Sentence examples for we renumbered from inspiring English sources

* Note that the figure numbers in the charts here are different from those in the book, because we renumbered the chapters after submitting the manuscript.

We renumbered one of the duplicates, depending on the neighborhood.

First, for the sake of convenient interpretation, we renumber the states of the QBD-M process, i.e. each ((i,j)) state now corresponds to state with assigned index (j* {mathcal {N}}+1)+i).

Moreover, all eigenvalues are real and bounded below by Corollaries 1 and 3. Therefore, we may renumber them as (lambda_{0} le lambda_{1} le lambda_{2} lecdots), which are counted according to their multiplicity.

Now, if there exists a subset B of {1,2,3,…..k} with n + 2 elements such that Inf i ∈ B W i > α Open image in new window, we will renumber the family W to give a family P= {P1,P2,….P k } such that Inf 1 ≤ i ≤ n + 2 P i > α Open image in new window.

First, we let β i  =  β(1 −  ɛ i ) and chose ten β i parameters uniformly on (0,1); we sorted and renumbered so that β10 was largest.

After recognizing this extensive synteny, we oriented and renumbered the Miscanthus linkage groups to emphasize this correspondence between Miscanthus and sorghum.

To calculate π for CDS and UTR sequences that spanned multiple fragments, we concatenated the VCF files and then renumbered the position field starting with position "1" through the total length of all concatenated fragments.

We removed the figure explaining the BED format and renumbered the figures.

We have added these data in a new Figure 4 figure supplement 2 (renumbered following removal of our original Figure 4, as per reviewers' suggestions) and include details of these analyses in the Methods.

Subsequent paragraphs renumbered.