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D i (A) forms a diagonal matrix holding the i th row of A on its main diagonal.
where S is a T C×K dictionary matrix of K spectrograms of clean speech, while A is the K×N activation matrix holding the linear combination coefficients.
The response variable was represented by a two-column matrix holding the number of 'successes' (positive recovery) and 'failures' (no recovery).
Let U be the matrix holding the ensemble members (U_{i} in R^{n},) U = (U_{1},U_{2}, ldots, U_{N} ) in R^{n times N} (10 where N is the number of ensemble members, and n is the size of the model state vector.
Let D be the matrix holding the ensemble of measurements (d_{i} in R^{m}): D = (d_{1},d_{2}, ldots, d_{N} ) in R^{m times N} (15)The corresponding measurement error covariance matrix is given by, R_{text{e}} = frac{{gamma gamma^{text{T}} }}{N - 1} (16)where (gamma = (epsilon_{1},epsildots2},epsilon_{siloN}{N} ) in R^{m times N}) is the ensemble of measurement perturbations.
The workflow of the method is such that it integrates three main components: metabolome data [26], [27], the stoichiometric matrix (holding the metabolic biochemical reactions in the organism) and the classical theory of modal analysis [28].
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Meanwhile, the weight matrix holds the basic function coefficients from the speech segment.
This matrix holds the transition probabilities, which depend on the model parameters and typically remain constant through time, between all possible states of the system within one time step.
After applying the first SVD to a 2-D matrix formed by the audio signal, he blended the intended watermark with the diagonal matrix holding singular values and then performed the second SVD on the modified matrix.
However, it is very costly and impractical in solving the shifted Hermitian subsystem with the coefficient matrix holding full and Toeplitz-like rather than Toeplitz structure.
The initial step of any clustering procedure is the computation of an upper triangular matrix holding similarity values between all pairs of compounds.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com