糖心TV

A Nugent, S Gomes, MT Wolfram, 2025, European Journal of Applied Mathematics, pp. 1–36. doi:10.1017/S0956792525100260

We extend a classical model of continuous opinion formation to explicitly include an age-structured population, considering both an SDE model and the corresponding mean field PDE. We rigorously prove the existence of stationary states in the PDE model, but also observe non-uniqueness of stationary states and periodic behaviour, an example of which is shown on the right. This figure shows the population opinion distribution (integrating over age) which has two large clusters that periodically move, merge and reform.

A Nugent, S Gomes, MT Wolfram, 2024, Chaos 1 July 2024; 34 (7): 073109.

We propose a novel control approach for opinion dynamics on evolving networks. Controls modify the strength of edges rather than influencing opinions directly, with the overall goal of steering the population towards a target opinion. The video shows the evolution in time of an example optimal control solution, with blue and red dots showing where edge weights are being increased and decreased respectively.

In the paper we study controllability, instantaneous control and optimal control. Each approach provides a different view on the complex relationship between opinion and network dynamics and raises interesting questions for future research.

A Nugent, S Gomes, MT Wolfram, 2024, Physica A: Statistical Mechanics and its Applications, 129886.

Most microscopic models of opinion dynamics are either agent-based models or differential equation models. We show how the latter can be obtained from the former by simultaneously reducing the time-step and the distance by which agents update their opinions after each random interaction. The video shows realisations of the ABM in solid lines and the limiting ODE in dashed lines.

This connection helps address questions in both settings, for example: the motivation of multiplicative noise terms in SDE models; the link between selection noise and mollification of interaction functions; and how the method for selecting interacting pairs can determine the normalisation in the corresponding ODE/SDE.

A Nugent, S Gomes, MT Wolfram, 2023, Physica D: Nonlinear Phenomena 456:133914.

We propose a new model for continuous time opinion dynamics on an evolving network, in which the network evolves through a system of ordinary differential equations for the edge weights. Each edge weight is interpreted as the strength of the relationship between a pair of individuals, with edges increasing in weight if pairs continually listen to each other鈥檚 opinions and decreasing if not. The model is examined partly through analytic results and partly through extensive numerical simulations of two case studies: one using bounded confidence interaction dynamics (as in the classical Hegselmann-Krause model) and one using an exponentially decaying interaction function. Particular focus is given to the impact of various edge dynamics on the opinion formation process itself: when does the dynamic network encourage consensus and when does it reinforce polarisation?

A Nugent, E Southall, L Dyson, 2022, Journal of Theoretical Biology, 554, p.111269.

Critical slowing down states that systems display increasing relaxation times prior to a critical transition, an effect that can be observed in timeseries statistics to give an early warning of the transition. However, in epidemiological models there is frequent disagreement with this general theory, moreover the alternative theory of critical speeding up predicts contradictory behaviour of early warning signals. We first describe the behaviour of common early warning signals in terms of a system鈥檚 potential surface and noise around a quasi-steady state, then describe an equation-free method to obtain these key features from timeseries, using a version of the SIS model as a case study. The figure shows example reconstructed potential surfaces.

Cyclists' Cardiac Conundrum (MathSys Group Project)

Supervised by: Professor Colm ConnaughtonLink opens in a new window, Ian Green (external partner from )

Collaborators: Jack BuckinghamLink opens in a new window, Yi Ting LooLink opens in a new window

Evidence suggests that those engaging in endurance sports training have an elevated risk of atrial fibrillation, this can be diagnosed accurately using an electrocardiogram (ECG), but this is often unavailable. Our goal in this project was to develop methods for quantifying the degree of the irregularity in readily available heart rate data, and test if this was correlated to self-reported heart rhythm problems.

Exploring approaches to modelling mass vaccination (URSS project)

Supervised by: Dr Louise DysonLink opens in a new window

During the role-out of COVID-19 vaccines, a key question was that of vaccine efficacy. We examined the different ways of incorporating vaccine efficacy into compartmental models, for example: a 90% efficacy could be interpreted as a 90% probability of moving to a fully immune class or a 90% reduction in the rate of infections. These different interpretations give different model structures and different conditions for controllability. In reality, vaccine efficacy has multiple components and should be included in compartmental models in multiple places.

Email: andrew.nugent@ucl.ac.uk

Office: D2.05 Zeeman Building