Search Results (168)

In this paper, we explore the connection between sensor networks and graph theory. Sensor networks represent distributed systems of interconnected devices that collect and transmit data, while graph theory provides a robust framework for modeling and analyzing complex networks. Specifically, we focus on vertex coloring, Eulerian paths, and Hamiltonian paths within the Delaunay graph associated with a sensor network. These concepts have critical applications in sensor networks, including connectivity analysis, efficient data collection, route optimization, task scheduling, and resource management. We derive theoretical results related to the chromatic number and the existence of Eulerian and Hamiltonian trails in the graph linked to the sensor network. Additionally, we complement this theoretical study with the implementation of several algorithmic procedures. A case study involving the monitoring of a sugarcane field, coupled with a computational analysis, demonstrates the performance and practical applicability of these algorithms in real-world scenarios. Full article

The study of unmanned aerial vehicle (UAV) coverage path planning is of great significance for ensuring maritime situational awareness and monitoring. In response to the problem of maritime multi-region coverage surveillance in complex obstacle environments, this paper proposes a global path planning method capable of simultaneously addressing the multiple traveling salesman problem, coverage path planning problem, and obstacle avoidance problem. Firstly, a multiple traveling salesmen problem–coverage path planning (MTSP-CPP) model with the objective of minimizing the maximum task completion time is constructed. Secondly, a method for calculating obstacle-avoidance path costs based on the Voronoi diagram is proposed, laying the foundation for obtaining the optimal access order. Thirdly, an improved discrete grey wolf optimizer (IDGWO) algorithm integrated with variable neighborhood search (VNS) operations is proposed to perform task assignment for multiple UAVs and achieve workload balancing. Finally, based on dynamic programming, the coverage path points of the area are solved precisely to generate the globally coverage path. Through simulation experiments with scenarios of varying scales, the effectiveness and superiority of the proposed method are validated. The experimental results demonstrate that this method can effectively solve MTSP-CPP in complex obstacle environments. Full article

River width is a crucial parameter that correlates and reflects the hydrological, geomorphological, and ecological characteristics of the channel. However, the width data with high spatial resolution is limited owing to the difficulties in extracting channel width under complex and variable riverine surroundings. To address this issue, we aimed to develop an automatic framework specifically for delineating river channels and measuring the bankfull widths at small spatial intervals along the channel. The DeepLabV3+ Convolutional Neural Network (CNN) model was employed to accurately delineate channel boundaries and a Voronoi Diagram approach was complemented as the river width algorithm (RWA) to calculate river bankfull widths. The CNN model was trained by images across four river types and performed well with all the evaluating metrics (mIoU, Accuracy, F1-score, and Recall) higher than 0.97, referring to the accuracy over 97% in prediction. The RWA outperformed other existing river width calculation methods by showing lower errors. The application of the framework in the Lillooet River, Canada, presented the capacity of this methodology to obtain detailed distributions of hydraulic and hydrological parameters, including flow resistance, flow energy, and sediment transport capacity, based on high-resolution channel widths. Our work highlights the significant potential of the newly developed framework in acquiring high-resolution channel width information and characterizing fluvial dynamics based on these widths along river channels, which contributes to facilitating cost-effective integrated river management. Full article

Designing scaffolds similar to the structure of trabecular bone requires specialised algorithms. Existing scaffold designs for bone tissue engineering have repeated patterns that do not replicate the random stochastic porous structure of the internal architecture of bones. In this research, the Voronoi tessellation method is applied to create random porous biomimetic structures. A volume mesh created from the shape of a Zygoma fracture acts as a boundary for the generation of random seed points by point spacing to create Voronoi cells and Voronoi diagrams. The Voronoi lattices were obtained by adding strut thickness to the Voronoi diagrams. Gradient Voronoi scaffolds of pore sizes (19.8 µm to 923 µm) similar to the structure of the trabecular bone were designed. A Finite Element Method-based computational fluid dynamics (CFD) simulation was performed on all designed Voronoi scaffolds to predict the pressure drops and permeability of non-Newtonian blood flow behaviour using the power law material model. The predicted permeability (0.33 × 10⁻⁹ m² to 2.17 × 10⁻⁹ m²) values of the Voronoi scaffolds from the CFD simulation are comparable with the permeability of scaffolds and bone specimens from other research works. Full article

