NOTE day and time of this seminar
In this talk I will primarily discuss the Multiset Sampler (MSS): a general ensemble based Markov Chain Monte Carlo (MCMC) method for sampling from complicated stochastic models. After which, I will briefly introduce the audience to my interactive visual analytics based research.

Proposal distributions for complex structures are essential for virtually all MCMC sampling methods. However, such proposal distributions are difficult to construct so that their probability distribution match that of the true target distribution, in turn hampering the efficiency of the overall MCMC scheme. The MSS entails sampling from an augmented distribution that has more desirable mixing properties than the original target model, while utilizing a simple independent proposal distributions that are easily tuned. I will discuss applications of the MSS for sampling from tree based models (e.g. Bayesian CART; phylogenetic models), and for general model selection, model averaging and predictive sampling.

In the final 10 minutes of the presentation I will discuss my research interests in interactive visual analytics and the Visual To Parametric Interaction (V2PI) paradigm. I'll discuss the general concepts in V2PI with an application of Multidimensional Scaling, its technical merits, and the integration of such concepts into core statistics undergraduate and graduate programs.

161011102333

NOTE day and time of this seminar
Spectral clustering is a computationally feasible and model-free method widely used in the identification of communities in networks. We introduce a data-driven method, namely Network Change Points Detection (NCPD), which detects change points in the network structure of a multivariate time series, with each component of the time series represented by a node in the network. Spectral clustering allows us to consider high dimensional time series where the number of time series is greater than the number of time points. NCPD allows for estimation of both the time of change in the network structure and the graph between each pair of change points, without prior knowledge of the number or location of the change points. Permutation and bootstrapping methods are used to perform inference on the change points. NCPD is applied to various simulated high dimensional data sets as well as to a resting state functional magnetic resonance imaging (fMRI) data set. The new methodology also allows us to identify common functional states across subjects and groups. Extensions of the method are also discussed. Finally, the method promises to offer a deep insight into the large-scale characterisations and dynamics of the brain.

161007094119

The Metropolis-Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution, usually to estimate an expected value. At each step, the algorithm proposes a new random sample, and then decides whether to accept or not. Efficiency depends on the computational cost per random sample, and the correlation of the sequence - a sequence of independent random samples is ideal.

I analyse the efficiency of Metropolis-Hastings algorithms with stochastic autoregressive proposals. These include many existing methods, such as the Metropolis-Adjusted Langevin Algorithm (MALA), the preconditioned Crank-Nicolson algorithm (pCN) and the Hybrid Monte Carlo algorithm (HMC). Previously, each of these algorithms required their own separate analyses. Using my analysis I can extend what is known about these algorithms as well as analysing new algorithms.

161005102453

NOTE day and time of this seminar
Many scientific disciplines have strong traditions of developing models to approximate nature. Traditionally, statistical models have not included scientific models and have instead focused on regression methods that exploit correlation structures in data. The development of Bayesian methods has generated many examples of forward models that bridge the gap between scientific and statistical disciplines. The ability to fit forward models using Bayesian methods has generated interest in paleoclimate reconstructions, but there are many challenges in model construction and estimation that remain.

I will present two statistical reconstructions of climate variables using paleoclimate proxy data. The first example is a joint reconstruction of temperature and precipitation from tree rings using a mechanistic process model. The second reconstruction uses microbial species assemblage data to predict peat bog water table depth. I validate predictive skill using proper scoring rules in simulation experiments, providing justification for the empirical reconstruction. Results show forward models that leverage scientific knowledge can improve paleoclimate reconstruction skill and increase understanding of the latent natural processes.

161007103441

NOTE day and time of this seminar
When making inferences concerning the environment, ground truthed data will frequently be available as point referenced (geostatistical) observations accompanied by a rich ensemble of potentially relevant remotely sensed and in-situ observations.
Modern soil mapping is one such example characterised by the need to interpolate geostatistical observations from soil cores and the availability of data on large numbers of environmental characteristics for consideration as covariates to aid this interpolation.

In this talk I will outline my application of Least Absolute Shrinkage Selection Opperator (LASSO) regularized multiple linear regression (MLR) to build models for predicting full cover maps of soil carbon when the number of potential covariates greatly exceeds the number of observations available (the p > n or ultrahigh dimensional scenario). I will outline how I have applied LASSO regularized MLR models to data from multiple (geographic) sites and discuss investigations into treatments of site membership in models and the geographic transferability of models developed. I will also present novel visualisations of the results of ultrahigh dimensional variable selection and briefly outline some related work in ground cover classification from remotely sensed imagery.

