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Dr Stephen MᶜAteer

Error estimation of Net Promoter Score

Person filling in a survey.

Abstract: Net Promotor Score (NPS) is a system used to gauge customer loyalty, and their likelihood to recommend products and services to others. In this presentation, we discuss 3 methods for estimating NPS error - that is, the uncertainty in the NPS due to limited sample-size.

Three methods are considered: a method based on a normality assumption, a bootstrapping method, and a method based on the trinomial distribution (i.e. the multinomial distribution corresponding to trials with 3 possible outcomes). The former two methods are standard, but a cursory literature-search failed to uncover applications of the trinomial distribution to NPS error estimation.

The precision, computational power and implementation difficulty of the three methods are also discussed.

(Presented to the Analytics Team Knowledge Sharing Session (Telstra), June 2016. Image credit: andibreit (Pixabay).)

The Friedman Test

Portrait of Milton Friedman

Abstract: 6 wine tasters taste 8 wines to be rated out of 10. How can we tell if any of the wines are outstandingly good (or bad)? One difficulty is that wine tasters don’t all rate on the same scale – Alice’s 2 is Bob’s 6 (Bob has a drinking problem). Another difficulty is that we don’t know how individual taster’s ratings are distributed – Alice rates everything either 2 or 9, Bob’s ratings are binomially distributed about 7.

The Friedman test is a nonlinear statistical test (on the rank sums of the ratings) designed to answer this type of question (caveat, caveat, caveat). This test was used to assess the output of a recent Navy expert elicitation session carried out by MCA in Sydney. In this session, I discuss the test and how we used it (I will not discuss the results of the assessment in order to keep the talk UNCLASSIFIED).

(Presented to the DSTO Mathematics Community of Practice in November 2015. Title and abstract approved for public release. Image credit: The Friedman Foundation for Educational Choice.)

Consider the risks: there's no safe way to do math

Bela Lugosi in 'The Devil Bat' (1940)

Abstract: Mathematical training changes the way you view the world around you – it causes a kind of brain damage! We don’t see a soccer ball, we see a truncated icosahedron; when we see a shoelace, we can’t help but think about whether it is knotted or unknotted. This presentation is intended to be humorous and engaging for the intended audience of year 10 students considering further studies in mathematics (and STEM in general). While the overt message is “don’t do math”, this is simply a vehicle for talking about the mathematical way of thinking.

(Presented to 10th grade STEM students as part of DSTO's outreach programme in October 2015. Title and abstract approved for public release. Image credit: Producers Releasing Corporation.)

Bobbing up and down like this: weather data as a predictor of patrol boat hull strain measurements

ATLANTIC OCEAN (Feb. 9, 2010) Waves crash against the hull of the Military Sealift Command fleet replenishment oiler USNS Leroy Grumman (T-AO 195) during a refueling-at-sea with the Nimitz-class aircraft carrier USS Carl Vinson (CVN 70). Carl Vinson is taking part in Southern Seas 2010 as part of a scheduled homeport shift from Norfolk to San Diego. (U.S. Navy photo by Mass Communication Specialist 2nd Class Daniel Barker/Released)

Katrina Kelleher (supervised by Stephen Mc Ateer)

Abstract: Driving a boat in high seas causes hull strain. Hull strain can cause fatigue and costly damage. The Royal Australian Navy (RAN) has a fleet of 14 Armidale Class Patrol Boats (ACPBs) – 57 meter, aluminium hulled patrol boats. The primary role of the ACPB fleet is border and fisheries protection on Australia's northern approaches. The ACPBs have suffered structural damage as a result of prolonged high operational demands.

In this paper, we investigate the feasibility of using weather data to predict hull strain measurements in patrol boats. The weather data is sourced from the Bureau of Meteorology and contains the values of various wave attributes (e.g. wave height and period) across the world’s oceans. The weather data is combined with Global Positioning System location data to develop a weather experience profile for a given ship. The reference strain data used in this study is a derived measure, “slams per hour”, and was generated by the Defence Science and Technology Organisation’s Maritime Division for the purposes of a separate study. The measure is based on sensors placed on board ACPB HMAS Glenelg. This study required the use of interpolation, linear regression and big data techniques such as machine learning to investigate the interrelation of the data sets.

Current methods of detecting ACPB hull damage require a ship to stay in port for several days while engineers manually investigate indicators of fatigue. During these maintenance periods, the ship and crew are unavailable to engage in operations and this results in reduced fleet capability. The approach discussed in this paper would allow maintenance inefficiencies to be reduced as a ship would potentially only require manual inspection when its weather experience profile indicates necessity.

The ACPB fleet has an approximate whole of life cost of $1 billion; finding efficiencies in the maintenance cycle has the potential to save the RAN millions of dollars.

