Polygonal Research Articles

Reusable energy-absorbers design harnessing snapping-through buckling of tailored multistable architected materials

Abstract Multistable metamaterials are artificially engineered materials that possess microarchitectures capable of maintaining multiple stable configurations. However, the realization of mechanical metamaterials with numerous programmable stable configurations using Double-Curved Beam (DCB) elements remains an ongoing challenge. In this study, we exploit the snapping-through buckling phenomenon exhibited by architected DCB structures to devise a mechanical metamaterial with a unique deformation mode, encompassing Multi-stability, Multi-path, Multi-platform, and Multi-step characteristics, hence referred to as a 4M mechanical metamaterial. By employing DCB as fundamental building block elements, architected metamaterials with two-dimensional (2D) series or parallel lattices are successfully constructed, as well as three-dimensional (3D) tubular geometries, denoted as DCB-n-m-C and DCB-n-m-M metamaterials, respectively. These metamaterials exhibit reversible energy absorption characteristics and the stiffness can be transformed from positive to negative under both small and large elastic deformations. Functional gradient design and tailored deformation capability are given by adjusting the wall thickness of each layer of double-curved beams, thereby demonstrating the multi-path deformation features inherent in 4M metamaterials. DCB-n-m-M metamaterials has multiple energy platforms in the process of snapping-through, which reflects the multi-platform characteristics of 4M metamaterial. Consequently, novel properties such as multistability, programmability, and reusable energy absorption characteristics are achieved. To comprehensively understand the mechanical response of the metamaterials, a thorough investigation into the influence of geometric parameters is conducted, including the number of polygonal edges, the number of the layers, and the aspect ratio Q. This investigation involves a combination of theoretical analyses, numerical simulations, and experimental verifications. The introduced design strategy paves a way for the innovative design of multistable, multi-step, tailored, and reversible deformation metamaterials.

Security Improvement of UAV Group IoT in Polygonal Area Based on Similarity Clustering Algorithm

Abstract Currently, unmanned aerial vehicle (UAV) group Internet of Things (IoT) has poor stability, poor endurance, and low security. In this regard, we report a polygon area UAV group IoT clustering algorithm for large-scale, high-speed mobile IoT environment. First, the UAV group IoT was divided into a polygon area and a few cluster heads were used to cover the polygon area uniformly. Then, the clustering index in the maximum speed similarity clustering algorithm was induced into the weighted clustering algorithm. Simultaneously, the link retention rate, relative node degree, and node residual energy ratio were improved to select the IoT node with the maximum weight as the cluster head. Finally, the IoT security was improved by reputation calculation. The results show that the clustering algorithm in this paper can reduce the number of clusters and lower the handover rate between clusters, improve the stability of clustering, prolong the survival time of the minimum node, improve the overall endurance of the IoT, and have high security.

Dispersion problem on a convex polygon

Given a set P={p1,p2,…,pn} of n points in R2 and a positive integer k(≤n), we wish to find a subset S of P of size k such that the cost of a subset S, cost(S)=min⁡{d(p,q)|p,q∈S}, is maximized, where d(p,q) is the Euclidean distance between two points p and q. The problem is called the max-min k-dispersion problem. In this article, we consider the max-min k-dispersion problem, where a given set P of n points are vertices of a convex polygon. We refer to this variant of the problem as the convex k-dispersion problem.We propose an 1.733-factor approximation algorithm for the convex k-dispersion problem. In addition, we study the convex k-dispersion problem for k=4. We propose an iterative algorithm that returns an optimal solution of size 4 in O(n3) time.

About polygon area uncertainty in GIS and its implications on agro-forestry estimates

Error affecting calculation of a polygon area from a digital map is an issue that is commonly neglected by remote sensing and Geographic information system (GIS) users. In this work, a method is presented aimed at estimating the uncertainty related to area calculation of polygons in a vector map. Additionally, area error relationship with polygon geometric features was analyzed, as well. A multivariate regression-based approach was applied for this task. After presenting the method, to demonstrate its operational capabilities, it was applied to 2 case studies corresponding (i) to a forest map and (ii) to the map from the Geo Spatial Aid Application used for in the framework of the EU Common Agriculture Policy. Estimated uncertainty (percentage) median values were found to be 0.01% and 0.02% for (i) and (ii), respectively. It was also demonstrated that the same polygon shape built using less vertices (longer vectors) generates area estimates that are less accurate than the ones from polygons built using a higher number of vertices (shorter vectors).

