Galerkin projection is performed using the extracted basis to yield a low dimensional I/O approximation of the original nonlinear model.
Table 1 Reduction of number of genes for different sample size in dataset Sample size Rank of the extracted basis (steps 1 and 2) Nb of genes with Kendall rank correlation (<0.5) (step 3) Number of final selected genes (step 5) 60 60 33 3 55 55 31 4 50 50 28 22 45 45 13 7 40 40 11 9.
Table 5 Reduction of number of genes for different sample size in dataset Sample size Rank of the extracted basis (steps 1 and 2) Nb of genes with Kendall rank correlation (<0.5) (step 3) Final selected genes (step 5) 80 26 5 75 75 31 3 70 70 34 10 60 60 34 10 50 50 2434 10 50 50 24 8. Table 6 presents the genes occurrences with their cross validation percentages.
Figure 3 shows the final extracted basis spectral signatures, after these spectral calibrations, corresponding to the four selected tissue types; epithelial tissue, lamina propria, collagen and lymphatic tissue.
Well-delineated unmixing with small residuals further demonstrates the purity of the extracted basis spectra as signatures of each tissue type.
Overall, however the fitting performance shown is fairly good, supporting our earlier conclusions that the extracted basis spectra well represent, and are capable of identifying the chosen basic tissue types within GI tissues.
The assays were carried out in triplicate; total flavonoid contents were expressed on an extract weight basis as mg/g rutin equivalents, rutin mg/100 g of extract.
Extruded linseed supplement (275 g/kg ether extract, DM basis) was included in treatment diets at 50 g/kg of DM.
Step 2: For (j= 1,ldots, p), sort (mathbb {X}_j) in descending order according to (eta ^2_j) values, and extract a basis of the first ({p}^prime) linearly independent variables, following the process of Gram-Schmidt ([49]).
If is the canonical basis of, then a basis of (respectively ) can be found considering the set for (respectively ) and then extracting a basis from it.
