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Chunk #14 — II. Methods and Material — C. MSC

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On the recording reference contribution to EEG correlation, phase synchrony, and coherence.
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that the conclusion is true only for positive cross correlations in (11). The reason is that the cross-power Sb1b2(w) may be negative, and in (12), only the absolute value of the cross-power Sb1b2(w) is used. In (11), if we further assume that Sb1b1(w)=Sb2b2(w)=1, which is similarly assumed in [36], (11) becomes (13)MSCx1x2=(Sb1b2(w)+SRR(w))2(1+SRR(w))2. Therefore, given Sb1b2(w), MSCx1x2 is a function of SRR(w) (> 0). If Sb1b2(w)>0, then the right-hand side of (13) is the same as the upper bound in (12) and MSCx1x2 monotonically increases to one as SRR(w) increases in [0, +∞), which is discussed in [36]. In Fig. 1(F), one can see that MSCx1x2 is a monotonic increasing function of reference signal power for each given positive cross-power Sb1b2(w). Hence, in this case, the MSC value of two referential signals x1 and x2 is always greater than that of nonreferential signals b1 and b2, i.e., the reference signal always increases MSC in this case, and only in this case is the conclusion in [36] true. If Sb1b2(w)<0, then it is easy to get the critical point at SRR(w)=−Sb1b2(w) from (13). In this case, MSCx1x2 monotonically decreases to zero as SRR(w) varies in [0,−Sb1b2(w)) and monotonically increases to one as