## 3 Results
### Habituation to the Series of Perturbations
Figure 4: Mean ML CoP positions during the fast and slow phases of the stimulation cycles (FL–EC condition) and their asymptotic values obtained by the exponential fit (ensemble averaged group means). (**A**) During the fast phase to the left (dark blue circles), the mean ML CoP position shifted to the right side of the force platform. During the slow phase (light blue circles) it moved to the left (arrows) with respect to the position reached during the fast phase. In the last cycles, the ML CoP position during the slow phase was close to the pre-stimulation position. (**B**) Mean values of the time constant of the exponential function fitted to the ML CoP position during the fast and during the slow phases. The bars with the blue outline refer to FL, and the bars with the red outline to FR. Grey filling denotes EC, and white filling EO. (**C**) For each subject, the mean post-stimulation ML CoP position was plotted against the difference in the asymptotic value of the ML CoP position between the fast and the slow phase for the FL-EC (grey filling with blue outlined circles), FL-EO (white filling with blue outline), FR–EC (grey filling with red outline) and FR–EO (white filling with red outline). (**D**) The mean values of the asymptotes of the fast and the slow phases were reported. Circles with blue outlines refer to FL and the circles with red outlines to FR condition. Grey filling refers to EC, and white filling to EO. The blue and red dotted lines are the mean ML post-stimulation CoP positions in the four conditions. The mean value of the ML CoP asymptotic position, calculated by the exponential fits for the _fast_ phase of the cycles, was always different from the initial ML CoP position (\(t\)-test, \(p<0.01\), d \(>0.93\) and \(\pi>0.8\) for all comparisons). The mean asymptote for the _slow_ half-cycles was instead close to the pre-stimulation position (\(t\)-test, \(p>0.20\) for all comparisons). ANOVA on the asymptotic values showed a difference between cycle profiles (main effect, FR vs. FL, F(1.19) = 13.2, \(p<0.01\), d = 1.67, \(\pi=0.94\)) and an interaction between the cycle profiles and fast or slow phase (F(1.19) = 46.15, \(p<0.0001\), d = 3.11, \(\pi=0.99\)). ANOVA showed no main effect of visual conditions (F(1.19) = 0.038, \(p=0.85\)). Figure 4D shows that the asymptotic values of the fast phase were opposite between the FL and FR conditions (post hoc, \(p<0.0001\) for all comparisons), but not different between FL and FR during the slow phase (post hoc, \(p>0.2\) for all comparisons) both under EC and EO condition. The post hoc test showed a significant difference between the asymptotic value of the fast and of the slow phase within each visual and perturbation profile condition (post hoc, \(p<0.0001\) for all comparisons). Moreover, there was an association between the ML CoP post-stimulation and the displacements of the CoP measured between the fast and the slow phases of the translation cycles. Panel C of Figure 4 shows that, across all participants (FR and FL conditions and EO and EC collapsed), there was a significant relationship between the CoP position post-stimulation and the difference in the asymptotic values of the functions fit the mean CoP positions during the fast and slow phases (regression line, \(y=-0.2\)x \(-0.09\), R\({}^{2}=0.16\), \(p<0.001\)). As a way of summarizing these findings, Figure 4D shows the mean values of the asymptote calculated by the exponential fit on the ML CoP position during the fast and the slow phases of the perturbation cycles. The shift (arrows) from the position imposed by the fast half-cycle to that recorded during the slow half-cycle brings the CoP very close to the post-stimulation position (the dotted horizontal segments).