Journal Description
Mathematics
Mathematics
is a peer-reviewed, open access journal which provides an advanced forum for studies related to mathematics, and is published semimonthly online by MDPI. The European Society for Fuzzy Logic and Technology (EUSFLAT) and International Society for the Study of Information (IS4SI) are affiliated with Mathematics and their members receive a discount on article processing charges.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, SCIE (Web of Science), RePEc, and other databases.
- Journal Rank: JCR - Q1 (Mathematics) / CiteScore - Q1 (General Mathematics)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 16.9 days after submission; acceptance to publication is undertaken in 2.6 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Sections: published in 13 topical sections.
- Companion journals for Mathematics include: Foundations, AppliedMath, Analytics, International Journal of Topology, Geometry and Logics.
Impact Factor:
2.4 (2022);
5-Year Impact Factor:
2.3 (2022)
Latest Articles
Music Genre Classification Based on VMD-IWOA-XGBOOST
Mathematics 2024, 12(10), 1549; https://doi.org/10.3390/math12101549 (registering DOI) - 15 May 2024
Abstract
Music genre classification is significant to users and digital platforms. To enhance the classification accuracy, this study proposes a hybrid model based on VMD-IWOA-XGBOOST for music genre classification. First, the audio signals are transformed into numerical or symbolic data, and the crucial features
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Music genre classification is significant to users and digital platforms. To enhance the classification accuracy, this study proposes a hybrid model based on VMD-IWOA-XGBOOST for music genre classification. First, the audio signals are transformed into numerical or symbolic data, and the crucial features are selected using the maximal information coefficient (MIC) method. Second, an improved whale optimization algorithm (IWOA) is proposed for parameter optimization. Third, the inner patterns of these selected features are extracted by IWOA-optimized variational mode decomposition (VMD). Lastly, all features are put into the IWOA-optimized extreme gradient boosting (XGBOOST) classifier. To verify the effectiveness of the proposed model, two open music datasets are used, i.e., GTZAN and Bangla. The experimental results illustrate that the proposed hybrid model achieves better performance than the other models in terms of five evaluation criteria.
Full article
Open AccessArticle
Beyond Event-Centric Narratives: Advancing Arabic Story Generation with Large Language Models and Beam Search
by
Arwa Alhussain and Aqil M. Azmi
Mathematics 2024, 12(10), 1548; https://doi.org/10.3390/math12101548 - 15 May 2024
Abstract
In the domain of automated story generation, the intricacies of the Arabic language pose distinct challenges. This study introduces a novel methodology that moves away from conventional event-driven narrative frameworks, emphasizing the restructuring of narrative constructs through sophisticated language models. Utilizing mBERT, our
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In the domain of automated story generation, the intricacies of the Arabic language pose distinct challenges. This study introduces a novel methodology that moves away from conventional event-driven narrative frameworks, emphasizing the restructuring of narrative constructs through sophisticated language models. Utilizing mBERT, our approach begins by extracting key story entities. Subsequently, XLM-RoBERTa and a BERT-based linguistic evaluation model are employed to direct beam search algorithms in the replacement of these entities. Further refinement is achieved through Low-Rank Adaptation (LoRA), which fine-tunes the extensive 3 billion-parameter BLOOMZ model specifically for generating Arabic narratives. Our methodology underwent thorough testing and validation, involving individual assessments of each submodel. The ROCStories dataset provided the training ground for our story entity extractor and new entity generator, and was also used in the fine-tuning of the BLOOMZ model. Additionally, the Arabic ComVE dataset was employed to train our commonsense evaluation model. Our extensive analyses yield crucial insights into the efficacy of our approach. The story entity extractor demonstrated robust performance with an F-score of 96.62%. Our commonsense evaluator reported an accuracy of 84.3%, surpassing the previous best by 3.1%. The innovative beam search strategy effectively produced entities that were linguistically and semantically superior to those generated using baseline models. Further subjective evaluations affirm our methodology’s capability to generate high-quality Arabic stories characterized by linguistic fluency and logical coherence.
