Results 51 to 60 of about 1,143,028 (268)
Persistent Homology of Semialgebraic Sets
SIAM Journal on Applied Algebra and Geometry, 2023 We give an algorithm with singly exponential complexity for computing the barcodes up to dimension $\ell$ (for any fixed $\ell \geq 0$) of the filtration of a given semi-algebraic set by the sub-level sets of a given polynomial. Our algorithm is the first algorithm for this problem with singly exponential complexity, and generalizes the corresponding ...
Saugata Basu, Negin Karisani
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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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Stable comparison of multidimensional persistent homology groups with torsion [PDF]
, 2010 The present lack of a stable method to compare persistent homology groups with torsion is a relevant problem in current research about Persistent Homology and its applications in Pattern Recognition.
Frosini, Patrizio
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Probing Multipartite Entanglement Through Persistent Homology [PDF]
Communications in Mathematical Physics, 2023 We propose a study of multipartite entanglement through persistent homology, a tool used in topological data analysis. In persistent homology, a 1-parameter filtration of simplicial complexes called a persistence complex is used to reveal persistent ...
Greg A. Hamilton, Felix Leditzky
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G-invariant persistent homology [PDF]
Mathematical Methods in the Applied Sciences, 2014 Classical persistent homology is not tailored to study the action of transformation groups different from the group Homeo(X) of all self-homeomorphisms of a topological space X. In order to obtain better lower bounds for the natural pseudo-distance d_G associated with a subgroup G of Homeo(X), we need to adapt persistent homology and consider G ...
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Homological Algebra for Persistence Modules [PDF]
Foundations of Computational Mathematics, 2021 41 pages, accepted by Foundations of Computational ...
Bubenik, Peter, Milićević, Nikola
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A Spatiotemporal Brain Network Analysis of Alzheimer’s Disease Based on Persistent Homology
Frontiers in Aging Neuroscience, 2022 Current brain network studies based on persistent homology mainly focus on the spatial evolution over multiple spatial scales, and there is little research on the evolution of a spatiotemporal brain network of Alzheimer’s disease (AD).
Jiacheng Xing +4 more
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On the effectiveness of persistent homology [PDF]
Neural Information Processing Systems, 2022 Persistent homology (PH) is one of the most popular methods in Topological Data Analysis. Even though PH has been used in many different types of applications, the reasons behind its success remain elusive; in particular, it is not known for which ...
Renata Turkevs +2 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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Persistent homological cell tracking technology
Scientific Reports, 2023 AbstractIn this paper, we develop a cell tracking method based on persistent homological figure detection technology. We apply our tracking method to 9 different time-series cell images and extract several kinds of cell movements. Being able to analyze various images with a single method allows researchers to systematically understand and compare ...
Haruhisa Oda +4 more
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