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Estimation of Directed Effective Connectivity from fMRI Functional Connectivity Hints at Asymmetries of Cortical Connectome

Fig 2

Iterative optimization to recover C from empirical Q.

A Estimation based on theoretical covariances. Evolution of Q⁰ and Q^τ errors between the model and theoretical objectives (blue curves), as well as C error between the original and model connectivity (red). The theoretical objectives are calculated using Eqs (6) and (7). Errors are calculated using the normalized matrix distance in Eq (25). The optimization relies on Eq (15) with time shift τ_est = 1 s. B Details of the match of the model and objective matrices for Q^τ (blue dots) and C (red crosses) at three stages of the optimization in A. The black line indicates a perfect match. C Similar plot to A with empirical Q as objectives, evaluated using Eq (2) for 50 simulations of the same network as in A. D Similar plot to B for the optimization in C.

doi: https://doi.org/10.1371/journal.pcbi.1004762.g002