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The mixture fraction, which is affected by the mixing process only, requires the least number of eigenmodes, and yields a sufficient representation of the original data with only two to three eigenmodes.
Figure 4 provides the results regarding the number of basis vectors needed for a sufficient representation of patient heterogeneity from AD. Apparently, the larger the dictionary size, the lower the representation error.
By repeating this procedure for all available cell facets matrix, a sufficient representation of the analysed problem is obtained.
In fact, the female library had the smallest number of exclusive unigenes with a sufficient representation (289 unigenes).
In such data sets, only TEs and other repetitive DNA sequences are expected to have a sufficient representation in the pool of reads to be assembled.
Once the mismatch has been accounted for in neural terms, the predictions are a sufficient representation of the sensory input (Mumford 1992; Rao and Ballard 1999; Friston 2003).
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However, this might not be a good and sufficient representation of the concept of equilibrium of Ying and Yang in Chinese medicine.
These findings demonstrate the feasibility of creating and maintaining a hESC bank with sufficient representation to support a large number of patients.
Recruitment was undertaken until sufficient representation of a range of midwifery hospitals and services was obtained for the pilot and expression of interest received prior to the cut-off date.
The range of the values used in the scenarios is an additional indicator for the sufficient representation of uncertainty (see Figs. 2 and 3 for climate scenarios and supplementary information for socio-economic developments).
Nonetheless, the study involved a large cohort of women ensuring sufficient representation from minority ethnic groups who are more resistant to agreeing to participate in prospective studies as we found out when we prospectively assessed psychosocial status.
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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