Probability density functions of the applied noise.

<p>Three types of noise distributions (normal, uniform and lognormal) with three different standard deviations were considered. For each type of distribution, the expectation value of the noise is zero, whereas the standard deviation <i>σ</i>_<i>N</i> varies from 0.5 to 2, resulting in different noise levels.</p

Actual and estimated correction gain <i>B</i>.

<p>Time series with actual correction gains <i>B</i> of 0.25, 0.5 and 0.75; different trial length <i>n</i> (from 10 to 800); and three distributions of noise (normal, uniform, and lognormal) were generated using <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0158466#pone.0158466.e008" target="_blank">Eq 7</a>. The correction gain <i>B</i> was estimated for each time series using both the Levenberg-Marquardt least-square algorithm (red) and the Adjusted Yule-Walker (AYW) method (blue), and then compared with the actual correction gain <i>B</i> (green). The simulations were repeated 1000 times for each algorithm and each <i>n</i>. The estimation by the Levenberg-Marquardt algorithm yielded a substantial bias, whereas the AYW method significantly reduced the bias for large enough <i>n</i>. These results remained unchanged for the noise sampled from a Gaussian (A), a uniform (B), or an asymmetric lognomal (C) distribution. In addition, the bias from the Levenberg-Marquardt algorithm and the improvement by the AYW method were not affected by the magnitude of the noise level <i>σ</i>_<i>N</i> (D).</p

Illustration of the analysis method and a representative data set.

<p>Illustration of the analysis method and a representative data set.</p

Absence of systematic changes in the release velocity with practice.

<p>The release velocities for each subject in each group are shown for all practice trials. Linear fits to the last three days are also shown. There was no systematic decreases in velocity as would be expected from speed-accuracy trade-off. Data were smoothed with a third-order Savitzky-Golay filter with frame size = 101.</p

Error amplification led to modest increases in participants’ error correction gain <i>B</i>, but larger decreases in execution and planning noise variance, <i>σ</i>_<i>EX</i>² and <i>σ</i>_<i>PL</i>², respectively.

<p>Bars show: Day 3 (before error amplification), Day 6 (last day of practice with error amplification), and the change from Day 6 –Day 3. Error bars show the between-subjects standard deviation. The manipulation conditions were: C = control (black); D = deterministic error amplification (red), S = stochastic error amplification (blue). *Groups significantly different than the control at <i>p</i> < 0.05.</p

Neuromotor Noise Is Malleable by Amplifying Perceived Errors

<div><p>Variability in motor performance results from the interplay of error correction and neuromotor noise. This study examined whether visual amplification of error, previously shown to improve performance, affects not only error correction, but also neuromotor noise, typically regarded as inaccessible to intervention. Seven groups of healthy individuals, with six participants in each group, practiced a virtual throwing task for three days until reaching a performance plateau. Over three more days of practice, six of the groups received different magnitudes of visual error amplification; three of these groups also had noise added. An additional control group was not subjected to any manipulations for all six practice days. The results showed that the control group did not improve further after the first three practice days, but the error amplification groups continued to decrease their error under the manipulations. Analysis of the temporal structure of participants’ corrective actions based on stochastic learning models revealed that these performance gains were attained by reducing neuromotor noise and, to a considerably lesser degree, by increasing the size of corrective actions. Based on these results, error amplification presents a promising intervention to improve motor function by decreasing neuromotor noise after performance has reached an asymptote. These results are relevant for patients with neurological disorders and the elderly. More fundamentally, these results suggest that neuromotor noise may be accessible to practice interventions.</p></div

Experimental design and protocol.

<p>Three subject groups received deterministic error amplification (DEA) of varying amplitudes <i>A</i> with a gain of 1.5, 2.0, and 2.5. Three other groups received stochastic error amplification (SEA), in which a sample from a uniform white noise was added to the amplified error (with mean amplification factors <i>A</i> of 1.5, 2.0, and 2.5). A control group received no error manipulation. All groups practiced the task for three days without manipulations; on three subsequent days, the six experimental groups, DEA and SEA, received error amplification.</p

Summary data showing that error amplification decreased the error <i>D-min</i>.

<p>Bars show: Day 3 (before error amplification), Day 6 (last day of practice with error amplification), and the change from Day 6 –Day 3. Participants received either deterministic (D; red) or stochastic (S; blue) error amplification on the last three practice days with amplification factors of 1.5, 2.0, or 2.5. The control group (C; black) received no error amplification. Error bars: between-subjects standard deviation. *Groups significantly different than the control at <i>p</i> < .05.</p

Changes in release velocity variability with practice.

<p>The six error amplification groups showed no significant changes. The control group slightly increased the variability of their release velocity with continued practice. Panels <b>A-C</b> shows the standard deviation of the release velocity for the last day of practice with no manipulation (Day 3) and three subsequent days (Day 4–6) in which subjects received either no error amplification (controls; panel <b>A</b>) or different magnitudes of deterministic or stochastic error amplification (DEA or SEA, respectively; panels <b>B</b> and <b>C</b>). Data were averaged in 20-trial bins. The insets in each plot show the averaged data for all six practice days. Panel <b>D</b> shows the change from Day 6 –Day 3. Error bars: between-subjects standard deviation. *Indicated that the change is significantly different from zero <i>p</i> < .05. C = control (no manipulation; black); D = deterministic error amplification (red), S = stochastic error amplification (blue).</p

With error amplification execution noise <i>σ</i>_<i>EX</i>² decreased consistently; planning noise <i>σ</i>_<i>PL</i>² dropped more abruptly.

<p>The estimated <i>σ</i>_<i>EX</i>² and <i>σ</i>_<i>PL</i>² are shown for the last day without manipulation (Day 3), and the three days with error amplification (Day 4–6). The data are averaged across all subjects in each group. Three levels of amplification were used for each DEA and SEA group: 1.5, 2.0, and 2.5.</p