FIG. 1.

Illustration of superposition for two-rate, linear time-invariant state-space model (SSM_LTI,2) [a_slow = 0.992, b_slow = 0.02, a_fast = 0.59, b_fast = 0.21, taken from the empirical estimates reported by Smith and colleagues (2006)] in the counterperturbation paradigm (CP). See Eq. 2 in the main text for the state-space model. The left column shows the input perturbation functions (abscissa is movement number n), whereas the right column shows both the outputs [equivalently in terms of directional error (red) and net sensorimotor map (black)] and the state variables [slow (blue) and fast (green)]. The rows correspond to a decomposition of the net input [(from top): initial adaptation stimulus, counterperturbation stimulus, readaptation stimulus, summed inputs]. As a consequence of superposition, the shaded plot in the bottom right corner is equal to both 1) the sum of the outputs to the separate inputs (sum down right column) and 2) the output to the summed inputs (transform from left to right in the bottom row). In the CP paradigm, superposition leads to obvious savings (i.e., a faster apparent rate of adaptation during the readaptation phase compared with the initial adaptation phase). Perturbation function for this CP paradigm: 0° for 1 ≤ n ≤ 10, 30° for 11 ≤ n ≤ 100, −30° for 101 ≤ n ≤ 103, 30° for 104 ≤ n ≤ 150.