Regular Maps Research Articles

Fixed point theorems for $ b $-generalized contractive mappings with weak continuity conditions

<abstract><p>The purpose of this paper was to introduce several $ b $-generalized contractive mappings in the framework of cone $ b $-metric spaces over Banach algebras. The obtained contractions generalized and extended the counterparts in metric spaces, cone metric spaces, and $ b $-metric spaces. Moreover, via weakening the completeness of the spaces, we gave some fixed point theorems for asymptotically regular mappings without considering the orbital continuity and $ k $-continuity of the mappings. Those who need a specification is our results do not rely on the continuity of $ b $-metric and the normality of cones. In addition, some nontrivial examples were presented to illustrate the superiority of our fixed point theorems.</p></abstract>

ERA*: Enhanced Relaxed A* algorithm for solving the shortest path problem in regular grid maps

This paper introduces a novel algorithm for solving the point-to-point shortest path problem in a static regular 8-neighbor connectivity (G8) grid. This algorithm can be seen as a generalization of Hadlock algorithm to G8 grids, and is shown to be theoretically equivalent to the relaxed A⁎ (RA⁎) algorithm in terms of the provided solution's path length, but with substantial time and memory savings, due to a completely different computation strategy, based on defining a set of lookup matrices. Through an experimental study on grid maps of various types and sizes (1290 runs on 43 maps), it is proven to be 2.25 times faster than RA⁎ and 17 times faster than the original A⁎, in average. Moreover, it is more memory-efficient, since it does not need to store a G score matrix.

TOWARDS DETECTING SPEED BUMPS FROM MLS POINT CLOUDS DATA

Abstract. High definition maps contain a high level of information about the road and its features. This includes traffic signs, speed limits and lane markings, that are not generally included on regular maps. However, they may still lack critical information, such as the locations of speed bumps. Without the information about the whereabouts of speed bumps the passengers’ comfort and safety, as well as the condition of the car may be jeopardized. There are currently methods for detecting speed bumps that use changes in acceleration or 3D cameras. However, these approaches are susceptible to external influences interfering with the recorded data. Hence, it is desirable to have this information stored and available through HD maps. In this work, we tested two deep learning-based approaches (PointNet++ and PointCNN) and compared the results with conventional region growing method, in order to find out pros and cons of the modern deep learning-based methods. For our test, we used MLS (mobile laser scanning) point clouds data in Trondheim, Norway.

The Evolving Landscape of Frailty Research: A Bibliometric Analysis

Purpose: This bibliometric analysis aimed to map global frailty research focused on older adults over the past four decades, illuminating growth, contributors, seminal works, and knowledge frontiers. Methodology: Frailty publications were retrieved from Scopus and Web of Science using keywords "frail*" AND "older adult*" without date restrictions. Data cleaning and analysis utilized ScientoPy, VOSviewer, and Biblioshiny to examine trends in output, countries, institutions, journals, citations, keywords, and concepts from 1980-2023. Findings: Among 3809 publications, output exponentially increased from <10 papers annually in the 1980s to 294 in 2021. The US and UK led production. Top universities were in Europe and Australia. Geriatrics and gerontology were the dominant subject, but multidisciplinary contribution highlighted frailty's complex etiology. Core topics included assessments, interventions, care models, sarcopenia, and adverse outcomes. Newer focus areas like integrated care and nurse-led models were rising. Originality: This robust longitudinal mapping elucidates the structure and evolution of the global frailty literature over the past four decades using multidimensional bibliometrics. Implications: Analysing quantitative growth, key contributors, seminal works, and conceptual shifts provides insights to inform frailty research priorities and policies for aging populations worldwide. Limitations: Database biases and search strategy constraints. Future studies can enrich visualizations, qualitative analyses, and regular knowledge mapping updates.

On the automorphism groups of regular maps

On the automorphism groups of regular maps

Approximation and homotopy in regulous geometry

Let $X$ , $Y$ be nonsingular real algebraic sets. A map $\varphi \colon X \to Y$ is said to be $k$ -regulous, where $k$ is a nonnegative integer, if it is of class $\mathcal {C}^k$ and the restriction of $\varphi$ to some Zariski open dense subset of $X$ is a regular map. Assuming that $Y$ is uniformly rational, and $k \geq 1$ , we prove that a $\mathcal {C}^{\infty }$ map $f \colon X \to Y$ can be approximated by $k$ -regulous maps in the $\mathcal {C}^k$ topology if and only if $f$ is homotopic to a $k$ -regulous map. The class of uniformly rational real algebraic varieties includes spheres, Grassmannians and rational nonsingular surfaces, and is stable under blowing up nonsingular centers. Furthermore, taking $Y=\mathbb {S}^p$ (the unit $p$ -dimensional sphere), we obtain several new results on approximation of $\mathcal {C}^{\infty }$ maps from $X$ into $\mathbb {S}^p$ by $k$ -regulous maps in the $\mathcal {C}^k$ topology, for $k \geq 0$ .

