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The importance of computational thinking (CT) as a 21st-century skill for future generations has been a key consideration in the reforms of many national and regional educational systems. Much attention has been paid to integrating CT into the traditional subject classrooms. This paper describes a scoping review of learning tools for integrating CT and mathematics in current empirical studies published from 2015 to 2021. The review showed that most of the studies implemented CT-intensive Math-connected integration. Five major types of CT tools had been identified, i.e., digital tangibles, apps and games, programming languages, formative or summative assessments, and other technological tools. In many instances, the tools also provide functions of assessment of CT skills. The most assessed CT competencies were including algorithms and algorithmic thinking, abstraction, testing and debugging, loops, and sequences. Geometry and Measurement was the most assessed mathematics topic. Our scoping review is beneficial in the investigation of the literature on CT and mathematics education, as well as guides those who are interested in developing curriculum, programs, or assessments that involve the integration of CT and mathematics.

Describes origami, the oriental art of paper folding as an activity to teach upper elementary students concepts and skills in geometry involving polygons, angles, measurement, symmetry, and congruence. (PK)

The article examines astronomers' use of an obscure paper astronomical instrument when calculating syzygies in the 15th and 16th centuries. Syzygies are computations made by astronomers in order to establish the straight-line positioning of the Earth, Sun, and Moon, and are therefore useful when studying eclipses. The author describes the design and construction of this instrument. He then goes on to discuss the use of the instrument's graphical design and computation algorithm. The author then presents astronomical computations developed by his own use of the instrument.

Abstract: In a recent paper (Computer Aided Geometric Design 23 (3), 243–260), Yang presented a novel kind of nonlinear and geometry driven subdivision scheme for curve interpolation. The author declared that this scheme was shape preserving when all free parameters were explicitly selected by some specific rules. In this note, we demonstrate that the author (a) ignored the consistency of the definition to straight edges, and also (b) did not give a perfect scheme and proof for the shape preserving subdivision. [Copyright &y& Elsevier]

A deep learning-based Visual Inertial SLAM technique is proposed in this paper to ensure accurate autonomous localization of mobile robots in environments with dynamic objects. Addressing the limitations of real-time performance in deep learning algorithms and the poor robustness of pure visual geometry algorithms, this paper presents a deep learning-based Visual Inertial SLAM technique. Firstly, a non-blocking model is designed to extract semantic information from images. Then, a motion probability hierarchy model is proposed to obtain prior motion probabilities of feature points. For image frames without semantic information, a motion probability propagation model is designed to determine the prior motion probabilities of feature points. Furthermore, considering that the output of inertial measurements is unaffected by dynamic objects, this paper integrates inertial measurement information to improve the estimation accuracy of feature point motion probabilities. An adaptive threshold-based motion probability estimation method is proposed, and finally, the positioning accuracy is enhanced by eliminating feature points with excessively high motion probabilities. Experimental results demonstrate that the proposed algorithm achieves accurate localization in dynamic environments while maintaining real-time performance. [ABSTRACT FROM AUTHOR]

In the model (m:n), to improve the autonomous collaborative interception capability for air vehicle, a new autonomous cross-collaborative interception algorithm based on GTSMC (Global Terminal Sliding Mode Control) and real-time virtual geometry is proposed in this paper. Firstly, the conception of an autonomous cross-collaboration is defined and the multi-air vehicle for the multi- object interception problem is formulated. Then, this paper presents the dynamic situation assessment function, which considers the real-time flight status and cooperative status of the air vehicle during the interception of the object. At the same time, this paper states the condition of whether the air vehicle is in a cooperative state and proves it. After completing the dynamic situation assessment, and considering the dynamic of the air vehicles, a new controller is designed by using GTSMC and the idea of backstepping method. Simultaneously, this paper gives a stability analysis of the closed-loop system by using Lyapunov theory. Finally, to demonstrate the effectiveness of the proposed algorithm, several simulation cases which consider different interception scenarios are given. The simulation results show that the new collaborative interception algorithm can provide better autonomous cross-collaborative interception capability and higher accuracy. [ABSTRACT FROM AUTHOR]

