ANZIAM2020 was held in the lower Hunter Valley in NSW, Australia, from 2-6 February. Bringing together the applied mathematics communities of both Australia and New Zealand, it also included speakers from the US, the UK and Japan. This made for a fascinating series of talks over four days, with the daily schedule consisting of three plenary talks separated by series of 15 minute presentations.
Peter Taylor (University of Melbourne), the 2019 ANZIAM Medallist, opened the conference with a plenary talk on resource allocation problems. The talk introduced the seminal work of A. K. Erlang who developed the Erlang probability distribution to model the number of telephone calls which might be made simultaneously to the operators of switching stations. Taylor's work considered an expanded network of resources, and found that localised allocation conditions were more effective than network-wide allocation conditions in distributing the resources most efficiently. He introduced his most recent work on a restless multi-armed bandit formulation of the problem.
The plenary talks generally had a focus on collaboration with industry, particularly Ryan Loxton's talk (Curtin University) on optimal control in crane dynamics with continuous inequality constraints. A construction company had been unsuccessfully using trial and error to automate smooth load carrying by its cranes. The company approached Loxton, who applied control theory to provide a number of solutions that would ensure adequately stable dynamics under external factors such as wind. An interesting takeaway was that while in academia, optimal solutions are desired, in Loxton's real world contexts, engineers are happy to sacrifice up to 5% of the convergence of the cost function so that the solution is physically feasible.
Given the ongoing climate crises in Australia, Elizabeth Bradley's talk (University of Colorado) was a timely insight into the state of ice-core data analysis. Bradley showed that climate dynamics based on ice-core data cannot yet be derived using non-linear time series analysis, and showed her work using tools from information theory instead, specifically permutation entropy. Bradley stressed that as the ice-core data is gradually compiled, it needs an increasing effort from the applied mathematics community to be analysed.
Ami Radunskaya (Pomona College) presented a fascinating collection of collaborative efforts with academia and industry. Radunskaya first showed work with medical collaborators proving that certain anti-blood clotting medications don't adequately take blood flow into account. Radunskaya alos showed that if you model a reactionary stabilising force using a delay differential equation, adding noise to the dynamics of the object being stabilised increases the number of delayed corrections the force makes, and also improves the average performance of the stabiliser. These results could have implications for remedial therapy, in which electric pulses would be transmitted into achilles tendons to help people learning to walk again. Most impressively, Radunskaya showed recent work in which she found discrepancies between the DNA of healthy and cancerous cells. Using graphs of DNA data from the medical literature, she used graph theoretical techniques and statistical tests to show that certain proteins behave differently, results that were subsequently corroborated in medical experiments.
The non-plenary talks varied from beer production planning (Stephen Maher, University of Exeter) to modelling task-switching using heteroclinic networks (Gray Manicom, University of Auckland), from algebra between matrices of ordinarily disagreeable dimensions (Christina Pospisil, University of Massachusetts Boston) to the student prize talk on Lagrangian coherent data assimilation (Rose Crocker, University of Adelaide).
We learnt that when localised and highly concentrated locust food sources arise in agricultural settings, locusts can form plagues which devastate agricultural industries, particularly in West Africa. Behind removing such food sources, a secondary measure exploits the fact that `gregarious' locusts have different coloured hind legs to `solitary' locusts, so that simply painting the hind legs of the former the same color as those of the latter will also restrict plague formation (Fillipe Georgiou, University of Newcastle).
We learnt that despite Australia's incessant drought, erosion under train lines caused by flooding remains of utmost concern to the railway industry, prevention of which requires modelling of fluid flow through porous media (Michael Meylan, University of Newcastle).
We learnt that during kidney stone removal via miniscule internal tracks, debris being cleared out become trapped in vortices resulting from the fluid flow, extending the overall runtime of the procedure. This is addressed by disturbing the flow in such a way that debris is forced into streamlines around the ureteroscope (Jessica Williams, University of Oxford).
My personal favourite was Gary Froyland's talk (University of New South Wales) on spectral clustering via his and his collaborators' Sparse Eigenbasis Approximation (SEBA) algorithm. The method extracts almost-invariant or coherent sets from the eigenvectors of transfer operators, and was shown to be effective and remarkably computationally efficient when locating ocean eddies in the North Atlantic Ocean from 90 days of satellite data.
ANZIAM once again provided a valuable opportunity for the applied mathematics community to share research ideas and opinions, with a wide breadth of topics on display. ANZIAM2021 at Cape Schanck in Victoria is expected to be another great experience.