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A feature vector is derived from a covariance matrix by taking its upper triangular part.

When the fracture is complete, we create the velocity matrix by taking the inverse of the elements of W times the discretization length: V x,y) = frac{a}{W x,y)}.

The correlation coefficients were converted into a distance matrix, by taking 1-correlation - that is, a correlation of 1 would give a distance of zero.

We approximate the elements of the information matrix by taking a second-order Taylor series about the mean eigenvalue of (1 − θ).

The pairwise correlation matrices for different species can be merged into a consensus correlation matrix by taking the minimum correlation for each metagene pair.

Finally, given multiple separate cost matrices, we can construct a single cost matrix by taking a simple weighted sum: (4) where is a vector of (log) weights.

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It is easy to see that A is a strictly α-diagonally dominant M-matrix by taking (alpha=0.5), and A is not a strictly diagonally dominant matrix.

In this section we disclose an elegant way of obtaining better commuting matrices by taking advantage of the bilinear transform, which is a good discrete substitute for the derivative operator.

Results: We design several techniques to combine kernel matrices by taking more involved, geometry inspired means of these matrices instead of convex linear combinations.

With any given gap cost, the probability of a residue aligned with a gap can be calculated proportionally from a given gap cost and other values from the un-scaled scoring matrices by taking anti-log of the log-odd values or score matrix.

From cluster indicator matrix to microbial clusters: Similar to [ 32], we obtained microbial clusters from cluster indicator matrix H by taking the threshold τ to assign a sample to a cluster when its weight for the cluster exceeded τ.

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