Key references:
Fitzpatrick, B. R., Lamb, D. W., & Mengersen, K. (2016). Ultrahigh Dimensional Variable Selection for Interpolation of Point Referenced Spatial Data: A Digital Soil Mapping Case Study. PLoS ONE, 11(9): e0162489.
Fitzpatrick, B. R., Lamb, D. W., & Mengersen, K. (2016). Assessing Site Effects and Geographic Transferability when Interpolating Point Referenced Spatial Data: A Digital Soil Mapping Case Study. https://arxiv.org/abs/1608.00086

161007111343

There have long been concerns about the numeracy of many undergraduates, based on anecdotal evidence. We now have data from two schools within the university that document the issue. This seminar will provide a definition of what is meant by numeracy at the university level and will describe issues around its assessment and the impact of current University Entrance requirements.

160712144406

Viscoplastic materials such as Bingham or Heschel Bulkley fluids have a yield stress which must be exceeded before they flow. Their behaviour lies somewhere between liquids and solids. In this talk I will first present a microscopic Gibbs field model that mimics the macroscopic yielding behaviour of a viscoplastic fluid as a means to qualitative validate our constitutive model. In the second part of the talk we look at laminar unsteady pipe flow of a Carbopol gel, which is a model viscoplastic fluid. By looking in detail at the solid-fluid transition of this material, we found a strong coupling between the irreversible deformation states and the phenomenon of wall slip (where the fluid behaves as if it is sliding along the wall).

160712144623

Note day, time and venue of this special seminar
Semiclassical analysis arose as a set of techniques for studying the high energy (or semiclassical) limit of quantum mechanics. These techniques have the advantage that intuition derived from the quantum-classical correspondence principle can guide our technical development. In this talk I will introduce some of the key techniques and discuss results such as the $L^{p}$ growth for products of Laplacian eigenfunctions and high energy phase space concentration estimates.

160817131553

Note day and time of this special seminar
In a one-dimensional homogeneous medium, linear wave scattering by an array of inclusions, e.g. beads on a string, can be reduced to a multiple reflection/transmission problem, in which the reflected and transmitted waves by an inclusion become incident waves on the adjacent inclusions. Under time-harmonic conditions, fast iterative methods can be used to obtain the solution of this class of scattering problems. In a two-dimensional medium, however, such methods cannot be directly extended as there is no natural way of uniquely ordering a finite number of arbitrarily positioned inclusions, e.g. circles, in the plane. A semi-analytical method was devised to solve deterministically the scattering of time-harmonic waves by a large finite array of inclusions in two dimensions. The method consists of clustering the inclusions into adjacent parallel slabs. The solution is obtained by combining plane wave expansions of the scattered field by each slab and a fast iterative technique for slab-slab interactions similar to the one-dimensional method mentioned above.

In this talk, I will describe this so-called slab-clustering method (SCM) and demonstrate how it provides a convenient framework to analyse the evolution of a multi-directional wave field through a large random array of inclusions. I will consider several applications of the methods in acoustics and water waves science. In particular, I will discuss some model predictions based on the SCM that generated key insights into the directional properties of water wave fields propagating in ice-covered oceans.

160817130802

Note day, time and venue of this special seminar
Biological cells are the fundamental building blocks of life. At a molecular level, a cell operates according to the hard mathematical laws of physics and chemistry. Encoded in the network of molecular interactions are robust mechanisms which collectively determine the properties of life itself. Mathematical insight into cell scale behaviour is fundamentally limited by the computational scalability and convergence of mathematical frameworks that are used to describe physical systems at molecular scales (both spatial and temporal). In this presentation, I will highlight the main problems with classical mathematical approaches used to study intracellular spatio-temporal environments and present multiscale methods I have developed in the last 5 years which have allowed for improved accuracy, and efficiency. The objective of this research is to lay mathematical foundations for progress in the highly interdisciplinary mission of whole cell simulation at the level of individual molecules, a goal which has been termed a `Grand Challenge of the 21st Century'. The mathematical content of this talk is rather varied, as is the nature of applied mathematics. This research draws on partial differential equation theory, perturbation theory, N-body theory, random walks and stochastic processes as well as a number of miscellaneous areas of mathematics.

160812100952

The aim of this talk is to introduce the initial boundary value problem (IBVP) for the conformal field equations (CFEs), and as an application study gravitational perturbations of a black hole space-time.

