International Journal of Computing Science and Mathematics (13 papers in press)

Regular Issues

• The Application of Mathematical Analysis in Solving Nonlinear Phenomena in Fluid Mechanics  
  by You Li, Gui Li, Xuan Leng 
  Abstract: In order to assist mathematical analysis in solving nonlinear problems, reduce the computational cost and accelerate the solution process, the study explores the common mathematical methods for nonlinear solution; followed by the introduction of an optimized arithmetic algorithm for improved precision. Experimental results showed the hybrid algorithm designed in the study achieves a recall of 0.893, corresponding to a precision of 0.9, and a ROC region of 0.913, which is better than other algorithms in the same experimental environment. The algorithm demonstrated fast convergence in loss curve, high computational efficiency, taking only 9.07s. The average absolute value error converges to 0.07, and the root mean square error converges to 0.532. The method takes the optimal values of Generation Distance, Hyper volume, Spacing and Spread indexes in the process of solving nonlinear equations. This study effectively combines the mathematical analytical method and computer technology to provide a new idea and method for the mathematical analysis of nonlinear phenomena, which enriches the research content of nonlinear science.
  Keywords: Mathematical analysis method; Solitons; Abnormal wave; Nonlinear phenomena; Arithmetic optimization algorithm; Nonlinear equation.
  DOI: 10.1504/IJCSM.2025.10072716
   
  
• Machine Learning Approach for Classification of Phishing Attacks with Particle Swarm Optimisation Technique  
  by Prakash Pathak, Akhilesh Shrivas 
  Abstract: Phishing is an online scam where an attacker creates fake websites or emails to collect secret information from the internet or email users. The main contribution of research work is to develop a robust and computationally efficient hybrid model using machine learning based classification techniques with Particle Swarm Optimisation (PSO) to facilitate the classification of phishing attacks. The study constructs a machine learning-based ensemble model empowered by particle swarm optimisation for effective phishing attack classification. A novel ensemble model is developed, amalgamating Support Vector Machine(SVM), Logistic Regression(LR), and Decision Trees (DT) through a voting scheme ensemble technique. Additionally, PSO feature selection techniques are applied to phishing datasets to streamline feature sets. Comparative analysis with existing classifiers and ensemble models, employing reduced feature sets, demonstrates that our proposed model achieves a remarkable 99.08% accuracy with 27 features. Consequently, our recommended model offers expedited computational time for phishing attack classification.
  Keywords: phishing attacks; machine learning; classification; ensemble model; particle swarm optimization (PSO); 10-fold cross-validation.
  DOI: 10.1504/IJCSM.2025.10072717
   
  
• Optimisation of Algebraic Event Structure using Trace Equivalence based on Gr  
  by Weidong Tang, Weiwen Ge, Meiling Liu 
  Abstract: The process of data flow exchange in complex concurrent systems is often redundant and uncertain, leading to resource inefficiency and "state explosion". Equivalence relationships identify processes of the same behaviour, remove redundancy to simplify system verification and analysis, and effectively mitigate the "state explosion" problem. In Glabbeek's equivalence spectrum, trace equivalence (systems that produce the same sequence of actions are considered equivalent) and bi-simulation equivalence (requiring bidirectional behaviour correspondence between systems) are widely accepted. In this paper, we discuss the method of trace equivalence judgment on the polynomial algebraic event structure, propose the judgment of polynomial event equivalence, and use Grobner basis for calculation. Grobner basis, as an algebraic tool to determine the equality of polynomial systems, has the advantages of accuracy and efficiency, and provides a strict mathematical basis for the equivalence determination. Finally, a practical case is presented to show the optimisation effect of this method.
  Keywords: state explosion; trace equivalence; bisimulation equivalence; polynomial algebraic event structure; Gröbner basis.
  DOI: 10.1504/IJCSM.2025.10072982
   
