Seminars

Tracy Craig (University of Cape Town)

The Academic Support Programme for Engineering in Cape Town

Tuesday, 6 December 2011, 11:00am
Room 447, Erskine Building

Abstract. Many of the students applying to study at the Universities of South Africa come from a disadvantaged educational background, due to the country's Apartheid legacy. In many cases the fact that these students reach or almost reach the university entrance requirements is a testimony to their academic strength and their work ethic.

I am the mathematics convenor in ASPECT, the programme in the Faculty of Engineering and the Built Environment at the University of Cape Town. ASPECT is a first year programme, setting the students on the path of an extended curriculum degree in Engineering. Our underlying structure is decreased load and increased contact time for the first year and, to a lesser extent, second year.

In this seminar I would like to describe what we do and what our challenges are. I invite commentary and look forward to hearing about any programmes in Canterbury which might inform or illuminate my circumstances.

Rachael Tappenden (University of Canterbury)

Development and Implementation of Algorithms for Fast Image Reconstruction

Thursday, 1 December 2011, 10:00am
Room 446, Erskine Building

Abstract. Signal and image processing is important in a wide range of areas, including medical and astronomical imaging, and speech and acoustic signal processing. There is often a need for the reconstruction of these objects to be very fast, as they have some cost (perhaps a monetary cost, although often it is a time cost) attached to them. This work considers the development of algorithms that allow these signals and images to be reconstructed quickly and without perceptual quality loss.

Merrilyn Goos (University of Queensland) and Mike Thomas (University of Auckland)

Transition from School to University Education in Mathematics: New Zealand and Australia Perspectives

Monday, 21 November 2011, 2.10pm Room 446, Erskine Building

Abstract. In recent years there has been a growing interest in the transition from school to university, which can prove difficult for many students. Reports identify problems in transition as a significant factor in learning mathematics, with international concerns about decreasing numbers of students opting to study mathematics at university and their decreasing levels of competence. Even students with good marks in school mathematics experience difficulties at university and sometimes fail the first year university mathematics courses. A widening gap between school and university mathematics appears to be a worldwide phenomenon and in many countries there is concern that differences in emphasis between school and tertiary mathematics may be increasing. In this talk we will report on some findings from recent projects on the transition from secondary to university education in mathematics in New Zealand and Australia. We also discuss practical recommendations arising from the projects, in particular student perspectives on transition, the effect of changes in mathematical emphasis and possible ways to improve communication and dialogue between members of the two sectors - school teachers and university lecturers. The seminar will be useful for lecturers who teach first-year mathematics courses and also for those interested in mathematics education.

About the speakers:
Merrilyn Goos is Professor of Mathematics Education and Director of the Teaching & Educational Development Institute at The University of Queensland and President of the Mathematics Education Research Group of Australasia. Mike Thomas is Professor of Mathematics Education in the Mathematics Department at The University of Auckland and is Chair of the 2012 International Congress on Mathematics Education Survey Team on ‒Key Mathematical Concepts in the Transition from Secondary to University–.

Robert Hannah (Department of Classics, Otago University)

The Antikythera Mechanism: celestial physics or metaphysics?

Thursday, 3 November 2011, 3.10pm
Room 031, Erskine Building
Interdisciplinary Colloquium Talk

Abstract. Discovered by chance in an ancient shipwreck in 1901, the fragmentary Antikythera Mechanism is now recognised as the most sophisticated scientific instrument from Greek and Roman antiquity. Its like would not be seen again for a thousand years, when Arabic science reintroduced similar mechanisms. It originally comprised over 30 interlocking, toothed gears, and several plates that were interrelated by their capacity to mark time in various ways an Egyptian calendar, a zodiac calendar, a star calendar (parapegma) and a local civil calendar. CT scanning has recently demonstrated that the Mechanism also tracked at least two of the five planets known to antiquity, and that it could calculate eclipses as well. For some reason it also had a dial to signal even the two- and four-yearly games festivals at Olympia, Isthmia, Dodona and Delphi.

