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This corresponds to a two-level model, with the first level representing the sensors and the second level representing the sources: where Y is an Ns (sensors) × Nt (time points) matrix of sensor data; L is a Ns × Np (sources) matrix representing the "forward model", and J is the Np × Nt matrix of unknown dipole currents; that is, the model parameters that we wish to estimate.
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Then, the image matrix was decomposed into a mixing matrix and a source matrix.
The (Z-transformed) source matrix was used for visualization and labelling of structural components.
The reason to specify the source matrix, which will be known for any forward transformation, is to enable inverse transformations from the target to the source (when the dimensions of the source matrix would be unknown otherwise).
The source matrix demonstrates how each component contributes to different GM voxels and thus involves spatial information about the structural components.
Geographical information of each component identified in the source matrix was used in the visual inspection step to exclude artefact components in further analyses.
Thus, the 92 subject-by-the number of GM voxels matrix was decomposed to a 92 subject-by-6 components matrix (mixing matrix) and a 6 component-by-GM voxels matrix (source matrix).
where the source matrix and the direction matrix are shown as follows (4).
According to noncircular property, the source matrix can be denoted by S = ψ S 0. (7).
Then, the source matrix is estimated using a standard linear programming algorithm.
Step 5. LS update for the source matrix Ω according to (22).
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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