Argues that the vast majority of adults have no use for the specialized mathematics taught in high schools and required by colleges--algebra, geometry, or calculus. Suggests that colleges should accept applicants who have studied percents, formulas, logic, computer commands, and basic statistics. (TE)

This paper presents an efficient algorithm for voxelizing the surface of triangular meshes in a single compute pass. The algorithm uses parallel equidistant lines to traverse the interior of triangles, minimizing costly memory operations and avoiding visiting the same voxels multiple times. By detecting and visiting only the voxels in each line operation, the proposed method achieves better performance results. This method incorporates a gap detection step, targeting areas where scanline‐based voxelization methods might fail. By selectively addressing these gaps, our method attains superior performance outcomes. Additionally, the algorithm is written entirely in a single compute GLSL shader, which makes it highly portable and vendor independent. Its simplicity also makes it easy to adapt and extend for various applications. The paper compares the results of this algorithm with other modern methods, comprehensibly comparing the time performance and resources used. Additionally, we introduce a novel metric, the 'Slope Consistency Value', which quantifies triangle orientation's impact on voxelization accuracy for scanline‐based approaches. The results show that the proposed solution outperforms existing, modern ones and obtains better results, especially in densely populated scenes with homogeneous triangle sizes and at higher resolutions. [ABSTRACT FROM AUTHOR]

CAD-CAE software companies have introduced numerous tools aimed at facilitating topology optimization through Finite Element Simulation, thereby enhancing accessibility for designers via user-friendly interfaces. However, the imposition of intricate constraint conditions or additional restrictions during calculations may introduce instability into the resultant outcomes. In this paper, an algorithm for updating the design variables called Adaptive Variable Design is proposed to keep the final design space volume of the optimized part consistently under the target value while giving the main algorithm multiple chances to update the optimization parameters and search for a valid design. This algorithm aims to produce results that are more conducive to manufacturability and potentially more straightforward in interpretation. A comparison between several commercial software packages and the proposed algorithm, implemented in MATLAB R2023a, is carried out to prove the robustness of the latter. By simulating identical parts under similar conditions, we seek to generate comparable results and underscore the advantages stemming from the adoption and comprehension of the proposed topology optimization methodology. Our findings reveal that the integrated enhancements within MATLAB pertaining to the topology optimization process yield favourable outcomes with respect to discretization and the manufacturability of the resultant geometries. Furthermore, we assert that the methodology evaluated within MATLAB holds promise for potential integration into commercial packages, thereby enhancing the efficiency of topology optimization processes. [ABSTRACT FROM AUTHOR]

Computational design and shape grammars hold a growing appeal in the architectural curricula. This paper aims to assess shape grammars as a visual teaching method that integrates manual exploration based on "learning by doing" in early education curricula without digital software. As a primary outcome of a visual design course at the British university in Egypt, four self-structured pavilions are fabricated by first-year architecture students. Experimentation occurs through a process of visual computing which develops a deeper understanding of material qualities. A comparison of design parameters is conducted through hands-on experiments that include design principles, unit transformations, connection types, assembly process, and functional aspects. The paper examines the skills that students acquired during the course. This study concludes that by applying shape grammars in design studios, students are adequately prepared at the foundational level for their transition towards learning computational design. [ABSTRACT FROM AUTHOR]