Full article
(This article belongs to the Section Mathematics and Computer Science)
Open AccessArticle
Key Selection Factors Influencing Animation Films from the Perspective of the Audience
by
Wendong Jiang
Mathematics 2024, 12(10), 1547; https://doi.org/10.3390/math12101547 - 15 May 2024
Abstract
The animation industry is an important part of China’s cultural and creative industries. In fact, it is the leading cultural and creative industry in China. However, there is insufficient research on the audience’s views in China’s animation industry, which has become an important
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The animation industry is an important part of China’s cultural and creative industries. In fact, it is the leading cultural and creative industry in China. However, there is insufficient research on the audience’s views in China’s animation industry, which has become an important research gap. Thus, an integrated approach of FAHP and GRA is proposed in this study, to analyse and evaluate the key selection factors for the Chinese animation industry from the perspective of a Chinese audience. In this research, in both FAHP and GRA models, factors such as visual appealing character, interesting performance of character animation, and easy-to-understand storyline are prioritised conditions for the selection of Chinese animation from the perspective of Chinese audiences. The main contribution of this research is to underscore the value of the hybrid MCDM model to aid Chinese animation companies in aligning their productions with audience expectations and making informed decisions. Finally, this study offers a systematic and objective model for Chinese animation selection, providing practical insights that can be applied in the industry and can serve as a valuable reference for future research in similar domains.
Full article
(This article belongs to the Special Issue Selected Papers from the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM))
Open AccessArticle
A Dynamic Programming Approach to the Collision Avoidance of Autonomous Ships
by
Raphael Zaccone
Mathematics 2024, 12(10), 1546; https://doi.org/10.3390/math12101546 - 15 May 2024
Abstract
The advancement of autonomous capabilities in maritime navigation has gained significant attention, with a trajectory moving from decision support systems to full autonomy. This push towards autonomy has led to extensive research focusing on collision avoidance, a critical aspect of safe navigation. Among
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The advancement of autonomous capabilities in maritime navigation has gained significant attention, with a trajectory moving from decision support systems to full autonomy. This push towards autonomy has led to extensive research focusing on collision avoidance, a critical aspect of safe navigation. Among the various possible approaches, dynamic programming is a promising tool for optimizing collision avoidance maneuvers. This paper presents a DP formulation for the collision avoidance of autonomous vessels. We set up the problem framework, formulate it as a multi-stage decision process, define cost functions and constraints focusing on the actual requirements a marine maneuver must comply with, and propose a solution algorithm leveraging parallel computing. Additionally, we present a greedy approximation to reduce algorithm complexity. We put the proposed algorithms to the test in realistic navigation scenarios and also develop an extensive test on a large set of randomly generated scenarios, comparing them with the RRT* algorithm using performance metrics proposed in the literature. The results show the potential benefits of an autonomous navigation or decision support framework.
Full article
(This article belongs to the Special Issue Dynamic Programming)
Open AccessArticle
On Some Multipliers Related to Discrete Fractional Integrals
by
Jinhua Cheng
Mathematics 2024, 12(10), 1545; https://doi.org/10.3390/math12101545 - 15 May 2024
Abstract
This paper explores the properties of multipliers associated with discrete analogues of fractional integrals, revealing intriguing connections with Dirichlet characters, Euler’s identity, and Dedekind zeta functions of quadratic imaginary fields. Employing Fourier transform techniques, the Hardy–Littlewood circle method, and a discrete analogue of
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This paper explores the properties of multipliers associated with discrete analogues of fractional integrals, revealing intriguing connections with Dirichlet characters, Euler’s identity, and Dedekind zeta functions of quadratic imaginary fields. Employing Fourier transform techniques, the Hardy–Littlewood circle method, and a discrete analogue of the Stein–Weiss inequality on product space through implication methods, we establish bounds for these operators. Our results contribute to a deeper understanding of the intricate relationship between number theory and harmonic analysis in discrete domains, offering insights into the convergence behavior of these operators.
