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Mathematics
Volume 13
Issue 11
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Mathematics, Volume 13, Issue 11 (June-1 2025) – 206 articles

Cover Story (view full-size image): In this paper, we present two symbolic methods, in particular, the method starting from the source identity, umbra identity, for constructing identities of s-Appell polynomials related to Stirling numbers and binomial coefficients. We discuss some properties of s-Appell polynomial sequences related to Riordan arrays, Sheffer matrices, and their q analogs. View this paper
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22 pages, 1148 KiB  
Article
Research on a PTSD Risk Assessment Model Using Multi-Modal Data Fusion
by Youxi Luo, Yucui Shang, Dongfeng Zhu, Tian Zhang and Chaozhu Hu
Mathematics 2025, 13(11), 1901; https://doi.org/10.3390/math13111901 - 5 Jun 2025
Viewed by 522
Abstract
Post-traumatic stress disorder (PTSD) is a complex psychological disorder caused by multiple factors, which are not only related to individual psychological states but also closely linked to physiological responses, social environments, and personal experiences. Therefore, traditional single data source assessment methods are difficult [...] Read more.
Post-traumatic stress disorder (PTSD) is a complex psychological disorder caused by multiple factors, which are not only related to individual psychological states but also closely linked to physiological responses, social environments, and personal experiences. Therefore, traditional single data source assessment methods are difficult to fully understand and evaluate the complexity of PTSD. To overcome this challenge, the focus of this study is on developing a PTSD risk assessment model based on multi-modal data fusion. The importance of multi-modal data fusion lies in its ability to integrate data from different dimensions and provide a more comprehensive PTSD risk assessment. For multi-modal data fusion, two sets of solutions are proposed: the first is to extract EEG features using B-spline basis functions, combined with questionnaire data, to construct a multi-modal Zero-Inflated Poisson regression model; the second is to build a multi-modal deep neural network fusion prediction model to automatically extract and fuse multi-modal data features. The results show that the multi-modal data model is more accurate than the single data model, with significantly improved prediction ability. Zero-inflated Poisson models are prone to over-fitting when data is limited, while deep neural network models show superior performance in both training and prediction sets, especially the Hybrid LSTM-FCNN model, which not only has high accuracy but also strong generalization ability. This study proves the potential of multi-modal data fusion in PTSD prediction, and the Hybrid LSTM-FCNN model stands out for its high accuracy and good generalization ability, providing scientific evidence for early warning of PTSD in rescue personnel. Future research can further explore model optimization and clinical applications to promote the mental health maintenance of rescue personnel. Full article
(This article belongs to the Section D: Statistics and Operational Research)
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15 pages, 296 KiB  
Article
On the Product of Zeta-Functions
by Nianliang Wang, Kalyan Chakraborty and Takako Kuzumaki
Mathematics 2025, 13(11), 1900; https://doi.org/10.3390/math13111900 - 5 Jun 2025
Viewed by 426
Abstract
In this paper, we study the Bochner modular relation (Lambert series) for the kth power of the product of two Riemann zeta-functions with difference α, an integer with the Voronoĭ function weight Vk. In the case of [...] Read more.
In this paper, we study the Bochner modular relation (Lambert series) for the kth power of the product of two Riemann zeta-functions with difference α, an integer with the Voronoĭ function weight Vk. In the case of V1(x)=e−x, the results reduce to Bochner modular relations, which include the Ramanujan formula, Wigert–Bellman approximate functional equation, and the Ewald expansion. The results abridge analytic number theory and the theory of modular forms in terms of the sum-of-divisor function. We pursue the problem of (approximate) automorphy of the associated Lambert series. The α=0 case is the divisor function, while the α=1 case would lead to a proof of automorphy of the Dedekind eta-function à la Ramanujan. Full article
(This article belongs to the Special Issue Analytic Methods in Number Theory and Allied Fields)
16 pages, 339 KiB  
Article
An Efficient Numerical Method for the Fractional Bagley–Torvik Equation of Variable Coefficients with Robin Boundary Conditions
by S. Joe Christin Mary, Sekar Elango, Muath Awadalla and Rabab Alzahrani
Mathematics 2025, 13(11), 1899; https://doi.org/10.3390/math13111899 - 5 Jun 2025
Viewed by 294
Abstract
In this paper, we propose a numerical method for the fractional Bagley–Torvik equation of variable coefficients with Robin boundary conditions. The problem is approximated using a finite difference scheme on a uniform mesh that combines the L1 scheme with central differences. We prove [...] Read more.
In this paper, we propose a numerical method for the fractional Bagley–Torvik equation of variable coefficients with Robin boundary conditions. The problem is approximated using a finite difference scheme on a uniform mesh that combines the L1 scheme with central differences. We prove that this numerical method is almost first-order convergent. The error bounds for the numerical approximation are derived. The numerical calculations carried out for the given examples validate the theoretical results. Full article
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23 pages, 1723 KiB  
Article
A Comprehensive Study on the Different Approaches of the Symmetric Difference in Nilpotent Fuzzy Systems
by Luca Sára Pusztaházi, György Eigner and Orsolya Csiszár
Mathematics 2025, 13(11), 1898; https://doi.org/10.3390/math13111898 - 5 Jun 2025
Viewed by 285
Abstract
This paper comprehensively examines symmetric difference operators within logical systems generated by nilpotent t-norms and t-conorms, specifically addressing their behavior and applicability in bounded and Łukasiewicz fuzzy logic systems. We identify two distinct symmetric difference operators and analyze their fundamental properties, revealing their [...] Read more.
