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Note that each element in matrix X can either be classified as a signal (denoted by '1') or as noise (represented as '0'), based on a predefined threshold η.
So, the optical field over the focal plane Σ can be represented as Based on the coordinate system displayed in Fig. 2, we get For paraxial approximation, it can be re-written as Here k x, k y are spatial frequencies and F [ U (x 0, y 0 ) ] is the Fourier transform of U (x 0, y 0 ) with respect to spatial frequencies (k x, k y ).
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This is a general representation theorem proving that algebras for modal systems can be represented as algebras based on the power set of the set K in the corresponding Kripke's structures.
The molecule has been represented as modular based on the division into three homology regions corresponding to the N-terminal TPR motifs, a large central region of uncertain function, and the C-terminal UCS domain [4].
The decisions were represented as being based on strategic and rational planning and careful considerations that take into account the strategy of the municipality as a whole.
It represents as many as 1920 x 1200 pixels (guesstimate based on the resolution of the 17-inch MacBook Pro — but might it be even more?) floating in your lap.
The step A models are represented as M (model based on microarray data) and G (model based on genomics data), and the step C model based on both microarray and genomics data as MG.
Finally, fastq files were converted to fasta format using seqtk (part of the samtools package), and bases that failed the depth and quality filters (represented as lowercase bases in the vcfutils.pl output) were converted to ambiguity characters (Ns).
The works of L. Ron Hubbard, the Scientology founder, are well represented, as are books based on the Star Trek series.
Starting from an embedding space such as the visual hull, we will first conduct robust 3D depth estimation (represented as 3D points) based on image correlation.
The synchronization of processes across the boundaries in our case, where a space is represented as a cells based spatial grid, is achieved by specifying a buffered region of a certain size.
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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