In this paper I talk about the history of the discovery of the Mechanism, discuss its possible functions, and try to situate the Mechanism within a broader cultural background in antiquity.

Govind Menon (Division of Applied Mathematics, Brown University)

Algorithmic Design of Self-folding Polyhedron

Thursday, 20 October 2011, 3.10pm
Room 446, Erskine Building
Colloquium Talk

Abstract. Nature uses self-assembly to construct biomolecules and biocontainers such as the viral capsid. A fascinating new direction in materials chemistry is the development of self-assembling materials and devices, typically inspired by such biological systems.

I will describe one such set of experiments on ‒self-folding polyhedra– and a little associated theory. Little background knowledge will be presumed. This work is in collaboration with David Gracias’s group at Johns Hopkins.

Daniel Stouffer (School of Biological Sciences, University of Canterbury)

The Tragedy of the Commons in Mutualistic Networks

Thursday, 13 October 2011, 3.10pm
Room 446, Erskine Building
Interdisciplinary Colloquium Talk

Abstract. Mutualistic interactions form the basis of many biological and human systems of cooperation and competition. Mutualistic networks are composed of mutually beneficial interactions between individual participants or nodes of two distinct sets, such as plant species and their pollinators. Within these networks, one pattern in particular—nestedness—appears ubiquitous. This nested architecture minimizes interspecific competition and allows the network to support greater biodiversity. However, it is not known whether this benefit is received by each node in proportion to its contribution to overall network structure.

We address this question by applying a suite of structural and dynamic methods to an ensemble of flowering plant/insect pollinator networks. We find that nodes contribute heterogeneously to the overall nested architecture and that the removal of a strong contributor tends to decrease overall network persistence more than the removal of a weak contributor. Intriguingly, strong contributors 'do not gain individual survival benefits but are in fact the nodes most vulnerable to extinction. We explore the generality of these results by analysing a 15-year time series of the interactions between firms in the New York garment industry. As with the ecological networks, a firm's survival probability decreases as its individual nestedness contribution increases. Our results, therefore, introduce a new paradox into the study of the persistence of cooperative networks, and potentially address questions about the impact of invasive species in ecological systems and new competitors in economic systems.

Speaker's Bio-Sketch:
Dr. Daniel Stouffer joined the School of Biological Sciences at UC in February 2011 in the position of Lecturer. His educational background is in chemical engineering, though he did his PhD at Northwestern University studying ecological networks under the supervision of a physicist. While at Northwestern his training was explicitly interdisicplinary and he participated in the NSF funded IGERT about "Dynamics of Complex Systems in Science and Engineering." Before joining UC, he was a postdoctoral fellow at the Estación Biológica de Doñana in Sevilla, Spain where he continued his work on complexity in ecology and complex systems in general. At UC, he plans to lead a research group based around these two general themes and to maintain a constant mix of biologists, physicists, engineers, and mathematicians.

Charles Semple (University of Canterbury)

Submodular Functions and Optimizing Biodiversity

Thursday, 6 October 2011, 3.10pm
Erskine Room 446
Colloquium Talk

Abstract. One of the fascinations of mathematics is that common notions frequently arise in unexpected settings. Recognizing such occurrences, and then exploiting the theory of the common notion, often leads to elegant arguments and results.

In this talk, we describe such a fascination in the context of optimizing biodiversity, where the common notion arising is submodular functions. This is joint work with Magnus Bordewich (Durham University).

Stefan Winkler (Geological Sciences, University of Canterbury)

Glaciers - Good Indicators of Past and Present Climate Change?!

