andmodular forms. We will discuss a generalisation ofthis correspondence to Siegel modular forms andsome associated properties.

16.12. The Arithmetic of Consecutive PolynomialSequences over Finite Fields

Min Sha (University of New South Wales)

15:40 Thu 1 October 2015 – SSN223

Dr Min Sha

In this talk, I will present some recent work onsequences of polynomials whose coefficients arechosen consecutively from a sequence in a finitefield of odd prime characteristic. These includebounds for the largest degree of irreducible fac-tors, the number of irreducible factors, as well asfor the number of such sequences of fixed length inwhich all the polynomials are irreducible. This isjoint work with Domingo Gomez-Perez and AlinaOstafe.

16.13. Every prime greater than 61 has threeconsecutive primitive roots

Timothy Trudgian (Australian National University)

16:05 Thu 1 October 2015 – SSN223

Dr Timothy Trudgian

Very little is known about the distribution ofprimitive roots modulo a prime p. Carlitz showedthat for a given n, all sufficiently large p haven consecutive primitive roots. This was madeexplicit in 2013 by Tanti and Thangadurai whoshowed that p > 1044000 is sufficient to showthat p has 3 consecutive primitive roots. Ishall present work, joint with Stephen Cohen andTomas Oliveira e Silva, which shows that p > 61is sufficient: this condition is best possible.

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17. Operator Algebras and Function Analysis

17.1. C*-algebras associated to graphs of groups

Nathan Brownlowe (University of Wollongong)


Dr Nathan Brownlowe

We start with a brief recap of Bass-Serre theory,which concerns the relationship between graphsof groups and the actions of groups on trees. Toa class of graphs of groups we build two C*-algebras: a universal C*-algebra built from gen-erators and relations encoding the algebraic andgeometric data in the graph of groups, and thecrossed product C*-algebra induced from the ac-tion of the fundamental group of a graph of groupson the boundary of the universal covering tree ofa graph of groups. We will examine the relation-ship between these C*-algebras. This is ongoingjoint work with Alexander Mundey, David Pask,Jack Spielberg and Anne Thomas.

17.2. Stable finiteness of k-graph algebras

Aidan Sims (University of Wollongong)


Dr Aidan Sims

It is relatively easy to decide when the C*-algebraof a graph is stably finite (meaning that no matrixalgebra over it contains an infinite projection).This is because every graph algebra is a crossed-product of an approximately finite-dimensional al-gebra by the integers, and a theorem of NateBrown says exactly when such algebras are stablyfinite. It is much more difficult to decide whena k-graph algebra is stably finite because it is acrossed product by the rank-k free abelian grouprather than just the integers, and Brown’s resultdoesn’t apply. I’ll describe recent joint work withLisa Orloff Clark and Astrid an Huef that answersthis question.

17.3. Dualities in real K-theory and physicalapplications

Guo Chuan Thiang (The University of Adelaide)


Dr Guo Chuan Thiang

The study of topological phases in physics involvesK-theory invariants of C*-algebras determinedby the underlying symmetry data. Real KR-theory enters when Real or Quaternionic struc-tures are provided by antiunitary symmetry oper-ations such as time reversal. The bulk-boundarycorrespondence/heuristic can be formulated math-ematically as a topological boundary map arisingfrom C*-algebra extensions. We illustrate howsuch maps can be T-dualized into simpler mapsinvolving ordinary real K-theory.

The talk is based on recent joint work with V.Mathai, arXiv:1503.01206, arXiv:1505.05250, andarXiv:1506.04492.

17.4. Magnetic spectral gap-labelling conjectures

Mathai Varghese (The University of Adelaide)


Prof Mathai Varghese

We generalise the spectral gap-labelling conjec-ture of Bellissard to the case with non-zero mag-netic field, and prove it in low dimensional cases.Given a constant magnetic field on p-dimensionalEuclidean space determined by a skew-symmetric(p×p) matrix Θ, and a lattice-invariant probabil-ity measure on the disorder set, we conjecture thatthe corresponding Integrated Density of States ofany self-adjoint operator affiliated to the twistedcrossed product algebra in this context takes onvalues on spectral gaps in an explicit Z-moduleinvolving Pfaffians of Θ and its sub-matrices thatwe describe, with multiplier associated to Θ. Thisis joint work with M. Benameur.

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18.1. Convexity on Groups and Semigroups

Jonathan Borwein (The University of Newcastle)


Dr Jonathan Borwein and Dr Ohad Giladi

Title: Convex analysis on groups and semigroups,I

Speaker: Jonathan Borwein Abstract: In this talkwe will show how we can canonically define thenotion of convexity on additive groups and semi-groups - so that in a vector space we have theclassical notion. It turns out that even in rela-tively simple groups, convex sets can look quitedifferent than in the classical vector space set-ting. Nevertheless, for large classes of groupsand semigroups, many known results from con-vex analysis still hold in this more general set-ting. (This is joint work with Ohad Giladi. Seehttps://www.carma.newcastle.edu.au/jon/ConvOnGroups.pdf.)

============================

Title: Convexity on topological groups and semi-groups, II

Speaker: Ohad Giladi (CARMA, University ofNewcastle)

Abstract: In this talk, we will discuss some as-pects of convex analysis in topological groups. Inparticular, we will discuss a group-theoretic ver-sion of the Krein-Milman Theorem, as well asthe Minimax Theorem. (This is joint work withJonathan Borwein. See https://www.carma.newcastle.edu.au/jon/LCGroups.pdf.)

