Abstract:
This study uses the biharmonic spline interpolation method to create surfaces that help analyze the interactions and synergies of multiple Sustainable Development Goals (SDGs). The detailed analysis reveals two unique interpolation surfaces: The Global Reporting Initiative (GRI) and Environmental, Social, and Governance (ESG). The GRI surface is formed from a linear combination of three GRI pillars, displaying two harmonic patterns. Six convex harmonics, labeled A to F, consistently score below the 0.6 level, while the concave harmonic G exceeds the 0.8 level. This surface converts complex three-dimensional data into a simpler two-dimensional GRI contour plot, which shows seven unique contours labeled A to G. A crucial boundary at the 0.7 level is introduced in the plot, which is key to identifying specific synergies within the GRI contour plot. Conversely, the ESG surface arises from the linear combination of three ESG pillars, creating 12 unique patterns, labeled A to L. Interestingly, the concave harmonics A to F consistently surpass the 0.9 level, while the convex harmonics G to L stay below the 0.7 level. The ESG surface accurately represents complex three-dimensional data, making it suitable for the contour plot. The ESG contour plot is an important analytical tool that helps identify a critical boundary set at the 0.8 level, crucial for understanding the pattern of interactions and synergies depicted in the ESG contour plot. In conclusion, the study confirms that both the GRI and ESG interpolation surfaces, along with their respective contour plots, are effective tools for analyzing the interactions and synergies among the top 100 schools featured in THE Impact Rankings.
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