Emergence of scaling in complex substitutive systems.

Diffusion processes are central to human interactions. One common prediction of the current modelling frameworks is that initial spreading dynamics follow exponential growth. Here we find that, for subjects ranging from mobile handsets to automobiles and from smartphone apps to scientific fields, early growth patterns follow a power law with non-integer exponents. We test the hypothesis that mechanisms specific to substitution dynamics may play a role, by analysing unique data tracing 3.6 million individuals substituting different mobile handsets. We uncover three generic ingredients governing substitutions, allowing us to develop a minimal substitution model, which not only explains the power-law growth, but also collapses diverse growth trajectories of individual constituents into a single curve. These results offer a mechanistic understanding of power-law early growth patterns emerging from various domains and demonstrate that substitution dynamics are governed by robust self-organizing principles that go beyond the particulars of individual systems.

Product diffusion through on-demand information-seeking behaviour.

Most models of product adoption predict S-shaped adoption curves. Here we report results from two country-scale experiments in which we find linear adoption curves. We show evidence that the observed linear pattern is the result of active information-seeking behaviour: individuals actively pulling information from several central sources facilitated by modern Internet searches. Thus, a constant baseline rate of interest sustains product diffusion, resulting in a linear diffusion process instead of the S-shaped curve of adoption predicted by many diffusion models. The main experiment seeded 70 000 (48 000 in Experiment 2) unique voucher codes for the same product with randomly sampled nodes in a social network of approximately 43 million individuals with about 567 million ties. We find that the experiment reached over 800 000 individuals with 80% of adopters adopting the same product-a winner-take-all dynamic consistent with search engine driven rankings that would not have emerged had the products spread only through a network of social contacts. We provide evidence for (and characterization of) this diffusion process driven by active information-seeking behaviour through analyses investigating (a) patterns of geographical spreading; (b) the branching process; and (c) diffusion heterogeneity. Using data on adopters' geolocation we show that social spreading is highly localized, while on-demand diffusion is geographically independent. We also show that cascades started by individuals who actively pull information from central sources are more effective at spreading the product among their peers.

Detecting climate adaptation with mobile network data in Bangladesh: anomalies in communication, mobility and consumption patterns during cyclone Mahasen.

Large-scale data from digital infrastructure, like mobile phone networks, provides rich information on the behavior of millions of people in areas affected by climate stress. Using anonymized data on mobility and calling behavior from 5.1 million Grameenphone users in Barisal Division and Chittagong District, Bangladesh, we investigate the effect of Cyclone Mahasen, which struck Barisal and Chittagong in May 2013. We characterize spatiotemporal patterns and anomalies in calling frequency, mobile recharges, and population movements before, during and after the cyclone. While it was originally anticipated that the analysis might detect mass evacuations and displacement from coastal areas in the weeks following the storm, no evidence was found to suggest any permanent changes in population distributions. We detect anomalous patterns of mobility both around the time of early warning messages and the storm's landfall, showing where and when mobility occurred as well as its characteristics. We find that anomalous patterns of mobility and calling frequency correlate with rainfall intensity (r = .75, p < 0.05) and use calling frequency to construct a spatiotemporal distribution of cyclone impact as the storm moves across the affected region. Likewise, from mobile recharge purchases we show the spatiotemporal patterns in people's preparation for the storm in vulnerable areas. In addition to demonstrating how anomaly detection can be useful for modeling human adaptation to climate extremes, we also identify several promising avenues for future improvement of disaster planning and response activities.