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PERSISTENT DIRECTED FLAG LAPLACIAN.

Benjamin Jones1, Guo-Wei Wei1,2,3

  • 1Department of Mathematics, Michigan State University MI 48824, USA.

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Summary
This summary is machine-generated.

This study introduces the persistent directed flag Laplacian (PDFL), a novel method extending topological data analysis (TDA). PDFL offers a new approach for analyzing directed flag complexes in scientific applications.

Keywords:
Persistent topological LaplaciansPrimary: 55N31clique complexdirected flag Laplaciansdirected flag complextopological data analysis

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Area of Science:

  • Mathematics
  • Computer Science
  • Data Analysis

Background:

  • Topological data analysis (TDA) is a powerful tool for understanding complex data.
  • Persistent homology is a key TDA technique with limitations.
  • Persistent topological Laplacians (PTLs) address some limitations of persistent homology.

Purpose of the Study:

  • Extend PTLs to directed flag complexes.
  • Introduce the directed flag Laplacian.
  • Develop and validate the persistent directed flag Laplacian (PDFL).

Main Methods:

  • Generalization of PTLs to directed flag complexes.
  • Introduction of the directed flag Laplacian.
  • Development of the persistent directed flag Laplacian (PDFL).

Main Results:

  • The PDFL provides a distinct method for analyzing directed flag complexes.
  • Demonstration of PDFL's potential through example calculations.
  • PDFL offers new insights into geometric and topological object behavior.

Conclusions:

  • The PDFL is a valuable extension of TDA methods.
  • PDFL has potential for real-world applications in science and engineering.
  • This work advances the analysis of directed flag complexes.