Colloquium

Colloquium

Colloquium

The Departmental Colloquia are held on Friday afternoons, from 3:00 to 4:00pm, during the teaching semesters and are followed by refreshments.

2019 Session 2 Series

Week 13 - 08  November

Date: Friday, 8 November 2019 
Speaker: Dr Sam Mallinson (Memjet)

Venue:  E7B 146 ACE room

Title:

Abstract:

Week 12 - 01 November

Date: Friday, 01 November 2019 
Speaker: Dr Daniel Murfet (The University of Melbourne)

Venue:  E7B 146 ACE room

Title: The mathematics of AlphaGo

Abstract: AlphaGo is an algorithm trained by deep reinforcement learning to play the board game Go. The study of algorithms of this kind, which are learned rather than written, is an interesting new direction in computer science which touches on several areas of mathematics. I’ll explain in detail what AlphaGo is, how it works (fixed point theorems!), and what it means for mathematics.

Week 12 - 31 October

Date: Thursday, 31 October 2019 @ 1:00pm
Speaker: Prof. Herbert Huppet (University of Cambridge) Australian Academy of Sciences Selby Public Lecture 2019

Venue: 9WW  room 102

Title: Lava flows:  theory, lab experiments and field data

Abstract: Worldwide, unconstrained lava flows kill people almost every year and cause extensive damage, costing millions of pounds. Defending against lava flows is possible by using topographic variations sensibly, placing buildings considerately, constructing defending walls of appropriate size and the like. Hinton, Hogg and Huppert have recently published two rather mathematical papers outlining how viscous flows down slopes interact with a variety of geometrical shapes; evaluating, in particular, the conditions under which “dry zones” form – safe places for people and belongings – and the size of a protective wall required to defend a given size building. Following a desktop experimental demonstration, we will discuss these analyses and their consequences.

Week 11 - 25 October

Date: Friday, 25 October 2019 
Speaker: Dr Peter Humburg (Macquarie University)

Venue:  E7B 146 ACE room

Title: Statistical Consulting for the Human Sciences - A Report from the Trenches

Abstract: Many research projects in the Faculty of Human Sciences produce large, complex datasets, including, e.g., eye tracking and brain imaging data. Until recently, analyses of these data have relied predominantly on relatively simple methods. Here I will present a series of case studies to illustrate how the introduction of more sophisticated statistical techniques has helped researchers to improve the quality of their analyses.

Week 10 - 18 October

Date: Friday, 18 October 2019 
Speaker: Dr Andrew Milne (Western Sydney University)

Venue:  E7B 146 ACE room

Title: My Mathematical Journey Through Music

Abstract: My core interest is music — how it “works”, how it communicates, how we can algorithmically generate it, and facilitate its performance. Answers to these questions typically require mathematical representations of the structures common in music. They also require statistical techniques that can represent underlying structures of the data generation process and can reflect the inevitable uncertainties that arise from perceptual and psychological investigations. In my account of this mathematical journey through music, I will discuss some, or all, of: using mathematical characterisations of the frequency spectra of musical sounds to partially account for perceived consonance/dissonance, musical fit, and affective valence; describing scales and rhythms with the discrete Fourier transform for the purpose of analysis; the “balance" and “evenness" of musical rhythms and their relevance to algorithmic music and to perception; multilevel Bayesian regression; the playability and learnability of different spatial representations of pitch in new musical instruments.

Week 9 - 11 October

Date: Friday, 11 October 2019 
Speaker: Dr Anne Thomas (University of Sydney)

Venue:  E7B 146 ACE room

Title: Divergence in Coxeter groups

Abstract: Coxeter groups are groups generated by reflections, and they play important roles in algebra, combinatorics and geometry. We will discuss some history of these groups and introduce several key examples, before describing some results on the large-scale geometry of Coxeter groups, specifically, the divergence of geodesics in their Cayley graphs. This is joint work with Pallavi Dani, Yusra Naqvi and Ignat Soroko.

