Sentence examples for sets implies from inspiring English sources
But the perfect set property for co-analytic sets implies that the first uncountable cardinal, $\aleph_1$, is a large cardinal in the constructible universe $L$ (see Section 7), namely a so-called inaccessible cardinal (see Section 10), which implies that one cannot prove in ZFC that every co-analytic set has the perfect set property.
Setting up a Bland and Altman method to compare two data sets implies the following computing: (i) the average of repeated measurements for each sample and each method, and the within-sample standard deviation in each method (si HR-CS FAAS and si ICP-OES); (ii) the within-method standard deviation s wHR - CSFAAS = ∑ s iHR - CSFAAS 2 n (1).
Having identical ancestor sets implies identical functionality in terms of the GO tree; therefore, a value of 1 implies identical functionality.
The short-list of candidate genes was then culled from associated pathologies hypothesizing that frequent co-occurrence in causal gene sets implies functional relationship with a known disease gene (Methods).
While we had identified a related set of genes previously using fibroblast cells that had not been matched for site of origin, the significant differences between our previous and current gene sets implies that topology significantly influenced gene expression in our original set.
We define η c = min { ζ I ∗ : I ∈ D }. Stage 2: Nonbalanced sets imply (2).
In all cases, the former resulted in less variability of the performance indices between calibration and validation sets, implying better generalization ability than for the latter.
By the same elementary properties, the knowledge assumptions at the latter two information sets imply that Fiona and Alan have third-order mutual knowledge of the game and second-order mutual knowledge of rationality.
However, there was also a drawback since larger training data sets imply smaller test sets: in case of small test data set sizes, the variability of the prediction error estimates increased considerably.
Some of the variant alleles were also over-represented in the low-risk sets implying that many control subjects carried some risk for GBC.
Note that the values of the correlation coefficients do not vary sensibly in the <img src="http://journals.plos.org/plosone/article/asset?id=info?doi/10.1371/journal.pone.0016774.e141.PNG" class= inline-graphic"/> different training sets, implying that this choice of features is robust.