Thursday, 29 September 2011, 3.10pm
Room 446, Erskine Building
Interdisciplinary Colloquium Talk

Abstract. Glaciers are often recommended as perfect indicators of past and present climate change. International organizations like the IPCC (Intergovernmental Panel on Climate Change) and others frequently utilize global glacier data sets to demonstrate the development of the climate during the past decades. Glaciers are also in widespread use for visualization of the present "Global Warming" to the public by environmentalists as well as the media. In the talk, the popularity of glaciers as climate indicators is briefly explained, followed by a more critical review of their potential and limitations in a global context. With the help of a few case studies from New Zealand and Norway, it will be shown that e.g. the investigation and palaeoclimatological interpretation of glacial landforms is far more complicated than often anticipated. The need for spatial differentiation with the climate - glacier relationship will be emphasized alongside a look at some methodological uncertainties and challenges.

Speaker's Bio-Sketch:
Dr. Stefan Winkler joined the Department of Geological Sciences at UC in May 2010 in the position of a Senior Lecturer for Palaeoclimatology and Quaternary Geology. He has a scientific background as Physical Geographer and worked as Lecturer and Associate Professor at two German universities. He spent some years in Norway as guest scientist and during field work, and has close international collaborative connections. Before he took up his position at UC, he had already performed several field campaigns in the Southern Alps of New Zealand where his main interest is the Holocene climate and glacier history, i.e. the climate variations during the past several thousand years. In the immediate future, he wants to built up a research group within the department focussing on the reduction of the still existing uncertainties and contradictions in the palaeoclimatic interpretation of past glacier chronologies for New Zealand.

Note:
A primer for this Interdisciplinary Colloquium Talk will take place 4.15pm, Friday 23 September in KA04 when Christian Heining of Bayreuth University will talk on glacier flows. All welcome.

Douglas S. Bridges (University of Canterbury)

Permuting series, and computing projections

Thursday, 22 September 2011, 3.10pm
Room 446, Erskine Building

Building on Maarten McKubre-Jordens’s primer talk on constructive mathematics, this talk will discuss two disjoint topics in constructive analysis.

1. In the nineteenth century, G.F.B. Riemann proved two theorems about rearrangements of an infinite series ∑a_n of real numbers:

   RST₁ If ∑a_n is absolutely convergent, then every rearrangement of it converges to the same sum.

   RST₂ If ∑a_n is convergent but not absolutely convergent, then for any real number x, there exists a rearrangement of the series that converges to x. Moreover, there are rearrangements that diverge to ±∞.

   Michael Beeson asked, in 1974, whether one could prove these theorems constructively. The affirmative answer was given in 2009 by dsb and Josef Berger. A more interesting question then arose: can one prove, constructively, Riemann’s permutation theorem in the following form (which easily follows from RST₁ and RST₂ with classical logic)?

   RST₃ If every permutation of ∑a_n converges, then the series is absolutely convergent.

   The answer to this question takes us into the game of constructive reverse mathematics, bringing into play an important boundedness principle due to Hajime Ishihara.

2. The second part of my talk will deal with a constructive analysis of a classical algorithm, described in Paul Halmos’s Hilbert space problem book, for the computation of the infimum of two projections in a Hilbert space. Estimating the rate of convergence of this algorithm is not possible, in general, unless you allow unbounded searches. I will discuss conditions under which the algorithm’s convergence rate can be given; this will require me to introduce some facets of single-operator theory that are simply invisible to the eye of the classical analyst.

Ian Frigaard (University of British Columbia)

Math in the Mud?

Thursday, 15 September 2011, 3.10pm
Room 446, Erskine Building
Interdisciplinary colloquium seminar

Abstract. Oil and gas wells are subjected to a process called primary cementing, in which a cylindrical steel casing is cemented into the borehole, both sealing the well and giving mechanical support. At the core of this process the drilling mud that is in the borehole must be removed and replaced with a cement slurry. These two fluids are non-Newtonian and typically have significantly different densities and rheologies. The displacement flows can take place within both pipe and eccentric annular geometries, at inclinations ranging from 0 to 90 degrees, and can range from laminar to fully turbulent. Industrial design of the process is based on physical intuition that is translated into rules and recommended practices.

Complexity in the process physics makes this a difficult problem to model and analyse. Therefore a multi-disciplinary and multi-faceted approach is needed. However, as is often the case, some of the intuition is faulty, conservative or allows room for refinement. We outline some of the modelling approaches we have used over the past 10 years, showing where mathematics has made an impact in allowing dispelling some myths and giving improved process understanding.