Week 8 - 04 October

Date: Friday, 04 October 2019 
Speaker: Dr Patricia Campbell (VIDRL)

Venue:  E7B 146 ACE room

Title: Modelling to make robust decisions about infectious diseases control with limited information

Abstract: Infectious diseases have plagued human populations since the dawn of time.  Despite rapid advances in molecular methods allowing detailed characterization of the causative pathogens, for many infectious diseases the factors that drive transmission remain unknown, and in some cases, perhaps unknowable. Mathematical models provide a principled framework to study the drivers of infectious disease transmission and to define effective measures for control. How can such models be developed in situations when we have limited information about the natural history of a disease, especially the aspects that could be important to reducing the disease burden? In this presentation, I will demonstrate that we can make robust decisions about interventions to control infectious diseases, even when knowledge about the underlying mechanisms of transmission and immunity are incomplete, using pertussis (whooping cough) as a case study.

Week 7 - 13 September

Date: Friday, 13 September 2019 @ 2:00pm
Speaker: Prof Christopher Poulton (University of Technology Sydney)

Venue:  E7B 146 ACE room

Title: Modelling interactions between sound and light on the nanoscale

Abstract: The interaction between electromagnetic and elastodynamic vibrations has a long and distinguished history, dating from the work of Brillouin in the early 20th century. More recently researchers have begun to rediscover these interactions in the context of nanophotonics, in which light is trapped or guided within structures that possess features that are typically as large as the wavelength of light (and sound) in the material. These interactions can lead to several interesting and unusual effects, including "slow-light", by which the speed of light is reduced to a fraction of its value in vacuum. However at these small scales the mathematics of the different types of waves, and of the forces that cause them to interact, can become complicated, and modelling of the interlinked PDEs is a difficult task. Here we discuss the journey towards a comprehensive and accurate mathematical description of light-sound interactions, and review recent progress in using these models for comparison with experiments.

Week 6 - 06 September

Date: Friday, 06 September 2019 
Speaker: Dr Robyn Araujo (Queensland University of Technology)

Venue:  E7B 146 ACE room

Title: Cellular Cognition and the Robust Perfect Adaptation (RPA) Problem

Abstract: In this talk, I will give a brief discussion of my recent research on robustness in molecular signalling networks.   It has been a long-standing mystery how the extraordinarily complex communication networks inside living cells, comprising thousands of different interacting molecules, are able to function robustly since complexity is generally associated with fragility.  Our recent work has now suggested a resolution to this paradox through the discovery that robust adaptive signalling networks must be constructed from just a small number of well-defined universal modules (or "motifs"), connected together.  The existence of these newly-discovered modules has important implications for evolutionary biology, embryology and development, cancer research, and drug development.

Week 5 - 30 August

Date: Friday, 30 August 2019
Speaker: A/Prof Vidit Nanda (Oxford University)

Venue:  E7B 146 ACE room

Title: Path signatures in topology, dynamics and data analysis

Abstract: The signature of a path in Euclidean space resides in the tensor algebra of that space; it is obtained by systematic iterated integration of the components of the given path against one another. This straightforward definition conceals a host of deep theoretical properties and impressive practical consequences. In this talk, I will describe the homotopical origins of path signatures, their subsequent application to stochastic analysis, and how they facilitate efficient machine learning in topological data analysis. This last bit is joint work with Ilya Chevyrev and Harald Oberhauser.

Week 4 - 23 August

Date: Friday, 23 August 2019 
Speaker: Dr Rebecca Chisholm (University of Melbourne)

Venue:  E7B 146 ACE room

Title: Using mathematics to understand the emergence and early evolution of tuberculosis

Abstract: Tuberculosis is caused by the Mycobacterium tuberculosis complex (MTBC), a wildly successful group of organisms and the leading cause of death resulting from a single bacterial pathogen worldwide. It has an unusual natural history in that only a small fraction of its human hosts are infectious.  The vast majority of those infected with MTBC enter a latent state that is both non-infectious and devoid of any symptoms of disease.  It also has an unusual evolutionary history.  Evidence suggests that MTBC established itself in human populations in Africa over 50,000 years ago and that animal-infecting strains subsequently diverged from human strains.  This is unlike many other major human pathogens that have resulted from zoonotic transfers from wildlife or domesticated animals, such as HIV and influenza. Furthermore, when MTBC did emerge in humans, evidence suggests that it likely only caused active disease rather than mostly latent infection.  Yet, two crucial components of the origins and early evolution of MTBC remain a mystery.  First, what were the precise causal factors which led to its emergence in human populations? And second, if it began interactions with humans as an active disease without latency, how could it begin to evolve latency properties without incurring an immediate reproductive disadvantage? In this presentation, I will describe how we used mathematical models together with a synthesis of evidence from epidemiology, evolutionary genetics, and paleoanthropology to address these uncertainties surrounding the origins and early evolution of MTBC.

