Mathematics

29 pages, 899 KiB

Open AccessArticle

A Three-Level Meta-Frontier Framework with Machine Learning Projections for Carbon Emission Efficiency Analysis: Heterogeneity Decomposition and Policy Implications

by Xiaoxia Zhu, Tongyue Feng, Yuhe Shen, Ning Zhang and Xu Guo

Mathematics 2025, 13(9), 1542; https://doi.org/10.3390/math13091542 - 7 May 2025

Viewed by 203

Abstract

This study proposes a three-level meta-frontier framework enhanced with machine learning-driven projection methods to address the dual heterogeneity in carbon emission efficiency analysis arising from regional disparities and industrial diversification. Methodologically, we introduce two novel projection combinations—“exogenous-exogenous-accumulation (E-E-A) and exogenous-exogenous-consistent (E-E-C)”—to resolve the [...] Read more.

This study proposes a three-level meta-frontier framework enhanced with machine learning-driven projection methods to address the dual heterogeneity in carbon emission efficiency analysis arising from regional disparities and industrial diversification. Methodologically, we introduce two novel projection combinations—“exogenous-exogenous-accumulation (E-E-A) and exogenous-exogenous-consistent (E-E-C)”—to resolve the inconsistency of technology gap ratios (TGRs > 1) in traditional nonradial directional distance function (DDF) models. Reinforcement learning (RL) optimizes dynamic direction vectors, whereas graph neural networks (GNNs) encode spatial interdependencies to constrain the TGR within [0, 1]. Empirical analysis of 60 countries reveals that (1) E-E-C eliminates the TGR overestimation by 12–18% in energy-intensive sectors (e.g., reducing Asia’s secondary industry

T G R_{1}

from 1.160 to 1.000); (2) industrial heterogeneity dominates inefficiency in Asia (IHI = 0.207), whereas management gaps drive global secondary sector inefficiency (MI = 0.678); and (3) policy simulations advocate for decentralized renewables in Africa, fiscal incentives for Asian coal retrofits, and expanded EU carbon border taxes. Computational enhancements via Apache Spark achieve a 58% runtime reduction. The framework advances environmental efficiency analysis by integrating machine learning with meta-frontier theory, offering both methodological rigor (via regularization and GNN constraints) and actionable decarbonization pathways. Limitations include static heterogeneity assumptions and data granularity gaps, prompting the future integration of IoT-enabled dynamic models. Full article

(This article belongs to the Special Issue Computational and Mathematical Methods in Information Science and Engineering, 2nd Edition)

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23 pages, 443 KiB

Open AccessArticle

Revocable Attribute-Based Encryption with Efficient and Secure Verification in Smart Health Systems

by Zhou Chen, Lidong Han and Baokun Hu

Mathematics 2025, 13(9), 1541; https://doi.org/10.3390/math13091541 - 7 May 2025

Viewed by 160

Abstract

By leveraging Internet of Things (IoT) technology, patients can utilize medical devices to upload their collected personal health records (PHRs) to the cloud for analytical processing or transmission to doctors, which embodies smart health systems and greatly enhances the efficiency and accessibility of [...] Read more.

By leveraging Internet of Things (IoT) technology, patients can utilize medical devices to upload their collected personal health records (PHRs) to the cloud for analytical processing or transmission to doctors, which embodies smart health systems and greatly enhances the efficiency and accessibility of healthcare management. However, the highly sensitive nature of PHRs necessitates efficient and secure transmission mechanisms. Revocable and verifiable attribute-based encryption (ABE) enables dynamic fine-grained access control and can verify the integrity of outsourced computation results via a verification tag. However, most existing schemes have two vital issues. First, in order to achieve the verifiable function, they need to execute the secret sharing operation twice during the encryption process, which significantly increases the computational overhead. Second, during the revocation operation, the verification tag is not updated simultaneously, so revoked users can infer plaintext through the unchanged tag. To address these challenges, we propose a revocable ABE scheme with efficient and secure verification, which not only reduces local computational load by optimizing the encryption algorithm and outsourcing complex operations to the cloud server, but also updates the tag when revocation operation occurs. We present a rigorous security analysis of our proposed scheme, and show that the verification tag retains its verifiability even after being dynamically updated. Experimental results demonstrate that local encryption and decryption costs are stable and low, which fully meets the real-time and security requirements of smart health systems. Full article

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33 pages, 7332 KiB

Open AccessArticle

Synergistic Integration of Edge Computing and 6G Networks for Real-Time IoT Applications

by Ahmed M. Alwakeel

Mathematics 2025, 13(9), 1540; https://doi.org/10.3390/math13091540 - 7 May 2025

Viewed by 297

Abstract

The rapid proliferation of Internet of Things (IoT) applications necessitates real-time data processing and low-latency communication, challenging traditional cloud computing paradigms. This research addresses these challenges by integrating edge computing with emerging 6G networks, proposing the ARMO (Adaptive Resource Management and Offloading) model. [...] Read more.

The rapid proliferation of Internet of Things (IoT) applications necessitates real-time data processing and low-latency communication, challenging traditional cloud computing paradigms. This research addresses these challenges by integrating edge computing with emerging 6G networks, proposing the ARMO (Adaptive Resource Management and Offloading) model. The ARMO model leverages intelligent task scheduling, dynamic resource allocation, and energy-efficient strategies to enhance the performance of edge computing environments. Our comprehensive methodology involves collecting and preprocessing data from IoT devices, extracting relevant features, predicting resource demand, optimizing task offloading, and continuously monitoring and adjusting resource allocation using advanced machine learning techniques. The results demonstrate significant improvements, including a 47% reduction in average latency, a 40% decrease in total energy consumption, and a 20% increase in resource utilization. Additionally, the model achieved a 98% task completion rate and consistently higher network throughput compared to previous models. These findings underscore the ARMO model’s potential to support the next generation of real-time IoT applications, providing a robust, efficient, and scalable solution for integrating edge computing with 6G networks. Full article

(This article belongs to the Special Issue Application of Artificial Intelligence in Decision Making)

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43 pages, 7821 KiB

Open AccessArticle

Network Optimization of Fresh Products Cold Chain Considering Supply Disruption and Demand Fluctuation Under the Dual-Carbon Policy

by Haojie Ran, Dichen He and Huajun Tang

Mathematics 2025, 13(9), 1539; https://doi.org/10.3390/math13091539 - 7 May 2025

Viewed by 178

Abstract

Against global industrial upgrading and China’s “dual-carbon” policy, the cold chain for fresh products faces numerous challenges such as supply disruptions, demand fluctuations, and low-carbon transformation. This study focuses on introducing the key optimization goals of the cold chain network for fresh products: [...] Read more.

