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Subjective weighting methods are widely employed to determine criteria weights in multi-criteria decision-making (MCDM) environment. Inputs from decision-makers, including opinions, assessments, assumptions, evaluations, interpretations, expectations, and judgments, are primarily relied upon in these methods. Significant challenges are faced due to two primary factors: the inherent uncertainty in inputs and the process of pairwise comparisons. These challenges increase the uncertainty regarding the derived weights, raising concerns about the reliability of such approaches. This paper introduces a novel MCDM method called Soft Clusters-Rectangles (SCR) to overcome such limitations. This method distinguishes itself by avoiding pairwise comparisons and adopting a fuzzy approach to address uncertainty. Weights are calculated based on criteria membership values across three defined clusters, namely immaterial, mediocre, and vital. Each cluster represents a distinct range of importance. Analytic geometry is also used by computing the areas of multiple rectangles to determine the final weights. The application of SCR method is demonstrated through a case study on autonomous vehicle route selection problem. The results are thoroughly examined through comprehensive analysis. The findings reveal that this method not only avoids the challenges posed by pairwise comparison-based methodologies but also exhibits similarities with objective weighting techniques, often yielding results more comparable to those produced by hybrid methods. [ABSTRACT FROM AUTHOR]

Given a set of integers A⊂Z$A \subset \mathbb {Z}$, we consider the smallest family B$\mathcal {B}$ invariant by translations that contains the rectangles R=Ia1×⋯×Ian−1×I−(a1+⋯+an−1)$$\begin{equation*} R = I_{a_1} \times \dots \times I_{a_{n-1}} \times I_{-(a_1+\dots +a_{n-1})} \end{equation*}$$for any a1,⋯,an−1∈An−1$a_1,\dots,a_{n-1} \in A^{n-1}$ and where Ik=[0,2k]$I_k = [0,2^k]$ for k$k$ integer. We prove that if A$A$ contains arbitrary large arithmetic progression, then the maximal operator MB$M_{\mathcal {B}}$ associated to the family B$\mathcal {B}$ satisfies a weak‐type estimate of the form MBf>t≲n∫Rn|f|t1+log+|f|tn−1$$\begin{equation*} {\left|{\left\lbrace M_{\mathcal {B}}f > t \right\rbrace} \right|} \lesssim _n \int _{\mathbb {R}^n} \frac{|f|}{t} {\left(1 + \log ^+ \frac{|f|}{t} \right)}^{n-1} \end{equation*}$$but does not satisfy a weak‐type estimate of the form MBf>t≲n∫Rnϕ|f|t$$\begin{equation*} {\left|{\left\lbrace M_{\mathcal {B}}f > t \right\rbrace} \right|} \lesssim _n \int _{\mathbb {R}^n} \phi {\left(\frac{|f|}{t}\right)} \end{equation*}$$for any nonnegative convex increasing function ϕ$\phi$ such that ϕ(x)=o(x(1+log+x)n−1)$\phi (x) = o(x(1+ \log ^+ x)^{n-1})$ as x$x$ tends to infinity. [ABSTRACT FROM AUTHOR]

The five-bar linkage, used in the form of a planar manipulator, benefits from easy controllability and relatively simple kinematic structures, which mean that it can be used in several applications in robotics, rehabilitation, and haptic devices, etc. This paper proposes an optimal synthesis method for a symmetrical five-bar linkage of type 5-RRRRR, with a singularity-free dexterous workspace, based on workspaces with predefined shapes, like squares, rectangles, triangles, circles, and ellipses. The synthesis conditions, to avoid singularities, are given as inequations, which can be further substituted with a system of equations, by introducing the supraunitary coefficient, k. The analytical solutions of the resulting system of equations enable the computation of the link lengths of the five-bar linkage. The optimization method provides the optimal value of the supraunitary coefficient, in order to obtain a maximum value for the minimum input transmission angle and a minimum value for the manipulator size. In this paper, the authors present an analytical approach to the optimal synthesis of a symmetrical five-bar linkage for different shapes of workspace, with the same surface and coordinates in terms of the mass center, as well as the resulting link lengths. In regard to the numerical examples, the authors considered and compared performance indices, such as manipulability, the condition number, and stiffness. The considered examples showed that an equilateral triangle-shaped workspace achieved higher global manipulability, a square-shaped workspace achieved higher global dexterity and the minimum input transmission angle, and circular workspaces achieved the highest mean stiffness and total surface size. It was observed that the synthesis method generates structures that are well-suited to singularity-free dexterous workspaces, with nonzero stiffness values. [ABSTRACT FROM AUTHOR]

Purpose: To characterize the dose‐response, energy dependence, postexposure changes, orientation dependence, and spatial capabilities of LD‐V1, a new low‐dose Gafchromic film for low‐energy x‐ray dosimetry. Methods: A single sheet of LD‐V1 Gafchromic film was cut into 15 × 20 mm2 rectangles with a notch to track orientation. Eight different doses between 5 and 320 mGy were delivered by an MXR‐160/22 x‐ray tube using x‐ray beams of 90, 100, and 120 kVp filtered with 3 mm of Al and 2 mm of Ti. The 120 kVp films were scanned at 1, 1.5, 2, 3, 12, 24, 48, 72, and 168 h postexposure in portrait orientation and additionally scanned in landscape orientation at 24 h. The 90 and 100 kVp films were scanned at 24 h postexposure in portrait orientation. Lastly, a 20 × 200 mm2 strip of film was irradiated using a thin‐slit imaging collimator and scanned 24 h postexposure to test the film performance in an x‐ray imaging application. Results: Of the three color channels, the red channel was found to produce a dose‐response curve with a large range of net optical density (netOD) values across the considered dose range. A prominent energy dependence was discovered, resulting in dose discrepancies on the scale of 17 mGy between 90 and 120 kVp for a dose of 80 mGy. The measured postexposure changes suggest that the calibration irradiation‐to‐scan time should be longer than 12 h with a ± 4 h scanning time window for dose errors of <0.5%. An average dose difference of 3.4% was found between the two scanning orientations. Lastly, noise of 4% was measured in the thin slit collimator film for a dose of 30 mGy. Conclusions: We have characterized the LD‐V1 film for low‐energy, low‐dose x‐ray dosimetry. Energy, scan‐time, and orientation dependencies should be considered when using this film. [ABSTRACT FROM AUTHOR]