Week 3 - 16 August

Date: Friday, 16 August 2019 
Speaker: A/Prof Daniel Chan (University of New South Wales)

Venue:  E7B 146 ACE room

Title: Diagrams of linear maps and moduli spaces

Abstract: In linear algebra, one studies a single linear map or matrix, typically by finding nice changes of bases which transform the matrix to a simple canonical form e.g. Jordan canonical form. In this talk, we look more generally at the situation where there are several linear maps and the problem of classifying such diagrams of linear maps up to change of bases. We approach the problem by looking at moduli spaces parametrising such diagrams of linear maps and describing the intriguing relationship between the geometry of these moduli spaces with the algebraic classification problem.

Week 2 - 09 August

Date: Friday, 09 August 2019
Speaker: Dr David Price (University of Melbourne)

Venue:  E7B 146 ACE room

Title: Optimal allocation of resources to understand infectious diseases

Abstract: Design of experiments is not a new concept. However, much of the classical experimental design work was developed for the purpose of hypothesis testing – i.e., how many resources (e.g., individuals, mice, blood samples, etc.), are required to ensure sufficient statistical power to test a formal hypothesis. In contrast, many basic science experiments (e.g., microbiology, immunology or chemistry) and observational studies (e.g., sampling populations or the environment to understand an ongoing phenomenon), are often exploratory – concerned with estimation of a quantity or learning about a system, rather than hypothesis testing. This talk will introduce the optimal design framework, a decision-theoretic approach to the problem of allocating limited resources to optimise statistical information. We will consider scenarios where the purpose is to either estimate parameters or discriminate between competing models as well as possible. Examples in each case will relate to understanding infectious disease dynamics.

Week  1 - 02 August

Date: Friday, 02 August 2019
Speaker: Jia Wu (Macquarie University)

Venue:  E7B 146 ACE room

Title: Towards Multi-instance Learning with Discriminative Bag Mapping

Abstract: Multi-instance learning (MIL) is a useful tool for tackling labeling ambiguity in learning because it allows a bag of instances to share one label. Bag mapping transforms a bag into a single instance in a new space via instance selection and has drawn significant attention recently. To date, most existing work is based on the original space, using all instances inside each bag for bag mapping, and the selected instances are not directly tied to an MIL objective. As a result, it is difficult to guarantee the distinguishing capacity of the selected instances in the new bag mapping space. We propose a discriminative mapping approach for multi-instance learning (MILDM) that aims to identify the best instances to directly distinguish bags in the new mapping space. Accordingly, each instance bag can be mapped using the selected instances to a new feature space, and hence any generic learning algorithm, such as an instance-based learning algorithm, can be used to derive learning models for multi-instance classification. Experiments and comparisons on eight different types of real-world learning applications demonstrate that MILDM outperforms the state-of-the-art bag mapping multi-instance learning approaches. Results also confirm that MILDM achieves balanced performance between runtime efficiency and classification effectiveness.

2019 Session 1 Series
12 July

Date: Friday, 12 July 2019 
Speaker: A/Prof Ad Ridder (Vrije Universiteit)

Venue:  E7B 146 ACE room

Title: Efficient Computations of Insurance Risk Models with Cubic Variance Functions

Authors: Ad Ridder (VU Amsterdam, Netherlands) and Shaul Bar-lev (University of Haifa, Israel)

Abstract: In this paper, we consider the problem of computing tail probabilities of the distribution of a random sum of positive random variables. We assume that the individual variables follow a reproducible natural exponential family (NEF) distribution and that the random number has a NEF counting distribution with a cubic variance function. This specific modelling is supported by data of the aggregated claim distribution of an insurance company. Large tail probabilities are important as they reflect the risk of large losses, however, analytic or numerical expressions are not available. We propose several simulation algorithms which are based on an asymptotic analysis of the distribution of the counting variable and on the reproducibility property of the claim distribution. For large risk levels, we propose to apply efficient importance sampling simuations. We conclude by numerical experiments of these algorithms.