Seminar Primer
4.10pm, Friday 9 September, Kirkwood Village (by the Staff Club).
Subject: “A Quickie of Rheology Part 1” by Miguel Moyers-Gonzales. (Area: Dynamical Systems)

Dr Phil Wilson (University of Canterbury)

Bodies Clashing in Fluids

Thursday, 8 September 2011, 3.10pm
Room 446, Erskine Building

Abstract. Ship slamming, aircraft icing, pyroclastic flows, arterial plaques, bouncing bob sleighers: these few examples involve a body or bodies moving through a fluid and clashing, bouncing, or skimming against a solid wall, one another, or a layer of a different fluid.

In this talk, we will look at solid-solid or solid-fluid impacts, concentrating especially on the fluid-structure interaction in the pre-impact phase. The framework is of a thin body impacting obliquely in a channel. The influences of body thickness and camber are of some interest here. Our approach combines an interaction between asymptotic analysis and numerical methods.

The level of presentation should be accessible to all.

Michael Pauley

Cubics and negative curvature

Friday, 26 August 2011, 9:00am
Room 445, Erskine Building

Abstract. Riemannian cubics are curves that generalise cubic polynomials to arbitrary Riemannian manifolds, in the same way that geodesics generalise straight lines. In any complete Riemannian manifold, geodesics can be extended indefinitely. In this talk I will discuss the question of whether Riemannian cubics can be extended indefinitely. The sectional curvature of the manifold plays a role.

Maarten McKubre-Jordens (University of Canterbury)

Critical Phenomena and Distortion Functionals

Thursday, 25 August 2011, 2:00pm
Room 446, Erskine Building

Abstract. In this seminar we consider some theoretical motivations for certain critical phenomena in materials science. In particular we investigate minimisers of weighted distortion functionals, and consider the mean distortion for regions in the complex plane. These considerations connect a conjecture from Nitsche concerning the nonexistence of harmonic mappings between doubly connected regions to a problem now referred to as the Grötzsch problem and demonstrate conditions under which no deformation of minimal energy is possible among mappings of finite distortion. We also discuss some interpretations of the weight function to provide insight into physically relevant phenomena and possible directions for future investigation.

Richard Brown (University of Canterbury)

Numerical techniques for simulating cerebral bloodflow autoregulation ODE systems on a large-scale binary tree network.

Thursday, 25 August 2011, 9:00am
Room 446, Erskine Building

Abstract. Under certain assumptions the network of cerebral blood vessels can be modeled by a purely resistive binary tree where each vessel is characterised by a single resistance, computed as a function of its length and radius. Each vessel has the ability to vasoconstrict or vasodilate, hence changing its resistance, in response to local variables such as cellular Ca2+ concentration within the vessel. In this way the network of vessels collectively regulate the cerebral bloodflow. The dynamics of each vessel are nonlinear and can be described phenomenologically by a system of ODEs for each vessel.

Mathematically, the overall system is a large network of coupled ODEs, which can comprise up to millions of variables. The overall system is highly coupled, and can exhibit stiffness, so solution by traditional sequential ODE algorithms can be very expensive. The tree structure suggests an obvious parallelisation of the problem into subtrees, where the coupling between subtrees can be captured by a single variable: the blood pressure at the junction where the trees are coupled. The system can then be solved iteratively by a waveform relaxation variant, however convergence can be slow.

As an alternative approach to simulating the full system, we also investigate generating approximate solutions using linear reduced order models. These models are developed by computing a projection of the linearisation of the nonlinear system about its equilibrium onto a state space of much lower dimension.