Learning from Safe-by-Design for Safe-and-Sustainable-by-Design: Mapping the current landscape of Safe-by-Design reviews, case studies, and frameworks

With the introduction of the European Commission's “Safe and Sustainable-by-Design” (SSbD) framework, the interest in understanding the implications of safety and sustainability assessments of chemicals, materials, and processes at early-innovation stages has skyrocketed. Our study focuses on the “Safe-by-Design” (SbD) approach from the nanomaterials sector, which predates the SSbD framework.In this assessment, SbD studies have been compiled and categorized into reviews, case studies, and frameworks. Reviews of SbD tools have been further classified as quantitative, qualitative, or toolboxes and repositories. We assessed the SbD case studies and classified them into three categories: safe(r)-by-modeling, safe(r)-by-selection, or safe(r)-by-redesign. This classification enabled us to understand past SbD work and subsequently use it to define future SSbD work so as to avoid confusion and possibilities of “SSbD-washing” (similar to greenwashing). Finally, the preexisting SbD frameworks have been studied and contextualized against the SSbD framework.Several key recommendations for SSbD based on our analysis can be made. Knowledge gained from existing approaches such as SbD, green and sustainable chemistry, and benign-by-design approaches needs to be preserved and effectively transferred to SSbD. Better incorporation of chemical and material functionality into the SSbD framework is required. The concept of lifecycle thinking and the stage-gate innovation model need to be reconciled for SSbD. The development of high-throughput screening models is critical for the operationalization of SSbD. We conclude that the rapid pace of both SbD and SSbD development necessitates a regular mapping of the newly published literature that is relevant to this field.

Post-Earthquake Reconnaissance of a Dam with Stabilizing Fill using Drone Photogrammetry

Post-earthquake reconnaissance is an important process for assessing the safety of massive structures. Dams are critical structures that require evaluation following an earthquake, as dam failure can lead to significant damage to the surrounding area. This paper presents drone (unmanned aerial vehicle) photogrammetry-based reconnaissance of the Angat Dam (Philippines), which has stabilizing fill, following the M 6.1 Luzon earthquake in April 2019. The author presents the results of visual inspection, drone digital mapping, and seismically induced deformation monitoring, as well as a general interpretation of dam safety. Analysis of the instrumentation data did not indicate that any significant changes in crest settlement, piezometric head, or seepage rate resulted from the earthquake. However, seismically induced longitudinal cracking along the dam crest was observed in the drone photogrammetry. The digital surface model, orthoimage, and as-built GIS geometry characterizations generated using the drone photogrammetry facilitated the geospatial analysis of seismic cracking and deformation. It is found that the uplift deformation was caused by counteracting effects between the existing dam body and its stabilizing fill. It is concluded that the results obtained using drone digital mapping are a valuable reference for future deformation monitoring using regular mapping methods in a 3D geospatial digital model.

Disaster Mitigation Model for Sustainable Tourism Development at the Nam Salu Openpit Geosite: Insights from the Belitong UNESCO Global Geopark

This research aims to develop an effective disaster mitigation model to support sustainable tourism development at the Nam Salu Openpit Geosite, which is an integral part of the Belitong UNESCO Global Geopark. The qualitative approach method uses descriptive methods through case studies, namely the Open Pit Nam Salu (OPNS) geosite. The results of research conducted regarding the Open Pit Nam Salu (OPNS) Geosite in East Belitung revealed that the potential threat of disaster to this tourist site is very significant. The main factors influencing the vulnerability of OPNS Geosites to natural disasters include ecosystem damage due to unmanaged mining activities, changes in the landscape caused by intensive mining practices, and disruption of slope stability due to excessive exploitation of natural resources. In addition, climate change can also worsen the risk of disasters, including landslides and coastal erosion. Therefore, it is necessary to carry out structured disaster mitigation measures, including an early warning system, emergency management training, regular risk mapping, evacuation planning, development of a disaster information center, as well as education and public awareness programs to maintain the sustainability of the OPNS Geosite as a safe tourist destination. and sustainable.