Full article
(This article belongs to the Special Issue Fractional Calculus and Mathematical Applications, 2nd Edition)
Open AccessArticle
Blockchain-Based Unbalanced PSI with Public Verification and Financial Security
by
Zhanshan Wang and Xiaofeng Ma
Mathematics 2024, 12(10), 1544; https://doi.org/10.3390/math12101544 - 15 May 2024
Abstract
Private set intersection (PSI) enables two parties to determine the intersection of their respective datasets without revealing any information beyond the intersection itself. This paper particularly focuses on the scenario of unbalanced PSI, where the sizes of datasets possessed by the parties can
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Private set intersection (PSI) enables two parties to determine the intersection of their respective datasets without revealing any information beyond the intersection itself. This paper particularly focuses on the scenario of unbalanced PSI, where the sizes of datasets possessed by the parties can significantly differ. Current protocols for unbalanced PSI under the malicious security model exhibit low efficiency, rendering them impractical in real-world applications. By contrast, most efficient unbalanced PSI protocols fail to guarantee the correctness of the intersection against a malicious server and cannot even ensure the client’s privacy. The present study proposes a blockchain-based unbalanced PSI protocol with public verification and financial security that enables the client to detect malicious behavior from the server (if any) and then generate an irrefutable and publicly verifiable proof without compromising its secret. The proof can be verified through smart contracts, and some economic incentive and penalty measures are executed automatically to achieve financial security. Furthermore, we implement the proposed protocol, and experimental results demonstrate that our scheme exhibits low online communication complexity and computational overhead for the client. At the same time, the size of the generated proof and its verification complexity are both , enabling cost-effective validation on the blockchain.
Full article
(This article belongs to the Special Issue Applied Mathematics in Blockchain and Intelligent Systems)
Open AccessArticle
A Fluid Dynamic Approach to Model and Optimize Energy Flows in Networked Systems
by
Massimo de Falco, Luigi Rarità and Alfredo Vaccaro
Mathematics 2024, 12(10), 1543; https://doi.org/10.3390/math12101543 - 15 May 2024
Abstract
In this paper, attention is focused on the analysis and optimization of energy flows in networked systems via a fluid-dynamic approach. Considering the real case of an energy hub, the proposed model deals with conservation laws on arcs and linear programming problems at
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In this paper, attention is focused on the analysis and optimization of energy flows in networked systems via a fluid-dynamic approach. Considering the real case of an energy hub, the proposed model deals with conservation laws on arcs and linear programming problems at nodes. Optimization of the energy flows is accomplished by considering a cost functional, which estimates a term proportional to the kinetic energy of the overall system in consideration. As the real optimization issue deals with an integral formulation for which precise solutions have to be studied through variational methods, a decentralized approach is considered. First, the functional is optimized for a simple network having a unique node, with an incoming arc and two outgoing ones. The optimization deals with distribution coefficients, and explicit solutions are found. Then, global optimization is obtained via the local optimal parameters at the various nodes of the real system. The obtained results prove the correctness of the proposed approach and show the evident advantages of optimization procedures dealing with variational approaches.
Full article
(This article belongs to the Topic Mathematical Modeling)
Open AccessArticle
Deep Learning-Driven Interference Perceptual Multi-Modulation for Full-Duplex Systems
by
Taehyoung Kim and Gyuyeol Kong
Mathematics 2024, 12(10), 1542; https://doi.org/10.3390/math12101542 - 15 May 2024
Abstract
In this paper, a novel data transmission scheme, interference perceptual multi-modulation (IP-MM), is proposed for full-duplex (FD) systems. In order to unlink the conventional uplink (UL) data transmission using a single modulation and coding scheme (MCS) over the entire assigned UL bandwidth, IP-MM
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In this paper, a novel data transmission scheme, interference perceptual multi-modulation (IP-MM), is proposed for full-duplex (FD) systems. In order to unlink the conventional uplink (UL) data transmission using a single modulation and coding scheme (MCS) over the entire assigned UL bandwidth, IP-MM enables the transmission of UL data channels based on multiple MCS levels, where a different MCS level is applied to each subband of UL transmission. In IP-MM, a deep convolutional neural network is used for MCS-level prediction for each UL subband by estimating the potential residual self-interference (SI) according to the downlink (DL) resource allocation pattern. In addition, a subband-based UL transmission procedure is introduced from a specification point of view to enable IP-MM-based UL transmission. The benefits of IP-MM are verified using simulations, and it is observed that IP-MM achieves approximately 20% throughput gain compared to the conventional UL transmission scheme.