Week 13 - 7  June

Date: Friday, 7 June 2019 
Speaker: Dr Trent Mattner (The University of Adelaide)

Venue:  E7B 146 ACE room

Title: Large-eddy simulations of turbulence using the stretched-vortex subgrid model

Abstract: Turbulent flows are characterised by irregular three-dimensional motion over a wide range of spatial and temporal scales. In a direct numerical simulation of turbulent flow, the entire range of scales must be resolved by the computational grid. In many applications, the range of scales is so enormous that it is not computationally feasible to resolve them all. In a large-eddy simulation, only the large scales are resolved. This reduces computational requirements, but a model is needed to account for the effects of the fine subgrid scales. In this talk, I will discuss the stretched-vortex subgrid model, in which the subgrid scales are modelled as an ensemble of stretched spiral vortices. As with many other subgrid models, simulations using the stretched-vortex model are sensitive to the numerical scheme. High-order schemes with low numerical dissipation are usually preferred, but it is sometimes necessary to relax these requirements. Recent work shows that it is possible to obtain reasonably accurate results using the stretched-vortex model with low-order numerical schemes and artificial damping, provided suitable care is taken.

Week 12 - 31 May

Date: Friday, 31 May 2019 
Speaker: Dr Sophie Hautphenne (The University of Melbourne)

Venue:  E7B 146 ACE room

Title: The Markovian binary tree applied to demography and conservation biology

Abstract: Markovian binary trees form a general and tractable class of continuous-time branching processes, which makes them well-suited for real-world applications. Thanks to their appealing probabilistic and computational features, these processes have proven to be an excellent modelling tool for applications in population biology. Typical performance measures of these models include the extinction probability of a population, the distribution of the population size at a given time, the total progeny size until extinction, and the asymptotic population composition. Besides giving an overview of the main performance measures and the techniques involved to compute them, we discuss recently developed statistical methods to estimate the model parameters, depending on the accuracy of the available data. We illustrate our results in human demography and in conservation biology.

Week 11 - 24 May

Date: Friday, 24 May 2019 
Speaker: Dr Anthony M. Licata (The Australian National University)

Venue:  E7B 146 ACE room

Title: Groups, curves, and categories

Abstract: Abstract: In the 1980s, W. Thurston and others developed tools to understand symmetry groups (mapping class groups) of 2-dimensional manifolds.  In addition to its relevance for topology and geometry, Thurston's theory is important because it has parallels in other parts of group theory, such as the study of arithmetic groups, or the in the study of automorphisms of the free group.  In this talk, I'll explain a bit about Thurston thinks about curves on surfaces, and then try to tell you something about how similar structure arises when one tries to understand the symmetry groups of triangulated categories.

Week 10 - 17 May

Date: Friday, 17 May 2019 
Speaker: A/Prof Sharon Stephen (University of Sydney)

Venue:  E7B 146 ACE room

Title: Hydrodynamic stability of non-Newtonian shear flows

Abstract: I will discuss results from studies to investigate the effect of non-Newtonian viscosity on the transition process from a laminar flow to a turbulent flow at large Reynolds number for two-dimensional and three-dimensional flows. The focus is to determine whether non-Newtonian flows can be used to delay transition to turbulence in practical applications. Numerical and asymptotic methods are used to determine the basic flows and the neutral stability curves, revealing the stabilising or destabilising effect of non-Newtonian viscosity. The original motivation came from experiments in the oil recovery industry revealing spiral corrosion patterns on marble rotating discs in viscoelastic gelled acids. This lead to our first investigations on the stability of non-Newtonian rotating flows, specifically the effect of different viscosity models on the stability of crossflow vortices due to flow over a rotating disc. Subsequently, we considered the stability of the Blasius boundary layer for a non-Newtonian flow. These studies and ongoing work on the effect of non-Newtonian viscosity for the asymptotic suction boundary will be discussed. The results suggest that the choice of viscosity model for shear flows is important. In particular, the power-law viscosity model may not be appropriate. Attention is now focussed on the alternative Carreau viscosity model which is more realistic for small and large shear rates. Recent results relating to nanofluids will also be discussed.

