Persistent homology of groups [PDF]
Journal of Group Theory, 2010 We introduce and investigate notions of persistent homology for p-groups and for coclass trees of p-groups. Using computer techniques we show that persistent homology provides fairly strong homological invariants for p-groups of order at most 81.
Ellis, Graham, King, Simon A.
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Predicting Affinity Through Homology (PATH): Interpretable binding affinity prediction with persistent homology. [PDF]
PLoS Computational BiologyAccurate binding affinity prediction (BAP) is crucial to structure-based drug design. We present PATH+, a novel, generalizable machine learning algorithm for BAP that exploits recent advances in computational topology.
Yuxi Long, Bruce R Donald
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Dynamic ECG signal quality evaluation based on persistent homology and GoogLeNet method. [PDF]
Front Neurosci, 2023 Cardiovascular disease is a serious health problem. Continuous Electrocardiograph (ECG) monitoring plays a vital role in the early detection of cardiovascular disease. As the Internet of Things technology continues to mature, wearable ECG signal monitors
Ren Y +5 more
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Persistent Homology Approach for Human Presence Detection from 60 GHz OTFS Transmissions. [PDF]
Sensors (Basel), 2023 Orthogonal Time Frequency Space (OTFS) is a new, promising modulation waveform candidate for the next-generation integrated sensing and communication (ISaC) systems, providing environment-awareness capabilities together with high-speed wireless data ...
Maršálek R +6 more
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Persistent Homology-Based Machine Learning Method for Filtering and Classifying Mammographic Microcalcification Images in Early Cancer Detection. [PDF]
Cancers (Basel), 2023 Simple Summary The appearance of microcalcifications in mammogram images is an essential predictor for radiologists to detect early-stage breast cancer.
Malek AA +5 more
europepmc +2 more sources
Persistent Homology and String Vacua [PDF]
Journal of High Energy Physics, 2015 We use methods from topological data analysis to study the topological features of certain distributions of string vacua. Topological data analysis is a multi-scale approach used to analyze the topological features of a dataset by identifying which ...
Cirafici, Michele
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Topological Signals of Singularities in Ricci Flow [PDF]
Axioms, 2017 We implement methods from computational homology to obtain a topological signal of singularity formation in a selection of geometries evolved numerically by Ricci flow.
Paul M. Alsing +6 more
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A Spatiotemporal Brain Network Analysis of Alzheimer’s Disease Based on Persistent Homology [PDF]
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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Computing Persistent Homology by Spanning Trees and Critical Simplices [PDF]
Research, 2023 Topological data analysis can extract effective information from higher-dimensional data. Its mathematical basis is persistent homology. The persistent homology can calculate topological features at different spatiotemporal scales of the dataset, that is,
Dinghua Shi +3 more
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Categorification of persistent homology [PDF]
Discrete & Computational Geometry, 2014 We redevelop persistent homology (topological persistence) from a categorical point of view. The main objects of study are diagrams, indexed by the poset of real numbers, in some target category.
A. Zomorodian +18 more
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