This paper comprehensively examines symmetric difference operators within logical systems generated by nilpotent t-norms and t-conorms, specifically addressing their behavior and applicability in bounded and Łukasiewicz fuzzy logic systems. We identify two distinct symmetric difference operators and analyze their fundamental properties, revealing their inherent non-associativity. Recognizing the limitations posed by non-associative behavior in practical multi-step logical operations, we introduce a novel aggregated symmetric difference operator constructed through the arithmetic mean of the previously defined operators. The primary theoretical contribution of our research is establishing the associativity of this new aggregated operator, significantly enhancing its effectiveness for consistent multi-stage computations. Moreover, this operator retains critical properties including symmetry, neutrality, antitonicity, and invariance under negation, thus making it particularly valuable for various computational and applied domains such as image processing, pattern recognition, fuzzy neural networks, cryptographic schemes, and medical data analysis. The demonstrated theoretical robustness and practical versatility of our associative operator provide a clear improvement over existing methodologies, laying a solid foundation for future research in fuzzy logic and interdisciplinary applications. Our broader aim is to derive and study symmetric difference operators in both bounded and Łukasiewicz systems, as this represents a new direction of research. Full article
(This article belongs to the Special Issue New Approaches to Data Analysis and Data Analytics)
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35 pages, 432 KiB  
Article
Correctness of Fuzzy Inference Systems Based on f-Inclusion
by Carolina Díaz-Montarroso, Nicolás Madrid and Eloísa Ramírez-Poussa
Mathematics 2025, 13(11), 1897; https://doi.org/10.3390/math13111897 - 5 Jun 2025
Viewed by 224
Abstract
Recent work has shown that the f-index of inclusion can serve as a foundation for modeling Generalized Modus Ponens. In this paper, we develop a novel fuzzy inference system based on this inference rule. To establish its soundness, we connect it to [...] Read more.
Recent work has shown that the f-index of inclusion can serve as a foundation for modeling Generalized Modus Ponens. In this paper, we develop a novel fuzzy inference system based on this inference rule. To establish its soundness, we connect it to a Fuzzy Description Logic LU enriched with fuzzy modifiers (also known as fuzzy hedges). This logic background provides to the approach a strength absent in most fuzzy inference systems in the literature, which allows us to formally prove a series of results that culminate in a final correctness theorem for the proposed fuzzy inference system. This paper also presents a running example aimed at showing the potential applicability of the proposal. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
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23 pages, 2180 KiB  
Article
Leveraging Advanced Mathematical Methods in Artificial Intelligence to Explore Heterogeneity and Asymmetry in Cross-Border Travel Satisfaction
by Yan Xu, Huajie Yang, Zibin Ye, Xiaobo Ma, Lei Tong and Xinyi Yu
Mathematics 2025, 13(11), 1896; https://doi.org/10.3390/math13111896 - 5 Jun 2025
Viewed by 327
Abstract
The cross-border port serves as a crucial cross-border travel connecting mainland China with Hong Kong and Macau, directly impacting the overall satisfaction of cross-border travel. While previous studies on neighborhoods, communities, and other areas have thoroughly examined the heterogeneity and asymmetry in satisfaction, [...] Read more.
The cross-border port serves as a crucial cross-border travel connecting mainland China with Hong Kong and Macau, directly impacting the overall satisfaction of cross-border travel. While previous studies on neighborhoods, communities, and other areas have thoroughly examined the heterogeneity and asymmetry in satisfaction, research on the satisfaction of cross-border travel at ports remains notably limited. This paper explores the heterogeneity and asymmetry of cross-border travel satisfaction using gradient boosted decision trees (GBDT) and k-means cluster analysis under the framework of three-factor theory, aiming to demonstrate the latest scientific research results on the fundamental theories and applications of artificial intelligence. The results show prevalent asymmetric relationships between factors and cross-border travel satisfaction, with the factor structure exhibiting heterogeneity across different groups. High-income individuals were more likely to prioritize the reliability of cross-border travel, whereas low-income individuals tended to emphasize the convenience of travel. Finally, this paper proposes improvement priorities for different types of passengers, reflecting the practical application of advanced mathematical methods in artificial intelligence to drive intelligent decision-making. Full article
(This article belongs to the Special Issue Artificial Intelligence Applications with Advanced Mathematical Methods)
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30 pages, 5325 KiB  
Article
Carbon Dioxide Emission Forecasting Using BiLSTM Network Based on Variational Mode Decomposition and Improved Black-Winged Kite Algorithm
by Yueqiao Yang, Shichuang Li, Haijun Liu and Jidong Guo
Mathematics 2025, 13(11), 1895; https://doi.org/10.3390/math13111895 - 5 Jun 2025
Viewed by 269
Abstract
With the growing severity of global climate change, forecasting and managing carbon dioxide (CO2) emissions has become one of the critical tasks in addressing climate change. To improve the accuracy of CO2 emission forecasting, an innovative framework based on variational [...] Read more.
With the growing severity of global climate change, forecasting and managing carbon dioxide (CO2) emissions has become one of the critical tasks in addressing climate change. To improve the accuracy of CO2 emission forecasting, an innovative framework based on variational mode decomposition (VMD), improved black-winged kite algorithm (IBKA), and BiLSTM networks is proposed. This framework aims to address the challenges associated with predicting non-stationary data and optimizing model hyperparameters. Initially, experiments were conducted on 29 benchmark functions using the IBKA algorithm, demonstrating its superior performance in highly nonlinear and complex environments. Subsequently, the BiLSTM model optimized by IBKA was employed to predict CO2 emission trends across four major industries in China, confirming its enhanced prediction accuracy. Finally, a comparative analysis with other mainstream machine learning and deep learning models revealed that the BiLSTM model consistently achieved the best predictive performance across all industries. This research proposes an efficient and practical technical pathway for intelligent carbon emission prediction under the “dual-carbon” strategic goals, offering scientific support for policy formulation and the low-carbon transition. Full article
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34 pages, 418 KiB  
Review
Queues with Working Vacations: A Survey
by Dieter Fiems
Mathematics 2025, 13(11), 1894; https://doi.org/10.3390/math13111894 - 5 Jun 2025
Viewed by 271
Abstract
In this paper, we present an extensive literature review on queueing systems with working vacations. The concept of a working vacation generalises the concept of server vacations, which are time periods during which the server is absent and cannot serve waiting customers. During [...] Read more.