(Presented at MODSIM 2015, winner of MODSIM 2015 Student Award, based on Katrina Kelleher's honours thesis. Image credit: Daniel Barker, US Navy)

Royal Australian Navy: navigating our way into navigational data

US Navy 090721-N-9123L-010 Quartermaster 1st Class Jory Mason of Chicago, Ill. and Royal Australian Navy Seaman Andrew Smith of guided-missile frigate HMAS Newcastle (FFG 06) review a chart aboard guided-missile destroyer USS M...

Abstract: In the past few years evidence based decision making has become one of the catch cries of the big data phenomenon. This has seen both Google and Facebook efforts leading to open source software to analyse big data sets as part of the Hadoop ecosystem. Additionally, the role of data scientist has been declared as the sexiest job of the 21st century.

The Royal Australian Navy (RAN) has a vast array of information available via electronic navigational display systems. Amongst other things, this includes: position; velocity; water depth; weather information; and maritime traffic information. With recent Navy 2-star sponsorship, all vessels are required to submit their navigational log files to the Defence Science and Technology Organisation for analysis; this could amount to 1 terabyte of plain text data each year.

Demonstrating the value of this data, we have undertaken three rapid studies. The first study provided the RAN with analysis of patrol boat speed profiles categorized by activity. The second study concerned patrol boat wharf-space usage in Darwin. And the final study (ongoing) seeks correlations between navigational and meteorological data and precursors of hull damage. These studies contribute to evidence-based decision making for patrol boat replacement.

These examples lead to a discussion of military big data challenges in Australia, and the techniques we propose to overcome them. These include the use of big data techniques, heuristic methods for pattern recognition and statistical data exploration. Finally, we share our vision of how RAN’s future could be enhanced by embracing big data.

(based on work with Justin Beck, Katrina Kelleher and Timothy J. Surendonk, talk given at the Defence Operations Research Symposium, October 2014, and the 83rd Symposium of the Military Operations Research Society, June 2015, title and abstract approved for public release -- won Gus Schaeffer Award for best paper at DORS 2014, image credit: U.S. Navy photo by Mass Communication Specialist 2nd Class Byron C. Linder)

Why 100 duck-sized horses are scarier than 1 horse-sized duck (and how we set up our Hadoop cluster)

Cubieboard HADOOP cluster

Abstract: In this presentation we give a brief overview of the benefits and modern techniques of distributed parallel computation (MapReduce) and storage (Hadoop Distributed File System). That is, we teach you a healthy fear of duck-sized horses. We will then go through the steps involved in setting up a Hadoop cluster pre-loved desktops. Finally we provide a tour of an actual, real-life cluster.

(based on work with Ross Ashman, Justin Beck and Timothy J. Surendonk, presented at the DST Group, MCA MSTC seminar series, 27 February 2015, title and abstract approved for public release, image credit: Cubie Team)

Discrete event simulation of hydrographic launch and recovery operations

US Navy 060130-N-7676W-142 The Seahorse-class Autonomous Underwater Vehicle (AUV) is moved into position with Sea Fighter's (FSF-1) stern ramp during launch.

Abstract: Australia's national hydrographic survey and charting programme (hydroscheme) is carried out by the Australian Hydrographic Service of the Royal Australian Navy. Hydrographic survey involves using sonar to measure the depth of the sea floor and for feature detection. For the most part, this is carried out through the use of organic systems such as hull-mounted sonar but emerging technology will allow more surveys to be carried out by off-board unmanned vehicles (UV). This new technological paradigm raises a number of questions:

  • What is the maximum number of UVs that a single vessel can operate effectively in tandem?
  • In the case that the deploying vessel also has organic sensors, what is the effect of transiting between survey areas on the overall rate of effort?
  • What effect do UV parameters such as endurance, deployment and recovery times have on the overall rate of effort?
In this study we investigate these UV operational issues using discrete event simulation and explore options available to Navy for the execution of the hydroscheme in the future.

(based on work with Justin D. Beck, title and abstract approved for public release, in Piantadosi, J., Anderssen, R.S. and Boland J. (eds) MODSIM2013, 20th International Congress on Modelling and Simulation, Modelling and Simulation Society of Australia and New Zealand, December 2013, pg. 236. ISBN 978-0-9872143-2-4, PDF, image credit: U.S. Navy photo by Mr. John F. Williams)

The algebraic Bethe Ansatz -- a diagrammatic approach

Abstract: I will present an easily digested and elementary description of the algebraic Bethe Ansatz (ABA). This may be of particular interest to Stat Mech students/others who want an introduction to the topic. I'll start off from the very basics and describe the ABA using diagrammatic tensor notation. This will be a very informal session.

(talk given on 19 March 2012)

A diagrammatic representation of the $sl(n)$ $F$-matrix

Abstract: I will describe diagrammatic tensor notation and introduce factorizing $F$-matrices. I will then present a diagrammatic representation of the factorizing $F$-matrix of Albert, Boos, Flume and Ruhlig, for the quantum spin chain with $sl(n)$ symmetry. This representation uses partial $F$-matrices, as in the construction of the $sl(2)$ factorizing $F$-matrix by Maillet and Sanchez de Santos, and leads to an easy proof of the factorizing property.