This study investigates plate analyses employing the method of initial functions (MIFs) across various plate geometries and loading conditions. The conclusions derived from thick rectangular plates highlight substantial thickness‐induced effects on deflection and stress distributions. For thicker plates, the classical assumption of constant deflection fails, with maximum deflection often occurring at surfaces other than the middle plane. The classical and Reissner theories' constant deflection assumption leads to significant discrepancies in thick plate deflection estimates, emphasizing the need for MIFs more accurate approach. Similarly, in the case of thick circular plates, deviations from classical theory are evident in radial and shear stress distributions, particularly pronounced closer to the plate edge and support. These deviations dissipate further away from these regions. Moreover, the study delves into free vibration analyses for rectangular and circular plates, revealing that classical theory tends to overestimate frequencies, especially as plate dimensions increase. Mindlin's theory and MIF approaches showcase improved accuracy with increasing order, converging toward exact solutions. Additionally, Mindlin's theory effectively captures the behavior of higher vertical modes, showcasing sign changes in characteristic quantities of the plate. The findings underscore the limitations of classical theories in accurately predicting plate behaviors, especially in thicker plates and higher modes of vibration. Conversely, the MIF method, alongside Mindlin's theory, proves effective in providing nuanced insights into plate behaviors under various conditions, thus offering valuable implications for structural design and analysis. [ABSTRACT FROM AUTHOR]

Deep neural networks have been remarkably successful as models of the primate visual system. One crucial problem is that they fail to account for the strong shape-dependence of primate vision. Whereas humans base their judgements of category membership to a large extent on shape, deep networks rely much more strongly on other features such as color and texture. While this problem has been widely documented, the underlying reasons remain unclear. We design simple, artificial image datasets in which shape, color, and texture features can be used to predict the image class. By training networks from scratch to classify images with single features and feature combinations, we show that some network architectures are unable to learn to use shape features, whereas others are able to use shape in principle but are biased towards the other features. We show that the bias can be explained by the interactions between the weight updates for many images in mini-batch gradient descent. This suggests that different learning algorithms with sparser, more local weight changes are required to make networks more sensitive to shape and improve their capability to describe human vision. Author summary: When humans recognize objects, the cue they rely on most is shape. In contrast, deep neural networks mostly use local features like color and texture to classify images. We investigated how this difference arises, using images of simple shapes like rectangles and the letters L and T, combined with color and texture features. By testing different feature combinations, we show that some networks are generally unable to learn about shape, whereas others could learn to recognize shapes in isolation, but ignored shape if another feature was present. We show that this bias for color and texture arises from the way in which networks are trained: by averaging the learning signal over many images, the training algorithm favors simple features that are relatively similar in many images and removes sparser, more varied shape features. These insights can help build networks that are more sensitive to shape and work better as models of human vision. [ABSTRACT FROM AUTHOR]

Mathematics is a difficult subject for elementary school students. One of the causes is errors in mathematical concepts and principles made by students. For this reason, efforts need to be made to improve the concept and principles of quadrilaterals. The aim of this research is to design student learning trajectories in finding the perimeter and area of a rectangle in the context of a fishing pond. This is research with a design research approach. The subjects of this research were 50 students divided into two groups, 25 people each. Data collection techniques through observation, interviews and documentation. The data analysis technique used is qualitative and is developed through certain relationship patterns. The results of this research show that the mathematics learning trajectory design was implemented very well. It improves the ability of understanding about quadrilaterals. The learning path is activity-1: students create a representation of the context of a fishing pond and a rectangular image. Activity-2: students determine the perimeter of a rectangular image by placing match sticks around the rectangle in sequence, holding them tightly together. Activity-3: students determine the circumference of the fishing pond. Activity-4: students determine how to calculate the circumference of the pond by drawing a rectangle using matchsticks. Activity-5: students discover the principle of perimeter of a rectangle. The conclusion of this research is that the mathematics learning trajectory design is valid, practical, and increases the ability to understand concepts and principles from quadrilaterals. [ABSTRACT FROM AUTHOR]

This paper puts forward a novel affine relaxation-based algorithm for solving the minimax affine fractional program problem (MAFPP) over a polyhedron set. First of all, some new variables are introduced for deriving the equivalence problem (EP) of the MAFPP. Then, for the EP, the affine relaxation problem (ARP) is established by using the two-stage affine relaxation method. The method provides a lower bound by solving the ARP in the branch-and-bound searching process. By subdividing the output space rectangle and solving a series of ARPs continuously, the feasible solution sequence generated by the algorithm converges to a global optimal solution of the initial problem. In addition, the algorithmic maximum iteration in the worst case is estimated by complexity analysis for the first time. Lastly, the practicability and effectiveness of the algorithm have been verified by numerical experimental results. [ABSTRACT FROM AUTHOR]