18.2. Proper Efficiency and ProperKarushKuhnTucker Conditions for SmoothMultiobjective Optimization Problems

Regina Burachik (University of South Australia)

16:05 Thu 1 October 2015 – HUM115

Assoc Prof Regina Burachik

ProperKarushKuhnTucker (PKKT) conditions aresaid to hold when all the multipliers of the objec-tive functions are positive. In 2012, Burachik andRizvi introduced a new regularity condition underwhich PKKT conditions hold at every Geoffrion-properly efficient point. In general, the set of Bor-wein properly-efficient points is larger than the setof Geoffrion-properly efficient points. Our aim isto extend the PKKT conditions to the larger setof Borwein-properly efficient points.

18.3. Orbital Geometry and Eigenvalueoptimization

Andrew Eberhard (RMIT University)

15:15 Thu 1 October 2015 – HUM115

Prof Andrew Eberhard and Dr Vera Roshchina

The aim of this talk is to summarise, relate,explain some generalisations of results in non-smooth, and predominantly nonconvex analysis,that exploit the symmetry of underlying prob-lems. We will concentrate on results that general-ize the characterization of the proximal subdiffer-ential of group invariant functions. These resultscan be placed in a similar framework that revolvesaround the application of groups of symmetriesand notions of orbits of finite reflection groups.We discuss the characterization of the subdif-ferential of group invariant eigenvalue functionsthat are nonconvex and invariant with respect togroups that differ from the standard permutationgroups. Some applications are discussed.

18.4. An Improvement for the Conjugate GradientAnalysis Method

Soorena Ezzati (Federation University Australia)


Mr Soorena Ezzati, Dr David Yost

Reliability-based design optimisation (RBDO) mod-els are widely used in real world problems. Onechallenging step in solving an RBDO problem isevaluation of its probabilistic constraint. Thisevaluation is done in the inner loop of double-loop RBDO problems, in which many reliabil-ity analysis methods are available. It has beenreported that the conjugate gradient analysis(CGA) method is an efficient method to solve reli-ability analysis problems. An initial design pointis updated in this method based on the conju-gate gradient direction. However, it is found thatthe CGA method is not efficient enough to eval-uate a number of highly nonlinear performancefunctions. An amendment of the CGA method isintroduced in this talk in order to overcome thisdrawback. The improved method which we pro-pose is based on a self-adaptive conjugate searchdirection. Several numerical experiments are per-formed to compare efficiency of this method withthe existing CGA method. It will be shownthat the new method converges in a shorter timeand needs less iteration than the CGA method.Thus, it can be concluded that the improved CGAmethod is more efficient than the CGA method.

18.5. Convexity on topological groups andsemigroups, II

Ohad Giladi (The University of Newcastle)


Dr Ohad Giladi

In this talk, we will discuss some aspects of con-vex analysis in topological groups. In particular,we will discuss a group-theoretic version of the

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Krein-Milman Theorem, as well as the MinimaxTheorem. (This is joint work with Jonathan Bor-wein.)

18.6. Solving some variational problems withiterated function systems

Markus Hegland (Australian National University)


Prof Markus Hegland

Popular numerical solvers of elliptic variationalproblems involving integral and (partial)differentialoperators are based on piecewise polynomial func-tion approximations using the Ritz method. Herewe will discuss a more general approach basedon functions which are defined by iterated func-tion systems and which are using the collage fit,a variant of least squares. This is joint work withMichael Barnsley and Peter Massopust.

18.7. Alternating direction method of multipliersfor inverse problems

Qinian Jin (Australian National University)


Dr Qinian Jin

Alternating direction method of multipliers (ADMM)is an efficient and popular method for solvingstructured optimization problems due to its de-composability and superior flexibility. When ap-plied to deal with inverse problems, ADMM isusually used to solve a regularised minimisationproblem in which the regularisation parameteris assumed to be chosen properly. It is naturalto ask if it is possible to apply ADMM to solveinverse problems directly. In this talk we pro-pose an iterative method using ADMM strategyto solve linear inverse problems in Hilbert spaceswith general convex penalty term. When the datais given exactly, we give a convergence analysis ofour ADMM algorithm. In case the data containsnoise, we show that our method is a regularisationmethod as long as it is terminated by a suitablestopping rule. Numerical simulations are reportedto test the efficiency of the method. This is ajoint work with Yuling Jiao, Xiliang Lu and Wei-jie Wang.

18.8. Duality and Computations forControl-constrained Optimal Control Problems

Yalcin Kaya (University of South Australia)

16:30 Thu 1 October 2015 – HUM115

Walter Alt, Regina S. Burachik, C. Yalcin Kaya,

Saba N. Majeed, Christopher Schneider

We derive the Fenchel dual of control-constrainedlinear-quadratic optimal control problems, includ-ing the ones in which the control variable appearslinearly. We show that strong duality and saddle

point properties hold. In the case when the con-trol variable appears linearly in the control prob-lem, the optimal control is well-known to be acombination of bang–bang and singular control, asopposed to continuous optimal control in the caseof positive definite quadratic control term in theobjective functional. We assume that the optimalcontrol in the former case is bang–bang, and usea quadratic regularization in the objective func-tional to make the problem tractable. We providenew results on discretization of the dual prob-lem. We carry out numerical experiments withthe discretized primal and dual formulations ofthe problem. We illustrate that by solving thedual of the optimal control problem, instead ofthe primal one, significant computational savingscan be achieved. Other numerical advantages arealso discussed.

18.9. Optimal control of 1,3-propanediolproduction processes

Ryan Loxton (Curtin University of Technology)


Assoc Prof Ryan Loxton

This talk is concerned with the batch and fed-batch fermentation processes for producing 1,3-propanediol, an important industrial polymer withapplications to cosmetics, adhesives, lubricants,and medicines. For the batch fermentation pro-cess, we consider an optimal control problem inwhich the goal is to maximize process yield andminimize system sensitivity with respect to pa-rameter uncertainties; for the fed-batch process,we consider another optimal control problem inwhich the goal is to maximize yield and mini-mize feeding rate variation. We show that eachof these non-standard optimal control problemscan be solved using a combination of computa-tional techniques, including control parameteri-zation, nonlinear programming, and variationalanalysis. Numerical examples using real data willbe discussed in the talk.

