Mathematics

27 pages, 5316 KB

Open AccessArticle

Lie Symmetry, Conservation Laws, and Dynamical Analysis of Ionic Currents in the Microtubule Model

by Beenish and Abdulaziz Khalid Alsharidi

Mathematics 2025, 13(23), 3891; https://doi.org/10.3390/math13233891 - 4 Dec 2025

Viewed by 277

In this article, we investigate the dynamical analysis and soliton solutions of the microtubule equation. First, the Lie symmetry method is applied to the considered model to reduce the governing partial differential equation into an ordinary differential equation. Next, the multivariate generalized exponential [...] Read more.

In this article, we investigate the dynamical analysis and soliton solutions of the microtubule equation. First, the Lie symmetry method is applied to the considered model to reduce the governing partial differential equation into an ordinary differential equation. Next, the multivariate generalized exponential rational integral function method is employed to derive exact soliton solutions. Finally, the bifurcation analysis of the corresponding dynamical system is discussed to explore the qualitative behavior of the obtained solutions. When an external force influences the system, its behavior exhibits chaotic and quasi-periodic phenomena, which are detected using chaos detection tools. We detect the chaotic and quasi-periodic phenomena using 2D phase portrait, time analysis, fractal dimension, return map, chaotic attractor, power spectrum, and multistability. Phase portraits illustrating bifurcation and chaotic patterns are generated using the RK4 algorithm in Matlab version 24.2. These results offer a powerful mathematical framework for addressing various nonlinear wave phenomena. Finally, conservation laws are explored. Full article

(This article belongs to the Special Issue Applied Mathematics in Nonlinear Dynamics and Chaos)

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22 pages, 1108 KB

Open AccessArticle

Micromechanics-Based Strength Criterion for Root-Reinforced Soil

by Wei Luo, Fu Cao, Yang Wang, Guiyou Xiao and Enlong Liu

Mathematics 2025, 13(23), 3890; https://doi.org/10.3390/math13233890 - 4 Dec 2025

Viewed by 196

Abstract

To address the limitation of using experimental parameters in the macroscopic strength criterion, a micromechanical strength criterion for root-reinforced soil is developed. In this model, a micromechanical model for a three-phase composite (“root—cemented soil matrix—frictional element”) is constructed, and the novel combination of [...] Read more.

To address the limitation of using experimental parameters in the macroscopic strength criterion, a micromechanical strength criterion for root-reinforced soil is developed. In this model, a micromechanical model for a three-phase composite (“root—cemented soil matrix—frictional element”) is constructed, and the novel combination of energy equivalence principles with the M-T method is used to determine the meso-scale prestress and strength criterion for root-reinforced soil under freeze–thaw cycles. The representative volume element (RVE) of root-reinforced soil is conceptualized as a composite material consisting of a bonded element (a cemented-soil matrix with root inclusions) and frictional inclusions. By applying micromechanics, along with the Mori–Tanaka method, the LCC method, limit analysis theory, and macro–micro energy equivalence principles (incorporating both strain and dissipated energy), a micromechanical strength criterion is formulated, revealing failure mechanisms at the microscale. The previously used stepwise procedure for deriving the stationary function is improved, and the microscale prestress is determined through the Mori–Tanaka method combined with macro–micro strain-energy equivalence. The proposed micromechanical strength criterion effectively models the primary strength variation in root-reinforced soil under freeze–thaw cycles, extending the existing shear criterion for soil. Full article

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26 pages, 2929 KB

Open AccessArticle

Label-Driven Optimization of Trading Models Across Indices and Stocks: Maximizing Percentage Profitability

by Abdulmohssen S. AlRashedy and Hassan I. Mathkour

Mathematics 2025, 13(23), 3889; https://doi.org/10.3390/math13233889 - 4 Dec 2025

Viewed by 1023

Abstract

Short-term trading presents a high-dimensional prediction problem, where the profitability of trading signals depends not only on model accuracy but also on how financial labels are defined and aligned with market dynamics. Traditional approaches often apply uniform modeling choices across assets, overlooking the [...] Read more.

Short-term trading presents a high-dimensional prediction problem, where the profitability of trading signals depends not only on model accuracy but also on how financial labels are defined and aligned with market dynamics. Traditional approaches often apply uniform modeling choices across assets, overlooking the asset-specific nature of volatility, liquidity, and market response. In this work, we introduce a structured, label-aware machine learning pipeline aimed at maximizing short-term trading profitability across four major benchmarks: S&P 500 (SPX), NASDAQ-100 (NDX), Dow Jones Industrial Average (DJI), and the Tadāwul All-Share Index (TASI and twelve of their most actively traded constituents). Our solution systematically evaluates all combinations of six model types (logistic regression, support vector machines, random forest, XGBoost, 1-D CNN, and LSTM), eight look-ahead labeling windows (3 to 10 days), and four feature subset sizes (44, 26, 17, 8 variables) derived through Random Forest permutation-importance ranking. Backtests are conducted using realistic long/flat simulations with zero commission, optimizing for Percentage Profit and Profit Factor on a 2005–2021 train/2022–2024 test split. The central contribution of the framework is a labeling-aware search mechanism that assigns to each asset its optimal combination of model type, look-ahead horizon, and feature subset based on out-of-sample profitability. Empirical results show that while XGBoost performs best on average, CNN and LSTM achieve standout gains on highly volatile tech stocks. The optimal look-ahead window varies by market from 3-day signals on liquid U.S. shares to 6–10-day signals on the less-liquid TASI universe. This joint model–label–feature optimization avoids one-size-fits-all assumptions and yields transferable configurations that cut grid-search cost when deploying from index level to constituent stocks, improving data efficiency, enhancing robustness, and supporting more adaptive portfolio construction in short-horizon trading strategies. Full article

(This article belongs to the Special Issue Financial Econometrics and Machine Learning)

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13 pages, 534 KB

Open AccessArticle

Certain Geometric Investigations of Three Normalized Bessel-Type Functions of a Complex Variable

by Rabab Alyusof, Shams Alyusof, Rabha M. El-Ashwah and Alaa H. El-Qadeem

Mathematics 2025, 13(23), 3888; https://doi.org/10.3390/math13233888 - 4 Dec 2025

Viewed by 245

Abstract

We recall the normalized forms for the three Bessel-type functions; these functions are the Bessel function, Lommel function, and Struve function of the first kind. By using convolution, we define normalized forms. The essential purpose is to introduce necessary and sufficient bounds of [...] Read more.