The emerging wireless energy transfer technology enables sensor nodes to maintain perpetual operation. However, maximizing the network performance while preserving short charging delay is a great challenge. In this work, a Wireless Mobile Charger (MC) and a directional charger (DC) were deployed to transmit wireless energy to the sensor node to improve the network’s throughput. To the best of our knowledge, this is the first work to optimize the data sensing rate and charging delay by the joint scheduling of an MC and a DC. We proved we could transmit maximum energy to each sensor node to obtain our optimization objective. In our proposed work, a DC selected a total horizon of 360° and then selected the horizon of each specific 90∘ area based on its antenna orientation. The DC’s orientation was scheduled for each time slot. Furthermore, multiple MCs were used to transmit energy for sensor nodes that could not be covered by the DC. We divided the rechargeable wireless sensor network into several zones via a Voronoi diagram. We deployed a static DC and one MC charging location in each zone to provide wireless charging service jointly. We obtained the optimal charging locations of the MCs in each zone by solving Mix Integral Programming for energy transmission. The optimization objective of our proposed research was to sense maximum data from each sensor node with the help of maximum energy. The lifetime of each sensor network could increase, and the end delay could be maximized, with joint energy transmission. Extensive simulation results demonstrated that our RWSNs were designed to significantly improve network lifetime over the baseline method. Full article

Matched line segments are crucial geometric elements for reconstructing the desired 3D structure in stereo satellite imagery, owing to their advantages in spatial representation, complex shape description, and geometric computation. However, existing line segment matching (LSM) methods face significant challenges in effectively addressing co-linear interference and the misdirection of parallel line segments. To address these issues, this study proposes a “continuous–discrete–continuous” cyclic LSM method, based on the Voronoi diagram, for stereo satellite images. Initially, to compute the discrete line-point matching rate, line segments are discretized using the Bresenham algorithm, and the pyramid histogram of visual words (PHOW) feature is assigned to the line segment points which are detected using the line segment detector (LSD). Next, to obtain continuous matched line segments, the method combines the line segment crossing angle rate with the line-point matching rate, utilizing a soft voting classifier. Finally, local point-line homography models are constructed based on the Voronoi diagram, filtering out misdirected parallel line segments and yielding the final matched line segments. Extensive experiments on the challenging benchmark, WorldView-2 and WorldView-3 satellite image datasets, demonstrate that the proposed method outperforms several state-of-the-art LSM methods. Specifically, the proposed method achieves F1-scores that are 6.22%, 12.60%, and 18.35% higher than those of the best-performing existing LSM method on the three datasets, respectively. Full article

One of the most significant applications of mathematical numerical methods in biology is the theoretical description of the convectional reaction–diffusion of chemical compounds. Initial biological objects must be appropriately mimicked by digital domains that are suitable for further use in computational modeling. In the present study, an algorithm for the creation of a digital phantom describing a local part of nervous tissue—namely, a synaptic contact—is established. All essential elements of the synapse are determined using a set of consistent Boolean operations within the COMSOL Multiphysics software 6.1. The formalization of the algorithm involves a sequence of procedures and logical operations applied to a combination of 3D Voronoi diagrams, an experimentally defined inner synapse area, and a simple ellipsoid under different sets of biological parameters. The obtained digital phantom is universal and may be applied to different types of neuronal synapses. The clear separation of the designed domains reveals that the boundary’s conditions and internal flux dysconnectivity functions can be set up explicitly. Digital domains corresponding to the parts of a synapse are appropriate for further application of the derived numeric meshes, with various capacities of the included elements. Thus, the obtained digital phantom can be effectively used for further modeling of the convectional reaction–diffusion of chemical compounds in nervous tissue. Full article

