A1 Functional advantages of cell-type heterogeneity in neural circuits

Limits in Percolation Models: Slight changes in the number of connections within a network that form at random (for example, connections in social networks) can lead to a huge increase in connectivity, a phenomenon termed "explosive percolation." These percolation transitions are often studied with Erdös and Rényi models, in which edges connecting pairs of vertices in a network are added randomly or according to a rule. Whether these transitions are continuous in nature has been the subject of several recent studies. Cho et al. (p. 1185 ; see the Perspective by Ziff ) examined the effect of avoiding bridge bonds that create a spanning cluster (one that completes the percolation path) on the continuity of transitions for a d -dimensional lattice (up to six dimensions). Analytical arguments and numerical studies reveal a critical value for the number of bonds m below which the percolation transition is continuous and above which it is discontinuous. The critical value depends on d and on the fractal dimension of the bridge bonds of the clusters.

The first passage time (FPT) for random walks is a key indicator of how fast information diffuses in a given system. Despite the role of FPT as a fundamental feature in transport phenomena, its behavior, particularly in heterogeneous networks, is not yet fully understood. Here, we study, both analytically and numerically, the scaling behavior of the FPT distribution to a given target node, averaged over all starting nodes. We find that random walks arrive quickly at a local hub, and therefore, the FPT distribution shows a crossover with respect to time from fast decay behavior (induced from the attractive effect to the hub) to slow decay behavior (caused by the exploring of the entire system). Moreover, the mean FPT is independent of the degree of the target node in the case of compact exploration. These theoretical results justify the necessity of using a random jump protocol (empirically used in search engines) and provide guidelines for designing an effective network to make information quickly accessible.

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.

We investigate a reversible percolation system showing unipolar resistance switching in which percolating paths are created and broken alternately by the application of an electric bias. Owing to the dynamical changes in the percolating paths, different from those in classical percolating paths, a detailed understanding of the structure is demanding and challenging. Here, we develop a scaling theory that can explain the transport properties of these conducting paths; the theory is based on the fractal geometry of a percolating cluster. This theory predicts that two scaling behaviors emerge, depending on the topologies of the conducting paths. We confirm these theoretical predictions experimentally by observing material-independent universal scaling behaviors in unipolar resistance switching.