A network-based threshold model for the spreading of fads in society and markets

We investigate the behavior of a threshold model for the spreading of fads and similar phenomena in society. The model is giving the fad dynamics and is intended to be confined to an underlying network structure. We investigate the whole parameter space of the fad dynamics on three types of network models. The dynamics we discover is rich and highly dependent on the underlying network structure. For some range of the parameter space, for all types of substrate networks, there are a great variety of sizes and life-lengths of the fads -- what one see in real-world social and economical systems

Influence networks

Some behaviors, ideas or technologies spread and become persistent in society, whereas others vanish. This paper analyzes the role of social influence in determining such distinct collective outcomes. Agents are assumed to acquire information from others through a certain sampling process that generates an influence network, and they use simple rules to decide whether to adopt or not depending on the observed sample. We characterize, as a function of the primitives of the model, the diffusion threshold (i.e., the spreading rate above which the adoption of the new behavior becomes persistent in the population) and the endemic state (i.e., the fraction of adopters in the stationary state of the dynamics). We find that the new behavior will easily spread in the population if there is a high correlation between how influential (visible) and how easily influenced an agent is, which is determined by the sampling process and the adoption rule. We also analyze how the density and variance of the out-degree distribution affect the diffusion threshold and the endemic state.social influence, networks, diffusion threshold, endemic state

Nonequilibrium phase transition in the coevolution of networks and opinions

Models of the convergence of opinion in social systems have been the subject of a considerable amount of recent attention in the physics literature. These models divide into two classes, those in which individuals form their beliefs based on the opinions of their neighbors in a social network of personal acquaintances, and those in which, conversely, network connections form between individuals of similar beliefs. While both of these processes can give rise to realistic levels of agreement between acquaintances, practical experience suggests that opinion formation in the real world is not a result of one process or the other, but a combination of the two. Here we present a simple model of this combination, with a single parameter controlling the balance of the two processes. We find that the model undergoes a continuous phase transition as this parameter is varied, from a regime in which opinions are arbitrarily diverse to one in which most individuals hold the same opinion. We characterize the static and dynamical properties of this transition

Thought and Behavior Contagion in Capital Markets

Prevailing models of capital markets capture a limited form of social influence and information transmission, in which the beliefs and behavior of an investor affects others only through market price, information transmission and processing is simple (without thoughts and feelings), and there is no localization in the influence of an investor on others. In reality, individuals often process verbal arguments obtained in conversation or from media presentations, and observe the behavior of others. We review here evidence concerning how these activities cause beliefs and behaviors to spread, affect financial decisions, and affect market prices; and theoretical models of social influence and its effects on capital markets. Social influence is central to how information and investor sentiment are transmitted, so thought and behavior contagion should be incorporated into the theory of capital markets.capital markets; thought contagion; behavioral contagion; herd behavior; information cascades; social learning; investor psychology; accounting regulation; disclosure policy; behavioral finance; market efficiency; popular models; memes

Self-organized model of cascade spreading

We study simultaneous price drops of real stocks and show that for high drop thresholds they follow a power-law distribution. To reproduce these collective downturns, we propose a minimal self-organized model of cascade spreading based on a probabilistic response of the system elements to stress conditions. This model is solvable using the theory of branching processes and the mean-field approximation. For a wide range of parameters, the system is in a critical state and displays a power-law cascade-size distribution similar to the empirically observed one. We further generalize the model to reproduce volatility clustering and other observed properties of real stocks.Comment: 8 pages, 6 figure

Incorporating Betweenness Centrality in Compressive Sensing for Congestion Detection

This paper presents a new Compressive Sensing (CS) scheme for detecting network congested links. We focus on decreasing the required number of measurements to detect all congested links in the context of network tomography. We have expanded the LASSO objective function by adding a new term corresponding to the prior knowledge based on the relationship between the congested links and the corresponding link Betweenness Centrality (BC). The accuracy of the proposed model is verified by simulations on two real datasets. The results demonstrate that our model outperformed the state-of-the-art CS based method with significant improvements in terms of F-Score

The Dynamics of Public Opinion in Complex Networks

This paper studies the problem of public opinion formation and concentrates on the interplays among three factors: individual attributes, environmental influences and information flow. We present a simple model to analyze the dynamics of four types of networks. Our simulations suggest that regular communities establish not only local consensus, but also global diversity in public opinions. However, when small world networks, random networks, or scale-free networks model social relationships, the results are sensitive to the elasticity coefficient of environmental influences and the average connectivity of the type of network. For example, a community with a higher average connectivity has a higher probability of consensus. Yet, it is misleading to predict results merely based on the characteristic path length of networks. In the process of changing environmental influences and average connectivity, sensitive areas are discovered in the system. By sensitive areas we mean that interior randomness emerges and we cannot predict unequivocally how many opinions will remain upon reaching equilibrium. We also investigate the role of authoritative individuals in information control. While enhancing average connectivity facilitates the diffusion of the authoritative opinion, it makes individuals subject to disturbance from non-authorities as well. Thus, a moderate average connectivity may be preferable because then the public will most likely form an opinion that is parallel with the authoritative one. In a community with a scale-free structure, the influence of authoritative individuals keeps constant with the change of the average connectivity. Provided that the influence of individuals is proportional to the number of their acquaintances, the smallest percentage of authorities is required for a controlled consensus in a scale free network. This study shows that the dynamics of public opinion varies from community to community due to the different degree of impressionability of people and the distinct social network structure of the community.Public Opinion, Complex Network, Consensus, Agent-Based Model

Phase transition for the Maki-Thompson rumour model on a small-world network

We consider the Maki-Thompson model for the stochastic propagation of a rumour within a population. We extend the original hypothesis of homogenously mixed population by allowing for a small-world network embedding the model. This structure is realized starting from a $k$-regular ring and by inserting, in the average, $c$ additional links in such a way that $k$ and $c$ are tuneable parameter for the population architecture. We prove that this system exhibits a transition between regimes of localization (where the final number of stiflers is at most logarithmic in the population size) and propagation (where the final number of stiflers grows algebraically with the population size) at a finite value of the network parameter $c$. A quantitative estimate for the critical value of $c$ is obtained via extensive numerical simulations.Comment: 24 pages, 4 figure