Related papers: Digital Shy Maps
Topological strategies for navigation meaningfully reduce the space of possible actions available to a robot, allowing use of heuristic priors or learning to enable computationally efficient, intelligent planning. The challenges in…
In this paper, we study instances of complex neural networks, i.e. neural netwo rks with complex topologies. We use Self-Organizing Map neural networks whose n eighbourhood relationships are defined by a complex network, to classify handwr…
In this chapter, we discuss applications of topological data analysis (TDA) to spatial systems. We briefly review the recently proposed level-set construction of filtered simplicial complexes, and we then examine persistent homology in two…
We investigate a family of one dimensional maps for which the bifurcation diagram looks differently than the usual ones. We describe and exemplify various unique and interesting phenomena arising for this family of maps.
In this paper, using the classical covering theory, we introduce a generalization of covering maps of a space $X$ with respect to a topology $\tau$ on the fundamental group of $X$. We show that the famous notions, covering, semicovering,…
We discuss the study of topological characteristics of random fields that are used for numerical simulation of oil and gas reservoirs and numerical algorithms (see arXiv:1302.3669), for computing such characteristics, for which we…
State-of-the-art autonomous driving systems rely on high definition (HD) maps for localization and navigation. However, building and maintaining HD maps is time-consuming and expensive. Furthermore, the HD maps assume structured environment…
The use of satellite networks has increased significantly in recent years due to their advantages over purely terrestrial systems, such as higher availability and coverage. However, to effectively provide these services, satellite networks…
In our paper, we introduce special-generic-like maps or SGL maps as smooth maps and study their several algebraic topological and differential topological properties. The new class generalize the class of so-called special generic maps.…
Schematic maps are in daily use to show the connectivity of subway systems and to facilitate travellers to plan their journeys effectively. This study surveys up-to-date algorithmic approaches in order to give an overview of the state of…
We study geometrically finite one-dimensional mappings. These are a subspace of $C^{1+\alpha}$ one-dimensional mappings with finitely many, critically finite critical points. We study some geometric properties of a mapping in this subspace.…
Topological data analysis refers to approaches for systematically and reliably computing abstract ``shapes'' of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest…
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…
We show that the spaces of holomorphic and continuous maps from a smooth complex projective variety to a projective space have the same homology in a range depending on the degree of the maps.
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…
Data hiding is the art of concealing messages with limited perceptual changes. Recently, deep learning has enriched it from various perspectives with significant progress. In this work, we conduct a brief yet comprehensive review of…
We study the topology of the complex points of the algebraic loop space of a smooth curve.
We introduce a notion of discrete topological complexity in the setting of simplicial complexes, using only the combinatorial structure of the complex by means of the concept of contiguous simplicial maps. We study the links of this new…
This paper regroups some of the basic properties of Lipschitz maps and their flows. Many of the results presented here are classical in the case of smooth maps. We prove them here in the Lipschitz case for a better understanding of the…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…