Results 101 to 110 of about 521,410 (206)

A Comprehensive Review of Matrix Equations in Dynamical Systems and Control Theory

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
Matrix equations are of foundational importance in the modeling, investigation, and control of dynamical systems. This review discusses various classes of matrix equations, their solutions, and their relevance in control theory and dynamical systems.
Chacha Stephen Chacha, Arpan Hazra
wiley   +1 more source

Some generalized metric properties on hyperspaces with the Vietoris topology

, 2019
18
Lin, Fucai, Shen, Rongxin, Liu, Chuan
openaire   +2 more sources

Generalized metric properties at a subset on the Vietoris hyperspace F(X)

Filomat
In this paper, we study generalized metric properties at a subset on the hyperspace F (X) of finite subsets of a space X endowed with the Vietoris topology. We prove that X has the covering property ? at A if and only if F (X) has the covering property ?
L. Tuyen, O. Tuyen
semanticscholar   +1 more source

When does the Fell topology on a hyperspace of closed sets coincide with the meet of the upper Kuratowski and the lower Vietoris topologies?

Topology and its Applications, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nogura, Tsugunori, Shakhmatov, Dmitri
openaire   +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

An Adaptation of the Vietoris Topology for Ordered Compact Sets

We discuss a natural topology on powers of a space that is inspired by the Vietoris topology on compact subsets. We then place this topology in context with other product topologies; specifically, we compare this topology with the Tychonoff product, the box product, and Bell's uniform box topology.
Caruvana, Christopher, Holshouser, Jared
openaire   +2 more sources

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

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

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.
Shin, Jaesun, Jeon, Eunjoo, Cho, Taewon, Cho, Namkyeong, Gwon, Youngjune   +4 more
openaire   +2 more sources

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

Coincidence of Vietoris and Wijsman topologies: A new proof

, 1997
Summary: Let \((X,d)\) be a metric space and \(\text{CL}(X)\) the family of all nonempty closed subsets of \(X\). We provide a new proof of the fact that the coincidence of the Vietoris and Wijsman topologies induced by the metric \(d\) forces \(X\) to be a compact space.
openaire   +2 more sources