  
• Linear Polynomial Algebra Migration System for Program Equivalence and Approximate Optimisation  
  by Weiwen Ge, Weidong Tang, Meiling Liu 
  Abstract: Program structure simplification constitutes a critical research domain in software engineering. With increasing system complexity, traditional simplification approaches remain predominantly confined to deterministic equivalence verification, lacking substantial investigation into approximate equivalence, error quantification, and control mechanisms. This paper develops a novel concept of common algebraic set bi-simulation equivalence by integrating Wu's characteristic series within a linear polynomial algebraic migration system framework. To address non-deterministic equivalence problems, this work introduces novel least squares solution metrics and singular value thresholding control mechanisms. These innovations establish an approximate bi-simulation equivalence theory that quantifies program behaviour differences while maintaining controllable error bounds. Consequently, approximately equivalent systems can replace the original complex systems, thereby simplifying program architecture. Experimental validation using a concurrent communication program demonstrates the efficacy of our proposed methodology in program optimisation.
  Keywords: Wu's characteristic series; linear polynomial algebra migration system; least squares solution; singular value thresholding; approximate bisimulation equivalence.
  DOI: 10.1504/IJCSM.2025.10073023
   
  
• News Recommendation Optimisation Path based on Improved GAT Algorithm  
  by Kunlong Yang, Minjing Wang 
  Abstract: To solve the problem of recommending massive news information mentioned above, a semantic representation model based on news text information fusion is proposed. The innovation lies in the use of capsule networks and Transformers for feature extraction and fusion, while proposing a perceptual model for graphic attention networks to enhance the capture of relevant information. In the accuracy recall analysis, the research model achieved an accuracy of 0.962 in sports news scenarios, which is superior to the other two models. In the comparison of recommendation accuracy, the model showed the best performance with recommendation accuracy of 0.915 and 0.961 on the Yahoo and MIND datasets, respectively. It can be seen that the research model meets the requirements of news and user development. The research content will provide important technical references for the effective dissemination of news and the improvement of recommendation techniques.
  Keywords: GAT; News recommendations; Capsule network; Transformer; Perception model.
  DOI: 10.1504/IJCSM.2025.10073091
   
  
• REC-YoloPose: a Lightweight Model for Enhancing Human Pose Estimation Performance in Multi-Scale and Complex Scenes  
  by Weize Chen, Chenyang Shi, Donglin Zhu, Changjun Zhou 
  Abstract: Human pose estimation is a computer vision research area, but it faces challenges in balancing model complexity and accuracy. To address this problem, this study proposes an improved model named REC-YoloPose, based on Yolov8sPose. Firstly, the contextual guidance (CG block) is employed to replace traditional convolution, and efficient local attention (ELA) is introduced into the backbone, enhancing the models feature extraction capability. Secondly, inspired by Repvit, the original Cross-Stage Partial fusion module (C2f) is improved, striking a balance between model parameters and recognition accuracy. Experimental results demonstrate that the proposed model achieves AP50 scores of 93.1% and 87.0% on Leeds sports pose (LSP) dataset and common objects in context (COCO) dataset respectively. Compared with other mainstream pose estimation algorithms, this model reduces computational parameters by 16.9% to 80.5% while maintaining high detection accuracy. Finally, REC-YoloPose is applied to human posture classification, showcasing its practical value in real-world tasks.
  Keywords: Human pose estimation;ELA;RepC2f;Context Guided Block;SMLP.
  DOI: 10.1504/IJCSM.2025.10073104
   
