SIGM can be written as a function of time t (see Appendix), SIGM =[1+3 exp -8λ t/3)]/4 [3] whexp -8λs the average rate of substitution per site per evolutionary time unit, and t is the time after sequence homogenization (concerted evolution).
Because Q H can also be written as (see Appendix) (12) we see that Q H vanishes for non-associative (non-modular) networks, because when color is assigned randomly to nodes we have so that Tr e = 1/ N c.
At first, the whitening filter W− 1/2in (27) can be written as follows: [see Appendix] W - 1 ∕ 2 = α I 2 γ H 1, i H 2, i H γ H 2, i H 1, i H β I 2, (30).
After some algebraic manipulations, Equation (12) can be written as (see the Appendix for the proof): y p + 1 = V F p + 1, ω Σ − 1 U H r = ∑ n = 1 N f n p + 1, ω u n H r σ n v n (18).
The algorithm is written as Algorithm 1 (see Appendix).
"Certain final questions of identification remain unsettled," he wrote in an appendix to this essay in November, 1944.
"The god of machine-logic was overthrown," Herbert writes in an appendix, "and a new concept was raised: 'Man may not be replaced.& 8217 " This watershed moment, known as the Butlerian Jihad, resulted in a spiritual awakening, which put into place the religious structures that ultimately produce the messiah, Paul Atreides.
After an uncertain start, Dr. Stritmatter writes in an appendix, he turned to scholarly works on Shakespeare's biblical references and, "one by one, I began to tick off a growing list of verses marked in the de Vere Bible which these scholars had identified as influential on Shakespeare".
The details to estimate G are in Appendix A. The model can be written as, where g is a vector of N random genome-wide effects for all animals.
