Network reconstructions with partially available data
Chaoyang Zhang1(),Yang Chen2,Gang Hu3()
1. Department of Physics, Ningbo University, Ningbo 315211, China 2. School of Sciences, Beijing University of Posts and Telecommunications, Beijing 100876, China 3. Department of Physics, Beijing Normal University, Beijing 100875, China
Many practical systems in natural and social sciences can be described by dynamical networks. Day by day we have measured and accumulated huge amounts of data from these networks, which can be used by us to further our understanding of the world. The structures of the networks producing these data are often unknown. Consequently, understanding the structures of these networks from available data turns to be one of the central issues in interdisciplinary fields, which is called the network reconstruction problem. In this paper, we considered problems of network reconstructions using partially available data and some situations where data availabilities are not sufficient for conventional network reconstructions. Furthermore, we proposed to infer subnetwork with data of the subnetwork available only and other nodes of the entire network hidden; to depict group-group interactions in networks with averages of groups of node variables available; and to perform network reconstructions with known data of node variables only when networks are driven by both unknown internal fast-varying noises and unknown external slowly-varying signals. All these situations are expected to be common in practical systems and the methods and results may be useful for real world applications.
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