In this paper, we present an extensive literature review on queueing systems with working vacations. The concept of a working vacation generalises the concept of server vacations, which are time periods during which the server is absent and cannot serve waiting customers. During a working vacation, the server remains active, albeit at a reduced service rate. Our literature survey mainly highlights the structural properties of the Markov chains that underlie working vacation queueing models, as well as various methodological approaches to assessing the performance of queues with working vacations. Moreover, queueing games with working vacations and applications of queues with working vacations are discussed. Full article
(This article belongs to the Special Issue Queue and Stochastic Models for Operations Research, 3rd Edition)
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15 pages, 467 KiB  
Article
Linear Trend, HP Trend, and bHP Trend
by Hiroshi Yamada
Mathematics 2025, 13(11), 1893; https://doi.org/10.3390/math13111893 - 5 Jun 2025
Viewed by 295
Abstract
The modelling of the trend component of economic time series has a long history, and the most primitive and popular model displays the trend as a linear function of time. However, the residuals of such a linear trend frequently exhibit long-period fluctuations. The [...] Read more.
The modelling of the trend component of economic time series has a long history, and the most primitive and popular model displays the trend as a linear function of time. However, the residuals of such a linear trend frequently exhibit long-period fluctuations. The Hodrick–Prescott (HP) filter is able to capture such long-period fluctuations well, resulting in a very realistic trend-cycle decomposition. It may be queried whether the HP trend residuals no longer contain useful long-period fluctuations. If such long-period fluctuations are present, then taking them into consideration could improve the HP trend. In a recent article, a new approach to address this issue, the boosted HP (bHP) filter, was proposed. The three trends mentioned above, i.e., the linear trend, the HP trend, and the bHP trend, can be treated in a unified manner. In this paper, we demonstrate the relationship in detail. We show how the bHP trend is constructed from the linear/HP trend, and long-period fluctuations remained in their trend residuals. Full article
(This article belongs to the Special Issue Recent Advances in Time Series Analysis)
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23 pages, 2098 KiB  
Article
Modeling Time Series with SARIMAX and Skew-Normal and Zero-Inflated Skew-Normal Errors
by M. Alejandro Dinamarca, Fernando Rojas, Claudia Ibacache-Quiroga and Karoll González-Pizarro
Mathematics 2025, 13(11), 1892; https://doi.org/10.3390/math13111892 - 5 Jun 2025
Viewed by 339
Abstract
This study proposes an extension of Seasonal Autoregressive Integrated Moving Average models with exogenous regressors (SARIMAX) by incorporating skew-normal and zero-inflated skew-normal error structures to better accommodate asymmetry and excess zeros in time series data. The proposed framework demonstrates improved flexibility and robustness [...] Read more.
This study proposes an extension of Seasonal Autoregressive Integrated Moving Average models with exogenous regressors (SARIMAX) by incorporating skew-normal and zero-inflated skew-normal error structures to better accommodate asymmetry and excess zeros in time series data. The proposed framework demonstrates improved flexibility and robustness compared to traditional Gaussian-based models. Simulation experiments reveal that the skewness parameter significantly affect forecasting accuracy, with reductions in mean absolute error (MAE) and root mean square error (RMSE) observed across both positively and negatively skewed scenarios. Notably, in negative-skew contexts, the model achieved an MAE of 0.40 and RMSE of 0.49, outperforming its symmetric-error counterparts. The inclusion of zero-inflation probabilities further enhances model performance in sparse datasets, yielding superior values in goodness-of-fit criteria such as the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). To illustrate the practical value of the methodology, a real-world case study is presented involving the modeling of optical density (OD600) data from Escherichia coli during stationary-phase growth. A SARIMAX(1,1,1) model with skew-normal errors was fitted to 200 time-stamped absorbance measurements, revealing significant positive skewness in the residuals. Bootstrap-derived confidence intervals confirmed the significance of the estimated skewness parameter (α=14.033 with 95% CI [12.07, 15.99]). The model outperformed the classical ARIMA benchmark in capturing the asymmetry of the stochastic structure, underscoring its relevance for biological, environmental, and industrial applications in which non-Gaussian features are prevalent. Full article
(This article belongs to the Special Issue Applied Statistics in Management Sciences)
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25 pages, 510 KiB  
Article
An Adaptive Evolutionary Causal Dynamic Factor Model
by Qian Wei and Heng-Guo Zhang
Mathematics 2025, 13(11), 1891; https://doi.org/10.3390/math13111891 - 5 Jun 2025
Viewed by 241
Abstract
Background: With COVID-19 having a significant impact on economic activity, it has become difficult for the existing dynamic factor models (nowcasting models) to forecast macroeconomics with high accuracy. The real-time monitoring of macroeconomics has become an important research problem faced by banks, governments, [...] Read more.
Background: With COVID-19 having a significant impact on economic activity, it has become difficult for the existing dynamic factor models (nowcasting models) to forecast macroeconomics with high accuracy. The real-time monitoring of macroeconomics has become an important research problem faced by banks, governments, and corporations. Subjects and Methods: This paper proposes an adaptive evolutionary causal dynamic factor model (AcNowcasting) for macroeconomic forecasting. Unlike the classical nowcasting models, the AcNowcasting algorithm has the ability to perform feature selection. The criteria for feature selection are based on causality strength rather than being based on the quality of the prediction results. In addition, the factors in the AcNowcasting algorithm have the capacity for adaptive differential evolution, which can generate the best factors. These two abilities are not possessed by classical nowcasting models. Results: The experimental results show that the AcNowcasting algorithm can extract common factors that reflect macroeconomic fluctuations better, and the prediction accuracy of the AcNowcasting algorithm is more accurate than that of traditional nowcasting models. Contributions: The AcNowcasting algorithm provides a new prediction theory and a means for the real-time monitoring of macroeconomics, which has good theoretical and practical value. Full article
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18 pages, 7765 KiB  
Article
Secure Parallel Image Cryptographic Hash Function Using a Novel 2D High-Randomness Hyperchaotic Map
by Mingrui Qi and Dongdong Wang
Mathematics 2025, 13(11), 1890; https://doi.org/10.3390/math13111890 - 5 Jun 2025
Viewed by 329
Abstract
For image data, the processing of each pixel using a cryptographic hash function is linear, and the existing cryptographic hash function lacks parallel processing of image width and height. In order to improve the computational efficiency and ensure the security of the hash [...] Read more.