Space non-cooperative target recognition is crucial for on-orbit servicing. Multi-satellite cooperation has great potential for broadening the observation scope and enhancing identification efficiency. However, there is currently a lack of research on recognition methods tailored for multi-satellite cooperative observation. In this paper, we propose a novel space non-cooperative target recognition method to identify satellites and debris in images from multi-satellite observations. Firstly, we design an image-stitching algorithm to generate space-wide-area images. Secondly, we propose a two-stage multi-target detection model, a lighter CNN model with distance merge threshold (LCNN-DMT). Specifically, in the first stage, we propose a novel foreground extraction model based on a minimum bounding rectangle with the threshold for distance merging (MBRT-D) to address redundant detection box extraction for satellite components. Then, in the second stage, we propose an improved SqueezeNet model by introducing separable convolution and attention mechanisms for target classification. Moreover, due to the absence of a public multi-target detection dataset containing satellites and debris, we construct two space datasets by introducing a randomized data augmentation strategy. Further experiments demonstrate that our method can achieve high-precision image stitching and superior recognition performance. Our LCNN-DMT model outperforms mainstream algorithms in target localization accuracy with only 0.928 M parameters and 0.464 GFLOPs, making it ideal for on-orbit deployment. [ABSTRACT FROM AUTHOR]

Cutting and Packing problems have been recognized as a sub-discipline of operation research for more than half a century. Such problems are involved in a range of circumstances such as pallet loading, wood or glass cutting, strip packing, and positioning problems. The focus of this study is on 2D rectangular strip packing problems in which rectangle items are not oriented and guillotine constraint is not considered aiming to pack all these items without overlapping into an open-ended bin called a strip of fixed width while the objective is obtaining the minimum total height of cutting. The main aim of this paper is to introduce two proposed heuristics for solving the problem under study. The two heuristics are improved versions of the known Best Fit heuristics, Tower Checker Best Fit (TCBF) and Waste Priority Best Fit (WPBF). The performance of the proposed heuristics is tested using well-known benchmark problems. The computational analysis of the results shows that the proposed heuristics can generate near-optimal solutions to large-scale problems. In addition, the performance of the heuristics outperforms other well-known heuristics from literature by 3%. [ABSTRACT FROM AUTHOR]

In recent years, deep-learning methods have significantly improved the classification results in the field of plant-leaf recognition. However, limited by the model input, the original image needs to be compressed to a certain size before it can be input into the convolutional neural network. This results in great changes in the shape and texture information of some samples, thus affecting the classification accuracy of the model to a certain extent. Therefore, a minimum enclosing quadrate (MEQ) method is proposed to standardize the sample datasets. First, the minimum enclosing rectangle (MER) of the leaf is obtained in the original image, and the target area is clipped. Then, the minimum enclosing quadrate of the leaf is obtained by extending the short side of the rectangle. Finally, the sample is compressed to fit the input requirements of the model. In addition, in order to further improve the classification accuracy of plant-leaf recognition, an EC-ResNet50 model based on transfer-learning strategy is proposed and further combined with the MEQ method. The Swedish leaf, Flavia leaf, and MEW2012 leaf datasets are used to test the performance of the proposed methods, respectively. The experimental results show that using the MEQ method to standardize datasets can significantly improve the classification accuracy of neural networks. The Grad-CAM visual analysis reveals that the convolutional neural network exhibits a higher degree of attention towards the leaf surface features and utilizes more comprehensive feature regions during recognition of the leaf samples processed by MEQ method. In addition, the proposed MEQ + EC-ResNet50 method also achieved the best classification results among all the compared methods. This experiment provides a widely applicable sample standardization method for leaf recognition research, which can avoid the problem of sample deformation caused by compression processing and reduce the interference of redundant information in the image to the classification results to a certain degree. [ABSTRACT FROM AUTHOR]

The second mode is the main instability factor in hypersonic flow and shows the characteristics of acoustic disturbance. The stabilization effect of a porous surface on the second mode in a hypersonic boundary layer is studied according to the acoustic disturbance characteristics—including the flow characteristics of the porous surface, the effects of porous parameters, and the effect of mechanics—by direct numerical simulation. A rectangle is the basic structure of pores (slots) with a two-dimensional porous surface. The results show that the porosity (φ) and the number of pores (n) are the primary and secondary primary factors affecting the inhibition effect on the second mode by the porous surface. By influencing the amplitude and phase distribution of the pressure disturbance, the porous surface affects the wall normal transport between the mainstream and the porous surface in the near wall region, and it finally inhibits the growth of the second mode. [ABSTRACT FROM AUTHOR]

License plate recognition is currently used in various situations, such as parking lot vehicle management and the tracking of wanted vehicles. These applications require recognition from all possible camera angles. Therefore, we propose a method for license plate recognition in images captured from various camera angles. First, the license plate area is detected from the input image using the YOLOv5 object detection method. The subsequent process can be performed in two manners: by rotating the license plate to the front using projective transformation and trapezoidal correction, or by using graph matching. The first method performs Hough transforms or linear approximations as preprocessing, and then calculates the rectangle surrounding the license plate from the YOLOv5 output. After performing trapezoidal correction, the maximally stable extremal regions (MSER) are used to detect character candidates, and characters are recognized using 3D rotated character recognition. The second method performs character candidate detection and recognition without trapezoidal correction, followed by graph matching. These methods are versatile because they do not depend on the layout of license plates, which varies among countries and regions. Two types of datasets were used: a set of images containing Japanese license plates collected by ourselves, and a set of publicly available images containing Taiwanese license plates. Two recognition rates were evaluated: the license plate character recognition rate and license plate recognition rate in which all characters in one plate are recognized. The license plate character recognition rates using graph matching were 91.9% for the Japanese license plates and 89.3% for the Taiwanese license plates. The license plate recognition rates were 84.0% and 84.5%, respectively. [ABSTRACT FROM AUTHOR]

