publications

2026

1. Neural Netw.

   Anatomical Connectivity Reconstruction of Biological Neuronal Networks Using Granger Causality

   Bo Wang, Kai Chen, Shouwei Luo, Yanyang Xiao, Songting Li, and 1 more author

   Neural Networks, 198, 108528, Jan 2026

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   Accessing to the anatomical connectivity of the cortical network is crucial for understanding the dynamics and functions of the brain. While direct experimental measurements of anatomical connectivity are costly, effective connectivity methods offer a potential alternative approach to reconstructing anatomical connections with the help of statistical tools. Granger causality (GC) is one of the most widely used tools for network effective connection estimations in brain networks. However, whether the effective connectivity estimated by GC can help to reliably capture the information of the underlying anatomical connectivity of neuronal networks remains largely unknown. In this work, we demonstrate that GC can effectively reconstruct the anatomical connectivity of Hodgkin-Huxley (HH) neuronal networks using neuronal voltage time series data across various dynamical regimes. Moreover, we uncover the quantitative mechanisms underlying the accurate reconstruction capabilities of GC. Furthermore, we extend our analysis from HH type point neuronal networks to multi-compartment neuronal networks, and from voltage data to spike-train data. The GC-based reconstruction remains consistently effective across these different scenarios. Finally, we investigate GC-based reconstruction using real experimental data from Allen Institute, demonstrating that GC-reconstructed connectivities exhibit high consistency across different stimulus conditions. Overall, our findings provide a strong theoretical foundation for the use of GC in realistic neuronal network reconstructions.

2025

1. arXiv

   Network structural change point detection and reconstruction for balanced neuronal networks

   Kai Chen, Mingzhang Wang, Songting Li,  and  Douglas Zhou

   arXiv, , 2025
2. arXiv

   Nonlinear Network Reconstruction by Pairwise Time-delayed Transfer Entropy

   Kai Chen, Zhong-qi K. Tian, Yifei Chen, Songting Li,  and  Douglas Zhou

   arXiv, , 2025
3. CSIAM-LS

   The Asymptotic Behavior of Conditional Granger Causality with Respect to Sampling Interval

   Jinlong Mei, Kai Chen, Yanyang Xiao, Songting Li,  and  Douglas Zhou

   CSIAM Transactions on Life Sciences, 1 (1), 45–66, 2025

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   Granger causality (GC) stands as a powerful causal inference tool in time series analysis. Typically estimated from time series data with finite sampling rate, the GC value inherently depends on the sampling interval τ. Intuitively, a higher data sampling rate leads to a time series that better approximates the real signal. However, previous studies have shown that the bivariate GC converges to zero linearly as τapproaches zero, which will lead to mis-inference of causality due to vanishing GC value even in the presence of causality. In this work, by performing mathematical analysis, we show this asymptotic behavior remains valid in the case of conditional GC when applying to a system composed of more than two variables. We validate the analytical result by computing GC value with multiple sampling rates for the simulated data of Hodgkin-Huxley neuronal networks and the experimental data of intracranial EEG signals. Our result demonstrates the hazard of GC inference with high sampling rate, and we propose an accurate inference approach by calculating the ratio of GC to τas τapproaches zero.

2024

1. CSIAM-LS

   The Asymptotic Behavior of Conditional Granger Causality with Respect to Sampling Interval (Online)

   Jinlong Mei, Kai Chen, Yanyang Xiao, Songting Li,  and  Douglas Zhou

   CSIAM Transactions on Life Sciences, , Jun 2024
2. PNAS

   Causal Connectivity Measures for Pulse-Output Network Reconstruction: Analysis and Applications