For image data, the processing of each pixel using a cryptographic hash function is linear, and the existing cryptographic hash function lacks parallel processing of image width and height. In order to improve the computational efficiency and ensure the security of the hash function in image cryptography, we design a 2D hyperchaotic map, whose good chaotic dynamics and randomness fully meet the needs of the hash function. Based on the proposed mapping, we propose an image-specific chaotic hash function for confusion diffusion and extraction in both width and height dimensions in parallel. The designed hash function of image cryptography can set some common hash lengths and also support the setting of key. For image data, the proposed method has higher computational efficiency than other common hash functions and has good encryption security and anti-collision characteristics. Full article
(This article belongs to the Special Issue Complex System Dynamics and Image Processing)
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26 pages, 1610 KiB  
Article
Forecasting Stock Market Volatility Using CNN-BiLSTM-Attention Model with Mixed-Frequency Data
by Yufeng Zhang, Tonghui Zhang and Jingyi Hu
Mathematics 2025, 13(11), 1889; https://doi.org/10.3390/math13111889 - 5 Jun 2025
Viewed by 721
Abstract
Existing stock volatility forecasting models predominantly rely on same-frequency market data while neglecting mixed-frequency integration and face particular challenges in incorporating low-frequency macroeconomic variables that exhibit temporal mismatches with financial market dynamics. To address this limitation, this study develops a novel hybrid approach [...] Read more.
Existing stock volatility forecasting models predominantly rely on same-frequency market data while neglecting mixed-frequency integration and face particular challenges in incorporating low-frequency macroeconomic variables that exhibit temporal mismatches with financial market dynamics. To address this limitation, this study develops a novel hybrid approach for stock market volatility forecasting, which synergistically combines a deep learning model (CNN-BiLSTM-Attention) with the GARCH-MIDAS model. The GARCH-MIDAS model can fully exploit mixed-frequency information, including daily returns, monthly macroeconomic variables, and EPU. The deep learning model can effectively capture both spatial and temporal patterns of multivariate time-series data, thus effectively improving prediction accuracy and generalization ability in stock market volatility forecasting. The results indicate that the CNN-BiLSTM-Attention model yields the most accurate forecasts compared to the benchmark models. Furthermore, incorporating additional predictors, such as macroeconomic indicators and the Economic Policy Uncertainty Index, also provides valuable information for stock market volatility prediction, notably enhancing the model’s forecasting effect. Full article
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3 pages, 142 KiB  
Editorial
Preface to the Special Issue “Advanced Applications of Multi-Criteria Decision-Making Methods in Operational Research”
by Marcio Pereira Basilio, Valdecy Pereira and Marcos dos Santos
Mathematics 2025, 13(11), 1888; https://doi.org/10.3390/math13111888 - 5 Jun 2025
Viewed by 712
Abstract
Decision-making is a consistent part of the daily activities of individuals and organizations [...] Full article
16 pages, 503 KiB  
Article
Overcoming Class Imbalance in Incremental Learning Using an Elastic Weight Consolidation-Assisted Common Encoder Approach
by Engin Baysal and Cüneyt Bayılmış
Mathematics 2025, 13(11), 1887; https://doi.org/10.3390/math13111887 - 4 Jun 2025
Viewed by 537
Abstract
Incremental learning empowers models to continuously acquire knowledge of new classes while retaining previously learned information. However, catastrophic forgetting and class imbalance often impede this process, especially when new classes are introduced sequentially. We propose a hybrid method that integrates Elastic Weight Consolidation [...] Read more.
Incremental learning empowers models to continuously acquire knowledge of new classes while retaining previously learned information. However, catastrophic forgetting and class imbalance often impede this process, especially when new classes are introduced sequentially. We propose a hybrid method that integrates Elastic Weight Consolidation (EWC) with a shared encoder architecture to overcome these obstacles. This approach provides robust feature extraction, while EWC safeguards vital parameters and preserves prior knowledge. Moreover, task-specific output layers enable flexible adaptation to new classes. We evaluated our method using the CICIoT2023 dataset, a class-incremental IoT anomaly detection benchmark. Our results demonstrated a 15.3% improvement in the macro F1-score and a 1.28% increase in overall accuracy compared to a baseline model that did not incorporate EWC, with particular advantages for underrepresented classes. These findings underscore the effectiveness of the EWC-assisted shared encoder framework for class-imbalanced incremental learning in streaming environments. Full article
(This article belongs to the Special Issue New Insights in Machine Learning (ML) and Deep Neural Networks)
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13 pages, 1542 KiB  
Article
Reducing the Primary Resonance Vibrations of a Cantilever Beam Using a Proportional Fractional-Order Derivative Controller
by M.N. Abd El-Salam and Rageh K. Hussein
Mathematics 2025, 13(11), 1886; https://doi.org/10.3390/math13111886 - 4 Jun 2025
Viewed by 243
Abstract
Many studies aim to suppress vibrations in vibrating dynamic systems, such as bridges, highways, and aircraft. In this study, we scrutinize the primary resonance of a cantilever beam excited by an external force via a proportional fractional-order derivative controller (PFD). The average method [...] Read more.