Against global industrial upgrading and China’s “dual-carbon” policy, the cold chain for fresh products faces numerous challenges such as supply disruptions, demand fluctuations, and low-carbon transformation. This study focuses on introducing the key optimization goals of the cold chain network for fresh products: maximizing the service level while minimizing operating costs and carbon emissions. To this end, this study proposes a high-dimensional multi-objective optimization model for the cold chain network of fresh products and designs four resilience strategies to address supply disruption and demand fluctuation scenarios. To solve this model, this study innovatively designs a hybrid algorithm combining neighborhood search and swarm intelligence, integrating the advantages of local exploration and global optimization to balance the relationships among multiple objectives efficiently. In addition, this study conducts a real-world case analysis to verify the effectiveness of the proposed model and the algorithm. Furthermore, by deeply exploring the comprehensive impacts of supply disruptions and demand fluctuations on the cold chain network for fresh products, the mechanism of action of resilience strategies in dealing with supply chain risks is highlighted. The research results provide valuable decision-making support for fresh cold chain enterprises to develop resilient and low-carbon network optimization strategies for cost reduction, efficiency improvement, and sustainable development. Full article

(This article belongs to the Section E2: Control Theory and Mechanics)

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17 pages, 1451 KiB

Open AccessArticle

Correctness Coverage Evaluation for Medical Multiple-Choice Question Answering Based on the Enhanced Conformal Prediction Framework

by Yusong Ke, Hongru Lin, Yuting Ruan, Junya Tang and Li Li

Mathematics 2025, 13(9), 1538; https://doi.org/10.3390/math13091538 - 7 May 2025

Viewed by 165

Abstract

Large language models (LLMs) are increasingly adopted in medical question answering (QA) scenarios. However, LLMs have been proven to generate hallucinations and nonfactual information, undermining their trustworthiness in high-stakes medical tasks. Conformal Prediction (CP) is now recognized as a robust framework within the [...] Read more.

Large language models (LLMs) are increasingly adopted in medical question answering (QA) scenarios. However, LLMs have been proven to generate hallucinations and nonfactual information, undermining their trustworthiness in high-stakes medical tasks. Conformal Prediction (CP) is now recognized as a robust framework within the broader domain of machine learning, offering statistically rigorous guarantees of marginal (average) coverage for prediction sets. However, the applicability of CP in medical QA remains to be explored. To address this limitation, this study proposes an enhanced CP framework for medical multiple-choice question answering (MCQA) tasks. The enhanced CP framework associates the non-conformance score with the frequency score of the correct option. The framework generates multiple outputs for the same medical query by leveraging self-consistency theory. The proposed framework calculates the frequency score of each option to address the issue of limited access to the model’s internal information. Furthermore, a risk control framework is incorporated into the enhanced CP framework to manage task-specific metrics through a monotonically decreasing loss function. The enhanced CP framework is evaluated on three popular MCQA datasets using off-the-shelf LLMs. Empirical results demonstrate that the enhanced CP framework achieves user-specified average (or marginal) error rates on the test set. Moreover, the results show that the test set’s average prediction set size (APSS) decreases as the risk level increases. It is concluded that it is a promising evaluation metric for the uncertainty of LLMs. Full article

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18 pages, 1139 KiB

Open AccessArticle

Expressions for the First Two Moments of the Range of Normal Random Variables with Applications to the Range Control Chart

by Don G. Wardell

Mathematics 2025, 13(9), 1537; https://doi.org/10.3390/math13091537 - 7 May 2025

Viewed by 112

Abstract

A common and simple estimate of variability is the sample range, which is the difference between the maximum and minimum values in the sample. While other measures of variability are preferred in most instances, process owners and operators regularly use range (R) control [...] Read more.

A common and simple estimate of variability is the sample range, which is the difference between the maximum and minimum values in the sample. While other measures of variability are preferred in most instances, process owners and operators regularly use range (R) control charts to monitor process variability. The center line and limits of the R charts use constants that are based on the first two moments (mean and variance) of the distribution of the range of normal random variables. Historically, the computation of moments requires the use of tabulated constants approximated using numerical integration. We provide exact results for the moments for sample sizes 2 through 5. For sample sizes from 6 to 1000, we used the differential correction method to find Chebyshev minimax rational-function approximations of the moments. The rational function we recommend for the mean (R-chart constant d₂) has a polynomial of order two in the numerator and six in the denominator and achieves a maximum error of 4.4 × 10⁻⁶. The function for the standard deviation (R-chart constant d₃) has a polynomial of order two in the numerator and seven in the denominator and achieves a maximum error of 1.5 × 10⁻⁵. The exact and approximate expressions eliminate the need for table lookup in the control chart design phase. Full article

(This article belongs to the Section D: Statistics and Operational Research)

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25 pages, 873 KiB

Open AccessArticle

Statistical Inference for Two Lomax Populations Under Balanced Joint Progressive Type-II Censoring Scheme

by Yuanqi Wang, Jinchen Xiang and Wenhao Gui

Mathematics 2025, 13(9), 1536; https://doi.org/10.3390/math13091536 - 7 May 2025

Viewed by 120

Abstract

In recent years, joint censoring schemes have gained significant attention in lifetime experiments and reliability analysis. A refined approach, known as the balanced joint progressive censoring scheme, has been introduced in statistical studies. This research focuses on statistical inference for two Lomax populations [...] Read more.

In recent years, joint censoring schemes have gained significant attention in lifetime experiments and reliability analysis. A refined approach, known as the balanced joint progressive censoring scheme, has been introduced in statistical studies. This research focuses on statistical inference for two Lomax populations under this censoring framework. Maximum likelihood estimation is employed to derive parameter estimates, and asymptotic confidence intervals are constructed using the observed Fisher information matrix. From a Bayesian standpoint, posterior estimates of the unknown parameters are obtained under informative prior assumptions. To evaluate the effectiveness and precision of these estimators, a numerical study is conducted. Additionally, a real dataset is analyzed to demonstrate the practical application of these estimation methods. Full article

(This article belongs to the Section D1: Probability and Statistics)

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13 pages, 2179 KiB

Open AccessArticle

Semi-Supervised Clustering via Constraints Self-Learning

by Xin Sun

Mathematics 2025, 13(9), 1535; https://doi.org/10.3390/math13091535 - 7 May 2025

Viewed by 117

Abstract

So far, most of the semi-supervised clustering algorithms focus on finding a suitable partition that well satisfies the given constraints. However, insufficient supervisory information may lead to over-fitting results and unstable performance, especially on complicated data. To address this challenge, this paper attempts [...] Read more.