The CFEs are a different mathematical representation of Einstein's field equations that allow one to study “infinity” of a space-time without any sort of limiting procedure. This is of interest as in general relativity infinity is the only place that energy is well defined.

In this talk, the main ideas of the CFEs will be discussed, along with the issues associated with forming an IBVP for them. A framework for the IBVP will be presented and numerical evidence of its success will be given. As an application I will discuss the problem of shooting a gravitational wave into a black hole. In particular, I will discuss how the IBVP is formulated for this situation and how to calculate the so-called "Bondi-energy" at infinity. The resulting expression is found to reproduce the famous Bondi-Sachs mass loss.

160712143109

Note day and time of this special seminar
Stochastic partial differential equations (SPDEs, for short) are mathematical models for evolutions in space and time, which are influenced by noise. They are aimed at describing phenomena in physics, chemistry, epidemiology, economics, and many other disciplines. Although we can prove existence and uniqueness of a solution to various classes of such equations, in general, we do not have an explicit representation of this solution. Thus, in order to make those models ready to use for applications, we need efficient numerical methods for approximating their solutions. And to determine the efficiency of an approximation method, we usually need to analyse the regularity of the target object, which is, in our case, the solution of the SPDE.

The aim of this talk is to present some recent results concerning the regularity of SPDEs and to point out their relevance for the question of developing efficient numerical methods for solving these equations. Before doing this, we first explain the meaning of the different parts of a typical SPDE. For simplicity, we focus on the most basic example, the stochastic heat equation driven by a (cylindrical) Wiener process. It arises from the common deterministic heat equation if we add what is called 'white noise'.

160812100405

The representation theory of the symmetric groups is closely related to combinatorial objects. For example, the simple ordinary and modular representations of the symmetric groups are parametrised by partitions and p-restricted partitions respectively. In this seminar, we discuss various relations between the properties of partitions and the structures of the classical modular representations of the symmetric groups. In particular, I will present a new combinatorial property which gives us the exact label of a signed Young module which is isomorphic to a simple Specht module.

This is a joint work with Susanne Danz.

Note day, time and venue of this special seminar

160801125732

Free analysis provides an analytic framework for dealing with quantities with the highest degree of noncommutativity, such as large random matrices. In the talk we will explore a natural extension of the notion of convexity to matrix spaces, the so-called matrix convex sets. We shall give an appropriate analog of the Hahn-Banach theorem and present some of its applications.

160412133900

The finite volume method is a numerical method mainly used in computational fluid dynamics. It is well suited to solving conservation law PDEs because it can exactly preserve the conserved quantity. In this talk I describe how to use a finite volume method to approximate the Frobenius-Perron operator; an operator that describes the time evolution of a probability density function in a dynamical system. The finite volume method will be shown to exactly preserve two essential properties of probability density functions, they must integrate to 1 and be positive. The positivity preserving property is new for finite volume methods and requires a CFL condition is satisfied. The finite volume method can be used instead of the Kalman filter, and produces accurate results even when the probability density function is multi-modal.

160223102439

STATISTICS
Michel de Lange :Deep learning
Georgia Anderson : Probabilistic linear discriminant analysis
Nick Gelling : Automatic differentiation in R

15-MINUTE BREAK 2.40-2.55

MATHEMATICS
Alex Blennerhassett : Toeplitz algebra of a directed graph
Zoe Luo : Wavelet models for evolutionary distance
Xueyao Lu : Making sense of the λ-coalescent
Terry Collins-Hawkins : Reactive diffusion in systems with memory
Josh Ritchie : Linearisation of hyperbolic constraint equations

Also
CJ Marland : Extending matchings of graphs: a survey
This one mathematics project presentation takes place at 12 noon on Thursday 26 May, room 241

160520092655

My interest in mathematics research was ignited by my secondary mathematics teacher. Robin Patterson introduced our class to some (then unsolved) Mathematical Problems. An examination of Euler's prime generating quadratics at High School was the seed for my first published paper 12 years later. Fermat's Last Theorem and the 4-colour conjecture motivated me through graduate study and steered me into Algebraic Number Theory for my PhD. Although I played no part in their subsequent proofs, I gained a lot of useful research techniques and knowledge from tinkering with them. Perhaps their greatest influence was in whetting my appetite for mathematics research. Hadamard's conjecture remains unsolved - but my investigation into that problem was pivotal to a breakthrough in modeling Molecular Phylogenetics.
In this seminar I will reflect on the role that each of these 4 problems had in my own career as a researcher in mathematics and give an outline of each problem. I hope others might also see that "playing" with such problems could be useful in motivating and training future mathematics researchers.