Pipat Wongsaart

A Semiparametric Autoregressive Conditional Duration Model

Friday, 15 July 2011
Room 445, Erskine Building

Abstract. Most of the existing extensions of the Engle and Russell's (1998) Autoregressive Conditional Duration (ACD) model in the literature are aimed at providing additional flexibility on the dynamic specification of the conditional duration model and/or the shape of the hazard function. This paper introduces an alternative semiparametric regression approach to a nonlinear ACD modeling. The use of a semiparametric functional form on the dynamics of the duration process suggests the model being called the Semiparametric ACD (SEMI-ACD) model. The model allows useful generalizations of both components of the ACD class of models, particularly because of the fact that the semiparametric technique employed does not require an arbitrary assumption on the conditional distribution of the durations. To estimate the model, we extend an existing iterative estimation algorithm to the semiparametric setting and provide an alternative proof of its statistical consistency to the approach that is currently available in the literature. To ensure the statistical rigor of the SEMI-ACD estimation procedure, the asymptotic properties of the semiparametric estimators are established. These asymptotic results are presented in conjunction with simulated examples that illustrate a robust finite sample performance of the model. Finally, the paper applies the proposed method to model the price duration process in foreign exchange market.

Anna MacDonald (University of Canterbury)

Threshold estimation using a flexible extremal mixture model

Monday, 11 July 2011
Room 446, Erskine Building

Abstract. A plethora of recent articles have proposed various extreme value mixture models for threshold estimation and quantifying the corresponding uncertainty. These mixture models typically treat the threshold as a parameter, so it can be objectively estimated using standard inference tools, avoiding the aforementioned graphical diagnostics which require expert (subjective) judgment. These mixture models are typically easy to automate for application to multiple datasets, or in forecasting situations, for which various adhoc adaptations have had to be made in the past to overcome the threshold estimation problem.

This talk will outline one particularly flexible mixture model which splices together the usual extreme value model for the upper tail behaviour, with the threshold as a parameter, and the “bulk” of the distribution below the threshold captured by a non-parametric kernel density estimator. This representation avoids the need to specify a-priori a particular parametric model for the bulk distribution, and only really requires the trivial assumption of a smooth density which is realistic in most applications. This model overcomes sensitivity to the specification of the bulk distribution (and in particular it’s lower tail), which is known to be an issue with most of the existing mixture models. Inference for all the parameters, including threshold and kernel bandwidth, is carried out in a Bayesian paradigm, potentially allowing sources of expert information to be included which can help with the inherent sparsity of extremal sample information.

Travis Horton (University of Canterbury, Geological Sciences)

Orientation during Vertebrate Migration: how Maths and Stats can help solve a 3,000 year-old problem

Thursday, 7 July 2011
Room 446, Erskine Building

Abstract. Despite decades of experimental research, the scientific community remains far from understanding the cues and controls on animal migration. Recent advances in tracking technology have revolutionised animal migration research, presenting unprecedented opportunities to quantitatively analyse observed animal movements, and thousands of animals have been tracked over millions of kilometres during the past decade. The ecological community has used this data to identify migratory destinations, corridors, and the spatial, temporal, and environmental conditions of animal migration. Yet, many basic questions unanswered. What constitutes a 'departure' from a seasonal habitat? Are animal movements random or patterned? If they are patterned, what readily ailable exogenous cues are being using for spatial orientation? What's the spatial reference datum(a) of orientation? Are there seasonal, lunar, circadian cycles in the temporal patterning of animal movements? Answers to these questions will come from trans-disciplinary collaborations among biologists, geophysicists, astronomers, computer programmers, and mathematicians in the years ahead.

In this talk I will present a brief historical overview of migration research and the leading theoretical frameworks of spatial orientation during migration (magnetic orientation, solar orientation, etc.). Examples of seminal and cutting-edge data-based research, spanning diverse taxa, will also be presented.

Dennis Prangle (Lancaster University)

Summary statistics for Approximate Bayesian Computation

Friday, 24 June 2011
Room 101, Erskine Building

Abstract. Many modern statistical applications involve inference for complex stochastic models, where it is easy to simulate from the models, but difficult or impossible to calculate likelihoods. Approximate Bayesian Computation (ABC) is a method of inference for such models. It replaces calculation of the likelihood by a step which involves simulating artificial data for different parameter values, and comparing summary statistics of the simulated data to summary statistics of the observed data. The results are samples from an approximation to the Bayesian posterior distribution, whose quality depends crucially on the summary statistics. The question of how best to choose these has been an open problem. This talk reviews ABC methods and presents recent research on a method to provide summary statistics.

