Term 1

Term 1 Abstracts

Week 10. Benedict Russell (MathSys, Warwick) | STV Manipulation: How to win an election by supporting your opponent

We study potential manipulations of the single transferable vote (STV) voting rule, where a coalition of voters may vote strategically to change the result of an election in their favour. First outlining landmarks theorems in electoral science, we improve on a manipulation algorithm and use the result to derive a new stability measure. We explore the monotonic properties of the measure and how the stability measure changes under simulated STV elections.

Week 10. Matthew Bowditch (MathSys, Warwick) | Adversarial Purification using Diffusion Models

Neural network-based image classification models have been shown to be vulnerable to adversarial attacks, which is a large concern if they are to be used in a real-world setting. Small, carefully crafted pixel perturbations can be subtly introduced to an image by an attacker, deceiving these classifiers while preserving the image’s visual similarity to the original. One recent approach seeks to defend against such attacks by introducing a diffusion model before classification. This diffusion model acts as a "purifier", removing adversarial perturbations from the image prior to classification. In this talk, I will explore this method and discuss potential modifications to improve its effectiveness. These modifications utilise methods that change semantic content of images during the reverse diffusion process.

Week 8. Chen Lyu (Computer Science, Warwick) | Faithfulness and Factuality in NLP

Faithfulness and factuality are essential for ensuring the reliability and trustworthiness of Natural Language Processing (NLP) systems, particularly in high-stakes domains like healthcare, law, and education. This talk explores these intertwined concepts, focusing on the challenges of maintaining alignment between generated text and source content (faithfulness) and ensuring accuracy against real-world facts (factuality). While large language models (LLMs) bring unprecedented capabilities, they often introduce hallucinations and inconsistencies that undermine trust. This presentation will cover state-of-the-art techniques, including entailment-based methods, chain-of-thought reasoning, and external knowledge integration, alongside their applications in summarization, question answering, and domain-specific tasks. By examining case studies and current benchmarks, the talk provides insights into building NLP systems that prioritize both faithfulness and factuality for more reliable outputs.

Week 8. Mark Lynch (MathSys, Warwick) | Modelling the Role of Empathy in Epidemic Spread

Human behaviour is a key contributor to the spread of an infectious disease. People typically do not want to infect others if they themselves are infected. How empathetic does a population need to be in order to rationally suppress a disease through social distancing? When is this possible if the disease is asymptomatic? This population behaviour can be viewed as a “differential game”: Rational, well informed individuals seek to maximise their own utility function by modifying their behaviour. When the costs in the utility only pertain to the individual, infected individuals never socially distance because modifying their behaviour cannot improve their situation. We study the case where individuals care about other members of the population, in order to protect others from incurring the cost of being infected and/or of having to socially distance. We quantify the degree to which individuals must care about the population in order to rationally target disease eradication through social distancing. This work is then extended to an asymptomatic case, where susceptible behaviour is performed by a subset of infected individuals.

Week 7. Byron Tzamarias (MathSys, Warwick)

Week 6. Kipp Freud (University of Bristol) | AutoVec: Automatic generation of data and vector embeddings for arbitrary domains and cross-domain mappings using LLMs

We present AutoVec, a novel method for the fully unsupervised construction of interpretable embedding spaces applicable to arbitrary domains. Our approach automates costly data acquisition by leveraging the knowledge embedded in large language models (LLMs), facilitating similarity assessments between entities for meaningful positioning within vector spaces. Additionally, our method enables intelligent mappings between vector space representations of disparate domains, using a novel form of cross-domain similarity analysis. AutoVec is both a valuable tool for data synthesis, and facilitates a novel form of recommendation system; we can recommend entities from one domain based on entities from other domains. What movie should I watch if I enjoy the book Red Rising? What song should I listen to while I play the board game Risk? If King Charles was a vegetable, what vegetable would he be? Finally, such questions can be answered with AutoVec.

Week 6. Max Butler (MathSys, Warwick) | Kernel Methods for SDE Parameter Inference

Stochastic Differential Equations (SDEs) are being increasingly used in many Scientific disciplines to model real-world phenomena. SDEs allow practitioners to utilise their understanding of the deterministic dynamics or trends while also capturing, stochastically, the elements that are not yet understood or are not yet measurable. Once a SDE model has been devised it has to be fit to the observed data, exact analytical inference is often not possible especially with models that capture non-linear dynamics, meaning simulation based or approximate numerical methods must be used. Simulation based methods have the problem that doing the large amount of simulation required is computationally expensive and many approximate numerical methods don’t capture the full law the distribution. In this talk I'll present a novel method of SDE inference that combines the speed of approximate numerical methods with the accuracy of more expensive simulation based methods.

Week 4. Grega Saksida (Warwick Maths CDT) | Random walks in spin systems.

Spin systems, a very active topic in statistical mechanics, are models that describe how spin particles behave and interact with each other. A common question in this field is whether, and at what temperature, does a material transition between a "normal" and a magnetic state. One can usually represent objects in spin systems in terms of random walks, which allows us to apply techniques of random walks on spin systems. In this talk, I will first define a typical object we study in statistical mechanics: a two-point function. This can be studied using a technique called lace expansion. I will give an outline of the technique, using a self-avoiding walk as an example.

Week 4. Joseph Duque Lopez (HetSys, Warwick)

Atomistic simulations using Density Functional Theory can only capture femtoseconds worth of data within a limited simulation cell size. In order to predict the long-term effects of irradiation on the material properties of Tungsten, we require a continuum approach to simulate the interactions of dislocation loops in Tungsten due to irradiation. Contemporary continuum models of stress fields from dislocation loops are tricky to handle due to the presence of singularities near the core of the dislocations. We present a method to regularise such models while producing accurate predictions for the far-field interactions between loops. Such models must be informed by lower length scale simulations so that the physics of the problem is correctly captured by the model, therefore verification via atomistic simulations is still important to perform. We present the current model and its advantages, and how it compares against predictions produced by atomistic simulations, particularly how the decay rate of atomic displacements scale in the continuum and atomistic simulations.

Week 3. Andrew Nugent (MathSys, Warwick) | Heterogeneous mean-field limits: when different is actually the same.​

When studying large systems of interacting particles, such as in opinion formation, bird flocking or pedestrian dynamics, it can be useful to consider the limit as the population becomes infinitely large. This 'mean-field limit' provides a single partial differential equation describing the density of opinions/birds/pedestrians, thus avoiding tracking a large number of individuals. However, an additional challenge arises when the population is heterogeneous, such as when interactions occur over a network rather than in a well-mixed population. Inspired by the works of Pierre-Emmanuel Jabin and Fabio Coppini, this talk will discuss the use of heterogeneous mean-field limits, using their application to opinion dynamics on networks as a running example. We will examine when the heterogeneous mean-field limit differs from the 'classical' one and, perhaps most interestingly, when it does not.

Week 3. Aria Ahari (Statistics, Warwick) | Boundary crossing problems and functional transformations for Ornstein–Uhlenbeck processes