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Legendre-Weighted Residual Methods for System of Fractional Order Differential Equations

Journal of applied mathematics and Physics 2024年第9期12卷 3163-3184页

作者： Umme Ruman Md. Shafiqul Islam Department of Computer Science & Engineering Green University of Bangladesh Dhaka Bangladesh Department of Applied Mathematics University of Dhaka Dhaka Bangladesh

The numerical approach for finding the solution of fractional order systems of boundary value problems (BPVs) is derived in this paper. The implementation of the weighted residuals such as Galerkin, Least Square, and Collocation methods are included for solving fractional order differential equations, which is broadened to acquire the approximate solutions of fractional order systems with differentiable polynomials, namely Legendre polynomials, as basis functions. The algorithm of the residual formulations of matrix form can be coded efficiently. The interpretation of Caputo fractional derivatives is employed here. We have demonstrated these methods numerically through a few examples of linear and nonlinear BVPs. The results in absolute errors show that the present method efficiently finds the numerical solutions of fractional order systems of differential equations.

关键词： Fractional Differential Equations System of Fractional Order BVPs Weighted Residual Methods Modified Legendre Polynomials

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Enhancing Timely Graduations: An Explainable AI Approach to Predict Academic Risks in South African Students

Enhancing Timely Graduations: An Explainable AI Approach to ...

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2023 IEEE International Conference on Electrical, computer and Energy Technologies, ICECET 2023

作者： Bokgoshi, Lenny Sixhaxa, Khanyisile Jadhav, Ashwini Nyamane, Seipati Ajoodha, Ritesh School of Computer Science and Applied Mathematics University of Witwatersrand Johannesburg South Africa University of Witwatersrand Science Teaching and Learning Unit Faculty of Science Johannesburg South Africa Sol Plaatje University Department of Computer Science and Information Technology Kimberley South Africa

ISBN: (纸本)9798350327816

With rising dropout rates and extended degree completion times in South African institutions, there's a pressing need to better understand and address the hurdles faced by students during their academic journey. This research harnesses the power of explainable AI to predict and classify students based on their likelihood of not completing their degrees on time. Utilizing synthetic data generated via a Bayesian network, we used predictive models that categorize students into four distinct risk profiles. This clarity in prediction not only illuminates the underlying causes of academic delays but also empowers faculty, advisors, and student support services with actionable insights. The goal of this research is to facilitate timely interventions, tailored support, and seamless transitions for students transferring between universities, ensuring more students can realize their academic aspirations within expected time frames. © 2023 IEEE.

关键词： academic performance at-risk students classification models Machine learning student attrition

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Constructive Alignment in Software Engineering Education

Constructive Alignment in Software Engineering Education

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Conference on Software Engineering Education & Training (CSEE&T)

作者： Axel Böttcher Department of Computer Science and Mathematics HM University of Applied Sciences München

ISBN: (数字)9798350378979

ISBN: (纸本)9798350378986

The principle of constructive alignment requires that learning objectives, exam objectives and learning methods should be aligned with each other. This talk focuses on the alignment of learning objectives and exams for modern educational settings in software-related courses. As the use of LLM-based tools such as github-copilot or chatGPT has become an integral part of software technology, knowledge about LLM-based tools and their responsible use will also be addressed. For our courses on software-related topics we as instructors need to formulate learning objectives at different levels of granularity: from module descriptions down to fine-grained objectives for a single lecture or learning nugget. The definition of competence-oriented learning objectives at all levels of granularity is discussed, based on Anderson and Krathwohl's revision of Bloom's six-level taxonomy. For the assessment process, it is necessary to find appropriate forms of examinations that are constructively aligned with the learning objectives. Assessing programming skills requires forms other than just pen-and-paper exams. Suggestions for hands-on lab exams are discussed as well as tasks that can be used.

关键词： Learning systems Education Chatbots Software programming profession Software engineering

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Analysis of Nonlinear Processes in the P-I-N Diodes Plasma by the Perturbation Theory Methods 13

Analysis of Nonlinear Processes in the P-I-N Diodes Plasma b...

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13th International Conference on Advanced computer Information Technologies, ACIT 2023

作者： Bomba, Andrii Moroz, Igor National University of Water and Environmental Engineering Department of Computer Science and Applied Mathematics Rivne Ukraine Rivne State University of Humanities Department of Information Technologies and Modeling Rivne Ukraine

A nonlinear singularly perturbed boundary value problem of the electron-hole plasma state predicting in the p-i-n diodes active region is considered. The search for solutions to the problem is carried out by the asymptotic method of boundary corrections. The decomposition of the original problem is carried out, the results are analyzed, and the existence of its asymptotic solutions is proved. © 2023 IEEE.

关键词： Plasma diodes

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Implementation and performance analysis of sequential versus parallelized algorithms for solving multivariate equations of CFD Poisson processes 27

Implementation and performance analysis of sequential versus...

