Physics

The flourishing of fake news is favored by recommendation algorithms of online social networks which, based on previous users activity, provide content adapted to their preferences and so create filter bubbles. We introduce an analytically tractable voter model with personalized information, in which an external field tends to align the agent opinion with the one she held more frequently in the past. Our model shows a surprisingly rich dynamics despite its simplicity. An analytical mean-field approach, confirmed by numerical simulations, allows us to build a phase diagram and to predict if and how consensus is reached. Remarkably, polarization can be avoided only for weak interaction with the personalized information and if the number of agents is below a threshold. We analytically compute this critical size, which depends on the interaction probability in a strongly non linear way.

Opinion polarization is on the rise, causing concerns for the openness of public debates. Additionally, extreme opinions on different topics often show significant correlations. The dynamics leading to these polarized ideological opinions pose a challenge: How can such correlations emerge, without assuming them a priori in the individual preferences or in a preexisting social structure? Here we propose a simple model that qualitatively reproduces ideological opinion states found in survey data, even between rather unrelated, but sufficiently controversial, topics. Inspired by skew coordinate systems recently proposed in natural language processing models, we solidify these intuitions in a formalism of opinions unfolding in a multidimensional space where topics form a non-orthogonal basis. Opinions evolve according to the social interactions among the agents, which are ruled by homophily: two agents sharing similar opinions are more likely to interact. The model features phase transitions between a global consensus, opinion polarization, and ideological states. Interestingly, the ideological phase emerges by relaxing the assumption of an orthogonal basis of the topic space, i.e. if topics thematically overlap. Furthermore, we analytically and numerically show that these transitions are driven by the controversialness of the topics discussed, the more controversial the topics, the more likely are opinion to be correlated. Our findings shed light upon the mechanisms driving the emergence of ideology in the formation of opinions.

We model power grids as graphs with heavy-tailed sinks, which represent demand from cities, and study cascading failures on such graphs. Our analysis links the scale-free nature of blackout sizes to the scale-free nature of city sizes, contrasting previous studies suggesting that this nature is governed by self-organized criticality. Our results are based on a new mathematical framework combining the physics of power flow with rare event analysis for heavy-tailed distributions, and are validated using various synthetic networks and the German transmission grid.

Models of interacting social agents often represent agents as very simple entities having a small number of degrees of freedom, as exemplified by binary opinion models for instance. Understanding how such simple individual characteristics may emerge from potentially much more complex agents is thus a natural question. It has been proposed recently in [E. Bertin, P. Jensen, C.R. Phys. 20, 329 (2019)] that some types of interactions among agents with many internal degrees of freedom may lead to a `simplification' of agents, which are then effectively described by a small number of internal degrees of freedom. Here, we generalize the model to account for agents intrinsic heterogeneity. We find two different simplification regimes, one dominated by interactions, where agents become simple and identical as in the homogeneous model, and one where agents remain strongly heterogeneous although effectively having simple characteristics.

The complexities involved in modeling the transmission dynamics of COVID-19 has been a major roadblock in achieving predictability in the spread and containment of the disease. In addition to understanding the modes of transmission, the effectiveness of the mitigation methods also needs to be built into any effective model for making such predictions. We show that such complexities can be circumvented by appealing to scaling principles which lead to the emergence of universality in the transmission dynamics of the disease. The ensuing data collapse renders the transmission dynamics largely independent of geopolitical variations, the effectiveness of various mitigation strategies, population demographics, etc. We propose a simple two-parameter model -- the Blue Sky model -- and show that one class of transmission dynamics can be explained by a solution that lives at the edge of a blue sky bifurcation. In addition, the data collapse leads to an enhanced degree of predictability in the disease spread for several geographical scales which can also be realized in a model-independent manner as we show using a deep neural network. The methodology adopted in this work can potentially be applied to the transmission of other infectious diseases and new universality classes may be found. The predictability in transmission dynamics and the simplicity of our methodology can help in building policies for exit strategies and mitigation methods during a pandemic.

The success of modern civilization is built upon widespread cooperation in human society, deciphering the mechanisms behind has being a major goal for centuries. A crucial fact is, however, largely missing in most prior studies that games in the real world are typically played simultaneously and interactively rather than separately as assumed. Here we introduce the idea of interacting games that different games coevolve and influence each other's decision-making. We show that as the game-game interaction becomes important, the cooperation phase transition dramatically improves, a fairly high level of cooperation is reached for all involved games when interaction goes to be strong. A mean-field theory indicates that a new mechanism -- \emph{the dynamical reciprocity}, as a counterpart to the well-known network reciprocity, is at work to foster cooperation, which is confirmed by the detailed analysis. This revealed reciprocity is robust against variations in the game type, the population structure, and the updating rules etc, and more games generally yield a higher level of cooperation. Our findings point out the great potential towards high cooperation for many issues are interwoven with each other in the real world, and also the possibility of sustaining decent cooperation even in extremely adverse circumstances.

In order to understand controlling a complex system, an estimation of the required effort needed to achieve control is vital. Previous works have addressed this issue by studying the scaling laws of energy cost in a general way with continuous-time linear dynamics. However, continuous-time linear dynamics is unable to capture conformity behavior, which is common in many complex social systems. Therefore, to understand controlling social systems with conformity, discrete-time modelling is used and the energy cost scaling laws are derived. The results are validated numerically with model and real networks. In addition, the energy costs needed for controlling systems with and without conformity are compared, and it was found that controlling networked systems with conformity features always requires less control energy. Finally, it is shown through simulations that heterogeneous scale-free networks are less controllable, requiring a higher number of minimum drivers. Since the conformity-based model relates to various complex systems, such as flocking, or evolutionary games, the results of this paper represent a step forward towards developing realistic control of complex social systems.

We propose an agent-based model of collective opinion formation to study the wisdom of crowds under social influence. The opinion of an agent is a continuous positive value, denoting its subjective answer to a factual question. The wisdom of crowds states that the average of all opinions is close to the truth, i.e. the correct answer. But if agents have the chance to adjust their opinion in response to the opinions of others, this effect can be destroyed. Our model investigates this scenario by evaluating two competing effects: (i) agents tend to keep their own opinion (individual conviction β ), (ii) they tend to adjust their opinion if they have information about the opinions of others (social influence α ). For the latter, two different regimes (full information vs. aggregated information) are compared. Our simulations show that social influence only in rare cases enhances the wisdom of crowds. Most often, we find that agents converge to a collective opinion that is even farther away from the true answer. So, under social influence the wisdom of crowds can be systematically wrong.

Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into account the natural information geometry of probability distributions. We apply this framework to the Gibbs distribution of random graphs obtained with constraints on the node connectivity. The information geometry for this graph ensemble is calculated and the dynamical process is obtained as a diffusion equation. We compare the steady state of this dynamics to degree distributions found on real-world networks.

We study a multi-type SIR epidemic process among a heterogeneous population that interacts through a network. When we base social contact on a random graph with given vertex degrees, we give limit theorems on the fraction of infected individuals. For a given social distancing individual strategies, we establish the epidemic reproduction number R 0 which can be used to identify network vulnerability and inform vaccination policies. In the second part of the paper we study the equilibrium of the social distancing game, in which individuals choose their social distancing level according to an anticipated global infection rate, which then must equal the actual infection rate following their choices. We give conditions for the existence and uniqueness of equilibrium. For the case of random regular graphs, we show that voluntary social distancing will always be socially sub-optimal.