  
• Research on High-Precision Insulator Classification Using an Improved Hybrid Attention Mechanism in the Context of Un-Manned Aerial Vehicles  
  by Qi Cao, Song Yang, Hao Lin Li, Xin Qiang Wu, Ming Liu, Zhijun Qin, Feng Wang 
  Abstract: With the increasing reliance on unmanned aerial vehicles (UAVs) for power transmission line inspections, there has been a growing need for more sophisticated image classification methods to analyse the vast number of images captured during these operations. Traditional methods often struggle with the accurate identification of critical components, such as insulators, which are essential for maintaining the integrity of power lines. In this study, we present an improved vision transformer (ViT) model specifically designed to classify insulator conditions into three categories: damaged, flashover, and normal. To facilitate this, we constructed a dedicated dataset featuring these three conditions of insulators. Our enhanced ViT model demonstrates superior performance compared to conventional deep learning models, offering higher accuracy and robustness in identifying insulator conditions. The experimental results highlight the models effectiveness, with significant improvements in classification accuracy, making it a valuable tool for enhancing the reliability and safety of power transmission line inspections.
  Keywords: Power Transmission Line Inspection; Insulator Condition Classification; Unmanned Aerial Vehicle (UAV); Deep Learning; Im-age Classification.
  DOI: 10.1504/IJCSM.2025.10073609
   
  
• Sports Pose Estimation based on Adaptive Complementary Data Fusion Algorithm  
  by Jinchi Yu, Xiaomin Gu 
  Abstract: Accurately estimating athlete pose is of great significance for improving training quality and preventing sports injuries. The current vision-based estimation methods are susceptible to environmental lighting interference, while inertial sensors suffer from cumulative errors. To optimize the accuracy and stability of athlete pose estimation, a motion pose estimation method based on adaptive complementary data fusion algorithm is proposed. A motion sensor data fusion algorithm based on Kalman filtering algorithm is designed to improve its accuracy. When the number of samples was 300, the pitch angle was 9After UKF filtering, the maximum Roll angle was 20 and the minimum Roll angle was 85. The Yaw angle error was reduced, with a maximum Yaw angle of 80 and a minimum Yaw angle of 100. The experimental data proves the effectiveness and superiority of the proposed algorithm.
  Keywords: Kalman filtering algorithm; pose estimation; athletic sports; adaptive algorithm; sensor data fusion.
  DOI: 10.1504/IJCSM.2025.10073775
   
  
• Construction of Practical Teaching Data Classification Model Based on ROF-SSA-LGBM and Its Application in Physical Education Teaching and Management  
  by Xinjiao Zhang 
  Abstract: Under the background of informatization, To better assist the management of practical teaching, a data classification model based on ROF-ISSA-LGBM is proposed. Firstly, rotation forest algorithm (ROF) is used to screen importance features of practical teaching data set. Then, improved sparrow search algorithm (ISSA) is adopted to optimise hyperparameters of Lightweight Gradient Boosting Machine (LGBM). Finally, ISSA-LGBM is used as the classifier and applied to the classification of practical teaching datasets. The results reveal that on Haberman and Iris datasets with smaller sample sizes, average accuracy, macro average, and micro average of the constructed model reach 80.96%, 95.38% and 95.44%, respectively, its performance is better than that of commonly used classification models, which means the constructed model has high classification accuracy. Therefore, the constructed model can be used for deep mining of potential information in the data set of physical education practice teaching data, and shows high classification accuracy.
  Keywords: rotating forest algorithm; physical education practice teaching; sparrow search algorithm; lightweight gradient boosting machine; combination model; macro average.
  DOI: 10.1504/IJCSM.2025.10073777
   
  
• Research on Optical Music Recognition based on Improved CRNN Network and its Application in Piano Teaching  
  by Jianing Wang 
  Abstract: The traditional optical music recognition method has the problem of low recognition accuracy and efficiency. An optical music recognition method based on convolutional recurrent neural network (CRNN) is proposed. Firstly, residual depthwise separable convolution is introduced into convolutional layer of CRNN network. Then, after convolution operation, squeeze-excitation module in attention mechanism is introduced. Finally, parameters of cross entropy function are adjusted at transcription layer. The results reveal that error rate of note recognition and sequence recognition in optical music is 1.26% and 7.31% respectively, which is significantly lower than those of CRNN model and SE-BiLSTM model. This model can improve training speed, and its recognition time is only 6.44s, which is 7.89s and 14.65s lower than that of other two methods, respectively. It shows that recognition efficiency of the proposed model is significantly improved, which can meet the actual teaching needs of piano classrooms.
  Keywords: CRNN network; optical music recognition; SE module; note feature extraction; piano teaching.
  DOI: 10.1504/IJCSM.2025.10073780
   
