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The resulting global descriptors can be made invariant to multiple arbitrary transformation groups while retaining good discriminativeness.
We consider lumping by means of n̂ (n̂ ⩽ n -dimensional arbitrary tran -dimensional= h(y).
The additional terms with coefficients g j are used to partially compensate unknown arbitrary transformation in the initial stage.
Admittedly, he sided with Petrizi in this point: Petrizi's interpretation of Proclus's philosophy should be accepted rather than its arbitrary transformation by modern Armenian and Georgian interpreters.
Over the previous year, he had been determined to find a gravitation theory that was generally covariant, that is, whose equations were unchanged by arbitrary transformation of the spacetime coordinates.
Therefore, an arbitrary transformation of those values is subsequently needed to avoid distortion of the mean value.
Similar(53)
A combination of several of these basic gates are required for arbitrary transformations, thus integrating them in a stable manner will be required.
While progress has been made in the last few years, it is still unclear how to perform arbitrary transformations with high fidelity and near unitary efficiency in a fast and reliable way.
Thus the "absoluteness" of rotation arises precisely from singling out one type of frame, by one type of transformation, instead of allowing arbitrary transformations and arbitrary frames.
This generous choice has been made to cover also worst case scenarios, i.e., arbitrary transformations, without throughput degradation and might be reduced by a factor up to five when the necessary image transformations are small.
One possible explanation for this phenomenon is that two diagonalizable matrices have the same spectrum if they are similar via an arbitrary similarity transformation rather than just via a permutation transformation, and this suggests considering features of a matrix that are invariant under permutation similarities but not more general ones.
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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