We recall the normalized forms for the three Bessel-type functions; these functions are the Bessel function, Lommel function, and Struve function of the first kind. By using convolution, we define normalized forms. The essential purpose is to introduce necessary and sufficient bounds of these normalized functions so these functions are starlike and convex of order

γ

and type

δ

. Full article

(This article belongs to the Special Issue Current Topics in Geometric Function Theory, 2nd Edition)

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18 pages, 1117 KB

Open AccessArticle

An Enhanced, Lightweight Large Language Model-Driven Time Series Forecasting Approach for Air Conditioning System Cooling Load Forecasting

by Cong Zhu, Yongkuan Yang, Haiping Chen and Miao Zeng

Mathematics 2025, 13(23), 3887; https://doi.org/10.3390/math13233887 - 4 Dec 2025

Viewed by 434

Abstract

Accurate cooling load forecasting in high-efficiency chiller plants with ice storage systems is essential for intelligent control, energy conservation, and maintaining indoor comfort. However, conventional forecasting methods often struggle to model the complex nonlinear dependencies among influencing variables, limiting their predictive performance. To [...] Read more.

Accurate cooling load forecasting in high-efficiency chiller plants with ice storage systems is essential for intelligent control, energy conservation, and maintaining indoor comfort. However, conventional forecasting methods often struggle to model the complex nonlinear dependencies among influencing variables, limiting their predictive performance. To address this, this paper introduces Time-LLM, a novel time series forecasting framework that leverages a frozen large language model (LLM) to improve the accuracy and generalization of cooling load forecasting. Time-LLM extracts features from historical data, reformulates them as natural language prompts, and uses the LLM for temporal sequence modeling; a linear projection layer then maps the LLM output to final predictions. To enable lightweight deployment and improve temporal feature prompting, we propose ETime-LLM, an enhanced variant of Time-LLM. ETime-LLM significantly reduces deployment costs and mitigates the original model’s response lag during trend transitions by focusing on possible turning points. Extensive experiments demonstrate that ETime-LLM consistently outperforms or matches state-of-the-art baselines across short-term, long-term, and few-shot forecasting tasks. Specifically, in the commonly used 24 h forecasting horizon, compared with the original model, ETime-LLM achieves an approximately 17.3% reduction in MAE and a 19.3% reduction in RMSE. It achieves high-quality predictions without relying on costly external data, offering a robust and scalable solution for green and energy-efficient HVAC system management. Full article

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28 pages, 1641 KB

Open AccessArticle

Bayesian Estimation of R-Vine Copula with Gaussian-Mixture GARCH Margins: An MCMC and Machine Learning Comparison

by Rewat Khanthaporn and Nuttanan Wichitaksorn

Mathematics 2025, 13(23), 3886; https://doi.org/10.3390/math13233886 - 4 Dec 2025

Viewed by 561

Abstract

This study proposes Bayesian estimation of multivariate regular vine (R-vine) copula models with generalized autoregressive conditional heteroskedasticity (GARCH) margins modeled by Gaussian-mixture distributions. The Bayesian estimation approach includes Markov chain Monte Carlo and variational Bayes with data augmentation. Although R-vines typically involve computationally [...] Read more.

This study proposes Bayesian estimation of multivariate regular vine (R-vine) copula models with generalized autoregressive conditional heteroskedasticity (GARCH) margins modeled by Gaussian-mixture distributions. The Bayesian estimation approach includes Markov chain Monte Carlo and variational Bayes with data augmentation. Although R-vines typically involve computationally intensive procedures limiting their practical use, we address this challenge through parallel computing techniques. To demonstrate our approach, we employ thirteen bivariate copula families within an R-vine pair-copula construction, applied to a large number of marginal distributions. The margins are modeled as exponential-type GARCH processes with intertemporal capital asset pricing specifications, using a mixture of Gaussian and generalized Pareto distributions. Results from an empirical study involving 100 financial returns confirm the effectiveness of our approach. Full article

(This article belongs to the Special Issue Contemporary Bayesian Analysis: Methods and Applications)

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42 pages, 571 KB

Open AccessFeature PaperReview

Integrating Cognitive, Symbolic, and Neural Approaches to Story Generation: A Review on the METATRON Framework

by Hiram Calvo, Brian Herrera-González and Mayte H. Laureano

Mathematics 2025, 13(23), 3885; https://doi.org/10.3390/math13233885 - 4 Dec 2025

Viewed by 950

Abstract

The human ability to imagine alternative realities has long supported reasoning, communication, and creativity through storytelling. By constructing hypothetical scenarios, people can anticipate outcomes, solve problems, and generate new knowledge. This link between imagination and reasoning has made storytelling an enduring topic in [...] Read more.

The human ability to imagine alternative realities has long supported reasoning, communication, and creativity through storytelling. By constructing hypothetical scenarios, people can anticipate outcomes, solve problems, and generate new knowledge. This link between imagination and reasoning has made storytelling an enduring topic in artificial intelligence, leading to the field of automatic story generation. Over the decades, different paradigms—symbolic, neural, and hybrid—have been proposed to address this task. This paper reviews key developments in story generation and identifies elements that can be integrated into a unified framework. Building on this analysis, we introduce the METATRON framework for neuro-symbolic generation of fiction stories. The framework combines a classical taxonomy of dramatic situations, used for symbolic narrative planning, with fine-tuned language models for text generation and coherence filtering. It also incorporates cognitive mechanisms such as episodic memory, emotional modeling, and narrative controllability, and explores multimodal extensions for text–image–audio storytelling. Finally, the paper discusses cognitively grounded evaluation methods, including theory-of-mind and creativity assessments, and outlines directions for future research. Full article

(This article belongs to the Special Issue Mathematical Foundations in NLP: Applications and Challenges)

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35 pages, 4295 KB

Open AccessArticle

Simulation-Driven Deep Transfer Learning Framework for Data-Efficient Prediction of Physical Experiments

by Soo-Young Lim, Han-Bok Seo and Seung-Yop Lee

Mathematics 2025, 13(23), 3884; https://doi.org/10.3390/math13233884 - 4 Dec 2025

Viewed by 373

Abstract

Transfer learning, which utilizes extensive simulation data to overcome the limitations of scarce and expensive experimental data, has emerged as a powerful approach for predictive modeling in various physical domains. This study presents a comprehensive framework to improve the predictive performance of transfer [...] Read more.

