Control of opinion dynamics in multiple dimensions

研究的背景意见动态的基本概念，即一组个体随着时间的推移相互作用并更新他们的意见，已经在越来越多的模型中得到了体现。在一个简单的模型中，个体通过对周围人的意见进行加权平均，以离散的时间步长更新他们的意见，从而形成一个线性动力系统。对于这样的系统，存在明确的条件，当共识可以出现和方法来预测什么样的意见，该集团将达成。这个简单的模型已经在一系列不同的方向上发展，一些包括更现实的特征，如在线媒体或顽固的个人，提出不同的交互条件，应用替代数学技术，或进行任何数量的其他调整。一个主要的贡献是Hegselmann和Krause的模型，以及Deffuant等人。个人只有在他们的观点已经足够接近的情况下才能互动。这种情况造成了非线性，并可能导致意见集群的形成。这种最初的离散时间模型已被改编成连续时间模型，然后到随机模型，最后到相应的PDE模型描述的意见分布在一个大的人口的演变。在不同的参数制度下，这些模型可以表现出一系列有趣的行为：在某些情况下，意见合并或随着时间的推移变得更加温和，在其他情况下，多个不同的意见持续存在，在某些情况下，根本没有明确的意见出现。由于前所未有地接触到世界各地人们的意见，很容易看到真实的生活中的可比情况，来自社交媒体的数据使缩小数学模型和新观察到的动态之间的差距成为可能。在线交流的不可改变的影响使得我们越来越需要了解个人和群体的观点是如何形成的，以及如何避免潜在危险的虚假信息的传播。由于意见动态的复杂性，特别是在个人代理，无延迟社交网络或非线性互动的模式下，通常需要通过大量的模拟来探索模型的行为。本项目旨在通过将多维意见和动态网络结构与现有模型相结合来提高意见动态模型的准确性，并研究在这样的系统中控制的可能性。目标是将意见动力学模型扩展到多个维度，探索节点基于其对不同主题的意见进行交互的不同方式。整合动态网络结构，以反映个人关系如何随着时间的推移而演变，以应对他们对各种主题的（不）一致意见。使用网络结构和情绪分析从Twitter数据观察真实的多维意见形成，并将其与模型中观察到的行为进行比较。研究方法的新奇性加权他人的意见自然会创建一个网络结构，因此社交网络对意见动态的影响已经被探索。然而，一个动态网络的结论，特别是一个网络结构与个人意见相结合的网络，是一个新的发展。潜在的影响，应用和好处如果它被发现，纳入多个意见提供了一个更现实的意见形成模型，了解如何控制这样的系统可以在设计促销活动，减少错误信息的影响或鼓励/阻止不同组织之间的合作。该项目福尔斯属于数学科学研究领域。外部合作伙伴-不可能-将提供开发数据驱动模型的专业知识，将提供技术支持。

The context of the researchThe fundamental concept of opinion dynamics, that a collection of individuals interacts and updates their opinions over time, has been represented in an ever-growing varity of models. In a simple model individuals update their opinions in discrete time steps by taking a weighted average of the opinions of those around them, leadinf to a linear dynamical system. For such systems there exists clear condistions for when consensus can arise and methods to predict what opinion the group will reach. This simple model has been develpoed in a range of different directions, some include more realistic features such as online media or stubborn individuals , propose different conditions for interaction, apply alternative mathematical techniques, or make any number of other adaptations.A major contribution is the models of Hegselmann and Krause, and Deffuant et al. which independently introduced bounded confidence: the idea that individuals only interact if thier opinions are already sufficeintly close. This condition creates nonlinearity and can lead to the formation of opinion clusters. This originally discrete time models has been adapted into continuous time models, then into stochastic models and finally into corrsponding PDE models describing the evolution of the opinion distribution in a large population. Under various parameter regimes these models can exhibit a range of interesting behaviours: in some scenarios opinions coalesce or become more moderate over time, in other cases multiple distinct opinions persist and in some cases no clear opinions emerge at all. With unprecendented access to the opinions of people across the world it is easy to see compareable situations in real life, with data from social media allowing the possibility of narrowing the gap between meathematical models and newly observable dynamics. The undeinable impact of online communication makes it increasingly important to develop our understnading of how individuals and groups opinions are formed and what can be done to avoid the spread of potentially dangerous disinformation.Due to the complex nature of opinion dynamics, especially in modes with individulaised agents, undelaying social networks or nonlinear interactions, it is often necessary to explore the behaviour of the model through extensive simulation.This project aims to improve the accuracy of opinion dynamics models by combining multidomensional opinions and dynamic network structure with existing models, and investigate the possibility of control in such systems.The objectives are to exten opinion dynamics models into multiple dimensions exploring different ways in which nodes may interact based on their opinions on various topics. Incorporate dynamic network structure to mirror how individuals relationships may evolve over time in response to their (dis)agreement on various topics. Use network structure and sentiment analaysis from Twitter data to observe real multidimensional opinion formation and compare this to the behaviuors observed in models.The novelty of the research methodologyWeighting the opinions of others natrually creates a network structure, and so the influence of social networks on opinion dynamics has been explored. However the conclusion of a dynamic network, in particular one in which the network structure is coupled with individuals opinions, is a novel development.The potential impact, applications and benefitsIf it is found that incorporating multiple opinions provides a more realistic model of opinion formation, an understanding of how such systems can be controlled could be useful in designing promotional campaigns, reducing the impace of misinformation or encoraging/ discouraging cooperation between different organisations.This project falls into the mathematical sciences research area.External Partener - Improbable - will provide expertise in developing data driven models, will provide technical support.