Uncertainty of data, the degree to which data are inaccurate, imprecise, untrusted, and undetermined, is inherent in many contemporary database applications, and numerous research endeavours have been devoted to efficiently answer skyline queries over uncertain data. The literature discussed two different methods that could be used to handle the data uncertainty in which objects having continuous range values. The first method employs a probability-based approach, while the second assumes that the uncertain values are represented by their median values. Nevertheless, neither of these methods seem to be suitable for the modern high-dimensional uncertain databases due to the following reasons. The first method requires an intensive probability calculations while the second is impractical. Therefore, this work introduces an index, non-probability framework named Constrained Skyline Query processing on Uncertain Data (CSQUiD) aiming at reducing the computational time in processing constrained skyline queries over uncertain high-dimensional data. Given a collection of objects with uncertain data, the CSQUiD framework constructs the minimum bounding rectangles (MBRs) by employing the X-tree indexing structure. Instead of scanning the whole collection of objects, only objects within the dominant MBRs are analyzed in determining the final skylines. In addition, CSQUiD makes use of the Fuzzification approach where the exact value of each continuous range value of those dominant MBRs' objects is identified. The proposed CSQUiD framework is validated using real and synthetic data sets through extensive experimentations. Based on the performance analysis conducted, by varying the sizes of the constrained query, the CSQUiD framework outperformed the most recent methods (CIS algorithm and SkyQUD-T framework) with an average improvement of 44.07% and 57.15% with regards to the number of pairwise comparisons, while the average improvement of CPU processing time over CIS and SkyQUD-T stood at 27.17% and 18.62%, respectively. [ABSTRACT FROM AUTHOR]

An inerter‐based dynamic vibration absorber (IDVA) is proposed and applied to suppress the vibration of a plate. The dynamic model of a thin rectangular plate attached with an IDVA is established and the frequency response function of the transverse displacement of the plate is derived through the classical vibration theory and the analysis in the s$s$ domain. In addition, the equation for frequency ratios of fixed points is obtained, and the condition for the existence of four fixed points is found by investigating the problem of solving quartic equations. Moreover, the extended fixed‐point method is employed to analytically obtain the optimal parameters of the IDVA attached to a plate, the expressions of the optimal damping ratio and other dimensionless qualities are presented. [ABSTRACT FROM AUTHOR]

Packing problems have been studied for a long time and have great applications in real-world scenarios. In recent times, with problems in the industrial world increasing in size, exact algorithms are often not a viable option and faster approaches are needed. We study Monte Carlo tree search, a random sampling algorithm that has gained great importance in literature in the last few years. We propose three approaches based on MCTS and its integration with metaheuristic algorithms or deep learning models to obtain approximated solutions to packing problems that are also interpretable by means of MCTS exploration and from which knowledge can be extracted. We focus on two-dimensional rectangle packing problems in our experimentation and use several well known benchmarks from literature to compare our solutions with existing approaches and offer a view on the potential uses for knowledge extraction from our method. We manage to match the quality of state-of-the-art methods, with improvements in time with respect to some of them and greater interpretability. [ABSTRACT FROM AUTHOR]

We show that the linear brittle Griffith energy on a thin rectangle Γ -converges after rescaling to the linear one-dimensional brittle Euler–Bernoulli beam energy. In contrast to the existing literature, we prove a corresponding sharp compactness result, namely a suitable weak convergence after subtraction of piecewise rigid motions with the number of jumps bounded by the energy. [ABSTRACT FROM AUTHOR]

In the dynamic field of cryptography, lightweight ciphers play a pivotal role in overcoming resource constraints in modern applications. This paper introduces a lightweight cryptographic algorithm by seamlessly merging the proven characteristics of the Feistel cipher CLEFIA with the advanced substitution-permutation network (SPN) framework of RECTANGLE for key generation. The algorithm incorporates a specially optimized feather S-box, balancing efficiency and security in both CLEFIA and RECTANGLE components. The RECTANGLE key generation, vital for the proposed lightweight technique, enhances overall cryptographic security and efficiency. Meticulous consideration of resource limitations maintains the algorithm's lightweight nature, making it well-suited for applications with restricted computational resources. To validate the efficacy of the lightweight algorithm, extensive evaluation on encrypted data is conducted using National Institute of Standards and Technology (NIST) tools, known for assessing cryptographic algorithm quality. Results reveal a high degree of randomness, indicative of robust resistance against cryptographic attacks. This manuscript provides a comprehensive examination of the lightweight algorithm, emphasizing key attributes, security enhancements, and successful integration of the optimized feather S-box. Rigorous testing, particularly NIST tool-based randomness analysis, offers empirical evidence of the algorithm's resilience against attacks, establishing its suitability for secure data encryption in resource-limited environments. [ABSTRACT FROM AUTHOR]

A formula for the Hausdorff dimension of typical limsup sets generated by randomly distributed isotropic rectangles in Heisenberg groups is derived in terms of directed singular value functions. [ABSTRACT FROM AUTHOR]

In this paper, we study the spectral properties of a class of degenerate third-order partial differential operators with variable coefficients presented in a rectangle. Conditions are found to ensure the existence and compactness of the inverse operator. A theorem on estimates of approximation numbers is proven. Here, we note that finding estimates of approximation numbers, as well as extremal subspaces, for a set of solutions to the equation is a task that is certainly important from both a theoretical and a practical point of view. The paper also obtained an upper bound for the eigenvalues. Note that, in this paper, estimates of eigenvalues and approximation numbers for the degenerate third-order partial differential operators are obtained for the first time. [ABSTRACT FROM AUTHOR]

