Reconstructing propagation networks with natural diversity and identifying hidden sources

Abstract

Our ability to uncover complex network structure and dynamics from data is fundamental to understanding and controlling collective dynamics in complex systems. Despite recent progress in this area, reconstructing networks with stochastic dynamical processes from limited time series remains to be an outstanding problem. Here we develop a framework based on compressed sensing to reconstruct complex networks on which stochastic spreading dynamics take place. We apply the methodology to a large number of model and real networks, finding that a full reconstruction of inhomogeneous interactions can be achieved from small amounts of polarized (binary) data, a virtue of compressed sensing. Further, we demonstrate that a hidden source that triggers the spreading process but is externally inaccessible can be ascertained and located with high confidence in the absence of direct routes of propagation from it. Our approach thus establishes a paradigm for tracing and controlling epidemic invasion and information diffusion in complex networked systems.

Transitions between dynamical behaviors of oscillator networks induced by diversity of nodes and edges

“…If the different susceptibilities for a certain dynamics are interpreted in terms of robustness of the initial (or the target) state, our findings may inform previous studies that aim at controlling the dynamics on and of complex networks. [69][70][71][72][73][74] …”

Topology inference of uncertain complex dynamical networks and its applications in hidden nodes detection

“…In this article, the auxiliary network only receives control input from the considered one. Moreover, the network models and designed controllers can be further employed to detect hidden nodes (or latent variables), which is an interesting but challenging problem gradually sprung up in recent years [24,39,40].…”

Predicting and Controlling Complex Networks

“…One would hope that, applying the procedure to each node would lead to the complete weighted adjacency matrix, W. In previous works on reconstruction of complex networks based on stochastic dynamical correlations [29,30] or compressive sensing [33,37], the existent (real) links can be distinguished from the nonexistent links by setting a single threshold value in certain quantitative measure. The success relies on the fact that the dynamics at various nodes are of the same type, and the reconstruction algorithm is tailored toward the specific type of dynamical process.…”

“…In these works, the success of mapping out the entire network structure and estimating the nodal dynamical equations partly relies on taking advantage of the particular properties of the system dynamics in terms of the specific types and rules. For example, depending on the detailed dynamical processes such as continuous-time oscillations [29,30,32], evolutionary games [33], or epidemic spreading [37], appropriate mathematical frameworks uniquely tailored at the specific underlying dynamical process can be formulated to solve the inverse problem.…”