160222132801

Stochastic partial differential equations (SPDEs) are mathematical models for evolutions in space and time, which are corrupted by noise. Although we can prove existence and uniqueness of a solution to various classes of such equations, in general, we do not have an explicit representation of this solution. Thus, in order to make those models ready to use for applications, we need efficient numerical methods for approximating their solutions. And to determine the efficiency of an approximation method, we usually need to analyse the regularity of the target object, which is, in our case, the solution of the SPDE.
The aim of this talk is to present some recent results concerning the regularity of SPDEs and to point out their relevance for the question of developing efficient numerical methods for solving these equations. Before doing this, we first explain the meaning of the different parts of a typical SPDE. For simplicity, we focus on the most basic example, the stochastic heat equation driven by a (cylindrical) Wiener process. It arises from the common deterministic heat equation if we add what is called `white noise'.

160223102542

NOTE TIME AND VENUE
Detailed medical insurance claims data from the US in 2009 allow us to explore the spatial dynamics of a pandemic in greater depth than ever before. This talk will outline what we observed in terms of spatial and temporal dynamics of the pandemic in the US. Modelling work allows us to test hypothesis on the importance of different factors such as whether schools were in session, climate and city population size, to see which were important in determining the dynamics of disease spread.

Here I will also show results from ongoing studies with collaborators and some of the challenges. We have very fine-grained spatial data, and clearly we would like to us this but disaggregating too far leaves us with little signal. With fitted models and a bit of mathematical creativity, we can infer likely transmission routes during the pandemic and hypothesize what the phylogeography (spatial distribution of viral variants) might look like. Finally, looking at different age groups separately reveal a little more about why the pandemic wave was so slow.

160322163530

UNIVERSITY OF OTAGO PUBLIC LECTURE
Mathematics is an essential tool for helping us understand and control infectious diseases, from the scale of a single virus particle through to a global pandemic. Using detailed data and the toolkit of mathematical modelling,we explore the 2009 influenza pandemic at a greater depth than was possible for any previous pandemic. The results are surprising. We know the modern world is astonishingly well connected internationally so things should spread quickly. However, influenza does not like to conform to our expectations!

160322162831

Start by placing piles of indistinguishable chips on the vertices of a graph. A vertex can fire if it's supercritical; i.e., if its chip count exceeds its valency. When this happens, it sends one chip to each neighbour and annihilates one chip. Initialize a game by firing all possible vertices until no supercriticals remain. Then drop chips one-by-one on randomly selected vertices, at each step firing any supercritical ones. Perhaps surprisingly, this seemingly haphazard process admits analysis. And besides having diverse applications (e.g., in modelling avalanches, earthquakes, traffic jams, and brain activity), chip-firing reaches into numerous mathematical crevices. The latter include, alphabetically, algebraic combinatorics, discrepancy theory, enumeration, graph theory, stochastic processes, and the list could go on (to zonotopes). I'll share some joint work - with Dave Perkins - that touches on a few items from this list. The talk will be accessible to non-specialists, I promise.

160223101943

University of Otago Public Lecture
In 1916 Einstein predicted on the basis of his new theory of general relativity that gravitational waves should exist. Since the early 1960s scientists tried to measure them but the search has been unsuccessful until very recently. On the 14th of September 2015 the two LIGO detectors measured a gravitational wave signal which could only have come from a binary black hole system. What does this measurement mean for science and for us?

160318132038

The optimization of wave energy farms requires numerical models aimed at predicting as accurately as possible the production of a single device on a given site over long periods (typically a year).

Such models have been developed as specialized software, generally using Boundary Element Methods (BEM), in the framework of the theory of potential flow for the description of wave/device interaction. They are globally efficient for the optimization of one device alone or a small group of devices under simplified and rather idealized conditions.

But now as we advance towards application to real cases of multiMW farms featuring, for instance, O(100) machines, these models can no longer be used for optimization and a new generation of fast-running computer codes must be developed.

160225085439

We present new methods for efficiently computing likelihoods of visible physical traits (phenotypes) of species which are connected by an evolutionary tree. These methods combine an existing dynamic programming algorithm for likelihood computation with methods for numerical integration. We have already applied these particular methods to a dataset on extrafloral nectaries (EFNs) across a large evolutionary tree connecting species of Fabales plants. We compare the different numerical integration techniques that can be applied to the dynamic programming algorithm. In addition, we compare our numerical integration results to the published results of a “precursor” model applied to the same EFN dataset. These results include not only likelihood approximations, but also changes in phenotype along the tree and the Akaike Information Criterion (AIC), which is used to determine the relative quality of a statistical model.