Many studies aim to suppress vibrations in vibrating dynamic systems, such as bridges, highways, and aircraft. In this study, we scrutinize the primary resonance of a cantilever beam excited by an external force via a proportional fractional-order derivative controller (PFD). The average method is used to obtain the approximate solution of the vibrating system. The stability of the control system is illustrated using the Routh–Hurwitz criterion. We investigate the performance of some chosen parameters of the studied system to generate response curves. The performance of the linear fractional feedback control is studied at different values of the fractional order. Full article
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31 pages, 1581 KiB  
Article
Dynamic Portfolio Return Classification Using Price-Aware Logistic Regression
by Yakubu Suleiman Baguda, Hani Moaiteq AlJahdali and Altyeb Altaher Taha
Mathematics 2025, 13(11), 1885; https://doi.org/10.3390/math13111885 - 4 Jun 2025
Viewed by 466
Abstract
The dynamic and uncertain nature of financial markets presents significant challenges in accurately predicting portfolio returns due to inherent volatility and instability. This study investigates the potential of logistic regression to enhance the accuracy and robustness of return classification models, addressing challenges in [...] Read more.
The dynamic and uncertain nature of financial markets presents significant challenges in accurately predicting portfolio returns due to inherent volatility and instability. This study investigates the potential of logistic regression to enhance the accuracy and robustness of return classification models, addressing challenges in dynamic portfolio optimization. We propose a price-aware logistic regression (PALR) framework to classify dynamic portfolio returns. This approach integrates price movements as key features alongside traditional portfolio optimization techniques, enabling the identification and analysis of patterns and relationships within historical financial data. Unlike conventional methods, PALR dynamically adapts to market trends by incorporating historical price data and derived indicators, leading to more accurate classification of portfolio returns. Historical market data from the Dow Jones Industrial Average (DJIA) and Hang Seng Index (HSI) were used to train and test the model. The proposed scheme achieves an accuracy of 99.88%, a mean squared error (MSE) of 0.0006, and an AUC of 99.94% on the DJIA dataset. When evaluated on the HSI dataset, it attains a classification accuracy of 99.89%, an AUC of 99.89%, and an MSE of 0.011. The results demonstrate that PALR significantly improves classification accuracy and AUC while reducing MSE compared to conventional techniques. The proposed PALR model serves as a valuable tool for return classification and optimization, enabling investors, assets, and portfolio managers to make more informed and effective decisions. Full article
(This article belongs to the Special Issue Machine Learning and Finance)
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21 pages, 12520 KiB  
Article
Stress Estimation in Viscous Flows Using an Iterative Tikhonov Regularized Stokes Inverse Model
by Yuanhao Gao, Yang Wang and Jizhou Zhang
Mathematics 2025, 13(11), 1884; https://doi.org/10.3390/math13111884 - 4 Jun 2025
Viewed by 237
Abstract
In this paper, we propose and develop a stationary Stokes Inverse Model (SIM) to estimate the stress distributions that are difficult to measure directly in flows. We estimate the driving stresses from the velocities by solving the inverse problem governed by Stokes equations [...] Read more.
In this paper, we propose and develop a stationary Stokes Inverse Model (SIM) to estimate the stress distributions that are difficult to measure directly in flows. We estimate the driving stresses from the velocities by solving the inverse problem governed by Stokes equations under iterative Tikhonov (IT) regularization. We investigate the heuristic L-curve criterion to determine the proper regularization parameter. The solution existence and uniqueness for the Stokes inverse problem have been analyzed. We also conducted convergence analysis and error estimation for perturbed data, providing a fast and stable convergence. The finite element method is applied to the numerical approach. Following the theoretical investigation and formulation, we validate the model and demonstrate that the velocity data closely match the velocity fields that were reconstructed using the computed stress distributions. In particular, the proposed SIM can be used to reliably derive the stress distributions for the flows governed by the Stokes equations with small Reynolds number. Additionally, the model is robust to a certain number of perturbations, which enables the precise and effective estimation of the stress distributions. The proposed stationary SIM may be widely applicable in the estimation of stresses from experimental velocity fields in engineering and biological applications. Full article
(This article belongs to the Special Issue Mathematical Modeling for Fluid Mechanics)
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18 pages, 737 KiB  
Article
A Cloud-Edge-End Collaboration Framework for Fixed-Time Distributed Optimization of Virtual Power Plants
by Kai Kang, Nian Shi, Keqi Zhang, Si Cai, Liang Zhang, Xinan Shao, Lei Shu, Renjie Hu and Leimin Wang
Mathematics 2025, 13(11), 1883; https://doi.org/10.3390/math13111883 - 4 Jun 2025
Viewed by 270
Abstract
As the power grid expands, concerns about system computation speed and information privacy are becoming more critical. While distributed optimization methods protect individual privacy effectively, they struggle with computational efficiency in complex topologies. To address these issues, this paper proposes a cloud–edge–end collaboration [...] Read more.
As the power grid expands, concerns about system computation speed and information privacy are becoming more critical. While distributed optimization methods protect individual privacy effectively, they struggle with computational efficiency in complex topologies. To address these issues, this paper proposes a cloud–edge–end collaboration framework consisting of a cloud server and multiple edge servers. This framework enables parallel computation of multiple distributed optimization algorithms. Additionally, a distributed fixed-time optimization consensus algorithm is designed for virtual power plants, allowing the convergence time to be predetermined offline. The fixed-time convergence of the algorithm is proven and its effectiveness and superiority are demonstrated through simulation cases. Full article
(This article belongs to the Special Issue Finite-Time/Fixed-Time Stability and Control of Dynamical Systems)
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28 pages, 11557 KiB  
Review
Physics-Informed Neural Networks for Higher-Order Nonlinear Schrödinger Equations: Soliton Dynamics in External Potentials
by Leonid Serkin and Tatyana L. Belyaeva
Mathematics 2025, 13(11), 1882; https://doi.org/10.3390/math13111882 - 4 Jun 2025
Viewed by 614
Abstract
This review summarizes the application of physics-informed neural networks (PINNs) for solving higher-order nonlinear partial differential equations belonging to the nonlinear Schrödinger equation (NLSE) hierarchy, including models with external potentials. We analyze recent studies in which PINNs have been employed to solve NLSE-type [...] Read more.
