The original version of this Article contained an error in the Abstract, which incorrectly read: ‘Here, we show theoretically, and experimentally with a multi-robot system, that such a transition from simple to complex contagion can also bed observed in an archetypal model of distributed decision-making devoid of any thresholds or nonlinearities.’ The correct form of the fourth sentence in the Abstract is: ‘Here, we show theoretically, and experimentally with a multi-robot system, that such a transition from simple to complex contagion can also be observed in an archetypal model of distributed decision-making devoid of any thresholds or nonlinearities.’@en

Apart from the role the clustering coefficient plays in the definition of the small-world phenomena, it also has great relevance for practical problems involving networked dynamical systems. To study the impact of the clustering coefficient on dynamical processes taking place on networks, some authors have focused on the construction of graphs with tunable clustering coefficients. These constructions are usually realized through a stochastic process, either by growing a network through the preferential attachment procedure, or by applying a random rewiring process. In contrast, we consider here several families of static graphs whose clustering coefficients can be determined explicitly. The basis for these families is formed by the k-regular graphs on N nodes, that belong to the family of so-called circulant graphs denoted by CN,k. We show that the expression for the clustering coefficient of CN,k reported in literature, only holds for sufficiently large N. Next, we consider three generalizations of the circulant graphs, either by adding some pendant links to CN,k, or by connecting, in two different ways, an additional node to some nodes of CN,k. For all three generalizations, we derive explicit expressions for the clustering coefficient. Finally, we construct a family of pairs of generalized circulant graphs, with the same number of nodes and links, but with different clustering coefficients.@en

Hydrodynamic sensing is instrumental to fish and some amphibians. It also represents, for underwater vehicles, an alternative way of sensing the fluid environment when visual and acoustic sensing are limited. To assess the effectiveness of hydrodynamic sensing and gain insight into its capabilities and limitations, we investigated the forward and inverse problem of detection and identification, using the hydrodynamic pressure in the neighbourhood, of a stationary obstacle described using a general shape representation. Based on conformal mapping and a general normalization procedure, our obstacle representation accounts for all specific features of progressive perceptual hydrodynamic imaging reported experimentally. Size, location and shape are encoded separately. The shape representation rests upon an asymptotic series which embodies the progressive character of hydrodynamic imaging through pressure sensing. A dynamic filtering method is used to invert noisy nonlinear pressure signals for the shape parameters. The results highlight the dependence of the sensitivity of hydrodynamic sensing not only on the relative distance to the disturbance but also its bearing.@en

How does the spread of behavior affect consensus-based collective decision-making among animals, humans or swarming robots? In prior research, such propagation of behavior on social networks has been found to exhibit a transition from simple contagion—i.e, based on pairwise interactions—to a complex one—i.e., involving social influence and reinforcement. However, this rich phenomenology appears so far limited to threshold-based decision-making processes with binary options. Here, we show theoretically, and experimentally with a multi-robot system, that such a transition from simple to complex contagion can also bed observed in an archetypal model of distributed decision-making devoid of any thresholds or nonlinearities. Specifically, we uncover two key results: the nature of the contagion—simple or complex—is tightly related to the intrinsic pace of the behavior that is spreading, and the network topology strongly influences the effectiveness of the behavioral transmission in ways that are reminiscent of threshold-based models. These results offer new directions for the empirical exploration of behavioral contagions in groups, and have significant ramifications for the design of cooperative and networked robot systems.@en