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Using simply one additional SU per cell (i.e., M=6) would require matrices of length 612.
For example, matrices of length 4 have not been considered for a P-value equal to 10-3, and matrices of length smaller than 10 have not be considered for a P-value equal to 10-6.
Lemma 6 Let M and N be two matrices of length m such that there exists a permutation π on {1,..., m} satisfying, for each letter x of Σ, M i, x) = N(π i, x).
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μ s (l− k) is the mean value of (5) over all sub-matrices of length l− k along the diagonal of A, and can be pre-computed for a given A. We disallow domains where there are fewer than 100 sub-matrices available to compute the mean.
Lemma 5 Let M be a matrix of length m.
So a matrix of length m cannot not achieve a P-value smaller than 1 4 m MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGacaGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqaIXaqmaeaacqaI0aandaahaaqabeaacqWGTbqBaaaaaaaa@2FDC@.
The resultant p value and correlation matrices were merged across the 11 data sets by taking the median values (across the sets in which the gene was contained), giving a final matrix of length 20,121.
Lemma 2 Let M be a matrix of length m, let α and β be two score bounds defining a score range for which we want to compute the score distribution Q.
We tried several P-values, from 10-3 to 10-6, for all matrices of suitable length.
Regarding the precoding complexity: The SDMA precoder on each subchannel can be seen as a size 12N T ×2N R matrix filter of length equal to N+L−1, where L is the fixed length of the channel impulse responses (see the Appendix 1 for the details).
For example, Figure 2 shows the logo [ 13] of the matrix MA0045 of length 16 from the Jaspar database.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com