Morse theory for filtrations and efficient computation of persistent homology
Morse Theory for Filtrations and Efficient Computation of Persistent Homology |
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[HTML][HTML] Phat–persistent homology algorithms toolbox
Phat is an open-source C++ library for the computation of persistent homology by matrix
reduction, targeted towards developers of software for topological data analysis. We aim for …
reduction, targeted towards developers of software for topological data analysis. We aim for …
Parallel computation of 2D Morse-Smale complexes
N Shivashankar, M Senthilnathan… - IEEE Transactions on …, 2011 - ieeexplore.ieee.org
The Morse-Smale complex is a useful topological data structure for the analysis and
visualization of scalar data. This paper describes an algorithm that processes all mesh …
visualization of scalar data. This paper describes an algorithm that processes all mesh …
Towards personalized diagnosis of glioblastoma in fluid-attenuated inversion recovery (FLAIR) by topological interpretable machine learning
Glioblastoma multiforme (GBM) is a fast-growing and highly invasive brain tumor, which
tends to occur in adults between the ages of 45 and 70 and it accounts for 52 percent of all …
tends to occur in adults between the ages of 45 and 70 and it accounts for 52 percent of all …
Efficient computation of 3D Morse–Smale complexes and persistent homology using discrete Morse theory
We propose an efficient algorithm that computes the Morse–Smale complex for 3D gray-
scale images. This complex allows for an efficient computation of persistent homology since …
scale images. This complex allows for an efficient computation of persistent homology since …
Persistent homology of unweighted complex networks via discrete Morse theory
Topological data analysis can reveal higher-order structure beyond pairwise connections
between vertices in complex networks. We present a new method based on discrete Morse …
between vertices in complex networks. We present a new method based on discrete Morse …
Computational topology in text mining
In this paper we present our ongoing research on applying computational topology to
analysis of structure of similarities within a collection of text documents. Our work is on the …
analysis of structure of similarities within a collection of text documents. Our work is on the …
Discrete morse theory for computing zigzag persistence
We introduce a theoretical and computational framework to use discrete Morse theory as an
efficient preprocessing in order to compute zigzag persistent homology. From a zigzag …
efficient preprocessing in order to compute zigzag persistent homology. From a zigzag …
[PDF][PDF] Discrete Morse theory for filtrations
V Nanda - 2012 - rucore.libraries.rutgers.edu
We provide a brief synopsis of definitions and results from homological algebra in Section
2.2 and combinatorial topology in Section 2.5 while referring the reader to the excellent …
2.2 and combinatorial topology in Section 2.5 while referring the reader to the excellent …
Forman-Ricci curvature and persistent homology of unweighted complex networks
We present the application of topological data analysis (TDA) to study unweighted complex
networks via their persistent homology. By endowing appropriate weights that capture the …
networks via their persistent homology. By endowing appropriate weights that capture the …