Student Speakers
Name: Wilfred Armfield
Title: The Forward Loop-Erased Ant process and uniform spanning trees
Abstract: The Ant process was first introduced by Kious, Mailler and Schapira in 2020 to model the collective learning behaviours of ant colonies. In the new Forward Loop-Erased (FLE) variant of the model we are able to draw upon the extensive literature of loop-erased random walks. In particular, this talk will highlight how the link with Uniform Spanning Trees and Wilson’s algorithm allows us to prove geodesic results for the FLE Ants process in a more general setting than that of Kious, Mailler and Schapira.
Name: Sebastian Quintanilla
Title: Exploring genetic ancestry with Coalescent Trees
Abstract: The genetic history of living beings is encoded in their DNA, and these sequences can be traced back to a common ancestor. A simple way to represent this ancestry is through phylogenetic trees— graphical models that depict the times at which pairs of sequences last shared a common ancestor. Since the true genealogical history is not directly observable, a probabilistic model known as the Coalescent is used to simulate this unseen history, while the observed genetic data guides the inference of likely ancestral trees.
In this talk, I will introduce basic concepts from population genetics, and present an example from my research, where we simulate coalescent trees with a fixed length to explore the effects of constrained evolutionary timelines.
Name: Beth Stokes
Title: Should I stay, or should I go: Sex ratio response drives a diverse range of (anti-)correlated intra-species behaviours
Abstract: The decision of an individual or group to leave its current environment may be influenced by various factors. These include external or inter-species factors such as the presence of predators or food availability, and also intra-species dynamics like mate searching or the strength of social ties within a group. Understanding the consequences of these behaviours on the population level dynamics is non-trivial. In this work, we explore a stochastic model describing the movement of males and females of a species between localised patches, in which the movement rates are dependent on the sex ratio within the patch. By deriving a system of stochastic differential equations governing the fluctuations in these patches we can model a diverse range of intra-species behaviours driven solely by an individual’s response to local sex ratio. We subsequently uncover and explore how various individual behaviours can give rise to large scale (anti-)correlated movements between the sexes.
Name: Robert Johnson
Title: A new algorithm for ptychography
Abstract: Ptychography is an inverse problem that aims to recover the phase and amplitude of a sample under illumination from its complex diffraction patterns. Recovery algorithms use an iterative approach to recover the phase and amplitude by looking at the difference of the diffraction pattern of the true sample, to the diffraction pattern of the current best guess of the sample. In this talk a new algorithm for recovery using the L-BFGS optimization algorithm will be presented and compared to existing recovery algorithms, on synthetically generated data and on real samples.
Name: Veronika Chronholm
Title: Simplified proton transport models for treatment planning and uncertainty quantification
Abstract: Proton Beam Therapy (PBT) is a type of radiotherapy used for cancer treatment. Due to the sharply peaked dose-depth curve characteristic of protons, and the fact that protons stop at a finite depth inside the tissue, PBT is especially useful when treating tumours situated close to vital organs, which need to be spared from radiation damage.
In terms of both treatment planning and uncertainty quantification, a physically accurate model for proton transport that is also quick to evaluate is needed. This talk will cover some possible models for proton radiation, as well as their application to clinically relevant problems.
Name: Elliot Butterworth
Title: Lobsters and the evolution of complexity
Abstract: Tagmosis is the process by which the number of and differentiation between body segments changes. This talk focusses on tagmosis in a highly simplified model of a lobster’s legs. The legs are assumed to perform three core functions: movement, food gathering and eating. By constructing a fitness function based on these necessary tasks, we investigate how a model lobster can maximise its fitness and how this fittest state varies as the level of differentiation between its legs changes. We use this model to consider the nature of constraints in shaping the fitness of organisms. Further, we discuss the evolution of complexity in light of these findings, highlighting two stages, both leading to an increase in complexity. The range of applicability of these findings is considered.
