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Accurate detection of geospatial objects, particularly landslides, is a critical challenge in geospatial data analysis due to the complex nature of the data and the significant consequences of these events. This paper introduces an innovative topological knowledge-based (Topological KB) method that leverages the integration of topological, geometrical, and contextual information to enhance the precision of landslide detection. Topology, a fundamental branch of mathematics, explores the properties of space that are preserved under continuous transformations and focuses on the qualitative aspects of space, studying features like connectivity and exitance of loops/holes. We employed persistent homology (PH) to derive candidate polygons and applied three distinct strategies for landslide detection: without any filters, with geometrical and contextual filters, and a combination of topological with geometrical and contextual filters. Our method was rigorously tested across five different study areas. The experimental results revealed that geometrical and contextual filters significantly improved detection accuracy, with the highest F1 scores achieved when employing these filters on candidate polygons derived from PH. Contrary to our initial hypothesis, the addition of topological information to the detection process did not yield a notable increase in accuracy, suggesting that the initial topological features extracted through PH suffices for accurate landslide characterization. This study advances the field of geospatial object detection by demonstrating the effectiveness of combining geometrical and contextual information and provides a robust framework for accurately mapping landslide susceptibility. [ABSTRACT FROM AUTHOR]

Indoor navigation has attracted significant attention from both academic and industrial perspectives. Indoor positioning is a critical component of indoor navigation. Several solutions or technologies have been proposed, such as Wi-Fi, UWB, and Bluetooth. Among them, Bluetooth Low Energy (BLE) is cost-effective, easily deployable, flexible, and efficient. This paper focuses on indoor positioning solely based on BLE. Motivated by two observations, namely, that (i) involving more anchor nodes can enhance positioning accuracy, and that (ii) narrowing the area for unknown location determination can also lead to improved accuracy, a new distance-based method, the Weighted Centroid of the Convex Polygon (WC-CP), is proposed. While it is generally acknowledged that incorporating more anchor nodes can enhance indoor positioning performance, the current state of the art lacks a robust methodology for selecting and utilizing these nodes. The WC-CP approach addresses this gap by introducing a systematic and efficient method for identifying and employing the most suitable anchor nodes. By avoiding nodes that could potentially introduce significant errors or lead to incorrect localization, our method ensures more accurate and reliable indoor positioning. The efficacy of WC-CP is demonstrated in an indoor environment, achieving an RMSE of 1.35 m. This result shows significant improvements over three state-of-the-art approaches, about 34.15% better than LSBM, 32.50% better than TWCBM, and 30.05% better than ITWCBM. These findings underscore the potential of WC-CP for enhanced accuracy and reliability in indoor positioning based on BLE. [ABSTRACT FROM AUTHOR]

Layer 2 solutions have emerged in recent years as a valuable alternative to increase the throughput and scalability of blockchain-based architectures. The three primary types of Layer 2 solutions are state channels, sidechains, and rollups. The rollups are particularly promising, allowing significant improvements in transaction throughput, security, and efficiency, and have been adopted by many real-world projects, such as Polygon and Optimistic. However, the adoption of Layer 2 solutions has led to other challenges, such as the data availability problem, where transaction data processed off-chain must be posted back on the main chain. This is crucial to prevent data withholding attacks and ensure all participants can independently verify the blockchain state. This paper provides a comprehensive survey of existing rollup-based Layer 2 solutions with a focus on the data availability problem and discusses the major advantages and disadvantages of them. Finally, an analysis of open challenges and future research directions is provided. [ABSTRACT FROM AUTHOR]

Research on topological interlocking (TI) assemblies indicates that the geometry of blocks plays a significant role in the performance of a configuration. The current TI generation methods can return assemblies of uniform antiprisms, tetrahedra, cubes, and octahedra. However, other shapes (both convex and concave) are well qualified for use in TI assemblies. This paper presents a framework to generate blocks for TI assembly. Starting from a seed polygon, evolution steps translate and reshape the polygon, contracting it eventually to a point, a line segment, or another polygon. Our framework generalizes and unifies previous-generation methods based on tilting angles and height parameters. We show how the proposed method systematically generates novel TI solids and previously reported others. [ABSTRACT FROM AUTHOR]

Graffiti represents a multi-disciplinary social behavior. It is used to annotate urban landscapes under the assumption that building façades will constantly evolve and acquire modified skins. This study aimed to simulate the interaction between building façades and generative AI-based graffiti using Stable Diffusion® (SD v 1.7.0). The context used for graffiti generation considered the graffiti as the third skin, the remodeled façade as the second skin, and the original façade as the first skin. Graffiti was created based on plain-text descriptions, representative images, renderings of scaled 3D prototype models, and characteristic façades obtained from various seed elaborations. It was then generated from either existing graffiti or the abovementioned context; overlaid upon a campus or city; and judged based on various criteria: style, area, altitude, orientation, distribution, and development. I found that rescaling and reinterpreting the context presented the most creative results: it allowed unexpected interactions between the urban fabric and the dynamics created to be foreseen by elaborating on the context and due to the divergent instrumentation used for the first, second, and third skins. With context awareness or homogeneous aggregation, graphic partitions can thus be merged into new topologically re-arranged polygons that enable a cross-gap creative layout. Almost all façades were found to be applicable. AI generation enhances awareness of the urban fabric and facilitates a review of both the human scale and buildings. AI-based virtual governance can use generative graffiti to facilitate the implementation of preventive measures in an urban context. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new Best Uniform Rational Approximation-Semi-Discrete (BURA-SD) method taking into account the singularities of the solution of fractional diffusion problems in polygonal domains. The complementary capabilities of the exponential convergence rate of BURA-SD and the h p FEM are explored with the aim of maximizing the overall performance. A challenge here is the emerging singularly perturbed diffusion–reaction equations. The main contributions of this paper include asymptotically accurate error estimates, ending with sufficient conditions to balance errors of different origins, thereby guaranteeing the high computational efficiency of the method. [ABSTRACT FROM AUTHOR]

