Aug 2026· Zenodo (CERN European Organization for Nuclear Research)
Topological and Geometric Data Analysis
Abstract
This paper explores the potential of utilizing geometric analysis as a novel approach to understanding the complexity of biological systems. Biological systems, particularly protein folding and gene regulation, exhibit intricate geometric structures. This research proposes a framework to quantify and analyze these structures by employing topological concepts, establishing a bridge between mathematics and biological research. The core claim is to develop a method for comprehensively assessing the complexity of biological systems through the lens of geometric analysis, offering a fundamentally new perspective on the study of these systems. This work will examine the application of geometric topology, specifically measures of connectivity, curvature, and torsion, to reveal underlying patterns and quantify complexity. The goal is to move beyond traditional statistical methods and offer a more insightful, quantitative understanding of biological systems.
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