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Each left-out landmark on in vivo CT was then transformed using the corresponding transformation matrix.
Then, we propose a structured sparse representation model based on this new transformation matrix for image restoration, taking advantage of the sparse nature of the transform coefficients of image patches over the corresponding transformation matrices.
Different from other wavelet numerical methods adding wavelets directly, the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space via the corresponding transformation matrix.
However, because the voxel-by-voxel analysis showed that values correspond well after forward and backward transformations, it suggests that the corresponding transformation is practically invertible.
To be sure, the liberalisation of values, an increasing willingness to include strangers, and a corresponding transformation of collective identities can at best be stimulated through legal-administrative means.
The corresponding transformation algorithms are called algorithms for degree elevation of Bernstein polynomial representations.
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For more on changes of bases in the biset (Xcdot G) and the corresponding transformations of the wreath recursion see [35, 36].
Using this representation may look rather unnatural in biology; but corresponding transformations have been discussed in the flat case, though with a very different language: in [27, 31] they are called Shift-twist transformations.
Despite the case considered in Sections 2, 3 is more general, we derive here conditions of the solvability in detail since the corresponding transformations are based on the properties of operators and spaces as applied to the case under consideration.
Therefore, significant changes in the atomistic structure of 80GeSe2-20Ga2Se3 glasses from disordered amorphous to crystallized one are accompanied by corresponding transformations in the atomic-deficient void structure, the latter being defined by modifications in a void geometry [28].
We compared the alignment of interfaces from the different methods (Galinter, I2I-SiteEngine, and DaliLite) by examining the deviation of Cα atom coordinates of interface residues after corresponding transformations.
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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