Multiplex Decomposition of Non-Markovian Dynamics and the Hidden Layer Reconstruction Problem

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Elements composing complex systems usually interact in several different ways, and as such, the interaction architecture is well modeled by a network with multiple layers-a multiplex network-where the system's complex dynamics is often the result of several intertwined processes taking place at different levels. However, only in a few cases can such multilayered architecture be empirically observed, as one usually only has experimental access to such structure from an aggregated projection. A fundamental challenge is thus to determine whether the hidden underlying architecture of complex systems is better modeled as a single interaction layer or if it results from the aggregation and interplay of multiple layers. Assuming a prior of intralayer Markovian diffusion, here we show that by using local information provided by a random walker navigating the aggregated network, it is possible to determine, in a robust manner, whether these dynamics can be more accurately represented by a single layer or if they are better explained by a (hidden) multiplex structure. In the latter case, we also provide Bayesian methods to estimate the most probable number of hidden layers and the model parameters, thereby fully reconstructing its architecture. The whole methodology enables us to decipher the underlying multiplex architecture of complex systems by exploiting the non-Markovian signatures on the statistics of a single random walk on the aggregated network. In fact, the mathematical formalism presented here extends above and beyond detection of physical layers in networked complex systems, as it provides a principled solution for the optimal decomposition and projection of complex, non-Markovian dynamics into a Markov switching combination of diffusive modes.
Biological Physics, Complex Systems, Interdisciplinary Physics
Bibliographic citation
Lacasa, L., Mariño, I. P., Miguez, J., Nicosia, V., Roldán, É., Lisica, A., Grill, S. W., & Gómez-Gardeñes, J. (2018). Multiplex Decomposition of Non-Markovian Dynamics and the Hidden Layer Reconstruction Problem. Physical Review X 8(3).