Related papers: Topological characterizations to three types of co…
This paper proposes topology optimization for considering shielding and penetrating features. Based on the fictitious physical model, which is a useful approach to control geometric features, the proposed method analyzes fictitious…
In this note, we show some improvements for Theorem 7 and Example 8 in Shiping Wang[Information Sciences 263(1), 186-197, 2014]. Concretely, we study further the sixth lower and upper approximations of sets for covering approximation…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
In practical situations, it is of interest to investigate computing approximations of sets as an important step of knowledge reduction of dynamic covering decision information systems. In this paper, we present incremental approaches to…
In practical situations, calculating approximations of concepts is the central step for knowledge reduction of dynamic covering decision information system, which has received growing interests of researchers in recent years. In this paper,…
Topological Machine Learning (TML) is an emerging field that leverages techniques from algebraic topology to analyze complex data structures in ways that traditional machine learning methods may not capture. This tutorial provides a…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…
Dense prediction tasks such as depth perception and semantic segmentation are important applications in computer vision that have a concrete topological description in terms of partitioning an image into connected components or estimating a…
This article introduces and studies the tight approximation property, a property of algebraic varieties defined over the function field of a complex or real curve that refines the weak approximation property (and the known cohomological…
The introduction of covering-based rough sets has made a substantial contribution to the classical rough sets. However, many vital problems in rough sets, including attribution reduction, are NP-hard and therefore the algorithms for solving…
The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches…
In this paper, we introduce statistical bounded set on topological vector space. Also, we consider three classes of bounded operators from topological vector spaces to ordered topological vector spaces. Moreover, we give relations between…
In this paper, we will present some ideas to use 3D topology for quantum computing. Topological quantum computing in the usual sense works with an encoding of information as knotted quantum states of topological phases of matter, thus being…
Methods from computational topology are becoming more and more popular in computer vision and have shown to improve the state-of-the-art in several tasks. In this paper, we investigate the applicability of topological descriptors in the…
One of the main prerequisites for understanding sheaves on elementary toposes is the proof that a (Lawvere-Tierney) topology on a topos induces a closure operator on it, and vice-versa. That standard theorem is usually presented in a…
Hub Covering Problems arise in various practical domains, such as urban planning, cargo delivery systems, airline networks, telecommunication network design, and e-mobility. The task is to select a set of hubs that enable tours between…
Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster…
While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well developed. Despite increasing demands from applications this…
The theory of rough sets was firstly introduced by Pawlak (see \cite{p}). Many Mathematician has been studied the relations between rough sets and algebraic systems such as groups, rings and modules. In this paper we will introduce the…