Transfer learning, which utilizes extensive simulation data to overcome the limitations of scarce and expensive experimental data, has emerged as a powerful approach for predictive modeling in various physical domains. This study presents a comprehensive framework to improve the predictive performance of transfer learning, focusing on quasi-zero stiffness (QZS) systems with limited experimental datasets. The proposed framework systematically examines the interplay among three critical factors in the target domain: data augmentation, layer-freezing configurations, and neural network architecture. Simulation-driven synthetic data are generated to capture dynamic features not represented in the sparse experimental data. The optimal transfer depth is explored by evaluating different scenarios of selective layer freezing and fine-tuning. Results show that partial transfer strategies outperform both full-transfer and non-transfer approaches, leading to more stable and accurate predictions. To investigate hierarchical transfer, both symmetric and asymmetric network architectures are designed, embedding physically meaningful representations from simulations into the deeper layers of the target model. Furthermore, an attention mechanism is integrated to emphasize material-specific characteristics. Building on these components, the proposed simulation-driven framework predicts the full force–displacement responses of QZS systems using only 12 experimental samples. Through a systematic comparison of three datasets (direct transfer, linear correction, FEM-based correction), three network architectures, and seven layer-freezing scenarios, the framework achieves a best test performance of R² = 0.978 and MAE = 0.34 Newtons. Full article

(This article belongs to the Special Issue Advances in Neural Networks and Their Applications)

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22 pages, 3451 KB

Open AccessArticle

Critical-Path-Based Variable Neighborhood Descent for the Joint Scheduling of FJSP and AGVs

by Han Jia, Yaming Chen, Qian Tian, Dazhi Pan and Yan Yang

Mathematics 2025, 13(23), 3883; https://doi.org/10.3390/math13233883 - 4 Dec 2025

Viewed by 330

Abstract

This study addresses the joint scheduling problem of flexible job shop scheduling and automated guided vehicles with the objective of minimizing the makespan. We propose an efficient optimization approach based on a critical-path-driven variable neighborhood descent. The core contribution lies in the development [...] Read more.

This study addresses the joint scheduling problem of flexible job shop scheduling and automated guided vehicles with the objective of minimizing the makespan. We propose an efficient optimization approach based on a critical-path-driven variable neighborhood descent. The core contribution lies in the development of a critical path detection mechanism that incorporates transportation processes, along with the design of tailored neighborhood structures. Building on this foundation, a problem-specific variable neighborhood descent search strategy is implemented. Unlike traditional variable neighborhood descent approaches, the proposed critical path analysis accurately identifies bottleneck operations in both processing and transportation stages. The designed neighborhood structures effectively coordinate machine scheduling and automated guided vehicles transportation, enabling synergistic optimization. To enhance overall performance, auxiliary strategies such as an external memory archive and population diversity maintenance are integrated. Experimental results on multiple benchmark datasets demonstrate that the proposed method achieves significant improvements in solution quality compared to existing algorithms. Ablation experiments further confirm the critical role of the critical-path-driven variable neighborhood descent mechanism in enhancing algorithmic performance. Full article

(This article belongs to the Special Issue Mathematical Methods and Operation Research in Planning, Scheduling and Supply Chain Operations Management)

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20 pages, 3406 KB

Open AccessArticle

Efficient and Interpretable ECG Abnormality Detection via a Lightweight DSCR-BiGRU-Attention Network with Demographic Fusion

by Kan Luo, Longying Huang, Haixin He, Yu Chen, Lu You, Siluo Chen, Jian Chen and Chengyu Liu

Mathematics 2025, 13(23), 3882; https://doi.org/10.3390/math13233882 - 3 Dec 2025

Viewed by 495

Abstract

Deep learning has advanced automated electrocardiogram (ECG) interpretation, yet many models are computationally expensive, opaque, and overlook demographic factors. We propose DBA-ASFNet, a lightweight network that combines depthwise-separable convolutional residual blocks with a BiGRU and an attention mechanism to extract rich spatiotemporal features [...] Read more.

Deep learning has advanced automated electrocardiogram (ECG) interpretation, yet many models are computationally expensive, opaque, and overlook demographic factors. We propose DBA-ASFNet, a lightweight network that combines depthwise-separable convolutional residual blocks with a BiGRU and an attention mechanism to extract rich spatiotemporal features from 12-lead ECGs while maintaining low computational requirements. The Age-and-Sex Fusion (ASF) module integrates demographic information without enlarging the model, enabling personalized predictions. On the PTB-XL and CPSC2018 datasets, DBA-ASFNet achieves competitive multi-label performance with only ~0.03 million parameters and ~6.43 MFLOPs per inference. Real-time testing on a Raspberry Pi 5 achieved an average inference latency of ~2 ms, supporting deployment on resource-limited devices. Shapley additive explanations (SHAP) analysis shows that the model focuses on clinically meaningful ECG patterns and appropriately incorporates demographic factors, enhancing transparency. These results suggest that DBA-ASFNet is suited for accurate, efficient, and interpretable ECG analysis. Full article

(This article belongs to the Special Issue Advanced Artificial Intelligence Models and Its Applications, 2nd Edition)

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18 pages, 816 KB

Open AccessArticle

The Convergent Indian Buffet Process

by Ilsang Ohn

Mathematics 2025, 13(23), 3881; https://doi.org/10.3390/math13233881 - 3 Dec 2025

Viewed by 238

Abstract

We propose a new Bayesian nonparametric prior for latent feature models, called the Convergent Indian Buffet Process (CIBP). We show that under the CIBP, the number of latent features is distributed as a Poisson distribution, with the mean monotonically increasing but converging to [...] Read more.

