Related Experiment Video
Updated: Jan 16, 2026

Image-based Lagrangian Particle Tracking in Bed-load Experiments
Published on: July 20, 2017
PERSISTENT DIRECTED FLAG LAPLACIAN
Benjamin Jones1, Guo-Wei Wei1,2,3
1Department of Mathematics, Michigan State University MI 48824, USA.
None:
Topological data analysis (TDA) has had enormous success in science and engineering in the past decade. Persistent topological Laplacians (PTLs) overcome some limitations of persistent homology, a key technique in TDA, and provide substantial insight to the behavior of various geometric and topological objects. This work extends PTLs to directed flag complexes, which are an exciting generalization to flag complexes, also known as clique complexes, that arise naturally in many situations. We introduce the directed flag Laplacian and show that the proposed persistent directed flag Laplacian (PDFL) is a distinct way of analyzing these flag complexes. Example calculations are provided to demonstrate the potential of the proposed PDFL in real world applications.
More Related Videos
Related Concept Videos
Second Derivatives and Laplace Operator
Consider a scalar function. The curl of its...
Poisson's And Laplace's Equation
Region of Convergence of Laplace Tarnsform
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...
Definition of Laplace Transform
Properties of Laplace Transform-I
The Linearity property is foundational to the Laplace transform. It states that the transform of a linear combination of functions is equivalent to the same...
Properties of Laplace Transform-II
Time differentiation involves analyzing the rate of change of a function over time. Mathematically, it is the derivative of a function with respect to time. This concept can be likened to tracking...

