Figure 7. Relative speed and distance between neural trajectories during 1-2-3-Go.

a) t_s-independent (top) or t_s-dependent (bottom) representation of speed. b) Speed of each neural trajectory, ${\mathrm{\Omega }}^{\left[t_s\right]}$, compared to the speed of the reference trajectory, Ω^[800]. Colored lines show the progression of elapsed time on ${\mathrm{\Omega }}^{\left[t_s\right]}$ $\left({\mathbf{t}}^{[t_s]}\right)$ as a function of elapsed time on Ω^[800] (t^[800]) for different t_s. Shadings indicate median +/− 95% confidence intervals computed from n = 100 bootstrap resamples. Unity line corresponds to no difference in speed. Dashed lines represent the expected relationship between ${\mathbf{t}}^{[t_s]}$ and t^[800] under the internal model hypothesis for an observer with perfect knowledge of t_s. Insets: difference in RMSE under the assumption of t_s-independent speed (left of zero) versus t_s-dependent speed (right of zero). In S1-S2 epoch, both the open-loop and internal hypotheses (H_OL and H_IM) predict t_s-independent speed; t_s-dependent predictions were based on fits of EKF to behavior. In S2-S3 epoch, H_OL predicts t_s-independent speed, and H_IM predicts t_s-dependent speed; the data supports H_IM (red dashed line). In S2-S3 epoch, both hypotheses predict t_s-dependent speed. c) t_s-independent (top) or t_s-dependent (bottom) representation of the speed command. d) Distance $({\delta }^{t_s})$ between nearby states on ${\mathrm{\Omega }}^{\left[t_s\right]}$ and Ω^[800] as a function of time. Horizontal dashed line $\left({\delta }^{t_s}=0\right)$ corresponds to overlapping trajectories. The data supports H_IM (red dashed line). Shadings indicate median +/− 95% confidence intervals computed from n = 100 bootstrap resamples. See also Supplementary Figures 10, 11, and 12.