We propose a new Bayesian nonparametric prior for latent feature models, called the Convergent Indian Buffet Process (CIBP). We show that under the CIBP, the number of latent features is distributed as a Poisson distribution, with the mean monotonically increasing but converging to a certain value as the number of objects goes to infinity. That is, the expected number of features is bounded above even when the number of objects goes to infinity, unlike the standard Indian Buffet Process, under which the expected number of features increases with the number of objects. We provide two alternative representations of the CIBP based on a hierarchical distribution and a completely random measure, which are of independent interest. The proposed CIBP is assessed on a high-dimensional sparse factor model. Full article

(This article belongs to the Special Issue Application of the Bayesian Method in Statistical Modeling, 2nd Edition)

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16 pages, 282 KB

Open AccessArticle

A Minimax Diversification Approach to Dynamic Portfolio Optimization

by Hongyu Yang and Zijian Luo

Mathematics 2025, 13(23), 3880; https://doi.org/10.3390/math13233880 - 3 Dec 2025

Viewed by 273

Abstract

This paper investigates a multi-period investment problem in which an investor revises investment decisions at the beginning of each period. The objective is to maximize expected terminal wealth while simultaneously minimizing risk. This study quantifies risk using a dynamic risk function grounded in [...] Read more.

This paper investigates a multi-period investment problem in which an investor revises investment decisions at the beginning of each period. The objective is to maximize expected terminal wealth while simultaneously minimizing risk. This study quantifies risk using a dynamic risk function grounded in the minimax risk diversification principle. A key feature of the model is its flexibility: in each period, the investor constructs the risk function using either standard deviation, absolute deviation, or lower semi-absolute deviation, thereby accommodating diverse risk preferences. By employing dynamic programming, analytical solutions for the optimal investment strategy are derived. These solutions explicitly demonstrate the strategy’s dependence on the expected return rates of risky assets and the investor’s risk tolerance. Full article

(This article belongs to the Section E5: Financial Mathematics)

26 pages, 6495 KB

Open AccessArticle

Shaping Multi-Dimensional Traffic Features for Covert Communication in QUIC Streaming

by Dongfang Zhang, Dongxu Liu, Jianan Huang, Lei Guan and Xiaotian Yin

Mathematics 2025, 13(23), 3879; https://doi.org/10.3390/math13233879 - 3 Dec 2025

Viewed by 613

Abstract

Network covert channels embed secret data into legitimate traffic, but existing methods struggle to balance undetectability, robustness, and throughput. Application-independent channels at lower protocol layers are easily normalized or disrupted by network noise, while application-dependent streaming schemes rely on handcrafted traffic manipulations that [...] Read more.

Network covert channels embed secret data into legitimate traffic, but existing methods struggle to balance undetectability, robustness, and throughput. Application-independent channels at lower protocol layers are easily normalized or disrupted by network noise, while application-dependent streaming schemes rely on handcrafted traffic manipulations that fail to preserve the spatio-temporal dynamics of real encrypted flows and thus remain detectable by modern machine learning (ML)-based classifiers. Meanwhile, with the rapid adoption of HTTP/3, Quick UDP Internet Connections (QUIC) has become the dominant transport for streaming services, offering stable long-lived flows with rich spatio-temporal structure that create new opportunities for constructing resilient covert channels. In this paper, a QUIC streaming-based Covert Channel framework, QuicCC-SMD, is proposed that dynamically Shapes Multi-Dimensional traffic features to identify and exploit redundancy spaces for secret data embedding. QuicCC-SMD models the statistical and temporal dependencies of QUIC flows via Markov chain-based state representations and employs convex optimization to derive an optimal deformation matrix that maps source traffic to legitimate target distributions. Guided by this matrix, a packet-level modulation performs through packet padding, insertion, and delay operations under a periodic online optimization strategy. Evaluations on a real-world HTTP/3 over QUIC (HTTP/3-QUIC) dataset containing 18,000 samples across four video resolutions demonstrate that QuicCC-SMD achieves an average F1 score of 56% at a 1.5% embedding rate, improving detection resistance by at least 7% compared with three representative baselines. Full article

(This article belongs to the Special Issue Mathematical and Artificial Intelligence Applications in Network Information Security and Network Traffic Processing)

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16 pages, 1247 KB

Open AccessArticle

Sharp Coefficient Bounds for a Class of Analytic Functions Related to Exponential Function

by Adel Salim Tayyah, Sibel Yalçın and Hasan Bayram

Mathematics 2025, 13(23), 3878; https://doi.org/10.3390/math13233878 - 3 Dec 2025

Viewed by 264

Abstract

In this paper, we introduce a new class of analytic functions, denoted by

S (ν, φ_{ϑ, e})

, and provide illustrative examples to elucidate its properties. This class generalizes the starlike and convex functions previously defined by Khatter [...] Read more.

In this paper, we introduce a new class of analytic functions, denoted by

S (ν, φ_{ϑ, e})

, and provide illustrative examples to elucidate its properties. This class generalizes the starlike and convex functions previously defined by Khatter et al. in relation to the exponential function. A significant contribution of this work is the derivation of sharp bounds for various coefficient-related problems within this class. The computational challenges involved in deriving these bounds were effectively addressed using Mathematica^TM codes. Additionally, figures illustrating the geometric properties and essential computations have been incorporated into the paper. Full article

(This article belongs to the Special Issue Advanced Research in Complex Analysis Operators and Special Classes of Analytic Functions)

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20 pages, 2995 KB

Open AccessArticle

KAN-Former: 4D Trajectory Prediction for UAVs Based on Cross-Dimensional Attention and KAN Decomposition

by Junfeng Chen and Yuqi Lu

Mathematics 2025, 13(23), 3877; https://doi.org/10.3390/math13233877 - 3 Dec 2025

Viewed by 265

Abstract

To address the core challenges of multivariate nonlinear coupling and long-term temporal dependency in 4D UAV trajectory prediction, this study proposes an innovative model named KAN-Former. On a 21-dimensional multimodal UAV dataset, KAN-Former achieves statistically significant improvements over all baseline models, reducing the [...] Read more.