This paper devises an algorithm for finding the minimal set of axial lines that can represent a geometry of building and urban layout in two dimensions. Although axial lines are useful to analyze spatial configuration in the Space Syntax, existing methods for selecting axial lines seldom address the optimality of their solutions. The proposed algorithm uses linear programming to obtain a minimal set of axial lines. To minimize the number of axial lines that represent the entire geometry of building and urban layout, a linear programming problem is established in which a set of axial lines represents the entire geometry. The axial lines must have at least one intersection with every extension line of the wall edges to the sides of the reflex angles. If a solution to this linear programming problem exists, it will be guaranteed to be an optimum. However, some solutions of this general linear programming problem may include isolated lines, which are undesirable for an axial line analysis. To avoid isolated axial lines, this paper states a new formulation by adding a group of constraints to the original formulation. By examining the modified linear programming problem in various two-dimensional building maps and spatial layouts, this paper demonstrates that the proposed algorithm can guarantee a minimum set of axial lines to represent a two-dimensional geometry. This modified linear programming problem prevents isolated axial lines in the process of axial line reduction. [ABSTRACT FROM AUTHOR]

Purpose: This study aims to propose and evaluate the progress in the basic-pixel (a strategy to generate continuous trajectories that fill out the entire surface) algorithm towards performance gain. The objective is also to investigate the operational efficiency and effectiveness of an enhanced version compared with conventional strategies. Design/methodology/approach: For the first objective, the proposed methodology is to apply the improvements proposed in the basic-pixel strategy, test it on three demonstrative parts and statistically evaluate the performance using the distance trajectory criterion. For the second objective, the enhanced-pixel strategy is compared with conventional strategies in terms of trajectory distance, build time and the number of arcs starts and stops (operational efficiency) and targeting the nominal geometry of a part (operational effectiveness). Findings: The results showed that the improvements proposed to the basic-pixel strategy could generate continuous trajectories with shorter distances and comparable building times (operational efficiency). Regarding operational effectiveness, the parts built by the enhanced-pixel strategy presented lower dimensional deviation than the other strategies studied. Therefore, the enhanced-pixel strategy appears to be a good candidate for building more complex printable parts and delivering operational efficiency and effectiveness. Originality/value: This paper presents an evolution of the basic-pixel strategy (a space-filling strategy) with the introduction of new elements in the algorithm and proves the improvement of the strategy's performance with this. An interesting comparison is also presented in terms of operational efficiency and effectiveness between the enhanced-pixel strategy and conventional strategies. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamics of charged particles under a strong magnetic field in toroidal axi-symmetric geometry. Using modulated Fourier expansions of the exact and numerical solutions, the long-term drift motion of the exact solution in toroidal geometry is derived, and the error analysis of the large-stepsize modified Boris algorithm over long time is provided. Numerical experiments are conducted to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Visual SLAM algorithms can obtain a large amount of texture information from the environment and usually perform very well in static scenes, but there are a large number of irregular dynamic points when running in dynamic scenes, which can lead to increased error in SLAM feature point matching and loss of tracking localization. To address this challenge this paper proposes a SLAM system (YVG‐SLAM) that adapts to dynamic scenes. YVG‐SLAM is an improvement on the ORB‐SLAM3 algorithm, integrating the view geometry algorithm and the current powerful YOLOv5 algorithm, while proposing a dynamic feature removal strategy without a priori assumptions to reduce the influence of dynamic targets. In this paper, we first lighten the YOLOv5 algorithm, then process the image frame to get the bounding box, then use the view geometry algorithm to determine the dynamic feature points on the image frame, and finally remove the moving objects in the image frame according to the dynamic feature recognition strategy proposed in this paper. The performance of the algorithm is tested on the TUM RGB‐D and BONN RGB‐D datasets. The experimental results show that the robustness of the proposed algorithm on most video sequences is better than the existing SLAM algorithms dealing with dynamic scenes such as Detect‐SLAM and DynaSLAM, and the RMSE index of the absolute trajectory error measured on high‐speed dynamic video sequences can be significantly reduced by more than 93% compared to ORB‐SLAM3. © 2024 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