18.10. Scheduling for a Processor Sharing Systemwith Linear Slowdown

Yoni Nazarathy (The University of Queensland)


Dr Yoni Nazarathy

We consider the problem of scheduling arrivals toa congestion system with a finite number of usershaving identical deterministic demand sizes. Thecongestion is of the processor sharing type in thesense that all users in the system at any given timeare served simultaneously. However, in contrast toclassical processor sharing congestion models, theprocessing slowdown is proportional to the num-ber of users in the system at any time. That is, therate of service experienced by all users is linearly

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decreasing with the number of users. For eachuser there is an ideal departure time (due date).A centralized scheduling goal is then to select ar-rival times so as to minimize the total penaltydue to deviations from ideal times weighted withsojourn times. Each deviation is assumed qua-dratic, or more generally convex. But due to thedynamics of the system, the scheduling objectivefunction is non-convex. Specifically, the systemobjective function is a non-smooth piecewise con-vex function. Nevertheless, we are able to leveragethe structure of the problem to derive an algo-rithm that finds the global optimum in a (largebut) finite number of steps, each involving the so-lution of a constrained convex program. Further,we put forward several heuristics. The first is thetraversal of neighbouring constrained convex pro-gramming problems, that is guaranteed to reacha local minimum of the centralized problem. Thisis a form of a “local search”, where we use theproblem structure in a novel manner. The secondis a one-coordinate “global search”, used in coor-dinate pivot iteration. We then merge these twoheuristics into a unified “local-global” heuristic,and numerically illustrate the effectiveness of thisheuristic. Joint work with Liron Ravner.

18.11. New Algorithms to Generate the ParetoFront of Multiobjective Optimization Problems

Mohammed Mustafa Rizvi (University of South

Australia)

15:40 Thu 1 October 2015 – HUM115

Dr Mohammed Mustafa Rizvi

We present a new scalarization technique fornonconvex multiobjective optimization problems,which is particularly useful for disconnected Paretofronts or disconnected feasible sets. First we es-tablish the theoretical features of the proposedscalarization. Then, combining this scalariza-tion and existing grid generation techniques fromthe literature, we propose practical algorithms tosolve tri-objective and four-objective optimizationproblems. It is well-known that generating espe-cially the boundary of the (bounded) Pareto frontof problems with three or more objectives is quitea challenging task. We illustrate the algorithmswe propose on synthetic test problems, as wellas a problem involving a rocket injector design.We show that our algorithms outperform the ex-isting ones, such as the Normal Boundary Inter-sections method due to Das and Dennis and theSuccessive Approach due to Mueller-Gritschneder,Graeb and Schlichtmann.

18.12. Geometry of solution sets in multivariateChebyshev polynomial approximation problem

Vera Roshchina (RMIT University)


Dr Vera Roshchina, Dr Nadezda Sukhorukova, Dr.

Julien Ugon, A/Prof. David Yost

We revisit the problem of multivariate Chebyshevapproximation and address the question of whenthe solutions are unique and study the geometryof the solution sets.

18.13. Spaces of convex sets

Brailey Sims (The University of Newcastle)

14:50 Thu 1 October 2015 – HUM115

Theo Bendit and Brailey Sims (presenter)

Let C(X) denote the set of all non-empty closedbounded convex subsets of a normed linear spaceX. In 1952 Hans Radstrom described how C(X)equipped with the Hausdorff metric could be iso-metrically embedded in a normed lattice with theorder an extension of set inclusion. We call thislattice the Radstrom of X and denote it by R(X).We will:

(a) outline Radstrom construction,(b) survey the Banach space structure and

properties of R(X), including; complete-ness, density character, induced map-pings, inherited subspace structure, re-flexivity, and its dual space,

(c) explore possible synergies with metricfixed point theory.

18.14. Reconstruction Algorithms for BlindPtychographic Imaging

Matthew Tam (The University of Newcastle)


R. Hesse, D.R. Luke, S. Sabach and M.K. Tam

In scanning ptychography, an unknown specimenis illuminated by a localised illumination functionresulting in an exit-wave whose intensity is ob-served in the far-field. A ptychography datasetis a series of these observations, each of whichis obtained by shifting the illumination functionto a different position relative to the specimenwith neighbouring illumination regions overlap-ping. Given a ptychographic data set, the blindptychography problem is to simultaneously recon-struct the specimen, illumination function, andrelative phase of the exit-wave. In this talk Iwill discuss an optimisation framework which re-veals current state-of-the-art reconstruction meth-ods in ptychography as (non-convex) alternatingminimization-type algorithms. Within this frame-work, we provide a proof of global convergenceto critical points using the Kurdyka- Lojasiewiczproperty.

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19. Probability

19.1. Discrete multivariate approximation in totalvariation

Andrew David Barbour (Universitaet Zuerich)


A. D. Barbour, M. J. Luczak, A. Xia

When approximating the distribution of an inte-ger valued random variable, it is natural to tryto measure the error with respect to total vari-ation distance. For Poisson approximation, thishas been extraordinarily successful. In recentyears, it has also been shown that approxima-tion in total variation can be established in manycircumstances in which a normal approximationis good, strengthening the usual results based onKolmogorov distance. In our talks, we present arecipe for establishing total variation approxima-tion in 2 or more dimensions, using the discretenormal family, and illustrate it in the context ofStein’s method of exchangeable pairs.

