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Gianfranco (talk | contribs) (Created page with "== Model == Each of the j electrodes is described by an ordered pair (<math>x_j,y_j,z_j</math>) in 3-dimensional space. To complete this analysis, the electrodes were first projected onto the (<math>x,y</math>) plane, removing the depth of the head. Figure 1A shows the locations of each electrode in this 2d-space. Following this projection, the time courses for each of the 92 electrodes were Hilbert transformed and then normalized following the procedure listed using Eq...") |
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== Model == | == Model == | ||
Each of the j electrodes is described by an ordered pair (<math>x_j,y_j,z_j</math>) in 3-dimensional space. To complete this analysis, the electrodes were first projected onto the | Each of the j electrodes is described by an ordered pair (<math>x_j,y_j,z_j</math>) in 3-dimensional space. To complete this analysis, the electrodes were first projected onto the <math>( x,y )</math> plane, removing the depth of the head. Figure 1A shows the locations of each electrode in this 2d-space. Following this projection, the time courses for each of the 92 electrodes were Hilbert transformed and then normalized following the procedure listed using Eq. (2). A probability was defined in this electrode-position space as the square of the Hilbert transformed time course (Eq. 3), analogous to the wavefunctions of quantum mechanics. Eight regions Anterior L/R, Posterior L/R, Parietal L/R, Occipital L/R) were then defined by grouping the 92 electrodes, and the frequencies of entering each region fG were obtained by summing the probabilities electrodes within the group, then integrating in time. | ||
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| width="33%" | | | width="33%" | | ||
| width="33%" |{{CD1}}<math>Prob_G(t)=\sum_{j=1}^{92} \Psi_k^* (t)\times\Psi_k (t); f_G=\tfrac{1}{T}\sum_{j=1}^{T}Prob_G(t)</math>{{CD2}} | | width="33%" |{{CD1}} <math>Prob_G(t)=\sum_{j=1}^{92} \Psi_k^* (t)\times\Psi_k (t); f_G=\tfrac{1}{T}\sum_{j=1}^{T}Prob_G(t)</math> {{CD2}} | ||
| width="33%" align="right" |<math>(6)</math> | | width="33%" align="right" |<math>(6)</math> | ||
|} | |} |
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