Therefore, the penalty of the OAKFLEX mapping is reduced and results in a higher enrichment rate, because of the different flexibility properties.
As the success of association mapping is reduced by small effect sizes and limited power, linkage studies in laboratory-based model systems are still heavily used.
Furthermore, the accuracy of stochastic mapping is reduced with smaller data sets (limited number of gene families) due to unreliable estimation of branch lengths.
Therefore, the number of samples finally used for association mapping was reduced to 85.
After the quality control filters the number of useful and informative loci for mapping was reduced to 7,146.
We remark that (i) if (alpha_{i}=0) for every (i=1,2,ldots,N), then G-mapping is reduced to S-mapping; (ii) if (alpha_{i}=0) and (gamma_{i}=0) for every (i=1,2,ldots, N), then G-mapping is reduced to W-mapping; (iii) if (alpha_{i}=0) and (delta_{i}=0) for every (i=1,2,ldots, N), then G-mapping is reduced to K-mapping.
When a pair of complex conjugate eigenvalues of the Jacobian matrix cross the unit circle and satisfy the resonant condition λ04="1 or λ03= 1, the four-dimensional map is reduced to a two-dimensional one by the center manifold theorem, and the reduced map is put into its normal form by the method of normal form.
For every (i=1,2,ldots N), put (alpha^{i}_{3}=0) in Definition 4.5, then the S-mapping is reduced to the K-mapping generated by (alpha _{1}^{1}, alpha_{1}^{2},ldots, alpha_{1}^{N} ) where the K-mapping is defined by Kangtunyakarn and Suantai [19] as follows.
In this way, the similarity between two connection probability maps is reduced as a function of their anatomical proximity.
In this case, a weighted average of neighboring data points was used and apparent outliers given weights such that their effect on the resulting isopach map is reduced.
We see in Table 2, that the size of the extracted conserved domain pair is reduced from 83 to 45%, as the size v0 of the common equatorial domain used in the simulated maps is reduced from 100to25%5%.
