TY - JOUR
T1 - Validity and Limitations of the Detection Matrix to Determine Hidden Units and Network Size from Perceptible Dynamics
AU - Porfiri, Maurizio
N1 - Funding Information:
The author acknowledges financial support from the National Science Foundation under Grants No. CMMI-1561134, No. CMMI 1901697, and No. ECCS 1928614, and help of Alain Boldini in the preparation of the figures.
Publisher Copyright:
© 2020 American Physical Society.
PY - 2020/4/24
Y1 - 2020/4/24
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85084721914&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85084721914&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.124.168301
DO - 10.1103/PhysRevLett.124.168301
M3 - Article
C2 - 32383942
AN - SCOPUS:85084721914
SN - 0031-9007
VL - 124
JO - Physical Review Letters
JF - Physical Review Letters
IS - 16
M1 - 168301
ER -