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If T and G have the same ranked topology, then g i = i + 1.
For example, in Figure 1c, k2,0,1 = 1 and k2,1,1 = 2, while in Figure 1d, k2,0,1 = 2 and k2,1,1 = 3, although the two gene trees have the same ranked topology and m2 = 1 for both cases.
Similar(58)
However, when considering thousands of conformations, 13 categories are not sufficient for efficiently ranking, since many non-equivalent conformations have the same rank (granularity 0.05).
Logically equivalent claims have the same rank.
We assume that g and m have the same rank.
When v2 is ranked, nodes v1 and u1 are in set M and have the same rank r.
It is sometimes the case that a theory proposes that the population means on two variables should have the same rank order across a set of experimental conditions.
According to Equation 15, Hypothesis 1 is true only if all the Hbmin(α i ), where 1 ≤ i ≤ 2 m − 1, have the same rank.
Rank of the solution is the first priority for sorting and crowding distance is the second priority (i.e. the solution which has better rank number is prior but if two solutions have the same rank number, the solution that has bigger crowding distance is prior).
The individuals in population at the first time are selected based on rank and the member with the lower rank is chosen, but if two solutions have the same rank, the remainder of the population is selected based on crowding distance between members.
Assume that nodes v 1 and u 1 belong to the same layer of T spt(G[U∪C]), with v 2 and u 2 as their parents, respectively, and all of them have the same rank, then neither v 2 and u 1 nor u 2 and v 1 are adjacent in G[U∪C]; 3.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com