Satellite target detection algorithm for high-pressure dense channel based on deep learning

In order to improve the detection accuracy of high-voltage dense channel satellite image, a satellite target detection algorithm based on deep learning is proposed. The convolution neural network is selected to extract the feature map of high-voltage dense channel satellite image, and the extracted feature map is input into the optimized deformation convolution neural network. The value of each sampling point and the corresponding position authority of block convolution kernel are weighted by using the regular region sampling feature map. The feature map output by the convolution operation of pooling layer is used to obtain the depth features of the same dimension. The depth feature is input into the full connection layer to obtain the full connection feature of candidate target area, and the target detection in high-voltage dense channel satellite image is realized. The experimental results show that the target detection accuracy of the method is higher than 99% and the false alarm rate and false alarm rate are lower than 1.4%.

Generation of irregular grid maps for fingerprinting-based mobile radio localization using farthest-first traversal and low-discrepancy sequences

Localization techniques play a fundamental role in various applications like in the development of smart cities, making the improvement of such technologies indispensable. In this context, radio frequency (RF) fingerprinting (FP)-based localization methods are attractive due to their lower implementation cost, lower energy consumption, and better performance in non-line-of-sight conditions compared to GPS. With this in mind, we propose an RF FP-based localization method using an irregular grid map generation strategy. The grid map segmentation procedure is based on the assumption that the RF measurements collected in a region carry information on how users are often spatially distributed. The algorithms employed in the irregular grid map generation are the farthest-first traversal and low-discrepancy R-sequence. Different irregular grid map generators are compared with each other and with the regular grid map. We evaluate the generators in two different scenarios: with measurements obtained through simulation with ns-3 and via a driving-test procedure in an urban area. Numerical results indicate that our proposed irregular generator presents a lower localization error in both scenarios and is the only one capable of meeting one of the accuracy requirements stated by the Federal Communications Commission that demands a localization error of up to 50m in 80% of the emergency calls.

Efficiency of satellite data in the agro-ecological monitoring system

The article discusses the ecological value of the normalized vegetation index (NDVI). Generalization of scientific data on the possibility of use in forestry, agriculture, ecological research, modeling of ecosystems and monitoring of the earth’s surface has been carried out. It was found that, unlike the surveyor, the operational/satellite monitoring of crops makes it possible to automatically generate reports, control the condition of crops, forecast yields and plan agricultural operations taking into account the real ecological state and weather conditions. In particular, you can create electronic vegetation maps; develop images and field relief for a specific region. It has been established that the use of data from remote sensing of the Earth (RSE) ensures the determination of the objective state of crops (density, quantitative and qualitative changes in crops, obtaining information on chemical treatments) on large areas. The factors that influence the calculation of NDVI are given, and the necessity of using an approach focused on climatic conditions is indicated. It was found that the transformation of multispectral NDVI data into one image layer allows estimating the amount of available vegetation and the development of crops on a field scale. Regular field NDVI mapping helps identify and mitigate any crop problems, increase yields, and make agribusiness more profitable. NDVI has become one of the most important and frequently used indicators in precision agriculture, so it deserves further practical research. This is a numerical indicator of the quality and quantity of plants in the field. It is emphasized that NDVI has become one of the most important and frequently used indicators in precision agriculture. Therefore, deserves further practical investigation. Ecosystem service is a means of identifying threats to ecosystems in order to develop socially acceptable and effective solutions to environmental problems. The ecosystem approach allows predicting changes, which is extremely important for spatial planning and land use management. This approach is especially important when assessing and resolving conflict situations in nature management, when the economic benefit from the use of one or another natural resource becomes a strong argument. From the point of view of human benefit, operational monitoring becomes an ecosystem service. The use of spectral indices contributes to the production of high-quality «environmentally friendly» products, the preservation of environmental components, the reproduction of soil fertility, obtaining the maximum profit, along with the transition from a linear economy to a circular one (economic effect), saving resources, optimizing and diversifying agricultural production.

Simple eigenvalues of cubic vertex-transitive graphs

Abstract If ${\mathbf v} \in {\mathbb R}^{V(X)}$ is an eigenvector for eigenvalue $\lambda $ of a graph X and $\alpha $ is an automorphism of X, then $\alpha ({\mathbf v})$ is also an eigenvector for $\lambda $ . Thus, it is rather exceptional for an eigenvalue of a vertex-transitive graph to have multiplicity one. We study cubic vertex-transitive graphs with a nontrivial simple eigenvalue, and discover remarkable connections to arc-transitivity, regular maps, and number theory.

