A custom-built machine learning algorithm excels at the formidable task of predicting when a complex system is about to switch to a wildly different mode of behavior.

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Timothy LaRock, Ingo Scholtes, Tina Eliassi-Rad
Journal of Complex Networks, Volume 10, Issue 5, October 2022, cnac036,

The structure of complex networks can be characterized by counting and analysing network motifs. Motifs are small graph structures that occur repeatedly in a network, such as triangles or chains. Recent work has generalized motifs to temporal and dynamic network data. However, existing techniques do not generalize to sequential or trajectory data, which represent entities moving through the nodes of a network, such as passengers moving through transportation networks. The unit of observation in these data is fundamentally different since we analyse observations of trajectories (e.g. a trip from airport A to airport C through airport B), rather than independent observations of edges or snapshots of graphs over time. In this work, we define sequential motifs in trajectory data, which are small, directed and sequence-ordered graphs corresponding to patterns in observed sequences. We draw a connection between the counting and analysis of sequential motifs and Higher-Order Network (HON) models. We show that by mapping edges of a HON, specifically a kth-order DeBruijn graph, to sequential motifs, we can count and evaluate their importance in observed data. We test our methodology with two datasets: (1) passengers navigating an airport network and (2) people navigating the Wikipedia article network. We find that the most prevalent and important sequential motifs correspond to intuitive patterns of traversal in the real systems and show empirically that the heterogeneity of edge weights in an observed higher-order DeBruijn graph has implications for the distributions of sequential motifs we expect to see across our null models.

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Weihua Li, Sam Zhang, Zhiming Zheng, Skyler J. Cranmer & Aaron Clauset
Nature Communications volume 13, Article number: 4907 (2022)

While inequalities in science are common, most efforts to understand them treat scientists as isolated individuals, ignoring the network effects of collaboration. Here, we develop models that untangle the network effects of productivity defined as paper counts, and prominence referring to high-impact publications, of individual scientists from their collaboration networks. We find that gendered differences in the productivity and prominence of mid-career researchers can be largely explained by differences in their coauthorship networks. Hence, collaboration networks act as a form of social capital, and we find evidence of their transferability from senior to junior collaborators, with benefits that decay as researchers age. Collaboration network effects can also explain a large proportion of the productivity and prominence advantages held by researchers at prestigious institutions. These results highlight a substantial role of social networks in driving inequalities in science, and suggest that collaboration networks represent an important form of unequally distributed social capital that shapes who makes what scientific discoveries.

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Amahury Jafet López-Díaz, Fernanda Sánchez-Puig, Carlos Gershenson
Most models of complex systems have been homogeneous, i.e., all elements have the same properties (spatial, temporal, structural, functional). However, most natural systems are heterogeneous: few elements are more relevant, larger, stronger, or faster than others. In homogeneous systems, criticality — a balance between change and stability, order and chaos — is usually found for a very narrow region in the parameter space, close to a phase transition. Using random Boolean networks — a general model of discrete dynamical systems — we show that heterogeneity — in time, structure, and function — can broaden additively the parameter region where criticality is found. Moreover, parameter regions where antifragility is found are also increased with heterogeneity. However, maximum antifragility is found for particular parameters in homogeneous networks. Our work suggests that the “optimal” balance between homogeneity and heterogeneity is non-trivial, context-dependent, and in some cases, dynamic.

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What’s a message, really? Claude Shannon recognized that the elemental ingredient is surprise.

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