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To measure similarity to the TRANSFAC matrices we implemented the metrics described in [ 44], as used in the program MatInspector.
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One problem associated with ETD schemes is the accurate calculation of the necessary matrices; we implement and discuss in detail a variety of different methods including direct computation, contour integration, spectral expansions and recurrence relations.
However, as all non-zero elements in this matrix are 1, we implemented a specialized GPU kernel for this task, which simply sums the elements whose indices are stored in a look-up table.
For a likelihood analysis, we implemented the MtArt matrix in PhyML 3.0 [ 64].
In this work, we implemented the Non-negative Matrix Factorization (NMF) algorithm [ 18] to decompose and detect somatic mutation signatures in nine major cancers.
Then, instead of computing a percentage of similarity between sequences (which is difficult because we don't know how to implement a good substitution matrix for hypervariable regions of rRNA sequences) we implemented a Levenshtein distance calculation for clustering sequences.
A well suited method is the Minimum Covariance Determinant (MCD) that considers all subsets containing h% of the observations and estimates the variance of the mean on the data of the subset associated with the smallest covariance matrix determinant - we implement the Rousseeuw and van Driessen algorithm [54].
In particular, the results support the use of shrunken centroids and diagonal covariance matrices, and we have implemented this algorithm in the Clanc software [13].
The CAS wavelets operational matrices are implemented for the numerical solution of nonlinear Volterra integro-differential equations of arbitrary order in Saeedi et al. [5].
Constraints that reserve the positive and semi-positive definiteness and the inter-connectivity of the spatial matrices were implemented using semi-definite programming.
Pair wise identities by state (IBS) were calculated for all 966 samples based on autosomal SNPs using identity matrices as implemented in the GenABEL library [46].
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com