Synthesis of 1-DOF mechanisms for exact regular polygonal path generation based on non-circular gear transmissions

Design of one-degree-of-freedom (1-DOF) mechanisms is of paramount interest. This work deals with the generation of exact regular polygonal paths by using two particular 1-DOF mechanisms. The design of two-bar and three-bar mechanisms including non-circular gears is presented and evaluated. Differences in the kinematics of both mechanisms are discussed. The three-bar mechanism allows derivable velocity and acceleration curves during the whole trajectory, including the polygon vertices, a feature that cannot be achieved with the simpler two-bar mechanism. Hence, the three-bar mechanism makes it possible to generate perfect vertices using non-circular gears. To the best of the authors’ knowledge, this mechanism is the first 1-DOF mechanism with articulated links and a non-circular gear transmission that can generate exact regular polygonal paths. The proposed mechanisms can also be applied to generate two straight lines with a given angle, which is another novel contribution of this work. A prototype of the three-bar mechanism has been developed for experimental validation.

Multi-granularity learning of explicit geometric constraint and contrast for label-efficient medical image segmentation and differentiable clinical function assessment

Automated segmentation is a challenging task in medical image analysis that usually requires a large amount of manually labeled data. However, most current supervised learning based algorithms suffer from insufficient manual annotations, posing a significant difficulty for accurate and robust segmentation. In addition, most current semi-supervised methods lack explicit representations of geometric structure and semantic information, restricting segmentation accuracy. In this work, we propose a hybrid framework to learn polygon vertices, region masks, and their boundaries in a weakly/semi-supervised manner that significantly advances geometric and semantic representations. Firstly, we propose multi-granularity learning of explicit geometric structure constraints via polygon vertices (PolyV) and pixel-wise region (PixelR) segmentation masks in a semi-supervised manner. Secondly, we propose eliminating boundary ambiguity by using an explicit contrastive objective to learn a discriminative feature space of boundary contours at the pixel level with limited annotations. Thirdly, we exploit the task-specific clinical domain knowledge to differentiate the clinical function assessment end-to-end. The ground truth of clinical function assessment, on the other hand, can serve as auxiliary weak supervision for PolyV and PixelR learning. We evaluate the proposed framework on two tasks, including optic disc (OD) and cup (OC) segmentation along with vertical cup-to-disc ratio (vCDR) estimation in fundus images; left ventricle (LV) segmentation at end-diastolic and end-systolic frames along with ejection fraction (LVEF) estimation in two-dimensional echocardiography images. Experiments on nine large-scale datasets of the two tasks under different label settings demonstrate our model’s superior performance on segmentation and clinical function assessment.

Maximizing the Area of Polygons via Quasicyclic Polygons

Based on Peter’s work from 2003, quadrilaterals can be characterized in the following way: “among all quadrilaterals with given side lengths 𝑎, 𝑏, 𝑐 and 𝑑, those of the largest possible area are exactly the cyclic ones”. In this paper, we will give the corresponding characterization for every polygon, by means of quasicyclic polygons properties.

Herbo-Mineral Medicine, Lithom Exhibits Anti-Nephrolithiasis Activity in Rat Model of Hyperoxaluria by Attenuating Calcium Oxalate Crystal Formation and Oxidative Stress.

