Oliver E. Williams, Lucas Lacasa, Ana P. Millán & Vito Latora 

Nature Communications volume 13, Article number: 499 (2022)

How to best define, detect and characterize network memory, i.e. the dependence of a network’s structure on its past, is currently a matter of debate. Here we show that the memory of a temporal network is inherently multidimensional, and we introduce a mathematical framework for defining and efficiently estimating the microscopic shape of memory, which characterises how the activity of each link intertwines with the activities of all other links. We validate our methodology on a range of synthetic models, and we then study the memory shape of real-world temporal networks spanning social, technological and biological systems, finding that these networks display heterogeneous memory shapes. In particular, online and offline social networks are markedly different, with the latter showing richer memory and memory scales. Our theory also elucidates the phenomenon of emergent virtual loops and provides a novel methodology for exploring the dynamically rich structure of complex systems.

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Steven Strogatz

Infinite sums are among the most underrated yet powerful concepts in mathematics, capable of linking concepts across math’s vast web.

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Francis Heylighen

A wide variety of approaches and mechanisms have been proposed to “extend” the neo-Darwinist theory of evolution, including self-organization, symbiogenesis, teleonomy, systems biology and niche construction. These extensions share a focus on agents, networks and processes rather than on independent, static units, such as genes. To develop a new evolutionary synthesis, we therefore need to replace the traditional object-based ontology by one that is here called “relational agency”. The paper sketches the history of both object-based and relational worldviews, going back to their roots in animism and Greek philosophy. It then introduces the basic concepts of the relational agency model: condition-action rules, challenges, agents, reaction networks and chemical organizations. These are illustrated with examples of self-contained ecosystems, genes and cells. The fundamental evolutionary mechanism is that agencies and reactions mutually adapt so as to form a self- maintaining organization, in which everything consumed by one process is produced again by one or more other processes. Such autonomous organization defines a higher-level agency, which will similarly adapt, and thus become embedded in a network of relationships with other agencies.

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