This review summarizes the application of physics-informed neural networks (PINNs) for solving higher-order nonlinear partial differential equations belonging to the nonlinear Schrödinger equation (NLSE) hierarchy, including models with external potentials. We analyze recent studies in which PINNs have been employed to solve NLSE-type evolution equations up to the fifth order, demonstrating their ability to obtain one- and two-soliton solutions, as well as other solitary waves with high accuracy. To provide benchmark solutions for training PINNs, we employ analytical methods such as the nonisospectral generalization of the AKNS scheme of the inverse scattering transform and the auto-Bäcklund transformation. Finally, we discuss recent advancements in PINN methodology, including improvements in network architecture and optimization techniques. Full article
(This article belongs to the Special Issue New Trends in Nonlinear Dynamics and Nonautonomous Solitons)
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19 pages, 9413 KiB  
Article
A Novel High-Fidelity Reversible Data Hiding Method Based on Adaptive Multi-pass Embedding
by Xiaoxi Kong, Wenguang He and Zhanchuan Cai
Mathematics 2025, 13(11), 1881; https://doi.org/10.3390/math13111881 - 4 Jun 2025
Viewed by 316
Abstract
In reversible data hiding, prediction error generation plays a crucial role, with pixel value ordering (PVO) standing out as a prediction method that achieves high fidelity. However, conventional PVO approaches select predicted pixels and their predictions independently, failing to fully exploit the inherent [...] Read more.
In reversible data hiding, prediction error generation plays a crucial role, with pixel value ordering (PVO) standing out as a prediction method that achieves high fidelity. However, conventional PVO approaches select predicted pixels and their predictions independently, failing to fully exploit the inherent redundancy in ordered pixel sequences. This paper proposes a novel PVO-based prediction method that leverages the continuity and spatial correlation of ordering pixels. We first introduce a new prediction technique that exploits the redundancy of consecutive pixels. Our approach selects the most appropriate prediction method from preset prediction errors, considering both pixel position and value characteristics. Furthermore, we implement an adaptive strategy that dynamically selects multiple iteration parameters based on pixel content to obtain more expandable prediction errors and adjusts the modification of prediction errors accordingly. Unlike traditional fixed-parameter methods, our approach better utilizes the inherent structure and redundancy of image pixels, thereby improving data embedding efficiency while minimizing image distortion. We enhance performance by combining pairwise prediction-error expansion with content-based prediction error analysis. Experimental results demonstrate that the proposed scheme outperforms state-of-the-art solutions in terms of image fidelity while maintaining competitive embedding capacity, confirming the effectiveness of our method for efficient data embedding and image recovery. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
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21 pages, 14585 KiB  
Article
Unsupervised Contrastive Graph Kolmogorov–Arnold Networks Enhanced Cross-Modal Retrieval Hashing
by Hongyu Lin, Shaofeng Shen, Yuchen Zhang and Renwei Xia
Mathematics 2025, 13(11), 1880; https://doi.org/10.3390/math13111880 - 4 Jun 2025
Viewed by 428
Abstract
To address modality heterogeneity and accelerate large-scale retrieval, cross-modal hashing strategies generate compact binary codes that enhance computational efficiency. Existing approaches often struggle with suboptimal feature learning due to fixed activation functions and limited cross-modal interaction. We propose Unsupervised Contrastive Graph Kolmogorov–Arnold Networks [...] Read more.
To address modality heterogeneity and accelerate large-scale retrieval, cross-modal hashing strategies generate compact binary codes that enhance computational efficiency. Existing approaches often struggle with suboptimal feature learning due to fixed activation functions and limited cross-modal interaction. We propose Unsupervised Contrastive Graph Kolmogorov–Arnold Networks (GraphKAN) Enhanced Cross-modal Retrieval Hashing (UCGKANH), integrating GraphKAN with contrastive learning and hypergraph-based enhancement. GraphKAN enables more flexible cross-modal representation through enhanced nonlinear expression of features. We introduce contrastive learning that captures modality-invariant structures through sample pairs. To preserve high-order semantic relations, we construct a hypergraph-based information propagation mechanism, refining hash codes by enforcing global consistency. The efficacy of our UCGKANH approach is validated by thorough tests on the MIR-FLICKR, NUS-WIDE, and MS COCO datasets, which show significant gains in retrieval accuracy coupled with strong computational efficiency. Full article
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25 pages, 1292 KiB  
Article
Trust Domain Extensions Guest Fuzzing Framework for Security Vulnerability Detection
by Eran Dahan, Itzhak Aviv and Michael Kiperberg
Mathematics 2025, 13(11), 1879; https://doi.org/10.3390/math13111879 - 4 Jun 2025
Viewed by 386
Abstract
The Intel® Trust Domain Extensions (TDX) encrypt guest memory and minimize host interactions to provide hardware-enforced isolation for sensitive virtual machines (VMs). Software vulnerabilities in the guest OS continue to pose a serious risk even as the TDX improves security against a [...] Read more.
