Results 71 to 80 of about 416 (159)

Vietoris topology on hyperspaces associated to a noncommutative compact space

Mathematica, 2018
We study some topological spaces that can be considered as hyperspaces associated to noncommutative spaces. More precisely, for a NC compact space associated to a unital C*-algebra, we consider the set of closed projections of the second dual of the C*-algebra as the hyperspace of closed subsets of the NC space.
openaire   +2 more sources

Atom probe informed persistent homology analysis of precipitation topology and hardening

Materials & Design
Precipitation hardening (PH) in metals arises from the evolution of precipitate structures, where connectivity and spatial organisation critically influence mechanical performance.
Siying Zhu, Tao Zhou
doaj   +1 more source

Classification of Topological Contacts Between Phases in 3D Multiphase Systems by Betti Number Dynamics

Mathematics
A methodological approach to the quantitative description of the spatial relations between phases in multicomponent systems is developed, based on the comparison of Betti numbers of united phases.
Andrey O. Kalashnikov, Diana V. Manukovskaya   +1 more
doaj   +1 more source

Topological Study of β-Sparsified d-Uniform Hypergraph-Based Simplicial Complexes

Mathematics
Persistent Homology (PH) is a method of Topological Data Analysis that characterizes the topological structure of a space. Unfortunately, the computation of PH for high-dimensional and big data is not possible due to the exponential growth of the ...
Rohit P. Singh, Nicholas O. Malott, Raihan Rafeek, Philip A. Wilsey   +3 more
doaj   +1 more source

Topological Machine Learning for Financial Crisis Detection: Early Warning Signals from Persistent Homology

Computers
We propose a strictly causal early–warning framework for financial crises based on topological signal extraction from multivariate return streams. Sliding windows of daily log–returns are mapped to point clouds, from which Vietoris–Rips persistence ...
Ecaterina Guritanu, Enrico Barbierato, Alice Gatti   +2 more
doaj   +1 more source

Line Graph Vietoris-Rips Persistence Diagram for Topological Graph Representation Learning

J. Mach. Learn. Res.
While message passing graph neural networks result in informative node embeddings, they may suffer from describing the topological properties of graphs. To this end, node filtration has been widely used as an attempt to obtain the topological information of a graph using persistence diagrams.
Jaesun Shin, Eunjoo Jeon, Taewon Cho, Namkyeong Cho, Youngjune Gwon   +4 more
openaire   +3 more sources

Topological Data Analysis for Characterising Earthquake Damage Patterns in Urban Building Clusters: A Novel Computational Framework with Benchmark Validation

Buildings
The spatial pattern of building damage produced by an earthquake carries information that classical building-by-building vulnerability indices cannot capture.
Enio Deneko, Marjo Hysenlliu, Klodian Dhoska, Andres Annuk   +3 more
doaj   +1 more source

A unified spectral-persistent homology framework for stable and generalizable topological deep learning

Discover Computing
Topological Deep Learning (TDL) boosts the capabilities of neural networks by integrating topological features from complex data structures like graphs and simplicial complexes.
Saif Hameed Abbood Alwaeli, Ali A. Abdulsaeed, Shams Jamal Fayyadh, Muhammad I. Khan, Abdallah Yousif, Tanzila Saba, Saeed Ali Bahaj   +6 more
doaj   +1 more source

Enhancing the Vietoris–Rips simplicial complex for topological data analysis: applications in cancer gene expression datasets

International Journal of Data Science and Analytics
Abstract The aim of this study is to enhance the extraction of informative features from complex data through the application of topological data analysis (TDA) using novel topological overlapping measures. Topological data analysis has emerged as a promising methodology for extracting meaningful insights from complex datasets.
Lebohang Mashatola, Zubayr Kader, Naaziyah Abdulla, Mandeep Kaur   +3 more
openaire   +1 more source

Maximum persistent Betti numbers of Čech complexes. [PDF]

J Appl Comput Topol
Edelsbrunner H, Kahle M, Kanazawa S.
europepmc   +1 more source