(Oxford University)

Michael Coughlan (with Sam Howison, Ian Hewitt, Andrew Wells)

Arctic sea ice forms a thin but significant layer at the ocean surface, mediating key climate feedbacks. During summer, surface melting produces considerable volumes of water, which collect on the ice surface in ponds. These ponds have long been suggested as a contributing factor to the discrepancy between observed and predicted sea ice extent. When viewed at large scales ponds have a complicated, approximately fractal geometry and vary in area from tens to thousands of square meters. Increases in pond depth and area lead to further increases in heat absorption and overall melting, contributing to the ice-albedo feedback. 

Previous modelling work has focussed either on the physics of individual ponds or on the statistical behaviour of systems of ponds. In this talk I present a physically-based network model for systems of ponds which accounts for both the individual and collective behaviour of ponds. Each pond initially occupies a distinct catchment basin and evolves according to a mass-conserving differential equation representing the melting dynamics for bare and water-covered ice. Ponds can later connect together to form a network with fluxes of water between catchment areas, constrained by the ice topography and pond water levels. 

I use the model to explore how the evolution of pond area and hence melting depends on the governing parameters, and to explore how the connections between ponds develop over the melt season. Comparisons with observations are made to demonstrate the ways in which the model qualitatively replicates properties of pond systems, including fractal dimension of pond areas and two distinct regimes of pond complexity that are observed during their development cycle. 

Different perimeter-area relationships exist for ponds in the two regimes. The model replicates these relationships and exhibits a percolation transition around the transition between these regimes, a facet of pond behaviour suggested by previous studies. The results reinforce the findings of these studies on percolation thresholds in pond systems and further allow us to constrain pond coverage at this threshold - an important quantity in measuring the scale and effects of the ice-albedo feedback.

We propose a subspace Gauss-Newton method for nonlinear least squares problems that builds a sketch of the Jacobian on each iteration. We provide global rates of convergence for regularization and trust-region variants, both in expectation and as a tail bound, for diverse choices of the sketching matrix that are suitable for dense and sparse problems. We also have encouraging computational results on machine learning problems.

What do random spanning trees, graph embeddings, random walks, simplices and graph curvature have in common? As you may have guessed from the title, they are indeed all intimately connected to the effective resistance on graphs! While originally invented as a tool to study electrical circuits, the effective resistance has proven time and again to be a graph characteristic with a variety of interesting and often surprising properties. Starting from a number of equivalent but complementary definitions of the effective resistance, we will take a stroll through some classical theorems (Rayleigh monotonicity, Foster's theorem), a few modern results (Klein's metricity, Fiedler's graph-simplex correspondence) and finally discuss number of recent developments (variance on graphs, discrete curvature and graph embeddings).

We show how traders use immediate execution limit orders (IELOs) to liquidate a position when the time between a trade attempt and the outcome of the attempt is random, i.e., there is latency in the marketplace and latency is random. We frame our model as a delayed impulse control problem in which the trader controls the times and the price limit of the IELOs she sends to the exchange. The contribution of the paper is twofold: (i) Our paper is the first to study an optimal liquidation problem that accounts for random delays, price impact, and transaction costs. (ii) We introduce a new type of impulse control problem with stochastic delay, not previously studied in the literature. We characterise the value functions as the solution to a coupled system of a Hamilton-Jacobi-Bellman quasi-variational inequality (HJBQVI) and a partial differential equation. We use a Feynman-Kac type representation to reduce the system of coupled value functions to a non-standard HJBQVI, and we prove existence and uniqueness of this HJBQVI in a viscosity sense. Finally, we implement the latency-optimal strategy and compare it with three benchmarks:  (i)  optimal execution with deterministic latency, (ii) optimal execution with zero latency, (iii) time-weighted average price strategy. We show that when trading in the EUR/USD currency pair, the latency-optimal strategy outperforms the benchmarks between ten USD per million EUR traded and ninety USD per million EUR traded.

We consider sensitivity of a generic stochastic optimization problem to model uncertainty. We take a non-parametric approach and capture model uncertainty using Wasserstein balls around the postulated model. We provide explicit formulae for the first order correction to both the value function and the optimizer and further extend our results to optimization under linear constraints.  We present applications to statistics, machine learning, mathematical finance and uncertainty quantification. In particular, we prove that LASSO leads to parameter shrinkage, propose measures to quantify robustness of neural networks to adversarial examples and compute sensitivities of optimised certainty equivalents in finance. We also propose extensions of this framework to a multiperiod setting. This talk is based on joint work with Daniel Bartl, Samuel Drapeau and Jan Obloj.

In this talk we will discuss a problem that was worked on during MISGSA 2020, a Study Group held in January at The University of Zululand, South Africa.

We look at a communication network with two types of users - Primary users (PU) and Secondary users (SU) - such that we reduce the network to a set of overlapping sub-graphs consisting of SUs indexed by a specific PU. Within any given sub-graph, the PU may be communicating at a certain fixed frequency F. The respective SUs also wish to communicate at the same frequency F, but not at the expense of interfering with the PU signal. Therefore if the PU is active then the SUs will not communicate.

In an attempt to increase information throughput in the network, we instead allow the SUs to communicate at a different frequency G, which may or may not interfere with a different sub-graph PU in the network, leading to a multi-objective optimisation problem.

We will discuss not only the problem formulation and possible approaches for solving it, but also the pitfalls that can be easily fallen into during study groups.

Hawkes processes are a class of point processes used to model self-excitation and cross-excitation between different types of events. They are characterized by the auto-regressive structure of their conditional intensity, and there exists several extensions to the original linear Hawkes model. In this talk, we start by defining Hawkes processes and give a brief overview of some of their basic properties. We then review some approaches to parametric and non-parametric estimation of Hawkes processes and discuss some applications to problems with large data sets in high frequency finance and social networks.

Many manufacturing processes require the use of robots to transport parts around a factory line. Some parts, which are very thin (e.g. car doors)
are prone to elastic deformations as they are moved around by a robot. These should be avoided at all cost. A problem that was recently raised by
F.E.E. (Fleischmann Elektrotech Engineering) at the ESGI 158 study group in Barcelona was to ascertain how to determine the stresses of a piece when
undergoing a prescribed motion by a robot. We present a simple model using Kirschoff-Love theory of flat plates and how this can be adapted. We
outline how the solutions of the model can then be used to determine the stresses.