The Intel® Trust Domain Extensions (TDX) encrypt guest memory and minimize host interactions to provide hardware-enforced isolation for sensitive virtual machines (VMs). Software vulnerabilities in the guest OS continue to pose a serious risk even as the TDX improves security against a malicious hypervisor. We suggest a comprehensive TDX Guest Fuzzing Framework that systematically explores the guest’s code paths handling untrusted inputs. Our method uses a customized coverage-guided fuzzer to target those pathways with random input mutations following integrating static analysis to identify possible attack surfaces, where the guest reads data from the host. To achieve high throughput, we also use snapshot-based virtual machine execution, which returns the guest to its pre-interaction state at the end of each fuzz iteration. We show how our framework reveals undiscovered vulnerabilities in device initialization procedures, hypercall error-handling, and random number seeding logic using a QEMU/KVM-based TDX emulator and a TDX-enabled Linux kernel. We demonstrate that a large number of vulnerabilities occur when developers implicitly rely on values supplied by a hypervisor rather than thoroughly verifying them. This study highlights the urgent need for ongoing, automated testing in private computing environments by connecting theoretical completeness arguments for coverage-guided fuzzing with real-world results on TDX-specific code. We discovered several memory corruption and concurrency weaknesses in the TDX guest OS through our coverage-guided fuzzing campaigns. These flaws ranged from nested #VE handler deadlocks to buffer overflows in paravirtual device initialization to faulty randomness-seeding logic. By exploiting these vulnerabilities, the TDX’s hardware-based memory isolation may be compromised or denial-of-service attacks may be made possible. Thus, our results demonstrate that, although the TDX offers a robust hardware barrier, comprehensive input validation and equally stringent software defenses are essential to preserving overall security. Full article
(This article belongs to the Special Issue Cybersecurity and Data Protection: Modern Methods and New Applications)
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21 pages, 3197 KiB  
Review
Deploying AI on Edge: Advancement and Challenges in Edge Intelligence
by Tianyu Wang, Jinyang Guo, Bowen Zhang, Ge Yang and Dong Li
Mathematics 2025, 13(11), 1878; https://doi.org/10.3390/math13111878 - 4 Jun 2025
Viewed by 1128
Abstract
In recent years, artificial intelligence (AI) has achieved significant progress and remarkable advancements across various disciplines, including biology, computer science, and industry. However, the increasing complexity of AI network structures and the vast number of associated parameters impose substantial computational and storage demands, [...] Read more.
In recent years, artificial intelligence (AI) has achieved significant progress and remarkable advancements across various disciplines, including biology, computer science, and industry. However, the increasing complexity of AI network structures and the vast number of associated parameters impose substantial computational and storage demands, severely limiting the practical deployment of these models on resource-constrained edge devices. Although edge intelligence methods have been proposed to alleviate the computational and storage burdens, they still face multiple persistent challenges, such as large-scale model deployment, poor interpretability, privacy and security vulnerabilities, and energy efficiency constraints. This article systematically reviews the current advancements in edge intelligence technologies, highlights key enabling techniques including model sparsity, quantization, knowledge distillation, neural architecture search, and federated learning, and explores their applications in industrial, automotive, healthcare, and consumer domains. Furthermore, this paper presents a comparative analysis of these techniques, summarizes major trade-offs, and proposes decision frameworks to guide deployment strategies under different scenarios. Finally, it discusses future research directions to address the remaining technical bottlenecks and promote the practical and sustainable development of edge intelligence. Standing at the threshold of an exciting new era, we believe edge intelligence will play an increasingly critical role in transforming industries and enabling ubiquitous intelligent services. Full article
(This article belongs to the Special Issue New Advances in Distributed Systems, Edge Intelligence, and Artificial Intelligence)
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23 pages, 2623 KiB  
Article
An Inductive Logical Model with Exceptional Information for Error Detection and Correction in Large Knowledge Bases
by Yan Wu, Xiao Lin, Haojie Lian and Zili Zhang
Mathematics 2025, 13(11), 1877; https://doi.org/10.3390/math13111877 - 4 Jun 2025
Viewed by 311
Abstract
Some knowledge bases (KBs) extracted from Wikipedia articles can achieve very high average precision values (over 95% in DBpedia). However, subtle mistakes including inconsistencies, outliers, and erroneous relations are usually ignored in the construction of KBs by extraction rules. Automatic detection and correction [...] Read more.
Some knowledge bases (KBs) extracted from Wikipedia articles can achieve very high average precision values (over 95% in DBpedia). However, subtle mistakes including inconsistencies, outliers, and erroneous relations are usually ignored in the construction of KBs by extraction rules. Automatic detection and correction of these subtle errors is important for improving the quality of KBs. In this paper, an inductive logic programming with exceptional information (EILP) is proposed to automatically detect errors in large knowledge bases (KBs). EILP leverages the exceptional information problems that are ignored in conventional rule-learning algorithms such as inductive logic programming (ILP). Furthermore, an inductive logical correction method with exceptional features (EILC) is proposed to automatically correct these mistakes by learning a set of correction rules with exceptional features, in which respective metrics are provided to validate the revised triples. The experimental results demonstrate the effectiveness of EILP and EILC in detecting and repairing large knowledge bases, respectively. Full article
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19 pages, 1374 KiB  
Article
Source Identification for a Two-Dimensional Parabolic Equation with an Integral Constraint
by Miglena N. Koleva and Lubin G. Vulkov
Mathematics 2025, 13(11), 1876; https://doi.org/10.3390/math13111876 - 3 Jun 2025
Viewed by 263
Abstract
We consider a two-dimensional parabolic problem subject to both Neumann and Dirichlet boundary conditions, along with an integral constraint. Based on the integral observation, we solve the inverse problem of a recovering time-dependent right-hand side. By exploiting the structure of the boundary conditions, [...] Read more.
We consider a two-dimensional parabolic problem subject to both Neumann and Dirichlet boundary conditions, along with an integral constraint. Based on the integral observation, we solve the inverse problem of a recovering time-dependent right-hand side. By exploiting the structure of the boundary conditions, we reduce the original inverse problem to a one-dimensional formulation. We conduct a detailed analysis of the existence and uniqueness of the solution to the resulting one-dimensional loaded initial-boundary value problem. Furthermore, we derive estimates for both the solution and the unknown function. The direct and inverse problems are numerically solved by finite difference schemes. Numerical verification of the theoretical results is provided. Full article
(This article belongs to the Special Issue Numerical Methods in Multiphase Flow with Heat and Mass Transfer)
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30 pages, 394 KiB  
Article
Problems with Missing Tricomi Condition and Analog of Frankl Condition for One Class of Mixed Type Equations
by Assel Makulbay, Mirakhmat Mirsaburov, Abdumauvlen Berdyshev and Gulbakhor Mirsaburova
Mathematics 2025, 13(11), 1875; https://doi.org/10.3390/math13111875 - 3 Jun 2025
Viewed by 259
Abstract
In this paper, for a mixed elliptic-hyperbolic type equation with various degeneration orders and singular coefficients, theorems of uniqueness and existence of the solution to the problem with a missing Tricomi condition on boundary characteristic and with an analog of Frankl condition on [...] Read more.