Inequalities involving fractional operators have been an active area of research, which is crucial in establishing bounds, estimates, and stability conditions for solutions to fractional integrals. In this paper, we initially presented a new class that is known as coordinated left and right ℏ -pre-invex interval-valued mappings ( C · L · R - ℏ -pre-invex Ι · V - M ), as well classical convex and nonconvex are also obtained. This newly defined class enabled us to derive novel inequalities, such as Hermite–Hadamard and Pachpatte's type inequalities. Furthermore, the obtained results allowed us to recapture several special cases of known results for different parameter choices, which can be applications of the main results. Finally, we discussed the validity of the main outcomes. [ABSTRACT FROM AUTHOR]

A novel DIRECT-type algorithm is proposed to tackle box-constrained optimization problems. The algorithm incorporates bisection partitioning and diagonal sampling procedures, utilizing the Pareto approach to identify potential hyperrectangles. Furthermore, each hyperrectangle's size is determined based on the length of its longest side, in accordance with the infinity norm. This combination enhances convergence speed, facilitating the generation of a global optimal solution. The proposed algorithm's effectiveness is evaluated through numerical experiments, with detailed results demonstrating its efficacy. [ABSTRACT FROM AUTHOR]

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The investigation presented in this study delves into the analysis of Lie symmetries for the bistable Allen-Cahn (BAC) equation with a quartic potential, specifically applied to the biofilm model. By employing the Lie symmetry method, we have acquired the Lie infinitesimal generators for the considered model. Using a transformation method, the nonlinear partial differential equations (NPDEs) are converted into various nonlinear ordinary differential equations (NLODEs), providing the numerous closed-form solitary wave solutions. The obtained solutions manifest in various forms including dark, bright, kink, anti-kink, and periodic types using diverse strategies. To enhance the physical interpretation, the study presents 3D, 2D, and contour plots of the acquired solutions. Every graph's wave-like structure contains information about the structural behaviour of the bacteria that build biofilms on surfaces where rectangles have different densities. This analysis enhances comprehension of the complex dynamics present in areas like fluid dynamics, fiber optics, biology, ocean physics, coastal engineering, and nonlinear complex physical systems. [ABSTRACT FROM AUTHOR]

Yi literature is an indispensable part of Chinese ethnic minorities, and with the development of modern science and technology digitization, the traditional printed Yi language is gradually decreasing. However, with the development of deep learning, the work of digitizing Yi literature has made new progress. Firstly, this study self-made Yi literature annotation data set, data preprocessing, including character segmentation, etc., using CTPN network to detect Yi language, and then calculating the minimum circumscribed rectangle for each text, input to the residual network to identify Yi language. Thus, the Yi text can be formatted and output to better digitize the Yi language and protect the Yi language literature. [ABSTRACT FROM AUTHOR]

This paper approaches the role of Origami Art role in teaching Descriptive Geometry to students, future builders. Using the Art of Paper Folding in the application classes of Descriptive Geometry, we demonstrate that the acquiring of knowledge and skills in educational practice is complemented by the development of creativity, imagination, Aesthetics and team spirit. Origami turned into a source of inspiration for first-year students majoring in Civil, Industrial and Agricultural Construction to build a demountable assembly made of modular origami elements. The element is a modular triangle, made from a rectangle with a side ratio of 1:√2 known as the "Harmony Gate". The construction is original and executed on several levels, from white and colored A4 paper, whose density equals 80 g/m2. The number of origami elements used is calculated by a mathematical formula. [ABSTRACT FROM AUTHOR]

Considerable advances have been made recently in applying reinforcement learning (RL) to packing problems. However, most of these methods lack scalability and cannot be applied in dynamic environments. To address this research gap, we propose a hybrid algorithm called GraphPack to solve the strip packing problem. Two graph neural networks are designed to fully incorporate the problem's structure and enhance generalization performance. SkylineNet encodes the geometry of free space as the context feature, while PackNet, supporting the symmetry of rectangles, chooses the next rectangle to pack from the remaining rectangles at each timestep. We conduct fixed-scale, variable rectangle number and variable strip width experiments to test our method. The experimental results show that our method outperforms classical heuristic methods as well as previous RL methods. Notably, our method exhibits strong generalization ability and produces stable results even when the number of rectangles or strip width differs from that during training. [ABSTRACT FROM AUTHOR]

Aiming at the problem of cartoon piracy and plagiarism, this paper proposes a method of cartoon copyright recognition based on character personality actions. This method can be used to compare the original cartoon actions with the action characteristics of pirated or copied cartoons to identify whether there is piracy or plagiarism. Firstly, an image preprocessing scheme for character extraction is designed. GrabCut interactive image segmentation algorithm was used to obtain cartoon characters, and then binarization and morphological processing were performed on the results. Secondly, a feature extraction scheme based on character profile, moving character and character pose is designed. By extracting the perimeter and area of the character contour, the length-to-width ratio of the smallest rectangle and the inclination angle of the contour, the character contour features are obtained. The three-dimensional coordinates are established by the central point position of the cartoon character in the two-dimensional image and the change of the character's zoom in and out, and the character's motion angle characteristics are calculated. By skeletonizing a character to obtain the pose characteristics, and using deburring operation to remove redundant branches, then extract the skeleton joint angle information. Finally, feature fusion is performed on the extracted features. The experimental results show that the proposed method breaks the limitation of the conventional single feature based recognition, and can better extract the character features including contour feature, motion feature and pose feature through multi-feature based extraction, so as to protect the cartoon copyright. [ABSTRACT FROM AUTHOR]

In this paper, two-dimensional (2D) heat equations on disjoint rectangles are considered. The solutions are connected by interface Robin's-type internal conditions. The problem has external Dirichlet boundary conditions that, in the forward (direct) formulation, are given functions. In the inverse problem formulation, the Dirichlet conditions are unknown functions, and the aim is to be reconstructed upon integral observations. Well-posedness both for direct and inverse problems is established. Using the given 2D integrals of the unknown solution on each of the domains and the specific interface boundary conditions, we reduce the 2D inverse problem to a forward heat 1D one. The resulting 1D problem is solved using the explicit Saul'yev finite difference method. Numerical test examples are discussed to illustrate the efficiency of the approach. [ABSTRACT FROM AUTHOR]

