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The subensemble density matrix that corresponds to a particular outcome having occurred can still have a lower Gibbs-von Neumann entropy than the ensemble over all measurement outcomes.
To respect this condition, one more class of damage was introduced in the extended matrix that corresponds to the state of No damage (D0).
Transmission electron microscopy images indicate that calcium carbonate nanoparticles produced in the jet homogenizer have a multiple core structure, with primary particles (c.a. 6 nm in diameter) immersed in a protein matrix that corresponds to 35% of the total nanoparticle mass.
This is a rate R = 0.5 and length n = 12 parity-check matrix that corresponds to an LDPC code C = [p1, p2,..., p6, d1, d2,..., d6], where d1, d2,..., d6 are the information bits and p1, p2,..., p6 are the parity bits.
SeriesMatrix are summary text files related to a GEO series Experiment (GSE) that include sample and experiment metadata together with a tab-delimited matrix that corresponds to normalized expression data.
Although the binding of Mnt to DNA is not strictly additive [32], in these simulations we assume that the binding energy to any sequence is the sum of the energy values from the matrix that corresponds to that sequence.
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These two registrations generated rigid body transformation matrices that corresponded to the movement between L4-L5 and L5-S1, respectively.
For conventional NMF processing, the multiplicative update of matrix A that corresponds to the cost function given in Eq. (10) is defined as [13] mathbf{A} leftarrow mathbf{A} !.!* frac{(mathbf{R}mathbf{S})^{top} frac{mathbf{Y}}{mathbf{R}mathbf{S}mathbf{A}}}{(mathbf{R}mathbf{S})^{top} mathbf{1} + lambda}, (11).
The 5'ss, 3'ss, and branch site sequences of each SJ were scored based on the corresponding log-odds matrix by adding up the entities in the matrix that corresponded to the nucleotides at each position on the sequence.
The orthonormal vectors of the null space can be derived either by applying the spectral theorem on the correlation matrix D I in order to keep the vectors corresponding to zero eigenvalues, or by directly applying an eigenvalue decomposition to H I, keeping the vectors of the left orthonormal matrix that correspond to zero eigenvalues.
where refers to the original posture, denotes the lower-dimensional version of the posture represented using the aSpace, [e1,…,e b ] is the aSpace transformation matrix that correspond to the first b selected eigenvectors, and is the posture mean value that is formed by averaging all postures, which are assumed to be transformed into the aSpace.
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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