Where diag(C) denotes the diagonal matrix With the diagonal elements from C. The partial correlation between a pair of variables is the Pearson correlation coefficient of the residuals of the linear least-squares predictor of their activity based on all the other variables, excluding the pair [40, 51].

For example, the eigenvalue decomposition of the covariance matrix expresses shared correlated activity components across the population; common fluctuations of population activity may be accurately represented by only a few eigenvec-tors that affect all correlation coefficients .

The partial correlation coefficient between two neurons reflects their linear association conditioned on the activity of all the other recorded cells [40].

In our data, the sample correlation coefficients were largely positive and low.

The sample correlation coefficients were largely positive and low (Fig.

The average value of the correlation coefficient across sites ranged from 0.0065 to 0.051 with the mean across sites of 0.018.

F. Histogram of noise correlation coefficients in one site.

While goodness-of—fit measures for regression may not generally be appropriate for assessing proportionality, Zheng [28] eXplores the concordance correlation coefficient pC [29] which could be modified to provide an alternative measure of proportionality defined as and related to var(log(x/y)) by the terms in Equation 1.

Currently, there are many gene co-expression databases available that provide correlation coefficients for the relative expression levels of different genes, generally from multiple experiments with different experimental conditions (see e.g., [18]).

A 2D histogram of the correlation coefficient observed for the relative abundances of a given pair of mRNAs in a sample where the ten most abundant mRNAs have been removed, against the correlation coefficient observed for the relative abundances of that same pair, over all pairs.

While the distribution of the correlation coefficient pairs lies more on the diagonal than in the preceding figure, it is clear that correlation of relative abundances is sensitive to What is in (or out of) the

A 2D histogram of ¢(clr(xi), clr(xj)) for the relative abundances of a given pair (i, j) of mRNAs, against the correlation coefficient observed for the absolute abundances of that same pair, over all pairs.

Correlation Coefficient [39], which quantifies the quality of a binary classification.

Matthews Correlation Coefficient shows that IT K_CYCLE methods outperform ANOVA and F24 in the presence and absence of asymmetric time series.

The vertical axis shows the Matthews Correlation Coefficients (MCC) [39] for different Benjamini-Hochberg adjusted p-value cutoffs (FDR) along the X-aXis.