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=== Table 1 ===
Group averages of the centroids.

{| class="wikitable"
|+
!Stimulus
!<math>\langle x\rangle</math>
!<math>\langle y\rangle</math>
!<math>\langle p_x\rangle</math>
!<math>\langle p_y\rangle</math>
|-
|Taken
| colspan="1" rowspan="1" |<small><math>(-1.4\pm5.8)\times10^{-1}</math></small>
| colspan="1" rowspan="1" |<small><math>(2.4\pm8.0)\times10^{-1}</math></small>
| colspan="1" rowspan="1" |<small><math>(-5.8\pm27.0)\times10^{-2}</math></small>
| colspan="1" rowspan="1" |<small><math>(-1.0\pm4.1)\times10^{-1}</math></small>
|-
|Taken Scrambled
| colspan="1" rowspan="1" |<small><math>(-7.7\pm35.0)\times10^{-2}</math></small>
| colspan="1" rowspan="1" |<small><math>(1.1\pm9.3)\times10^{-1}</math></small>
| colspan="1" rowspan="1" |<small><math>(4.1\pm13.0)\times10^{-2}</math></small>
| colspan="1" rowspan="1" |<small><math>(6.3\pm35.0)\times10^{-2}</math></small>
|-
| colspan="1" rowspan="1" |Bang! You’re Dead
| colspan="1" rowspan="1" |<small><math>(1.2\pm4.7)\times10^{-1}</math></small>
| colspan="1" rowspan="1" |<small><math>(3.5\pm74.0)\times10^{-2}</math></small>
| colspan="1" rowspan="1" |<small><math>(2.6\pm33.0)\times10^{-2}</math></small>
| colspan="1" rowspan="1" |<small><math>(-3.0\pm42.0)\times10^{-1}</math></small>
|-
| colspan="1" rowspan="1" |Bang! You’re Dead Scrambled
| colspan="1" rowspan="1" |<small><math>(1.4\pm5.7)\times10^{-1}</math></small>
| colspan="1" rowspan="1" |<small><math>(-2.6\pm7.5)\times10^{-1}</math></small>
| colspan="1" rowspan="1" |<small><math>(-1.5\pm2.8)\times10^{-1}</math></small>
| colspan="1" rowspan="1" |<small><math>(-5.5\pm53.0)\times10^{-2}</math></small>
|-
| colspan="1" rowspan="1" |Rest (Pre-Taken)
| colspan="1" rowspan="1" |<small><math>(-1.3\pm4.6.0)\times10^{-1}</math></small>
| colspan="1" rowspan="1" |<small><math>(2.0\pm1.4)\times10^{0}</math></small>
| colspan="1" rowspan="1" |<small><math>(9.1\pm19.0)\times10^{-2}</math></small>
| colspan="1" rowspan="1" |<small><math>(-6.3\pm7.3)\times10^{-1}</math></small>
|-
| colspan="1" rowspan="1" |Rest (Pre-BYD)
| colspan="1" rowspan="1" |<small><math>(1.1\pm66.0)\times10^{-3}</math></small>
| colspan="1" rowspan="1" |<small><math>(1.9\pm1.2)\times10^{0}</math></small>
| colspan="1" rowspan="1" |<small><math>(1.0\pm26.0)\times10^{-2}</math></small>
| colspan="1" rowspan="1" |<small><math>(-4.3\pm7.5)\times10^{-1}</math></small>
|}

Significant differences are only noted for the rest acquired before Taken and Bang! You’re Dead when comparing the average y location to either of their task counterparts (scrambled and intact stimulus).

Group averages of the centroids.

This analysis revealed two notable findings. First, there was a lack of significant differences in the momenta of the brain along the x and y direction. Second, the averages in momenta were not significantly different from 0 at the group level. The positive or negative momenta come from the competing time derivative of the probability and location of the electrode. Since the momenta average to 0, there is an equal number of anterior and posterior electrodes with both increases and decreases in probability.

Further, we examined changes in the probability values in both resting and active states. Animations of the probability distributions are present in Supplementary Material 1. In these animations, the differences in rest and task are apparent through the evolution of probability in time.