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To obtain the unpaired LOH profile matrices, we applied the basic Hidden Markov Model method proposed by Beroukhim et al. (2006) to the cancer genome data.
To infer phylogenetic trees from three nucleotide matrices, we applied the maximum likelihood method with rapid bootstrapping of 1000 replicates in RAxML-HPC v7.2.8 available on http://www.phylo.org/ [ 80].
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To convert the matrix β of β-weights into a topological adjacency matrix, we applied a threshold to the absolute value of the elements of the matrix.
To estimate the noise covariance matrix, we applied an energy-based voice activity detector to detect the absence of speech signals.
To efficiently compute the kernel matrix we applied the Cholesky Decomposition (see Materials and Methods) because the naïve computation was too time consuming.
Based on the covariance matrix, we apply a technique known as SVD, in order to project out the signal space.
To avoid this problem and to estimate a heteroscedasticity robust covariance matrix, we apply the parametric bootstrap.
In order to show the fundamental importance of the Laguerre operational matrix, we apply it together with the spectral Laguerre tau method for the numerical solution of general linear multi-term FDEs on a semi-infinite interval.
In order to analyze the performance and characteristics of the Kronecker product measurement matrix, we apply the measurement matrix to a 2-D image acquisition simulation experiment and compare it with the Gaussian random matrix, Fourier matrix, Bernoulli matrix, Toeplitz matrix, polynomial matrix, and measurement matrix which are commonly used.
We assume the reasons of the occurrence of the non-zero diagonal values are similar to the reasons for the non-symmetricity of the matrix: the starting position, the rigidity of reference conformer, etc. Further, to make the non-symmetric matrix symmetric, we applied matrix transformations for clustering.
In the second approach for the data matrices construction we applied the same division into stripes also to direction X, to check if, by taking into account local variations in both directions, the parameter identification results more accurate, in spite of the variance inflation.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com