So far, most of the semi-supervised clustering algorithms focus on finding a suitable partition that well satisfies the given constraints. However, insufficient supervisory information may lead to over-fitting results and unstable performance, especially on complicated data. To address this challenge, this paper attempts to solve the semi-supervised clustering problem by self-learning sufficient constraints. The essential motivation is that constraints can be learned from the local neighbor structures within appropriate feature spaces, and sufficient constraints can directly divide the data into clusters. Hence, we first present a constraint self-learning framework. It performs an expectation–maximization procedure iteratively between exploring a discriminant space and learning new constraints. Then, a constraint-based clustering algorithm is proposed by taking advantage of sufficient constraints. Experimental studies on various real-world benchmark datasets show that the proposed algorithm achieves promising performance and outperforms the state-of-the-art semi-supervised clustering algorithms. Full article

(This article belongs to the Special Issue Artificial Intelligence Applications with Advanced Mathematical Methods)

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19 pages, 1196 KiB

Open AccessArticle

Fixed-Time Event-Triggered Consensus Power-Sharing Control for Hybrid AC/DC Microgrid Parallel Bi-Directional Interconnect Converters

by Junjie Wu, Siyu Lyu, Benhua Qian, Chuanyu Jiang, Ziqaing Song and Jun Xiao

Mathematics 2025, 13(9), 1534; https://doi.org/10.3390/math13091534 - 7 May 2025

Viewed by 100

Abstract

Although power sharing in hybrid AC/DC microgrids (HMGs) has been widely researched, traditional power-sharing control is based on an infinite time consensus method, and the communication bandwidth is large. Therefore, this paper proposes a power-sharing strategy for HMG parallel bi-directional interconnected converters (BICs) [...] Read more.

Although power sharing in hybrid AC/DC microgrids (HMGs) has been widely researched, traditional power-sharing control is based on an infinite time consensus method, and the communication bandwidth is large. Therefore, this paper proposes a power-sharing strategy for HMG parallel bi-directional interconnected converters (BICs) considering fixed-time stabilization and event-triggered control. Firstly, every BIC has a well-designed local control method to generate the corresponding power reference for the BIC, which provides the basis for further research. Secondly, a fixed-time-based power-sharing controller is designed in order to improve the convergence speed of power-sharing control for HMG parallel BICs. Finally, an event-triggered method is applied to reduce the system communication bandwidth and the frequency of controller updates. In this paper, we first transform the parallel BIC control problem into a multi-agent system (MAS) consensus problem. Furthermore, a fixed time based on an event trigger consensus method is proposed at the secondary control level. The energy flow between the two subgrids can be shared according to the rated power of each BIC. Finally, the effectiveness of the proposed fixed-time event-triggered power-sharing control is verified through simulation and experiments. Full article

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20 pages, 918 KiB

Open AccessArticle

The Linear Stability of a Power-Law Liquid Film Flowing Down an Inclined Deformable Plane

by Karim Ladjelate, Nadia Mehidi Bouam, Amar Djema, Abdelkader Belhenniche and Roman Chertovskih

Mathematics 2025, 13(9), 1533; https://doi.org/10.3390/math13091533 - 7 May 2025

Viewed by 126

Abstract

A linear stability analysis is performed for a power-law liquid film flowing down an inclined rigid plane over a deformable solid layer. The deformable solid is modeled using a neo-Hookean constitutive equation, characterized by a constant shear modulus and a nonzero first normal [...] Read more.

A linear stability analysis is performed for a power-law liquid film flowing down an inclined rigid plane over a deformable solid layer. The deformable solid is modeled using a neo-Hookean constitutive equation, characterized by a constant shear modulus and a nonzero first normal stress difference in the base state at the fluid–solid interface. To solve the linearized eigenvalue problem, the Riccati transformation method, which offers advantages over traditional techniques by avoiding the parasitic growth seen in the shooting method and eliminating the need for large-scale matrix eigenvalue computations, was used. This method enhances both analytical clarity and computational efficiency. Results show that increasing solid deformability destabilizes the flow at low Reynolds numbers by promoting short-wave modes, while its effect becomes negligible at high Reynolds numbers where inertia dominates. The fluid’s rheology also plays a key role: at low Reynolds numbers, shear-thinning fluids (

n < 1

) are more prone to instability, whereas at high Reynolds numbers, shear-thickening fluids (

n > 1

) exhibit a broader unstable regime. Full article

(This article belongs to the Special Issue Advances and Applications in Computational Fluid Dynamics)

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13 pages, 1366 KiB

Open AccessArticle

Structure Fault Tolerance of Fully Connected Cubic Networks

by Eminjan Sabir and Cheng-Kuan Lin

Mathematics 2025, 13(9), 1532; https://doi.org/10.3390/math13091532 - 7 May 2025

Viewed by 88

Abstract

An interconnection network is usually modeled by a graph, and fault tolerance of the interconnection network is often measured by connectivity of the graph. Given a connected subgraph L of a graph G and non-negative integer t, the t-extra connectivity [...] Read more.

An interconnection network is usually modeled by a graph, and fault tolerance of the interconnection network is often measured by connectivity of the graph. Given a connected subgraph L of a graph G and non-negative integer t, the t-extra connectivity

κ_{t} (G)

, the L-structure connectivity

κ (G; L)

and the t-extra L-structure connectivity

κ_{g} (G; L)

of G can provide new metrics to measure the fault tolerance of a network represented by G. Fully connected cubic networks

{FC}_{n}

are a class of hierarchical networks which enjoy the strengths of a constant vertex degree and good expansibility. In this paper, we determine

κ_{t} ({FC}_{n})

,

κ ({FC}_{n}; L)

and

κ_{t} ({FC}_{n}; L)

for

t = 1

and

L \in {K_{1, 1}, K_{1, 2}, K_{1, 3}}

. We also establish the edge versions

λ_{t} ({FC}_{n})

,

λ ({FC}_{n}; L)

and

λ_{t} ({FC}_{n}; L)

for

t = 1

and

L \in {K_{1, 1}, K_{1, 2}}

. Full article

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26 pages, 7904 KiB

Open AccessArticle

Sustainable PV Power Forecasting via MPA-VMD Optimized BiGRU with Attention Mechanism

by Yongmei Ding, Shangnan Zhou and Wenwu Deng

Mathematics 2025, 13(9), 1531; https://doi.org/10.3390/math13091531 - 7 May 2025

Viewed by 125

Abstract

Accurate photovoltaic (PV) power generation forecasting is crucial for optimizing grid management and enhancing the reliability of sustainable energy systems. This study creates a novel hybrid model—MPA-VMD-BiGRU-MAM—designed to improve PV power forecasting accuracy through advanced decomposition and deep learning techniques. Initially, the Kendall [...] Read more.