Origami exhibits the remarkable ability to transform into diverse shapes, including quadrilaterals, triangles, and more complex polygons. This unique property has inspired the integration of origami principles into engineering design, particularly in the development of foldable mechanisms. In the field of robotics, when combined with actuators, these foldable mechanisms are referred to as active origami. Origami-based mechanisms play a pivotal role as versatile end effectors or grippers, enabling them to accurately trace desired trajectories. The performance of these mechanisms heavily relies on their specific fold patterns. To shed light on their capabilities, this study focuses on five representative structures using spherical mechanisms: oriceps, Miura ori, MACIOR, and two hexagonal structures. To assess their potential, a comparative analysis is conducted, evaluating their kinematic and scaling performances. The analysis employs the "scaling factor" as a metric, which quantifies the mechanical advantage of these mechanisms. This metric aids in the selection of appropriate structures for various applications. [ABSTRACT FROM AUTHOR]

The advancement of information technology has led to the widespread application of remote measurement systems, where information in the form of images or videos, serving as measurement results, is transmitted over networks. However, this transmission is highly susceptible to attacks, tampering, and disputes, posing significant risks to the trustworthy transmission of measurement results from instruments and devices. In recent years, many encryption algorithms proposed for images have focused on encrypting the entire image, resulting in resource waste. Additionally, most encryption algorithms are designed only for single-object-type images. Addressing these issues, this paper proposes a multi-object region encryption algorithm based on an adaptive mechanism. Firstly, an adaptive mechanism is employed to determine the strategy for adjusting the sampling rate of encryption objects, achieved through an encryption resource allocation algorithm. Secondly, an improved polygon segmentation algorithm is utilized to separate single-object regions from multi-object images, dynamically adjusting the sequence of encryption objects based on the adaptive mechanism. Finally, encryption is achieved using a chaos fusion XOR encryption algorithm. Experimental validation using instrument images demonstrates that the proposed algorithm offers high efficiency and security advantages compared to other mainstream image encryption algorithms. [ABSTRACT FROM AUTHOR]

The insurance industry has used parametric solutions to transfer catastrophe risks since the 1990s. Instead of relying on a lengthy process to assess a claim, these products pay the insured a pre-agreed amount if the physical characteristics of the event fulfill pre-defined conditions. Cat-in-a-box or cat-in-a-circle triggers, commonly used tools for tropical cyclone risk transfer, provide a payout to the insured if the track of a hurricane crosses the perimeter of a geographic area defined by a polygon or a circle with a certain intensity. Cat-in-a-grid solutions are novel and more sophisticated. They rely on a set of multiple cat-in-a-box triggers arranged on an orthogonal grid. The consideration of multiple geographic domains instead of a single box or circle is helpful to reduce basis risk, i.e., the difference between the parametric loss estimate and the target loss. In the case study for Miami presented here, for instance, a cat-in-a-grid solution showed 18.5% less basis risk than a typical cat-in-a-box alternative. To organize the different types of triggers within a common framework, we classify the existing alternatives based on whether they use a single geographic domain (like a box or a circle) or multiple domains (like a grid). We discuss their advantages and disadvantages and describe the process required to calibrate any one solution with the help of a catastrophe-risk model. We focus, in particular, on the analysis and construction of cat-in-a-grid triggers, the alternative that we believe offers the greatest potential for global standardization and adoption. [ABSTRACT FROM AUTHOR]

TiCx/Al composites were successfully prepared in this study by dissolving graphite particles in Al-Ti melt based on the principle of a solid–liquid in situ reaction. It was observed that the microstructure of the TiCx/Al composites changed with changes in the reaction temperature and graphite particle size. With an increase in reaction temperature, the TiCx particles in the TiCx/Al composites transitioned from a spider-like distribution to being evenly dispersed in the Al matrix. Additionally, the morphology of the TiCx particles changed from polygons of various sizes to quasi-spherical shapes with a uniform particle size, while the presence of Al4C3 and Al3Ti in the matrix diminished. The size variation of the graphite particles had minimal impact on the particle size and stoichiometric ratio of TiCx generated in the sample. Furthermore, an appropriate graphite particle size was found to mitigate the agglomeration and residue of graphite particles during the in situ reaction. [ABSTRACT FROM AUTHOR]

To generate an orthophoto mosaic from a collection of aerial images, the original images are first orthorectified individually using a Digital Surface Model (DSM). Then, they are stitched together along some determined seamlines to form the orthophoto mosaic. Determining appropriate seamlines is a critical process, as it affects the visual and geometric quality of the results. The stitching process can usually be done in frame-to-frame or multi-frame modes. Although the latter is more efficient, both still involve a lot of pre-processing, such as creating individual orthophotos, image registration, and overlap extraction. This paper presents a novel coarse-to-fine approach that directly determines the seamline network without such pre-processing. Our method has been specifically applied for UAV photogrammetry projects where, due to the large number of images and the corresponding overlaps, the orthophoto mosaic generation can be very challenging and time-consuming. We established the seamlines simultaneously for all the images through a two-step process. First, a DSM was generated, and a low-resolution grid was overlayed. Then, for each grid point, an optimal image was selected. Then, the grid cells are grouped into polygons based on their corresponding optimal image. Boundaries of these polygons established our seamline network. Thereafter, to generate the orthophoto mosaic, we overlayed a higher/full resolution grid on the top of the DSM, the optimal image of each point of which was quickly identified via our low-resolution polygons. In this approach, not only seamlines were automatically generated, but also were the need for the creation, registration, and overlap extraction of individual orthophotos. Our method was systematically compared with a conventional frame-to-frame (CF) technique from different aspects, including the number of double-mapped areas, discontinuities across the seamlines network, and the amount of processing time. The outcomes revealed a 46% decrease in orthophoto generation time and a notable reduction in the number of double-mapped areas, sawtooth effects, and object discontinuities within the constructed orthophoto mosaic. [ABSTRACT FROM AUTHOR]

The study presents an analysis and guide for the synthesis of a spherical shaped gear mesh in kinematic sculptures. The specific conditions for generating such arrangements are investigated, like the mesh condition for constrained gear systems, the geometry of forming gears, possible patterns, choice of dimensions, and number of teeth. The starting geometry is also partially described, which is based on convex polyhedrons. It is a solid three-dimensional figure with flat polygonal faces that are closed, where all the angles between adjacent faces are less than or equal to 180 degrees, and there are no concave regions or indentations in its structure. Two different examples are presented based on two different polyhedrons with different gear arrangements. [ABSTRACT FROM AUTHOR]