Week 9 - 10 May

Date: Friday, 10 May 2019 
Speaker: Prof Jean Yang (University of Sydney)

Venue:  E7B 146 ACE room

Title: Integration and cell type identification of multiple single-cell transcriptomics datasets

Abstract:

Technological advances such as large-scale single cell transcriptome profiling has exploded in recent years and enabled unprecedented insight into the behaviour of individual cells. In particular, Single cell RNA-Sequencing (scRNA-Seq) technology allows for cell-type specific characterization of gene expression values, towards understanding underlying biological processes.  Concerted examination of multiple collections of scRNA-Seq data promises further biological insights that cannot be uncovered with individual datasets. However, such integrative analyses and cell type identification are challenging and require sophisticated methodologies. To enable effective interrogation of multiple scRNA-Seq datasets, we have developed a novel algorithm, named scMerge, that removes unwanted variation by identifying stably expressed genes and utilizing pseudo-replicates across datasets. Biological knowledge such as cell type information can be easily incorporated into scMerge to further improve performance. We evaluated scMerge using seven publicly available scRNA-Seq data collections and found our method effectively removed batch and dataset-specific effects across a wide range of biological systems. To identify cell types, we further employed statistical machine learning methodologies together with cell type information from an external dataset to identify cells in a hierarchically setting. We evaluated our novel approach scClassify and found that it consistently achieves low classification error rates as well as enables finer cell type identification.

Week 8 - 03 May

Date: Friday, 03 May 2019 
Speaker: Dr Nora Ganter (The University of Melbourne)

Venue:  E7B 146 ACE room

Title: Codes, periodicity and triality and all that

Abstract:

I will explain how the Hamming code H_8 is at the heart of some famous exceptional phenomena in dimension eight.

Week 7 - 12 April

Date: Friday, 12 April 2019 
Speaker: Professor Gareth Peters (Heriot-Watt University)

Venue:  E7B 146 ACE room

Title: Some Properties of Symmetric Non-Independent Increment Alpha-Stable Processes

Abstract:

In this presentation, I will discuss new approaches to characterize alpha-Stable stochastic processes which don't require independent increment requirements in their constructions. This will be obtained via a new class of sufficient conditions for right additivity of the covariation to be achieved with regard to restrictions on the spectral measure characterizing the process.

Week 6 - 05 April

Date: Friday, 05 April 2019 
Speaker: Professor Aidan Sims (University of Wollongong)

Venue:  E7B 146 ACE room

Title: Graphs, algebras and C*-algebras

Abstract:

I will tell the tale of a pair of long-lost siblings: graph C*-algebras, who grew up in the Analysis household, and Leavitt-path algebras, who were raised by the Algebraists. Starting from a brief and non-technical sketch of what each of these things is and why we might care about them, I’ll describe how a decade of work showed that what at first seemed like a collection of remarkable but isolated coincidences were actually the markers of a deep connection that has ended up linking much larger classes of C*-algebras and abstract algebras than anyone could originally have guessed. I won’t be assuming any background in either C*-algebras or abstract algebra – this talk should be accessible to everyone.

Week 5 - 29 March

Date: Friday, 29 March 2019 
Speaker: Dr Douglas Brumley (University of Melbourne)

Venue:  E7B 146 ACE room

Title: Bacteria push the limits of chemotactic precision to navigate dynamic chemical gradients

Abstract:

The limited precision of sensory organs places fundamental constraints on organismal performance. An open question, however, is whether organisms are routinely pushed to these limits, and how limits might influence interactions between populations of organisms and their environment. By combining a method to generate dynamic, replicable resource landscapes, high-speed tracking of freely moving bacteria, a new mathematical theory, and agent-based simulations, we show that sensory noise ultimately limits when and where bacteria can detect and climb chemical gradients. Our results suggest the typical chemical landscapes bacteria inhabit are dominated by noise that masks shallow gradients, and that the spatiotemporal dynamics of bacterial aggregations can be predicted by mapping the region where gradient signal rises above noise.

