Abstract: Multistability?understood as the existence of diverse stationary states under a fixed set of conditions?is ubiquitous in physics and in biology, it and leads to interesting spatial and temporal patterns. Motivated by several empirical observation of bimodal distributions of activity, we propose and analyze a theory for the self-organization to the point of phase-coexistence in systems exhibiting a first-order phase transition. It explains the emergence of regular avalanches patterns with attributes of scale-invariance which coexist with huge anomalous ones, with realizations in many fields.

Abstract: Since Turing?s seminal work, reaction-diffusion models have played a central role in the analysis of various self-organized spatio-temporal patterns in nature. As pointed out by Othmer and Scriven already in 1971, it is straightforward to generalize the reaction-diffusion models to networks, which gives us a wider perspective on pattern formation. In this talk, several topics on pattern formation and collective dynamics in reaction-diffusion models on random networks will be discussed. We consider formation of Turing patterns in activator-inhibitor systems on networks, where difference in diffusivity of chemical species leads to destabilization of uniform states and formation of patterns. It is shown that, for networks with degree heterogeneity, simple mean-field approximation of the network can account for backbones of the developed patterns. We will also see that essentially the same mechanism, called Benjamin-Feir instability, destabilizes uniformly synchronized state and leads to collective dynamics in coupled oscillators on networks. More general types of diffusion-induced instabilities in reaction-diffusion systems with three chemical species or in directed networks will also be discussed. Some related unsolved issues, such as self-consistency analysis of developed patterns, bifurcation analysis of instability, and localization properties of Laplacian eigenmodes on networks, will also be mentioned.

Abstract: Pattern formation has attracted the interest of the scientific communities of several fields since the Turing seminal paper on morphogenesis [1] first appeared. Recently, patterns emergence has been studied in complex networks [2], where a spontaneous differentiation of nodes in activator(inhibitor)-rich and activator(inhibitor)-poor nodes was observed in a two species reaction-diffusion system. From then, several extensions and generalizations have followed. In this talk we aim reviewing the main framework of our research on the pattern formation theory from the network prospective. Starting from the Turing instability mechanism we prove that the spontaneous segregation of the nodes in different groups extends far beyond Turing original conditions. In particular the network topology plays an active role in the initialization of the self-organization process as it happens for the directed networks [3]. In other cases the peculiarities of the network structure in layers (multiplex [4]) or product of sub-networks (Cartesian network [5]) explain why motifs are more likely to appear in such networks than others or how they emerge as a collective property of networks. Different applications from ecology to neuroscience can rise.

Abstract: TBA

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.