相关论文: Digital Shy Maps

Using digital topology approach, we construct digital models of closed surfaces as the intersection graphs of LCL covers of the surfaces. It is proved that digital models of closed surfaces are digital 2-dimensional surfaces preserving the…

We study properties of contiguity distance between simplicial maps. In particular, we show that simplicial versions of $LS$-category and topological complexity are particular cases of this more general notion.

In this article, we investigate some properties of the coincidence point set of digitally continuous maps. Following the Rosenfeld graphical model which seems more combinatorial than topological, we expect to achieve results that might not…

This paper considers generalizations of open mappings, closed mappings, pseudo-open mappings, and quotient mappings from topological spaces to generalized topological spaces. Characterizations of these classes of mappings are obtained and…

Freezing sets and cold sets have been introduced as part of the theory of fixed points in digital topology. In this paper, we introduce a generalization of these notions, the limiting set, and examine properties of limiting sets.

We continue the study of freezing sets in digital topology, introduced in [2]. We show how to find a minimal freezing set for a "thick" convex disk X in the digital plane Z^2. We give examples showing the significance of the assumption that…

Stable fold maps are fundamental tools in a generalization of the theory of Morse functions on smooth manifolds and its application to studies of geometric properties of smooth manifolds. Round fold maps were introduced as stable fold maps…

The majority of current approaches in autonomous driving rely on High-Definition (HD) maps which detail the road geometry and surrounding area. Yet, this reliance is one of the obstacles to mass deployment of autonomous vehicles due to poor…

Chaotic dynamics is widely used to design pseudo-random number generators and for other applications such as secure communications and encryption. This paper aims to study the dynamics of discrete-time chaotic maps in the digital (i.e.,…

In this paper, we introduce round and sleek topological spaces and study their properties.

We present a method for computing the topological entropy of one-dimensional maps. As an approximation scheme, the algorithm converges rapidly and provides both upper and lower bounds.

In this paper we define a numerical shape invariant of a continuous map called shape dimension of a map, which generalizes the shape dimension of a topological space. Some basic properties and applications of this invariant are given. The…

Mapping is an important part of many robotic applications. In order to measure the performance of the mapping process we have to measure the quality of its result: the map. The map is essential for robotic algorithms like localization and…

In this paper, we investigate topological modes of different physical systems defined on arbitrary two-dimensional curved surfaces. We consider the shallow water equations, inhomogeneous Maxwell's equations, Jackiw-Rebbi model and show how…

Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…

We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful bridge between network science and topology. Indeed, it has…

Most real-world networks are embedded in latent geometries. If a node in a network is found in the vicinity of another node in the latent geometry, the two nodes have a disproportionately high probability of being connected by a link. The…

We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…

Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…

We examine some kinds of discrete symmetries which are dynamically preserved, using the (generalized) Gowdy models of the first kind.