| الملخص: | This study introduces a fresh perspective on conventional notions of “shape” and “distribution” by utilizing the innovative framework of branch-length similarity (BLS) entropy. In our exploration of “shape,” we propose BLS entropy-based interpretations of circularity, elongation, and symmetry. We subject these novel concepts to quantitative evaluation against established benchmarks, highlighting their inherent advantages. The evaluation is conducted using a dataset of 1365 images from the MPEG-7 collection. Additionally, within the context of BLS entropy-driven “distributions,” we present an inventive approach involving the construction of networks that connect nodes through Delaunay triangles within a two-dimensional space. In this framework, we employ <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula> to quantify both local and global connectivity of individual nodes. To effectively demonstrate the utility of <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula>, we apply them to the analysis of intricate foraging dynamics exhibited by a school of fish. Through this application, we uncover shifts in both individual fish behavior and collective school dynamics, providing illuminating insights into their behavioral changes.
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