Calcium oxalate monohydrate (COM) forms the most common type of kidney stones observed in clinics, elevated levels of urinary oxalate being the principal risk factor for such an etiology. The objective of the present study was to evaluate the anti-nephrolithiatic effect of herbo-mineral formulation, Lithom. The in vitro biochemical synthesis of COM crystals in the presence of Lithom was performed and observations were made by microscopy and Scanning Electron Microscope (SEM) based analysis for the detection of crystal size and morphology. The phytochemical composition of Lithom was evaluated by Ultra-High-Performance Liquid Chromatography (UHPLC). The in vivo model of Ethylene glycol-induced hyperoxaluria in Sprague-Dawley rats was used for the evaluation of Lithom. The animals were randomly allocated to 5 different groups namely Normal control, Disease control (ethylene glycol (EG), 0.75%, 28 days), Allopurinol (50 mg/kg, q.d.), Lithom (43 mg/kg, b.i.d.), and Lithom (129 mg/kg, b.i.d.). Analysis of crystalluria, oxalate, and citrate levels, oxidative stress parameters (malondialdehyde (MDA), catalase, myeloperoxidase (MPO)), and histopathology by hematoxylin and eosin (H&E) and Von Kossa staining was performed for evaluation of Lithom. The presence of Lithom during COM crystals synthesis significantly reduced the average crystal area, feret's diameter, and area-perimeter ratio, in a dose-dependent manner. SEM analysis revealed that COM crystals synthesized in the presence of 100 and 300 μg/mL of Lithom exhibited a veritable morphological transition from irregular polygons with sharp edges to smoothened smaller cuboid polygons. UHPLC analysis of Lithom revealed the presence of Trigonelline, Bergenin, Xanthosine, Adenosine, Bohoervinone B, Vanillic acid, and Ellagic acid as key phytoconstituents. In EG-induced SD rats, the Lithom-treated group showed a decrease in elevated urinary oxalate levels, oxidative stress, and renal inflammation. Von Kossa staining of kidney tissue also exhibited a marked reduction in crystal depositions in Lithom-treated groups. Taken together, Lithom could be a potential clinical-therapeutic alternative for management of nephrolithiasis.

A compact and efficiently designed two-port MIMO antenna for N78/48 5G applications

A tightly packed irregular polygon with a distinctive protruding strip, specifically tailored for the N78/48 application, enhances a highly compact and effectively designed two-port MIMO (multiple-input, multiple-output) antenna. Its dimensions measure 20x31.5 × 1.6 mm3, with εr being 4.4 of FR-4 substrate, and it impressively delivers an extensive impedance bandwidth (Sxx < −10 dB) spanning the 3.25–3.85 GHz range. The design incorporates a MIMO antenna with closely spaced elements, merely 1.5 mm (0.012 λ0) apart. The microstrip inserts a feeding line with a partially truncated ground, a grounded stub, and a side stubs embedded in the ground plane, which improve isolation. Positioning T shaped decoupling elements between radiators helps the antenna's bandwidth enhance and improves isolation (S21) across the band. Extensive validation of the antenna's performance has been carried out through comprehensive s-parameter analysis, closely mirroring the results obtained through measurements. Despite its compact form, this antenna efficiently minimizes coupling, achieving S21 levels exceeding −19.25 dB throughout the band. Notably, the antenna attains an impressive peak gain of 3.3 dBi and exhibits a radiation efficiency of 92%. A total affective reflection coefficient (TARC) that starts at-10 dB, a MEG of 0.481 dB, and a channel capacity loss (CCL) of 0.3016 bits/s/Hz are some of the things that make up its MIMO diversity performance. The envelope correlation coefficient (ECC) is 0.0089. It's particularly suitable for 5G-NR sub-6GHz requirements, offering an efficient and compact solution.

A Convex Polygon of Twist Influenced by Nandakumar and Ramana Rao

In this study, the researchers address the conundrum: To divide a 2-dimensional convex polygonal region Q into a specified natural number n of convex pieces, all of which have equal areas although perimeters could be different, such that the total length of cuts used is maximized. With the aid of AutoCAD software, the results show that a convex polygon Q divided into n=2 equal area partitions must have its cut line λ¬ or its area bisector originate in some vertex "v" _"α" of Q with the least measure. We claim that this cut line λ is the maximum possible cut length that divides polygon Q into n=2 equal area partitions. The resulting proof of this conjecture can be used recursively for a convex polygon Q divided into n=2^k equal area partitions, where k∈N

MRI Extracellular Volume Fraction in Liver Fibrosis-A Comparison of Different Time Points and Blood Pool Measurements.

