Clear and compress: Computing persistent homology in chunks
We present a parallel algorithm for computing the persistent homology of a filtered chain
complex. Our approach differs from the commonly used reduction algorithm by first …
complex. Our approach differs from the commonly used reduction algorithm by first …
[KNJIGA][B] Discrete Morse Theory
NA Scoville - 2019 - books.google.com
Discrete Morse theory is a powerful tool combining ideas in both topology and
combinatorics. Invented by Robin Forman in the mid 1990s, discrete Morse theory is a …
combinatorics. Invented by Robin Forman in the mid 1990s, discrete Morse theory is a …
Matroid filtrations and computational persistent homology
This technical report introduces a novel approach to efficient computation in homological
algebra over fields, with particular emphasis on computing the persistent homology of a …
algebra over fields, with particular emphasis on computing the persistent homology of a …
Optimal topological simplification of discrete functions on surfaces
Given a function f on a surface and a tolerance δ> 0, we construct a function f δ subject to‖ f
δ− f‖∞≤ δ such that f δ has a minimum number of critical points. Our construction relies on …
δ− f‖∞≤ δ such that f δ has a minimum number of critical points. Our construction relies on …
Homological eigenvalues of graph -Laplacians
D Zhang - Journal of Topology and Analysis, 2023 - World Scientific
Inspired by persistent homology in topological data analysis, we introduce the homological
eigenvalues of the graph p-Laplacian Δ p, which allows us to analyze and classify non …
eigenvalues of the graph p-Laplacian Δ p, which allows us to analyze and classify non …
[HTML][HTML] Generalized morse theory of distance functions to surfaces for persistent homology
This paper brings together three distinct theories with the goal of quantifying shape textures
with complex morphologies. Distance fields are central objects in shape representation …
with complex morphologies. Distance fields are central objects in shape representation …
Duality in persistent homology of images
Duality in Persistent Homology of Images Page 1 Duality in Persistent Homology of Images
Adélie Garin Laboratory for Topology and Neuroscience, EPFL, Lausanne, Switzerland …
Adélie Garin Laboratory for Topology and Neuroscience, EPFL, Lausanne, Switzerland …
Notes on the simplification of the Morse-Smale complex
Abstract The Morse-Smale complex can be either explicitly or implicitly represented.
Depending on the type of representation, the simplification of the Morse-Smale complex …
Depending on the type of representation, the simplification of the Morse-Smale complex …
The Morse theory of Čech and Delaunay filtrations
Given a finite set of points in Rn and a positive radius, we study the Čech, Delaunay--Čech,
alpha, and wrap complexes as instances of a generalized discrete Morse theory. We prove …
alpha, and wrap complexes as instances of a generalized discrete Morse theory. We prove …
Piecewise linear Morse theory
R Grunert - 2017 - refubium.fu-berlin.de
Klassische Morsetheorie betrachtet glatte Mannigfaltigkeiten und auf ihnen definierte
Morsefunktionen, also glatte reellwertige Funktionen, deren kritische Punkte sämtlich nicht …
Morsefunktionen, also glatte reellwertige Funktionen, deren kritische Punkte sämtlich nicht …