19.2. Stochastic Two-dimensional Fluid Models:an operator approach

Nigel Bean (The University of Adelaide)


Prof Nigel Bean

A particular type of stochastic two-dimensionalfluid model can be approached in an analogousway to a traditional Stochastic Fluid Model byworking in the operator domain. The theoreti-cal basis for this has been published. However,trying to apply this work has lead to a numberof unexpected surprises. In this talk I’ll focus onexplaining these surprises.

19.3. Pricing discrete average options

Daniel Dufresne (The University of Melbourne)


Prof Daniel Dufresne, Prof Felisa Vazquez-Abad

Remarkable results have been obtained about thepricing of average (=Asian) options when the av-eraging is done continuously, but in real life thepayoffs depend on an ordinary discrete average.The discrete case is more difficult than the contin-uous one, u less there are just very few averagingpoints. A few approximations exist, some betterthan others, but there is still no computationallyefficient formula for pricing average options ac-curately, or to find the distribution of a discreteaverage of stock prices (in the Black-Scholes set-ting). We present a new type of approximationthat does very well in a large number of cases.Joint work with Professor Felisa Vazquez-Abad,City University of New York

19.4. SPDE limits for the age structure of apopulation

Jie Yen Fan (Monash University)


Jie Yen Fan, Kais Hamza, Peter Jagers, Fima

Klebaner

Consider a general branching process that is su-percritical (resp. subcritical) when the populationsize is below (resp. above) the carrying capacity,and whose reproduction parameters may dependon the age of the individual as well as the wholeage structure of the population. We give the law oflarge number and the central limit theorem of theage structure as the carrying capacity increases.

19.5. Bootstrap Random Walks

Kais Hamza (Monash University)


Dr Kais Hamza

Consider a one dimensional simple random walkX = (Xn)n≥0. We form a new simple symmet-ric random walk Y = (Yn)n≥0 by taking sums ofproducts of the increments of X and study thetwo-dimensional walk (X,Y ) = ((Xn, Yn))n≥0.We show that it is recurrent and when suitablynormalised converges to a two-dimensional Brow-nian motion with independent components; thisindependence occurs despite the functional depen-dence between the pre-limit processes. The pro-cess of recycling increments in this way is repeatedand a multi-dimensional analog of this limit theo-rem together with a transience result are obtained.The construction and results are extended to in-clude the case where the increments take valuesin a finite set (not necessarily −1,+1). Timepermitting, I will present a number of possible ex-tensions currently being investigated. This workis joint with Andrea Collevecchio and Meng Shi.

19.6. Approximations of stochastic system nearunstable fixed point

Fima Klebaner (Monash University)


Prof Fima Klebaner

We give new approximations of non linear sys-tems in the vicinity of unstable fixed point onincreasing time intervals. The approximation in-volves two steps, first it is approximated by a lin-ear stochastic process, and then by non linear de-terministic system. This talk is based on the pa-per with A. Barbour, K. Hamza, and H. Kaspi,Escape from the boundary of Markov Populationprocesses, Adv. Appl. Probab, 2015.

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19. Probability

19.7. False Alarm Control for Window-LimitedChange Detection

Julia Kuhn (The University of Queensland)


Ms Julia Kuhn

We are interested in statistical change point detec-tion problems where the maximum testing periodis large but bounded. Popular detection methods,such as CUSUM, non-parametric CUSUM andEWMA, typically proceed by sequentially evalu-ating a certain test statistic and comparing it toa predefined threshold; a change point is detectedas soon as the threshold is exceeded. The teststatistic is often related to the log-likelihood ra-tio, and its computation can be expensive if thedata sequences are not independent. In this talkwe therefore consider testing data in sliding win-dows of fixed size. Traditionally, the average runlength criterion – the expected time until the firstfalse detection – is then used to select a thresholdthat ensures the false detection rate is limited tospecified level. It can be argued, however, thatusing the average run length criterion may not berestrictive enough for window-limited testing. Wetherefore propose a different criterion that is prov-ably more stringent. We then outline methods forfinding a threshold such that this false detectioncriterion is satisfied, and comment on optimalityof CUSUM under this new criterion.

19.8. Slowing time: Markov-modulated Brownianmotion with a sticky boundary

Giang Nguyen (The University of Adelaide)


Dr Giang Nguyen

We analyze the stationary distribution of regu-lated Markov modulated Brownian motions (MMBM)modified so that their evolution is slowed downwhen the process reaches level zero level zero issaid to be sticky.

19.9. Whittaker-Kotel’nikov-Shannonapproximation of sub-Gaussian random processes

Andriy Olenko (La Trobe University)


Dr Andriy Olenko

We generalize some classical results and obtainnew truncation error upper bounds in the sam-pling theorem for bandlimited stochastic pro-cesses. Lp([0, T ]) and uniform approximations ofϕ-sub-Gaussian random processes by finite timesampling sums are investigated. Explicit trunca-tion error upper bounds are established. Somespecifications of the general results for which theassumptions can be easily verified are given. Di-rect analytical and probability methods are em-ployed to obtain the results.

The presentation is based on a joint paper withProf. Yu.Kozachenko.

19.10. A Simulation Algorithm for QueueingNetwork Stability Identification

Brendan Patch (The University of Queensland)


Brendan Patch

One of the first considerations in the design of aqueueing system is ensuring stability. This is aguarantee that the capacity of the system is suf-ficient to meet demand in the long run. Due tothis, the stability of queueing systems has longbeen an area of intense research by the appliedprobability community. The aim of this researchhas been to determine the set of parameters, suchas arrival or service rates, for which the number ofcustomers in a given queueing system will remainfinite over time. For us this means that the drift ofthe system’s size is expected to remain sublinear.We call the set of parameters satisfying this con-dition the stability region, and develop a methodto efficiently find it using simulation.

