arXiv research

Han discusses variants of digital covering maps and their equivalences.

In this paper, we show how to construct graph theoretical models of n-dimensional continuous objects and manifolds. These models retain topological properties of their continuous counterparts. An LCL collection of n-cells in Euclidean space is introduced and investigated. If an LCL collection of n-cells is a cover of a…

We study properties of shy maps in digital topology.

Study on cold and freezing sets in digital images.

Digital currencies and cryptocurrencies have hesitantly started to penetrate the investors, and the next step will be the regulatory risk management framework. We examine the Value-at-Risk and Expected Shortfall properties for the major digital currencies, Bitcoin, Ethereum, Litecoin, and Ripple. The methodology used i…

Maps are an important medium that enable people to comprehensively understand the configuration of cultural activities and natural elements over different times and places. Although massive maps are available in the digital era, how to effectively and accurately access the required map remains a challenge today. Previo…

We continue the work of [10], studying properties of digital images determined by fixed point invariants. We introduce pointed versions of invariants that were introduced in [10]. We introduce freezing sets and cold sets to show how the existence of a fixed point set for a continuous self-map restricts the map on the c…

CitySim dataset captures vehicle trajectories for safety research.

In "Rips complexes and covers in the uniform category" \cite{Rips} the authors define, following James \cite{J}, covering maps of uniform spaces and introduce the concept of generalized uniform covering maps. Conditions for the existence of universal uniform covering maps and generalized uniform covering maps are given…

Study of lifting maps in branched covers of 3-manifolds, showing non-injectivity.

Paper introduces a method to learn physics between digital twins using imperfect models.

The production and consumption of information about Bitcoin and other digital-, or 'crypto'-, currencies have grown together with their market capitalisation. However, a systematic investigation of the relationship between online attention and market dynamics, across multiple digital currencies, is still lacking. Here,…

The paper studies harmonic maps between surfaces homotopic to a covering map, proving uniqueness and injectivity of Hopf differential.

AI improves precision health through adaptive interventions.

The automatic digitizing of paper maps is a significant and challenging task for both academia and industry. As an important procedure of map digitizing, the semantic segmentation section mainly relies on manual visual interpretation with low efficiency. In this study, we select urban planning maps as a representative …

The paper studies liftable mapping class groups of cyclic covers of spheres.

This paper shows semi-equivelar toroidal maps are vertex-transitive covers.

Mapping the spatial distribution of poverty in developing countries remains an important and costly challenge. These "poverty maps" are key inputs for poverty targeting, public goods provision, political accountability, and impact evaluation, that are all the more important given the geographic dispersion of the remain…

Framework predicts responses in misspecified systems using GPLFM and BNNs.

We define Peano covering maps and prove basic properties analogous to classical covers. Their domain is always locally path-connected but the range may be an arbitrary topological space. One of characterizations of Peano covering maps is via the uniqueness of homotopy lifting property for all locally path-connected spa…

The Birman-Hilden theory is extended to infinite type surfaces and branched covers.

Taut foliations map leaves to branched 2-sphere covers.

The abstract covers various aspects of eBusiness and eGovernment, including digital currencies, m-government services, gender inclusivity, eLearning, export performance, SME digitalization, and banking customer behavior.

In this paper we develop analysis of the monopole maps over the universal covering space of a compact four manifold. We induce a property on local properness of the covering monopole map under the condition of closeness of the AHS complex. In particular we construct a higher degree of the covering monopole map when the…

Study Dirichlet-to-Neumann maps on manifolds, focusing on covering and total spaces.

The paper details folding of branched covers of the 3-sphere over knots.

ISOMORPH creates a digital twin for supply chain logistics, advancing time-series forecasting benchmarks.

There is a concept in digital topology of a shy map. We define an analogous concept for topological spaces: We say a function is shy if it is continuous and the inverse image of every path-connected subset of its image is path-connected. Some basic properties of such maps are presented. For example, every shy map onto …

New braid group representations into mapping class groups are derived from disk coverings.

Solve arc diagrams on surfaces via branched covers.

We say that a cover of surfaces S -> X has the Birman--Hilden property if the subgroup of the mapping class group of X consisting of mapping classes that have representatives that lift to S embeds in the mapping class group of S modulo the group of deck transformations. We identify one necessary condition and one suffi…

Harmonic maps from surfaces to CAT(k) spheres are branched coverings.

Overlays were introduced by R. H. Fox [6] as a subclass of covering maps. We offer a different view of overlays: it resembles the definition of paracompact spaces via star refinements of open covers. One introduces covering structures for covering maps and $p:X\to Y$ is an overlay if it has a covering structure that ha…

Flat connections induced over covering maps are studied and the trivial ones among them are described. In the sequel, we deal with the resulting holonomy bundles.

The study proves unique path lifting properties and their implications on quotient spaces and covering maps.

The study explores how the mapping class group acts on the homology of surface covers.

Let S be an orientable surface with negative Euler characteristic, let ψ\in\Mod(S) be a mapping class of S, and let T_ψ be the mapping torus of ψ. We study the action of lifts of ψon the homology of finite covers of S via the torsion homology growth of towers of finite covers of T_ψ. We show that ψadmits a lift to a fi…

In this note, we show that, if a pseudo-Anosov map $φ:S\to S$ admits a finite cover whose action on the first homology has spectral radius greater than $1$, then the monodromy of any fibered structure of any finite cover of the mapping torus $M_φ$ has the same property.

Open manifolds can be covered by $\mathbb{R}^m$ with finite or infinite degree.

Berestovskii and Plaut introduced the concept of a coverable uniform space when developing their theory of generalized universal covering maps for uniform spaces. Brodskiy, Dydak, LaBuz, and Mitra introduced the concept of a locally uniformly joinable uniform space when developing their theory of generalized uniform co…

Nonorientable surface mapping class group embeds quasi-isometrically in its orientable cover.

Orchestrating the Twin Transition in GBS: A Socio-Technical Framework

Study homology groups of mapping and Torelli groups for surfaces with abelian covers.

In this article we determine, for an infinite family of maps on the plane, the topology of the surface on which the minimal regular covering occurs. This infinite family includes all Archimedean maps.

We describe a novel spiking neural network (SNN) for automated, real-time handwritten digit classification and its implementation on a GP-GPU platform. Information processing within the network, from feature extraction to classification is implemented by mimicking the basic aspects of neuronal spike initiation and prop…

Notes on harmonic maps between manifolds, existence and regularity covered.

Proves manifolds with positive scalar curvature have inessential covers.

The paper formalizes robot environments using topological concepts.