  
• A Survey of Machine Learning Approaches to Solving NP-hard Problems  
  by Li Shuyun, Ma Huan, Wang Zhihui, Zhang Xinchang 
  Abstract: NP-hard problems have attracted considerable attention due to their computational complexity and widespread practical applications. Traditional algorithms often struggle to handle large-scale instances of these problems due to their exponential time complexity. In recent years, machine learning (ML) methodshaveemergedaseffectivetoolsforsolvingNP-hardproblems,leveraging their powerful pattern recognition capabilities, adaptability, and generalisation abilities. However, different types of NP-hard problems are suited to different ML methods, and there are significant differences in solving capabilities between ML methods and traditional algorithms. This paper systematically reviews the latest advancements in applying ML to the traveling salesman problem (TSP), bin packing problem (BPP), and Virtual Network Embedding Problem. It also compares the strengths and weaknesses of ML methods versus traditional algorithms in terms of algorithmic performance, computational complexity, and applicability. Finally, the paper analyses the key challenges faced by ML methods in solving NP-hard problems and outlines future research directions, aiming to provide a reference for subsequent research.
  Keywords: NP-hard problems; machine learning; combinatorial optimization; deep reinforcement learning.
  DOI: 10.1504/IJCSM.2025.10073807
   
  
• Application Research On Variation Analysis Model for Exchange Rate Based Lasso-BP  
  by Wei Xue, Peng Liu, Zhuan Xin, Jing Chen 
  Abstract: Aiming at the problem of low accuracy of exchange rate forecast in foreign exchange market data analysis, an exchange rate prediction model based on Lasso-IGWO-BP was proposed. Firstly, Lasso regression model is used as feature screening method of exchange rate data. Then, BP neural network is taken as the basic prediction method, and IGWO algorithm is introduced to optimize the parameters of BP neural network. Finally, the extracted features are input into the IGWO-BP model for classification prediction, thus achieving better exchange rate prediction effect. Experimental results show that compared with the Attention-LSTM, PSO-ELM and FWA-GA prediction models, the Lasso-IGWO-BP model constructed in this paper has significantly improved prediction accuracy. Therefore, exchange rate prediction model constructed can provide more reliable exchange rate data for foreign exchange market, which has certain feasibility.
  Keywords: exchange rate analysis; data prediction; Lasso; BP neural network; GWO.
  DOI: 10.1504/IJCSM.2025.10073841
   
  
• Bidirectional Optimised Auction Model for Carbon Emission Rights with Incremental Reserve Price Strategy  
  by Zenghua Du, Hongren Yan, Sheng Yang, ZhiGuo Hu 
  Abstract: Carbon emission trading has become a widely adopted and effective strategy for mitigating greenhouse gas emissions. Among the various trading mechanisms, auction-based models have demonstrated superior efficiency in allocating emission allowances. However, existing studies primarily emphasise revenue maximisation, often overlooking the critical role of the sellers reserve price. This paper argues that incorporating a reserve price not only safeguards the sellers interests but also incentivises buyers to engage in energy conservation and emission reduction efforts. We propose a novel multi-stage auction model that jointly optimises the revenues of both sellers and buyers across multiple bidding rounds, incorporating seller-defined, non-decreasing reserve price functions. Theoretical analysis confirms the correctness and convergence of the model, and illustrative examples are provided to demonstrate its practical applicability. Compared to existing approaches, our model offers a more realistic and balanced framework by explicitly considering the impact of dynamic reserve pricing on the benefits of both parties, thereby aligning more closely with the operational needs of carbon auction markets.
  Keywords: Auction Model; Carbon Emission Right; Reserve Price; Maximum Revenue.
  DOI: 10.1504/IJCSM.2025.10073855