Since determining the stability region of a givenqueueing network is often a highly non-trivialtask, results are primarily only available for spe-cific, relatively simple, systems. There does notcurrently exist a unified framework with which todetermine the stability region of a general queue-ing network. Moreover, for many systems a closedform expression for the stability region is notmathematically tractable. In this case a sensi-ble approach is to use an approximation methodthat provides a reasonable guarantee of determin-ing the stability region.

It is common to use simulation to establish sta-bility for a given choice of parameters. If a par-ticular parameter choice appears to result in thesimulated queue size becoming unbounded over along time frame, then this is often taken as anindication that the parameter choice is unstable.To determine the stability region more generallyrequires a sequence of simulations, and it is some-times possible to perform an exhaustive search (upto a chosen granularity) of the parameter set toidentify which choices appear to produce unstablebehaviour. In other cases, however, such a searchmay be computationally infeasible. It is thereforesensible to develop methods of ensuring that avail-able computational effort is allocated in the searchof the parameter space in an efficient manner.

In this talk we will discuss an approach to search-ing the parameter space which is based on thewell known simulated annealing optimisation al-gorithm. Our principle result shows that the sta-bility of a set of parameters for a given system canbe summarised using a single Markov chain that

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19. Probability

randomly searches the parameter space for an el-ement that is ‘most likely’ to induce instability.

Our algorithm is given informally as follows. Con-sider a set of Markov chains (Xλ : λ ∈ L), eachwith state space X , where L ⊂ Rn parameterisesdifferent configurations of the chain. For instance,λ ∈ L could parameterise the arrival rates of aqueueing network. The Markov chain generatedby the algorithm has state (x, λ) ∈ X ×L, wherex is the current state of the queueing system andλ is the parameterisation last considered by thealgorithm. Given this configuration, our algo-rithm then samples randomly from L a new can-didate parameter µ. After running the chain forτ time units from initial state x, it then samplesXµ(τ) = y. Here τ is chosen to be proportional to|x|. The next state of the Markov chain is chosenby comparing the new candidate solution (y, µ)and the old state (x, λ) according to the followingrule

(x′, λ′) =

(y, µ) with probability exp

(min0, |y| − |x|

),

(x, λ) otherwise.

We will show how to construct a Markov chainthat has greater expected drift than any chainproduced by the algorithm that has no measur-able subset of parameters which is unstable. Us-ing this chain we are able to derive a criterionfor rigorously testing (statistically) the hypothe-sis that the set of parameters is stable. In the talkwe will also apply the algorithm to some examplenetworks.

This is joint work with Neil Walton and MichelMandjes.

19.11. Population networks with local extinctionprobabilities that evolve over time

Philip Keith Pollett (University of Queensland)


Prof Philip Keith Pollett

I will describe a variant of Hanski’s incidence func-tion model that accounts for the evolution overtime of landscape characteristics affecting the per-sistence of local populations. In particular theprobability of local extinction is allowed to evolveaccording to a Markov chain. This covers thewidely studied case where patches are classifiedas being either suitable or unsuitable for occu-pancy. For large population networks the per-sistence and equilibrium levels of the populationare determined by the distribution of the life spanof local populations and not by the specific land-scape dynamics.

This is joint work with Ross McVinish and Jessica(Yui Sze) Chan

19.12. Statistical inference for phase-type scalemixtures

Leonardo Rojas Nandayapa (The University of

Queensland)


Dr Leonardo Rojas Nandayapa

An effective approach to approximate the MLEestimators for a classical phase-type distributionis the EM algorithm (Asmussen, et.al., 1996). Weextend this methodology to the case of phase-typescale mixtures, which can be seen as an extensionof classical phase-type distributions to infinite di-mensions in order to include heavy-tailed distri-butions.

I will introduce a couple of models and their corre-sponding EM estimators. Estimates of the FisherInformation will enable us to test if a data setcomes from specific family of heavy-tailed distri-butions. I will illustrate the results with a seriesof examples both with light and heavy tailed data.

19.13. Calculating optimal limits for transactingcredit card customers

Peter Gerrard Taylor (The University of

Melbourne)


Jonathan Budd and Peter Taylor

We present a model of credit card profitability,assuming that the card-holder always pays thefull outstanding balance. The motivation for themodel is to calculate an optimal credit limit,which requires an expression for the expected out-standing balance. We derive its Laplace trans-form, assuming that purchases are made accord-ing to a marked point process and that there is asimplified balance control policy in place to pre-vent the credit limit being exceeded.

We calculate optimal limits for a compound Pois-son process example and show that the optimallimit scales with the distribution of the purchas-ing process and that the probability of exceedingthe optimal limit remains constant.

Furthermore, we establish a connection with theclassic newsvendor model and use this to calcu-late bounds on the optimal limit for a more com-plicated balance control policy. Finally, we applyour model to real credit card purchase data.

131

20. Statistics

20.1. Inference for population dynamics in theNeolithic period

Richard Boys (The University of Newcastle UK)

14:50 Thu 1 October 2015 – SSN235

Prof Richard Boys

We consider parameter estimation for the spreadof the Neolithic incipient farming across Europeusing radiocarbon dates. We model the arrivaltime of farming at radiocarbon-dated, early Ne-olithic sites by a numerical solution to an advanc-ing wavefront. We allow for (technical) uncer-tainty in the radiocarbon data, lack-of-fit of thedeterministic model and use a Gaussian processto smooth spatial deviations from the model. In-ference for the parameters in the wavefront modelis complicated by the computational cost requiredto produce a single numerical solution. We there-fore employ Gaussian process emulators for thearrival time of the advancing wavefront at eachradiocarbon-dated site. We validate our modelusing predictive simulations.

