Many different approaches exist to determine functional connectivity from time series data (Pereda et al., 2005 (link)). Different methods employ distinct coupling measures (e.g., linear or nonlinear measures) and different strategies for assigning network edges. In this work we utilize two measures of linear coupling: the cross correlation and coherence. We outline here our particular data analysis approach; a detailed discussion, including the statistical properties and simulation results for the cross correlation measure, may be found in (Kramer et al., 2009 ). Before applying the coupling analysis, we process the ECoG data from each seizure and subject in the following way. For the cross correlation analysis, we first notch filter (third order Butterworth, zero-phase digital filtering) the data at 60 Hz and 120 Hz to remove line noise, high pass filter the data above 1 Hz to avoid slow drift, and low pass filter the data below 150 Hz to avoid higher frequency line noise harmonics. For the coherence measure we do not perform these filtering operations, and instead focus on frequency intervals that exclude narrowband noise peaks and slow drift oscillations. Next, we subtract the average reference from each electrode to reduce the contribution of the reference electrode to coupling (Towle et al., 1999 (link)). Then we divide the ECoG data into non-overlapping windows of duration 1.024s. We choose ~1s intervals here to balance the requirements of approximate stationarity of the time series (requiring short epochs) and of sufficient data to allow accurate coupling estimates (requiring long epochs). Finally, we normalize the data from each electrode within each window to have zero mean and unit variance.
With the data processed in this way, we construct functional networks for each window in three steps. We briefly describe these steps here; a complete discussion may be found in (Kramer et al., 2009 ). In the first step we choose two electrodes, and apply either the cross correlation or the coherence to the ECoG data. For the correlation, we select the maximum correlation within time delays of +/− 250 ms. This interval of delays allows an assessment of the variance in the cross correlation over time delays which is used to calculate the significance of the correlation (Kramer et al., 2009 ). For the coherence, we use the multitaper method with a time bandwidth product of 5 and 8 tapers. For the choices of window size (~1s) and time bandwidth product (5), the half-bandwidth is 5 Hz. We therefore analyze the coherence in evenly spaced 10 Hz bands (the full bandwidth) - {5–15 Hz, 15–25 Hz, 25–35 Hz, and 35–45 Hz} - for all electrode pairs. These bands cover traditional oscillatory classes: 5–15 Hz, theta and alpha; 15–25 Hz, beta; 25–35 Hz and 35–45 Hz, gamma (Buzsaki & Draguhn, 2004 (link)). Low frequencies are omitted to avoid low frequency drift in the data. Second, we determine the statistical significance of these coupling results through analytic procedures (Mitra & Bokil, 2008 ; Kramer et al., 2009 ). Third, we correct for multiple significance tests using a linear step-up procedure controlling the false detection rate (FDR) with q=0.05. For this choice of q, 5% of the network connections are expected to be falsely declared (Benjamini & Hochberg, 1995 ). This procedure results in a thresholding of the significance tests (i.e., the p-values) of the coupling measure - not of the correlation or coherence value itself - for each interval of data (Kramer et al., 2009 ). The resulting network in each window possesses an associated measure of uncertainty, namely the expected number of edges incorrectly declared present.
With the data processed in this way, we construct functional networks for each window in three steps. We briefly describe these steps here; a complete discussion may be found in (Kramer et al., 2009 ). In the first step we choose two electrodes, and apply either the cross correlation or the coherence to the ECoG data. For the correlation, we select the maximum correlation within time delays of +/− 250 ms. This interval of delays allows an assessment of the variance in the cross correlation over time delays which is used to calculate the significance of the correlation (Kramer et al., 2009 ). For the coherence, we use the multitaper method with a time bandwidth product of 5 and 8 tapers. For the choices of window size (~1s) and time bandwidth product (5), the half-bandwidth is 5 Hz. We therefore analyze the coherence in evenly spaced 10 Hz bands (the full bandwidth) - {5–15 Hz, 15–25 Hz, 25–35 Hz, and 35–45 Hz} - for all electrode pairs. These bands cover traditional oscillatory classes: 5–15 Hz, theta and alpha; 15–25 Hz, beta; 25–35 Hz and 35–45 Hz, gamma (Buzsaki & Draguhn, 2004 (link)). Low frequencies are omitted to avoid low frequency drift in the data. Second, we determine the statistical significance of these coupling results through analytic procedures (Mitra & Bokil, 2008 ; Kramer et al., 2009 ). Third, we correct for multiple significance tests using a linear step-up procedure controlling the false detection rate (FDR) with q=0.05. For this choice of q, 5% of the network connections are expected to be falsely declared (Benjamini & Hochberg, 1995 ). This procedure results in a thresholding of the significance tests (i.e., the p-values) of the coupling measure - not of the correlation or coherence value itself - for each interval of data (Kramer et al., 2009 ). The resulting network in each window possesses an associated measure of uncertainty, namely the expected number of edges incorrectly declared present.