As core algorithms of geographic computing, overlay analysis algorithms typically have computation-intensive and data-intensive characteristics. It is highly important to optimize overlay analysis algorithms by parallelizing the vector polygons after reasonable data division. To address the problem of unbalanced data partitioning in the task decomposition process for parallel polygon overlay analysis and calculation, this paper presents a data partitioning method based on shape complexity index optimization, which achieves data equalization among multicore parallel computing tasks. Taking the intersection operator and difference operator of the Vatti algorithm as examples, six polygon shape indexes are selected to construct the shape complexity model, and the vector data are divided in accordance with the calculated shape complexity results. Finally, multicore parallelism is achieved based on OpenMP. The experimental results show that when a data set with a large amount of data is used, the effect of the multicore parallel execution of the Vatti algorithm's intersection operator and difference operator based on shape complexity division is clearly improved. With 16 threads, compared with the serial algorithm, speedups of 29 times and 32 times can be obtained. Compared with the traditional multicore parallel algorithm based on polygon number division, the speed can be improved by 33% and 29%, and the load balancing index is reduced. For a data set with a small amount of data, the acceleration effect of this method is similar to that of traditional methods involving multicore parallelism. [ABSTRACT FROM AUTHOR]

In the open literature, there are numerous studies on the normal and extreme (flood and drought) behavior of wet and dry periods based on the understanding of the standard precipitation index (SPI), which provides a series of categorizations by considering the standard normal (Gaussian) probability distribution function (PDF). The numerical meaning of each categorization assessment is quite lacking in terms of future predictions of wet and dry period duration based on historical records. This paper presents a new approach for calculating possible formations of future wet and dry period durations based on historical records through an effective fractal geometric forecasting approach. The essence of the proposed methodology is based on the number of dry periods (steps) of non-overlapping monthly duration along consecutive broken line paths in the SPI classification for wet and dry period durations. It has been observed that the plot of periods on double logarithmic paper falls along a straight line against the number of such periods, implying a power function, which is the essence of fractal geometry. Extending the empirically derived straight line provides the number of periods that may occur in the future over a range of SPI levels. This methodology is referred to as SPI fractal (SPIF), and the classic SPI classification is converted into SPIF wet and dry polygons, which provide additional information about the drought period number within a valid polygonal area, compared to the classic SPI results. The wet and dry period features of any hydro-meteorology time series are constrained in SPIF polygons. The application of the methodology was carried out on monthly rainfall records on the European side of the Istanbul Florya meteorological station in Turkey. [ABSTRACT FROM AUTHOR]

Fingerprints are unique patterns used as biometric keys because they allow an individual to be unambiguously identified, making their application in the forensic field a common practice. The design of a system that can match the details of different images is still an open problem, especially when applied to large databases or, to real-time applications in forensic scenarios using mobile devices. Fingerprints collected at a crime scene are often manually processed to find those that are relevant to solving the crime. This work proposes an efficient methodology that can be applied in real time to reduce the manual work in crime scene investigations that consumes time and human resources. The proposed methodology includes four steps: (i) image pre-processing using oriented Gabor filters; (ii) the extraction of minutiae using a variant of the Crossing Numbers method which include a novel ROI definition through convex hull and erosion followed by replacing two or more very close minutiae with an average minutiae; (iii) the creation of a model that represents each minutia through the characteristics of a set of polygons including neighboring minutiae; (iv) the individual search of a match for each minutia in different images using metrics on the absolute and relative errors. While in the literature most methodologies look to validate the entire fingerprint model, connecting the minutiae or using minutiae triplets, we validate each minutia individually using n-vertex polygons whose vertices are neighbor minutiae that surround the reference. Our method also reveals robustness against false minutiae since several polygons are used to represent the same minutia, there is a possibility that even if there are false minutia, the true polygon is present and identified; in addition, our method is immune to rotations and translations. The results show that the proposed methodology can be applied in real time in standard hardware implementation, with images of arbitrary orientations. [ABSTRACT FROM AUTHOR]

DUS measurements for popliteal artery aneurysms (PAAs) specifically can be time-consuming, error-prone, and operator-dependent. To eliminate this subjectivity and provide efficient segmentation, we applied artificial intelligence (AI) to accurately delineate inner and outer lumen on DUS. DUS images were selected from a cohort of patients with PAAs from a multi-institutional platform. Encord is an easy-to-use, readily available online AI platform that was used to segment both the inner lumen and outer lumen of the PAA on DUS images. A model trained on 20 images and tested on 80 images had a mean Average Precision of 0.85 for the outer polygon and 0.23 for the inner polygon. The outer polygon had a higher recall score than precision score at 0.90 and 0.85, respectively. The inner polygon had a score of 0.25 for both precision and recall. The outer polygon false-negative rate was the lowest in images with the least amount of blur. This study demonstrates the feasibility of using the widely available Encord AI platform to identify standard features of PAAs that are critical for operative decision making. [ABSTRACT FROM AUTHOR]

The discrete fracture model (DFM) and the embedded discrete fracture model (EDFM) are both the most widely used methods to simulate fractured wells' production. In general, DFM represents fractures using an unstructured grid, and EDFM represents fractures using 2D virtual polygon grids embedded into 3D corner point grids. However, both EDFM and DFM suffer from non-orthogonal grid effects. Based on the non-linear flux approximation, this work presents a new flux scheme for DFM and EDFM that is capable of simulating fractured reservoir production in second-order accuracy. Two test cases are set to verify the accuracy of this method. Finally, this work is used to simulate the production of one fractured horizontal well belonging to the Y-oil field. Orthogonal design is used to optimize the parameters. The results show that this method is capable of improving accuracy while keeping the solution effective. This method exhibits good practicability and has practical significance for fractured reservoir development. [ABSTRACT FROM AUTHOR]

Chewing is a complex procedure that involves sensory feedback and motor impulses controlled by the trigeminal system in the brainstem. The analysis of mandibular movement is a first approximation to understanding these mechanisms. Several recording methods have been tested to achieve this. Video, ultrasound, the use of external markers and kinesiographs are examples of recording systems used in research. Electromagnetic articulography is an alternative method to those previously mentioned. It consists of the use of electromagnetic fields and receiver coils. The receiver coils are placed on the points of interest and the 3D coordinates of movement are saved in binary files. In the Oral Physiology Laboratory of the Dental Sciences Research Center (Centro de Investigación en Ciencias Odontológicas—CICO), in the Faculty of Dentistry at the Universidad de La Frontera (Temuco, Chile) several research studies have been carried out using the AG501 3D EMA articulograph (Carstens Medizinelektronik, Lenglern, Germany). With this device, they developed a series of protocols to record mandibular movement and obtain new information, such as the 3D Posselt polygon, the area of each polygon, individualized masticatory cycles and speed and acceleration profiles. Other investigations have analyzed these parameters, but separately. The AG501 allows for holistic analysis of all these data without altering natural movement. A limitation of this technology is the interference generated by its metallic elements. The aim of the present work is to show the developed methods used to record mandibular movement in the CICO, using the AG501 and compare them with others used in several research studies. [ABSTRACT FROM AUTHOR]

