The mathematical behavior of correlations at different angles was observed and correlation coefficients were determined by linear and first order exponential fits.
The behavior of correlation-based TDE methods has been studied theoretically [6] also in reverberant enclosures [7, 8].
However, we acknowledge that, given the low-to-moderate heritabilities of the traits evaluated in this study, it is not possible to discard nonnegligible sampling variability on the estimates of Spearman correlation coefficients or other statistical reasons related to unstable behavior of correlations within extreme tails.
Similarly to Table 1, Tables 2 and 3 list the time lags corresponding to the minimum and the maximum of the correlation C ij, and Figures 11, 12, and 13 show the heatmap representation of the behavior of the correlation as function of τ.
The LL displays very unique properties, e.g., the spin and charge separation and the power-law behavior of the correlation functions.
Figure 1a,b depicts the true correlation and complementary correlation functions of x t, Figure 1c,d the simulated simulated ones corresponding to model 1 and Figure 1e,f the simulated ones for model 2. We can see that the simulated trajectories of model 1 pick up adequately the behavior of the correlation function.
This behavior of the correlation indicates that most of the reactions are sequential and reversible.
A monotonic behavior of the correlation vs the time lag is observed for almost all the pairs of the species.
Figures 6, 7, and 8 are heatmap representations of the behavior of the correlation C ij for each possible pairwise combination of the biochemical species.
Open image in new window Fig. 5 Scatter diagram between measured mass transfer coefficient and that calculated from the equation of Venkatnarasaiah and Varma [17], Eq. 5 Table 4 Comparative fitting behavior of the correlations of mass transfer coefficient Equations R 2 SSE Venkatanarasaiah and Varma [17], Eq. 5 0.5042.3800 Developmentnt correlation, Eq. 7 0.7954 0.4462.
Another point focused is the behavior of the spatial correlation in discrete Markov random fields, here studied by the calculus of the practical semivariogram function in the binary Markov images, generated by using the Metropolis algorithm.
