Also, since we require P i ≥ 0, β i is substituted as 0, due to the complementary slackness condition [42].
That is, w ℓ substitutes (tilde {mathbf {x}}) in (11), and N, λ l, and x i are substituted by M, (lambda _{i}^{u}) and u ℓ, respectively.
Its elements, R ij, denote the rates at which a nucleotide i is substituted by a nucleotide j; diagonal elements are R ii = −∑ j ≠ i R ij, the total rate away from i.
In the matrix above, the rows and columns are labeled by nucleotides adenine, cytosine, guanine and thymine (in this order), so that entry (j, k) stands for the conditional probability that nucleotide j at the parent node of edge e i is substituted by nucleotide k at the child node.
"I didn't understand why I was substituted".
"Everyone was quiet but I stood up and said: 'How can you stand there and say that when we are only doing what you have been going on about all week.' "Rodgers looked at me and muttered: 'Whatever.' I was substituted 12 minutes later".
For me it endured for two years and ended with an inaccurate underarm toss of the armband to, I think, Stuart Pearce, when I was substituted in what turned out to be my final game for England in the European Championship in Sweden.
"When I was captain at Derby I once threw my boots off when I was substituted against Forest and he let me have it in front of everybody".
I was down and feeling sorry for myself after a nightmare performance against Iceland in which I was substituted at half-time.
I'm substituting cottage cheese here for the ricotta used in the classic version of this lasagna.
