Memory Effects for agents on Multilayer Networks  

We first proposed a procedure to generate dynamical networks with bursty, possibly repetitive and correlated temporal behaviors. Regarding any weighted directed graph as being composed of the accumulation of paths between its nodes, our construction uses random walks of variable length to produce time-extended structures with adjustable features. Our procedure enables one to obtain plausible and realistic instances of temporal networks when only the aggregated structure is known. Hence, it can be employed to compensate for the lack of time-resolved data or to provide alternative scenarios when access to empirical information is limited. Moreover, that the synthetic network has tunable properties is essential to assessing the influence of time- dependent features on the dynamical processes on networks, especially when only aggregated information is available. Finally, structural flexibility also makes it possible to test the relevance of various definitions of centrality measures for nodes and links in temporal networks.

We have defined a series of models of interacting agents, with tunable interaction rules. In particular, various interaction ingredients are based on memory effects empirically observed in human contact data, similar to rich-get-richer effects. While several memory effects are present at the same time in the data, the modeling framework allows us to analyze separately their individual roles in determining the complex phenomenology arising in the data, concerning in particular the heterogeneous distributions of contact durations and numbers and of inter-contact durations. We have hence disentangled the role of these mechanisms, shown which empirical characteristics emerge from each, and shown that the inclusion of all memory effects is necessary to recover an overall phenomenology fully resembling the one of the empirical data.

We have defined new network models to capture the non-Markovian nature of real-world datasets such as the interactions of mobile phone calls. In particular, in [Karsai2014] we have measured from a real-world dataset of mobile phone calls the activity of the agents that form the network and used such information to build a synthetic model that mimics the properties of real temporal networks. Such results provide a significant advance with respect to traditional modeling approaches, due to the inclusion of a number of realistic features in the modeling of temporal networks. 

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