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Updated: Dec 22, 2025
Photodiode-Based Optical Imaging for Recording Network Dynamics with Single-Neuron Resolution in Non-Transgenic Invertebrates
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Validity and Limitations of the Detection Matrix to Determine Hidden Units and Network Size from Perceptible Dynamics
1Department of Mechanical and Aerospace Engineering and Department of Biomedical Engineering, New York University, Tandon School of Engineering, Brooklyn, New York 11201, USA.
Abstract:
Determining the size of a network dynamical system from the time series of some accessible units is a critical problem in network science. Recent work by Haehne et al. [Phys. Rev. Lett. 122, 158301 (2019).PRLTAO0031-900710.1103/PhysRevLett.122.158301] has presented a model-free approach to address this problem, by studying the rank of a detection matrix that collates sampled time series of perceptible nodes from independent experiments. Here, we unveil a profound connection between the rank of the detection matrix and the control-theoretic notion of observability, upon which we conclude when and how it is feasible to exactly infer the size of a network dynamical system.
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