Effects of temporal correlations on cascades: Threshold models on temporal networks

A person's decision to adopt an idea or product is often driven by the decisions of peers, mediated through a network of social ties. A common way of modeling adoption dynamics is to use threshold models, where a node may become an adopter given a high enough rate of contacts with adopted neighbors. We study the dynamics of threshold models that take both the network topology and the timings of contacts into account, using empirical contact sequences as substrates. The models are designed such that adoption is driven by the number of contacts with different adopted neighbors within a chosen time. We find that while some networks support cascades leading to network-level adoption, some do not: the propagation of adoption depends on several factors from the frequency of contacts to burstiness and timing correlations of contact sequences. More specifically, burstiness is seen to suppress cascades sizes when compared to randomised contact timings, while timing correlations between contacts on adjacent links facilitate cascades.