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On the Structural Theorem of Persistent Homology [PDF]
Discrete & Computational Geometry, 2018 We study the categorical framework for the computation of persistent homology, without reliance on a particular computational algorithm. The computation of persistent homology is commonly summarized as a matrix theorem, which we call the Matrix Structural Theorem.
Killian Meehan +2 more
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Persistent Homology for Virtual Screening [PDF]
, 2018 Finding new medicines is one of the most important tasks of pharmaceutical companies. One of the best approaches to finding a new drug starts with answering this simple question: Given a known effective drug X, what are the top 100 molecules in our ...
Theodore L. Willke (5633319) +5 more
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Persistent Homology applied to location problems
MATEC Web of Conferences, 2018 Different approaches to solve location problems in transport and logistics have been developed in the literature. This article introduces a new approach using the concept of persistent homology which has been proved to be an efficient method in ...
Bennis Driss, Gharib Fouad, Lebbar Ghita
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Adaptive Approximation of Persistent Homology
Journal of Applied and Computational Topology, 2023 Abstract We study an important preprocessing step for the efficient calculation of persistent homology: coarsening a set of points while controlling the quality of the induced persistence diagram. This coarsening step is instrumental in reducing the overall runtime of state-of-the-art algorithms such as Ripser, GUDHI, or PHAT.
Maria Herick +2 more
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Formation of Machine Learning Features Based on the Construction of Tropical Functions
Моделирование и анализ информационных систем, 2022 One of the main methods of computational topology and topological data analysis is persistent homology, which combines geometric and topological information about an object using persistent diagrams and barcodes.
Sergey N. Chukanov, Ilya S. Chukanov
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Analysis of Dynamic Evolution of Complex Brain Networks Based on Persistent Homology
Chinese Journal of Magnetic Resonance, 2021 Some studies have shown that the cognitive state in Alzheimer's disease (AD) patients is related to the changes of the temporal characteristics of dynamic functional connection. Persistent homology index analysis method provides a deeper insight into the
JIA Jia-ying +3 more
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Distributed Computation of Persistent Homology [PDF]
, 2013 Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically -- as long as the algorithm does not exhaust the available memory.
Ulrich Bauer +2 more
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Topological data analysis for the string landscape
Journal of High Energy Physics, 2019 Persistent homology computes the multiscale topology of a data set by using a sequence of discrete complexes. In this paper, we propose that persistent homology may be a useful tool for studying the structure of the landscape of string vacua. As a scaled-
Alex Cole, Gary Shiu
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Model comparison via simplicial complexes and persistent homology
Royal Society Open Science, 2021 In many scientific and technological contexts, we have only a poor understanding of the structure and details of appropriate mathematical models. We often, therefore, need to compare different models.
Sean T. Vittadello, Michael P. H. Stumpf
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Stable volumes for persistent homology
Journal of Applied and Computational Topology, 2023 AbstractThis paper proposes a stable volume and a stable volume variant, referred to as a stable sub-volume, for more reliable data analysis using persistent homology. In prior research, an optimal cycle and similar ideas have been proposed to identify the homological structure corresponding to each birth-death pair in a persistence diagram. While this
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