Accurate photovoltaic (PV) power generation forecasting is crucial for optimizing grid management and enhancing the reliability of sustainable energy systems. This study creates a novel hybrid model—MPA-VMD-BiGRU-MAM—designed to improve PV power forecasting accuracy through advanced decomposition and deep learning techniques. Initially, the Kendall correlation coefficient is applied to identify key influencing factors, ensuring robust feature selection for the model inputs. The Marine Predator Algorithm (MPA) optimizes the hyperparameters of Variational Mode Decomposition (VMD), effectively segmenting the PV power time series into informative sub-modes. These sub-modes are processed using a bidirectional gated recurrent unit (BiGRU) enhanced with a multi-head attention mechanism (MAM), enabling dynamic weight assignment and comprehensive feature extraction. Empirical evaluations on PV datasets from Alice Springs, Australia, and Belgium indicate that our hybrid model consistently surpasses baseline methods and achieves a 38.34% reduction in Mean Absolute Error (MAE), a 19.6% reduction in Root Mean Square Error (RMSE), a 4.41% improvement in goodness of fit, and a 33.91% increase in stability (STA) for the Australian dataset. For the Belgian dataset, the model attains a 96.32% reduction in MAE, a 95.84% decrease in RMSE, an 11.92% enhancement in goodness of fit, and an STA of 92.08%. We demonstrate the model’s effectiveness in capturing seasonal trends and addressing the inherent variability in PV power generation, offering a reliable solution to the challenges of instability, intermittency, and unpredictability in renewable energy sources. Full article

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23 pages, 495 KiB

Open AccessArticle

Multi-View Graph Contrastive Neural Networks for Session-Based Recommendation

by Pengbo Huang and Chun Wang

Mathematics 2025, 13(9), 1530; https://doi.org/10.3390/math13091530 - 6 May 2025

Viewed by 269

Abstract

Session-based recommendation (SBR) aims to predict the next item a user may interact with based on an anonymous session, playing a crucial role in real-time recommendation scenarios. However, existing SBR models struggle to effectively capture local session dependencies and global item relationships, while [...] Read more.

Session-based recommendation (SBR) aims to predict the next item a user may interact with based on an anonymous session, playing a crucial role in real-time recommendation scenarios. However, existing SBR models struggle to effectively capture local session dependencies and global item relationships, while also facing challenges such as data sparsity and noisy information interference. To address these challenges, this paper proposes a novel Multi-View Graph Contrastive Learning Neural Network (MVGCL-GNN), which enhances recommendation performance through multi-view graph modeling and contrastive learning. Specifically, we construct three key graph structures: a session graph for modeling short-term item dependencies, a global item graph for capturing cross-session item transitions, and a global category graph for learning category-level relationships. In addition, we introduce simple graph contrastive learning to improve embedding quality and reduce noise interference. Furthermore, a soft attention mechanism is employed to effectively integrate session-level and global-level information representations. Extensive experiments conducted on two real-world datasets demonstrate that MVGCL-GNN consistently outperforms state-of-the-art baselines. MVGCL-GNN achieves 34.96% in P@20 and 16.50% in MRR@20 on the Tmall dataset, and 22.59% in P@20 and 8.60% in MRR@20 on the Nowplaying dataset. These results validate the effectiveness of multi-view graphs and contrastive learning in improving both accuracy and robustness for session-based recommendation tasks. Full article

(This article belongs to the Special Issue Advanced Image Processing and Computational Intelligence: Methodologies and Applications)

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25 pages, 3233 KiB

Open AccessFeature PaperArticle

Multi-Domain Controversial Text Detection Based on a Machine Learning and Deep Learning Stacked Ensemble

by Jiadi Liu, Zhuodong Liu, Qiaoqi Li, Weihao Kong and Xiangyu Li

Mathematics 2025, 13(9), 1529; https://doi.org/10.3390/math13091529 - 6 May 2025

Viewed by 207

Abstract

Due to the rapid proliferation of social media and online reviews, the accurate identification and classification of controversial texts has emerged as a significant challenge in the field of natural language processing. However, traditional text-classification methodologies frequently encounter critical limitations, such as feature [...] Read more.

Due to the rapid proliferation of social media and online reviews, the accurate identification and classification of controversial texts has emerged as a significant challenge in the field of natural language processing. However, traditional text-classification methodologies frequently encounter critical limitations, such as feature sensitivity and inadequate generalization capabilities. This results in a notably suboptimal performance when confronted with diverse controversial content. To address these substantial limitations, this paper proposes a novel controversial text-detection framework based on stacked ensemble learning to enhance the accuracy and robustness of text classification. Firstly, considering the multidimensional complexity of textual features, we integrate comprehensive feature engineering, i.e., encompassing word frequency, statistical metrics, sentiment analysis, and comment tree structure features, as well as advanced feature selection methodologies, particularly lassonet, i.e., a neural network with feature sparsity, to effectively address dimensionality challenges while enhancing model interpretability and computational efficiency. Secondly, we design a two-tier stacked ensemble architecture, which not only combines the strengths of multiple machine learning algorithms, e.g., gradient-boosted decision tree (GBDT), random forest (RF), and extreme gradient boosting (XGBoost), with deep learning models, e.g., gated recurrent unit (GRU) and long short-term memory (LSTM), but also implements the support vector machine (SVM) for efficient meta-learning. Furthermore, we systematically compare three hyperparameter optimization algorithms, including the sparrow search algorithm (SSA), particle swarm optimization (PSO), and Bayesian optimization (BO). The experimental results demonstrate that the SSA exhibits a superior performance in exploring high-dimensional parameter spaces. Extensive experimentation across diverse topics and domains also confirms that our proposed methodology significantly outperforms the state-of-the-art approaches. Full article

(This article belongs to the Special Issue Machine Learning Methods and Mathematical Modeling with Applications)

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21 pages, 2514 KiB

Open AccessFeature PaperArticle

United Prediction of Travel Modes and Purposes in Travel Chains Based on Multitask Learning Deep Neural Networks

by Chenxi Xiao, Zhitao Li, Jinjun Tang and Jeanyoung Jay Lee

Mathematics 2025, 13(9), 1528; https://doi.org/10.3390/math13091528 - 6 May 2025

Viewed by 157

Abstract

Predicting and analyzing travel mode choices and purposes are significant to improve urban travel mobility and transportation planning. Previous research has ignored the interconnection between travel mode choices and purposes and thus overlooked their potential contributions to predictions. Using individual travel chain data [...] Read more.

