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63 The canonical correlation provided a single, unbiased test of statistical significance, which takes into account the sample size, the number of variables in the analysis, and intercorrelations between and within sets of them, as well as the fact that it is a pair of linear combinations prederived to maximally correlate whose correlation is being tested for significance.
Another interesting aspect of Figure 2(b) is that away from the quantum critical point, the composite parameter is mostly composed of model parameter variations near the spins whose correlation is being evaluated.
When we searched for the coexpression of enzyme-coding genes directly connected to metabolite pairs whose correlation is conserved, only a small fraction of genes were coexpressed.
A point above the 45-degree line represents an analysis where the method whose predictive correlation is given on the vertical axis (RKHS, RBFNN, BRNN) outperformed the one whose correlation is given on the horizontal axis (BL).
The p-value, p (M (i, j)), is the probability of drawing by chance | M (i, j)| = k (i, j) terms whose correlation is greater than the observed minima.
The top anchor-partner scores are seen to lie within the correlation interval [0.257, 0.357], suggesting that anchor-partner SNP combinations whose correlation lies within this range are most useful for the AI test, consistent with our intuition that we should seek a partner SNP whose correlation is not "too high" and not "too low" with the anchor SNP.
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Fig. S3 Pairs of thorax metabolites whose mean values are unaffected by diet (P > 0.05) but whose correlations are significantly different between DR and AL.
By this definition, pairs of metabolites whose correlations are similar and high (i.e., r ij,18 ≈ r ij,27 → 1, where r ij,t is the correlation coefficient between two metabolites i and j at temperature t), are weighted more heavily than pairs of metabolites whose correlations are similar but non-significant (i.e., r ij,18 ≈ r ij,27 → 0).
A detailed characterization of upregulated genes belonging to this clade allowed us to identify a subset of 18 genes whose correlations were independently supported by different kind of studies as, for example, between YBX1 and SYNCRIP [ 44– 46] or between CCAR1 and WWTR1 [ 47].
The following five groups of items were identified, whose correlations were larger than 0.4 between items: (a) items relating to depressed mood (items 8, 32, and 39), (b) items relating to self-harm (items 20 and 43), (c) items relating to irritability/agitation (items 16, 26, and 42), (d) one item relating to drowsiness (item 37), and (e) one item relating to euphoria (item 38) (Table 2).
The influential CPD is mostly composed of parameters around the spins whose correlation function is being evaluated, except near the quantum critical point when other parameters also contribute.
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