Name: Chiara Boetti
Title: Network Time Series Models for Volatility Forecasting
Abstract: Accurate forecasting of volatility— the time-varying variability in a financial asset’s price— is essential for risk management and for designing optimal decision-making policies. The increasing availability of high-frequency data has exposed limitations in classical latent-variable models, which are unsuitable for handling data with long-range dependence. Although fractionally integrated models can accommodate this feature, they are computationally demanding. The heterogeneous autoregressive (HAR) model offers a more efficient alternative, combining simplicity with strong empirical performance, and has become a standard in the field.There is growing interest in multivariate extensions of the HAR model to effectively capture dependencies across different financial markets. In this talk, we focus on time series data defined over graphs and compare the forecasting performance of two recent network-based models: one built on fractional integration and the other on the HAR framework.
Name: Guannan Chen
Title: Quantum algorithms for the exponential of Hamiltonian matrices
Abstract: Computing the time evolution of quantum systems, by solving the Schrödinger equation and approximating matrix exponentials, is a fundamental task in quantum computing and numerical analysis. In this talk, we discuss some techniques for Hamiltonian simulation on quantum computers, including rational approximations, variational methods, and exponential splittings, with a focus on enabling long time steps that allow practical implementation on near-term quantum devices.
Name: Charlie Cameron
Title: Spatial regime conversion method
Abstract: We present a novel hybrid modelling approach for simulating one-dimensional, one-species reaction-diffusion systems that balances stochastic accuracy with computational efficiency. Our model automatically adapts to local particle concentrations, applying the Stochastic Simulation Algorithm (SSA) in regions where stochastic effects are significant, and switching to partial differential equations (PDEs) where particle numbers are high. This dynamic regime conversion removes the need for a predefined interface, allowing the model to respond flexibly to evolving system states.
To ensure consistency across regimes, we employ a moment-closure method that bridges the stochastic reaction network with its deterministic PDE counterpart. We demonstrate the model’s accuracy and efficiency on benchmark problems, including simple diffusion and the Fisher-KPP equation.
This method offers a scalable framework for simulating reaction-diffusion systems, especially those where stochasticity plays a critical role in low-density regions but becomes computationally intensive at scale.
Name: Paddy O’Toole
Title: Clustering of multivariate tail dependence using conditional methods
Abstract: Conditional extreme value models analyse joint tail behaviour by describing the distribution of a random vector’s components given one component exceeds a high threshold. Although flexible, estimates suffer high uncertainty due to the scarcity of extreme data. To our knowledge, clustering has not yet been explored for CE models.
We propose a clustering framework for CE models to summarise multivariate extremal dependence and identify sites with similar tail behaviour. Our approach defines a novel dissimilarity measure based on the Jensen-Shannon divergence and typical CE model assumptions, which is uniquely applicable in any dimension. We use k-medoids to cluster sites using this measure.
A simulation study demonstrates superior performance to existing bivariate methods across various extremal dependence structures and uniquely enables multivariate clustering. We also apply our framework to Irish meteorological data, revealing groups of sites with similar tail dependence between precipitation and wind speed.
Name: Diana de Armas Bellon
Title: Rough Mount Fuji accessibility percolation
Abstract: We consider a rooted tree where each vertex is labelled by an independent and identically distributed (i.i.d.) uniform(0,1) random variable, plus a parameter theta times its distance from the root. We study paths from the root to infinity along which the vertex labels are increasing. The existence of such increasing paths depends on both the structure of the tree and the value of theta. The goal is to determine the critical value of theta such that, above this value, increasing paths occur with positive probability, while below it, no such paths exist. Additionally, we extend this problem to consider the case of the integer lattice.
Name: Patrick Fahy
Title: Greedy Learning to Optimise with convergence guarantees.
Abstract: Learning to Optimise (L2O) uses training data to speed up optimisation problems. Traditional unrolling methods, while effective, are often limited by memory constraints and lack convergence guarantees. We propose a novel greedy L2O approach that learns iteration-specific parameters by minimising the next iteration’s function value.
This method allows for significantly longer training sequences with constant GPU memory. Our update parametrisation ensures that parameter learning is no more complex than solving the original optimisation problem, with convergence guarantees on test data. Empirical results on a Computed Tomography example show improved performance over classical algorithms like Nesterov’s Accelerated Gradient Method and L-BFGS.