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.

Despite this small discrepancy, the model is very accurate on the training data ( correlation coefficient of 0.97).

The Pearson correlation coefficient (PCC, also known as the Pearson’s r) was computed between hmndam predictions and the values in both databases.

Correlation coefficients are shown in the last column of Table 1.

When initiated with R = 1,000 random peptides, it achieves a correlation coefficient of 0.90 (CAMPs) and 0.93 (BPP).

The models are clearly predictive of ADCP, obtaining a mean Pearson correlation coefficient PCC = 0.64 (standard deviation 0.15) over the 200-replicate fivefold.

Performance was assessed by Pearson correlation coefficient (PCC), r, between observed and predicted function value; r assesses the linear correlation (between -1 for perfectly anticor-related and +1 for perfectly correlated), while 1'2 represents the fraction of the variation eXplained.

Filtered features were selected by choosing the feature most strongly correlated with the function within each cluster, in terms of the magnitude of the Pearson correlation coefficient (Fig 2A).

Antibody feature:function and feature:feature correlations were computed over the set of 80 vaccinated subjects and assessed using Pearson correlation coefficient and p-value.

Features were clustered based on the profile of their correlation coefficients over the set of all features.

Circular statistics tool-sets include some correlation metrics [24], such as the circular correlation coefficient [21] which corresponds to the COOP in the same case.

Specificically the circular correlation coefficient can only be used for uniform distributions (i.e.

In that special case, the circular correlation coefficient and the COOP converge to the same equation (SI Supplemental Text).

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.

Black line indicates a least-squares regression with correlation coefficient (R) and coefficient of determination (R2).

Black line indicates a least-squares regression With correlation coefficient (R) and coefficient of determination (R2).

Lines (Model-1: red; Model-2: blue) indicate least-squares regressions With respective correlation coefficient (R) and coefficient of determination (R2).

Lines (Model-1: red; Model-2: blue) indicate least-squares regressions with respective correlation coefficient (R) and 810 Fig.

Fig 4A and 4C clearly demonstrate a negative correlation between node degree and dPLI (Spearman correlation coefficient = - 0.61, p< 0.01) and positive correlation between node degree and amplitude of oscillators (Spearman correlation coefficient = 0.92, p<0.01) at coupling strength 8 = 3.

The strong negative correlation observed during the conscious state (Spearman correlation coefficient of -O.76 (p<0.01)) disappears during the unconscious state (Spearman correlation coefficient of -0.04 (p<0.01)).

However, the correlation between node degree and amplitude for the EEG network differs from the models (nonsignificant Spearman correlation coefficient of 0.266 (p = 0.1) for the conscious state).

The spearman correlation coefficient was used for evaluating the correlations among node degree, amplitude and dPLI of the 64 channels (“corr.m” in Matlab).

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.