Building outlines are important for emergency response, urban planning, and change analysis and can be quickly extracted from remote sensing images and raster maps using deep learning technology. However, such building outlines often have irregular boundaries, redundant points, inaccurate positions, and unclear turns arising from variations in the image quality, the complexity of the surrounding environment, and the extraction methods used, impeding their direct utility. Therefore, this study proposes a simplification and regularization algorithm for right-angled polygon building outlines with jagged edges. First, the minimum bounding rectangle of the building outlines is established and populated with a square grid based on the smallest visible length principle. Overlay analysis is then applied to the grid and original buildings to extract the turning points of the outlines. Finally, the building orientation is used as a reference axis to sort the turning points and reconstruct the simplified building outlines. Experimentally, the proposed simplification method enhances the morphological characteristics of building outlines, such as parallelism and orthogonality, while considering simplification principles, such as the preservation of the direction, position, area, and shape of the building. The proposed algorithm provides a new simplification and regularization method for right-angled polygon building outlines with jagged edges. [ABSTRACT FROM AUTHOR]

Object detection in deep learning provides a viable solution for detecting crop-pest-infected regions. However, existing rectangle-based object detection methods are insufficient to accurately detect the shape of pest-infected regions. In addition, the method based on instance segmentation has a weak ability to detect the pest-infected regions at the edge of the leaves, resulting in unsatisfactory detection results. To solve these problems, we constructed a new polygon annotation dataset called PolyCorn, designed specifically for detecting corn leaf pest-infected regions. This was made to address the scarcity of polygon object detection datasets. Building upon this, we proposed a novel object detection model named Poly-YOLOv8, which can accurately and efficiently detect corn leaf pest-infected regions. Furthermore, we designed a loss calculation algorithm that is insensitive to ordering, thereby enhancing the robustness of the model. Simultaneously, we introduced a loss scaling factor based on the perimeter of the polygon, improving the detection ability for small objects. We constructed comparative experiments, and the results demonstrate that Poly-YOLOv8 outperformed other models in detecting irregularly shaped pest-infected regions, achieving 67.26% in mean average precision under 0.5 threshold ( mA P 50 ) and 128.5 in frames per second (FPS). [ABSTRACT FROM AUTHOR]

Change and persistence are often richly entangled facets of landscapes. While many studies use land use/land cover (depicted as polygons) to illustrate landscape evolution, this paper draws on approaches from landscape archaeology to investigate how lines and points can also be used to examine landscape morphologies. The study uses three distinct spatial elements: points (graves), lines (field boundaries), and polygons (land use) to represent landscape transformations and reflect time depth in the landscape. The paper aims to identify the most enduring landscape elements within the region and uncover the underlying mechanisms of persistence. It is suggested that the time depth exhibited in field boundaries surpasses that of land use in this case. Field boundaries provide a useful way to examine agricultural intensification, whereas land use is more sensitive to agricultural commercialization and urbanization. In addition, the Chinese Feng Shui funeral culture emerges as a stabilizing force that encourages landscape persistence. This cultural driver ensures the persistence of field patterns surrounding graves, making these fields the most ancient plots within the study area. In conclusion, representing the time depth of landscapes through linear features and points can serve as an important supplement to the study of landscape change based on land use. [ABSTRACT FROM AUTHOR]

The Himalayan region is a hotspot in terms of expected future hydrological and geomorphological variations induced by climate change on proglacial areas and the related implications for human societies established along the downstream rivers. Due to the remoteness of the proglacial zones in the Himalayas and the associated logistical problems in carrying out traditional field and UAV-based morphological monitoring activities, remote sensing here plays a crucial role to monitor past and current fluvial dynamics, which could be used to anticipate future changes; however, there has been, so far, limited research on morphological changes in Himalayan proglacial rivers. To address this gap, a morphological classification model was designed to classify recent changes in Himalayan proglacial rivers using the Google Earth Engine platform. The model is the first of its kind developed for the Himalayan region and uses multispectral S-2 satellite data to delineate submerged water channels, vegetated surfaces, and emerged, unvegetated sediment bars, and then to track their variations over time. The study focused on three training sites: Langtang-Khola (Nepal), Saltoro (Pakistan), and Nubra (Jammu and Kashmir) rivers, and one testing site, the Ganga-Bhagirathi River (India). A total of 900 polygons were used as training samples for the random forest classifier, which were further divided into 70% calibration and 30% validation datasets for the training sites, and a separate validation dataset was acquired from the testing site to assess the model performance. The model achieved high accuracy, with an average overall accuracy of 96% and a kappa index of 0.94, indicating the reliability of the S2 data for modeling proglacial geomorphic features in the Himalayan region. Therefore, this study provides a reliable tool to detect past and current morphological changes occurring in the Himalayan proglacial rivers, which will be of great value for both research and river management purposes. [ABSTRACT FROM AUTHOR]

Shannon entropy quantifying bi-colored Ramsey complete graphs is introduced and calculated for complete graphs containing up to six vertices. Complete graphs in which vertices are connected with two types of links, labeled as α-links and β-links, are considered. Shannon entropy is introduced according to the classical Shannon formula considering the fractions of monochromatic convex α -colored polygons with n α-sides or edges, and the fraction of monochromatic β -colored convex polygons with m β-sides in the given complete graph. The introduced Shannon entropy is insensitive to the exact shape of the polygons, but it is sensitive to the distribution of monochromatic polygons in a given complete graph. The introduced Shannon entropies S α and S β are interpreted as follows: S α is interpreted as an average uncertainty to find the green α − polygon in the given graph; S β is, in turn, an average uncertainty to find the red β − polygon in the same graph. The re-shaping of the Ramsey theorem in terms of the Shannon entropy is suggested. Generalization for multi-colored complete graphs is proposed. Various measures quantifying the Shannon entropy of the entire complete bi-colored graphs are suggested. Physical interpretations of the suggested Shannon entropies are discussed. [ABSTRACT FROM AUTHOR]

