Reconstructing propagation networks with natural diversity and identifying hidden sources

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.Comment: 20 pages and 5 figures. For Supplementary information, please see http://www.nature.com/ncomms/2014/140711/ncomms5323/full/ncomms5323.html#

Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

Temporal similarity metrics for latent network reconstruction: The role of time-lag decay

When investigating the spreading of a piece of information or the diffusion of an innovation, we often lack information on the underlying propagation network. Reconstructing the hidden propagation paths based on the observed diffusion process is a challenging problem which has recently attracted attention from diverse research fields. To address this reconstruction problem, based on static similarity metrics commonly used in the link prediction literature, we introduce new node-node temporal similarity metrics. The new metrics take as input the time-series of multiple independent spreading processes, based on the hypothesis that two nodes are more likely to be connected if they were often infected at similar points in time. This hypothesis is implemented by introducing a time-lag function which penalizes distant infection times. We find that the choice of this time-lag strongly affects the metrics' reconstruction accuracy, depending on the network's clustering coefficient and we provide an extensive comparative analysis of static and temporal similarity metrics for network reconstruction. Our findings shed new light on the notion of similarity between pairs of nodes in complex networks

Model-agnostic network inference enhancement from noisy measurements via curriculum learning

Noise is a pervasive element within real-world measurement data, significantly undermining the performance of network inference models. However, the quest for a comprehensive enhancement framework capable of bolstering noise resistance across a diverse array of network inference models has remained elusive. Here, we present an elegant and efficient framework tailored to amplify the capabilities of network inference models in the presence of noise. Leveraging curriculum learning, we mitigate the deleterious impact of noisy samples on network inference models. Our proposed framework is model-agnostic, seamlessly integrable into a plethora of model-based and model-free network inference methods. Notably, we utilize one model-based and three model-free network inference methods as the foundation. Extensive experimentation across various synthetic and real-world networks, encapsulating diverse nonlinear dynamic processes, showcases substantial performance augmentation under varied noise types, particularly thriving in scenarios enriched with clean samples. This framework's adeptness in fortifying both model-free and model-based network inference methodologies paves the avenue towards a comprehensive and unified enhancement framework, encompassing the entire spectrum of network inference models. Available Code: https://github.com/xiaoyuans/MANIE

Reconstructing direct and indirect interactions in networked public goods game

W.-X.W. was supported by NNSFC under Grant No. 61573064 and Grant No. 61074116, Beijing Nova Programme, China, and the Fundamental Research Funds for the Central Universities. Y.-C.L. was supported by ARO under Grant W911NF-14-1-0504.Peer reviewedPublisher PD

Reconstructing direct and indirect interactions in networked public goods game

abstract: Network reconstruction is a fundamental problem for understanding many complex systems with unknown interaction structures. In many complex systems, there are indirect interactions between two individuals without immediate connection but with common neighbors. Despite recent advances in network reconstruction, we continue to lack an approach for reconstructing complex networks with indirect interactions. Here we introduce a two-step strategy to resolve the reconstruction problem, where in the first step, we recover both direct and indirect interactions by employing the Lasso to solve a sparse signal reconstruction problem, and in the second step, we use matrix transformation and optimization to distinguish between direct and indirect interactions. The network structure corresponding to direct interactions can be fully uncovered. We exploit the public goods game occurring on complex networks as a paradigm for characterizing indirect interactions and test our reconstruction approach. We find that high reconstruction accuracy can be achieved for both homogeneous and heterogeneous networks, and a number of empirical networks in spite of insufficient data measurement contaminated by noise. Although a general framework for reconstructing complex networks with arbitrary types of indirect interactions is yet lacking, our approach opens new routes to separate direct and indirect interactions in a representative complex system.The final version of this article, as published in Scientific Reports, can be viewed online at: https://www.nature.com/articles/srep3024