Predicting and analyzing travel mode choices and purposes are significant to improve urban travel mobility and transportation planning. Previous research has ignored the interconnection between travel mode choices and purposes and thus overlooked their potential contributions to predictions. Using individual travel chain data collected in South Korea, this study proposes a Multi-Task Learning Deep Neural Network (MTLDNN) framework, integrating RFM (Recency, Frequency, Monetary) to achieve a joint prediction of travel mode choices and purposes. The MTLDNN is constructed to share a common hidden layer that extracts general features from the input data, while task-specific output layers are dedicated to predicting travel modes and purposes separately. This structure allows for efficient learning of shared representations while maintaining the capacity to model task-specific relationships. RFM is then integrated to optimize the extraction of users’ behavioral features, which helps in better understanding the temporal and financial patterns of users’ travel activities. The results show that the MTLDNN demonstrates consistent input variable replacement modes and selection probabilities in generating behavioral replacement patterns. Compared to the multinomial logit model (MNL), the MTLDNN achieves lower cross-entropy loss and higher prediction accuracy. The proposed framework could enhance transportation planning, efficiency, and user satisfaction by enabling more accurate predictions. Full article

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17 pages, 467 KiB

Open AccessFeature PaperArticle

Multivariate Extension Application for Spearman’s Footrule Correlation Coefficient

by Liqi Xia, Sami Ullah and Li Guan

Mathematics 2025, 13(9), 1527; https://doi.org/10.3390/math13091527 - 6 May 2025

Viewed by 141

Abstract

This paper presents a simplified and computationally feasible multivariate extension. A correlation matrix is constructed using pairwise Spearman’s footrule correlation coefficients, and these coefficients are shown to jointly converge to a multivariate normal distribution. A global test statistic based on the Frobenius norm [...] Read more.

This paper presents a simplified and computationally feasible multivariate extension. A correlation matrix is constructed using pairwise Spearman’s footrule correlation coefficients, and these coefficients are shown to jointly converge to a multivariate normal distribution. A global test statistic based on the Frobenius norm of this matrix asymptotically follows a weighted sum of chi-square distributions. Simulation studies and two real-world applications (a sensory analysis of French Jura wines and the characterization of plant leaf specimens) demonstrate the practical utility of the proposed method, bridging the gap between theoretical rigor and practical implementation in multivariate nonparametric inference. Full article

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22 pages, 887 KiB

Open AccessArticle

On the Special Viviani’s Curve and Its Corresponding Smarandache Curves

by Yangke Deng, Yanlin Li, Süleyman Şenyurt, Davut Canlı and İremnur Gürler

Mathematics 2025, 13(9), 1526; https://doi.org/10.3390/math13091526 - 6 May 2025

Viewed by 156

Abstract

In the present paper, the special Viviani’s curve is revisited in the context of Smarandache geometry. Accordingly, the paper first defines the special Smarandache curves of Viviani’s curve, including the Darboux vector. Then, it expresses the resulting Frenet apparatus for each Smarandache curve [...] Read more.

In the present paper, the special Viviani’s curve is revisited in the context of Smarandache geometry. Accordingly, the paper first defines the special Smarandache curves of Viviani’s curve, including the Darboux vector. Then, it expresses the resulting Frenet apparatus for each Smarandache curve in terms of the Viviani’s curve. The paper is also supported by extensive graphical representations of Viviani’s curve and its Smarandache curves, as well as their respective curvatures. Full article

(This article belongs to the Special Issue Submanifolds in Metric Manifolds, 2nd Edition)

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22 pages, 387 KiB

Open AccessArticle

Sufficient Conditions for Optimal Stability in Hilfer–Hadamard Fractional Differential Equations

by Safoura Rezaei Aderyani, Reza Saadati and Donal O’Regan

Mathematics 2025, 13(9), 1525; https://doi.org/10.3390/math13091525 - 6 May 2025

Viewed by 135

Abstract

The primary objective of this study is to explore sufficient conditions for the existence, uniqueness, and optimal stability of positive solutions to a finite system of Hilfer–Hadamard fractional differential equations with two-point boundary conditions. Our analysis centers around transforming fractional differential equations into [...] Read more.

The primary objective of this study is to explore sufficient conditions for the existence, uniqueness, and optimal stability of positive solutions to a finite system of Hilfer–Hadamard fractional differential equations with two-point boundary conditions. Our analysis centers around transforming fractional differential equations into fractional integral equations under minimal requirements. This investigation employs several well-known special control functions, including the Mittag–Leffler function, the Wright function, and the hypergeometric function. The results are obtained by constructing upper and lower control functions for nonlinear expressions without any monotonous conditions, utilizing fixed point theorems, such as Banach and Schauder, and applying techniques from nonlinear functional analysis. To demonstrate the practical implications of the theoretical findings, a pertinent example is provided, which validates the results obtained. Full article

(This article belongs to the Special Issue Current Topics in Optimization, Inequalities and Convex Function Theory)

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26 pages, 5898 KiB

Open AccessArticle

Thermophysical Properties and Expectation Values for Pöschl–Teller-like Pseudo-Harmonic Oscillator

by Haifa I. Alrebdi, Uduakobong S. Okorie, Ridha Horchani, Gaotsiwe J. Rampho and Akpan N. Ikot

Mathematics 2025, 13(9), 1524; https://doi.org/10.3390/math13091524 - 6 May 2025

Viewed by 162

Abstract

The Nikiforov–Uvarov functional analysis (NUFA) formalism is employed to study approximately the eigensolutions of the Schrodinger equation with the Pöschl–Teller-like pseudo-harmonic oscillator (PTPO). The variations in the energy spectra and the wave functions as a function of the screening parameters for different quantum [...] Read more.

