We finally replace M by using the Boolean indicator matrix for symmetric nearest neighbors (mil = 1 if genes i and l are symmetric nearest neighbors, or 0 otherwise).
A pan-genome tree was constructed using the gene presence/absence indicator matrix for these genomes and our 16 draft genomes.
Let G j be the n × g j indicator matrix for variable j (j ∈ (1,... q)), with g j the number of categories of variable j.
That is for each j (j = 1,..., q) with G j the n × g j indicator matrix for variable j with g j the number of categories of variable j.
To derive the partial derivative, we begin by substituting the determinant formulation into our volume penalization and arrive at the following calculation: therefore, the gradient of log vol(K) is given by where the eigenvector z d satisfies the equality Qz d = λ d z d and E ij is the indicator matrix for the entry ij.
It follows immediately that the number of possible difference indicator matrices is less for M
In the following, we will show that the number of distinct difference indicator matrices is finite for bounded N, and that the sequence of difference indicator matrices {Δ t′} is stationary Markov and ergodic.
Using the cnaGENE function of SWITCHdna, the segment output file was converted into an indicator matrix, where for each sample, each gene's copy state was represented as −1 = loss, 0 = no change, 1 = gain.
To determine subtype-specific CNAs, the segment output file which had arisen from the SBL model and BE procedure was converted into an indicator matrix, where, for each sample, each gene's copy state was represented as −1 = loss, 0 = no change, and 1 = gain.
Both indicator matrices, though redundant, are useful for simplifying the presentation of the solutions.
