Simplicial complexes provide a mathematical structure for understanding higher-order interactions in complex systems. Based on frameworks from non-commutative geometry, particularly the topological Dirac operator and Connes’ spectral triplet, the authors introduce measures for analyzing simplicial complexes, including a definition of discrete curvature, and apply these tools to a dataset of musical compositions such as J. S. Bach’s sonatas and partitas for solo violin.
- Sara Najem
- Dima Mrad
- Mohammad Elsayed
