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Recall that T j is the transition matrix of Y j.
It is also shown that for the hierarchically ordered system of regression models, the D-optimal design does not depend on the covariance matrix of y.
Suppose that the transition matrix of Y j is T j ≡ T = ( 1 1 1 0 ) for j ∈ odd.
where R y is the covariance matrix of y i, which is R y = σ c 2 I + ℰ d c ( x ) c ( x ) H. (23).
Let X k (g)=[Ψ k,1 g,Ψ k,2 g,…,Ψ k,M g] denote the sparse representation matrix of Y k.
The covariance matrix of Y is C Y =α 2 F C X F T. Therefore, it follows that (sigma _{Y}^{2}=frac {1}{L}trace{pmb {F}^{T}pmb {F}pmb {C}_{X}}=alpha ^{2}sigma ^{2}sigma.
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where [L y Γ x, y)]' denotes the transposed matrix of L y [Γ x, y)].
Theorem 2.2 Suppose n = 2 k + r for some k ≥ 3, r = 0, 1. T o and T e are the transition matrices of Y o and Y e, respectively.
The original DHGLM algorithm in Rönnegård et al. [ 19] iterates between a linear mixed model for the phenotypic observations: y i = P i = phenotypic observation of animal i; and a Gamma GLM for the residual variance φ i, where φ i = E e ^ i 2 1 − h i, e ^ i 2 is the squared estimated residual of y i and h i is the diagonal element of the hat-matrix of y corresponding to y i [ 30].
Given another foreground gene y, (8) E y = A y S = A y α E Θ = β E Θ, where E y and A y are the gene expression and binding matrix of gene y and β = A y α infers the relationship between gene y and the seed genes.
Let the transition probability matrix of {Y k } k≥1 be P (with P(Y 2=j|Y 1=P)=P i j ) and the stationary distribution be π (with P(Y 1=i)=π i ).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com