Results 71 to 80 of about 707 (188)

Multiscale Cell–Cell Interactive Spatial Transcriptomics Analysis

Advanced Science, Volume 12, Issue 44, November 27, 2025.
In this study, we present the MultiScale Cell‐Cell Interactive Spatial Transcriptomics Analysis method, which unites the strengths of spatially resolved deep learning techniques with a topological representation of multi‐scale cell‐cell similarity relations.
Sean Cottrell, Guo‐Wei Wei
wiley   +1 more source

Topological data analysis reveals altered brain connectivity in Alzheimer’s disease [PDF]

AIP Advances
This study analyzed brain network topology by using persistent homology (PH) on resting-state functional magnetic resonance imaging data from the Alzheimer’s Disease Neuroimaging Initiative.
Weiwei Zhang, Xinhua Tang, Xianfu Zhang, Shengxiang Xia   +3 more
doaj   +1 more source

AN APPROACH TO THE CONCEPT OF SOFT VIETORIS TOPOLOGY

, 2016
WOS: 000388622400011In the present paper, we study the Vietoris topology in the context of soft set. Firstly, we investigate some aspects of first countability in the soft Vietoris topology.
Demir, İzzettin
core  

A geometric Vietoris-Begle theorem, with an application to convex subsets of topological vector lattices

Topology and its Applications, 2022
We show that if $L$ is a topological vector lattice, $u \colon L \to L$ is the function $u(x) = x \vee 0$, $C \subset L$ is convex, and $D = u(C)$ is metrizable, then $D$ is an ANR and $u|_C \colon C \to D$ is a homotopy equivalence and thus an AR.
openaire   +4 more sources

Sequences suffice for pointfree uniform completions

Journal of the London Mathematical Society, Volume 112, Issue 2, August 2025.
Abstract Completions of metric spaces are usually constructed using Cauchy sequences. However, this does not work for general uniform spaces, where Cauchy filters or nets must be used instead. The situation in pointfree topology is more straightforward: the correct completion of uniform locales can indeed be obtained as a quotient of a locale of Cauchy 
Graham Manuell
wiley   +1 more source

Butterfly points and hyperspace selections

Applied General Topology
If f is a continuous selection for the Vietoris hyperspace ℱ(X) of the nonempty closed subsets of a space X, then the point f(X)∊ X is not as arbitrary as it might seem at first glance. In this paper, we will characterise these points by local properties
Valentin Gutev
doaj   +1 more source

Lifting Dynamical Properties to Hyperspaces

Applied General Topology, 2014
For a dynamical system (X,f), the passage of various dynamical properties such as transitivity, total transitivity, weakly mixing, mixing, topological exactness, topological conjugacy, to the hyperspace C(X) of X consisting of nonempty closed connected ...
Dania Masood, Pooja Singh
doaj   +1 more source

Birational complexity and dual complexes

Proceedings of the London Mathematical Society, Volume 131, Issue 2, August 2025.
Abstract We introduce the notion of birational complexity of a log Calabi–Yau pair. This invariant measures how far the log Calabi–Yau pair is from being birational to a toric pair. We study fundamental properties of the new invariant, with a particular focus on the geometry of dual complexes.
Mirko Mauri, Joaquín Moraga
wiley   +1 more source

Topology-controlled Laplace–Beltrami operator on point clouds based on persistent homology

Graphical Models
Computing the Laplace–Beltrami operator on point clouds is essential for tasks such as smoothing and shape analysis. Unlike meshes, determining the Laplace–Beltrami operator on point clouds requires establishing neighbors for each point.
Ao Zhang, Qing Fang, Peng Zhou, Xiao-Ming Fu   +3 more
doaj   +1 more source