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In order to randomly allocate either of the interventions to the participants of the study, block permutation design was undertaken with ten blocks including four patients in each block.

This idea was inspired by a procedure described in [30] where the author focuses on the optimization of TC permutation design with the so-called almost regular permutation model.

Because of the nature of the adaptive permutation design, estimation of p-values for markers having a strong association with response is expected to take longer.

That means most pseudo pathways in our permutation design met the requirement of gene expression correlation, although we did not limit the correlation values of genes when generating pseudo pathways.

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From our verification, the proposed BIJTs can be applied in areas such as 3GPP ultra mobile broadband permutation matrices design, RM code design, diagonal channel, MIMO 4G LTE Alamouti code, and precoding design.

In a permutation flowshop design the machines arranged in series were the jobs are processed in a same order without eliminating any machine.

To determine the significance of the correlation differences we formulated a permutation test designed to define the null distribution of the correlations.

When combined with permutation tests designed to assess interactions, P-values can also be used to select SNPs with significant ReliefF scores (Greene et al., 2010b; Wongseree et al., 2009).

An additional 1000-fold permuteston test designed specifically to test the linear null hypothesis that the association effects are only additive confirmed the presence of non-additive (i.e. nonlinear) or epistatic effects (p = 0.013).

In order to assess whether the correlation between our predictions and changes in metabolite concentration was due to these broad patterns of expression changes versus the modulation of specific genes, we performed a permutation analysis designed to assess the specificity of our results (Fig.  1b).

Ptx ∈ ℝ M×M is a permutation matrix whose design depends on the overall system and it is used to decouple, in the receiver, the transmitted symbols, as we will show later.

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