# Functional Roles of Saccades for a Hand Movement
## 3 Results
### Circle-Drawing Task  
Following a training period, both monkeys were able to smoothly draw a circle from all eight start points in both directions of rotation at success rates up to around 90%. In total, 2,000 trials (two rotation directions \(\times\) eight start points \(\times\) 125 trials) were recorded from each monkey. All of the following analyses were applied to the successful trials in which cursor trajectory was within \(\pm\) 2 SD range from the average and the saccades that directed the gaze within \(\pm\) 3 SD range from the average trajectory of the cursor. [PERSON] performed the task with a movement time of \(0.90\pm 0.14\) s and \(0.97\pm 0.11\) s (mean \(\pm\) SD) in the counterclockwise and clockwise directions, respectively. _[PERSON]_ did it with a movement time of \(0.77\pm 0.08\) s and \(0.71\pm 0.07\) s (mean \(\pm\) SD) in the counterclockwise and clockwise directions, respectively. Similar to the hitting task, both monkeys made several saccades throughout the drawing task (Figure 5A). We focused on the saccades that led the gaze on the way to the target. Therefore, we excluded the saccade within the final 45\({}^{\circ}\) range of the phase and plotted the distribution of phase difference of the saccade against the cursor (Figure 5B). In Monkey H, the distribution seemed to be bimodal with peaks around at 0\({}^{\circ}\) and -100\({}^{\circ}\) in both rotation directions. In contrast, in _Monkey U_, it seemed to be unimodal with a peak around at 0\({}^{\circ}\) in both rotation directions. We defined LS and CS in the drawing task as a saccade that had the phase difference smaller than \(-\)35\({}^{\circ}\) and within \(\pm\)35\({}^{\circ}\), respectively. More than 40% of the saccades were the LS in Monkey H (46% in the counterclockwise  
Figure 4: Effects of the CS on accuracy and precision of the hand movement in the hitting task are shown. Trials are grouped into three depending on the types of saccades during the trial in Monkey H; those without (w/o) CS (520 trials), with CSa (199 trials), and with CSd (67 trials). As a comparison, the result of all trials in Monkey U (556 trials) is also shown. (**A**) Top and bottom panels: average and variance of the cursor position in x-coordinate are shown, respectively (* \(p<\) 0.05). They are evaluated at cursor acceleration maximum (Amax), velocity maximum (Vmax), and acceleration minimum (Amin) point during the hand movement. (**B**) Top and bottom panels: average and variance of movement direction (Dm) are shown, respectively. The current and subsequent trials are shown as filled boxes and white oblique-lined boxes, respectively. An error bar represents a standard deviation in all panels. rotation direction, 44% in the clockwise rotation direction). In contrast, the CS dominated in Monkey U (45% in the counterclockwise rotation direction, 76% in the clockwise rotation direction) (Figure 5C) (Table 2). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Subject**} & \multirow{2}{*}{**Direction 1**} & \multirow{2}{*}{**Trial**} & \multicolumn{3}{c}{**Saccade [Times/Trial] (Number of Trials)**} \\ \cline{4-5}  & & & & **All/Midway 2** & \\ \cline{4-5}  & & & **Total 3** & **LS** & **CS** \\ \hline \multirow{3}{*}{Monkey H} & CCW & 743 & 5.22 (741)/ & 2.33 (735)/ & 2.27 (694)/ \\  & CCW & 751 & 1.81 (723) & 0.83 (457) & 0.86 (447) \\ \cline{3-5}  & \multirow{3}{*}{CCW} & \multirow{3}{*}{749} & 4.77 (751)/ & 1.78 (714)/ & 2.22 (668)/ \\ \cline{3-5}  & & & 1.72 (648) & 0.75 (439) & 0.88 (441) \\ \cline{3-5}  & \multirow{3}{*}{CCW} & \multirow{3}{*}{749} & 4.70 (749)/ & 1.70 (691)/ & 1.80 (638) \\ \cline{3-5}  & & & 3.04 (749) & 0.89 (531) & 1.35 (624) \\ \cline{3-5}  & & & 4.60 (769)/ & 1.10 (679)/ & 2.60 (744)/ \\ \cline{3-5}  & & & 2.29 (769) & 0.16 (110) & 1.73 (729) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Occurrence probability of each type of saccades during the circle-drawing task. Figure 5: Two types of saccades during the circle-drawing task are depicted.