Extracellular volume (ECV) correlates with the degree of liver fibrosis. To analyze the performance of liver MRI-based ECV evaluations with different blood pool measurements at different time points. Prospective. 73 consecutive patients (n = 31 females, mean age 56 years) with histopathology-proven liver fibrosis. 3T acquisition within 90 days of biopsy, including shortened modified look-locker inversion recovery T1 mapping. Polygonal regions of interest were manually drawn in the liver, aorta, vena cava, and in the main, left and right portal vein on four slices before and after Gd-DOTA administration at 5/10/15 minutes. ECV was calculated 1) on one single slice on portal bifurcation level, and 2) averaged over all four slices. Parameters were compared between patients with fibrosis grades F0-2 and F3-F4 with the Mann-Whitney U and fishers exact test. ROC analysis was used to assess the performance of the parameters to predict F3-4 fibrosis. A P-value <0.05 was considered statistically significant. ECV was significantly higher in F3-4 fibrosis (35.4% [33.1%-37.6%], 36.1% [34.2%-37.5%], and 37.0% [34.8%-39.2%] at 5/10/15 minutes) than in patients with F0-2 fibrosis (33.3% [30.8%-34.8%], 33.7% [31.6%-34.7%] and 34.9% [32.2%-36.0%]; AUC = 0.72-0.75). Blood pool T1 relaxation times in the aorta and vena cava were longer on the upper vs. lower slices at 5 minutes, but not at 10/15 minutes. AUC values were similar when measured on a single slice (AUC = 0.69-0.72) or based on blood pool measurements in the cava or portal vein (AUC = 0.63-0.67 and AUC = 0.65-0.70). Liver ECV is significantly higher in F3-4 fibrosis compared to F0-2 fibrosis with blood pool measurements performed in the aorta, inferior vena cava, and portal vein at 5, 10, and 15 minutes. However, a smaller variability was observed for blood pool measurements between slices at 15 minutes. 1 TECHNICAL EFFICACY: Stage 3.

Gradient-based wind farm layout optimization with inclusion and exclusion zones

Abstract. Wind farm layout optimization is usually subjected to boundary constraints of irregular shapes. The analytical expressions of these shapes are rarely available, and, consequently, it can be challenging to include them in the mathematical formulation of the problem. This paper presents a new methodology to integrate multiple disconnected and irregular domain boundaries in wind farm layout optimization problems. The method relies on the analytical gradients of the distances between wind turbine locations and boundaries, which are represented by polygons. This parameterized representation of boundary locations allows for a continuous optimization formulation. A limitation of the method, if combined with gradient-based solvers, is that wind turbines are placed within the nearest polygons when the optimization is started in order to satisfy the boundary constraints; thus the allocation of wind turbines per polygon is highly dependent on the initial guess. To overcome this and improve the quality of the solutions, two independent strategies are proposed. A case study is presented to demonstrate the applicability of the method and the proposed strategies. In this study, a wind farm layout is optimized in order to maximize the annual energy production (AEP) in a non-uniform wind resource site. The problem is constrained by the minimum distance between wind turbines and five irregular polygon boundaries, defined as inclusion zones. Initial guesses are used to instantiate the optimization problem, which is solved following three independent approaches: (1) a baseline approach that uses a gradient-based solver; (2) approach 1 combined with the relaxation of the boundaries, which allows for a better design space exploration; and (3) the application of a heuristic algorithm, “smart-start”, prior to the gradient-based optimization, improving the allocation of wind turbines within the inclusion polygons based on the potential wind resource and the available area. The results show that the relaxation of boundaries combined with a gradient-based solver achieves on average +10.2 % of AEP over the baseline, whilst the smart-start algorithm, combined with a gradient-based solver, finds on average +20.5 % of AEP with respect to the baseline and +9.4 % of AEP with respect to the relaxation strategy.