Full article
(This article belongs to the Topic Application of Deep Learning Method in 6G Communication Technology)
Open AccessArticle
Retinex Jointed Multiscale CLAHE Model for HDR Image Tone Compression
by
Yu-Joong Kim, Dong-Min Son and Sung-Hak Lee
Mathematics 2024, 12(10), 1541; https://doi.org/10.3390/math12101541 - 15 May 2024
Abstract
Tone-mapping algorithms aim to compress a wide dynamic range image into a narrower dynamic range image suitable for display on imaging devices. A representative tone-mapping algorithm, Retinex theory, reflects color constancy based on the human visual system and performs dynamic range compression. However,
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Tone-mapping algorithms aim to compress a wide dynamic range image into a narrower dynamic range image suitable for display on imaging devices. A representative tone-mapping algorithm, Retinex theory, reflects color constancy based on the human visual system and performs dynamic range compression. However, it may induce halo artifacts in some areas or degrade chroma and detail. Thus, this paper proposes a Retinex jointed multiscale contrast limited adaptive histogram equalization method. The proposed algorithm reduces localized halo artifacts and detail loss while maintaining the tone-compression effect via high-scale Retinex processing. A performance comparison of the experimental results between the proposed and existing methods confirms that the proposed method effectively reduces the existing problems and displays better image quality.
Full article
(This article belongs to the Special Issue New Advances and Applications in Image Processing and Computer Vision)
Open AccessArticle
Reliability and Residual Life of Cold Standby Systems
by
Longlong Liu, Xiaochuan Ai and Jun Wu
Mathematics 2024, 12(10), 1540; https://doi.org/10.3390/math12101540 - 15 May 2024
Abstract
In this study, we conduct a reliability characterisation study of cold standby systems. Utilising synthetic rectangular formulas and cold preparedness equivalent models for cold standby systems, we analyse the lifetimes of several typical configurations, including series, parallel, and k/n:m voting systems. This study
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In this study, we conduct a reliability characterisation study of cold standby systems. Utilising synthetic rectangular formulas and cold preparedness equivalent models for cold standby systems, we analyse the lifetimes of several typical configurations, including series, parallel, and k/n:m voting systems. This study proposes system equivalent models for various types of cold standby systems, all composed of components that follow the same exponential distribution. We use the equivalent model to determine the optimal timing for the use of cold spares and derive the reliability function and residual lifetime function for each type of system. To demonstrate the validity of our model, the Monte Carlo simulation is strategically designed based on the system failure rate function. The experimental results are then compared with those obtained from the numerical model, highlighting that the numerical method incurs a lower time cost.
Full article
(This article belongs to the Special Issue Mathematical Modelling and Computational Methods in Reliability Engineering)
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Open AccessArticle
MSGC-YOLO: An Improved Lightweight Traffic Sign Detection Model under Snow Conditions
by
Baoxiang Chen and Xinwei Fan
Mathematics 2024, 12(10), 1539; https://doi.org/10.3390/math12101539 - 15 May 2024
Abstract
Traffic sign recognition plays a crucial role in enhancing the safety and efficiency of traffic systems. However, in snowy conditions, traffic signs are often obscured by particles, leading to a severe decrease in detection accuracy. To address this challenge, we propose an improved
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Traffic sign recognition plays a crucial role in enhancing the safety and efficiency of traffic systems. However, in snowy conditions, traffic signs are often obscured by particles, leading to a severe decrease in detection accuracy. To address this challenge, we propose an improved YOLOv8-based model for traffic sign recognition. Initially, we introduce a Multi-Scale Group Convolution (MSGC) module to replace the C2f module in the YOLOv8 backbone. Data indicate that MSGC enhances detection accuracy while maintaining model lightweightness. Subsequently, to improve the recognition ability for small targets, we introduce an enhanced small target detection layer, which enhances small target detection accuracy while reducing parameters. In addition, we replaced the original BCE loss with the improved EfficientSlide loss to improve the sample imbalance problem. Finally, we integrate Deformable Attention into the model to improve the detection efficiency and performance of complex targets. The resulting fused model, named MSGC-YOLOv8, is evaluated on an enhanced dataset of snow-covered traffic signs. Experimental results show that the MSGC-YOLOv8 model is used for snow road traffic sign recognition. Compared with the YOLOv8n model [email protected]:0.95, [email protected]:0.95 is increased by 17.7% and 18.1%, respectively, greatly improving the detection accuracy. Compared with the YOLOv8s model, while the parameters are reduced by 59.6%, [email protected] only loses 1.5%. Considering all aspects of the data, our proposed model shows high detection efficiency and accuracy under snowy conditions.
