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The remarkable robustness of many social systems has been associated with a peculiar triangular structure in the underlying social networks. Triples of people that have three positive relations (e.g., friendship) between each other are strongly overrepresented. Triples with two negative relations (e.g., enmity) and one positive relation are also overrepresented, and triples with one or three negative relations are drastically suppressed. For almost a century, the mechanism behind these very specific ("balanced") triad statistics remained elusive. Here, we propose a simple realistic adaptive network model, where agents tend to minimize social tension that arises from dyadic interactions. Both opinions of agents and their signed links (positive or negative relations) are updated in the dynamics. The key aspect of the model resides in the fact that agents only need information about their local neighbors in the network and do not require (often unrealistic) higher-order network information for their relation and opinion updates. We demonstrate the quality of the model on detailed temporal relation data of a society of thousands of players of a massive multiplayer online game where we can observe triangle formation directly. It not only successfully predicts the distribution of triangle types but also explains empirical group size distributions, which are essential for social cohesion. We discuss the details of the phase diagrams behind the model and their parameter dependence, and we comment on to what extent the results might apply universally in societies. [ABSTRACT FROM AUTHOR]

There are practically no quantitative tools for understanding how much stress a health care system can absorb before it loses its ability to provide care. We propose to measure the resilience of health care systems with respect to changes in the density of primary care providers. We develop a computational model on a 1-to-1 scale for a countrywide primary care sector based on patientsharing networks. Nodes represent all primary care providers in a country; links indicate patient flows between them. The removal of providers could cause a cascade of patient displacements, as patients have to find alternative providers. The model is calibrated with nationwide data from Austria that includes almost all primary care contacts over 2 y. We assign 2 properties to every provider: the "CareRank" measures the average number of displacements caused by a provider's removal (systemic risk) as well as the fraction of patients a provider can absorb when others default (systemic benefit). Below a critical number of providers, large-scale cascades of patient displacements occur, and no more providers can be found in a given region. We quantify regional resilience as the maximum fraction of providers that can be removed before cascading events prevent coverage for all patients within a district. We find considerable regional heterogeneity in the critical transition point from resilient to nonresilient behavior. We demonstrate that health care resilience cannot be quantified by physician density alone but must take into account how networked systems respond and restructure in response to shocks. The approach can identify systemically relevant providers. [ABSTRACT FROM AUTHOR]

Spatial patterning often occurs in ecosystems as a result of a selforganizing process caused by feedback between organisms and the physical environment. Here, we show that the spatial patterns observable in centuries-old Balinese rice terraces are also created by feedback between farmers' decisions and the ecology of the paddies, which triggers a transition from local to globalscale control of water shortages and rice pests. We propose an evolutionary game, based on local farmers' decisions that predicts specific power laws in spatial patterning that are also seen in a multispectral image analysis of Balinese rice terraces. The model shows how feedbacks between human decisions and ecosystem processes can evolve toward an optimal state in which total harvests are maximized and the system approaches Pareto optimality. It helps explain how multiscale cooperation from the community to the watershed scale could persist for centuries, and why the disruption of this self-organizing system by the Green Revolution caused chaos in irrigation and devastating losses from pests. The model shows that adaptation in a coupled human-natural system can trigger self-organized criticality (SOC). In previous exogenously driven SOC models, adaptation plays no role, and no optimization occurs. In contrast, adaptive SOC is a self-organizing process where local adaptations drive the system toward local and global optima. [ABSTRACT FROM AUTHOR]