To address the core challenges of multivariate nonlinear coupling and long-term temporal dependency in 4D UAV trajectory prediction, this study proposes an innovative model named KAN-Former. On a 21-dimensional multimodal UAV dataset, KAN-Former achieves statistically significant improvements over all baseline models, reducing the mean squared error (MSE) by 8.96% compared to the standard Transformer and by 2.66% compared to the strongest physics-informed baseline (PITA), while decreasing the mean absolute error (MAE) by 7.43% relative to TimeMixer/PatchTST. The model adopts a collaborative architecture with two key components: first, a “vertical–horizontal” cross-dimensional attention mechanism—where the vertical branch models physical correlations among multivariate variables using hierarchical clustering priors, and the horizontal branch employs a blockwise dimensionality reduction strategy to efficiently capture long-term temporal dynamics; second, it represents the first application of Kolmogorov–Arnold decomposition in trajectory prediction, replacing traditional feedforward networks with learnable combinations of B-spline basis functions to approximate high-dimensional nonlinear mappings. Ablation studies verify the effectiveness of each module, with the KAN module alone reducing MSE by 6.59%. Moreover, the model’s feature clustering results align closely with UAV physical characteristics, significantly improving interpretability. The demonstrated improvements in accuracy, interpretability, and computational efficiency make KAN-Former highly suitable for real-world applications such as real-time flight control and air traffic management, providing reliable trajectory forecasts for decision-making systems. This work offers a new paradigm for trajectory prediction in complex dynamic systems, successfully integrating theoretical innovation with practical value. Full article

(This article belongs to the Special Issue Artificial Intelligence, Algorithms, and Databases: Innovations and Cross-Disciplinary Impact)

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24 pages, 4004 KB

Open AccessArticle

Graph-Attention-Regularized Deep Support Vector Data Description for Semi-Supervised Anomaly Detection: A Case Study in Automotive Quality Control

by Taha J. Alhindi

Mathematics 2025, 13(23), 3876; https://doi.org/10.3390/math13233876 - 3 Dec 2025

Viewed by 295

Abstract

This paper addresses semi-supervised anomaly detection in settings where only a small subset of normal data can be labeled. Such conditions arise, for example, in industrial quality control of windshield wiper noise, where expert labeling is costly and limited. Our objective is to [...] Read more.

This paper addresses semi-supervised anomaly detection in settings where only a small subset of normal data can be labeled. Such conditions arise, for example, in industrial quality control of windshield wiper noise, where expert labeling is costly and limited. Our objective is to learn a one-class decision boundary that leverages the geometry of unlabeled data while remaining robust to contamination and scarcity of labeled normals. We propose a graph-attention-regularized deep support vector data description (GAR-DSVDD) model that combines a deep one-class enclosure with a latent k-nearest-neighbor graph whose edges are weighted by similarity- and score-aware attention. The resulting loss integrates (i) a distance-based enclosure on labeled normals, (ii) a graph smoothness term on squared distances over the attention-weighted graph, and (iii) a center-pull regularizer on unlabeled samples to avoid over-smoothing and boundary drift. Experiments on a controlled simulated dataset and an industrial windshield wiper acoustics dataset show that GAR-DSVDD consistently improves the F1 score under scarce label conditions. On average, F1 increases from 0.78 to 0.84 on the simulated benchmark and from 0.63 to 0.86 on the industrial case study relative to the best competing baseline. Full article

(This article belongs to the Special Issue Data Mining and Machine Learning with Applications, 2nd Edition)

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33 pages, 1944 KB

Open AccessArticle

Research on Data Product Operation Strategies Considering Dynamic Data Updates Under Different Power Structures

by Yazhou Liu, Wenxiu Hu, Qinfeng Gao, Zuhui Xia and Yan Shen

Mathematics 2025, 13(23), 3875; https://doi.org/10.3390/math13233875 - 3 Dec 2025

Viewed by 312

Abstract

As data product transactions become increasingly standardized, the operational strategies of data product manufacturers and service providers play a pivotal role in shaping market outcomes. This study develops a game-theoretic framework that incorporates dynamic data updates under alternative power structures to examine the [...] Read more.

As data product transactions become increasingly standardized, the operational strategies of data product manufacturers and service providers play a pivotal role in shaping market outcomes. This study develops a game-theoretic framework that incorporates dynamic data updates under alternative power structures to examine the equilibrium performance of pricing, demand, technological investment, update rates, and promotional effort. The results indicate that optimal prices under Stackelberg leadership exceed those in the Nash game, whereas demand, technological investment, update frequency, and promotion are consistently higher in the Nash setting. The effects of these decisions are moderated by end-user preference heterogeneity: when users exhibit stronger promotion preferences, service-provider leadership generates superior outcomes, while stronger quality preferences favor manufacturer leadership. Demand preferences and cost coefficients significantly influence profitability—enhanced preferences improve the leader’s returns, whereas high technological and promotional costs suppress profits for both parties. Cost savings in dynamic updates and increases in perceived value exert strong positive effects on market competitiveness, while higher update investment and data acquisition costs exert negative effects. Overall, this study deepens the theoretical understanding of how power structures interact with dynamic updating and user preferences, providing analytical insights and decision support for optimizing operational strategies in data product markets. Full article

(This article belongs to the Special Issue Quantitative Analysis and Mathematical Modeling in Economics and Financial Decision-Making)

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13 pages, 635 KB

Open AccessFeature PaperArticle

About Implementation of Magic State Injection in Heavy-Hexagon Structure

by Hansol Kim, Wonjae Choi and Younghun Kwon

Mathematics 2025, 13(23), 3874; https://doi.org/10.3390/math13233874 - 3 Dec 2025

Viewed by 689

Abstract

Implementing fault-tolerant quantum computing necessitates the realization of logical non-Clifford gates, which requires the preparation of specific quantum states known as magic states. However, IBM’s heavy-hexagon structure, which has limited qubit connectivity, presents challenges in adapting quantum error correction codes such as the [...] Read more.

Implementing fault-tolerant quantum computing necessitates the realization of logical non-Clifford gates, which requires the preparation of specific quantum states known as magic states. However, IBM’s heavy-hexagon structure, which has limited qubit connectivity, presents challenges in adapting quantum error correction codes such as the surface code. Several methods have been proposed to address these challenges by adapting the surface code to the heavy-hexagon architecture. In this study, we implement the magic state injection process within two distinct implementations of surface codes (standard and rotated methods) suitable for the heavy-hexagon structure and compare their logical error rates. Furthermore, we propose initialization methods to enhance the performance of magic state injection in the heavy-hexagon structure, thereby efficiently achieving logical non-Clifford gates with reduced error rates. Full article

(This article belongs to the Special Issue Recent Advances in Quantum Information and Quantum Computing)

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30 pages, 892 KB

Open AccessArticle

Addressing Daigou from the Perspective of Channel Competition: Strategy for Retail Management

by Keqin Chang, Rachael Kwai Fun Ip and Pak Hou Che

Mathematics 2025, 13(23), 3873; https://doi.org/10.3390/math13233873 - 3 Dec 2025

Viewed by 294

Abstract

In China’s on-demand service platforms, daigou agents utilize locational differences through proxy purchasing. Daigou creates an informal supply chain that directly competes with official channels. This study incorporates daigou arbitrage into the channel competition framework via a multi-stage Stackelberg game-theoretic model. An analysis [...] Read more.