160211094704

In this talk, I will show solution methods for computing the wave field through irregular media. The waves considered here are water waves over irregular seabed, and sound waves scattered by cylindrical obstacles. The mathematical models for these waves use the linear wave theory, that is, Laplace's equation for velocity potential of the incompressible water and Helmholtz equation for the sound pressure in air. Applied mathematicians and engineers are interested in the wave attenuation by these irregular properties. I will show how to represent mathematically the irregular/random seabed geometry in water wave problems, and the mixed boundary conditions for the cylinders in scattering problems. Engineers have been using the finite element or boundary element method to study these wave propagation problems in finer and finer details with the increasing computing power. However, it is difficult to find the underlying physics from these numerical methods. Furthermore, most of the computing packages are black boxes. Applied mathematicians have been working to extend the linear wave theory to incorporate the irregularities. I will talk about the recent progress made by the applied mathematicians, with whom I have been working.

151022085733

2.00 : Calum Nicholson, Wavelets and direct limits
2.25 : Pareoranga Luiten-Apirana, Morita equivalence of Leavitt path algebras
2.50 : Tom McCone, Primitive ideals in graph algebras

151020114521

The equations describing water waves in ideal fluids, known as the Euler equations, appear to be exceedingly complex. Certain assumptions on the waves amplitude and wavelength lead to mathematical models that simplify considerably the mathematics involved. In this talk we consider a class of such models known as Boussinesq systems. Boussinesq systems are comprised of partial differential equations with nonlinear and dispersive terms. We review some theoretical properties of these models such as the existence and uniqueness of smooth solutions. We also present and analyse Galerkin / Finite element methods for their numerical solution. Galerkin methods appear to be very efficient for the approximation of smooth solutions of Boussinesq models in plane domains with complicated boundaries. Applications to the propagation of solitary waves and the generation and propagation of tsunamis are discussed.

150623140632

Coding theory revolves around the question of what can be accomplished with only memory and redundancy. When we ask what enables the things that transmit and store information, we discover codes at work, connecting the world of geometry to the world of algorithms. This talk will focus on those connections that link the real world of Euclidean geometry to the world of binary geometry that we associate with Hamming. It will include the mathematical framework for error correction in quantum computing and code design for wireless communication with multiple antennas.

150907111814

This talk gives an overview of wavelets: what they are, how they work, why they are useful for image analysis and image compression. Then it will go on to discuss how they have been used recently for the study of paintings by e.g. Van Gogh, Goossen van der Weyden, Gauguin and Giotto.

150623133358

Numerical computation has long exploited that sparse matrices are special, and that there exist very fast algorithms to deal with them. In the last 15 years or so, mathematicians, engineers, computer scientists and statisticians have come to realize that "sparsity" can buy us much more: using it correctly is now crucially important in many computational contexts, and we will review a few.

150623140016

Software is transforming research and education. Mathematica is the leading software for mathematics with modelling. It has the natural language Wolfram Alpha web interface. It will show every step of the solution of common maths problems. With the cloud and free CDF player students can use interactive notebooks and 10000 demonstrations of concepts across the curriculum. Curated data provides a uniform environment for the arts and sciences; from modelling stereo chemistry to financial options, from 3D medical image processing to linguistic analysis, statistics and 'art': This session will be conducted in the computer lab Room 242.

150916104928

The number of phylogenetic (evolutionary) trees on $\ell$ taxa is a classical result in mathematical phylogenetics dating back to Schröder's work in 1870. This result also gives the number of such trees on $n$ labelled vertices. In contrast, the number of phylogenetic networks on $n$ labelled vertices is unknown. In this talk, we provide some answers to the problems of counting the numbers of phylogenetic networks. This is joint work with Colin McDiarmid and Dominic Welsh (University of Oxford).

150623140513

Many partial differential equations describing wave-like phenomena in nature are integrable. This has the consequence that their solutions can be obtained in terms of Theta functions associated to a Riemann surface. For several reasons it is useful to determine these functions explicitly. In this talk I will give an overview of the main ideas for developing computational schemes to determine the topological, geometrical and analytical structures of a Riemann surface which are needed to evaluate the Theta functions.