Harmonic-measure distribution functions of simply connected and doubly connected polygonal domains

The h-function encodes aspects of the behaviour of Brownian particles released from a specified fixed point inside the region. In turn, this behaviour is influenced by the shape of the region's boundary and the location of the fixed point. We compute the h-functions of numerous simply connected and doubly connected polygonal regions. The Schottky–Klein prime function plays a key role in computing h-functions of these regions. Also, in the computation, we use the Schwarz–Christoffel mappings, the Cayley-type mappings, and their generalisations, which are expressed in terms of the prime function. We also cross-check the validity of all the h-functions we find by rederiving them via numerical simulation of Brownian motion.

Effects of cell morphology, physiology, biochemistry and CHS genes on four flower colors of Impatiens uliginosa.

Flower color is one of the important ornamental traits in the plants, which plays an active role in attracting pollinators to pollinate plants and reproduce their offspring. The flower color of Impatiens uliginosa is rich, there are four main flower colors in nature: deep red, red, pink, and white. However, it remains unclear whether on four different flower colors mechanism of I. uliginosa. We investigate colorimetric measurement, observation of epidermal cells, cellular pH determination, extraction and determination of total anthocyanins and flavonoid, semi-quantitative determination of pigment components, and gene cloning and qRT-PCR of CHS genes to study four flower colors of I. uliginosa. The L* and b* values were the highest in white flower, while the a* values were the highest in pink flower. The same shape of epidermal cells was observed in different flower colors, which was all irregular flat polygons, and there were partial lignification. Their cellular pH values were weakly acidic, while the pH values of the deep red flower was the highest and the white flower was the lowest. The highest pigment content of the four flower colors was total anthocyanin content. And malvidin-3-galactosidechloride (C23H25ClO12), cyanidin-3-O-glucoside (C21H21O11) and delphinidin (C15H11O7) were the main pigment components affecting the color of four different flower colors. The anthocyanin synthesis gene IuCHS was expressed in four flowers, and all three copies of it had the highest expression level in pink flower and the lowest expression level in white flower. These results revealed the influence of main internal factors on four different flower colors of I. uliginosa, and provided a basis for further understanding of the intracellular and molecular regulatory mechanisms of flower color variation, and laid a foundation for the improvement of flower color breeding of Impatiens.

Dermoscopy in the Diagnosis of Darier’s Disease: A Precise Approach

Darier’s disease, a rare genetic condition with autosomal transmission that alters keratinization, clinically manifests as pruritic keratotic papules, mainly localized on seborrheic areas. Due to the similarity in presentation with other pathologies, dermoscopy plays a crucial role in diagnostic orientation. We report two observations of patients with Darier’s disease, highlighting distinctive dermoscopic structures, such as brownish polygonal areas surrounded by a whitish halo, thus contributing to a more accurate diagnosis.

Multi-Objective Optimization Design of an Origami-Inspired Combined Cushion Airbag

To improve the cushioning performance of soft-landing systems, a novel origami-inspired combined cushion airbag is proposed. The geometry size, initial pressure, and exhaust vent area of the cushion airbags are designed preliminarily using a theoretical model. The finite element models, including the returnable spacecraft and cushion airbags, are established via the control volume method (CVM) to analyze the impact dynamic behavior and cushioning performance during the landing attenuation process. The cushioning performance of the cushion airbags in complex landing environments are studied to investigate the influence of horizontal velocity, lateral velocity and nonhorizontal landing surfaces. Four design parameters of the cushion airbags, including the initial pressure, venting threshold pressure, exhaust vent area and polygon edge number, are employed to study their influence on the cushioning performance. A multi-objective optimization model of the cushion airbags based on the neural network and multi-objective water cycle algorithm is established to realize the rapid optimization design. The Pareto front of the maximum overload and specific energy absorption is obtained. The analysis results show that the maximum overload of the proposed combined cushion airbags is 7.30 g. The system with the anti-rollover design can avoid rollover and achieve outstanding cushioning performance in complex landing environments. The maximum overload of the returning spacecraft is decreased by 16.4% from 7.30 g to 6.10 g after multi-objective optimizations. This study could provide the technical support for the soft-landing system design of returnable spacecrafts.

