No Arabic abstract
During the COVID-19 pandemic, conflicting opinions on physical distancing swept across social media, affecting both human behavior and the spread of COVID-19. Inspired by such phenomena, we construct a two-layer multiplex network for the coupled spread of a disease and conflicting opinions. We model each process as a contagion. On one layer, we consider the concurrent evolution of two opinions -- pro-physical-distancing and anti-physical-distancing -- that compete with each other and have mutual immunity to each other. The disease evolves on the other layer, and individuals are less likely (respectively, more likely) to become infected when they adopt the pro-physical-distancing (respectively, anti-physical-distancing) opinion. We develop approximations of mean-field type by generalizing monolayer pair approximations to multilayer networks; these approximations agree well with Monte Carlo simulations for a broad range of parameters and several network structures. Through numerical simulations, we illustrate the influence of opinion dynamics on the spread of the disease from complex interactions both between the two conflicting opinions and between the opinions and the disease. We find that lengthening the duration that individuals hold an opinion may help suppress disease transmission, and we demonstrate that increasing the cross-layer correlations or intra-layer correlations of node degrees may lead to fewer individuals becoming infected with the disease.
As individuals communicate, their exchanges form a dynamic network. We demonstrate, using time series analysis of communication in three online settings, that network structure alone can be highly revealing of the diversity and novelty of the information being communicated. Our approach uses both standard and novel network metrics to characterize how unexpected a network configuration is, and to capture a networks ability to conduct information. We find that networks with a higher conductance in link structure exhibit higher information entropy, while unexpected network configurations can be tied to information novelty. We use a simulation model to explain the observed correspondence between the evolution of a networks structure and the information it carries.
The COVID-19 pandemic has led to significant changes in how people are currently living their lives. To determine how to best reduce the effects of the pandemic and start reopening societies, governments have drawn insights from mathematical models of the spread of infectious diseases. In this article, we give an introduction to a family of mathematical models (called compartmental models) and discuss how the results of analyzing these models influence government policies and human behavior, such as encouraging mask wearing and physical distancing to help slow the spread of the disease.
In an increasingly polarized world, demagogues who reduce complexity down to simple arguments based on emotion are gaining in popularity. Are opinions and online discussions falling into demagoguery? In this work, we aim to provide computational tools to investigate this question and, by doing so, explore the nature and complexity of online discussions and their space of opinions, uncovering where each participant lies. More specifically, we present a modeling framework to construct latent representations of opinions in online discussions which are consistent with human judgements, as measured by online voting. If two opinions are close in the resulting latent space of opinions, it is because humans think they are similar. Our modeling framework is theoretically grounded and establishes a surprising connection between opinions and voting models and the sign-rank of a matrix. Moreover, it also provides a set of practical algorithms to both estimate the dimension of the latent space of opinions and infer where opinions expressed by the participants of an online discussion lie in this space. Experiments on a large dataset from Yahoo! News, Yahoo! Finance, Yahoo! Sports, and the Newsroom app suggest that unidimensional opinion models may often be unable to accurately represent online discussions, provide insights into human judgements and opinions, and show that our framework is able to circumvent language nuances such as sarcasm or humor by relying on human judgements instead of textual analysis.
We study the problem of optimally investing in nodes of a social network in a competitive setting, where two camps aim to maximize adoption of their opinions by the population. In particular, we consider the possibility of campaigning in multiple phases, where the final opinion of a node in a phase acts as its initial biased opinion for the following phase. Using an extension of the popular DeGroot-Friedkin model, we formulate the utility functions of the camps, and show that they involve what can be interpreted as multiphase Katz centrality. Focusing on two phases, we analytically derive Nash equilibrium investment strategies, and the extent of loss that a camp would incur if it acted myopically. Our simulation study affirms that nodes attributing higher weightage to initial biases necessitate higher investment in the first phase, so as to influence these biases for the terminal phase. We then study the setting in which a camps influence on a node depends on its initial bias. For single camp, we present a polynomial time algorithm for determining an optimal way to split the budget between the two phases. For competing camps, we show the existence of Nash equilibria under reasonable assumptions, and that they can be computed in polynomial time.
Multilayer networked systems are ubiquitous in nature and engineering, and the robustness of these systems against failures is of great interest. A main line of theoretical pursuit has been percolation induced cascading failures, where interdependence between network layers is conveniently and tacitly assumed to be symmetric. In the real world, interdependent interactions are generally asymmetric. To uncover and quantify the impact of asymmetry in interdependence on network robustness, we focus on percolation dynamics in double-layer systems and implement the following failure mechanism: once a node in a network layer fails, the damage it can cause depends not only on its position in the layer but also on the position of its counterpart neighbor in the other layer. We find that the characteristics of the percolation transition depend on the degree of asymmetry, where the striking phenomenon of a switch in the nature of the phase transition from first- to second-order arises. We derive a theory to calculate the percolation transition points in both network layers, as well as the transition switching point, with strong numerical support from synthetic and empirical networks. Not only does our work shed light upon the factors that determine the robustness of multilayer networks against cascading failures, but it also provides a scenario by which the system can be designed or controlled to reach a desirable level of resilience.