150623140303

A joint seminar with the Department of Physics

It is not news to anyone working in scientific or STEM fields that the proportion of men and women in these careers is out of balance. Outreach targeted at encouraging young women into STEM careers has become rather fashionable, and discussion of both the numeric imbalances [1] and suggested explanations for the gender disparity [2] have become increasingly accessible. This talk will outline published literature on both the data that demonstrates gender disparity [3,4] and behavioural studies [5] that begin to explain why gender disparity in the sciences is persistent, with the aim of increasing general understanding of a rather complex issue. It will conclude with a discussion of what needs to change in order for gender equality to improve across the board, and discuss new studies that give insight into why some scientific disciplines, such as physics and mathematics, seem to perform so much worse than other disciplines such as biology in this respect.

[1] Nature 495, 5, 2224, 25-27, 28-31, (07 March 2013)
[2] The Economist, Promotion and Self-Promotion, (31 August 2013)
[3] Guiso, L.; Monte, F.; Sapienza, P.; Zingales, L. 2008. Culture, gender, and math. Science 320:11641165.
[4] Knobloch-Westerwick, S.; Glynn, C.J.; Huge, M. 2013. The Matilda Effect in science communication: An experiment on gender bias in publication quality perceptions and collaboration interest. Science Communication 35: 603625
[5] Moss-Racusin, C.A.; Dovidio, J.F.; Brescoll, V.L.; Graham, M.J.; Handelsman, J. 2012. Science faculty's subtle gender biases favor male students. Proceedings of the National Academy of Sciences 109:1647416479.

150623120014

Note day, time and venue of this Otago Logic Group seminar
The Axiom of Choice is probably the cause of more anxiety and unproductive disputation than any other proposition of pure mathematics. There is probably a majority of mathematicians who profess to believe it, but it's only a minority (even of the believers) who can state it correctly, and for most mathematicians its purpose and meaning are shrouded in smog. This talk is a backgrounder for a “General Pure'' audience (not logicians!). Technicalities will be kept to an absolute minimum.

150812163107

Wind energy represents one of the least cost methods of electricity generation, produces no carbon emissions, and is highly scaleable. However, the intermittency of wind and the passive nature of wind turbines mean spinning and scheduled reserves are required to ensure grid security. It is vital for transmission network planning that temporally and spatially accurate models of wind power are formulated. While there are many approaches to the simulation of wind speed time-series there is less information available to aid in characterising the dynamic transformation from wind speed time-series to wind power time-series. Wind farms comprise arrays of wind turbines, and individual wind turbines have well defined power curves, however the aggregation of the individual wind turbine power time-series is not independent; thus a temporally consistent model for the spatial correlation of the wind resource is required. Measurements made at a wind farm in New Zealand are used to construct two models and simulations compared with measured power. The first applies the Sandia method coupled with the convolution of a Gaussian function and the wind turbine power curve. The second method uses the Measure Correlate Predict methodology and Wavelet Multi-resolution Analysis. The MCP / WMA model is then applied to generate wind farm power curves for farms of differing topographies, and a simple model comprising Gaussian smoothing and a first order low pass filter matched to the results.

150623115649

In this talk I will briefly explain how certain classical fractional-in-space differential equations emerge in relation to scaling limits of random walks. I will discuss the main features of their solutions, in particular, in comparison to solutions of classical diffusion equations. Then I will show how to generalize these equations to model anomalous transport along flow lines. This is done using an abstract unbounded functional calculus for operator groups on Banach spaces, a construction which I will also briefly introduce in the talk. A movie (numerical simulation) will complete the entertainment.

150623115410

150717104304

To understand the retreat of the Arctic sea ice with the ongoing climate change is important for several reasons. First, Arctic sea ice plays a major role in the global climate due to its impact on global wind patterns. Second, the decline in sea ice extent has a large impact on the local flora and fauna. Finally, the opening of the Arctic sea allows for increased shipping activity and thus creates an opportunity to make trading in the northern hemisphere faster and cheaper.

The sea ice extent is correlated with ocean waves, generated by storms which have become stronger and more frequent in the past decades. My PhD project aims to contribute to our understanding of these interactions between water waves and sea ice. In the present talk I will present the current state of this project. The first part is concerned with viscoelastic continuum models. More recently I began to investigate the influence of the shape of ice floes on their scattering behavior. I will briefly introduce the idea of generalized polynomial chaos (gPC) which I want to use to model the scattering of water waves from a random-shaped ice floe.