Full article
(This article belongs to the Special Issue Deep Learning in Computer Vision: Theory and Applications)
Open AccessArticle
On Stock Volatility Forecasting under Mixed-Frequency Data Based on Hybrid RR-MIDAS and CNN-LSTM Models
by
Wenfeng Ma, Yuxuan Hong and Yuping Song
Mathematics 2024, 12(10), 1538; https://doi.org/10.3390/math12101538 - 15 May 2024
Abstract
Most of the deep-learning algorithms on stock price volatility prediction in the existing literature use data such as same-frequency market indicators or technical indicators, and less consider mixed-frequency data, such as macro-data. Compared with the traditional model that only inputs the same-frequency data
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Most of the deep-learning algorithms on stock price volatility prediction in the existing literature use data such as same-frequency market indicators or technical indicators, and less consider mixed-frequency data, such as macro-data. Compared with the traditional model that only inputs the same-frequency data such as technical indicators and market indicators, this study proposes an improved deep-learning model based on mixed-frequency big data. This paper first introduces the reserve restricted mixed-frequency data sampling (RR-MIDAS) model to deal with the mixed-frequency data and, secondly, extracts the temporal and spatial features of volatility series by using the parallel model of CNN-LSTM and LSTM, and finally utilizes the Optuna framework for hyper-parameter optimization to achieve volatility prediction. For the deep-learning model with mixed-frequency data, its RMSE, MAE, MSLE, MAPE, SMAPE, and QLIKE are reduced by 18.25%, 14.91%, 30.00%, 12.85%, 13.74%, and 23.42%, respectively. This paper provides a more accurate and robust method for forecasting the realized volatility of stock prices under mixed-frequency data.
Full article
(This article belongs to the Special Issue Looking at the New Era Challenges in Finance: Forecasting Modeling by Using Artificial Intelligence)
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Semi-Supervised Medical Image Classification with Pseudo Labels Using Coalition Similarity Training
by
Kun Liu, Shuyi Ling and Sidong Liu
Mathematics 2024, 12(10), 1537; https://doi.org/10.3390/math12101537 - 15 May 2024
Abstract
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The development of medical image classification models necessitates a substantial number of labeled images for model training. In real-world scenarios, sample sizes are typically limited and labeled samples often constitute only a small portion of the dataset. This paper aims to investigate a
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The development of medical image classification models necessitates a substantial number of labeled images for model training. In real-world scenarios, sample sizes are typically limited and labeled samples often constitute only a small portion of the dataset. This paper aims to investigate a collaborative similarity learning strategy that optimizes pseudo-labels to enhance model accuracy and expedite its convergence, known as the joint similarity learning framework. By integrating semantic similarity and instance similarity, the pseudo-labels are mutually refined to ensure their quality during initial training. Furthermore, the similarity score is utilized as a weight to guide samples away from misclassification predictions during the classification process. To enhance the model’s generalization ability, an adaptive consistency constraint is introduced into the loss function to improve performance on untrained datasets. The model achieved a satisfactory accuracy of 93.65% at 80% labeling ratio, comparable to supervised learning methods’ performance. Even with very low labeling ratio (e.g., 5%), the model still attained an accuracy of 74.28%. Comparison with other techniques such as Mean Teacher and FixMatch revealed that our approach significantly outperforms them in medical image classification tasks through improving accuracy by approximately 2%, demonstrating this framework’s leadership in medical image classification.