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27th International Conference on System Theory, Control and Computing, ICSTCC 2023

作者： Sbîrnă, Sebastian Sbîrnă, Liana-Simona DTU Compute Department Institute of Applied Mathematics and Computer Science Technical University of Denmark Kongens Lyngby Denmark Department of Chemistry Faculty of Sciences University of Craiova Craiova Romania

ISBN: (纸本)9798350337983

The present work aims to find computationally-efficient models for solving discretized partial differential equations. To accomplish that, we implement and compare the performance of a series of algorithmic models, both sequential and parallelized (using OpenMP libraries), which may be used for solving convergence problems. For demonstrating the results upon a real-world case scenario, the work introduces a CFD (computational fluid dynamics) Poisson process, which is numerically discretized and approximated using Jacobi and Gauss-Seidel algorithms. Performance of the parallelized implementations will be measured against a baseline, and the consequent model optimizations will be described. Finally, the scalability of the parallelized algorithms will be compared together, with regards to CPU thread count and memory handling. The results show that, compared with a sequential version, a parallelized Jacobi algorithm shows strong performance and scalability when introducing more threads. At the same time, a parallelized version of the Gauss-Seidel algorithm did not present substantial increases in performance over its sequential counterpart. © 2023 IEEE.

关键词： Computational fluid dynamics

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Education 4.0: Considering the Development of Teachers’ Psychological Dispositions Towards the Use of ICT with Kindergarten Children 14th

Education 4.0: Considering the Development of Teachers’ P...

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14th International Conference on Methodologies and Intelligent Systems for Technology Enhanced Learning, mis4TEL 2024

作者： Peretti, Sara Caruso, Federica Pino, Maria Chiara Di Mascio, Tania Centre of Excellence DEWS University of L’Aquila L’Aquila Italy Department of Information Engineering Computer Science and Mathematics University of L’Aquila L’Aquila Italy Department of Biotechnological and Applied Clinical Sciences L’Aquila Italy

ISBN: (纸本)9783031855603

Since 2020, the COVID-19 pandemic has forced teachers to rapidly adopt Information and Communication Technology (ICT) tools for distance learning, transforming education into an all-digital environment. This shift posed significant challenges, especially for kindergarten teachers accustomed to traditional, face-to-face methods. These changes will have long-term impacts on education, influencing teachers’ attitudes and beliefs, which take time to stabilize and evaluate. The present paper addresses this by posing the question: In 2024, four years after the COVID-19 pandemic, what attitudes have kindergarten teachers developed towards ICT integration in the classroom? For this purpose, the standardized "Intrapersonal Technology Integration Scale" was chosen to assess the beliefs of Italian kindergarten teachers. The study includes 49 kindergarten teachers, all women. Data analysis showed that they have a strong interest in using ICT, indicating a need for ongoing support and training initiatives. However, teachers did not report feeling self-efficacy in using ICT with children in the classroom. This finding is crucial as it can influence their expectations and motivation towards integrating these technologies into daily teaching activities. In conclusion, this study highlights the critical importance of teachers’ attitudes in shaping future learning environments within the Education 4.0 era and provides suggestions to maximize ICT integration starting from early education to better meet the needs of future citizens. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Teaching

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Discovering and exploring cases of educational source code plagiarism with Dolos

arXiv

引用

arXiv 2024年

作者： Maertens, Rien Van Neyghem, Maarten Geldhof, Maxiem Van Petegem, Charlotte Strijbol, Niko Dawyndt, Peter Mesuere, Bart Department of Applied Mathematics Computer Science and Statistics Ghent University Ghent Belgium

Source code plagiarism is a significant issue in educational practice, and educators need user-friendly tools to cope with such academic dishonesty. This article introduces the latest version of Dolos, a state-of-the-art ecosystem of tools for detecting and preventing plagiarism in educational source code. In this new version, the primary focus has been on enhancing the user experience. Educators can now run the entire plagiarism detection pipeline from a new web app in their browser, eliminating the need for any installation or configuration. Completely redesigned analytics dashboards provide an instant assessment of whether a collection of source files contains suspected cases of plagiarism and how widespread plagiarism is within the collection. The dashboards support hierarchically structured navigation to facilitate zooming in and out of suspect cases. Clusters are an essential new component of the dashboard design, reflecting the observation that plagiarism can occur among larger groups of students. To meet various user needs, the Dolos software stack for source code plagiarism detections now includes a web interface, a JSON application programming interface (API), a command line interface (CLI), a JavaScript library and a preconfigured Docker container. Clear documentation and a free-to-use instance of the web app can be found at https://***. The source code is also available on GitHub. © 2024, CC BY.