150623104032

1. The combined power of New Zealand’s best and brightest mathematicians will be harnessed to solve significant business challenges at New Zealand’s first Mathematics-in-Industry event, 29th June to 3rd July 2015 at Massey University, Auckland.
Successfully implemented in 20+ countries worldwide, these intensive week-long workshops offer a collaborative environment to solve problems arising in industry. Scientists participate from a range of mathematical disciplines such as dynamic systems, statistics, and operational research.
This unconventional model sees companies paying $6000 each up-front for the rare opportunity to have their meatiest challenges tackled by mathematicians from across the country. Support for students to come; post workshop contracts possible; and employment possibilities may arise.

2. Non-local calculus is a sorely neglected topic in the under-graduate, or even the graduate, curriculum. These problems arise when cause and effect are separated by time or space. They come from important applications surprisingly often. Usually the solution possesses a rich structure missing in the classical local models.
Examples will be given with emphasis on the highly valued rye-grass/clover mixtures model, often quoted as “one of the best pieces of science to come from AgResearch-NZ’s largest Crown Research Institute”, as stated by Dr Andy West, ex-CEO.

150526094803

STATISTICS
Yunan Wang: Binary segmentation for change-point detection in GPS time series
Patrick Brown: Investigating dynamic time series models to predict future tourism demand in New Zealand
Alastair Lamont: Hierarchical modelling approaches to estimate genetic breeding values
Lyco Wen: Effects of gene by environment interaction on hyperuricemia and related gout risk

15-MINUTE BREAK 2.20-2.35

MATHEMATICS
Callum Nicholson: Wavelets and direct limits
Pareoranga Luiten-Apirana: Morita eqivalence of Leavitt path algebras
Tom McCone: Primitive ideals in graph algebras

141008094300

Students have unique relationships with mathematics consisting of their views and feelings, sets of identities, knowledge and habits of engagement. Using this relationship structure, Naomi will profile a thriving and vulnerable mathematics student. She will then suggest ways in which a student's relationship with mathematics can be improved.

150226154805

Mathematical models of physiological phenomena can be extremely complicated. They typically include terms that mimic the behaviour of a number of different processes that contribute to the phenomenon, resulting in models with many variables and parameters and often containing several timescales.

A common first step in the analysis of such a model is to simplify the model by identifying and eliminating variables that evolve over the fastest or slowest timescales. Model simplification of this type can sometimes be rigorously justified, but in many cases it is done in an ad hoc way and results in important features of model dynamics being destroyed.

This talk will describe some recent results about simplification techniques for models with multiple timescales, pointing out common pitfalls and identifying conditions under which simplifications might be mathematically justified.

150226143136

Multidimensional scaling (MDS) is a data reduction and visualisation technique used for high-dimensional object display in a low-dimensional space. Objects are mapped to points in the low-dimensional space (usually 2D or 3D) so as to preserve, as much as possible, the distances between objects. In this talk we discuss the general problem of MDS and introduce a new agglomerative approach for solving it. The algorithm is extremely fast. Our initial results suggest that it out-performs existing algorithms for large scale MDS (>100,000's of points).

150219094615

NOTE DAY AND TIME OF THIS SPECIAL SEMINAR
We shall survey recent analytical and computational results for coupled macroscopic-microscopic bead-spring chain models that arise from the kinetic theory of dilute solutions of incompressible polymeric fluids with noninteracting polymer chains, involving the unsteady Navier-Stokes system in a bounded domain and a high-dimensional Fokker-Planck equation. The Fokker-Planck equation emerges from a system of (Itô) stochastic differential equations, which models the evolution of a vectorial stochastic process comprised by the centre-of-mass position vector and the orientation (or configuration) vectors of the polymer chain. We discuss the existence of global-in-time weak solutions to the coupled Navier-Stokes-Fokker-Planck system. The numerical approximation of this high-dimensional coupled system is a formidable computational challenge, complicated by the fact that for practically relevant spring potentials the drift term in the Fokker-Planck equation is unbounded.

150305155330

UNIVERSITY OF OTAGO PUBLIC LECTURE
Numerical solution of PDEs is a rich and active field of modern applied mathematics. The steady growth of the subject is stimulated by ever-increasing demands from the natural sciences, engineering and economics to provide accurate and reliable approximations to mathematical models involving partial differential equations (PDEs) whose exact solutions are either too complicated to determine in closed form or, in many cases, are not known to exist. While the history of numerical solution of ordinary differential equations is firmly rooted in 18th and 19th century mathematics, the mathematical foundations of the field of numerical solution of PDEs are much more recent: they were first formulated in the landmark paper Über die partiellen Differenzengleichungen der mathematischen Physik (On the partial difference equations of mathematical physics) by Richard Courant, Karl Friedrichs, and Hans Lewy, published in 1928. The aim of the lecture is to survey several modern developments in the theory of finite difference methods for partial differential equations that rely on tools from functional analysis, harmonic analysis and function space theory.

