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Thus, the similarity matrix constructed based on these representation coefficients could be used for data clustering (Elhamifar and Vidal 2013; Vidal 2011).
Then, a similarity matrix was constructed based on these representation coefficients (Fig. 1d), and spectral clustering was applied to generate individual parcellation for each subject (Fig. 1e f).
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Due to the low cardinality and size of the generators, mining based on these representations, which does not generate duplicates, is very efficient.
Due to the definition of the interval derivative (7) and two parametric representations (2) and (3) for interval-valued functions, in general, it cannot be expected that the derivative of an interval-valued function be equal based on these representations.
Based on these representations, we decided to exclude the 5 Fe-rich objects, which compressed the potential separation of other objects, and to exclude As because, as shown in Table 2, it was detected in only 5 out of 200 measurements (e.g. in objects n° 36521- a nail - and n°106647 - a sword).
Specifically, the task of ILGA is to learn (i) "affordances," representations of object features that indicate where it can be grasped, and (ii) motor parameters that can be used to successfully grasp objects based on these representations.
Based on these integral representation formulas, the boundary behavior of some singular integral operators, and the Clifford analytic approach, we prove that the fourth-order elliptic Riemann type problem in (mathbb{R}^{3}) is solvable.
However, they essentially extract fixed representations from pre-divided regions for each image and then perform matching based on these extracted representations.
Autoencoders try to learn some representations of the input in the hidden layer in a way that makes it possible to reconstruct the input in the output layer based on these intermediate representations.
Based on these perceptual representations, surface-related junctions are made explicit such that they could be interpreted to interact as to generate surface-segmentations in static or temporally varying images.
The network was then trained to generate the orthographic and phonological outputs based on these visual representations.
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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