To quantitatively describe the spatial distribution of voids in the specimen, probability functions such as two-point correlation, lineal-path, and two-point cluster functions are adopted.
Then, void density contour and probabilistic description methods, such as two-point correlation and lineal-path functions, are used to describe the void distribution inside the specimen.
We test the approach on five examples and show that the spatial dependencies within the microstructures are well preserved, as evaluated via correlation and lineal-path functions.
Here, low-order probability functions, such as two-point correlation and lineal-path functions, are used to examine the anisotropic insulation distribution, and their integrations are also utilized for the quantitative description.
Correlation analyses and lineal regression models were used to evaluate the association between ALT levels and HIRI.
The lineal equation was y=9803.3 x−3.2442 and the correlation coefficient was R=1, where y is the concentration of R-salbutamol sulfate in solution (μg/mL) and x is the peak area of absorbance.
Firstly, amino acids with a Pearson correlation coefficient above 0.8 were designated as lineal consanguinity, either paternity or fraternity.
To assess the clinical correlates of SF-36 HRQOL, lineal regression analyses were carried out.
Fig. 4 shows the probability functions of the virtual samples with anisotropic insulations in the x, y, and z directions; Fig. 4a c are the two-point correlation function ((P_{ii}(r))), and Fig. 4d f are the lineal-path function ((L_i(r))).
For characterization of the insulation distributions, probability functions, such as two-point correlation (Tewari et al. 2004; Gokhale et al. 2005) and lineal-path functions (Lu and Torquato 1992; Chung and Han 2010), were used.
