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Suppose we have a factorial experiment with m factors where the ith factor has Si levels, i = 1, 2,…, m.
The independent variables (X 1, X 2, X 3 and X 4) are calculated with Eq. (7) (Zhang et al. 2010), where, X 0 is X i value at the middle point and X D is the step change (difference/2), x i is the coded value of ith factor.
The prediction error for the ith factor is calculated as follows (Fig. 3): begin{aligned} mathrm{error_{ i}} = frac{mathrm{factor_{ i}}-mathrm{factor_{ i}^{NF}}}{mathrm{factor}_{ i}} * 100 end{aligned} Open image in new window Fig. 3 Difference between the output of training data in two cases: case 1 (a) and case 2 (b).
In the above formula according to the ANOVA results (Table 6), P i is contribution percentage, SS i is sum of square, DOF i is degree of freedom of ith factor, and MSerror is mean sum of square of error (Azadi Moghaddam and Kolahan 2014).
The topology of (I_{f}) is induced from the product topology of (I^{mathbb{N}}), with the basic open sets in (I_{f}) given by U_{leftarrow}=bigl(f^{i-1}(U ,f^{i-2}(U ,f^{i-2},f^{-1}(U ,ldots}(U),ldotsbigr), where U is an open sU ,f^{-2}the ith factor space I, and i ranges over (mathbb{N}) (see e.g. Theorem 3 on p.79 in [10]).
The higher level factors are encoded in vector h, where h i is the ith factor.
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Each column of matrix S corresponds to an independent component or factor, and the ith element of a column is the "activation" level of the ith gene in that factor.
A Tricluster M I,J,K) = m i j k, where i ∈ I, j ∈ J and k ∈ K, is called a perfect shifting tricluster if each element of the submatrix M is represented as: m i j k = Γ + α i + β j + η k, where Γ is a constant value for the tricluster, α i, β j and η k are shifting factors of ith gene, jth samples/experimental condition and kth time point, respectively.
So, suppose the length of the promoter region of the jth gene is N, N- L+ 1 match values can be calculated and the maximal value is adopted as the match score, S ij, to reflect the binding ability of the ith transcription factor in the jth gene promoter region.
(5) E i j k 2 = 1 1 + e − M jk + C i / S i With consideration of the DNA methylation effect, the binding ability of the ith transcription factor in the jth gene promoter region can be modified as binding score B ij from match score M ij.
For each patient, we determined the 10-year risk of CVD using the Framingham risk equation: where S0 t) is the baseline survival at follow-up time t, β i is the estimated regression coefficient (log hazard ratio; see Table 2 from D'Agostinho et al 1), X i is the log-transformed value of the ith risk factor (if continuous), X̄ i is the corresponding mean, and p denotes the number of risk factors.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com