title: 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.
authors.affiliation: School of Systems Science, Beijing Normal University, Beijing 100875, China.
authors.forename: Zhesi
authors.initials: Z
authors.lastname: Shen
authors.affiliation: 1] School of Systems Science, Beijing Normal University, Beijing 100875, China [2] School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA.
authors.forename: Wen-Xu
authors.initials: WX
authors.lastname: Wang
authors.affiliation: School of Systems Science, Beijing Normal University, Beijing 100875, China.
authors.forename: Ying
authors.initials: Y
authors.lastname: Fan
authors.affiliation: School of Systems Science, Beijing Normal University, Beijing 100875, China.
authors.forename: Zengru
authors.initials: Z
authors.lastname: Di
authors.affiliation: 1] School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA [2] Department of Physics, Arizona State University, Tempe, Arizona 85287, USA.
authors.forename: Ying-Cheng
authors.initials: YC
authors.lastname: Lai