关键词： Application programming interfaces (API)

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Pose Estimation of Spacecraft Using Dual Transformers and Efficient Bayesian Hyperparameter Optimization

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International Journal of Advanced computer science and Applications 2025年第4期16卷 629-644页

作者： Raja, N. Kannaiya Ramesh, Janjhyam Venkata Naga El-Ebiary, Yousef A. Baker Muniyandy, Elangovan Reddy, N. Konda Kumar, Vanipenta Ravi Devarasetty, Prasad School of Computing Science and Engineering VIT Bhopal University Madhya Pradesh Bhopal466114 India Department of CSE Graphic Era Hill University Dehradun248002 India Department of CSE Graphic Era Deemed To Be University Uttarakhand Dehradun248002 India Faculty of Informatics and Computing UniSZA University Malaysia Department of Biosciences Saveetha School of Engineering Saveetha Institute of Medical and Technical Sciences Chennai602 105 India Applied Science Research Center Applied Science Private University Amman Jordan Department of Engineering Mathematics K L University Greenfields Guntur Dist Andhra Pradesh Vaddeswaram522302 India Department of Mathematics Annamacharya University New Boyanapalli Rajampet India Department of Computer Science and Engineering DVR & Dr HS MIC College of Technology Andhra Pradesh Kanchikacherla India

Spacecraft pose estimation is an essential contribution to facilitating central space mission activities like autonomous navigation, rendezvous, docking, and on-orbit servicing. Nonetheless, methods like Convolutional Neural Networks (CNNs), Simultaneous Localization and Mapping (SLAM), and Particle Filtering suffer significant drawbacks when implemented in space. Such techniques tend to have high computational complexity, low domain generalization capacity for varied or unknown conditions (domain generalization problem), and accuracy loss with noise from the space environment causes such as fluctuating lighting, sensor limitations, and background interference. In order to overcome these challenges, this study suggests a new solution through the combination of a Dual-Channel Transformer Network with Bayesian Optimization methods. The innovation is at the center with the utilization of EfficientNet, augmented with squeeze-and-excitation attention modules, to extract feature-rich representations without sacrificing computational efficiency. The dual-channel architecture dissects satellite pose estimation into two dedicated streams—translational data prediction and orientation estimation via quaternion-based activation functions for rotational precision. Activation maps are transformed into transformer-compatible sequences via 1×1 convolutions, allowing successful learning in the transformer's encoder-decoder system. To maximize model performance, Bayesian Optimization with Gaussian Process Regression and the Upper Confidence Bound (UCB) acquisition function makes the optimal hyperparameter selection with fewer queries, conserving time and resources. This entire framework, used here in Python and verified with the SLAB Satellite Pose Estimation Challenge dataset, had an outstanding Mean IOU of 0.9610, reflecting higher accuracy compared to standard models. In total, this research sets a new standard for spacecraft pose estimation, by marrying the versatility of deep le

关键词： Convolutional neural networks

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Multilevel Skeletonization Using Local Separators

arXiv

引用

arXiv 2023年

作者： Bærentzen, J. Andreas Christensen, Rasmus Emil Gæde, Emil Toftegaard Rotenberg, Eva Department of Applied Mathematics and Computer Science DTU Denmark

In this paper we give a new, efficient algorithm for computing curve skeletons, based on local separators. Our efficiency stems from a multilevel approach, where we solve small problems across levels of detail and combine these in order to quickly obtain a skeleton. We do this in a highly modular fashion, ensuring complete flexibility in adapting the algorithm for specific types of input or for otherwise targeting specific applications. Separator based skeletonization was first proposed by Bærentzen and Rotenberg in [ACM Tran. Graphics'21], showing high quality output at the cost of running times which become prohibitive for large inputs. Our new approach retains the high quality output, and applicability to any spatially embedded graph, while being orders of magnitude faster for all practical purposes. We test our skeletonization algorithm for efficiency and quality in practice, comparing it to local separator skeletonization on the University of Groningen Skeletonization Benchmark [Telea'16]. Copyright © 2023, The Authors. All rights reserved.

关键词： Separators

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A Shoe Shopping System based on Convolutional Neural Network Image Recognition 5

A Shoe Shopping System based on Convolutional Neural Network...

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5th IEEE Eurasia Conference on IOT, Communication and Engineering, ECICE 2023

作者： Chang, Chin-Chih Wei, Chi-Hung Chen, Chen-Sheng Chen, Jian-An Yeh, Shih-Hsien Hsiao, Sean Chung Hua University Department of Computer Science and Information Engineering Hsinchu Taiwan Chung Hua University Program in Engineering Science Hsinchu Taiwan Chang Gung University Department of Computer Science and Information Engineering Taoyuan Taiwan Chung Hua University Program in Applied Foreign Language and Smart Commerce Hsinchu Taiwan

ISBN: (纸本)9798350314694

In this article, we present an innovative approach to enhance the online shoe shopping experience. The convolutional neural network (CNN) image recognition technology was used to enhance shoe classification and recommendations. By training the CNN model on an extensive dataset, unique shoe features and styles were learned. Integrated into a user-friendly online platform, the system offers real-time image recognition, allowing users to snap a photo of a desired shoe for instant identification, including brand, price, and availability details. Moreover, the CNN-based recommendation engine provides personalized suggestions based on style, color, and customer preferences, enriching the shopping experience. Evaluation results confirmed the system's feasibility, and user feedback highlighted its effectiveness in simplifying the shopping process and enhancing satisfaction. This innovative system presents a significant leap in merging AI and e-commerce and shows the potential of image recognition to transform online marketplaces, benefiting consumers, offering valuable insights for retailers, and ultimately reshaping the future of online shoe shopping. © 2023 IEEE.

关键词： convolutional neural network (CNN) deep learning image recognition recommender system

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