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Open AccessArticle
maGENEgerZ: An Efficient Artificial Intelligence-Based Framework Can Extract More Expressed Genes and Biological Insights Underlying Breast Cancer Drug Response Mechanism
by
Turki Turki and Y-h. Taguchi
Mathematics 2024, 12(10), 1536; https://doi.org/10.3390/math12101536 - 15 May 2024
Abstract
Understanding breast cancer drug response mechanisms can play a crucial role in improving treatment outcomes and survival rates. Existing bioinformatics-based approaches are far from perfect and do not adopt computational methods based on advanced artificial intelligence concepts. Therefore, we introduce a novel computational
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Understanding breast cancer drug response mechanisms can play a crucial role in improving treatment outcomes and survival rates. Existing bioinformatics-based approaches are far from perfect and do not adopt computational methods based on advanced artificial intelligence concepts. Therefore, we introduce a novel computational framework based on an efficient support vector machine (esvm) working as follows: First, we downloaded and processed three gene expression datasets related to breast cancer responding and non-responding to treatments from the gene expression omnibus (GEO) according to the following GEO accession numbers: GSE130787, GSE140494, and GSE196093. Our method esvm is formulated as a constrained optimization problem in its dual form as a function of λ. We recover the importance of each gene as a function of λ, y, and x. Then, we select p genes out of n, which are provided as input to enrichment analysis tools, Enrichr and Metascape. Compared to existing baseline methods, including deep learning, results demonstrate the superiority and efficiency of esvm, achieving high-performance results and having more expressed genes in well-established breast cancer cell lines, including MD-MB231, MCF7, and HS578T. Moreover, esvm is able to identify (1) various drugs, including clinically approved ones (e.g., tamoxifen and erlotinib); (2) seventy-four unique genes (including tumor suppression genes such as TP53 and BRCA1); and (3) thirty-six unique TFs (including SP1 and RELA). These results have been reported to be linked to breast cancer drug response mechanisms, progression, and metastasizing. Our method is available publicly on the maGENEgerZ web server.
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(This article belongs to the Special Issue Advanced Artificial Intelligence Models and Its Applications, 2nd Edition)
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Open AccessArticle
Mathematical Analysis of the Wind Field Characteristics at a Towering Peak Protruding out of a Steep Mountainside
by
Mohammed Nabil, Fengqi Guo, Huan Li and Qiuliang Long
Mathematics 2024, 12(10), 1535; https://doi.org/10.3390/math12101535 - 15 May 2024
Abstract
Wind field characteristics in a complex topography are significantly influenced by the nature of the surrounding terrains. This study employs onsite measurements to investigate the wind field characteristics at a towering peak protruding out of a steep mountainside, where butterfly−lookalike landscape platform will
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Wind field characteristics in a complex topography are significantly influenced by the nature of the surrounding terrains. This study employs onsite measurements to investigate the wind field characteristics at a towering peak protruding out of a steep mountainside, where butterfly−lookalike landscape platform will be constructed; the impact of the surrounding topography on the wind flow is highlighted. The results showed that the blocking effect of the mountains in the mountainous side of the valley caused a significant drop in the mean wind speed from that direction. The stationary test (reverse arrangement test) indicated that the wind speed had a strong nonstationary characteristic, necessitating the employment of a steady and nonstationary wind speed model to assess the wind turbulence characteristics. The three directions’ wind turbulence integral scales were critically influenced by the occurrence of the wind speedup effect, unexpectedly resulting in the vertical turbulence integral scale being the greatest of the three. Furthermore, the measured wind turbulence properties under both wind speed models showed certain variations from the recommended specifications. Consequently, the impact of the local terrain and the speedup effect on the wind characteristics must be thoroughly evaluated to ensure the structural stability of structures installed at a similar topography.
