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Real systems showing regime shifts, such as ecosystems, are often composed of many dynamical elements interacting on a network. Various early warning signals have been proposed for anticipating regime shifts from observed data. However, it is unclear how one should combine early warning signals from different nodes for better performance. Based on theory of stochastic differential equations, we propose a method to optimize the node set from which to construct an early warning signal. The proposed method takes into account that uncertainty as well as the magnitude of the signal affects its predictive performance, that a large magnitude or small uncertainty of the signal in one situation does not imply the signal's high performance, and that combining early warning signals from different nodes is often but not always beneficial. The method performs well particularly when different nodes are subjected to different amounts of dynamical noise and stress. Early warning signals for rapid regime shifts in complex networks are of importance for ecology, climate and epidemics, where heterogeneities in network nodes and connectivity make construction of early warning signals challenging. The authors propose a method for selecting an optimal set of nodes from which a reliable early warning signal can be obtained. [ABSTRACT FROM AUTHOR]

Studying extreme ideas in routine choices and discussions is of utmost importance to understand the increasing polarization in society. In this study, we focus on understanding the generation and influence of extreme ideas in routine conversations which we label "eccentric" ideas. The eccentricity of any idea is defined as the deviation of that idea from the norm of the social neighborhood. We collected and analyzed data from two sources of different nature: public social media and online experiments in a controlled environment. We compared the popularity of ideas against their eccentricity to understand individuals' fascination towards eccentricity. We found that more eccentric ideas have a higher probability of getting a greater number of "likes". Additionally, we demonstrate that the social neighborhood of an individual conceals eccentricity changes in one's own opinions and facilitates generation of eccentric ideas at a collective level. [ABSTRACT FROM AUTHOR]