20.2. Hybrid Fractionally Integrated STAR andGenetic Algorithm for Modeling Foreign-ExchangeRates

Irhamah Irhamah (Institut Teknologi Sepuluh

Nopember)

15:40 Thu 1 October 2015 – SSN235

Dr Irhamah Irhamah

Foreign Exchange Rates data is indicated to belong memory and non linear. In this study, Frac-tionally Integrated Smooth Transition Autore-gressive (FISTAR) is used for simultaneously cap-turing those two features, but FISTAR parameterestimation model still leaves a problem about itsconvergence. Genetic Algorithm (GA) as searchtechnique, has been proven to be an efficient andpowerful method for numerous general optimisa-tion problem since it flexibility to handle variousobjective functions and constrains, and also canlead to global optimum. Thus we propose hybridFISTAR with GA to obtain better parameter es-timates and higher forecasting accuracy in model-ing Foreign Exchange rates. The results are alsocompared with Autoregressive Fractionally Inte-grated Moving Average (ARFIMA) time seriesmodel that captures long and short memories.

Keywords: time series, long memory, non linear,FISTAR, genetic algorithm

20.3. Mixture of two Transmuted Weibulldistributions

Muhammad Shuaib Khan (The University of

Newcastle)


Muhammad Shuaib Khan, Robert King, Irene

Hudson

This research investigates the mixture model oftwo transmuted Weibull distributions (MTTWD)and studies its statistical properties. We obtainthe analytical shapes of the density, reliability andhazard functions. The identifiability property ofthe MTTWD is proved. Maximum likelihood es-timation is used for estimating the unknown pa-rameters. We evaluate the performance of MLEthrough Monte Carlo simulations.

20.4. Analysis of Proteomics Imaging MassSpectrometry Data

Inge Koch (The University of Adelaide)


Dr Inge Koch

Mass spectrometry (MS) has become a versatileand powerful tool in proteomics for the analysisof complex biological systems. Much of the recentresearch has been motivated by the requirementsin cancer research to differentiate cell populationsand tissue types of such data accurately and effi-ciently.

In this talk we give an overview of different ap-proaches to proteomics MS data and the statisti-cal methods used in the analyses of such data. Forthe more recent imaging MS data we illustrate ina combined cluster analysis/feature extraction ap-proach the potential for distinguishing cancer tis-sue from non-cancerous tissue regions and for se-lecting features which are candidates for biomark-ers.

20.5. Simple Method to Define Extreme Events formultiple dataset

Heri Kuswanto (Institut Teknologi Sepuluh

Nopember)


Dr Heri Kuswanto

Developing method to properly define extremestill becomes main interest for statisticians work-ing on meteorological field. This research pro-poses procedure to investigate the occurrence ofextreme involving multiple dataset. It is a com-mon case in meteorology or hydrology that thedataset is collected from several sites (eg. stationsor rain gauges). To identify the extreme dates, athreshold value in each site is determined by using

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20. Statistics

Peak Over Threshold (POT). Considering the factthat the time series dataset may contain a certaindegree of autocorrelation, declustering procedureis applied to ensure the independence of events.The declustering mechanism can be considered asa way of setting block with the length dependingon the information generated from the autocor-relation. All extremes from each site are com-bined to obtain a proper definition covering allsites. Investigation extreme rainfall and extremehigh temperature events in Indonesia is given asillustration.

20.6. Bayesian inference for Vector SmoothTransition Autoregressive model

Darfiana Nur (Flinders University)

16:05 Thu 1 October 2015 – SSN235

Mr Glen Livingston Jr and Dr Darfiana Nur

The Vector Smooth Transition Autoregressive withorder k [(VSTAR)(k)] model is a nonlinear multi-variate time series model that represents changingin regime, which is often applied in finance andhydrology, to mention a few. The main aim ofthis paper is to perform a fully Bayesian analysisof VSTAR(k) models including coefficient and im-plicit parameters as well as the model orders (k).To achieve this aim, the joint posterior distribu-tion of model orders, coefficient and implicit pa-rameters in the logistic VSTAR(k) model is firstlybeing presented. The conditional posterior distri-butions are then shown, followed by the design of aposterior simulator using a combination of MCMCalgorithms which includes Metropolis-Hastings,Gibbs Sampler, Reversible Jump MCMC algo-rithms respectively. Following this, extensive sim-ulation studies and a case study are being detailedat the end.

20.7. Heterogeneity in meta-analysis

Elizabeth Stojanovski (The University of

Newcastle)

16:30 Thu 1 October 2015 – SSN235

Dr Elizabeth Stojanovski

Studies have demonstrated that those in theMediterranean area to be among the healthiest.Their diets have become known as the Mediter-ranean diet which has been shown to be protectiveagainst heart disease, depression, stroke, Parkin-sons disease and some cancers. Some recent stud-ies have suggested the Mediterranean diet to beeffective for reducing one’s risk for diabetes. Arandom effects meta-analysis will be presented tocombine results from several studies to investigatethe link between elements of the Mediterraneandiet and diabetes. Given the limited number ofstudies, studies will be excluded to test the ro-bustness of the results from the meta-analysis.