The Nikiforov–Uvarov functional analysis (NUFA) formalism is employed to study approximately the eigensolutions of the Schrodinger equation with the Pöschl–Teller-like pseudo-harmonic oscillator (PTPO). The variations in the energy spectra and the wave functions as a function of the screening parameters for different quantum states were investigated. With the energy expression of PTPO, the partition function and other thermodynamic function were obtained as a function of temperature for different values of the screening parameters using the Euler–Maclaurin formula. Using the Hellmann–Feynman theorem (HFT), we evaluate the expectation values of PTPO numerically and graphically for various values of the screening parameters and quantum states. It is observed that the eigensolutions, thermodynamic functions and expectation values of PTPO system are influenced by quantum states, screening parameters and temperature. Full article

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19 pages, 9204 KiB

Open AccessArticle

Numerical Study of Salt Ion Transport in Electromembrane Systems with Ion-Exchange Membranes Having Geometrically Structured Surfaces

by Evgenia Kirillova, Natalia Chubyr, Anna Kovalenko and Mahamet Urtenov

Mathematics 2025, 13(9), 1523; https://doi.org/10.3390/math13091523 - 6 May 2025

Viewed by 215

Abstract

This article is devoted to numerically modeling the effect of the geometric modification of the surfaces of ion-exchange membranes in electromembrane systems (EMSs) on the salt ion transport using a 2D mathematical model of the transport process in the desalination channel based on [...] Read more.

This article is devoted to numerically modeling the effect of the geometric modification of the surfaces of ion-exchange membranes in electromembrane systems (EMSs) on the salt ion transport using a 2D mathematical model of the transport process in the desalination channel based on boundary value problems for the coupled system of Nernst–Planck–Poisson and Navier–Stokes equations. The main patterns of salt ion transport are established taking into account diffusion, electromigration, forced convection, electroconvection, and the geometric modification of the surface of ion-exchange membranes. It is shown that the geometric modification of the surface of ion-exchange membranes significantly changes both the formation and development of electroconvection. A significant combined effect of electroconvection and geometric modification of the surface of ion-exchange membranes in the desalination channel on the salt ion transport is shown, as well as a complex, nonlinear, and non-stationary interaction of all the main effects of concentration polarization in the desalination channel. Full article

(This article belongs to the Special Issue Mathematical Applications in Electrical Engineering, 2nd Edition)

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28 pages, 1418 KiB

Open AccessArticle

Variable Selection for Additive Quantile Regression with Nonlinear Interaction Structures

by Yongxin Bai, Jiancheng Jiang and Maozai Tian

Mathematics 2025, 13(9), 1522; https://doi.org/10.3390/math13091522 - 5 May 2025

Viewed by 225

Abstract

In high-dimensional data analysis, main effects and interaction effects often coexist, especially when complex nonlinear relationships are present. Effective variable selection is crucial for avoiding the curse of dimensionality and enhancing the predictive performance of a model. In this paper, we introduce a [...] Read more.

In high-dimensional data analysis, main effects and interaction effects often coexist, especially when complex nonlinear relationships are present. Effective variable selection is crucial for avoiding the curse of dimensionality and enhancing the predictive performance of a model. In this paper, we introduce a nonlinear interaction structure into the additive quantile regression model and propose an innovative penalization method. This method considers the complexity and smoothness of the additive model and incorporates heredity constraints on main effects and interaction effects through an improved regularization algorithm under marginality principle. We also establish the asymptotic properties of the penalized estimator and provide the corresponding excess risk. Our Monte Carlo simulations illustrate the proposed model and method, which are then applied to the analysis of Parkinson’s disease rating scores and further verify the effectiveness of a novel Parkinson’s disease (PD) treatment. Full article

(This article belongs to the Section D1: Probability and Statistics)

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32 pages, 876 KiB

Open AccessArticle

Physics-Informed Neural Networks and Fourier Methods for the Generalized Korteweg–de Vries Equation

by Rubén Darío Ortiz Ortiz, Ana Magnolia Marín Ramírez and Miguel Ángel Ortiz Marín

Mathematics 2025, 13(9), 1521; https://doi.org/10.3390/math13091521 - 5 May 2025

Viewed by 323

Abstract

We conducted a comprehensive comparative study of numerical solvers for the generalized Korteweg–de Vries (gKdV) equation, focusing on classical Fourier-based Crank–Nicolson methods and physics-informed neural networks (PINNs). Our work benchmarks these approaches across nonlinear regimes—including the cubic case (

ν = 3

)—and [...] Read more.

We conducted a comprehensive comparative study of numerical solvers for the generalized Korteweg–de Vries (gKdV) equation, focusing on classical Fourier-based Crank–Nicolson methods and physics-informed neural networks (PINNs). Our work benchmarks these approaches across nonlinear regimes—including the cubic case (

ν = 3

)—and diverse initial conditions such as solitons, smooth pulses, discontinuities, and noisy profiles. In addition to pure PINN and spectral models, we propose a novel hybrid PINN–spectral method incorporating a regularization term based on Fourier reference solutions, leading to improved accuracy and stability. Numerical experiments show that while spectral methods achieve superior efficiency in structured domains, PINNs provide flexible, mesh-free alternatives for data-driven and irregular setups. The hybrid model achieves lower relative

L^{2}

error and better captures soliton interactions. Our results demonstrate the complementary strengths of spectral and machine learning methods for nonlinear dispersive PDEs. Full article

(This article belongs to the Special Issue Asymptotic Analysis and Applications)

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25 pages, 1867 KiB

Open AccessArticle

Nonlinear Mathematical Modeling and Robust Control of UAV Formation Under Parametric Variations and External Disturbances

by Claudia Verónica Vera Vaca, Stefano Di Gennaro, Claudia Carolina Vaca García and Cuauhtémoc Acosta Lúa

Mathematics 2025, 13(9), 1520; https://doi.org/10.3390/math13091520 - 5 May 2025

Viewed by 340

Abstract

This paper introduces a robust formation control strategy for Unmanned Aerial Vehicles (UAVs) designed to maintain coordinated trajectories and relative positioning in three-dimensional space. The proposed methodology addresses the challenges of parametric uncertainties and external disturbances by employing a backstepping-based framework with integrated [...] Read more.