In China’s on-demand service platforms, daigou agents utilize locational differences through proxy purchasing. Daigou creates an informal supply chain that directly competes with official channels. This study incorporates daigou arbitrage into the channel competition framework via a multi-stage Stackelberg game-theoretic model. An analysis of the subgame perfect Nash equilibrium shows that daigou activity disrupts the manufacturer’s profits. We have thus developed a strategy based on mathematical optimization and compared its effectiveness and side effects with those of existing methods. We came to identify purchase restrictions as one of the most powerful strategies. Equilibrium analysis and numerical experiments confirm that proper purchase restriction choices reduce daigou arbitrage and minimize negative impacts on legitimate demand. This work provides the first game-theoretic model that integrates informal proxy-purchase supply chains into dual-channel competitions. Full article

(This article belongs to the Special Issue Theoretical and Applied Mathematics in Supply Chain Management)

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33 pages, 1150 KB

Open AccessArticle

Modified Heisenberg Commutations Relations and Its Standard Hamiltonian Interpretation

by Mauricio Contreras González, Roberto Ortiz Herrera and José Mauricio González

Mathematics 2025, 13(23), 3872; https://doi.org/10.3390/math13233872 - 3 Dec 2025

Viewed by 292

Abstract

This paper analyzes the modified canonical Heisenberg commutation relations or GUP, from a standard Hamiltonian point of view. For a one-dimensional system, a such modified canonical Heisenberg commutation relation is defined by the commutator between a position

\hat{x}

and a momentum operator [...] Read more.

This paper analyzes the modified canonical Heisenberg commutation relations or GUP, from a standard Hamiltonian point of view. For a one-dimensional system, a such modified canonical Heisenberg commutation relation is defined by the commutator between a position

\hat{x}

and a momentum operator

\hat{p}

(called the deformed momentum), which becomes a function F of the same operators:

[\hat{x}, \hat{p}] = F (\hat{x}, \hat{p})

, that is, the Heisenberg algebra closes itself in general in a nonlinear way. The function F also depends on a parameter that controls the deformation of the Heisenberg algebra in such a way that for a null parameter value, one recovers the usual Heisenberg algebra

[\hat{x}, {\hat{p}}_{0}] = i ℏ I

. Thus, it naturally raises the following questions: What does a relation of this type mean in Hamiltonian theory from a standard point of view? Is the deformed momentum the canonical variable conjugate to the position in such a relation? Moreover, what are the canonical variables in this model? The answer to these questions comes from the existence of two different phase spaces: The first one, called the non-deformed phase (which is obtained for control parameter value equal to zero), is defined by the Cartesian

\hat{x}

coordinate and its non-deformed conjugate momentum

{\hat{p}}_{0}

, which satisfies the standard quantum mechanical Heisenberg commutation relation. The second phase space, the deformed one, is given by the deformed momentum

\hat{p}

and a new position coordinate

\hat{y}

, which is its canonical conjugate variable, so

\hat{y}

and

\hat{p}

also satisfy standard commutation relations. We construct a classical canonical transformation that maps the non-deformed phase space into the deformed one for a specific class of deformation functions F. Additionally, a quantum mechanical operator transformation is found between the two non-commutative phase spaces, which allows the Schrödinger equation to be written in both spaces. Thus, there are two equivalent quantum mechanical descriptions of the same physical process associated with a deformed commutation relation. Full article

(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering, 3rd Edition)

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19 pages, 754 KB

Open AccessArticle

Communication-Computation Co-Optimized Federated Learning for Efficient Large-Model Embedding Training

by Yingying Luo, Xi Jin, Changqing Xia, Chi Xu and Yiming Sun

Mathematics 2025, 13(23), 3871; https://doi.org/10.3390/math13233871 - 3 Dec 2025

Viewed by 373

Abstract

With the rapid development of the Industrial Internet of Things (IIoT) and intelligent manufacturing, massive amounts of heterogeneous and non-independent, identically distributed (non-IID) data are continuously generated in industrial environments. Large models have demonstrated strong generalization and transfer capabilities, offering new possibilities for [...] Read more.

With the rapid development of the Industrial Internet of Things (IIoT) and intelligent manufacturing, massive amounts of heterogeneous and non-independent, identically distributed (non-IID) data are continuously generated in industrial environments. Large models have demonstrated strong generalization and transfer capabilities, offering new possibilities for predictive maintenance, anomaly detection, and intelligent decision-making in IIoT scenarios. However, the deployment of such models in industrial environments faces challenges due to resource constraints in communication and computation. To address this problem, this paper proposes a collaborative optimization framework that integrates client-side feature learning, a hierarchical client–edge–cloud federated aggregation, and network-computing resource scheduling for efficient large-model embedding training. A parameter search method based on the Kepler Optimization Algorithm (PSKOA) is introduced to jointly optimize the three interdependent dimensions: client-side model structure parameter, federated aggregation parameters, and scheduling strategy. Evaluations demonstrate that the proposed method significantly reduces model loss by 41.7% and shortens training time by 13.4% compared to the traditional Genetic Algorithm-based method. Additionally, the proposed method achieves 12.5% lower model loss and 3.1% faster training time compared to the Particle Swarm Optimization-based method. These results highlight that the proposed method effectively enhances both training efficiency and convergence performance by jointly optimizing communication, computation, and model structure, making it a practical and scalable solution for large-model embedding training in resource-constrained IIoT environments. Full article

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23 pages, 4330 KB

Open AccessArticle

Surrogate Model-Based Optimization of a Dual-Shield Total Temperature Probe for Aero-Engine Applications

by Xuetao Zhang, Yufang Wang, Qi Lei, Jian Zhao and Yudi Ai

Mathematics 2025, 13(23), 3870; https://doi.org/10.3390/math13233870 - 3 Dec 2025

Viewed by 389

Abstract

The design of high-precision total temperature probes for aero-engines is constrained by the massive computational cost of high-fidelity simulations. This paper overcomes this barrier by introducing a surrogate model-based optimization framework for a dual-shield probe. A computationally efficient data-driven framework is established, merging [...] Read more.