This paper describes a system which takes user input of a pattern of regular polygons around one vertex and attempts to construct a uniform tiling with the same pattern at every vertex by adding one polygon at a time. The system constructs spherical, planar, or hyperbolic tilings when the sum of the interior angles of the user-specified regular polygons is respectively less than, equal to, or greater than 360 ∘ . Other works have catalogued uniform tilings in tables and/or illustrations. In contrast, this system was developed as an interactive educational tool for people to learn about symmetry and tilings by trial and error through proposing potential vertex patterns and investigating whether they work. Users can watch the rest of the polygons being automatically added one by one with recursive backtracking. When a trial polygon addition is found to violate the conditions of a regular tiling, polygons are removed one by one until a configuration with another compatible choice is found, and that choice is tried next. [ABSTRACT FROM AUTHOR]

In this paper, we present a workflow that combines supervised and unsupervised methods for the reconstruction of geometric models with architectural information from unordered 3D data. Our method uses a downsampling strategy to enrich features to provide scalability for large datasets, increase robustness, and be independent of the sensor used. A Neural Network is then used to segment the resulting point cloud into basic structures. This removes furniture and clutter and preserves the relevant walls, ceilings, floors, and openings. A 2D projection combined with a graph structure is used to find a Region of Interest within the cleaned point cloud, indicating a potential room. Each detected region is projected back into a 3D data patch to refine the room candidates and allow for more complex room structures. The resulting patches are fitted with a polygon using geometric approaches. In addition, architectural features, such as windows and doors, are added to the polygon. To demonstrate that the presented approach works and that the network provides usable results, even with changing data sources, we tested the approach in different real-world scenarios with different sensor systems. [ABSTRACT FROM AUTHOR]

This study focuses on the positional accuracy of Digital Elevation Models (DEMs) and 3D vector features by considering that both datasets can be used as a product to assess or as a reference. The main objective is to provide an alternative method to the traditional use of checkpoints by using check-surfaces in order to avoid identification issues. The methodology includes the determination of a set of polygons with a significant height in relation to the surrounding area (elevated or depressed) and those cells extracted from the DEM that match these elements. The check-surfaces are obtained after a triangulation of these polygons. The methodology uses procedures based on buffers to provide several results in the form of distribution functions of accuracies (2D, vertical and 3D). The trial has been carried out using a large set of data representing buildings obtained from official institutions. The results show consistent 2D, vertical and 3D accuracy values related to commonly used confidence levels. The application has demonstrated the viability of this approach for obtaining horizontal and vertical accuracies individually and jointly at any confidence level. In addition, the study includes the analysis of the results of specific zones, considering several characteristics. [ABSTRACT FROM AUTHOR]

Following the discovery of an artificial protein cage with a paradoxical geometry, we extend the concept of homogeneous symmetric congruent equivalent near-miss polyhedral cages, for which all the faces are equivalent, and define bi-homogeneous symmetric polyhedral cages made of two different types of faces, where all the faces of a given type are equivalent. We parametrise the possible connectivity configurations for such cages, analytically derive p-cages that are regular, and numerically compute near-symmetric p-cages made of polygons with 6 to 18 edges and with deformation not exceeding 10%. [ABSTRACT FROM AUTHOR]

The generalized Petersen graphs are a type of cubic graph formed by connecting the vertices of a regular polygon to the corresponding vertices of a star polygon. This graph has many interesting graph properties. As a result, it has been widely researched. In this work, the edge metric dimensions of the generalized Petersen graphs GP(2l + 1, l) and GP(2l, l) are explored, and it is shown that the edge metric dimension of GP(2l + 1, l) is equal to its metric dimension. Furthermore, it is proved that the upper bound of the edge metric dimension is the same as the value of the metric dimension for the graph GP(2l, l). [ABSTRACT FROM AUTHOR]

Planning an achievable trajectory for a mobile robot usually consists of two steps: (i) finding a path in the form of a sequence of discrete waypoints and (ii) transforming this sequence into a continuous and smooth curve. To solve the second problem, this paper proposes algorithms for automatic dynamic smoothing of the primary path using a tracking differentiator with sigmoid corrective actions. Algorithms for setting the gains of the differentiator are developed, considering a set of design constraints on velocity, acceleration, and jerk for various mobile robots. When tracking a non-smooth primary path, the output variables of the differentiator generate smooth trajectories implemented by a mechanical plant. It is shown that the tracking differentiator with a different number of blocks also generates derivatives of the smoothed trajectory of any required order, taking into account the given constraints. Unlike standard analytical methods of polynomial smoothing, the proposed algorithm has a low computational load. It is easily implemented in real time on the on-board computer. In addition, simple methods for modeling a safety corridor are proposed, taking into account the dimensions of the vehicle when planning a polygon with stationary obstacles. Confirming results of numerical simulation of the developed algorithms are presented. [ABSTRACT FROM AUTHOR]

Featured Application: Transfer case of hybrid vehicle. The internal–external composite meshing mechanism should be the best way to improve the transmission performance of a silent chain drive, but there is no internal–external composite meshing Hy-Vo chain under the classical design approach. In this research, by building the Hy-Vo chain meshing system, the difference between the meshing of the chain–sprocket and the meshing of the rack–gear is deeply analyzed. By rigidifying the external meshing Hy-Vo chain as a rack, the fluctuation range of the pitch line of the external meshing Hy-Vo chain is analyzed. Based on the relations between the actual chain pitch line and the rigid chain pitch line, the design method for the internal meshing profile of the internal–external composite meshing Hy-Vo chain is deduced, the necessary conditions are obtained, and the meshing characteristics are analyzed. By conducting comparative multi-body dynamics experiments, the results prove that the design method of the internal–external composite meshing Hy-Vo chain proposed in this study is effective and feasible. The results also show that the description of the internal–external composite meshing in the classical meshing theory is not completely correct. In fact, the internal–external composite meshing mechanism cannot reduce the meshing impact of the Hy-Vo chain system and can only improve the system polygon action, the meshing performance, and the transmission stability. [ABSTRACT FROM AUTHOR]

