Abstract: Chimera states are complex spatio-temporal patterns that consist of coexisting domains of spatially coherent and incoherent dynamics. This counterintuitive phenomenon was first observed in 2002 in systems of identical oscillators with symmetric coupling topology. During the last decade, chimera states have been theoretically investigated in a wide range of networks, where different kinds of coupling schemes varying from regular nonlocal to completely random topology have been considered. Potential applications of chimera states in nature include the phenomenon of unihemispheric sleep in birds and dolphins, bump states in neural systems, power grids, and social systems. We discuss current state-of-the-art in studies of chimera states, and demonstrate recent findings. In particular, we analyze properties of chimera states in the systems of nonlinear oscillators, the role of local dynamics and network topologies. We also address the robustness of chimeras due to inhomogeneities, and possible strategies of their control.

Abstract: We define a new structural property of large-scale communication networks consisting of the persistent patterns of communication among users. We claim these patterns represent a best-estimate at real information spread, and term them "persistent cascades." Using metrics of inexact tree matching, we group these cascades into classes which we then argue represent the fundamental communication structure of a local network. This differs from existing work in that (1) we are focused on recurring patterns among specific users, not abstract motifs (e.g. the prevalence of ?triangles? or other structures in the graph, regardless of user), and (2) we allow for inexact matching (not necessarily isomorphic graphs) to better account for the noisiness of human communication patterns. We find that analysis of these classes of cascades reveals new insights about information spread and the influence of certain users, based on three large mobile phone record datasets. For example, we find distinct groups of "weekend" vs "workweek" spreaders not evident in the standard aggregated network. Finally, we create the communication network induced by these persistent structures, and we show the effect this has on measurements of centrality or diffusion.

Abstract: We develop a dynamic network formation model that explains the observed nestedness in email communication networks inside organizations. Utilizing synchronization we enhance Konig et al. (2014)'s model with dynamic communication patterns. By endogenizing the probability of the removal of agents we propose a theoretical explanation why some agents become more important to a firm's informal organization than others, despite being ex ante identical. We also propose a theoretical framework for measuring the coherence of internal email communication and the impact of communication patterns on the informal organization structure as agents come and go. In situations with a high agent turnover rate, networks with high hierarchy outperform what we term "egalitarian" networks (i.e. all agents are of equal degree) for communication efficiency and robustness. In contrast, in situations with a low agent turnover, networks with low hierarchy outperform what we term "totalitarian" networks for communication efficiency and robustness. We derive a trade-off that accounts for the network communication performance in terms of both measures. Using the example for a consulting firm we show that the model fits real-world email communication networks.