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The basic method is a generalization of NL2SOL - an adaptive nonlinear least-squares algorithm [ 34], which uses a model/trust-region technique for computing trial steps along with an adaptive choice for the Hessian model.
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In Figure 6, we compute the trial-to-trial variability in the number and the spatial organization of the activated synapses following WD.
We therefore computed the trial-to-trial correlation for each unit under each condition ("autocorrelation"; see Experimental Procedures), and found that single-unit responses were indeed more reliable enhanced in the daylight condition.
Once the simpler viscoelastic model is validated, it is then employed to compute the trial resonance frequencies (which are the solutions of an eigenvalue problem associated with this model) during the inversion process.
At the kth iterate, we compute a trial step by solving the following quadratic problem, begin{aligned} &Q(x_{k},H_{k},rho_{k} mbox quad min g_{k}^{T}d+frac{1}{2}d^{T}H_{k}d &hphantom{Q(x_{k},H_{k},rho_{k} mboxquad}quad text{s.t.
In addition to the raw estimates of system compliance, absolute estimation errors of the compliance rate (AEEC) were computed per trial by the formula AEEC=sqrt{{left {C}_{estimated}-{C}_{actual}right)}^2} (1)where C estimAEEC=sqrt{{left {C}_{estimated}-{C}_{actual}righty a participant in that trial and C actual was the compliance rate that was actually presented to the participant that trial.
For each brain region, mean coherograms were obtained by averaging coherograms computed per trial across all rats.
The algorithm first computes a trial-averaged FR aligned to a marker of interest (in our case movement onset).
This analysis could only be computed for trials with at least one number repetition.
The weights were then used to compute single-trial time series for each source.
The ANCOVA was conducted over items because problem size can only be computed for trials but not participants.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com