Furthermore, pair wise sample correlations of genome- and transcript-aligned read frequencies had very similar correlation coefficients (data not shown).
Read frequencies exhibited much higher correlation coefficients in pair wise sample comparisons (r2 = 0.93 0.99) than array hybridization (r2 = 0.83 0.88; Fig. 5 and 6).
Overlaid kernel density estimates, univariate distribution results, Mahalanobis distances, correlation coefficients of pair wise sample comparisons, unsupervised principal component analysis (by Pearson product-moment correlation) and Ward hierarchical clustering of Pearson product-moment correlations of read frequencies were performed with JMP Genomics, Version 3.2 (SAS Institute, Cary, NC).
Next feature would be to display the data for the whole ensemble of pair wise sample distances on a single picture.
The study first compared vegetation, water velocity, sediment deposition rate, sediment properties and benthic communities between invasive S. alterniflora and native Scirpus mariqueter patches using a pair-wise sampling design at 3 sites (Dongtan, Jiuduansha and Nanhui) in four seasons.
Then, the measurement matrix Φ ′, composed of L different block-wise sampling operators, is adopted to these decompositions with one operator for each level.
We used a pair-wise sampling protocol to control for spatial heterogeneity.
Computing the variance of this Horvitz-Thompson estimator requires either weighting each quadruplet by the quadruple-wise sampling probabilities, i.e., working with a matrix of size N'(N'-1)(N'-2)(N'-3), or bootstrapping the case-cohort data.
Specifically, we proposed sample selection methods using (i) repeated random draws, (ii) a genetic algorithm, and (iii) pair-wise sample compatibilities.
Experiments on simulated data demonstrate the effectiveness of all three approaches, with a consistently superior performance exhibited by the pair-wise sample compatibilities-based method.
