First we calculated the baseline probability of obtaining swap errors by chance.
Our aim is to repeatedly find a candidate to swap with, where, such that the weight of the new mapping,, where and are the edges obtained by swapping e and, is higher than.
The solution to the adjoint system is separated into two parts, namely the self-adjoint part, which is linearly proportional to the solution of the governing equation; and the non-self-adjoint part, which is obtained by swapping the locations of the incident wave and the receiving planes in the simulation model.
where now r ˜ denotes the vector r in the frame obtained by swapping two Cartesian coordinates.
where snr b [k] is defined as in Definition 2. Also, let R 5[k], R 6[k], and R 7[k] be obtained by swapping the indices a and b in R 2[k], R 3[k], and R 4[k], respectively.
Given a vector p and the corresponding d=X×p, any differently sorted vector of durations would be obtained by swapping the rows of X. Further, note that X does not have an inverse matrix, and therefore there is no linear transformation from durations to events.
(H ) Cross-correlation function obtained after swapping the green channels between pairs of time traces (shuffled data) also reveals the absence of technical bias.
By the symmetry between strain a and strain b, R 0 a (Q b *) can be obtained by swapping the indexes a and b in the above equations.
Similar results were obtained on swapping GFP and mRFP reporter sequences, ruling out potential artefacts due to differences in their coding sequences or stability of the reporter proteins (supplementary Fig S4B online).
For subsequent analyses, we focused on the 16907 and 2307 high-confidence sites (Additional file 2: sFile 1), which had higher statistical significance than any of the "negative" peaks obtained by swapping the ChIP-Seq and control channels.