Identifying dynamic objects in dynamic scenes remains a challenge for traditional simultaneous localization and mapping (SLAM) algorithms. Additionally, these algorithms are not able to adequately inpaint the culling regions that result from excluding dynamic objects. In light of these challenges, this study proposes a novel visual SLAM (vSLAM) algorithm based on improved Vision Transformer semantic segmentation in dynamic scenes (VTD-SLAM), which leverages an improved Vision Transformer semantic segmentation technique to address these limitations. Specifically, VTD-SLAM utilizes a residual dual-pyramid backbone network to extract dynamic object region features and a multiclass feature transformer segmentation module to enhance the pixel weight of potential dynamic objects and to improve global semantic information for precise identification of potential dynamic objects. The method of multi-view geometry is applied to judge and remove the dynamic objects. Meanwhile, according to static information in the adjacent frames, the optimal nearest-neighbor pixel-matching method is applied to restore the static background, where the feature points are extracted for pose estimation. With validation in the public dataset TUM (The Entrepreneurial University Dataset) and real scenarios, the experimental results show that the root-mean-square error of the algorithm is reduced by 17.1 % compared with dynamic SLAM (DynaSLAM), which shows better map composition capability. [ABSTRACT FROM AUTHOR]

Very recently, the BERT graph convolutional network (BertGCN) model has attracted much attention from researchers due to its good text classification performance. However, just using original documents in the corpus to construct the topology of graphs for GCN-based models may lose some effective information. In this paper, we focus on sentiment classification, an important branch of text classification, and propose the multistream BERT graph convolutional network (MS-BertGCN) for sentiment classification based on cross-document learning. In the proposed method, we first combine the documents in the training set based on within-class similarity. Then, each heterogeneous graph is constructed using a group of combinations of documents for the single-stream BertGCN model. Finally, we construct multistream-BertGCN (MS-BertGCN) based on multiple heterogeneous graphs constructed from different groups of combined documents. The experimental results show that our MS-BertGCN model outperforms state-of-the-art methods on sentiment classification tasks. [ABSTRACT FROM AUTHOR]

Purpose: In furthering numerical optimization techniques for the light-weighting of components, it is paramount to produce algorithms that closely mimic the physical behavior of the specific manufacturing method under which they are created. The continual development in topology optimization (TO) has reduced the difference in the optimized geometry from what can be physically realized. As the reinterpretation stage inevitably deviates from the optimal geometry, each progression in the optimization code that renders the final solution more realistic is beneficial. Despite the efficacy of material extrusion (MEx) in producing complex geometries, select manufacturing constraints are still required. Thus, the purpose of this paper is to develop a TO code which demonstrates the incorporation of MEx specific manufacturing constraints into a numerical optimization algorithm. Design/methodology/approach: A support index is derived for each element of the finite element mesh that is used to penalize elements, which are insufficiently supported, discouraging their existence. The support index captures the self-supporting angle and maximum allowable bridging distance for a given MEx component. The incorporation of the support index into a TO code is used to demonstrate the efficacy of the method on multiple academic examples. Findings: The case studies presented demonstrate the methodology is successful in generating a resulting topology that is self-supporting given the manufacturing parameters specified in the code. Comparative to a general TO problem formulation, the optimal material distribution results in a minimally penalized design on a compliance normalization metric while fully adhering to the MEx specific parameters. The methodology, thus, proves useful in generating an infill geometry is fully enclosed regions, where support material extraction is not a possibility. Originality/value: The work presented is the first paper to produce a novel methodology that incorporates the manufacturing-specific constraint of bridging distance for MEx into TO code. The results generated allow for the creation of printed components with hollow inclusions that do not require any additional support material beyond the intended structure. Given the advancement, the numerical optimization technique has progressed to a more realistic representation of the physical manufacturing method. [ABSTRACT FROM AUTHOR]