This paper considers the problem of finding maximum volume (axis-aligned) inscribed boxes in a compact convex set, defined by a finite number of convex inequalities, and presents optimization and geometric approaches for solving them. Several optimization models are developed that can be easily generalized to find other inscribed geometric shapes such as triangles, rhombi, and squares. To find the largest volume axis-aligned inscribed rectangles in the higher dimensions, an interior-point method algorithm is presented and analyzed. For two-dimensional space, a parametrized optimization approach is developed to find the largest area (axis-aligned) inscribed rectangles in convex sets. The optimization approach provides a uniform framework for solving a wide variety of relevant problems. Finally, two computational geometric (1−ε) –approximation algorithms with sublinear running times are presented that improve the previous results. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms—Continuous. Funding: The author is grateful for the support of Northeastern University for this research. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0239) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0239). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

In the context of the unstructured and fast-changing construction environment, the adaptability of robots to human improvisation is crucial. However, existing construction robots are limited in understanding spatial goals communicated spontaneously in the workplace and require substantial human-user training. Incorporating deictic gestures into human–robot interfaces holds promise for enhancing the intuitive operation of construction robots and for on-site collaboration. However, applying deictic gestures in precision-demanding construction tasks presents challenges because in a large-scale work environment, humans have limited accuracy in pointing at objects at a distance. This study introduces LaserDex, a novel interface for distant spatial tasking based on a global-to-local identification approach, in which the human first guides the robot toward the general area of the task using a deictic gesture and then indicates the precise area by dynamically using a laser pointer. Our user study with 11 participants demonstrated that LaserDex can achieve an intersection over union (IoU) of 0.830 when outlining a rectangular drywall opening (compared with an IoU of 0.514 for the baseline, a handheld controller), and an 11.4-mm distance error of the center of the estimated rectangle compared with the center of the targeted rectangle. The findings of this study underscore the potential of LaserDex to seamlessly combine intuitive human–robot interaction with precise robot operations. [ABSTRACT FROM AUTHOR]

We report the results of large-scale molecular dynamics simulations of adsorption nanoparticles on solid surfaces. The particles were modeled as stiff aggregates of spherical segments. Three types of particles were studied: rods, rectangles, and triangles built of the same number of segments. We show how the particle shape affects the adsorption, the structure of the surface layer, and the degree of the removal of particles from the solvent. The systems with different segment–segment and segment–surface interactions and different concentrations of particles were investigated. The ordered structures formed in adsorption monolayers were also analyzed. The results are consistent with experimental observations. [ABSTRACT FROM AUTHOR]

Vibration of aircraft wings and the dynamic stress concentration at the clamped edge are important research topics due to concerns on the safety of aircrafts. To have a better understanding of the problem, the free and forced vibration response of a ribbed rectangular cantilever plate representing a section of an aircraft wing is investigated in this study. A new analytical solution is developed for the vibration analysis of rib stiffened cantilever plates using Mindlin plate and Timoshenko beam theories alongside the finite integral transform technique. The one- and two-dimensional integral transforms are applied to the governing equations of beams and plates, respectively, where the coupling force components at the interface between the base plate and the beam(s) can be automatically defined during the integral transform. Eventually, the partial differential equations are transformed into a system of linear algebraic equations in which its derivation is rigorous and easily implemented. Good agreements are found between the results of analytical solution, finite element analysis (FEA) and related literature. The solution is then employed to study the vibration suppression of cantilever plates and the shear force at the clamped edge. It is found that the insertion of a pair of orthogonal ribs in the plate can effectively reduce its vibration. An optimum orthogonal ribbing pattern is obtained using multi-objective particle swarm optimization (MOPSO) algorithm, taking into consideration both the vibration suppression of the plate and the maximum induced shear force at the corners of the clamped edge. [ABSTRACT FROM AUTHOR]

A logotype is a rectangular region defined by a set of characteristics, which come from the pixel information and region shape, that differ from those of the text. In this paper, a new method for automatic logo detection is proposed and tested using the public Tobacco800 database. Our method outputs a set of regions from an official document with a high probability to contain a logo using a new approach based on the variation of the feature rectangles method available in the literature. Candidate regions were computed using the longest increasing run algorithm over the document blank lines' indices. Those regions were further refined by using a feature-rectangle-expansion method with forward checking, where the rectangle expansion can occur in parallel in each region. Finally, a C4.5 decision tree was trained and tested against a set of 1291 official documents to evaluate its performance. The strategic combination of the three previous steps offers a precision and recall for logo detention of 98.9% and 89.9%, respectively, being also resistant to noise and low-quality documents. The method is also able to reduce the processing area of the document while maintaining a low percentage of false negatives. [ABSTRACT FROM AUTHOR]

We study the problem of perfect tiling in the plane and explore the possibility of tiling a rectangle using integral distinct squares. Assume a set of distinguishable squares (or equivalently a set of distinct natural numbers) is given, and one has to decide whether it can tile the plane or a rectangle or not. Previously, it has been proved that tiling the plane is not feasible using a set of odd numbers or an infinite sequence of natural numbers including exactly two odd numbers. The problem is open for different situations in which the number of odd numbers is arbitrary. In addition to providing a solution to this special case, we discuss some open problems to tile the plane and rectangles in this paper. [ABSTRACT FROM AUTHOR]

