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Sensorimotor Learning of Dexterous Manipulation 35

manipulation experience with the object. For this comparison, we normal-
ized the T com from the transfer trial (context B) by the negative sign of its
T target , therefore avoiding the statistical complication caused by the different
signs of the two contexts.
Statistical analyses (repeated measures ANOVAs) were designed to assess
within-block learning, interblock interactions, and the effect of the break
duration using the T com and a RI for different experimental conditions.
All tests were performed at the P < .05 significance level. Comparisons of
interest exhibiting statistically significant differences were further analyzed
using posthoc tests with Bonferroni corrections.

3.2.3.2 Model and Simulation
To facilitate the interpretation of our experimental findings, we first tested
a modified version of a dual-rate multiple contexts model (DRMC, [14]),
which supported the protection of a learned context by assuming a
context-independent fast process and a context-dependent slow process.
In this model, the two learning processes have different learning rates
(i.e., fast and slow), but both of them are driven by the motor error from
previous trials. However, using Bayesian Information Criterion, this model
had less accuracy to fit our data in comparison with our following proposed
model (see [33] for details). Here, we propose a novel computational model
based on the nonlinear interactions between two sensorimotor processes
(dual-processes nonlinear interaction model, DPNI). Similar to the DRMC
model, the DPNI model also consists of two sensorimotor adaptation
processes. However, we model the context independent process differently
as a use-dependent sensorimotor memory. Most importantly, to account for
our data, we propose a nonlinear interaction between the two processes
instead of linear summation.
In trial n, the motor error e is determined by the difference between the
motor output y and the ideal compensatory torque to be generated at the lift
onset (i.e., T target ):

enðÞ ¼ T target nðÞ ynðÞ (3.1)
The error-based update equation follows:
x n +1Þ ¼ A nðÞ•x nðÞ + B nðÞ•enðÞ (3.2)
ð
where x is a 2-d vector that represents the internal estimate of the task
dynamics of the two contexts. A and B denote the retention and learning
rates, respectively, that can vary trial-by-trial according to the context of