Compactification of level maps of moduli spaces of Drinfeld shtukas

We define Drinfeld level structures for Drinfeld shtukas of any rank and show that their moduli spaces are regular and admit finite flat level maps. In particular, the moduli space of Drinfeld shtukas with Drinfeld Γ0(pn)-level structures provides a good integral model and a relative compactification of the moduli space of shtukas with naive Γ0(pn)-level defined using shtukas for dilated group schemes.

Utilization of brain scans to create realistic phosphene maps for cortical visual prosthesis simulation studies.

It has been shown that we can restore sensations of light by stimulating the visual cortex. Cortical prosthetic vision consists of light perception in the visual field named phosphenes. Phosphenes are like pixels on a monitor which we can control to form the desired perception. However, the locations of phosphenes evoked vary between individuals. One of the biggest challenges is how to utilize phosphenes to present recognizable patterns that represent real-world scenes. Because of the difficulties of recruiting participants, and the risks of neurosurgery, researchers have used computer simulations to investigate the outcome of cortical visual prostheses. Previous simulations used regular phosphene maps, which may overestimate the visual ability cortical visual prosthesis can provide. This study aims to develop a more realistic simulation for cortical visual prostheses. We derived realistic phosphene maps using an existing cortical retinotopy dataset and decided implant placement by considering neurosurgery restrictions. We rendered some visual stimuli to evaluate the usability of those phosphene maps. The results indicate that presenting information on phosphenes maps may be more challenging than previously estimated.

Regular maps with an alternating or symmetric group as automorphism group

This paper provides a complete determination of which of the alternating groups An and the symmetric groups Sn occur as the automorphism group of some regular or chiral map on an orientable surface, and which of them occur as the automorphism group of a regular map on a non-orientable surface. The situation for some given types (m,k) is also considered, where k is the valency and m is the face-size, with special focus on types with m=3, and more particularly with (m,k)=(3,7) or (3,8), or their duals. Some observations are made also about what happens for regular and orientably-regular maps with given valency, and for regular and chiral polyhedra. Much but certainly not all of what is presented follows from theorems in previous papers by the author and others, and this one brings them and some new observations together into a single reference.

Stability Analysis of Modified General Version of Gauss-type Proximal Point Method for Solving Generalized Equations Using Metrically Regular Mapping

A modified general version of Gauss-type proximal point algorithm (GGPPA) is presented in this article for solving the parameterized generalized equation y ∈ F(x), where y is a parameter and a set-valued mapping F: X ⇉ 2Y is acting between two different Banach spaces X and Y. We demonstrate the existence of any sequence produced by the modified GGPPA by taking certain presumptions into account, and we use metrically regular mapping to demonstrate the uniformity of semi-local and local convergence findings. Finally, we present a numerical experiment to verify the uniformity of semi-local convergence result.

Common stationary point of multivalued asymptotically regular mappings

We establish a relationship between asymptotic regularity and common stationary points of multivalued mappings on a metric space. As a consequence of our results, we obtain a new common fixed point result for two asymptotically regular single-valued mappings. Our work significantly improves and complements comparable results in the literature.

Dominating real algebraic morphisms

Let X and Y be nonsingular real algebraic varieties, dim⁡X≥dim⁡Y. Assume that the variety Y is malleable, compact and connected. Our main result implies that each regular map from X to Y is homotopic to a surjective regular map. The class of malleable varieties includes all homogeneous spaces for linear real algebraic groups.

Bifurcations and transition to chaos in generalized fractional maps of the orders 0 < α < 1.

In this paper, we investigate the generalized fractional maps of the orders 0<α<1. Commonly used in publications, fractional and fractional difference maps of the orders 0<α<1 belong to this class of maps. As an example, we numerically solve the equations, which define asymptotically periodic points to draw the bifurcation diagrams for the fractional difference logistic map with α=0.5. For periods more than four (T>4), these bifurcation diagrams are significantly different from the bifurcation diagrams obtained after 105 iterations on individual trajectories. We present examples of transition to chaos on individual trajectories with positive and zero Lyapunov exponents. We derive the algebraic equations, which allow the calculation of bifurcation points of generalized fractional maps. We use these equations to calculate the bifurcation points for the fractional and fractional difference logistic maps with α=0.5. The results of our numerical simulations allow us to make a conjecture that the cascade of bifurcations scenarios of transition to chaos in generalized fractional maps and regular maps are similar, and the value of the generalized fractional Feigenbaum constant δf is the same as the value of the regular Feigenbaum constant δ=4.669….