Abstract
This paper introduces "Kabirian-based optinalysis (KBO)," a pioneering framework that addresses the longstanding challenges in estimating symmetry/asymmetry, similarity/dissimilarity, and identity/unidentity within mathematical structures and biological sequences. The existing methods often lack a strong theoretical foundation, leading to inconsistencies and limitations. Kabirian-based optinalysis draws inspiration from isomorphism and automorphism, providing a theoretically grounded framework that unifies estimation methodologies. It introduces the concept of optiscale, autoreflective pairing, isoreflective pairing, and others ensuring invariance and robustness under various mathematical transformations and establishing functional bijectivity for isomorphic or automorphic structures. This not only overcomes previous limitations but also offers precise and interpretable estimations. Additionally, the framework introduces "geometrical pairwise analysis" to improve sensitivity to position-specific and character-specific variations in biological sequences. This novel approach enhances the accuracy of sequence similarity assessments, surpassing the constraints of conventional methods. The novelty of this work extends beyond mathematics and biology, impacting diverse fields such as computer science, data analysis, pattern recognition, and evolutionary biology. Kabirian-based optinalysis presents a holistic and theoretically grounded solution that has the potential to revolutionize the analysis of complex structures and sequences, opening new horizons for interdisciplinary research.•Inspired by automorphism and isomorphism, Kabirian-based optinalysis introduces a new paradigm-shifting and unified approach to estimations in mathematical structures and biological sequences with a solid conceptual and theoretical foundation.•The GPA method enhances pairwise sequence similarity estimation by being sensitive to position-specific and character-specific variations and providing a comprehensive characterization of these features.