Opinion dynamics over complex networks: Kinetic modelling and numerical methods

We survey some recent developments on the mathematical modeling of opinion dynamics. After an introduction on opinion modeling through interacting multi-agent systems described by partial differential equations of kinetic type, we focus our attention on two major advancements: optimal control of opinion formation and influence of additional social aspects, like conviction and number of connections in social networks, which modify the agents\u2019 role in the opinion exchange process

Opinion dynamics with varying susceptibility to persuasion

A long line of work in social psychology has studied variations in people's susceptibility to persuasion -- the extent to which they are willing to modify their opinions on a topic. This body of literature suggests an interesting perspective on theoretical models of opinion formation by interacting parties in a network: in addition to considering interventions that directly modify people's intrinsic opinions, it is also natural to consider interventions that modify people's susceptibility to persuasion. In this work, we adopt a popular model for social opinion dynamics, and we formalize the opinion maximization and minimization problems where interventions happen at the level of susceptibility. We show that modeling interventions at the level of susceptibility lead to an interesting family of new questions in network opinion dynamics. We find that the questions are quite different depending on whether there is an overall budget constraining the number of agents we can target or not. We give a polynomial-time algorithm for finding the optimal target-set to optimize the sum of opinions when there are no budget constraints on the size of the target-set. We show that this problem is NP-hard when there is a budget, and that the objective function is neither submodular nor supermodular. Finally, we propose a heuristic for the budgeted opinion optimization and show its efficacy at finding target-sets that optimize the sum of opinions compared on real world networks, including a Twitter network with real opinion estimates

Phase Transition of the 2-Choices Dynamics on Core-Periphery Networks

Consider the following process on a network: Each agent initially holds either opinion blue or red; then, in each round, each agent looks at two random neighbors and, if the two have the same opinion, the agent adopts it. This process is known as the 2-Choices dynamics and is arguably the most basic non-trivial opinion dynamics modeling voting behavior on social networks. Despite its apparent simplicity, 2-Choices has been analytically characterized only on networks with a strong expansion property -- under assumptions on the initial configuration that establish it as a fast majority consensus protocol. In this work, we aim at contributing to the understanding of the 2-Choices dynamics by considering its behavior on a class of networks with core-periphery structure, a well-known topological assumption in social networks. In a nutshell, assume that a densely-connected subset of agents, the core, holds a different opinion from the rest of the network, the periphery. Then, depending on the strength of the cut between the core and the periphery, a phase-transition phenomenon occurs: Either the core's opinion rapidly spreads among the rest of the network, or a metastability phase takes place, in which both opinions coexist in the network for superpolynomial time. The interest of our result is twofold. On the one hand, by looking at the 2-Choices dynamics as a simplistic model of competition among opinions in social networks, our theorem sheds light on the influence of the core on the rest of the network, as a function of the core's connectivity towards the latter. On the other hand, to the best of our knowledge, we provide the first analytical result which shows a heterogeneous behavior of a simple dynamics as a function of structural parameters of the network. Finally, we validate our theoretical predictions with extensive experiments on real networks

