Optimal gain model.

<p>A) Error estimation model. The random errors are Gaussian distributed. For any given error as indicated by the green dot the estimate for that error is contaminated by perceptual noise of the form . Depending on the current perceptual noise instance the participant will either answer correctly for the left/right judgement task (white area under the curve) or incorrectly (grey area). The higher the variance in perceptual noise compared to the motor noise the higher the chance of perceiving the error incorrectly in which case correction movements would lead to bigger errors on average. Thus, to be able to correct for the perceived error in an optimal way to minimize end-point variance the level of perceptual noise has to be weighed against prior knowledge of the distribution of the pointing errors . B) Theoretical ratio between the standard deviations in final endpoint after correcting and initial error versus the correction gain for several different levels of perceptual noise. Values below one mean better performance after making the corrections. Values above one mean worse performance. Optimal gains can be estimated by determining the gains for which the end point variance after correcting is lowest (red curve).</p

Generalisation results for Experiments 2 and 3.

<p>A) Results for the 2-Pair Condition of Experiment 2. B) Results for the 5-Pair Condition of Experiment 2. C) Results for Experiment 3 in which 3 training pairs were used. In each graph the numbers in the lower right corner indicate how many participants learned and the total number of participants for that condition. Axes and colour coding are the same as for <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004172#pcbi.1004172.g003" target="_blank">Fig. 3</a>. The results indicate that extrapolation of learning does not occur in a linear manner. The Mixture-of-Kalman-Filters performs better at capturing the generalisation results.</p

The Mixture-of-Kalman-Filters Model.

<p>A) The updating process of a single Kalman filter. On each trial a prior internal estimate (blue) is combined with sensory feedback (red) to obtain a posterior estimate (black) of the mapping that should have been used. This posterior estimate serves as the prior estimate for the next trial through propagation in time, which is not noise free (thus adding <i>σ</i>_{<i>process</i>}). B) Mixture-of-Kalman-Filters. For each shape along the shape scale a separate Kalman Filter updates the associated mapping. C) Mixture-of-Kalman-Filters updates over time. The initial prior estimates for each Kalman Filter (left) are being updated on each trial according to the shape seen and the feedback received (middle) to obtain the posterior estimates (right). The feedback is most precise for the shape on the current trial (indicated in red) and the precision of the feedback decreases for shapes further away along the shape scale. After only a few iterations the pattern for generalisation already starts to emerge in the estimates of the Mixture-of-Kalman-Filters Model.</p

Experimental design and setup.

<p>A) Participants were seated in front of a touch screen on which targets were displayed. Participants performed pointing movement either towards the touch screen with their index finger or on a graphics tablet using a stylus. To control for visual feedback participants wore shutter glasses that were only transparent as long as a mouse button was being held. A chin rest restricted head movements. B) The complexity of the visuomotor mapping depends on the response mode (direct–touch screen vs. indirect–graphics tablet). Direct condition (top): for touch screen responses the pointing movement is directly towards the visual target location. Indirect condition (bottom): for tablet responses the pointing movement is on the horizontal plane of the tablet involving an additional mapping from the vertical image screen to the horizontal response plane. C) Sequence for a single trial. Participants initiated stimulus onset and shutter glasses transparency by pressing the right mouse button, such that with the onset of the movement visual feedback was prevented. After movement completion participants indicated whether they thought they had landed left or right of target. At the end of each trial they received a score based on absolute pointing accuracy.</p

Generalisation results of Experiment 1.

<p>Results are shown for participants that learned the cued mappings (7 out of 12 participants). The x-axis indicates the training and test shape morph factors. The y-axis indicates the mapping that participants applied for each shape. The continuous horizontal and tilted black lines indicate the no-learning prediction and the trained linear relationship, respectively. The black dashed line indicates the prediction for linear inter/extrapolation based on the linear fits of the training results. Coloured disks indicate single participant results for the corresponding test shape (red, blue and green disks represent trained shapes, interpolation shapes and extrapolation shapes, respectively). Black circles and error bars indicate the mean and standard deviation across participants. The yellow line and shaded area show the Mixture-of-Kalman-Filters Model mean and standard deviation across participants. The results indicate that the learning for 2 trained shape-mappings pairs transfers to the other shapes on the same morph scale. Both linear generalisation and the Mixture-of-Kalman-Filters Model seem to capture the observed pattern of generalisation.</p

Shape definition parameters.