The design of high-precision total temperature probes for aero-engines is constrained by the massive computational cost of high-fidelity simulations. This paper overcomes this barrier by introducing a surrogate model-based optimization framework for a dual-shield probe. A computationally efficient data-driven framework is established, merging conjugate-heat-transfer Computational Fluid Dynamics (CFDs), a Support Vector Regression (SVR) model, and a Genetic Algorithm (GA), which collectively replace the traditional costly design loop. The surrogate model’s exceptional predictive fidelity is confirmed, and this approach obtains improvement in measurement accuracy, successfully reducing the temperature deviation and meeting the stringent requirement. Finally, the demonstrated framework is geometry-agnostic, establishing a generalizable and cost-effective strategy for the rapid design of high-performance thermometric components in gas turbine systems. Full article

(This article belongs to the Special Issue Intelligent Optimization and Control Modeling in Power and Energy System)

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33 pages, 2022 KB

Open AccessArticle

Evolutionary Computation for Feature Optimization and Image-Based Dimensionality Reduction in IoT Intrusion Detection

by Hessah A. Alsalamah and Walaa N. Ismail

Mathematics 2025, 13(23), 3869; https://doi.org/10.3390/math13233869 - 2 Dec 2025

Viewed by 352

Abstract

The exponential growth of the Internet of Things (IoT) has made it increasingly vulnerable to cyberattacks, where malicious manipulation of network and sensor data can lead to incorrect data classification. IoT data are inherently heterogeneous, comprising sensor readings, network flow records, and device [...] Read more.

The exponential growth of the Internet of Things (IoT) has made it increasingly vulnerable to cyberattacks, where malicious manipulation of network and sensor data can lead to incorrect data classification. IoT data are inherently heterogeneous, comprising sensor readings, network flow records, and device metadata that differ significantly in scale and structure. This diversity motivates transforming tabular IoT data into image-based representations to facilitate the recognition of intrusion patterns and the analysis of spatial correlations. Many deep learning models offer robust detection performance, including CNNs, LSTMs, CNN–LSTM hybrids, and Transformer-based networks, but many of these architectures are computationally intensive and require significant training resources. To address this challenge, this study introduces an evolutionary-driven framework that mathematically formalizes the transformation of tabular IoT data into image-encoded matrices and optimizes feature selection through metaheuristic algorithms. Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Variable Neighborhood Search (VNS) are employed to identify optimal feature subsets for Random Forest (RF) and Extreme Gradient Boosting (XGBoost) classifiers. The approach enhances discrimination by optimizing multi-objective criteria, including accuracy and sparsity, while maintaining low computational complexity suitable for edge deployment. Experimental results on benchmark IoT intrusion datasets demonstrate that VNS-XGBoost configurations performed better on the IDS2017 and IDS2018 benchmarks, achieving accuracies up to 0.99997 and a significant reduction in Type II errors (212 and 6 in tabular form, reduced to 4 and 1 using image-encoded representations). These results confirm that integrating evolutionary optimization with image-based feature modeling enables accurate, efficient, and robust intrusion detection across large-scale IoT systems. Full article

(This article belongs to the Special Issue Evolutionary Computation for Feature Selection and Dimensionality Reduction)

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26 pages, 2983 KB

Open AccessArticle

Global Dynamics and Optimal Control of a Dual-Target HIV Model with Latent Reservoirs

by Fawaz K. Alalhareth, Fahad K. Alghamdi, Mohammed H. Alharbi and Miled El Hajji

Mathematics 2025, 13(23), 3868; https://doi.org/10.3390/math13233868 - 2 Dec 2025

Cited by 2 | Viewed by 296

Abstract

In this paper, we develop a mathematical model to investigate HIV infection dynamics, where we focus on the virus’s dual-target mechanism involving both CD

4^{+}

T cells and macrophages. Our model is structured as a system of seven nonlinear ordinary differential equations [...] Read more.

In this paper, we develop a mathematical model to investigate HIV infection dynamics, where we focus on the virus’s dual-target mechanism involving both CD

4^{+}

T cells and macrophages. Our model is structured as a system of seven nonlinear ordinary differential equations describing the interactions between susceptible, latent, and infected cells, alongside free virus particles. We derive the basic reproduction number,

R_{0}

, as two components,

R_{01}

and

R_{02}

, which quantify the respective contributions of CD

4^{+}

T cells and macrophages to viral spread. It is deduced that the infection-free steady state is globally asymptotically stable once

R_{0} \leq 1

, ensuring viral eradication. For

R_{0} > 1

, a stable endemic steady state emerges, indicating the persistence of the infection. Later, we develop an optimal control strategy to study the impact of reverse transcriptase and protease inhibitors. This analysis identifies a critical drug efficacy threshold,

ϵ^{*} = 1 - \frac{1}{R_{0}}

, necessary for viral eradication. The numerical simulations and the sensitivity analysis provide key parameters that drive viral dynamics, offering practical insights for designing targeted therapies, particularly during the early stages of infection. Full article

(This article belongs to the Special Issue Modeling, Control and Optimization of Biological Systems)

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16 pages, 307 KB

Open AccessFeature PaperArticle

Characterizations for S-Convex-Averaging Domains via Two-Dimensional Diffusion-Wave Equations

by Jianwei Wang, Nan Jiang and Ming Liu

Mathematics 2025, 13(23), 3867; https://doi.org/10.3390/math13233867 - 2 Dec 2025

Viewed by 176

Abstract

In this paper, we introduce the concept of s-convex-averaging domains, which are extensions of circular and irregular convex domains, by using s-convex functions and generalized Orlicz norms. Based on the quasi-hyperbolic metric and L^p-averaging domains, several fundamental properties of [...] Read more.