Assessing the quality of maize seedlings is crucial for field management and germplasm evaluation. Traditional methods for evaluating seedling quality mainly rely on manual field surveys, which are not only inefficient but also highly subjective, while large-scale satellite detection often lacks sufficient accuracy. To address these issues, this study proposes an innovative approach that combines the YOLO v8 object detection algorithm with Voronoi spatial analysis to rapidly evaluate maize seedling quality based on high-resolution drone imagery. The YOLO v8 model provides the maize coordinates, which are then used for Voronoi segmentation of the field after applying the Convex Hull difference method. From the generated Voronoi diagram, three key indicators are extracted: Voronoi Polygon Uniformity Index (VPUI), missing seedling rate, and repeated seedling rate to comprehensively evaluate maize seedling quality. The results show that this method effectively extracts the VPUI, missing seedling rate, and repeated seedling rate of maize in the target area. Compared to the traditional plant spacing variation coefficient, VPUI performs better in representing seedling uniformity. Additionally, the R² for the estimated missing seedling rate and replanting rate based on the Voronoi method were 0.773 and 0.940, respectively. Compared to using the plant spacing method, the R² increased by 0.09 and 0.544, respectively. The maize seedling quality evaluation method proposed in this study provides technical support for precision maize planting management and is of great significance for improving agricultural production efficiency and reducing labor costs. Full article

The modeling of the concrete matrix serves as a foundation for mesoscale analysis of concrete, which provides a crucial avenue for investigating the crack propagation and strength characteristics of concrete. However, the primary prerequisite for conducting such analyses is the generation of aggregate models. By combining the advantages of Voronoi diagrams and the random walk algorithm (RWA), a Voronoi–random walk algorithm is proposed in this paper. The algorithm overcomes the limitations of traditional methods, including constraints on aggregate volume fraction, low computational efficiency, and insufficient randomness in aggregate distribution. The meso-structure of a concrete block was modeled by the proposed method, and then its failure behavior under uniaxial compression was simulated using the finite element method. The numerical results agreed well with the experimental observations, indicating the effectiveness and accuracy of the proposed approach. Full article

This study examines the link between food deserts and cardiovascular health in older adults in Santiago’s Metropolitan Region, Chile. As the population ages and chronic diseases rise, understanding the impact of food accessibility on health is essential. Using multiscale geographically weighted regression, we analyzed data from the Cardiovascular Health Program, socioeconomic indicators, and food desert maps, sourced from the Chilean Ministry of Health and other databases. Spatial analysis, including Voronoi diagrams, assessed the influence of food deserts on health outcomes. Findings show a significant correlation between limited access to healthy foods and higher cardiovascular disease rates, especially in economically disadvantaged areas. The regression model is significant to contribute to the explanation of disease prevalence, emphasizing the impact of food availability on health. This study highlights the importance of considering spatial factors in urban planning and public health policies. By showcasing the role of food environments in health disparities, it advocates for integrated health interventions. Targeted urban planning to address food deserts can enhance access to healthy foods, improving cardiovascular health and well-being among Santiago’s elderly. The findings provide insights for policymakers to create healthier urban environments and stress the need for sustainable food systems to support public health. Full article

A mathematical procedure enabling the transformation of an arbitrary tessellation of a surface into a bi-colored, complete graph is introduced. Polygons constituting the tessellation are represented by vertices of the graphs. Vertices of the graphs are connected by two kinds of links/edges, namely, by a green link, when polygons have the same number of sides, and by a red link, when the polygons have a different number of sides. This procedure gives rise to a semi-transitive, complete, bi-colored Ramsey graph. The Ramsey semi-transitive number was established as Rtrans(3,3)=5 Shannon entropies of the tessellation and graphs are introduced. Ramsey graphs emerging from random Voronoi and Poisson Line tessellations were investigated. The limits ζ=limN→∞NgNr, where N is the total number of green and red seeds, Ng and Nr, were found ζ= 0.272 ± 0.001 (Voronoi) and ζ= 0.47 ± 0.02 (Poisson Line). The Shannon Entropy for the random Voronoi tessellation was calculated as S= 1.690 ± 0.001 and for the Poisson line tessellation as S = 1.265 ± 0.015. The main contribution of the paper is the calculation of the Shannon entropy of the random point process and the establishment of the new bi-colored Ramsey graph on top of the tessellations. Full article