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(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering, 2nd Edition)
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Research on Virus Propagation Network Intrusion Detection Based on Graph Neural Network
by
Xianer Ying, Mengshuang Pan, Xiner Chen, Yiyi Zhou, Jianhua Liu, Dazhi Li, Binghao Guo and Zihao Zhu
Mathematics 2024, 12(10), 1534; https://doi.org/10.3390/math12101534 - 14 May 2024
Abstract
The field of network security is highly concerned with intrusion detection, which safeguards the security of computer networks. The invention and application of intrusion detection technology play indispensable roles in network security, and it is crucial to investigate and comprehend this topic. Recently,
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The field of network security is highly concerned with intrusion detection, which safeguards the security of computer networks. The invention and application of intrusion detection technology play indispensable roles in network security, and it is crucial to investigate and comprehend this topic. Recently, with the continuous occurrence of intrusion incidents in virus propagation networks, traditional network detection algorithms for virus propagation have encountered limitations and have struggled to detect these incidents effectively and accurately. Therefore, updating the intrusion detection algorithm of the virus-spreading network is imperative. This paper introduces a novel system for virus propagation, whose core is a graph-based neural network. By organically combining two modules—a standardization module and a computation module—this system forms a powerful GNN model. The standardization module uses two methods, while the calculation module uses three methods. Through permutation and combination, we obtain six GNN models with different characteristics. To verify their performance, we conducted experiments on the selected datasets. The experimental results show that the proposed algorithm has excellent capabilities, high accuracy, reasonable complexity, and excellent stability in the intrusion detection of virus-spreading networks, making the network more secure and reliable.
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(This article belongs to the Special Issue Advanced Research on Information System Security and Privacy)
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Quadratic Tracking Control of Linear Stochastic Systems with Unknown Dynamics Using Average Off-Policy Q-Learning Method
by
Longyan Hao, Chaoli Wang and Yibo Shi
Mathematics 2024, 12(10), 1533; https://doi.org/10.3390/math12101533 - 14 May 2024
Abstract
This article investigates the optimal tracking control problem for data-based stochastic discrete-time linear systems. An average off-policy Q-learning algorithm is proposed to solve the optimal control problem with random disturbances. Compared with the existing off-policy reinforcement learning (RL) algorithm, the proposed average off-policy
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This article investigates the optimal tracking control problem for data-based stochastic discrete-time linear systems. An average off-policy Q-learning algorithm is proposed to solve the optimal control problem with random disturbances. Compared with the existing off-policy reinforcement learning (RL) algorithm, the proposed average off-policy Q-learning algorithm avoids the assumption of an initial stability control. First, a pole placement strategy is used to design an initial stable control for systems with unknown dynamics. Second, the initial stable control is used to design a data-based average off-policy Q-learning algorithm. Then, this algorithm is used to solve the stochastic linear quadratic tracking (LQT) problem, and a convergence proof of the algorithm is provided. Finally, numerical examples show that this algorithm outperforms other algorithms in a simulation.
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(This article belongs to the Special Issue Dynamics and Control of Complex Systems and Robots)
Open AccessArticle
New Oscillation Criteria for Sturm–Liouville Dynamic Equations with Deviating Arguments
by
Taher S. Hassan, Clemente Cesarano, Loredana Florentina Iambor, Amir Abdel Menaem, Naveed Iqbal and Akbar Ali
Mathematics 2024, 12(10), 1532; https://doi.org/10.3390/math12101532 - 14 May 2024
Abstract
The aim of this study is to refine the known Riccati transformation technique to provide new oscillation criteria for solutions to second-order dynamic equations over time. It is important to note that the convergence or divergence of some improper integrals on time scales
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The aim of this study is to refine the known Riccati transformation technique to provide new oscillation criteria for solutions to second-order dynamic equations over time. It is important to note that the convergence or divergence of some improper integrals on time scales depends not only on the integration function but also on the integration time scale. Therefore, there has been a motivation to find new oscillation criteria that can be applicable regardless of whether is convergent or divergent, in contrast to what has been followed in most previous works in the literature. We have provided an example to illustrate the significance of the obtained results.
