## 2 Materials and Methods
### Data Acquisition and Treatment  
The position of the CoP was recorded for the entire duration of the trials by the force platform (Kistler 9286 BA, Winterthur, Switzerland) at a sampling frequency of 140 Hz, and was expressed in platform coordinates. No artefacts were produced on the force-platform output by the translations of the motorized platform. The force-platform data were stored in a PC for offline analysis. For each participant and condition, the mean ML and AP CoP positions were calculated on a time window of 1 min duration, just before the onset of platform motion (these mean CoP values were the reference for further analysis) and at the end of the last platform translation cycle. For the same time windows, the standard deviation (SD) of the ML and AP CoP traces over time were also calculated and accepted as an index of the CoP sway around its mean position. The pre-/post-stimulation difference in the SD of the ML CoP trace in the quiet stance periods (visual conditions collapsed) was plotted against the extent of the pre-/post-stimulation ML CoP displacement. This distribution was studied by a linear regression model and the coefficient of determination (R\({}^{2}\)) was calculated to assess the goodness of the fit.  
The mean ML position of the CoP was also calculated cycle by cycle, for each of the successive perturbation cycles, during both the fast and the slow phases of the translations using a software developed in LabVIEW (National Instruments, Austin, TX, USA). These mean positions, averaged across all subjects, changed over time featuring an exponential trend from the early to the late trials. The data were therefore fitted with an exponential model (y = A + Be\({}^{-t/\tau}\)) for each participant and for each condition by means of the iterative conjugate gradient method of the Excel(r) Solver Utility [39]. A, B and \(\tau\) (tau) parameters were computed by using the minimum sum squared algorithm. Tau is the time-constant of the exponential function expressed in cycles, where the duration of an entire translation cycle is 3.8 s (the fast phase lasted 1 s and the slow phase lasted 2.8 s). A is the value at steady state of the function (asymptote), and A + B the value of the intercept with the ordinate at the first cycle [40]. The difference between the asymptotic value of the ML CoP position during the fast and the slow phases of the translation cycles was calculated and plotted against the ML CoP position post-stimulation. This relationship was studied by a linear regression model (asymmetric translation profile and visual conditions collapsed) and the coefficient of determination (R\({}^{2}\)) was calculated.  
The duration of the post-effect produced by the stimulation on the ML CoP position was estimated for each participant according to the following procedure. Each successive sample of the CoP position acquired in the post-stimulation epoch was compared by the one-sample Student's \(t\)-test to the mean position of the CoP computed during 1 min pre-stimulation. The time-period during which the \(t\)-value of the above comparison bypassed the critical \(t\)-value corresponding to a probability of \(\alpha\) = 0.05 and remained above that value for at least 500 ms was taken as the duration of the post-effect [41]. The relationship between the amplitude of the ML CoP position post-stimulation and the duration of the post-effect was studied by a linear regression model and the R\({}^{2}\) was calculated.