Mesh quality is critical to the accuracy and efficiency of finite element calculations, and mesh smoothing is an essential means of reducing the number of poor elements and improving mesh quality. The deep Q-network-based optimization algorithm for planar Delaunay mesh (unconstrained DQN) has attracted increasing attention due to its advantages in autonomous optimization. However, the unconstrained DQN model does not constrain the movement area of the central node during the training process, and element quality easily falls into a local optimum, resulting in a low generalization of the DQN model. In this paper, an updateable iterative inner polygon is proposed as a constraint to limit the central node's movement and control the element's angle. Next, the performance of different neural networks when training the same dataset is analyzed, and the appropriate neural network is selected. After that, the effectiveness and generalization of the method were analyzed. Finally, the results were compared with those obtained by existing methods. The results show that the proposed algorithm can improve the minimum angle of global elements and the shape of poor elements, and the trained DQN model has a high generalization. [ABSTRACT FROM AUTHOR]

A polygon with n nodes can be divided into two subpolygons by an internal diagonal through node n. Splitting the polygon along diagonal δ i , n and diagonal δ n − i , n , i ∈ { 2 , ... , ⌊ n / 2 ⌋ } results in mirror images. Obviously, there are ⌊ n / 2 ⌋ − 1 pairs of these reflectively symmetrical images. The influence of the observed symmetry on polygon triangulation is studied. The central result of this research is the construction of an efficient algorithm used for generating convex polygon triangulations in minimal time and without generating repeat triangulations. The proposed algorithm uses the diagonal values of the Catalan triangle to avoid duplicate triangulations with negligible computational costs and provides significant speedups compared to known methods. [ABSTRACT FROM AUTHOR]

The boundary element method (BEM) is used by applying Cauchy's formula to the boundary of the water movement domain under a dam. By approximating the border with a polygon through linear interpolation, the relationships between the complex velocities on each edge of the polygon are analytically deduced. For the case of the flow domain described by a semi- circular closed contours, the numerical values of the velocity are computed and compared with those obtained only analytically. Conclusions on the analytical and numerical context are drawn. [ABSTRACT FROM AUTHOR]

The present paper focuses on vehicle simulator fidelity, particularly the effect of motion cues intensity on driver performance. The 6-DOF motion platform was used in the experiment; however, we mainly focused on one characteristic of driving behavior. The braking performance of 24 participants in a car simulator was recorded and analyzed. The experiment scenario was composed of acceleration to 120 km/h followed by smooth deceleration to a stop line with prior warning signs at distances of 240, 160, and 80 m to the finish line. To assess the effect of the motion cues, each driver performed the run three times with different motion platform settings–no motion, moderate motion, and maximal possible response and range. The results from the driving simulator were compared with data acquired in an equivalent driving scenario performed in real conditions on a polygon track and taken as reference data. The driving simulator and real car accelerations were recorded using the Xsens MTi-G sensor. The outcomes confirmed the hypothesis that driving with a higher level of motion cues in the driving simulator brought more natural braking behavior of the experimental drivers, better correlated with the real car driving test data, although exceptions were found. [ABSTRACT FROM AUTHOR]

We consider the central configurations of the 1 + N -body problem, where N bodies are infinitesimal and the remaining one body is dominant. For regular polygon central configurations, we prove that the masses of all the infinitesimal bodies are equal when N is odd and the masses of the alternate infinitesimal bodies must be equal when N is even. Moreover, in the case of N being even, we present the relationship of the mass parameters between two consecutive infinitesimal bodies. [ABSTRACT FROM AUTHOR]

Image reconstruction is an interesting yet challenging optimization problem that has several potential applications. The task is to reconstruct an image using a fixed number of transparent polygons. Traditional gradient-based algorithms cannot be applied to the problem since the optimization objective has no explicit expression and cannot be represented by computational graphs. Metaheuristic search algorithms are powerful optimization techniques for solving complex optimization problems, especially in the context of incomplete information or limited computational capability. In this paper, we developed a novel metaheuristic search algorithm named progressive learning hill climbing (ProHC) for image reconstruction. Instead of placing all the polygons on a blank canvas at once, ProHC starts from one polygon and gradually adds new polygons to the canvas until reaching the number limit. Furthermore, an energy-map-based initialization operator was designed to facilitate the generation of new solutions. To assess the performance of the proposed algorithm, we constructed a benchmark problem set containing four different types of images. The experimental results demonstrated that ProHC was able to produce visually pleasing reconstructions of the benchmark images. Moreover, the time consumed by ProHC was much shorter than that of the existing approach. [ABSTRACT FROM AUTHOR]

Indoor space information is the basis of indoor location services such as indoor navigation, path planning, emergency evacuation, etc. Focusing on indoor navigation needs, this paper proposes a fast construction algorithm for a complex indoor space topology model based on disjoint set for the problem of lacking polygon description and topological relationship expression of indoor space entity objects in building plan drawings. Firstly, the Tarjan algorithm is used for identifying the hanging edges existing in the indoor space. Secondly, each edge is stored as two different edges belonging to two adjacent polygons that share the edge. A ring structure is introduced to judge the geometric position of walls, and then an efficient disjoint set algorithm is used to perform set merging. After that, disjoint set is queried to obtain all indoor space contours and external boundary contours, thereby the complete indoor space topological relationship at multiple levels is established. Finally, the connectivity theory of graph is used for solving the problem of a complex isolated polygon in topology information generation. The experimental results show that the proposed algorithm has generality to efficiently complete the automatic construction of a topological model for complex scenarios, and effectively acquire and organize indoor space information, thus providing a good spatial cognition mode for indoor navigation. [ABSTRACT FROM AUTHOR]

We consider a problem in computational origami. Given a piece of paper as a convex polygon P and a point f located within, we fold every point on a boundary of P to f and compute a region that is safe from folding, i.e., the region with no creases. This problem is an extended version of a problem by Akitaya, Ballinger, Demaine, Hull, and Schmidt that only folds corners of the polygon. To find the region, we prove structural properties of intersections of parabola-bounded regions and use them to devise a linear-time algorithm. We also prove a structural result regarding the complexity of the safe region as a variable of the location of point f, i.e., the number of arcs of the safe region can be determined using the straight skeleton of the polygon P. [ABSTRACT FROM AUTHOR]