In this paper, for a mixed elliptic-hyperbolic type equation with various degeneration orders and singular coefficients, theorems of uniqueness and existence of the solution to the problem with a missing Tricomi condition on boundary characteristic and with an analog of Frankl condition on different parts of the cut boundary along the degeneration segment in the mixed domain are proved. On the degeneration line segment, a general conjugation condition is set, and on the boundary of the elliptic domain and degeneration segment, the Bitsadze–Samarskii condition is posed. The considered problem, based on integral representations of the solution to the Dirichlet problem (in elliptic part of the domain) and a modified Cauchy problem (in hyperbolic part of the domain), is reduced to solving a non-standard singular Tricomi integral equation with a non-Fredholm integral operator (featuring an isolated first-order singularity in the kernel) in non-characteristic part of the equation. Non-standard approaches are applied here in constructing the solution algorithm. Through successive applications of the theory of singular integral equations and then the Wiener–Hopf equation theory, the non-standard singular Tricomi integral equation is reduced to a Fredholm integral equation of the second kind, the unique solvability of which follows from the uniqueness theorem for the problem. Full article
(This article belongs to the Section C1: Difference and Differential Equations)
16 pages, 3426 KiB  
Article
Noise Improves Multimodal Machine Translation: Rethinking the Role of Visual Context
by Xinyu Ma, Jun Rao and Xuebo Liu
Mathematics 2025, 13(11), 1874; https://doi.org/10.3390/math13111874 - 3 Jun 2025
Viewed by 367
Abstract
Multimodal Machine Translation (MMT) has long been assumed to outperform traditional text-only MT by leveraging visual information. However, recent studies challenge this assumption, showing that MMT models perform similarly even when tested without images or with mismatched images. This raises fundamental questions about [...] Read more.
Multimodal Machine Translation (MMT) has long been assumed to outperform traditional text-only MT by leveraging visual information. However, recent studies challenge this assumption, showing that MMT models perform similarly even when tested without images or with mismatched images. This raises fundamental questions about the actual utility of visual information in MMT, which this work aims to investigate. We first revisit commonly used image-must and image-free MMT approaches, identifying that suboptimal performance may stem from insufficiently robust baseline models. To further examine the role of visual information, we propose a novel visual type regularization method and introduce two probing tasks—Visual Contribution Probing and Modality Relationship Probing—to analyze whether and how visual features influence a strong MMT model. Surprisingly, our findings on a mainstream dataset indicate that the gains from visual information are marginal. We attribute this improvement primarily to a regularization effect, which can be replicated using random noise. Our results suggest that the MMT community should critically re-evaluate baseline models, evaluation metrics, and dataset design to advance multimodal learning meaningfully. Full article
(This article belongs to the Special Issue Artificial Intelligence: Deep Learning and Computer Vision)
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19 pages, 289 KiB  
Article
Some New Sobolev-Type Theorems for the Rough Riesz Potential Operator on Grand Variable Herz Spaces
by Ghada AlNemer, Ghada Ali Basendwah, Babar Sultan and Ioan-Lucian Popa
Mathematics 2025, 13(11), 1873; https://doi.org/10.3390/math13111873 - 3 Jun 2025
Viewed by 265
Abstract
In this paper, our first objective is to define the idea of grand variable Herz spaces. Then, our main goal is to prove boundedness results for operators, including the rough Riesz potential operator of variable order and the fractional Hardy operators, on grand [...] Read more.
In this paper, our first objective is to define the idea of grand variable Herz spaces. Then, our main goal is to prove boundedness results for operators, including the rough Riesz potential operator of variable order and the fractional Hardy operators, on grand variable Herz spaces under some proper assumptions. To prove the boundedness results, we use Holder-type and Minkowski inequalities. In the proof of the main result, we use different techniques. We divide the summation into different terms and estimate each term under different conditions. Then, by combining the estimates, we prove that the rough Riesz potential operator of variable order and the fractional Hardy operators are bounded on grand variable Herz spaces. It is easy to show that the rough Riesz potential operator of variable order generalizes the Riesz potential operator and that the fractional Hardy operators are generalized versions of simple Hardy operators. So, our results extend some previous results to the more generalized setting of grand variable Herz spaces. Full article
(This article belongs to the Special Issue Advances on Complex Analysis, 2nd Edition)
13 pages, 2752 KiB  
Article
Chaos, Hyperchaos and Transient Chaos in a 4D Hopfield Neural Network: Numerical Analyses and PSpice Implementation
by Victor Kamdoum Tamba, Gaetant Ngoko, Viet-Thanh Pham and Giuseppe Grassi
Mathematics 2025, 13(11), 1872; https://doi.org/10.3390/math13111872 - 3 Jun 2025
Viewed by 317
Abstract
The human brain is an extremely sophisticated system. Several neural models have been proposed to mimic and understand brain function. Most of them incorporate memristors to simulate autapse or self-coupling, electromagnetic radiation and the synaptic weight of the neuron. This article introduces and [...] Read more.
The human brain is an extremely sophisticated system. Several neural models have been proposed to mimic and understand brain function. Most of them incorporate memristors to simulate autapse or self-coupling, electromagnetic radiation and the synaptic weight of the neuron. This article introduces and studies the dynamics of a Hopfield neural network (HNN) consisting of four neurons, where one of the synaptic weights of the neuron is replaced by a memristor. Theoretical aspects such as dissipation, the requirements for the existence of attractors, symmetry, equilibrium states and stability are studied. Numerical investigations of the model reveal that it develops very rich and diverse behaviors such as chaos, hyperchaos and transient chaos. These results obtained numerically are further supported by the results obtained from an electronic circuit of the system, constructed and simulated in PSpice. Both approaches show good agreement. In light of the findings from the numerical and experimental studies, it appears that the 4D Hopfield neural network under consideration in this work is more complex than its original version, which did not include a memristor. Full article
(This article belongs to the Special Issue Chaotic Systems and Their Applications, 2nd Edition)
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