Andrew Nugent
Hello, I am a PhD student at the MathSys II CDT, supervised by Susana Gomes and Marie-Therese Wolfram.
My interests are in opinion dynamics, interacting particle systems and evolving networks.
My personal website can be found at: https://sites.google.com/view/andrew-nugent/homeLink opens in a new window
Recorded talks
Below are some recordings of talks given at the SPAAM (Statistics, Probability, Analysis and Applied Maths) seminar at the University of Warwick. A full list of talks and conferences can be found below.
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Publications
Steering opinion dynamics through control of social networksLink opens in a new window
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.
Bridging the gap between agent based models and continuous opinion dynamics.Link opens in a new window
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.
On evolving network models and their influence on opinion formation.Link opens in a new window
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’s 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?
Exploring the role of the potential surface in the behaviour of early warning signals.Link opens in a new window
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’s 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.
Past Projects
Cyclists' Cardiac Conundrum (MathSys Group Project)
Supervised by: Professor Colm ConnaughtonLink opens in a new window, Ian Green (external partner from CricklesLink opens in a new window)
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.
Conferences and Talks
- SPAAM Seminar | University of Warwick, Oct 24 | Talk on "Heterogeneous Mean-Field Limits: When different is actually the same" YouTube Link opens in a new window.
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UK Mathematical Systems and Control Theory NetworkLink opens in a new window | University of Warwick, Sep 24
- AMP24Link opens in a new window | University of Warwick, July 24 | Talk on "Steering opinion dynamics through control of social networks" Slides Link opens in a new window.
- Frontiers in Interacting Particle Systems, Aggregation-Diffusion Equations & Collective BehaviorLink opens in a new window | Research school at CIRM, Marseille, July 24
- BECMCLink opens in a new window | University of Birmingham, June 24 | Talk on "Steering opinion dynamics through control of social networks" Slides Link opens in a new window.
- Festival of Postgraduate ResearchLink opens in a new window | University of Warwick, May 24 | Visual presentation.
- MathSys Annual Retreat | Apr 24 | Poster on "Optimal network control for opinion dynamics" Poster Link opens in a new window.
- SPAAM Seminar | University of Warwick, Apr 24 | Talk on "Steering opinion dynamics through control of social networks" YouTube Link opens in a new window.
- British Applied Mathematics ColloquiumLink opens in a new window | Newcastle University, Apr 24 | Talk on "Bridging the gap between ABMs and continuous opinion dynamics" Slides Link opens in a new window.
- MINDS Seminar | Heriot-Watt University, Mar 24 | Talk on "Scaling in opinion dynamics".
- Junior Applied Maths SeminarLink opens in a new window | University of Oxford, Jan 24 | Talk on "Scaling in opinion dynamics".
- Postgraduate SeminarLink opens in a new window | University of Warwick, Jan 24 | Talk on "Approaches to modelling opinion formation" Slides Link opens in a new window .
- SPAAM seminarLink opens in a new window | University of Warwick, Nov 23 | Talk on "Scaling in opinion dynamics" Slides Link opens in a new window YouTube Link opens in a new window.
- Dynamics Days EuropeLink opens in a new window | Naples, Sep 23 | Poster on evolving network models.
- BECMCLink opens in a new window | University of Birmingham, July 23 | Talk on "Evolving networks in opinion dynamics".
- Interdisciplinary Workshop on Opinion Dynamics and Collective DecisionsLink opens in a new window | Constructor University, Bremen, July 23 | Poster "On evolving network models and their influence on opinion formation" Poster Link opens in a new window.
- Topics on Neuroscience, Collective Migration and Parameter Estimation Link opens in a new windowworkshop | Oxford, July 23.
- MathSys Summer School on Data Visualisation | University of Warwick, June 23.
- SPAAM seminar | University of Warwick, June 23 | Talk "On evolving network models and their influence on opinion formation" Slides Link opens in a new window, YouTube Link opens in a new window.
- MathSys Annual Retreat | Apr 23 | Presentation on representing multi-dimensional opinions Poster Link opens in a new window.
- Warwick Maths Society | University of Warwick, Jan 23 | Talk on "Models of opinion formation" Slides Link opens in a new window.
- Mir@W Day Opinion Formation in Complex SocietiesLink opens in a new window | University of Warwick, Oct 22.
- SPAAM seminar | University of Warwick, Oct 22 | Talk on "Exploring the role of the potential surface in the behaviour of early warning signals".
- Mathematical Models in Social InnovationLink opens in a new window summer school | University of L'Aquila, Sep 22
- MathSys Annual Retreat | Apr 22 | Poster on "Cyclists' Cardiac Conundrum" Poster Link opens in a new window.
- SIAM Annual MeetingLink opens in a new window | Online, July 21 | Poster on "Analysing early warning signals of disease elimination by approximating the potential surface" Poster Link opens in a new window.
- Society for Mathematical Biology Annual MeetingLink opens in a new window | Online, June 21 | Talk on "Investigating the potential of early warning signals of disease elimination" Slides Link opens in a new window.
Teaching Experience
- Teaching assistant for MA933 Stochastic Modelling and Random ProcessesLink opens in a new window | University of Warwick | 22/23 and 23/24 academic years
- Teaching assistant for ES98D Particle-based modellingLink opens in a new window | University of Warwick | 23/24 academic year
- First year supervisor | University of Warwick | 20/21, 22/23 and 23/24 academic years. Modules covered include: Analysis I and II, Calculus I, Sets and Numbers, Mathematical Methods and Modelling, Linear Algebra.
- A-level tutor | President Kennedy School | 19/20 academic year
- Peer tutor | University of Warwick | 19/20 academic year
Education
- PhD Mathematics of Systems | University of Warwick MathSys II CDT | Oct 22 - Present
- MSc Mathematics of Systems (Distinction) | University of Warwick MathSys II CDT | Sep 21 - Sep 22
- MMath Master of Mathematics (First Class) | University of Warwick | Sep 17 - July 22
Other Activities
- President of the Warwick SIAM-IMA Student ChapterLink opens in a new window committee | 24/25 academic year
- Reviewer for Chaos: An Interdisciplinary Journal of Non-linear Science
- Organising committee for AMP Conference 2024Link opens in a new window, which was recently featured in SIAM NewsLink opens in a new window.
- Seminar organiser for SPAAM seminarLink opens in a new window | 23/24 academic year
- Member of Warwick SIAM-IMA Student Chapter committee | 23/24 academic year
- Student representative to MathSys Advisory Board | June 22 - Present
- Secretary of MathSys SSLC | 21/22 academic year
- Executive Committee of Warwick Taichi and Chigong SocietyLink opens in a new window | 20/21 and 21/22 academic years
Email: a.nugent@warwick.ac.uk
Office: D2.05 Zeeman Building