<p>Each shape has a separate morph factor which is defined by the ratio between the inner and outer radii of the shape </p><p></p><p><mi>ρ</mi><mo>=</mo></p><p></p><p><mi>r</mi><mi>i</mi></p><p><mi>r</mi><mi>o</mi></p><p></p><p></p><p></p>. The bulgy spikes are obtained by making the radius <i>r</i> dependent on the angle <i>θ</i> within the shape via: <p></p><p><mi>r</mi><mo stretchy="false">(</mo><mi>θ</mi><mo stretchy="false">)</mo><mo>=</mo></p><p><mi>r</mi><mi>i</mi></p><mo></mo><p><mi>e</mi></p><p></p><p><mo stretchy="true">(</mo></p><p></p><p><mi>θ</mi><mo>−</mo></p><p><mi>θ</mi><mi>i</mi></p><p></p><p></p><p><mi>θ</mi><mi>o</mi></p><mo>−</mo><p><mi>θ</mi><mi>i</mi></p><p></p><p></p><mo stretchy="true">)</mo><p></p><mi>ln</mi><p><mo stretchy="true">(</mo></p><p></p><p><mi>r</mi><mi>i</mi></p><p><mi>r</mi><mi>o</mi></p><p></p><mo stretchy="true">)</mo><p></p><p></p><p></p><p></p><p></p>. The inner and outer radii for each <i>ρ</i> were chosen such that the surface area matched that of a circular disk with radius <i>R</i> = 1.3 deg (12.5 mm). The two radii were defined as: <p></p><p></p><p><mi>r</mi><mi>o</mi></p><mo>=</mo><mi>R</mi><p></p><p></p><p><mn>2</mn><mo></mo><mi>ln</mi></p><p><mo stretchy="true">(</mo><mi>ρ</mi><mo stretchy="true">)</mo></p><p></p><p></p><p><mi>ρ</mi><mn>2</mn></p><mo>−</mo><mn>1</mn><p></p><p></p><p></p><p></p><p></p> for (0 < <i>ρ</i> < 1), <i>r</i>_<i>o</i> = <i>R</i> for (<i>ρ</i> = 1) and <i>r</i>_<i>i</i> = <i>ρ</i><i>r</i>_<i>o</i>. For a full description of the shape definition see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004172#pcbi.1004172.s001" target="_blank">S1 Text</a>.<p></p

Results Experiment 2: secondary corrections.

<p>A) and B) shows the perceptual noise for the left/right discrimination of the errors before and after making secondary corrective movements and the standard deviation in random error respectively. The median and 25% and 75% percentiles across participants for each condition are indicated by the bars and the error bars respectively (median and 75% percentile for the after correction are 144 mm and approaching infinity respectively). The separate points indicate the results for individual participants (filled symbols indicate performance significantly above chance). C) The measured correction gain vs. the optimal gain for each participant. The predicted optimal gains are generally relatively low which is consistent with participants' behavior. D) Measured ratio between the standard deviations in final endpoint and initial error versus the predicted error ratio. Values below one mean that participants' variance was reduced after making the corrections. Values of one mean no change and values above one mean participants' performance became worse by making corrections. As predicted from the level of perceptual noise and the resulting low correction gains participants hardly improve through correcting.</p

Results Experiment 3: visual feedback.

<p>Similar to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0078757#pone-0078757-g003" target="_blank">Figure 3</a> except that participants received either unreliable or reliable visual feedback of their initial pointing position. A,B) shows the perceptual noise for the left/right discrimination of the errors and the motor noise respectively, before and after making secondary corrective movements. The median and 25% and 75% percentiles across participants for each condition are indicated by the bars and the error bars respectively (medians for after corrections approach infinity). The separate points indicate the results for individual participants (filled symbols indicate performance significantly above chance). The dashed line shows the average across participants for the standard deviation in initial random pointing error . C) Behavioral gain vs. the optimal gain for each participant for the two correction conditions with visual feedback. With more reliable visual feedback correction gains generally increase as predicted. D) Behavioral endpoint versus initial error ratio vs. the predicted error ratio. With more reliable visual feedback end-point variance is reduced the most.</p

Haptic adaptation to slant:no transfer between exploration modes

\u3cp\u3eHuman touch is an inherently active sense: to estimate an object's shape humans often move their hand across its surface. This way the object is sampled both in a serial (sampling different parts of the object across time) and parallel fashion (sampling using different parts of the hand simultaneously). Both the serial (moving a single finger) and parallel (static contact with the entire hand) exploration modes provide reliable and similar global shape information, suggesting the possibility that this information is shared early in the sensory cortex. In contrast, we here show the opposite. Using an adaptation-and-transfer paradigm, a change in haptic perception was induced by slant-adaptation using either the serial or parallel exploration mode. A unified shape-based coding would predict that this would equally affect perception using other exploration modes. However, we found that adaptation-induced perceptual changes did not transfer between exploration modes. Instead, serial and parallel exploration components adapted simultaneously, but to different kinaesthetic aspects of exploration behaviour rather than object-shape per se. These results indicate that a potential combination of information from different exploration modes can only occur at down-stream cortical processing stages, at which adaptation is no longer effective.\u3c/p\u3