This article deals with the issue of the automatic setting of machines on their base. The focus is on machines with a selfsupporting frame, freestanding, on more than three supports. The alignment uses the previously presented method of precise and repeatable machine placement on the foundation. As a result, the machine has the necessary parameters in terms of its geometry, and at the same time a defined weight distribution on the individual building elements is guaranteed. The paper presents a new method for automatic machine alignment using so-called "smart feet". Due to this, the process of machine alignment is clearly defined, repeatable and does not depend on the experience of the personnel performing the alignment. The presented algorithm makes it possible to automate the entire machine-setting process. The article includes the presentation of a machine placement on its base, which is used for testing and verification of the functionality of the alignment algorithm. [ABSTRACT FROM AUTHOR]

Acoustic emission (AE) source localization is a fundamental element of rock fracture damage imaging. To improve the efficiency and accuracy of AE source localization, this paper proposes a joint method comprising a three-dimensional (3D) AE source localization simplex method and grid search scanning. Using the concept of the geometry of simplexes, tetrahedral iterations were first conducted to narrow down the suspected source region. This is followed by a process of meshing the region and node searching to scan for optimal solutions, until the source location is determined. The resulting algorithm was tested using the artificial excitation source localization and uniaxial compression tests, after which the localization results were compared with the simplex and exhaustive methods. The results revealed that the localization obtained using the proposed method is more stable and can be effectively avoided compared with the simplex localization method. Furthermore, compared with the global scanning method, the proposed method is more efficient, with an average time of 10%–20% of the global scanning localization algorithm. Thus, the proposed algorithm is of great significance for laboratory research focused on locating rupture damages sustained by large-sized rock masses or test blocks. [ABSTRACT FROM AUTHOR]

This paper describes the application of a machine learning (ML) algorithm using a convolution neural network, first developed in Boyer et al. ["Classification and prediction of detachment in DIII-D using neural networks trained on C III imaging," Nucl. Fusion (submitted) (2024)], to detect divertor detachment in DIII-D. Detachment detection is based on images from tangentially viewing upper and lower filtered divertor cameras that measure CIII emission at 465 nm. Separate ML models are developed for lower single null and upper single null configurations with mostly closed divertor shapes. Due to the viewing angle and divertor geometry, camera images of the upper divertor show a stark contrast in CIII emission between attached and detached conditions and the model identified detachment with 100% accuracy in the test dataset. For the lower divertor images, the contrast between attached and detached conditions is lower and the model identifies detachment with 96% accuracy. This ML model will be applied to the image data after each shot to provide a rapid assessment of divertor detachment to aid operation of DIII-D with the potential extension to other devices in the future. [ABSTRACT FROM AUTHOR]