Assessing Wet and Dry Periods Using Standardized Precipitation Index Fractal (SPIF) and Polygons: A Novel Approach

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.

Phase Correction of the Channels of a Fully Populated Randomized Multielement Therapeutic Array Using the Acoustic Holography Method

The acoustic holography method was used to characterize a therapeutic focused fully populated 256-element ultrasonic transducer array. Elements of the array with the shape of equal area polygons are densely arranged in an irregular pattern on a spherically concave surface with a radius of curvature of 150 mm and a diameter of 200 mm. The array has a central frequency of 1.2 MHz and is designed to operate in water. The performance of individual array elements was studied based on the holographically reconstructed normal velocity distribution over the array surface. It was shown that with the same electrical signals applied to the elements, their acoustic responses had a phase deviation relative to the nominal values, which can be caused either by the asphericity of the array surface, or by the introduction of additional phase delays by the electrical matching network. To compensate for the detected parasitic phase shifts of the elements and restore the effective sphericity of the radiating surface, the Verasonics V-1 control system was used. The hologram measured after making the correction, as well as the shape of the focal region and acoustic pressure magnitude at the focus, separately measured by a hydrophone, showed that the proposed method reconstructed the nominal operating parameters of the array with high accuracy.

Exploring Geometry and Art through Tessellations

In this lesson, elementary school students explore geometric shapes and tessellations using a Cricut Maker 3. During Part 1 of the activity, students review geometric concepts of regular versus irregular polygons and lines of symmetry. This includes using shapes cut by the Cricut machine to determine which regular polygons form a tessellation when put together. Then students answer reflection questions. During Part 2, there is a discussion about how the artist MC Escher used different types of symmetry (e.g., translations, rotations, and reflections) to modify irregular shapes to create tessellations. In Part 3, students are given materials to prototype their own tessellation using regular and irregular shapes and at least one type of symmetry transformation.

Lagrangian and Eulerian modelling of river plumes in the Great Barrier Reef system, Australia

In this paper, we describe methods to verify the adequacy and accuracy of Lagrangian particles from a Lagrangian model to reproduce the concentrations of a passive tracer from an Eulerian-model in river plumes. The modelling simulates plumes from two major rivers discharging in the Great Barrier Reef (GBR), Australia, under real-world scenarios. The study has been a part of a major project to aid in the protection of the GBR system from the impacts of extreme events and climate change. We employ the Regional Ocean Modelling System (ROMS) activated with its built-in Lagrangian model, and forced with wind fields from global models and recorded river volume discharges. The ROMS-Lagrangian model tracks the Lagrangian particles using the spatially interpolated velocities computed on the Eulerian ROMS three-dimensional (3D) grid. The Lagrangian particles are released in the river in proportion to the measured river volume flux. We apply a novel technique that exploits Voronoi polygon areas to convert Lagrangian particle separation into a concentration field. This facilitates comparison with the passive tracer concentrations driven by the Eulerian velocities computed on the ROMS 3D grid. We evaluate the fate of Lagrangian particles activated on a 4-km grid resolution with those of equivalent Eulerian tracer concentrations. For validation, we compare the Lagrangian particles with the Eulerian passive tracer simulated using a higher model grid resolution of 500-m, and found that the computed Lagrangian particle concentrations showed similar overall patterns compared to the passive tracer concentrations from both the coarse 4-km, and high-resolution 500-m Eulerian models. The spatial extent of the particles was in better agreement with the coarse 4-km model than with the higher resolution 500-m model. The clustering of particles resulted in structures at finer scales than the Eulerian model, over the high particle density areas that compared well against observations. The Lagrangian particles are able to capture the general river plume patterns seen in the satellite MODIS images and the satellite derived Chlorophyll-a. We further compare the online ROMS model with an offline particle tracker, OceanPARCELS and determined the similarity of results from both online and offline methods. Overall, our study demonstrates the viability to use Lagrangian particles to reproduce the Eulerian tracer properties, which can be combined with particle properties include tracer age providing to enhance the guidance on the distribution and concentration of effluent from localised flooding river events.