This paper introduces a robust formation control strategy for Unmanned Aerial Vehicles (UAVs) designed to maintain coordinated trajectories and relative positioning in three-dimensional space. The proposed methodology addresses the challenges of parametric uncertainties and external disturbances by employing a backstepping-based framework with integrated proportional-integral virtual controls. The control strategy stabilizes tracking errors in the x, y, and z axes, ensuring that the UAVs maintain a cohesive formation even in the presence of dynamic model variations and environmental perturbations. The approach combines dynamic models of UAV motion, incorporating translational and rotational behaviors, with a decomposition of relative distances in the leader’s local reference frame to ensure precise formation control. This framework enhances stability, trajectory tracking, and disturbance rejection. Validation through MATLAB-Simulink simulations demonstrates the effectiveness of the proposed strategy, showcasing its ability to maintain formation and trajectory adherence under diverse operating conditions. The results emphasize the robustness and flexibility of the control approach, making it suitable for demanding applications requiring precise multi-UAV coordination. Full article

(This article belongs to the Special Issue Advances in Nonlinear Control Theory Applied to Dynamic Systems)

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15 pages, 983 KiB

Open AccessArticle

Task-Oriented Local Feature Rectification Network for Few-Shot Image Classification

by Ping Li and Xiang Zhu

Mathematics 2025, 13(9), 1519; https://doi.org/10.3390/math13091519 - 5 May 2025

Viewed by 229

Abstract

Few-shot image classification aims to classify unlabeled samples when only a small number of labeled samples are available for each class. Recently, local feature-based few-shot learning methods have made significant progress. However, existing methods often treat all local descriptors equally, without considering the [...] Read more.

Few-shot image classification aims to classify unlabeled samples when only a small number of labeled samples are available for each class. Recently, local feature-based few-shot learning methods have made significant progress. However, existing methods often treat all local descriptors equally, without considering the importance of each local descriptor in different tasks. Therefore, the few-shot learning model is easily disturbed by class-irrelevant features, which results in a decrease in accuracy. To address this issue, we propose a task-oriented local feature rectification network (TLFRNet) with two feature rectification modules (support rectification module and query rectification module). The former module uses the relationship between each local descriptor and prototypes within the support set to rectify the support features. The latter module uses a CNN to rectify the similarity tensors between the query and support local features and then models the importance of the query local features. Through these two modules, our model can effectively reduce the intra-class variation of class-relevant features, thus obtaining more accurate image-to-class similarity for classification. Extensive experiments on five datasets show that TLFRNet achieves more superior classification performance than the related methods. Full article

(This article belongs to the Topic Soft Computing and Machine Learning)

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27 pages, 1276 KiB

Open AccessArticle

Transient Post-Buckling of Microfluid-Conveying FG-CNTs Cylindrical Microshells Embedded in Kerr Foundation and Exposed to a 2D Magnetic Field

by Mohammed Sobhy

Mathematics 2025, 13(9), 1518; https://doi.org/10.3390/math13091518 - 5 May 2025

Viewed by 174

Abstract

Dynamic post-buckling behavior of microscale cylindrical shells reinforced with functionally graded carbon nanotubes (FG-CNTs) and conveying microfluid is discussed for the first time. The microshell is embedded in a Kerr foundation and subjected to an axial compressive load and a two-dimensional magnetic field [...] Read more.

Dynamic post-buckling behavior of microscale cylindrical shells reinforced with functionally graded carbon nanotubes (FG-CNTs) and conveying microfluid is discussed for the first time. The microshell is embedded in a Kerr foundation and subjected to an axial compressive load and a two-dimensional magnetic field effect. CNTs dispersion across the shell thickness follows a power law, with five distribution types developed. The modified couple stress theory is applied to incorporate the small-size effect using a single material parameter. Furthermore, the Knudsen number is used to address the small-size effect on the microfluid. The external force between the magnetic fluid and microshell is modeled by applying the Navier–Stokes equation depending on the fluid velocity. Nonlinear motion equations of the present model are derived using Hamilton’s principle, containing the Lorentz magnetic force. According to the Galerkin method, the equations of motion are transformed into an algebraic system to be solved, determining the post-buckling paths. Numerical results indicate that the presence of the magnetic field, CNT reinforcement, and fluid flow improves the load-bearing performance of the cylindrical microshells. Also, many new parametric effects on the post-buckling curves of the FG-CNT microshells have been discovered, including the shell geometry, magnetic field direction, length scale parameter, Knudsen number, and CNT distribution types. Full article

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32 pages, 5779 KiB

Open AccessArticle

Modeling Rural Labor Responses to Digital Finance: A Hybrid IGSA-Random Forest Approach

by Zhiru Lin and Yishuai Tian

Mathematics 2025, 13(9), 1517; https://doi.org/10.3390/math13091517 - 4 May 2025

Viewed by 447

Abstract

The application of digital inclusive finance in various industries, particularly in rural areas, is gaining significant attention. The traditional agricultural sector, which focuses on rural labor economics (RLE), is more sensitive to financial innovations due to geographical and other constraints. This paper investigates [...] Read more.

The application of digital inclusive finance in various industries, particularly in rural areas, is gaining significant attention. The traditional agricultural sector, which focuses on rural labor economics (RLE), is more sensitive to financial innovations due to geographical and other constraints. This paper investigates how digital inclusive finance affects RLE by integrating the Improved Gravitational Search Algorithm Random Forest (IGSA-RF) with the Gini coefficient, Out-of-Bag (OOB) coefficient, and the Gini-OOB coupling coefficient. Focusing on Jiangsu Province, China, this study uses rural labor economic indicators to examine the underlying influence mechanisms of digital finance on labor dynamics in rural regions. The findings suggest that (1) digital inclusive finance has a long-term positive impact on consumption, gross regional product, and the average wage index of rural workers; (2) there is a growing trend in agricultural machinery power over time. However, the study found that gender, age, and the development of labor-intensive industries did not show significant improvement. The study provides a data-driven framework for understanding and enhancing rural labor development through digital financial innovation. Full article

(This article belongs to the Special Issue Mathematical Modelling in Financial Economics)

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23 pages, 3914 KiB

Open AccessArticle

Tensor-Based Uncoupled and Incomplete Multi-View Clustering

by Yapeng Liu, Wei Guo, Weiyu Li, Jingfeng Su, Qianlong Zhou and Shanshan Yu

Mathematics 2025, 13(9), 1516; https://doi.org/10.3390/math13091516 - 4 May 2025

Viewed by 164

Abstract

Multi-view clustering demonstrates strong performance in various real-world applications. However, real-world data often contain incomplete and uncoupled views. Missing views can lead to the loss of latent information, and uncoupled views create obstacles for cross-view learning. Existing methods rarely consider incomplete and uncoupled [...] Read more.

