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When more than one expression value was present for a gene (multiple probe sets per gene), the gene was considered up- or down-regulated if the direction of change (up/down) was consistent between all probe sets, and at least one of the probe sets satisfied the -0.6/0.6 threshold on log ratios.
We determined that 277,346 of the 493,710 (56.2%) analyzed probe sets were non-core and we decided to interrogate 189,460 intronic regions.We note that 49,588 of these non-core probe sets satisfied the expression filtering criteria, including 2037 which showed expression variations between tumor samples and mapping to 1725 intronic regions.
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Thus, all analytic sets satisfy the CH.
These collections of data sets satisfy all the characteristics of Big Data (the 5 Vs).
The generalization of Gradecast to sets satisfies the three Gradecast properties.
Furthermore, each of those sets satisfies the limiting property ; for each and any given.
However, the efforts to prove that co-analytic sets satisfy the CH would not succeed, as this is not provable in ZFC.
For example, in one of the earliest results in the subject, Cantor and Bendixson showed that every closed set is either countable or has the size of the continuum; in other words, the closed sets satisfy CH.
Conventional works on fuzzy logic assume that fuzzy sets satisfy the conditions of convexity and normality (the height is one) which are called fuzzy numbers.
A matroid is a mathematical structure in which certain sets of elements are defined to be independent, in such a way that the independent sets satisfy properties modeled after the properties of linear independence in a vector space.
In Data Set 1, 53.6% of bad probe sets and 39.4% of good probe sets satisfy this condition.
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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