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However, we observe a breakdown of the slice invariance for other representations.
The paper focuses on the boundary representation, although some ideas are more general and can be used for other representations, too.
He ends his book with a blast of cartographical analysis, and suggests that weather maps have created the template for other representations of volatile geographic phenomena such as the incidence of crime and disease.He may well be right.
The framework developed is general and can be used for other representations such as mel-frequency cepstrum coefficients, higher resolution PSDs, as well as other models such as GMMs, HMMs, and NMF.
For other representations of chemical structures like SMILES, InChI or IUPAC names such an enumeration is only possible for the most common substances.
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Over the last 20 years, and especially during New Labour's modernising project, poor, working-class communities have looked for other representation, sometimes in the form of Ukip.
"Dealers certainly don't like it if you bad mouth them but, of course, why are you shifting and looking around if you aren't unhappy?" Hagin noted that she "sniffed around... put out the word that I was looking for other representation... talked to people who knew me and knew which dealers were looking for what" and, finally, found the right match.
As can be seen in Table 2, for each of the IBO levels of interest, the values of and and measured for the representations with the minimum NLS are the minimal or very close to the minimal values of and and measured for the other representations.
The same is true for many other representations of motifs.
Many other representations for fractional derivative operator exists.
Therefore, one might expect that other representations, for which the human brain may have less specialized circuitry [ 36, 37], will also be task independent.
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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