(talk given at Correlation Functions of Quantum Integrable Models on Thursday, 8 September 2011, Dijon, France)

On factorising \( F \)-tensors by diagrammatic tensor notation

Abstract: In 1996 Maillet and Sanchez de Santos introduced the factorising \( F \)-matrix (really a tensor). This tensor factorises products of \( R \)-tensors indexed by permutations (the ubiquitous transfer matrix and indeed entire lattices of \( R \)-tensors are in this class. In this talk I define and describe some properties of the factorising \( F \)-tensors using diagrammatic tensor notation.

(talk given for the University of Melbourne, Department of Mathematics, Mathematical Physics Reading Group on Tuesday, 8 March 2011)

Introduction to the Bethe Ansatz

Abstract: The algebraic Bethe Ansatz is a method which is used to solve two dimensional lattice models such as the 6-vertex model. Over two sessions, I will introduce the key ideas and describe how the method works in specific cases. In the first session I will introduce the big picture, and in the second I will hone in on the details.

(talk given over two weeks for the graduate student seminar series on Friday, 6 and Friday, 13 August 2010)

MathML: \( \mathrm{\LaTeX} \) is Not the Only Fruit.

Abstract: \( \mathrm{\LaTeX} \) has been a staple of mathematical publication for a some time now, however it is not designed with online publication in mind. Enter MathML; Mathematical Markup Language. MathML produces beautiful mathematics, fully integrated into a webpage. I will give a brief introduction into the language, by the end of which audience members should be able to start creating their own gorgeous mathematical webpages without the need to link to a PDF every time a formula appears. I will also discuss some other advantages MathML has over other standards such as searchability and ease of production.

(talk given on 25 February 2010)

Some Solvable Nonlinear Differential Equations *sigh* or Another Mysterious and Wonderful Beast Bites the Dust

Abstract: We are often told that solvable nonlinear differential equations are rare - if you write down a random nonlinear DE, it's an extremely safe bet that it's not going to be solvable. We are then presented with a solvable example and we stand rightly in awe. Where did it come from? How does it have any right to be? In this talk I will follow a discussion presented in a manuscript by M. Noumi & T Takebe. Lots of solvable nonlinear DEs are constructed in a reasonably pedestrian manner. If time permits, I will also discuss other interesting results presented in the manuscript.

(talk given for the graduate student seminar series on 29 January 2010)

Happy-snaps from \(\{ f\ |\ f:\mathbb{C} \rightarrow \mathbb{C} \}\) - visualisation of complex valued functions

Abstract: Complex valued functions are much talked about but rarely seen. But their graphs live in (something like) \(\mathbb{R}^4\), so how can we hope to see them? I will discuss one way to do this which produces some quite cute pictures - and can on occasion lead to some degree of insight.

(talk given for the graduate student seminar series on 29 May 2009)

On a connection between the Calogero-Moser hierarchy & the KP hierarchy

Abstract: I will discuss the result that the roots of a polynomial tau-function of the KP hierarchy obey a Hamiltonian system of Calogero-Moser type. On the one hand we have a function which describes waves propagating in a weakly dispersing medium; solutions to KP -- on the other we have a system of particles moving in time according to a particular Hamiltonian.

(talk given for the math-phys reading group on 19 May 2009)

A discussion of Kuperberg's proof of the alternating sign matrix conjecture

Abstract: I will discuss Kuperberg's alternate proof of the alternating sign matrix conjecture; that there are \[ A(n) = \frac{1!4!7!...(3n-2)!}{n!(n+1)!...(2n-1)!} \] alternating sign matrices of order \( n \). \( A(n) \) also ennumerates the totally symmetric self complimentary plane partitions of size \( 2n \) and many other objects, but there is no known bijective proof of this fact.

(talk given for the University of Melbourne, Department of Mathematics, Mathematical Physics Reading Group on 24 Febuary 2009)

An aspect of the large $n$ behaviour of the partitions of $n$

Abstract: A probability distribution, which is related to hook length, is defined for the set of partitions of a given number $n$. We then ask questions about the expected shape of a partition for large $n$. It turns out that the distribution concentrates on a partition whose Young diagram has a boundary of a particular simple shape.

(talk given for the math-phys reading group on 18 November 2008)

Unjamming as structural instability

Abstract: Granular materials are known to exhibit multiple personalities. In this presentation, the transition from solid-like to liquid-like behaviour of granular materials is investigated through analysis of mechanical stability on the scale of clusters of particles in the mesoscopic domain. Mesoscopic structures emerge inside the material during deformation: like any structure, these are subject to instabilities that ultimately lead to failure. The failures of such structures on the mesoscale serve as precursors to unjamming of the granular material on the macroscopic scale.

(talk given for my honours presentation on 23 November 2007)

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