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The argumentation is sophisticated, but the upshot is that one can achieve the same logical results by simply replacing all occurrences of the expression "so-and-so exists" (e.g., numbers exist) by occurrences of the expression "so-and-so is assumed (or hypothesized) to exist".
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No differences in the levels and time occurrence of the expression of early (aP2) or late (HSL) differentiation related genes (determined by qPCR) were observed (data not shown) showing that the up-regulation of DNA-PK is not a required event to the differentiation process.
The main elements of one widely used notation are the following: if α is an expression containing some free occurrence of x, the expression {x : α} is used to stand for the class of objects fulfilling the condition expressed by α.
To further confirm the occurrence of BLT, the expressions of basal and luminal markers were analyzed by immunoblotting of total cell lysates prepared from LRBM cultures.
Thus, the occurrence of the Crx expression peaks a few hours before the peak of Aanat expression additionally supports the concept that homeodomain proteins act as regulatory factors of the daily expression profile of Aanat in the rodent pineal gland with CRX in a central position.
The times of occurrence (counts) of the expressions from level 1 through level 6 for each group are listed in Table 1.
We also examined a link between the occurrence of the aberrant expression and human papillomavirus (HPV).
In the case of e-CCC-Biclusters with sign-changes we compute the statistical significance of B, using the p-value(B), by obtaining the probability of a random occurrence under H0 of the expression patterns in the e-Neighborhoods of the patterns in the p B and, K = | I|-1 times in n = | R| -1 independent trials.
In fact, although the source of LinkedIn' group search algorithm is not available, we observed that it searches the occurrence of the search expressions not only in the groups of interest's name and description, but also in the groups of interest's discussions information.
From an entirely different angle, [ 21] provided an approach that screened genomic sequences against a database of putative regulatory motifs, evaluating the contribution of the occurrences of the motif on the gene expression by comparing the expression profiles of genes containing this motif against those that do not.
Summarized probe-level data is recommended as input, as this will eliminate the occurrence of improper combinations of the expression values of different probes into a single-gene value [ 14].
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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