There is a contradiction at the heart of our current understanding of individual and collective mobility patterns. On one hand, a highly influential stream of literature on human mobility driven by analyses of massive empirical datasets finds that human movements show no evidence of characteristic spatial scales. There, human mobility is described as scale-free. 1-3 On the other hand, in geography, the concept of scale, referring to meaningful levels of description from individual buildings through neighborhoods, cities, regions, and countries, is central for the description of various aspects of human behavior such as socio-economic interactions, or political and cultural dynamics. 4, 5 Here, we resolve this apparent paradox by showing that day-to-day human mobility does indeed contain meaningful scales, corresponding to spatial containers restricting mobility behavior. The scale-free results arise from aggregating displacements across containers. We present a simple model, which given a person's 1 arXiv:2109.07381v1 [physics.soc-ph] 15 Sep 2021trajectory, infers their neighborhoods, cities, and so on, as well as the sizes of these geographical containers. We find that the containers characterizing the trajectories of more than 700 000 individuals do indeed have typical sizes. We show that our model generates highly realistic trajectories without overfitting and provides a new lens through which to understand the differences in mobility behaviour across countries,

Many real-world networks represent dynamic systems with interactions that change over time, often in uncoordinated ways and at irregular intervals. For example, university students connect in intermittent groups that repeatedly form and dissolve based on multiple factors, including their lectures, interests, and friends. Such dynamic systems can be represented as multilayer networks where each layer represents a snapshot of the temporal network. In this representation, it is crucial that the links between layers accurately capture real dependencies between those layers. Often, however, these dependencies are unknown. Therefore, current methods connect layers based on simplistic assumptions that do not capture node-level layer dependencies. For example, connecting every node to itself in other layers with the same weight can wipe out dependencies between intermittent groups, making it difficult or even impossible to identify them. In this paper, we present a principled approach to estimating node-level layer dependencies based on the network structure within each layer. We implement our node-level coupling method in the community detection framework Infomap and demonstrate its performance compared to current methods on synthetic and real temporal networks. We show that our approach more effectively constrains information inside multilayer communities so that Infomap can better recover planted groups in multilayer benchmark networks that represent multiple modes with different groups and better identify intermittent communities in real temporal contact networks. These results suggest that node-level layer coupling can improve the modeling of information spreading in temporal networks and better capture intermittent community structure.

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