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(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena, 2nd Edition)
Open AccessArticle
Energy Mutual Aid Device of Electric Vehicles: Quadratic Boost Converter with Modified Voltage-Mode Controller
by
Jun Xiao, Shuo Zhai, Wei Jia, Weisheng Wang, Zhiyuan Zhang and Baining Guo
Mathematics 2024, 12(10), 1531; https://doi.org/10.3390/math12101531 - 14 May 2024
Abstract
Electric vehicles are becoming a mainstay of road transport. However, the uneven distribution of the electric vehicle charging piles in cities has led to the problem of “mileage anxiety”. This has become a significant concern of consumers in purchasing electric vehicles. At the
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Electric vehicles are becoming a mainstay of road transport. However, the uneven distribution of the electric vehicle charging piles in cities has led to the problem of “mileage anxiety”. This has become a significant concern of consumers in purchasing electric vehicles. At the same time, it also hinders the development of the electric vehicle industry. For this reason, this paper designs an electric vehicle energy mutual aid device. In the event that the power battery of an electric vehicle is low on energy and there are no suitable charging piles around, the device can also seek energy supplementation from surrounding electric vehicles with sufficient energy. This device should satisfy the characteristics of wide gain, high power, small size, and light weight. Firstly, the quadratic boost converter and its state space model are constructed. It uses only one electrical switching element to realize the light weight of the device, and it also provides wide voltage gain to fulfill the needs of electric vehicle charging. Secondly, an improved voltage mode controller is proposed to address the shortcomings of the conventional voltage mode controller of the quadratic boost converter. It avoids the tradeoff between the transient and steady-state performance due to the integration action of the conventional voltage mode controller. Also, this controller uses less feedback to make the controlled system output the required DC power, reducing the weight of the device. Finally, the effectiveness of the proposed energy mutual aid device is verified by simulations and experiments.
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(This article belongs to the Special Issue Mathematical Applications in Electrical Engineering)
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Investigating the Dynamic Behavior of Integer and Noninteger Order System of Predation with Holling’s Response
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Kolade M. Owolabi, Sonal Jain and Edson Pindza
Mathematics 2024, 12(10), 1530; https://doi.org/10.3390/math12101530 - 14 May 2024
Abstract
The paper’s primary objective is to examine the dynamic behavior of an integer and noninteger predator–prey system with a Holling type IV functional response in the Caputo sense. Our focus is on understanding how harvesting influences the stability, equilibria, bifurcations, and limit cycles
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The paper’s primary objective is to examine the dynamic behavior of an integer and noninteger predator–prey system with a Holling type IV functional response in the Caputo sense. Our focus is on understanding how harvesting influences the stability, equilibria, bifurcations, and limit cycles within this system. We employ qualitative and quantitative analysis methods rooted in bifurcation theory, dynamical theory, and numerical simulation. We also delve into studying the boundedness of solutions and investigating the stability and existence of equilibrium points within the system. Leveraging Sotomayor’s theorem, we establish the presence of both the saddle-node and transcritical bifurcations. The analysis of the Hopf bifurcation is carried out using the normal form theorem. The model under consideration is extended to the fractional reaction–diffusion model which captures non-local and long-range effects more accurately than integer-order derivatives. This makes fractional reaction–diffusion systems suitable for modeling phenomena with anomalous diffusion or memory effects, improving the fidelity of simulations in turn. An adaptable numerical technique for solving this class of differential equations is also suggested. Through simulation results, we observe that one of the Lyapunov exponents has a negative value, indicating the potential for the emergence of a stable-limit cycle via bifurcation as well as chaotic and complex spatiotemporal distributions. We supplement our analytical investigations with numerical simulations to provide a comprehensive understanding of the system’s behavior. It was discovered that both the prey and predator populations will continue to coexist and be permanent, regardless of the choice of fractional parameter.
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(This article belongs to the Special Issue Numerical Solution of Differential Equations and Their Applications)
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