Subdivision schemes are equipped with some rules that take a polygon as an input and produce smooth curves or surfaces as an output. This presents the issue of how accurately the polygon approximates the limit curve and surface. What number of iterations/levels would be necessary to achieve the required shape at a user-specified error tolerance? In fact, several methods have been introduced in the case of stationary schemes to address the issue in terms of the error bounds (distance between polygon/polyhedron and limiting shape) and subdivision depth (the number of iterations required to obtain the result at a user-specified error tolerance). However, in the case of non-stationary schemes, this topic needs to be further studied to meet the requirements of new practical applications. This paper highlights a new approach based on a convolution technique to estimate error bounds and subdivision depth for non-stationary schemes. The given technique is independent of any condition on the coefficient of the non-stationary subdivision schemes, and it also produces the best results with the least amount of computational effort. In this paper, we first associated constants with the vectors generated by the given non-stationary schemes, then formulated an expression for the convolution product. This expression gives real values, which monotonically decrease with the increase in the order of the convolution in both the curve and surface cases. This convolution feature plays an important role in obtaining the user-defined error tolerance with fewer iterations. It achieves a trade-off between the number of iterations and user-specified errors. In practice, more iterations are needed to achieve a lower error rate, but we achieved this goal by using fewer iterations. [ABSTRACT FROM AUTHOR]

On 15 September 2022, the Ethereum network adopted a proof-of-stake (PoS) consensus mechanism. We study the impact on the network and competing platforms in a two month event window around the Beacon chain merge. We find that the transition to PoS has reduced energy consumption by 99.98%. Miners have not transformed into validators, and total block reward income (in USD) has fallen by 97%, though transaction fees (in ETH) for Ether have increased nearly 10%. The Herfindahl index for the top 10 is 1009; the network is 19% less concentrated after the merge. Ethereum supply growth has been deflationary since the merge. The time between consecutive blocks is now steady at 12 s and transactions per day are up 7.0%. On Polygon, Matic fees rose but token fees fell. Polygon also slows, processing 3.3% fewer transactions per day. Solana's fees fall by $0.0003, and transactions per day are down 48%. Stablecoin transfer volumes fall on Ethereum and Polygon, but rise on Solana. [ABSTRACT FROM AUTHOR]

This paper investigates one way to reduce the computational burden of continuous-time model predictive control (MPC) laws by representing the input/output signals and related models using B-spline functions. Such an approximation allows to implement the resulting feedback control law more efficiently, requiring less online computational effort. As a result, the proposed controller formulates the control signals as continuous polynomial spline functions. All constraints assumed over the prediction horizon are then expressed as constraints acting on the B-splines control polygon vertices. The performance of the proposed theoretical framework has been demonstrated with several real-time experiments using the well-known 2-DOF laboratory helicopter setup. The aim of the presented experiments was to track given step-like reference trajectories for pitch and yaw angles under notable parameter uncertainties. In order to suppress the influence of uncertainties, the control algorithm is implemented in an adaptive mode, equipped with the recursive least squares (RLS) estimation of model parameters and with the adaptation of stabilizing terminal set and terminal cost calculations. Thanks to the presented framework, it is possible to significantly reduce the computational burden, measured by the number of decision variables and input constrains, indicating the potential of the proposed concept for real-time applications, even when using embedded control hardware. [ABSTRACT FROM AUTHOR]

Nowadays, many museums publish virtual versions of the artifacts they keep in their collections in different 3D model viewers available on the Internet. However, despite the wide experience that some of them have in this field, it is still possible to find many virtual models that do not meet the desirable requirements for their publication on the Internet, especially regarding the optimization of the mesh and color textures needed for greater efficiency in the visualization and downloading of 3D objects. In this study, a sample of virtual models of objects belonging to multiple archaeological museums from different countries is analyzed. We considered multiple characteristics of the models, such as the number of polygons that compose them, the quality of the meshes, filter effects applied during post-processing, etc. The results of this research indicate that it is still necessary to make a greater effort to improve the training and digital skills of the professionals in charge of the digitization process in this area of cultural heritage. [ABSTRACT FROM AUTHOR]

Unmanned aerial vehicles (UAVs) employed as airborne base stations (BSs) are considered the essential components in future sixth-generation wireless networks due to their mobility and line-of-sight communication links. For a UAV-assisted ad hoc network, its total channel capacity is greatly influenced by the deployment of UAV-BSs and the corresponding coverage layouts, where square and hexagonal cells are partitioned to divide the zones individual UAVs should serve. In this paper, the total channel capacities of these two kinds of coverage layouts are evaluated using our proposed novel computationally efficient channel capacity estimation scheme. The mean distance (MD) between a UAV-BS in the network and its served users as well as the MD from these users to the neighboring UAV-BSs are incorporated into the estimation of the achievable total channel capacity. We can significantly reduce the computational complexity by using a new polygon division strategy. The simulation results demonstrate that the square cell coverage layout can always lead to a superior channel capacity (with an average increase of  7.67 %  to be precise) to the hexagonal cell coverage layout for UAV-assisted ad hoc networks. [ABSTRACT FROM AUTHOR]

This study proposes a new wall boundary condition for the grid-stamping on a polygon (G-StoP) model, which enables a simpler and more efficient handling of boundary surfaces of arbitrarily complex-shaped bodies represented using polygons (or meshes). For example, computer-aided design surface data can be used to analyze flow using a particle-based fluid-solver moving particle semi-implicit method. For coupling simulations of fluid–multibody dynamics, the Pusan-National-University-modified MPS method is improved, and the coupling analysis is performed using RecurDyn, a commercial software package for multibody (or flexible multibody) dynamics. To confirm the applicability of the developed G-StoP model, hydrostatic pressure simulations are conducted in a rectangular tank at various corner angles. Then, the hydrostatic pressure results are compared with previously proposed polygonal wall boundary model results and theoretical solutions. That is, in the case with a corner angle of 30°, it was confirmed that the relative error to the experiment of the polygon model was 11.3%, while that of the G-StoP model was 1.3%. This demonstrates that the proposed G-StoP model is exceptional for numerical stability and robustness even when it is difficult to secure information on neighboring particles as the corner angle of the object becomes small. In addition, the G-StoP model was applied to dam breaking, subaerial landslide tsunami, and wine sloshing problems, and its accuracy and applicability were tested through comparison with experimental and other simulation results. As a result, it was shown that the present simulation results were much closer to the experiments than other simulations. [ABSTRACT FROM AUTHOR]

