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Abstract 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. 

The social brain hypothesis posits that species with larger brains tend to have greater social complexity. Various lines of empirical evidence have supported the social brain hypothesis, including evidence from the structure of social networks. Cooperation is a key component of group living, particularly among primates, and theoretical research has shown that particular structures of social networks foster cooperation more easily than others. Therefore, we hypothesized that species with a relatively large brain size tend to form social networks that better enable cooperation. In the present study, we combine data on brain size and social networks with theory on the evolution of cooperation on networks to test this hypothesis in non-human primates. We have found a positive effect of brain size on cooperation in social networks even after controlling for the effect of other structural properties of networks that are known to promote cooperation. 

Successfully anticipating sudden major changes in complex systems is a practical concern. Such complex systems often form a heterogeneous network, which may show multi-stage transitions in which some nodes experience a regime shift earlier than others as an environment gradually changes. Here we investigate early warning signals for networked systems undergoing a multi-stage transition. We found that knowledge of both the ongoing multi-stage transition and network structure enables us to calculate effective early warning signals for multi-stage transitions. Furthermore, we found that small subsets of nodes could anticipate transitions as well as or even better than using all the nodes. Even if we fix the network and dynamical system, no single best subset of nodes provides good early warning signals, and a good choice of sentinel nodes depends on the tipping direction and the current stage of the dynamics within a multi-stage transition, which we systematically characterize. 

Cooperative networks are essential features of human society. Evolutionary theory hypothesizes that networks are used differently by men and women, yet the bulk of evidence supporting this hypothesis is based on studies conducted in a limited range of contexts and on few domains of cooperation. In this paper, we compare individual-level cooperative networks from two communities in Southwest China that differ systematically in kinship norms and institutions—one matrilineal and one patrilineal—while sharing an ethnic identity. Specifically, we investigate whether network structures differ based on prevailing kinship norms and type of gendered cooperative activity, one woman-centred (preparation of community meals) and one man-centred (farm equipment lending). Our descriptive results show a mixture of ‘feminine’ and ‘masculine’ features in all four networks. The matrilineal meals network stands out in terms of high degree skew. Exponential random graph models reveal a stronger role for geographical proximity in patriliny and a limited role of affinal relatedness across all networks. Our results point to the need to consider domains of cooperative activity alongside gender and cultural context to fully understand variation in how women and men leverage social relationships toward different ends. This article is part of the theme issue ‘Cooperation among women: evolutionary and cross-cultural perspectives’. 

Many complex dynamical systems in the real world, including ecological, climate, financial and power-grid systems, often show critical transitions, or tipping points, in which the system’s dynamics suddenly transit into a qualitatively different state. In mathematical models, tipping points happen as a control parameter gradually changes and crosses a certain threshold. Tipping elements in such systems may interact with each other as a network, and understanding the behaviour of interacting tipping elements is a challenge because of the high dimensionality originating from the network. Here, we develop a degree-based mean-field theory for a prototypical double-well system coupled on a network with the aim of understanding coupled tipping dynamics with a low-dimensional description. The method approximates both the onset of the tipping point and the position of equilibria with a reasonable accuracy. Based on the developed theory and numerical simulations, we also provide evidence for multistage tipping point transitions in networks of double-well systems. 

Collective design and innovation are crucial in organizations. To investigate how the collective design and innovation processes would be affected by the diversity of knowledge and background of collective individual members, we conducted three collaborative design task experiments which involved nearly 300 participants who worked together anonymously in a social network structure using a custom-made computer-mediated collaboration platform. We compared the idea generation activity among three different background distribution conditions (clustered, random, and dispersed) with the help of the “doc2vec” text representation machine learning algorithm. We also developed a new method called “Idea Geography” to visualize the idea utility terrain on a 2D problem domain. The results showed that groups with random background allocation tended to produce the best design idea with the highest utility values. It was also suggested that the diversity of participants’ backgrounds distribution on the network might interact with each other to affect the diversity of ideas generated. The proposed idea geography successfully visualized that the collective design processes did find the high utility area through exploration and exploitation in collaborative work.