Dennis Prangle is a research associate in the Statistics Department of Lancaster University. His current research investigates the evolution of Campylobacter Jejuni, the bacteria responsible for the majority of human gastroenteritis cases, extending tools for statistical inference of complex stochastic processes developed in his PhD in collaboration with Prof. Paul Fearnhead and using data from the mEpiLab group at Massey University. Other research interests include Bayesian statistics and models of infectious disease epidemics.

Mary Myerscough (University of Sydney)

Honeybee Demography: the vital role of foragers in maintaining colony populations

Thursday, 10 February, 3:10pm
Room 446, Erskine Building
30 minutes, followed by a break and 20 minutes of discussion.

Abstract. Within colonies of honeybees, adult bees are divided into behavioural castes, roughly on the basis of age. We focus on hive bees, who are younger and do work inside the hive and on foragers who are generally older bees who work outside the hive. The rate that hive bees become foragers depends not only on their age but also on the number of foragers that the hive has already. We construct a model for the number of bees in a hive which includes the way that these bees move through different behavioural castes. We show that the colony’s survival is highly sensitive to forager death rate, even when the bees inside the hive are healthy and that other factors such as food and brood (immature bees) are less important in maintaining hive health. We explore the effects on the hive of having a large number of younger bees in its foraging workforce. This research has potential applications to colony collapse events in honeybees.

Teodor I. Burghelea (Universite de Nantes)

Complex fluids: complexity without imaginary part

Wednesday, 9th February, 3:10pm
Room 446, Erskine Building

Abstract. The concept of “complex fluids” will be introduced by focusing on their microscopic structure and its coupling to a macroscopic flow field. It will be shown that in this context, the complexity refers to a non-trivial stress-strain relation which often translates into a strongly nonlinear hydrodynamic problem.

Two particular classes of “complex fluids” will be presented: dilute solutions of linear polymers (viscoelastic fluids) and physical gels (viscoplastic fluids). Some “exotic” flow phenomena will be illustrated for each class of complex fluids by time-lapse movies, images of the flow fields and direct visualization of various “unusual” flow patterns.

The talk will close with a brief description of some difficulties in modeling “complex fluids”. As an example, some recent progress (work done in collaboration with Dr. Miguel Moyers) in understanding the hydrodynamic stability of viscoplastic fluids will be presented.

Robert Snocken (University of Southampton)

Representation theory of finitely generated nilpotent groups

Wednesday, 9th February, 2:10pm
Room 446, Erskine Building

Abstract. In this talk we will discuss some aspects of the representation theory of finitely generated nilpotent groups. We will introduce the representation zeta function; this is a complex function which encodes information about the group. We will then discuss the interplay between the analytic and arithmetic features of the zeta function and the algebraic properties of the group.

Alexander Danis (Uppsala University)

Parameter Estimation for Differential Equations by Rigorous and Non-rigorous Methods

Thursday, 27th January, 3:10pm
Room 446, Erskine Building

Abstract. Estimating parameters of a vector field from observations is a challenging inverse problem. In this talk we will introduce constraint propagation on directed acyclic graphs of arithmetical expressions of parametric families of vector fields. The talk should be accessible to a general maths/stats audience.

Jan Saxl (University of Cambridge)

Variations on Themes of Frobenius and Burnside

Wednesday, 26th January, 3:10pm
Room 446, Erskine Building
30 minutes, followed by a break and 20 minutes of discussion.

Abstract. The second edition of Burnside’s book, Theory of Groups of Finite Order, was published in 1911. In this talk, we shall first mention a few remarkable results of Frobenius and Burnside which appear in this book, and then present some related themes on permutation groups which are very much more recent.