The necessity for compact and relatively low cost x-ray sources with monochromaticity, continuous tunability of x-ray energy, high spatial coherence, straightforward polarization control, and high brightness has led to the rapid development of Thomson scattering x-ray sources. To meet the requirement of in-situ monochromatic computed tomography (CT) for large-scale and/or high-attenuation materials based on this type of x-ray source, there is an increasing demand for effective algorithms to correct the energy-angle correlation. In this paper, we take advantage of the parametrization of the x-ray attenuation coefficient to resolve this problem. The linear attenuation coefficient of a material can be decomposed into a linear combination of the energy-dependent photoelectric and Compton cross-sections in the keV energy regime without K-edge discontinuities, and the line integrals of the decomposition coefficients of the above two parts can be determined by performing two spectrally different measurements. After that, the line integral of the linear attenuation coefficient of an imaging object at a certain interested energy can be derived through the above parametrization formula, and monochromatic CT can be reconstructed at this energy using traditional reconstruction methods, e.g., filtered back projection or algebraic reconstruction technique. Not only can monochromatic CT be realized, but also the distributions of the effective atomic number and electron density of the imaging object can be retrieved at the expense of dual-energy CT scan. Simulation results validate our proposal and will be shown in this paper. Our results will further expand the scope of application for Thomson scattering x-ray sources. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel rigid-body motion segmentation algorithm that uses randomized voting to assign high scores to correctly estimated models and low scores to wrongly estimated models. This algorithm is based on an epipolar geometrical representation of the camera motion, and computes scores using the distance between the feature point and the corresponding epipolar line. These scores are accumulated and utilized for motion segmentation. To evaluate the efficacy of our algorithm, we conduct a series of experiments using the Hopkins 155 data set and the UdG data set, which are representative test sets for rigid motion segmentation. Among several state-of-the-art data sets, our algorithm achieves the most accurate motion segmentation results and, in the presence of measurement noise, achieves comparable results to the other algorithms. Finally, we analyze why our motion segmentation algorithm works using probabilistic and theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper introduces the use of graph theory for the study of the work of Candilis–Josic–Woods. Α short introduction to the architects' main strategies as members of Team Χ and CIAM (Congrès Internationaux d'Architecture Moderne) critics is given. Geometry and computational design methods for city planning and design are briefly discussed. Definitions of the minimum spanning tree, the shortest walk tree and the Steiner tree are then developed. The research projects these methods onto the main principles of Candilis–Josic–Woods' planning and urban design approach to reinforce their strategic concepts. Distance-related and proximity-based ideas and their importance are sought in the literature related to Candilis–Josic–Woods' body of work. Algorithmic based examples approximating a Euclidean Steiner tree are shown and discussed in the context of Candilis–Josic–Woods' syntax. This paper argues that the generation of additional points through the use of a Euclidean Steiner tree algorithmic process is of importance in the work of Candilis–Josic–Woods as it allows for a systematic but emerging creation of hubs that can be activated as space on the one hand, and facilitate pedestrian circulation on the other. The project seeks to demonstrate the relevance of the triplet's design methods to today's complex networks of urban environments. [ABSTRACT FROM AUTHOR]

Over the past three decades, describing the reality surrounding us using the language of complex networks has become very useful and therefore popular. One of the most important features, especially of real networks, is their complexity, which often manifests itself in a fractal or even multifractal structure. As a generalization of fractal analysis, the multifractal analysis of complex networks is a useful tool for identifying and quantitatively describing the spatial hierarchy of both theoretical and numerical fractal patterns. Nowadays, there are many methods of multifractal analysis. However, all these methods take into account only the fact of connection between nodes (and eventually the weight of edges) and do not take into account the real positions (coordinates) of nodes in space. However, intuition suggests that the geometry of network nodes' position should have a significant impact on the true fractal structure. Many networks identified in nature (e.g., air connection networks, energy networks, social networks, mountain ridge networks, networks of neurones in the brain, and street networks) have their own often unique and characteristic geometry, which is not taken into account in the identification process of multifractality in commonly used methods. In this paper, we propose a multifractal network analysis method that takes into account both connections between nodes and the location coordinates of nodes (network geometry). We show the results for different geometrical variants of the same network and reveal that this method, contrary to the commonly used method, is sensitive to changes in network geometry. We also carry out tests for synthetic as well as real-world networks. [ABSTRACT FROM AUTHOR]

In this paper, we study anabelian geometry of curves over algebraically closed fields of positive characteristic. Let X•=(X,DX)$X^{\bullet }=(X, D_{X})$ be a pointed stable curve over an algebraically closed field of characteristic p>0$p>0$ and ΠX•$\Pi _{X^{\bullet }}$ the admissible fundamental group of X•$X^{\bullet }$. We prove that there exists a group‐theoretical algorithm, whose input datum is the admissible fundamental group ΠX•$\Pi _{X^{\bullet }}$, and whose output data are the topological and the combinatorial structures associated with X•$X^{\bullet }$. This result can be regarded as a mono‐anabelian version of the combinatorial Grothendieck conjecture in the positive characteristic. Moreover, by applying this result, we construct clutching maps for moduli spaces of admissible fundamental groups. [ABSTRACT FROM AUTHOR]