相关论文: Digital Shy Maps

In this article, we investigate the relationship between the shadowing property of set-valued maps and their associated inverse limit systems. We show that if a set-valued map is expansive and open in the context of set-valued dynamics,…

A map is an abstract visual representation of a region, taken from a given space, usually designed for final human consumption. Traditional cartography focuses on the mapping of Euclidean spaces by using some distance metric. In this paper…

We investigate the separability of several well known classes of subgroups of the mapping class group of a surface.

Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…

We explore the experimental observation that complex networks of porous media exhibit the property that the porous coordination number is proportional to its size. Based in this geometry-topology duality we developed an analytical approach…

Quasi-vertex-transitive maps are the homogeneous maps on the plane with finitely many vertex orbits under the action of their automorphism groups. We show that there exist quasi-vertex-transitive maps of types $[p^3, 3]$ for $p \equiv 1$…

This is a survey article on distance-squared mappings and related topics.

We study connectivity preserving multivalued functions between digital images. This notion generalizes that of continuous multivalued functions studied mostly in the setting of the digital plane $Z^2$. We show that connectivity preserving…

We give a lower bound of the cochain type level of the diagonal map on the classifying space of a Lie group by using the ghostness of a shriek map. Moreover, in a derived category, we discuss the triviality of the shriek map which induces…

There is a lack of data on the location, condition, and accessibility of sidewalks across the world, which not only impacts where and how people travel but also fundamentally limits interactive mapping tools and urban analytics. In this…

The ability to autonomously navigate in unknown environments is important for mobile robots. The map is the core component to achieve this. Most map representations rely on drift-free state estimation and provide a global metric map to…

Following [6,12], we study coupled map networks over arbitrary finite graphs. An estimate from below for a topological entropy of a perturbed coupled map network via a topological entropy of an unperturbed network by making use of the…

The domains of mesh functions are strict subsets of the underlying space of continuous independent variables. Spaces of partial maps between topological spaces admit topologies which do not depend on any metric. Such topologies…

We describe the topology of singular real algebraic curves in a smooth surface. We enumerate and bound in terms of the degree the number of topological types of singular algebraic curves in the real projective plane.

Topological conjugateness of one dimensional unimodal dynamical systems, which are generated by interval [0, 1] into itself maps are studied. We study the smoothness and differentiability of the conjugacy of symmetrical and non-symmetrical…

This paper contains an expository account of persistent homology and its usefulness for topological data analysis. An alternative foundation for level-set persistence is presented using sheaves and cosheaves.

We review measures of street network structure proposed in the recent literature, establish their relevance to practice, and identify open challenges facing researchers. These measures' empirical values vary substantially across world…

Transformations of digital spaces preserving local and global topology play an important role in thinning, skeletonization and simplification of digital images. In the present paper, we introduce and study contractions of simple pair of…

We introduce a new memory architecture for navigation in previously unseen environments, inspired by landmark-based navigation in animals. The proposed semi-parametric topological memory (SPTM) consists of a (non-parametric) graph with…

This paper considers the problem of detecting topology variations in dynamical networks. We consider a network whose behavior can be represented via a linear dynamical system. The problem of interest is then that of finding conditions under…