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For such fixed points, we obtain a complete characterization by means of eigenfunctions of the Laplacian.
Assuming a curve representation by M = tmax discrete points, we obtain h = M/N.
By making a standard triangulation of the parameter points, we obtain a corresponding triangulation of the original data set.
For complex turning points, we obtain exponentially small reflection, a new result in the context of difference equations.
Based on the Melnikov method and numerical computations for Melnikov integrals, fixed points, and turning points, we obtain conditions for chaos suppression and generation.
Second, by collecting robotic motion data at a set of operating points, we obtain the quantitative mapping from GIM tuning parameters to robotic speed.
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Using the cutoff points, we obtained sensitivities, specificities, positive predictive values, and negative predictive values for incident MetS.
The cut-off points we obtained by ROC curve analysis are relatively higher than those suggested by previous studies [ 20, 30].
By sampling this period at five consecutive time points we obtained samples with different proportions of cells at the major morphogenetic stages.
Based on 18 RNA-Seq libraries from roots, stems, and leaves at different time points, we obtained transcriptome profiles and identified the DEGs upon benzoic acid stress.
After normalizing these concentration values, depicting them as a function of Zn (in logarithm), and smoothly connecting these simulated data points, we obtained the purple curve in Fig. 3d (please note that only three simulated data points for Zur assay are shown as small purple dots in this figure to avoid confusion with the experimental data points).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com