The percolation of the interfacial transition zone (ITZ) is generally regarded as an important factor that may accelerate the penetration of aggressive agents in concrete materials, and its threshold is largely determined by the features of aggregates. In most numerical studies about ITZ percolation, both fine aggregates and coarse aggregates are assumed to be the particles of uniform shape, and their size distributions are generally strung together by a single function, which is quite different from reality. To quantify the ITZ percolation associated with the polydispersity of aggregate shapes and size gradations in a more realistic way, the two-dimensional (2D) meso-scale model of concrete is generated by simplifying coarse aggregates and fine aggregates as polygons and ovals, respectively. Moreover, the size gradations of them are also represented by two separate expressions. By combining these models with percolation theory, the percolation of ITZ in the 2D case is explicitly simulated, and the influence of aggregate shape- and size-diversities on the critical threshold ϕagg,c is studied in detail. Based on the simulated results of ϕagg,c, an empirically analytical expression is further proposed to fast predict the ITZ percolation, and its reliability is verified. The results show that the ITZ thickness, average aggregate fineness, coarse aggregate shape, and fine aggregate shapes are the four main contributing factors to the ITZ percolation. Compared with the existing literature, the proposed model here has a broader range of applications (e.g., mortar, concrete, and other granular systems) in the 2D case and can provide the larger predicted results, which may be closer to reality. [ABSTRACT FROM AUTHOR]

The turning function is a tool in image processing that measures the difference between two polygonal shapes. We propose a localization algorithm for the optimal pose estimation of autonomous mobile robots using the scan-matching method based on the turning function algorithm. There are several methodologies aimed at moving the robots in the right way and carrying out their missions well, which involves the integration of localization and control. In the proposed method, the localization problem is implemented in the form of an optimization problem. Afterwards, the turning function algorithm and the simplex method are applied to estimate the localization and orientation of the robot. The proposed algorithm first receives the polygons extracted from two sensors' data and then allocates a histogram to each sensor scan. This algorithm attempts to maximize the similarity of the two histograms by converting them to a unified coordinate system. In this way, the estimate of the difference between the two situations is calculated. In more detail, the main objective of this study is to provide an algorithm aimed at reducing errors in the localization and orientation of mobile robots. The simulation results indicate the great performance of this algorithm. Experimental results on simulated and real datasets show that the proposed algorithms achieve better results in terms of both position and orientation metrics. [ABSTRACT FROM AUTHOR]

Adjusting the roll angle of a rover's body is a commonly used strategy to improve its traversability over sloped terrains. However, its range of adjustment is often limited, due to constraints imposed by the rover design and geometry factors such as suspension, chassis, size, and suspension travel. In order to improve the rover's traversability under these constraints, this paper proposes a reconfigurable rover design with a two-level (sliding and rolling) mechanism to adjust the body's roll angle. Specifically, the rolling mechanism is a bionic structure, akin to the human ankle joint which can change the contact pose between the wheel and the terrain. This novel adjustment mechanism can modulate the wheel–terrain contact pose, center-of-mass projection over the supporting polygon, wheel load, and the rover driving mode. Combining the wheel–load model and terramechanics-based wheel–terrain interaction model, we develop an integrated model to describe the system dynamics, especially the relationship between rover pose and wheel slippage parameters. Using this model, we develop an associated attitude control strategy to calculate the desired rover pose using particle swarm algorithm while considering the slip rate and angle constraints. We then adjust the sliding and rolling servo angles accordingly for slope traversing operations. To evaluate the proposed design and control strategies, we conduct extensive simulation and experimental studies. The results indicate that our proposed rover design and associated control strategy can double the maximum slope angles that the rover can negotiate, resulting in significantly improved traversability over soft sloped terrains. [ABSTRACT FROM AUTHOR]

As one of the best indicators of the periglacial environment, ice-wedge polygons (IWPs) are important for arctic landscapes, hydrology, engineering, and ecosystems. Thus, a better understanding of the spatiotemporal dynamics and evolution of IWPs is key to evaluating the hydrothermal state and carbon budgets of the arctic permafrost environment. In this paper, the dynamics of ground surface deformation (GSD) in IWP zones (2018–2019) and their influencing factors over the last 20 years in Saskylakh, northwestern Yakutia, Russia were investigated using the Interferometric Synthetic Aperture Radar (InSAR) and Google Earth Engine (GEE). The results show an annual ground surface deformation rate (AGSDR) in Saskylakh at −49.73 to 45.97 mm/a during the period from 1 June 2018 to 3 May 2019. All the selected GSD regions indicate that the relationship between GSD and land surface temperature (LST) is positive (upheaving) for regions with larger AGSDR, and negative (subsidence) for regions with lower AGSDR. The most drastic deformation was observed at the Aeroport regions with GSDs rates of −37.06 mm/a at tower and 35.45 mm/a at runway. The GSDs are negatively correlated with the LST of most low-centered polygons (LCPs) and high-centered polygons (HCPs). Specifically, the higher the vegetation cover, the higher the LST and the thicker the active layer. An evident permafrost degradation has been observed in Saskylakh as reflected in higher ground temperatures, lusher vegetation, greater active layer thickness, and fluctuant numbers and areal extents of thermokarst lakes and ponds. [ABSTRACT FROM AUTHOR]

In the planning stage of the fabrication process of physical models of cellular structures, a surface model of the structure needs to be adjusted to acquire the requisite properties, but errors emerge frequently at this stage. The main objective of this research was to repair or reduce the impact of deficiencies and errors before the fabrication of physical models. For this purpose, it was necessary to design models of cellular structures with different accuracy settings in PTC Creo and then compare them after the tessellation process using GOM Inspect. Subsequently, it was necessary to locate the errors occurring in the process of preparing models of cellular structures and propose an appropriate method of their repair. It was found that the Medium Accuracy setting is adequate for the fabrication of physical models of cellular structures. Subsequently, it was found that within regions where mesh models merged, duplicate surfaces emerged, and the entire model could be considered as manifesting non-manifold geometry. The manufacturability check showed that in the regions with duplicate surfaces inside the model, the toolpath creation strategy changed, causing local anisotropy within 40% of the fabricated model. A non-manifold mesh was repaired in the proposed manner of correction. A method of smoothing the model's surface was proposed, reducing the polygon mesh density and the file size. The findings and proposed methods of designing cellular models, error repair and smoothing methods of the models can be used to fabricate higher-quality physical models of cellular structures. [ABSTRACT FROM AUTHOR]