PMC

Delay errors. (a) 2° yaw angle and 0° pitch angle; (b) 0° yaw angle and 2° pitch angle; (c) 2° yaw angle and 2° pitch angle; (d) 3° yaw angle and 3° pitch angle.

Phase delay in rotated PPP. (a) Phase delay with no inclination among reference and object wavefronts. The solid blue line is for the proposed phase delay estimation, dashed orange curve is for phase delay from the paper []. (b) Phase delay dependence on inclination angle between reference and object wavefronts. The solid red line is phase shift, because of inclination on , a dotted orange curve is phase delay with , a dash-dot purple curve is phase delay with , and dashed orange curve is phase delay with .

Experimental data of the joint angle for negotiating a junction. (A) Time delay of the joint angle for the first joint (top) and the second joint (bottom). (B) Angle error of the joint between the desired angle and the actual angle of the joint (top). and shifted angle error of the joint between the desired angle and the actual angle moved forward 5 time steps (bottom). Angle error and shifted angle error of the 1–12th joints, the 13–24th joints, and the 25–36th joints are shown in the left, center, and right panel of the figures, respectively.

A. Cumulative reaction time distributions (pooled across all sessions). Green denotes short delay periods (0-300ms), and orange denotes long delay periods (300-600ms). Dotted lines denote the first 150 trials during adaptation, and solid lines denote the last 150 trials during adaptation. The p-values were obtained from the Wilcoxon rank-sum test and compare trials with short delay periods and trials with long delay periods.
B. Correlation between the length of the delay period on trial k and the mean error on that same trial k. Data were binned in 50ms bins. The p-values are for the F-test on the model, which tests whether the fit is significantly better than a model with only a constant term. The plotted data (same for (C) and (D)) is pooled across five sessions; the first 25 trials (i.e., ‘early learning’) are considered from each session. The delay length for Monkey P was drawn randomly on every trial from a uniform distribution from 0ms-500ms; for Monkey V this was between 250ms-600ms.
C. Correlation between the length of the delay period on trial k and the variance in the distribution of errors (in 50ms bins) on that same trial k. The p-values are for the F-test on the model, which tests whether the fit is significantly better than a model with only a constant term. Delay period distribution was the same as in (B).
D. Correlation between the length of the delay period on trial k and the mean error (in 50ms bins) on the next trial k+1. The p-values are for the F-test on the model, which tests whether the fit is significantly better than a model with only a constant term. Delay period distribution was the same as in (B).
E. Delay period neural activity from a representative session projected into a 2D subspace found using Principal Components Analysis on 200ms of trial-averaged neural activity from a baseline block. Small dots are two-trial-averages projected into the subspace; large circles are cluster centroids. Colors correspond to the seven reach directions shown in the inset (top left). Gray lines correspond to hypothetical baseline and −45° VMR trial neural trajectories during the delay period; angle (θ_t) is computed between the trajectories for each time point t at a 10ms resolution.
F. The angle between neural trajectories during the delay period (θ_t) is computed at a 50ms resolution between baseline and −45° (−60° for Monkey J) VMR trajectories; each trajectory is a 5-trial average. The gray ‘optimal angle’ line corresponds to the ‘anti-VMR’ angle, i.e., 45° and 60° for Monkeys P and J respectively. Plotted is the correlation between the time during the delay period and the angle (θ_t) between trajectories. The p-values are for the F-test on the model, which tests whether the fit is significantly better than a model with only a constant term. The delay length for Monkey P was drawn randomly on every trial from a uniform distribution from 0ms-650ms; for Monkey J this was between 0ms-750ms. Data is pooled across sessions such that a population of at least 50 tuned neural units (channels on the Utah electrode arrays for Monkey J; channels on the V-probe for Monkey P) during early learning (first 25 trials) are analyzed. Note that data is shown for Monkey J, and not Monkey V, in this panel (see for details).