TDA Software: PETLS, CACTIS | Persistent Laplacian & Flag Complex Tools
CACTIS: Coarse-grained Asymmetric Cycles in Time Series
CACTIS is a Python library for applying topological data analysis (TDA) to time series using directed flag complexes and persistent homology. It extracts coarse-grained asymmetric cycles from temporal data for applications in dynamical systems and climate science.
PETLS: Persistent Topological Laplacian Software
PETLS is a high-performance C++ library with Python bindings for efficiently computing persistent Laplacians in topological data analysis (TDA). It provides order-of-magnitude speedups over existing implementations for persistent Laplacian computations on various complexes including Rips complexes, alpha complexes, flag complexes, and cellular sheaves.
Key features:
- Fast persistent Laplacian eigenvalue computation
- Support for multiple complex types (Rips, Alpha, directed flag complexes)
- Python interface:
pip install petls - Applications to molecular biology, network analysis, and computational topology
Resources:
- PETLS Documentation
- GitHub Repository
- arXiv paper for PETLS
- AATRN YouTube Tutorial on Persistent Laplacians
Khovanov Laplacian and Khovanov Dirac
Mathematica implementation of Khovanov Laplacians for Khovanov homology applied to knot theory. This extends combinatorial Laplacian theory to the geometric topology of knots and links.
Persistent Directed Flag Laplacian (PDFL)
PDFL combines persistent topological Laplacians with directed flag complexes (directed clique complexes) for TDA on directed networks. Built on the Flagser library for fast persistent homology of directed flag complexes.