133

Index of Speakers

Albrecht, Amie (13.1), 112

Alekseevsky, Dmitri (5.1), 84Alexander, Tristram (13.2), 112

Alexander, Tristram (8.1), 92

Alper, Jarod (2.1), 72Anderssen, Robert Scott (3.1), 74

Baniasadi, Pouya (12.1), 107Banks, John (13.3), 112

Barbour, Andrew David (19.1), 129

Bardi, Martino (0.1), 65Bardini, Caroline (13.4), 113

Bean, Nigel (19.2), 129

Bender, Axel (7.1), 89Bhargava, Manjul (0.2), 65

Bhatia, Sangeeta (12.2), 107Bhatia, Sangeeta (7.2), 89

Binder, Benjamin (12.3), 107

Black, Andrew (12.4), 107Borwein, Jonathan (13.5), 113

Borwein, Jonathan (18.1), 126

Bottema, Murk (15.1), 121Bourne, Christopher (14.1), 119

Bowman, David (5.2), 84

Boys, Richard (20.1), 132Bradford, Elizabeth (3.2), 74

Brownlowe, Nathan (1.1), 69

Brownlowe, Nathan (17.1), 125Buenzli, Pascal R (12.5), 107

Bui, Anh (11.1), 103Burachik, Regina (18.2), 126

Burton, Benjamin (10.1), 98

Cairns, Grant (16.1), 123Calbert, Greg (7.3), 89Cattlin, Joann (13.6), 113

Chang, Ting-Ying (11.2), 103Chopin, Joshua (3.3), 74

Cirstea, Florica Corina (11.3), 103Clancy, Kieran (4.1), 80

Clarke, Simon (3.4), 75

Combe, Diana (4.2), 80Cooper, Shaun (16.2), 123

Coster, Adelle (12.6), 108Cromer, Deborah (12.7), 108Cudmore, Peter (8.2), 92

Curiel, Imma (9.1), 96

Curry, Sean (5.3), 84

Daners, Daniel (8.3), 92

Daniels, Tom (14.2), 119De Gier, Jan (14.3), 119

Dearricott, Owen (5.4), 84

Delaigle, Aurore (0.3), 65Demange, Marc (4.3), 80

Demmel, James (0.4), 65

Dilcher, Karl (16.3), 123Do, Norman (10.2), 98

Do, Thoan Thi Kim (10.3), 98

Dow, Ana (10.4), 98Dragicevic, Davor (8.4), 92

Dudek, Adrian (16.4), 123

Dufresne, Daniel (19.3), 129

Duong, Xuan (11.4), 103

East, James (1.2), 69

Eberhard, Andrew (18.3), 126

Edwards, Antony (13.7), 113Egri-Nagy, Attila (1.3), 69

Ejov, Vladimir (9.2), 96

Elder, Murray (1.4), 69Ezzati, Soorena (18.4), 126

Fan, Chenxi (6.1), 86Fan, Jie Yen (19.4), 129

Farrell, Troy (3.5), 75

Feischl, Michael (6.2), 86Filar, Jerzy (0.5), 66

Filar, Jerzy (9.3), 96

Fish, Alexander (1.5), 69Flegg, Jennifer (12.8), 108

Flegg, Mark (12.9), 109Foster, Kylie (3.6), 75

Franklin, David (11.5), 103

Froyland, Gary (6.3), 86

Gaitsgory, Vladimir (8.5), 92

Ghitza, Alexandru (16.5), 123

Giladi, Ohad (18.5), 126Glen, Amy (4.4), 80

Globke, Wolfgang (10.5), 98Glynn, David G (4.5), 80

Gomes, Sean (11.6), 103

Gontar, Amelia (15.2), 121Gonzalez-Tokman, Cecilia (8.6), 93

Gregory, James (11.7), 103

Guo, Zihua (11.8), 104Guttmann, Tony (4.6), 81

Hajek, Bronwyn (3.7), 75Hall, Joanne (4.7), 81

Ham, Lucy (4.8), 81

Hammerlindl, Andy (8.7), 93Hamza, Kais (19.5), 129

Han, Xiaolong (11.9), 104Hanson, Stijn (16.6), 123Harrison, John (1.6), 69Hassell, Andrew (11.10), 104

Hauer, Daniel (11.11), 104Haythorpe, Michael (9.4), 96

Hazrat, Roozbeh (1.7), 70Hegland, Markus (18.6), 127

Hegland, Markus (6.4), 86Henderson, Anthony (2.2), 72Heyman, Randell (16.7), 123

Hodgson, Craig (10.6), 98

Hoffman, Neil (10.7), 98Hongler, Clement (0.6), 66

Horadam, Kathy (1.8), 70Horadam, Kathy (3.8), 76Howie, Joshua (10.8), 99

Howlett, Phil (3.9), 76Huilgol, Raja Ramesh (3.10), 76Hussain, Mumtaz (16.8), 124

134

Index of Speakers

Irhamah, Irhamah (20.2), 132

Jackson, Deborah (13.8), 114Jackson, Marcel (1.9), 70

Jenner, Adrianne (12.10), 109

Jepps, Owen (12.11), 109Jin, Qinian (18.7), 127

Jin, Qinian (6.5), 86

Johnston, Barbara (12.12), 109Johnston, Peter (12.13), 110

Kalloniatis, Alexander (7.4), 90Kaya, Yalcin (18.8), 127

Kennett, Carolyn (13.9), 114

Khan, Muhammad Shuaib (20.3), 132Kirwan, Frances (0.7), 66

Klebaner, Fima (19.6), 129

Koch, Inge (20.4), 132Kolar, Martin (5.5), 84

Kowalski, Tomasz (4.9), 81

Kozic, Slaven (2.3), 72Kress, Jonathan (13.10), 114

Kuhn, Julia (19.7), 130

Kumar, Shrawan (2.4), 72Kuo, Frances (0.8), 66

Kuswanto, Heri (20.5), 132Kwok, Eric (8.8), 93

Lamichhane, Bishnu (6.6), 86

Larusson, Finnur (10.9), 99Lauret, Jorge (5.6), 84

Lay, Jeffrey (16.9), 124Le Gia, Quoc Thong (6.7), 87

Lee, Gobert (15.3), 121

Leopardi, Paul Charles (6.8), 87Li, Qirui (11.12), 104

Licata, Anthony (1.10), 70

Licata, Anthony (2.5), 72Licata, Joan (10.10), 99

Links, Jon (14.4), 119

Lischewski, Andree (10.11), 99Liu, Qing (8.9), 93

Loch, Birgit (13.11), 115

Loxton, Ryan (18.9), 127Lu, Rui-Sheng (15.4), 121Lukyanenko, Inna (14.5), 119

Luu, Steven (11.13), 104

Macourt, Simon (16.10), 124

Mallet, Dann (13.12), 115Mangelsdorf, Christine (13.13), 115

Mathews, Daniel (10.12), 99

McAndrew, Angus (16.11), 124McDougall, Robert (1.11), 70

Medvedev, Alexandr (10.13), 99Mendan, Stacey (4.10), 81Meylan, Francine (5.7), 85

