## 3 Results
### Habituation to the Series of Perturbations  
During the translation cycles, the CoP moved rapidly on the force platform over a large distance in the direction opposite to the fast-phase motion and returned toward a more central position during the slow phase (see Figure 1B,C). Opposite translation profiles produced very similar but reverse CoP motions. The displacements of the CoP during the sequence of the translation cycles were not constant (compare the first and last cycle in Figure 1) but exhibited a progressive decrease in peak-to-peak amplitude. Therefore, the hypothesis that the CoP position post-stimulation may be specified by the continuous postural adjustments occurring during the stimulation period was tested. The top panel (A) of Figure 4 shows the average value across the participants of the ML CoP positions (condition FL-EC) plotted over time, cycle-to-cycle, during the fast left (dark blue) and the slow right phases (light blue) of the translation cycles. At the first cycle, the fast translation to the left moved the CoP to the right of the force platform (upwards in the Figure). During the next slow phase, the CoP showed an ample shift to the left (downwards) to counteract the large perturbation. In the successive cycles, the CoP featured a progressive shift during the fast phases and a recovery towards the initial position during the slow phases (points near zero in the ordinate). Toward the end of the stimulation sequence, the CoP mean position was close to the pre-stimulation position during the slow phases and distant during the fast phases. The exponential fits through the data points (separately for the fast and the slow phases, and separately for all participants) allowed to identify a time constant and an asymptote, the value of which was assumed to indicate the steady state. When the stimulation was administered in the opposite direction (fast phase to the right, FR) a similar picture emerged (not shown in the Figure). Owing to the opposite profile of platform translation and CoP motion condition, the trend in the average ML CoP positions during the fast and the slow phases of the perturbation cycles was increasing during FL (Figure 4A) but decaying during FR. Figure 3: Duration of the post-stimulation effect on the ML CoP position. The bars with a blue outline refer to the fast left (FL) condition, and the bars with a red outline to the fast right (FR) condition. Grey filling refers to EC, white filling to EO. There was no difference in the duration of the post-effect regardless of the asymmetry of the stimulation-cycle profile or of the visual condition. Across all participants, the mean time course of this adaptation (Figure 4B) had a long time constant under all the tested conditions for both the fast and the slow phases (mean \(\pm\) SD; fast phase: FL-EC, 15.3 cycles \(\pm\) 10.9; FL-EO, 28.7 \(\pm\) 22.5; FR-EC, 17.7 \(\pm\) 14.6; FR-EO, 24.7 \(\pm\) 26.4; slow phase, FL-EC, 14.3 cycles \(\pm\) 12.8; FL-EO, 27.5 cycles \(\pm\) 21.6; FR-EC, 14.6 cycles \(\pm\) 19.6; FR-EO, 19.7 cycles \(\pm\) 21.2). Considering the duration of a complete translation cycle (3.8 s), these time constants range from about 1 to 2 min on average, and this variability explains the large SDs of the bars. ANOVA showed no differences between the time constants of the fast and of the slow phases (main effect, F(1.19) = 1.17, \(p\) = 0.29) and between the two translation profile conditions (FL vs. FR, main effect, F(1,19) = 0.22, \(p\) = 0.64). However, there was a significant difference in the time constants between the visual conditions (main effect, F(1,19) = 10.3, \(p\) < 0.01, d = 1.47, \(\pi\) = 0.86) due to the longer time constants with EO compared to with EC. This effect was present for all the cycle phases and profiles and in most of the participants (65% for FL, 55% for FR), revealing a robust effect of vision, whereby no-vision speeded up the achievement of the plateau.