150325101321

In a warming climate, ocean waves increasingly impact the morphology of the ice-covered Arctic and Southern Oceans, as intensified wave spectra have the ability to break sea ice deeper in the pack ice. This process is currently not modelled properly (or at all) in large scale climate models, so a significant effort is needed to provide these models with realistic parametrisations of wave/sea ice interactions. As waves travel through a sea ice cover, they experience scattering, which redistributes conservatively the energy across all directions, and dissipation, due to many non-linear processes e.g. collisions between floes, floe breaking, turbulences, viscous damping... Most existing scattering models are two dimensional (1 horizontal and 1 vertical dimension) or assume infinite periodic distributions of identical scatterers (i.e. floes), and therefore cannot properly describe the evolution of realistic directional wave spectra through large random distributions of ice floes. After briefly discussing these models and their limitations, I propose a new approach to remedy these shortcomings. The so-called slab-clustering method is devised to solve deterministically the scattering of multi-directional waves by arbitrary arrays of O(10⁴–10⁵) scatterers. The method is first described in the simpler context of 2D planar acoustic waves scattered by sound-hard inclusions and then applied to the wave-ice interaction problem. I will show preliminary results suggesting the model is appropriate to characterise the attenuation of ocean wave energy and the widening of its directional spread, as observed in the field.

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NOTE day, time and venue
The United States is realizing the need to achieve a level of quantitative literacy for its graduates to prepare them to thrive in the modern world. Given the prevalence of statistics in the media and workplace, individuals who aspire to a wide range of positions and careers require a certain level of statistical literacy. Because of the emphasis on data and statistical understanding, it is crucial for us as educators to consider how we can prepare a statistically literate population. Students must acquire an adequate level of statistical literacy through their education beginning in the first grade of education.
The Common Core State Standards for mathematics (that include statistics) in grades Kindergarten – 12 have been adopted by most states and the District of Columbia. These national standards for the teaching of statistics and probability range from counting the number in each category to determining statistical significance through the use of simulation and randomization tests. Soon, and for the first time, most of our entering college students will have been taught some statistics and probability, so our introductory college and university statistics courses will have to change. In addition, we must rethink the preparation of future K–12 teachers to teach this curriculum. Change in teacher preparation must thus be implemented in order to respond to the call from society for an increase in statistical understanding.
This presentation will provide a brief history of statistics at K-12 in the United States, an overview of the statistics and probability content of these standards, resources that support the K-12 standards in statistics, consider the effect in our introductory university statistics courses, and describe the knowledge and preparation needed by the future and current K–12 teachers who will be teaching using these standards. A new American Statistical Association strategic initiative, the Statistical Education of Teachers, will be outlined and the desired assessment of statistics at K-12 on the high stakes national tests will be explored.

This is a joint seminar by the Department of Mathematics and Statistics and Otago Mathematics Association (OMA)

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Advances in genomics technologies have enabled generation of genome-wide data on multiple individuals, creating new challenges for data management and analyses. Of particular interest to geneticists, are ‘signatures’ of natural and artificial selection within genome-wide data generated on populations. Recently, University of Otago researchers funded via the Virtual Institute of Statistical Genetics (VISG, www.visg.co.nz) developed an analytical pipeline to identify genomic regions that exhibit such signatures. In this seminar I will provide an overview of VISG, describe aspects of the analytical pipeline, and results from applying this to a gene (PPARGC1A) previously hypothesised to be subject to natural selection in Polynesians.

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NOTE DAY AND TIME OF THIS SPECIAL SEMINAR
In this talk I will present some preliminary results of coupling a directional scattering model of waves with sea ice break-up. The scattering model used is based on the multiple scattering model of Foldy (1945), and is the one used by many researchers (eg. Masson & LeBlond, 1987).

Retaining the scattered energy in the system (as it should be), instead of simply dissipating it as is currently done in early implementations of quasi-operational waves-in-ice models, has implications for the wave field in the ice, the amount of ice broken up by a given wave field that is arriving from the open ocean, and for momentum transfer from the waves to the ice.

I will also give some background to the problem of modeling waves-in-ice.

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