Nonlinear opinion models and other networked systems

Networks play a critical role in many physical, biological, and social systems. In this thesis, we investigate tools to model and analyze networked systems. We first examine some of the ways in which we can model social dynamics that take place on networks. We then study two recently developed data-analysis methods that employ a network framework and explore new ways in which they can be used to find meaningful signals in large data sets. In the first half of the thesis, we study opinion dynamics on networks. We begin by examining a class of opinion models, known as coevolving voter models (CVM), that couple the mechanisms of opinion formation and changing social connections. We then propose a version of CVMs that incorporates nonlinearity. In our models, we assume that individuals strive to achieve harmony and avoid disagreement, both by changing their social connections to reflect their opinions and by changing their opinions to reflect their social connections. By taking a minimalist approach to modeling social dynamics, we hope to gain a deeper understanding of how these two mechanisms can give rise to social phenomena such as the ``majority illusion''. Comparing several versions of CVMs, we find that seemingly small changes in update rules can lead to strikingly different behaviors. A particularly interesting feature of our nonlinear CVMs is that, under certain conditions, the opinion state that is held initially by a minority of the nodes can effectively spread to almost every node in a network if the minority nodes view themselves as the majority. We then discuss an ongoing project that involves another class of opinion models called bounded-confidence models. Specifically, we examine extensions of bounded-confidence models on hypergraphs and discuss some preliminary findings. In the second half of the thesis, we study problems in data analysis. We begin by considering topological structures as a tool to study integrated circuit (IC) devices. In particular, we examine a problem in the design and manufacturing of IC devices using topological data analysis (TDA), which is based on network structures called simplicial complexes. Failures in IC devices generally occur near the tolerance limits of photolithography systems, such as at the minimum separation distance between adjacent electronic components. However, for complex arrangements of electronic components, simply ensuring minimal separation is insufficient to guarantee that one can manufacture an IC design accurately and reliably. We apply tools from TDA to compare data from IC designs. Without inputting domain knowledge, we are able to infer several results about the IC design-manufacturing process. Finally, we discuss an ongoing project in the analysis of network data. Specifically, we explore applications of a recently developed algorithm called network dictionary learning (NDL) and discuss problems of network reconstruction and denoising using NDL on both synthetic and real-world networks

Expanding Social Network Modeling Software and Agent Models for Diffusion Processes

In an increasingly digitally interconnected world, the study of social networks and their dynamics is burgeoning. Anthropologically, the ubiquity of online social networks has had striking implications for the condition of large portions of humanity. This technology has facilitated content creation of virtually all sorts, information sharing on an unprecedented scale, and connections and communities among people with similar interests and skills. The first part of my research is a social network evolution and visualization engine. Built on top of existing technologies, my software is designed to provide abstractions from the underlying libraries, drive real-time network evolution based on user-defined parameters, and optionally visualize that evolution at each step of the process. My software provides a low maintenance interface for the creation of networks and update schemes for a wide array of experimental contexts, an engine to drive network evolution, and a visualization platform to provide real-time feedback about different aspects of the network to the researcher, as well as fine-grained debugging tools. We conducted investigations into the opinion dynamics of networks when multiple agent “archetypes” interact together with this platform. We modeled agents’ archetypes with respect to two attributes: their preference over their friends’ opinion profiles, and their tendency to change their opinion over time. We extended the current state of agent modeling in opinion diffusion by providing a unified 2D trajectory/preference space for agents that incorporates most common models in the literature. We investigated six agent archetypes from this space, and examined the behavior of the network as a whole and the individual agents in a variety of contexts. In another branch of work using our software, we developed a network of agents who must carry out both economic and social activities during a pandemic. Agents’ decisions about what actions to take (self-protective measures like masking, social distancing, or waiting to run errands) are based on several factors, including perception of risk (obtained from news reports, social connections, etc.) and economic need. We show with preliminary testing that this platform is able to execute standard pandemic models successfully with the incorporation of the economic and social dimensions, and that this paradigm may provide useful insight into effective agent-level response policies that can be used in concert with other top-down approaches that comprise most of the recent pandemic response research. We have investigated the implications of varying behavior profiles within a network of agents, and how those behavioral compositions affect the overall climate of the network in return, and this software will continue to facilitate similar research into the future

Mixing text mining analysis and agent based modelling methodologies.: A case study to analyze a controversy

This paper starts from methodological issues dealing with sociological and quantitative interpretation of qualitative and discontinued data when analyzing controversies from a large press corpus. Then authors offer a new approach mixing text mining analysis and agent based modeling. The study case dealing with the controversy of abnormal disappearance of honey bees (\textit{apis mellifera}) among French speaking journalistic during 13 years is mobilized to describe the different steps of this heuristic framework. First articles are tagged with three stances to report the problematic phenomenon, a uni-factor cause, i.e. the use of pesticides, a multi-factor cause, i.e. including one other factor different than pesticides at least, or the absence of understanding. Second, variations of the proportions of agents explaining the issue either with unifactor or multifactor causes are obtained with modeling. Assuming agents follow dispositional or positional social influence in their interactions to report the facts, their associated networks are extracted from the data applying a network randomized model of opinion dynamics. Third, from those distributions the possible topology of actor networks can be questioned back with others qualitative methods, either ethnographic or interviews