Week 4 - 22 March

Date: Friday, 22 March 2019 
Speaker: Prof Graham Farr (Monash University)

Venue:  E7B 146 ACE room

Title: Powerful sets: a generalisation of binary linear spaces

Abstract:

A set  S  of binary vectors, with positions indexed by  E, is said to be a powerful code if, for all subsets  X  of  E, the number of vectors in  S  that are zero in the positions indexed by X is a power of 2. By treating binary vectors as characteristic vectors of subsets of  E, we say that a set  S  of subsets of  E  is a powerful set if the set of characteristic vectors of sets in  S  is a powerful code. Powerful sets (codes) include binary linear codes (equivalently, cocircuit spaces of binary matroids), but much more besides.
In this talk, we investigate the combinatorial properties of powerful sets. We prove fundamental results on special elements (loops, coloops, frames, near-frames, and stars), their associated types of single-element extensions, various ways of combining powerful sets to get new ones, and constructions of nonlinear powerful sets. We show that every powerful set is determined by its collection of minimal nonzero members. Finally, we show that the number of powerful sets is doubly exponential, and hence that almost all-powerful sets are nonlinear.

(Joint work with Yezhou Wang, University of Electronic Science and Technology of China (UESTC).

Week 3 - 15 March

Date: Friday, 15 March 2019 
Speaker: Dr Vera Roshchina (University of New South Wales)

Venue:  E7B 146 ACE room

Title: Facial Structure of Convex Sets

Abstract:

Convex geometry is a foundation for several applied research areas, and many problems in this field originate from the challenges encountered in modelling and in the design of optimisation algorithms. This includes such well-known open problems as the generalised Lax conjecture and the 9th problem of Stephen Smale. I will discuss some subtleties pertaining to the facial structure of convex sets, and introduce new ideas for capturing irregularities in the facial arrangements based on lexicographic tangents and subtransversality. I will also demonstrate how some specific features of the facial structure affect the behaviour of optimisation algorithms, using examples from conic programming and projection methods.

Week 2 - 08 March

Date: Friday, 08 March 2019 @ 3:30pm
Speaker: Prof Nadja Klein (Humboldt-University, Berlin)

Venue:  E7B 146 ACE room

Title: Bayesian Effect Selection in Structured Additive Distributional Regression Models

Abstract: 

We propose a novel spike and slab prior specification with scaled beta prime marginals for the importance parameters of regression coefficients to allow for general effect selection within the class of structured additive distributional regression. This enables us to model effects on all distributional parameters for arbitrary parametric distributions, and to consider various effect types such as non-linear or spatial effects as well as hierarchical regression structures. Our spike and slab prior relies on a parameter expansion that separates blocks of regression coefficients into overall scalar importance parameters and vectors of standardised coefficients. Hence, we can work with a scalar quantity for effect selection instead of a possibly high-dimensional effect vector, which yields improved shrinkage and sampling performance compared to the classical normal-inverse-gamma prior. We investigate the propriety of the posterior, show that the prior yields desirable shrinkage properties, propose a way of eliciting prior parameters and provide efficient Markov Chain Monte Carlo sampling. Using both simulated and three large-scale data sets, we show that our approach is applicable for data with a potentially large number of covariates, multilevel predictors accounting for hierarchically nested data and non-standard response distributions, such as bivariate normal or zero-inflated Poisson.

Week  1 - 01 March

Date: Friday, 01 March 2019
Speaker: Zsuzsanna Dancso (University of Sydney)

Venue:  E7B 146 ACE room

Title: Loops on a punctured disk, and knotted tubes in R^4

Abstract: 

Classically, knots are one-dimensional strings knotted in three-dimesional space. In this talk we'll discuss two very different flavours ganeralised knot theory: one higher dimensional, one "very low dimensional". We'll end with a mystery: there is a correspondence between certain invariants of these two different knot theories, which must be rooted in a relationship between their topologies - and we don't understand how.

For past seminars, please go to our archive.

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