The article is devoted to the study of the genesis of the plans and ceilings of the Dunhuang cave sanctuaries. Based on the methods of graphic-and-analytical, defining features and system-structural analysis, the spread of types of plans and ceilings from dynasty to dynasty has been traced. With the help of a group of auxiliary methods of historical analysis, mathematical analysis and comparative analysis, a general picture of the development of the floating structure and constructive schemes of the Dunhuang sanctuaries from the Northern Liang period to the Yuan period was created. By counting the types of plans and ceilings in each period, a group of the most common types of plans was determined: with a combination of larger and smaller rectangles (where the smaller is the altar part of a square or rectangular shape), a plan in the form of a square with a protruding trapezoidal altar, an altar in outline close to a rectangle or trapezoids with rounded corners, a horizontally elongated plan rectangle, based on squares with protrusions. The most common type of ceilings is fu-dow-din with modifications. [ABSTRACT FROM AUTHOR]

This article examines the genesis of planning solutions and ceiling designs of Dunhuang cave shrines. Based on the methods of defining features, graphic-and-analytical and system-and-structural analysis, the spread of types of plans and ceilings from dynasty to dynasty has been traced. Using auxiliary methods of historical, mathematical, and comparative analysis, a general picture of the development of the planning structure and constructive schemes of Dunhuang shrines from the Northern Lian period to the Yuan period has been created. By counting the types of plans and ceilings in each period, a group of the most common types of plans was determined: with a combination of larger and smaller rectangles (where the smaller is the altar part of a square or rectangular shape), a plan in the form of a square with a protruding trapezoidal altar, an altar in outline close to a rectangle or trapezoids with rounded corners, a horizontally elongated plan rectangle, based on squares with protrusions. The most common type of ceiling is fu-dou-ding with modifications. [ABSTRACT FROM AUTHOR]

A dimension-reduced and linearly ordered (DRLOP) index structure for network-constrained moving objects is proposed to address the challenges posed by the rapid increase in the volume, diversity, and intensity of spatio-temporal data. The critical metadata rectangles are projected into reduced-dimensional phase points, and then arranged into a linear order structure to speed up retrieval through filtering and binary search. Using a dataset generated by a moving object generator from the underlying road network in Texas, our experimental results demonstrated the superior efficiency of the proposed index compared with the MON-Tree in terms of query and index creation. DRLOP exhibits the advantages of simple index structure, small storage space consumption, and high efficiency of spatio-temporal query operation, which is especially suitable for retrievals of large-scale historical trajectory data. [ABSTRACT FROM AUTHOR]

Based on the TRMM dataset, this paper compares the applicability of the improved MCE (minimum circumscribed ellipse), MBR (minimum bounding rectangle), and DIA (direct indexing area) methods for rain cell fitting. These three methods can reflect the geometric characteristics of clouds and apply geometric parameters to estimate the real dimensions of rain cells. The MCE method shows a major advantage in identifying the circumference of rain cells. The circumference of rain cells identified by MCE in most samples is smaller than that identified by DIA and MBR, and more similar to the observed rain cells. The area of rain cells identified by MBR is relatively robust. For rain cells composed of many pixels (N > 20), the overall performance is better than that of MCE, but the contribution of MBR to the best identification results, which have the shortest circumference and the smallest area, is less than that of MCE. The DIA method is best suited to small rain cells with a circumference of less than 100 km and an area of less than 120 km2, but the overall performance is mediocre. The MCE method tends to achieve the highest success at any angle, whereas there are fewer "best identification" results from DIA or MBR and more of the worst ones in the along-track direction and cross-track direction. Through this comprehensive comparison, we conclude that MCE can obtain the best fitting results with the shortest circumference and the smallest area on behalf of the high filling effect for all sizes of rain cells. [ABSTRACT FROM AUTHOR]

Over the last three decades, many attempts have been made to improve the DIRECT (DIviding RECTangles) algorithm's efficiency. Various novel ideas and extensions have been suggested. The main two steps of DIRECT-type algorithms are selecting and partitioning potentially optimal rectangles. However, the most efficient combination of these two steps is an area that has not been investigated so far. This paper presents a study covering an extensive examination of various candidate selection and partitioning techniques within the same DIRECT algorithmic framework. Twelve DIRECT-type algorithmic variations are compared on 800 randomly generated GKLS-type test problems and 96 box-constrained global optimization problems from DIRECTGOLib v1.1 with varying complexity. Based on these studies, we have identified the most efficient selection and partitioning combinations leading to new, more efficient, DIRECT-type algorithms. All these algorithms are included in the latest version of DIRECTGO v1.1.0 and are publicly available. [ABSTRACT FROM AUTHOR]

During the process of establishing the analytical quaternion ship domain model, the impact of ship traffic conditions and navigator state was not taken into consideration. However, the significance of these factors in the ship domain cannot be ignored. To create a more realistic representation of changes in the ship domain in real navigation environments, this study further considers the influence of ship encounter course, waterway traffic intensity, relative ship velocity, and the navigator state based on the quaternion ship domain model. As a result, a new dynamic quaternion ship domain model is proposed. To assess the changes in the size and shape of the ship domain under various navigation environments, ship domain scaling and shape transformation functions are introduced. Specifically, this study focuses on analyzing the ship traffic near the Lao Tie Shan Waterway, simulating the size and shape changes of the ship domain during the navigation process in this area. The findings indicate that the size of the ship domain dynamically adjusts to the traffic conditions. Additionally, when the navigator state is excellent, the ship domain takes on an irregular diamond shape with the smallest area, whereas when the navigator state is poor, the shape approximates a rectangle with the largest area. Furthermore, the dynamic quaternion ship domain model proposed in this study is compared to the ship domain models put forth by Goodwin, Davis, and co-authors. The results demonstrate that the dynamic quaternion ship domain model is more compatible and suitable for open waters compared to the static quaternion ship domain model. [ABSTRACT FROM AUTHOR]

