Reconstructing network topology and coupling strengths in directed networks of discrete-time dynamics

Abstract

Reconstructing network connection topology and interaction strengths solely from measurement of the dynamics of the nodes is a challenging inverse problem of broad applicability in various areas of science and engineering. For a discrete-time step network under noises whose noise-free dynamics is stationary, we derive general analytic results relating the weighted connection matrix of the network to the correlation functions obtained from time-series measurements of the nodes for networks with one-dimensional intrinsic node dynamics. Information about the intrinsic node dynamics and the noise strengths acting on the nodes can also be obtained. Based on these results, we develop a scheme that can reconstruct the above information of the network using only the time-series measurements of node dynamics as input. Reconstruction formulas for higher-dimensional node dynamics are also derived and illustrated with a two-dimensional node dynamics network system. Furthermore, we extend our results and obtain a reconstruction scheme even for the cases when the noise-free dynamics is periodic. We demonstrate that our method can give accurate reconstruction results for weighted directed networks with linear or nonlinear node dynamics of various connection topologies, and with linear or nonlinear couplings.

Directed effective connectivity and synaptic weights of in vitro neuronal cultures revealed from high-density multielectrode array recordings

“…For a class of networked systems having generic stationary dynamics modelled by a 40 set of stochastic differential equations with directional interactions, it has been shown 41 that the equal-time cross-covariance of the dynamics of the nodes does not carry 42 sufficient information to recover the effective connectivity [11,12], and the effective 43 connectivity matrix can instead be extracted using the theoretical relation between the 44 time-lagged cross-covariance and the equal-time cross-covariance [13]. Similar result has 45 been found for systems with discrete-time dynamics [14]. This covariance-relation based 46 method thus infers effective connectivity for a generic class of models and not only for a 47 specific model.…”

Local Tomography of Large Networks Under the Low-Observability Regime

“…One explanation for this behavior is the following. The choice of the constant τ in (35) -see (29). Thresholding stands for the tomography strategy where the entries of A S are thresholded with the threshold ηM determined in (45).…”

“…Strictly speaking, in the network literature the Laplacian and Metropolis rules are defined with weights that add up to one, which would correspond to(28) and(29) without the multiplying factor ρ. The multiplying factor ρ, which provides the matrix stability, is usually left separate and not absorbed into the combination matrix.…”

“…For instance, in the case of diffusion networks(14) we have ρ = 1 − µ, where µ is the step-size. In our treatment, it is more convenient to include this scaling factor into the combination matrix, as done in(28)and(29) May 24, 2018. DRAFT…”

Detecting directed interactions of networks by random variable resetting

“…The existing reconstruction methods propose to detect the dynamics of complex systems [7,8,9,10,11,12,13,14,15] or to detect network connectivity [16,17,18,19,20,21,22,23]. Controlling, as a proactive approach, is usually adopted in real systems, such as synchronization and desynchronization controlling.…”