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Abstract Engineering multilayer networks that efficiently connect sets of points in space is a crucial task in all practical applications that concern the transport of people or the delivery of goods. Unfortunately, our current theoretical understanding of the shape of such optimal transport networks is quite limited. Not much is known about how the topology of the optimal network changes as a function of its size, the relative efficiency of its layers, and the cost of switching between layers. Here, we show that optimal networks undergo sharp transitions from symmetric to asymmetric shapes, indicating that it is sometimes better to avoid serving a whole area to save on switching costs. Also, we analyze the real transportation networks of the cities of Atlanta, Boston, and Toronto using our theoretical framework and find that they are farther away from their optimal shapes as traffic congestion increases. 

Abstract Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex networks, the percolation transition can become discontinuous. However, little is known about percolation in networks with higher-order interactions. Here, we show that percolation can be turned into a fully fledged dynamical process when higher-order interactions are taken into account. By introducing signed triadic interactions, in which a node can regulate the interactions between two other nodes, we define triadic percolation. We uncover that in this paradigmatic model the connectivity of the network changes in time and that the order parameter undergoes a period doubling and a route to chaos. We provide a general theory for triadic percolation which accurately predicts the full phase diagram on random graphs as confirmed by extensive numerical simulations. We find that triadic percolation on real network topologies reveals a similar phenomenology. These results radically change our understanding of percolation and may be used to study complex systems in which the functional connectivity is changing in time dynamically and in a non-trivial way, such as in neural and climate networks. 

Abstract The 2021 Nobel Prize in Physics recognized the fundamental role of complex systems in the natural sciences. In order to celebrate this milestone, this editorial presents the point of view of the editorial board of JPhys Complexity on the achievements, challenges, and future prospects of the field. To distinguish the voice and the opinion of each editor, this editorial consists of a series of editor perspectives and reflections on few selected themes. A comprehensive and multi-faceted view of the field of complexity science emerges. We hope and trust that this open discussion will be of inspiration for future research on complex systems. 

Contemporary science has been characterized by an exponential growth in publications and a rise of team science. At the same time, there has been an increase in the number of awarded PhD degrees, which has not been accompanied by a similar expansion in the number of academic positions. In such a competitive environment, an important measure of academic success is the ability to maintain a long active career in science. In this paper, we study workforce trends in three scientific disciplines over half a century. We find dramatic shortening of careers of scientists across all three disciplines. The time over which half of the cohort has left the field has shortened from 35 y in the 1960s to only 5 y in the 2010s. In addition, we find a rapid rise (from 25 to 60% since the 1960s) of a group of scientists who spend their entire career only as supporting authors without having led a publication. Altogether, the fraction of entering researchers who achieve full careers has diminished, while the class of temporary scientists has escalated. We provide an interpretation of our empirical results in terms of a survival model from which we infer potential factors of success in scientific career survivability. Cohort attrition can be successfully modeled by a relatively simple hazard probability function. Although we find statistically significant trends between survivability and an author’s early productivity, neither productivity nor the citation impact of early work or the level of initial collaboration can serve as a reliable predictor of ultimate survivability.