Miklavcic, Stanley Joseph (3.11), 76Miller, Tony (3.12), 76

Misereh, Grace Omollo (10.14), 100

Mitchell, Lewis (8.10), 93Moeini, Asghar (9.5), 97

Moitsheki, Joel (3.13), 77

Morris, Richard Michael (3.14), 77Morrison, Scott (2.6), 72

Murray, Michael (10.15), 100

Murray, Rua (8.11), 93

Nakazono, Nobutaka (8.12), 94

Nazarathy, Yoni (18.10), 127Nekouei, Ehsan (9.6), 97

Neuzerling, Murray (4.11), 82

Newsam, Garry (6.9), 87

Ng, Michael (15.5), 122Nguyen, Giang (19.8), 130

Nichols, James Ashton (12.14), 110

Nikolayevsky, Yuri (10.16), 100Nur, Darfiana (20.6), 133

Olenko, Andriy (19.9), 130Onn, Uri (2.7), 73

Ortega Piwonka, Ignacio (3.15), 77

Ottazzi, Alessandro (5.8), 85

Patch, Brendan (19.10), 130

Penington, Catherine (3.16), 77Pincombe, Brandon (7.5), 90

Pineda-Villavicencio, Guillermo (10.17), 100

Pollett, Philip Keith (19.11), 131Prince, Geoffrey (10.18), 100

Pulemotov, Artem (10.19), 101

Quinn, Diana (13.14), 115

Radnovic, Milena (10.20), 101

Rao, Asha (4.12), 82Reid, Colin David (1.12), 70

Reid, Darryn (7.6), 90Rice, John William (13.15), 116

Ridout, David (14.6), 119

Rizvi, Mohammed Mustafa (18.11), 128Roberts, David (10.21), 101

Roffelsen, Pieter (11.14), 105

Rojas Nandayapa, Leonardo (19.12), 131Rose, Danya (8.13), 94

Roshchina, Vera (18.12), 128

Ruffer, Bjorn (8.14), 94

Sadykov, Timur (5.9), 85

Saha, Arnab (2.8), 73Sajeev, Shelda (15.6), 122

Schmalz, Gerd (5.10), 85

Seaton, Katherine Anne (13.16), 116Sha, Min (16.12), 124

Shah, Nirav Arunkumar (11.15), 105

Shearman, Donald (13.17), 116Shelley, Michael (0.9), 67

Shi, Yang (8.15), 94

Sikora, Adam (11.16), 105Simpson, Jamie (4.13), 82

Sims, Aidan (17.2), 125Sims, Brailey (18.13), 128

Sircar, Sarthok (12.15), 110

Slovak, Jan (10.22), 101Small, Michael (8.16), 94

Spreer, Jonathan (10.23), 101

Stojanovski, Elizabeth (20.7), 133Stokes, Yvonne (3.17), 78

Stoyanov, Luchezar (8.17), 94Sumner, Jeremy (12.16), 111Sun, Qiang (3.18), 78

Tacy, Melissa (11.17), 105Talbot, Kyle (11.18), 105

Tam, Matthew (18.14), 128

Tao, Terence (0.10), 67Taylor, Christopher (4.14), 82

Taylor, Don (1.13), 71Taylor, Peter Gerrard (19.13), 131Taylor, Richard (7.7), 91

Thiang, Guo Chuan (14.7), 120Thiang, Guo Chuan (17.3), 125Thomas, Alise (3.19), 79Thomas, Anne (1.14), 71Thornton, Lauren (1.15), 71

Tomczyk, Jakub (9.7), 97

135

Index of Speakers

Tran, Minh (7.8), 91

Trenholm, Sven (13.18), 117

Trudgian, Timothy (16.13), 124Truong, Tuyen (5.11), 85

Tsartsaflis, Ioannis (5.12), 85

Turner, Ian (6.10), 87Twiton, Michael (11.19), 106

van Heijster, Petrus (8.18), 95Varghese, Mathai (17.4), 125

Voineagu, Mircea (2.9), 73

Vozzo, Raymond (10.24), 101

Wang, Hang (2.10), 73

Wang, Yuguang (6.11), 88Ward, Lesley (13.19), 117

Wheeler, Glen (10.25), 101

Wheeler, Glen (11.20), 106White, Kevin (13.20), 117

Wiegand, Aaron (13.21), 117

Williams, Ruth (0.11), 67Williams, Simon (15.7), 122

Womersley, Robert (6.12), 88

Wood, Leigh (13.22), 118Wormald, Nicholas (4.15), 82

Worthington, Joachim (8.19), 95Wright, Paul (8.20), 95

Xu, Jon (2.11), 73

Zarembo, Konstantin (0.12), 67

Zhang, Zhou (10.26), 102

Zudilin, Wadim (0.13), 68Zuparic, Mathew (14.8), 120

136

Index of Speakers

27 - Central Library 28 - Matthew Flinders Theatre

31 - Humanities Courtyard 32 - Social Sciences North

Enter via Registry Rd at the bus stop, up the stairs past the Central Library, or via Humanities Rd near Carpark 5.

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