A matrix M is doubly stochastic, i.e., each column and each row of M sum to 1, if and only if for some N < ∞ there are permutation matrices σ1, …, σ N and positive scalars α1, …, α N ∈ [0,1] such that α1 + ⋯ + α n = 1 and M = α1 σ1 + ⋯ + α N σ N. Therefore, the weighted sum of the permutation matrices in Σ T yields a doubly stochastic matrix M T as introduced above.
During the recovery process, there is permutation ambiguity, that is, the order of the users may be lost and again the user signals will be recovered up to a scalar multiple.
In the case of the Cry3Bb1 response phenotype there are possible permutations between high and low response populations, and all permutations were used to create the null distribution.
For diapause versus non-diapause populations there are potential permutations, among which we randomly selected 1,000 to create the null distribution.
You are now able to sprint via the use of equipment permutations (there are other permutations, we just don't know what they are yet) available at certain points in the levels.
Today in art there are so many permutations and gradations of space that there could be dozens of names for them.
By one estimate there are 50,000 different permutations of carbon nanotubes alone.
The idea here is that the more states you put in play, the more permutations there are that lead to victory.
You might well wonder why it is that, given just how many Apple domain permutations there are out there (AppleiCloud, anyone?), Apple went for these two domains.
