隱藏節點對網絡動力學的影響

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姓名

何白莉(Beverly Gemao) 查詢紙本館藏

畢業系所

物理學系

論文名稱

隱藏節點對網絡動力學的影響
(Effects of Hidden Nodes on Noisy Network Dynamics)

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摘要(中)

我們研究了在無相關雜訊之下耦合的網路系統。在這個網路系統中，有一些節點無法被外在的世界觀察出來。這些隱藏的節點作用在被觀察到節點的動力學效應，可以視為作用在被觀察到節點的額外等效雜訊。這些等效雜訊擁有和隱藏的連接有關的空間以及時間的關聯性。我們分析研究了等效雜訊中空間以及時間的關聯性，而這些結果在有方向性以及無方向性的權重隨機網路和小世界網路的模擬中被證實。除此之外，利用對於觀察到的網路雜訊動力學的網路重建關係，我們提出了一個方法來推斷隱藏節點所造成的效應資訊，包括了被隱藏的節點數目，以及對於每一個被觀察到結點中所隱藏的連結權重。這些結果的有效性被明確的模擬結果證實。

摘要(英)

We consider a coupled network system under uncorrelated noises where some of the nodes cannot be observed from the external world. The effects of hidden nodes on the dynamics of the observed nodes can be viewed as having an extra effective noise acting on the observed nodes. These effective noises possess spatial and temporal correlations whose properties are related to the hidden connections. The spatial and temporal correlations of these effective noises are analysed analytically and the results are verified by simulations on undirected and directed weighted random networks and small-world networks.
Furthermore, by exploiting the network reconstruction relation for the observed network noisy dynamics, we propose a scheme to infer information of the effects of the hidden nodes such as the total number of hidden nodes and the weighted hidden connections on each observed nodes. The accuracy of these results are demonstrated by explicit simulations.

關鍵字(中)

★ 高斯雜訊下的網路
★ 遺漏節點效應
★ 網路完成問題

關鍵字(英)

★ networks under Gaussian noises
★ effects of missing nodes
★ network completion problem

論文目次

Abstract
Acknowledgements

1 INTRODUCTION
11.1Outline of my work
1.2Noisy Network Dynamics

2 A Brief Review on Networks and Network Reconstruction
2.1Network Terminologies and Properties
2.2Review on Network Reconstruction Methods Using Noise-Bridging Approach

3 Effects of Hidden Node on the Dynamics of the Observed Nodes
3.1Nature of effective noise on the observed nodes .
3.2Calculation and Approximation of the Effective Noise from Missing Nodes
3.2.1Unweighted Completely Connected Network . . . .
3.2.2Approximation for the Time-lag Correlation of the Effective Noises 213.3Spatial and Temporal Correlations of the Effective noises on the observed nodes: Simulation Results

4 Detecting Hidden Node Effects from Observed Time-series and Network Connections
4.1Inference of Weighted Node Effects using Reconstruction Formula in Sec. 2.2
4.2 Some Relations for Noisy Bidirectional Network

5 Conclusion

Appendices
A Spectral Decomposition of a diagonalizable Matrix
B Time-lag Correlation Matrices ofξ(t)56B.1 Completely Connected Network
B.1.1Alternative Derivation for (B.13)
B.2 An Approximation for the Time-lag Correlation of the Effective Noises
C More Relations for Unweighted Completely Connected Network

References

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指導教授

黎璧賢(Pik-Yin Lai)

審核日期

2021-1-22

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