Football players’ decision-making behaviours near the scoring target (finishing situations) emerge from the evolving spatiotemporal information directly perceived in the game’s landscape. In finishing situations, the ball carrier’s decision-making about shooting or passing is not an individual decision-making process, but a collective decision that is guided by players’ perceptions of match affordances. To sustain this idea, we collected spatiotemporal information and built a model to quantify the “Finishing Space Value” (FSV) that results from players’ perceived affordances about two main questions: (a) is the opponent’s target successfully reachable from a given pitch location?; and (b) from each given pitch location, the opposition context will allow enough space to shoot (low adversaries’ interference)? The FSV was calculated with positional data from high-performance football matches, combining information extracted from Voronoi diagrams (VD) with distances and angles to the goal line. FSV was tested using as a reference the opinion of a “panel of expert” (PE), composed by football coaches, about a questionnaire presenting 50 finishing situations. Results showed a strong association between the subjective perception scale used by the PE to assess how probable a shot made by the ball carrier could result in a goal and FSV calculated for that same situation (R2=0.6706). Moreover, we demonstrate the accuracy of the FSV quantification model in predicting coaches’ opinions about what should be the “best option” to finish the play. Overall, results indicated that the FSV is a promising model to capture the affordances of the shooting circumstances for the ball carrier’s decision-making in high-performance football. FSV might be useful for more precise match analysis and informing coaches in the design of representative practice tasks. Full article

Street design and land subdivision are significant tasks in the development and redevelopment planning process. Optimizing street and land subdivision layouts within a unified framework to achieve solutions that meet a set of objectives and constraints (e.g., minimizing parcel area deviation from standard values, minimizing land consumption for street construction, etc.) is a critical concern for planners, particularly in complex contexts such as blocks with irregular shapes and parcels of varying sizes and requirements. To address this challenge, a mathematical formulation is presented for the bi-level street network and land subdivision optimization problem. Subsequently, the solution procedure is outlined, which utilizes a genetic-based algorithm for street design and a memetic–genetic-based algorithm for land subdivision. Finally, two cases are presented, solved, and discussed to analyze and verify the proposed mathematical model and solution procedures. The results suggest that the formulated problem is suitable for addressing the coupled street network and land subdivision design problem, and it can be adapted and extended to other case studies. Additionally, the introduced ideas and algorithms satisfactorily solved the stated problem. Full article

In recent decades, multi-robot region coverage has played an important role in the fields of environmental sensing, target searching, etc., and it has received widespread attention worldwide. Due to the effectiveness in segmenting nearest regions, Voronoi diagrams have been extensively used in recent years for multi-robot region coverage. This paper presents a survey of recent research works on region coverage methods within the framework of the Voronoi diagram, to offer a perspective for researchers in the multi-robot cooperation domain. First, some basic knowledge of the Voronoi diagram is introduced. Then, the region coverage issue under the Voronoi diagram is categorized into sensor coverage and task execution coverage problems, respectively, considering the sensor range parameter. Furthermore, a detailed analysis of the application of Voronoi diagrams to the aforementioned two problems is provided. Finally, some conclusions and potential further research perspectives in this field are given. Full article

With the increasing utilization of sampling-based path planning methods in the field of mobile robots, the RRT* algorithm faces challenges in complex indoor scenes, including high sampling randomness and slow convergence speed. To tackle these issues, this paper presents an improved RRT* path-planning algorithm based on the generalized Voronoi diagram with an adaptive bias strategy. Firstly, the algorithm leverages the properties of the generalized Voronoi diagram (GVD) to obtain heuristic paths, and a sampling region with target bias is constructed, increasing the purposefulness of the sampling process. Secondly, the node expansion process incorporates an adaptive bias strategy, dynamically adjusting the step size and expanding direction. This strategy allows the algorithm to adapt to the local environment leading to improved convergence speed. To ensure the generation of smooth paths, the paper employs the cubic spline curve interpolation algorithm for trajectory optimization to ensure that the mobile robotic can obtain the best trajectory. Finally, the proposed algorithm is experimentally compared with existing algorithms, including the RRT* and Informed-RRT* algorithms, to verify the feasibility and stability. Full article