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Identifying structures of continuously-varying weighted networks.

ABSTRACT: Identifying network structures from dynamical observations is a fundamental problem currently pervading scientific research on complex systems, as understanding and modeling the structure of a complex network will lead to greater knowledge of its evolutionary mechanisms and to a better understanding of its functional behaviors. Usually, one needs to identify a network's structure through a limited number of observations. Particularly, couplings of many real-world networks are sparse and continuously varying with time. In this study, a new framework is developed via optimization for identifying structures of continuously-varying weighted networks formed by sparsely-connected dynamical systems. Furthermore, a regularization technique is employed to increase the numerical stability of the parameter estimation algorithm. Three numerical examples are provided to illustrate the feasibility and effectiveness of the proposed identification method. In comparison with other existing techniques, the main advantages of our method include its ability to identify structures of continuously-varying weighted networks in addition to static ones, as well as its requirement of a relatively small number of observations. The proposed method has a potential applicability to a variety of evolving complex dynamical networks.

SUBMITTER: Mei G

PROVIDER: S-EPMC4901193 | biostudies-literature | 2016 May

REPOSITORIES: biostudies-literature

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Identifying structures of continuously-varying weighted networks.

Mei Guofeng G Wu Xiaoqun X Chen Guanrong G Lu Jun-An JA

Scientific reports 20160531

Identifying network structures from dynamical observations is a fundamental problem currently pervading scientific research on complex systems, as understanding and modeling the structure of a complex network will lead to greater knowledge of its evolutionary mechanisms and to a better understanding of its functional behaviors. Usually, one needs to identify a network's structure through a limited number of observations. Particularly, couplings of many real-world networks are sparse and continuo ...[more]

PMID: 27241956

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Project description:BackgroundIt is a crucial task of brain science researches to explore functional connective maps of Biological Neural Networks (BNN). The maps help to deeply study the dominant relationship between the structures of the BNNs and their network functions.ResultsIn this study, the ideas of linear Granger causality modeling and causality identification are extended to those of nonlinear Granger causality modeling and network structure identification. We employed Radial Basis Functions to fit the nonlinear multivariate dynamical responses of BNNs with neuronal pulse firing. By introducing the contributions from presynaptic neurons and detecting whether the predictions for postsynaptic neurons' pulse firing signals are improved or not, we can reveal the information flows distribution of BNNs. Thus, the functional connections from presynaptic neurons can be identified from the obtained network information flows. To verify the effectiveness of the proposed method, the Nonlinear Granger Causality Identification Method (NGCIM) is applied to the network structure discovery processes of Spiking Neural Networks (SNN). SNN is a simulation model based on an Integrate-and-Fire mechanism. By network simulations, the multi-channel neuronal pulse sequence data of the SNNs can be used to reversely identify the synaptic connections and strengths of the SNNs.ConclusionsThe identification results show: for 2-6 nodes small-scale neural networks, 20 nodes medium-scale neural networks, and 100 nodes large-scale neural networks, the identification accuracy of NGCIM with the Gaussian kernel function was 100%, 99.64%, 98.64%, 98.37%, 98.31%, 84.87% and 80.56%, respectively. The identification accuracies were significantly higher than those of a traditional Linear Granger Causality Identification Method with the same network sizes. Thus, with an accumulation of the data obtained by the existing measurement methods, such as Electroencephalography, functional Magnetic Resonance Imaging, and Multi-Electrode Array, the NGCIM can be a promising network modeling method to infer the functional connective maps of BNNs.

Dataset Information

Identifying structures of continuously-varying weighted networks.

Publications

Identifying structures of continuously-varying weighted networks.

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