Mengbin Ye

Mengbin Ye, Minh Hoang Trinh, Young-Hun Lim et al.

In this paper, and inspired by the recent discrete-time model in [1,2], we study two continuous-time opinion dynamics models (Model 1 and Model 2) where the individuals discuss opinions on multiple logically interdependent topics. The logical interdependence between the different topics is captured by a `logic' matrix, which is distinct from the Laplacian matrix capturing interactions between individuals. For each of Model 1 and Model 2, we obtain a necessary and sufficient condition for the network to reach to a consensus on each separate topic. The condition on Model 1 involves a combination of the eigenvalues of the logic matrix and Laplacian matrix, whereas the condition on Model 2 requires only separate conditions on the logic matrix and Laplacian matrix. Further investigations of Model 1 yields two sufficient conditions for consensus, and allow us to conclude that one way to guarantee a consensus is to reduce the rate of interaction between individuals exchanging opinions. By placing further restrictions on the logic matrix, we also establish a set of Laplacian matrices which guarantee consensus for Model 1. The two models are also expanded to include stubborn individuals, who remain attached to their initial opinions. Sufficient conditions are obtained for guaranteeing convergence of the opinion dynamics system, with the final opinions generally being at a persistent disagreement. Simulations are provided to illustrate the results.

Zainab Zaidi, Mengbin Ye, Fergus John Samon et al.

Developing an understanding of the public discourse on COVID-19 vaccination on social media is important not only for addressing the current COVID-19 pandemic, but also for future pathogen outbreaks. We examine a Twitter dataset containing 75 million English tweets discussing COVID-19 vaccination from March 2020 to March 2021. We train a stance detection algorithm using natural language processing (NLP) techniques to classify tweets as `anti-vax' or `pro-vax', and examine the main topics of discourse using topic modelling techniques. While pro-vax tweets (37 million) far outnumbered anti-vax tweets (10 million), a majority of tweets from both stances (63% anti-vax and 53% pro-vax tweets) came from dual-stance users who posted both pro- and anti-vax tweets during the observation period. Pro-vax tweets focused mostly on vaccine development, while anti-vax tweets covered a wide range of topics, some of which included genuine concerns, though there was a large dose of falsehoods. A number of topics were common to both stances, though pro- and anti-vax tweets discussed them from opposite viewpoints. Memes and jokes were amongst the most retweeted messages. Whereas concerns about polarisation and online prevalence of anti-vax discourse are unfounded, targeted countering of falsehoods is important.

Manou Rosenberg, Mengbin Ye, Brian D. O. Anderson

The Euclidean Steiner tree problem, normally posed in two dimensions, seeks to connect a set of prescribed terminal nodes by placing additional nodes, known as Steiner points, with edges connecting such nodes either to another Steiner point or a terminal node, and with the placements minimising the sum of all the edge lengths of the associated tree. We consider a problem in which we start with a known solution to a Steiner tree problem, and the terminal positions are then perturbed. A first-order approximation theorem is established for efficiently updating the Steiner point positions to recover a Steiner tree solution after the perturbations to terminal nodes. Numerical examples illustrate the effectiveness of our approach (including a stepwise application for large perturbations) as well as its limitations.

Roberta Raineri, Mengbin Ye, Lorenzo Zino

In this paper, we consider a population of individuals who have actions and opinions, which coevolve, mutually influencing one another on a complex network structure. In particular, we formulate a control problem for this social network, in which we assume that we can inject into the network a committed minority -- a set of stubborn nodes -- with the objective of steering the population, initially at a consensus, to a different consensus state. Our study focuses on two main objectives: i) determining the conditions under which the committed minority succeeds in its goal, and ii) identifying the optimal placement for such a committed minority. After deriving general monotone convergence result for the controlled dynamics, we leverage these results to build a computationally-efficient algorithm to solve the first problem and an effective heuristics for the second problem, which we prove to be NP-complete. For both algorithms, we establish theoretical guarantees. The proposed methodology is illustrated though academic examples, and demonstrated on a real-world case study.

Lorenzo Zino, Mengbin Ye, Brian D. O. Anderson

We study a continuous-time dynamical system of nodes diffusively coupled over a hierarchical network to examine the efficiency and performance tradeoffs that organizations, teams, and command and control units face while achieving coordination and sharing information across layers. Specifically, after defining a network structure that captures real-world features of hierarchical organizations, we use linear systems theory and perturbation theory to characterize the rate of convergence to a consensus state, and how effectively information can propagate through the network, depending on the breadth of the organization and the strength of inter-layer communication. Interestingly, our analytical insights highlight a fundamental performance tradeoff. Namely, networks that favor fast coordination will have decreased ability to share information that is generated in the lower layers of the organization and is to be passed up the hierarchy. Numerical results validate and extend our theoretical results.

Ella C. Davidson, Lorenzo Zino, Ming Cao et al.

This paper proposes a mathematical model for the coevolution of actions and opinions for a population facing a social dilemma. In particular, we assume each person participates in a Public Goods Game (PGG), with their action being to cooperate or defect, and holds an opinion about which action they prefer. We propose a payoff function that combines the PGG with the Friedkin--Johnsen model from opinion dynamics to form a coevolutionary game. According to a discrete-time process, players asynchronously update their actions and opinions, aiming to maximise their individual payoff for the coevolutionary game using myopic best-response. We study the equilibria and provide conditions for the existence of the all-defection and all-cooperation consensus equilibria. We also establish conditions for global convergence to the all-defection equilibrium.

Mengbin Ye, Lorenzo Zino, Ming Cao

For a society to remain healthy and prosperous, people must collectively behave and act to contribute to the common good, even if there is often a tradeoff against their individual benefit. Paradigmatic examples include the adoption of sustainable behaviors and technologies to combat the climate crisis, and the mobilization for collective action to promote the rights and freedoms of repressed minorities. In this tutorial, we illustrate how game theory and network systems theory can be powerful tools to model and study this collective decision-making problem. We provide examples of how awareness of this tradeoff can impact collective change toward the societal good, exploring different problem contexts such as sustainable behavior and collective action. Finally, we review recent developments using systems and control-theoretic approaches to generate awareness and guide the emergent population dynamics towards a desired outcome, and conclude by highlighting new research and application frontiers.

James S. Russell, Mengbin Ye, Brian D. O. Anderson et al.

A GPS-denied UAV (Agent B) is localised through INS alignment with the aid of a nearby GPS-equipped UAV (Agent A), which broadcasts its position at several time instants. Agent B measures the signals' direction of arrival with respect to Agent B's inertial navigation frame. Semidefinite programming and the Orthogonal Procrustes algorithm are employed, and accuracy is improved through maximum likelihood estimation. The method is validated using flight data and simulations. A three-agent extension is explored.

James Russell, Mengbin Ye, Brian D. O. Anderson et al.

This paper presents a novel approach for localising a GPS (Global Positioning System)-denied Unmanned Aerial Vehicle (UAV) with the aid of a GPS-equipped UAV in three-dimensional space. The GPS-equipped UAV makes discrete-time broadcasts of its global coordinates. The GPS-denied UAV simultaneously receives the broadcast and takes direction of arrival (DOA) measurements towards the origin of the broadcast in its local coordinate frame (obtained via an inertial navigation system (INS)). The aim is to determine the difference between the local and global frames, described by a rotation and a translation. In the noiseless case, global coordinates were recovered exactly by solving a system of linear equations. When DOA measurements are contaminated with noise, rank relaxed semidefinite programming (SDP) and the Orthogonal Procrustes algorithm are employed. Simulations are provided and factors affecting accuracy, such as noise levels and number of measurements, are explored.