Multi-view clustering demonstrates strong performance in various real-world applications. However, real-world data often contain incomplete and uncoupled views. Missing views can lead to the loss of latent information, and uncoupled views create obstacles for cross-view learning. Existing methods rarely consider incomplete and uncoupled multi-view data simultaneously. To address these problems, a novel method called Tensor-based Uncoupled and Incomplete Multi-view Clustering (TUIMC) is proposed to effectively handle incomplete and uncoupled data. Specifically, the proposed method recovers missing samples in a low-dimensional feature space. Subsequently, the self-representation matrices are paired with the optimal views through permutation matrices. The coupled self-representation matrices are integrated into a third-order tensor to explore high-order information of multi-view data. An efficient algorithm is designed to solve the proposed model. Experimental results on five widely used benchmark datasets show that the proposed method exhibits superior clustering performance on incomplete and uncoupled multi-view data. Full article

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19 pages, 5504 KiB

Open AccessArticle

Progressive Domain Decomposition for Efficient Training of Physics-Informed Neural Network

by Dawei Luo, Soo-Ho Jo and Taejin Kim

Mathematics 2025, 13(9), 1515; https://doi.org/10.3390/math13091515 - 4 May 2025

Viewed by 326

Abstract

This study proposes a strategy for decomposing the computational domain to solve differential equations using physics-informed neural networks (PINNs) and progressively saving the trained model in each subdomain. The proposed progressive domain decomposition (PDD) method segments the domain based on the dynamics of [...] Read more.

This study proposes a strategy for decomposing the computational domain to solve differential equations using physics-informed neural networks (PINNs) and progressively saving the trained model in each subdomain. The proposed progressive domain decomposition (PDD) method segments the domain based on the dynamics of residual loss, thereby indicating the complexity of different sections within the entire domain. By analyzing residual loss pointwise and aggregating it over specific intervals, we identify critical regions requiring focused attention. This strategic segmentation allows for the application of tailored neural networks in identified subdomains, each characterized by varying levels of complexity. Additionally, the proposed method trains and saves the model progressively based on performance metrics, thereby conserving computational resources in sections where satisfactory results are achieved during the training process. The effectiveness of PDD is demonstrated through its application to complex PDEs, where it significantly enhances accuracy and conserves computational power by strategically simplifying the computational tasks into manageable segments. Full article

(This article belongs to the Special Issue Advanced Modeling and Design of Vibration and Wave Systems)

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19 pages, 4281 KiB

Open AccessArticle

Volatility Spillover Between China’s Carbon Market and Traditional Manufacturing

by Jining Wang, Dian Sheng and Lei Wang

Mathematics 2025, 13(9), 1514; https://doi.org/10.3390/math13091514 - 4 May 2025

Viewed by 287

Abstract

This study constructed a DGC-t-MSV model by integrating dynamic correlation and Granger causality into the MSV framework. Using daily closing price data from 4 January 2022 to 21 November 2024, it empirically analyzed volatility spillover effects between China’s carbon market and traditional manufacturing [...] Read more.

This study constructed a DGC-t-MSV model by integrating dynamic correlation and Granger causality into the MSV framework. Using daily closing price data from 4 January 2022 to 21 November 2024, it empirically analyzed volatility spillover effects between China’s carbon market and traditional manufacturing from an industrial heterogeneity perspective. The findings are as follows: (1) The carbon market exhibits significant unidirectional volatility spillover effects on carbon-intensive industries, such as steel, chemicals, shipbuilding, and automobile manufacturing, with the carbon market acting as the spillover source. (2) Bidirectional volatility spillover effects exist between the carbon market and industries such as forest products, textiles, construction engineering, and machinery manufacturing, with the carbon market predominantly acting as a recipient. (3) The carbon market exhibits general dynamic correlations with traditional manufacturing industries, where the correlation strength is positively associated with industry-level carbon emissions. Notably, the correlations with the steel, chemicals, machinery manufacturing, construction engineering, and automobile manufacturing industries are significant, whereas those with the textile industry and the forest products industry are relatively weaker. Furthermore, the carbon market demonstrates substantially higher volatility than traditional manufacturing industries. This study innovatively explored volatility spillover effects between China’s carbon market and traditional manufacturing from an industrial heterogeneity perspective, providing policy implications for their coordinated development. Full article

(This article belongs to the Special Issue Mathematics and Applications)

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37 pages, 1654 KiB

Open AccessArticle

CISMN: A Chaos-Integrated Synaptic-Memory Network with Multi-Compartment Chaotic Dynamics for Robust Nonlinear Regression

by Yaser Shahbazi, Mohsen Mokhtari Kashavar, Abbas Ghaffari, Mohammad Fotouhi and Siamak Pedrammehr

Mathematics 2025, 13(9), 1513; https://doi.org/10.3390/math13091513 - 4 May 2025

Viewed by 269

Abstract

Modeling complex, non-stationary dynamics remains challenging for deterministic neural networks. We present the Chaos-Integrated Synaptic-Memory Network (CISMN), which embeds controlled chaos across four modules—Chaotic Memory Cells, Chaotic Plasticity Layers, Chaotic Synapse Layers, and a Chaotic Attention Mechanism—supplemented by a logistic-map learning-rate schedule. Rigorous [...] Read more.

Modeling complex, non-stationary dynamics remains challenging for deterministic neural networks. We present the Chaos-Integrated Synaptic-Memory Network (CISMN), which embeds controlled chaos across four modules—Chaotic Memory Cells, Chaotic Plasticity Layers, Chaotic Synapse Layers, and a Chaotic Attention Mechanism—supplemented by a logistic-map learning-rate schedule. Rigorous stability analyses (Lyapunov exponents, boundedness proofs) and gradient-preservation guarantees underpin our design. In experiments, CISMN-1 on a synthetic acoustical regression dataset (541 samples, 22 features) achieved R² = 0.791 and RMSE = 0.059, outpacing physics-informed and attention-augmented baselines. CISMN-4 on the PMLB sonar benchmark (208 samples, 60 bands) attained R² = 0.424 and RMSE = 0.380, surpassing LSTM, memristive, and reservoir models. Across seven standard regression tasks with 5-fold cross-validation, CISMN led on diabetes (R² = 0.483 ± 0.073) and excelled in high-dimensional, low-sample regimes. Ablations reveal a scalability–efficiency trade-off: lightweight variants train in <10 s with >95% peak accuracy, while deeper configurations yield marginal gains. CISMN sustains gradient norms (~2300) versus LSTM collapse (<3), and fixed-seed protocols ensure <1.2% MAE variation. Interpretability remains challenging (feature-attribution entropy ≈ 2.58 bits), motivating future hybrid explanation methods. CISMN recasts chaos as a computational asset for robust, generalizable modeling across scientific, financial, and engineering domains. Full article

(This article belongs to the Special Issue Advances in Machine Learning and Graph Neural Networks)

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