Accurately estimating the pose of spacecraft is indispensable for space applications. However, such targets are generally non-cooperative, i.e., no markers are mounted on them, and they include no parts for operation. Therefore, the detection and measurement of a non-cooperative target is very challenging. Stereovision sensors are important solutions in the near field. In this paper, a rectangular natural feature recognition and pose measurement method for non-cooperative spacecraft is proposed. Solar panels of spacecraft were selected as detection objects, and their image features were captured via stereo vision. These rectangle features were then reconstructed in 3D Cartesian space through parallelogram fitting on the image planes of two cameras. The vertexes of rectangle features were detected and used to solve the pose of a non-cooperative target. An experimental system was built to validate the effectiveness of the algorithm. The experimental results show that the average position measurement error of the algorithm is about 10 mm and the average attitude measurement error is less than 1°. The results also show that the proposed method achieves high accuracy and efficiency. [ABSTRACT FROM AUTHOR]

This paper introduces novel enhancements to the most recent versions of DIRECT-type algorithms, especially when dealing with solutions located at the hyper-rectangle vertices. The BIRECT algorithm encounters difficulties in efficiently sampling points at the boundaries of the feasible region, leading to potential slowdowns in convergence. This issue is particularly pronounced when the optimal solution resides near the boundary. Our research explores diverse approaches, with a primary focus on incorporating a grouping strategy for hyper-rectangles of similar sizes. This categorization into different classes, constrained by a predefined threshold, aims to enhance computational efficiency, particularly involving a substantial number of hyper-rectangles of varying sizes. To further improve the new algorithm's efficiency, we implemented a mechanism to prevent oversampling and mitigate redundancy in sampling at shared vertices within descendant sub-regions. Comparisons with several DIRECT-type algorithms highlight the promising nature of the proposed algorithms as a global optimization solution. Statistical analyses, including Friedman and Wilcoxon tests, demonstrated the effectiveness of the improvements introduced in this new algorithm. [ABSTRACT FROM AUTHOR]

The buckling behavior of rectangular thin plates, which are supported at their four corner points with four edges free, is a matter of great concern in the field of plate and shell mechanics. Nevertheless, the complexities arising from the boundary conditions and governing equations present a formidable obstacle to the attainment of analytical solutions for these problems. Despite the availability of various approximate/numerical methods for addressing these challenges, the literature lacks accurate analytic solutions. In this study, we employ the symplectic superposition method, a recently developed method, to effectively analyze the buckling problem of rectangular thin plates analytically. These plates have four supported corners and four free edges. To achieve this, the problem is divided into two sub-problems and solve them separately using variable separation and symplectic eigen expansion, leading to analytical solutions. Finally, we obtain the resolution to the initial issue by superposing the sub-problems. The current solution method can be regarded as a logical, analytical, and rational approach as it begins with the basic governing equation and is systematically derived without assuming the forms of the solutions. To examine various aspect ratios and in-plane load ratios of rectangular thin plates, which are supported at their four corner points with four edges free, we provide numerical examples that demonstrate the buckling loads and typical buckling mode shapes. [ABSTRACT FROM AUTHOR]

We establish an estimate for arbitrary geometric maximal operators in the plane: we associate to any family B composed of rectangles and invariant by translations and central dilations a geometric quantity λB called its analytic split and satisfying log(λB) ≤p ∥MB∥pp for all 1 < p < ∞, where MB is the Hardy-Littlewood type maximal operator associated to the family B. [ABSTRACT FROM AUTHOR]

A generic rectangular partition is a partition of a rectangle into a finite number of rectangles provided that no four of them meet at a point. A graph H is called dual of a plane graph G if there is one-to-one correspondence between the vertices of G and the regions of H, and two vertices of G are adjacent if and only if the corresponding regions of H are adjacent. A plane graph is a rectangularly dualizable graph if its dual can be embedded as a rectangular partition. A rectangular dual R of a plane graph G is a partition of a rectangle into n-rectangles such that (i) no four rectangles of R meet at a point, (ii) rectangles in R are mapped to vertices of G, and (iii) two rectangles in R share a common boundary segment if and only if the corresponding vertices are adjacent in G. In this paper, we derive a necessary and sufficient for a rectangularly dualizable graph G to admit a unique rectangular dual upto combinatorial equivalence. Further we show that G always admits a slicible as well as an area-universal rectangular dual. [ABSTRACT FROM AUTHOR]

In this paper, for the first time are presented the full selection of finds of antler composite combs with a single row of teeth from Olbia Pontica. All of them belong to the Cherniakhiv culture and are related to the time of the last settlement of the territory of the ancient city. From a typological point of view, all of them can be divided into two groups: combs with semicircular or trapezoidal handle and, slightly older than them, comb handles of a complex shape, which is based on a rectangle with a semicircular middle part. [ABSTRACT FROM AUTHOR]

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This article examines the genesis of planning solutions and ceiling designs of Dunhuang cave shrines. Based on the methods of defining features, graphic-and-analytical and system-andstructural analysis, the spread of types of plans and ceilings from dynasty to dynasty has been traced. Using auxiliary methods of historical, mathematical, and comparative analysis, a general picture of the development of the planning structure and constructive schemes of Dunhuang shrines from the Northern Lian period to the Yuan period has been created. By counting the types of plans and ceilings in each period, a group of the most common types of plans was determined: with a combination of larger and smaller rectangles (where the smaller is the altar part of a square or rectangular shape), a plan in the form of a square with a protruding trapezoidal altar, an altar in outline close to a rectangle or trapezoids with rounded corners, a horizontally elongated plan rectangle, based on squares with protrusions. The most common type of ceiling is fu-dou-ding with modifications. [ABSTRACT FROM AUTHOR]