Reconstruction of dynamic networks with time-delayed interactions in the presence of fast-varying noises

Detecting hidden nodes in networks based on random variable resetting method

Reconstructing network connections from measurable data facilitates our understanding of the mechanism of interactions between nodes. However, the unmeasurable nodes in real networks, also known as hidden nodes, introduce new challenges for reconstruction. There have been some hidden node detection methods, but most of them are limited by system models, network structures, and other conditions. In this paper, we propose a general theoretical method for detecting hidden nodes based on the random variable resetting method. We construct a new time series containing hidden node information based on the reconstruction results of random variable resetting, theoretically analyze the autocovariance of the time series, and finally provide a quantitative criterion for detecting hidden nodes. We numerically simulate our method in discrete and continuous systems and analyze the influence of main factors. The simulation results validate our theoretical derivation and illustrate the robustness of the detection method under different conditions.

Full reconstruction of simplicial complexes from binary contagion and Ising data

Previous efforts on data-based reconstruction focused on complex networks with pairwise or two-body interactions. There is a growing interest in networks with higher-order or many-body interactions, raising the need to reconstruct such networks based on observational data. We develop a general framework combining statistical inference and expectation maximization to fully reconstruct 2-simplicial complexes with two- and three-body interactions based on binary time-series data from two types of discrete-state dynamics. We further articulate a two-step scheme to improve the reconstruction accuracy while significantly reducing the computational load. Through synthetic and real-world 2-simplicial complexes, we validate the framework by showing that all the connections can be faithfully identified and the full topology of the 2-simplicial complexes can be inferred. The effects of noisy data or stochastic disturbance are studied, demonstrating the robustness of the proposed framework.

Data-driven recovery of topology is challenging for networks beyond pairwise interactions. The authors propose a framework to reconstruct complex networks with higher-order interactions from time series, focusing on networks with 2-simplexes where social contagion and Ising dynamics generate binary data.

Exploring node interaction relationship in complex networks by using high-frequency signal injection

Many practical systems can be described by complex networks. These networks produce, day and night, rich data which can be used to extract information from the systems. Often, output data of some nodes in the networks can be successfully measured and collected while the structures of networks producing these data are unknown. Thus, revealing network structures by analyzing available data, referred to as network reconstruction, turns to be an important task in many realistic problems. Limitation of measurable data is a very common challenge in network reconstruction. Here we consider an extreme case, i.e., we can only measure and process the data of a pair of nodes in a large network, and the task is to explore the relationship between these two nodes while all other nodes in the network are hidden. A driving-response approach is proposed to do so. By loading a high-frequency signal to a node (defined as node A), we can measure data of the partner node (node B), and work out the connection structure, such as the distance from node A to node B and the effective intensity of interaction from A to B, with the data of node B only. A systematical smoothing technique is suggested for treating noise problem. The approach has practical significance.