We present a new initialisation of an adaptive batch strategy to compute the ε-approximate minimum volume covering ellipsoid (MVCE) for a set of n points. We focus on moderately sized datasets (up to dimension d = 100 and n = 1 000 000). The adaptive batch strategy works in an optimisation-deletion-adaptation cycle: we solve the MVCE problem using a smaller number of points, we delete points from consideration that are guaranteed to not lie on the boundary of the MVCE, and then carefully select a new batch of points. We propose a new initialisation, which involves selecting the points corresponding to some highest leverage scores. We show using numerical examples that this new initialisation tends to improve computation time as well as reduce the total number of cycles, as compared with initialising with a random selection of points.

A highly accurate and efficient method to compute the expected values of the count, sum, and squared norm of the sum of the centre vectors of a random maximal sized collection of non-overlapping unit diameter disks touching a fixed unit-diameter disk is presented. This extends earlier work on Renyi's parking problem [Magyar Tud. Akad. Mat. Kutato Int. Kozl. 3 (1–2), 1958, pp. 109–127]. Underlying the method is a splitting of the the problem conditional on the value of the first disk. This splitting is proven and then used to derive integral equations for the expectations. These equations take a lower block triangular form. They are solved using substitution and approximation of the integrals to very high accuracy using a polynomial approximation within the blocks.


 MISG 2020
 
 
 University of Newcastle, Australia
 
 
 28 January -- 1 February, 2020
 
 
 
 This special Section of the ANZIAM Journal (Electronic Supplement) contains the refereed papers from the 2020 Mathematics and Statistics in Industry Study Group (MISG 2020) held at the University of Newcastle from 28 January -- 1 February 2020. The MISG is a special interest meeting of ANZIAM, the Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) division of the Australian Mathematics Society. The MISG meetings take place annually and provide a forum where projects proposed by industry can be worked on intensively, by high profile scientists in the fields of Applied Mathematics, Statistics and Operations Research, from Australia, New Zealand and the world beyond, along with representatives from the industries proposing the projects.
 The writing of these papers was coordinated by the project moderators in consultation with the coauthors and company representatives. The manuscripts were submitted to the editors, Associate Professor Mike Meylan, Professor Ngamta Thamwattana and Professor Tony Roberts, and were subsequently refereed by two expert referees. On the advice of the referees, manuscripts were accepted for publication, subject to the recommended revisions, and formally approved by the editorial committee.
 At MISG 2020, six projects were presented from diverse industries, with 78 delegates participating.
 Industry Partners
 We gratefully acknowledge the support of our industry partners:
 
 Lovells Springs;
 Safearth;
 Concrush;
 Hyper Q Aerospace.
 
 Acknowledgements
 In addition to our industry partners, we gratefully acknowledge support from the following organisations:
 
 ANZIAM;
 Office of the NSW Chief Scientist \& Engineer, Department of Industry, NSW Government;
 Priority Research Centre: Computer Assisted Research Mathematics and its Applications, The University of Newcastle;
 Faculty of Science, The University of Newcastle.
 
 We are also grateful to Professor Ryan Loxton from the Centre for Optimisation and Decision Science, Curtin University, for giving a public lecture on power of optimisation research in mining, energy, and agriculture industries, as part of the MISG's outreach event and acknowledge the support from the Hunter Branch of the Royal Society of NSW in promoting the public lecture. We are also grateful to Professor Mark McGuinness (Victoria University of Wellington), Professor Troy Farrell (Queensland University of Technology), Associate Professor Amie Albrecht (University of South Australia) and Dr Neville Fowkes (University of Western Australia) for their helpful advice and comments in organising the MISG 2020.
 MISG2020 Organising Committee
 
 Professor Ngamta Thamwattana (Co-Director)
 Associate Professor Mike Meylan (Co-Director)
 Mrs Juliane Turner (Administrative Support)
 Dr David Allingham (Technical Support)
 
 

This paper investigates spatial data on the unit sphere. Traditionally, isotropic Gaussian random fields are considered as the underlying mathematical model of the cosmic microwave background (CMB) data. We discuss the generalized multifractional Brownian motion and its pointwise Hölder exponent on the sphere. The multifractional approach is used to investigate the CMB data from the Planck mission. These data consist of CMB radiation measurements at narrow angles of the sky sphere. The results obtained suggest that the estimated Hölder exponents for different CMB regions do change from location to location. Therefore, the CMB temperature intensities are multifractional. The methodology developed is used to suggest two approaches for detecting regions with anomalies in the cleaned CMB maps. doi:10.1017/S1446181122000104

We consider a local projection stabilisation based on biorthogonal systems and adaptive refinement for convection-diffusion-reaction differential equations. The local projection stabilisation and adaptive finite element method are both based on a biorthogonal system. We investigate the numerical efficiency of the approach when compared to the standard finite element method. Numerical examples are presented to demonstrate the performance of the approach.

A vital input for steel manufacture is a coal-derived solid fuel called coke. Digital reconstructions and simulations of coke are valuable tools to analyse and test coke properties. We implement biased voxel iteration into a simulated annealing method via a kernel convolution to reduce the number of iterations required to generate a digital coke microstructure. We demonstrate that voxel connectivity assumptions impact the number of iterations and reduce the normalised computation time required to generate a digital microstructure by as much as 70%.

In 2016, a Mathematics-in-Industry Study Group (MISG) project considered the construction of mining sequences, that is, the process connecting ore extraction with specific orders. In particular, the meeting considered the potential for using knowledge about geological variability within the ore. This article revisits this MISG project and the approach developed for thinking about the problem as the build for an order progresses. We provide new perspectives on this approach and outline possible ways for further development.

In this work, we discuss elasticity equations on a two-dimensional domain with random boundaries and we apply these equations to modelling human corneas.

Aggregations abound in nature, from cell formations to locust swarms. One method of modelling these aggregations is the non-local aggregation equation with the addition of degenerate diffusion. In this article we develop a finite volume based numerical scheme for this style of equation and perform an error, computation time, and convergence analysis. In addition we investigate two methods for approximating the non-local component.

Several numerical studies have shown that non-convex sparsity-induced regularization can outperform the convex ℓ1-penalty. In this article, we introduce a new non-convex and non-smooth regularization. This new regularization is a continuous and separable function which provides a tighter approximation to the cardinality function than any ℓq-penalty (0 < q < 1). We then apply the Proximal Gradient Method to solve a regularized optimization problem with the new regularization. The convergence analysis shows that the algorithm converges to a critical point and we also provide a pseudo-code for fast implementation. In addition, we conduct a simple numerical experiment with a regularized least square problem to illustrate the performance of the new regularization.