Results 61 to 70 of about 1,043,448 (307)
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 ...
openaire +7 more sources
Homological Algebra for Persistence Modules [PDF]
Foundations of Computational Mathematics, 2021 41 pages, accepted by Foundations of Computational ...
Bubenik, Peter, Milićević, Nikola
openaire +2 more sources
Persistent Homology analysis of Phase Transitions [PDF]
, 2016 Persistent homology analysis, a recently developed computational method in algebraic topology, is applied to the study of the phase transitions undergone by the so-called XY-mean field model and by the phi^4 lattice model, respectively.
De Nigris, Sarah +6 more
core +5 more sources
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
openaire +3 more sources
The Comparison of Diffeomorphic Images Based on the Construction of Persistent Homology
Моделирование и анализ информационных систем, 2019 An object shape analysis is a problem that is related to such areas as geometry, topology, image processing and machine learning. For analyzing the form, the deformation between the source and terminal form of the object is estimated.
Sergey N. Chukanov
doaj +1 more source
Persistent Homology in Machine Learning: Applied Sciences Review
Proceedings of the International Conference on Applied Innovations in IT, 2023 Topological Data Analysis (‘TDA’) has become a vibrant and quickly developing field in recent years, providing topology-enhanced data processing and Machine Learning (‘ML’) applications.
Oleksandr Yavorskyi +2 more
doaj +1 more source
BPS Spectra, Barcodes and Walls [PDF]
, 2019 BPS spectra give important insights into the non-perturbative regimes of supersymmetric theories. Often from the study of BPS states one can infer properties of the geometrical or algebraic structures underlying such theories.
Cirafici, Michele
core +3 more sources