   Zhong-qi K. Tian, Kai Chen, Songting Li, David W. McLaughlin,  and  Douglas Zhou

   Proceedings of the National Academy of Sciences, 121 (14), e2305297121, Apr 2024

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   The causal connectivity of a network is often inferred to understand network function. It is arguably acknowledged that the inferred causal connectivity relies on the causality measure one applies, and it may differ from the network’s underlying structural connectivity. However, the interpretation of causal connectivity remains to be fully clarified, in particular, how causal connectivity depends on causality measures and how causal connectivity relates to structural connectivity. Here, we focus on nonlinear networks with pulse signals as measured output, e.g., neural networks with spike output, and address the above issues based on four commonly utilized causality measures, i.e., time-delayed correlation coefficient, time-delayed mutual information, Granger causality, and transfer entropy. We theoretically show how these causality measures are related to one another when applied to pulse signals. Taking a simulated Hodgkin–Huxley network and a real mouse brain network as two illustrative examples, we further verify the quantitative relations among the four causality measures and demonstrate that the causal connectivity inferred by any of the four well coincides with the underlying network structural connectivity, therefore illustrating a direct link between the causal and structural connectivity. We stress that the structural connectivity of pulse-output networks can be reconstructed pairwise without conditioning on the global information of all other nodes in a network, thus circumventing the curse of dimensionality. Our framework provides a practical and effective approach for pulse-output network reconstruction.

   @article{tian2024causal,
     title = {Causal Connectivity Measures for Pulse-Output Network Reconstruction: {{Analysis}} and Applications},
     author = {Tian, Zhong-qi K. and Chen, Kai and Li, Songting and McLaughlin, David W. and Zhou, Douglas},
     year = {2024},
     month = apr,
     journal = {Proceedings of the National Academy of Sciences},
     volume = {121},
     number = {14},
     pages = {e2305297121},
     issn = {0027-8424, 1091-6490},
     doi = {10.1073/pnas.2305297121},
     copyright = {All rights reserved},
     dimensions = {true},
   }

2023

1. bioRxiv

   Quantitative relations among causality measures with applications to pulse-output nonlinear network reconstruction

   Zhong-qi K. Tian, Kai Chen, Songting Li, David W. McLaughlin,  and  Douglas Zhou

   bioRxiv, , 2023

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   The causal connectivity of a network is often inferred to understand the network function. It is arguably acknowledged that the inferred causal connectivity relies on the causality measure one applies, and it may differ from the network’s underlying structural connectivity. However, the interpretation of causal connectivity remains to be fully clarified, in particular, how causal connectivity depends on causality measures and how causal connectivity relates to structural connectivity. Here, we focus on nonlinear networks with pulse signals as measured output, e.g., neural networks with spike output, and address the above issues based on four intensively utilized causality measures, i.e., time-delayed correlation coefficient, time-delayed mutual information, Granger causality, and transfer entropy. We theoretically show how these causality measures are related to one another when applied to pulse signals. Taking the simulated Hodgkin-Huxley neural network and the real mouse brain network as two illustrative examples, we further verify the quantitative relations among the four causality measures and demonstrate that the causal connectivity inferred by any of the four well coincides with the underlying network structural connectivity, therefore establishing a direct link between the causal and structural connectivity. We stress that the structural connectivity of networks can be reconstructed pairwise without conditioning on the global information of all other nodes in a network, thus circumventing the curse of dimensionality. Our framework provides a practical and effective approach for pulse-output network reconstruction.Significance Statement Inferring network connectivity is a key challenge in many diverse scientific fields. We investigate networks with pulse signal as measured output and solve the above reverse-engineering issue by establishing a direct link between the network’s causal connectivity and structural connectivity. Here, the causal connectivity can be inferred by any one of the four causality measures, i.e., time-delayed correlation coefficient, time-delayed mutual information, Granger causality, and transfer entropy. We analytically reveal the relationship among these four measures and show that they are equally effective to fully reconstruct the network connectivity pairwise. Our work provides a practical framework to reconstruct the structural connectivity in general pulse-output nonlinear networks or subnetworks.Competing Interest StatementThe authors have declared no competing interest.

   @article{Tian2023,
     author = {Tian, Zhong-qi K. and Chen, Kai and Li, Songting and McLaughlin, David W. and Zhou, Douglas},
     title = {Quantitative relations among causality measures with applications to pulse-output nonlinear network reconstruction},
     elocation-id = {2023.04.02.535284},
     year = {2023},
     doi = {10.1101/2023.04.02.535284},
     publisher = {Cold Spring Harbor Laboratory},
     journal = {bioRxiv}
   }

2. Nonlinear Pulse-coupled Network Reconstruction by Pairwise Time-delayed Transfer Entropy (in preparation)

   Zhong-qi K. Tian, Kai Chen, Wei P. Dai, Songting Li,  and  Douglas Zhou

   , 2023