In this paper, we introduce the concept of s-convex-averaging domains, which are extensions of circular and irregular convex domains, by using s-convex functions and generalized Orlicz norms. Based on the quasi-hyperbolic metric and L^p-averaging domains, several fundamental properties of s-convex-averaging domains are characterized. These properties are applied to the domains of a class of two-dimensional diffusion-wave equations. Furthermore, we establish intrinsic relationships between the considered partial differential equations and the geometric structure of s-convex-averaging domains. Finally, the embedding inequality for the solutions of these kinds of partial differential equations is derived. Full article

(This article belongs to the Special Issue Theory and Application of Difference and Differential Equations in Life Sciences)

21 pages, 14302 KB

Open AccessFeature PaperArticle

Improved Post-Assembly Magnetization Performance of Spoke-Type PMSM Using a 5-Times Divided Magnetizer with Auxiliary Pole Winding

by Seung-Heon Lee, Jong-Hyun Kim and Won-Ho Kim

Mathematics 2025, 13(23), 3866; https://doi.org/10.3390/math13233866 - 2 Dec 2025

Viewed by 244

Abstract

Due to the reinforcement of energy efficiency regulations and the pursuit of sustainable development goals, the demand for high-efficiency electric motors has been steadily increasing. Rare-earth permanent magnets such as neodymium (Nd) and samarium (Sm) provide high power density, but their high cost [...] Read more.

Due to the reinforcement of energy efficiency regulations and the pursuit of sustainable development goals, the demand for high-efficiency electric motors has been steadily increasing. Rare-earth permanent magnets such as neodymium (Nd) and samarium (Sm) provide high power density, but their high cost and unstable supply chains have led to growing interest in ferrite-based motors. Ferrite magnets offer excellent cost-effectiveness; however, their relatively low remanent flux density and coercivity result in reduced motor performance. To compensate for these limitations, a spoke-type flux-concentrating structure is commonly employed to enhance the air-gap flux density. Nevertheless, in spoke-type motors, the magnets are deeply embedded within the rotor, making it difficult to achieve a sufficient magnetization rate during post-assembly magnetization. In this study, an optimized magnetizing yoke is proposed to achieve a post-assembly magnetization rate of over 99% while suppressing the irreversible demagnetization of untargeted magnets. Finite element analysis (FEA) results for a 10-pole ferrite rotor confirm that the proposed structure demonstrates excellent magnetization performance and effectively mitigates irreversible demagnetization. Full article

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

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36 pages, 1682 KB

Open AccessArticle

Structural Properties and a Revised Value Iteration Algorithm for Dynamic Capacity Expansion and Reduction

by Jazeem Abduljaleel and Mohammad M. AlDurgam

Mathematics 2025, 13(23), 3865; https://doi.org/10.3390/math13233865 - 2 Dec 2025

Viewed by 223

Abstract

This manuscript introduces a generalized Markov Decision Process (MDP) model for dynamic capacity planning in the presence of stochastic time-nonhomogeneous demand, wherein system capacity may be flexibly increased or decreased throughout a finite planning horizon. The model includes investment, disinvestment, maintenance, operational, and [...] Read more.

This manuscript introduces a generalized Markov Decision Process (MDP) model for dynamic capacity planning in the presence of stochastic time-nonhomogeneous demand, wherein system capacity may be flexibly increased or decreased throughout a finite planning horizon. The model includes investment, disinvestment, maintenance, operational, and shortage costs, in addition to a salvage value at the end of the planning horizon. Under very realistic conditions, we investigate the structural properties of the optimal policy and demonstrate its monotonic structure. By leveraging these properties, we propose a revised value iteration algorithm that capitalizes on the intrinsic structure of the problem, thereby achieving enhanced computational efficiency compared to traditional dynamic programming techniques. The proposed model is applicable across a range of sectors, including manufacturing systems, cloud-computing services, logistics systems, healthcare resource management, power capacity planning, and other intelligent infrastructures driven by Industry 4.0. Full article

(This article belongs to the Special Issue Mathematical Methods of Operational Research and Data Analytics in Operations Planning and Scheduling)

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19 pages, 998 KB

Open AccessArticle

Optimal Impulsive Control and Stabilization of Dynamic Systems Based on Quasi-Variational Inequalities

by Wenxuan Wang, Chuandong Li and Mingchen Huan

Mathematics 2025, 13(23), 3864; https://doi.org/10.3390/math13233864 - 2 Dec 2025

Viewed by 226

Abstract

In this paper, we investigate the optimal control problem regarding a class of dynamic systems, aiming to address the challenge of simultaneously ensuring cost minimization and system asymptotic stability. The theoretical framework proposed in this paper integrates the value function concept from optimal [...] Read more.

In this paper, we investigate the optimal control problem regarding a class of dynamic systems, aiming to address the challenge of simultaneously ensuring cost minimization and system asymptotic stability. The theoretical framework proposed in this paper integrates the value function concept from optimal control theory with Lyapunov stability theory. By setting the impulse cost at any finite time to be strictly positive, we exclude Zeno behavior, and a set of sufficient conditions is established that simultaneously guarantees system asymptotic stability and cost minimization based on Quasi-Variational Inequalities (QVIs). To address the challenge of solving the Hamilton–Jacobi–Bellman (HJB) equation in high-dimensional nonlinear systems, we employ an inverse optimal control framework to synthesize the strategy and its corresponding cost function. Finally, we validate the feasibility of our method by applying the theoretical results obtained to three numerical examples. Full article

(This article belongs to the Special Issue Mathematics and Simulation of Brain-Inspired Computing: From Dynamic Models to Visual Intelligence)

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18 pages, 1822 KB

Open AccessArticle

Information Misreporting Behavior and Optimal Pricing Strategy in Dual-Channel Supply Chain Under Different Dominant Power Structures

by Guangming Zhang, Shinan Zhao, Yingying Yang and Chunqi Li

Mathematics 2025, 13(23), 3863; https://doi.org/10.3390/math13233863 - 2 Dec 2025

Viewed by 234

Abstract

This study explores the information misreporting behavior among channel members and the optimal pricing strategies in a dual-channel supply chain under information asymmetry, where the manufacturer operates an online channel, and the retailer operates an offline channel. More specifically, Stackelberg game models are [...] Read more.

This study explores the information misreporting behavior among channel members and the optimal pricing strategies in a dual-channel supply chain under information asymmetry, where the manufacturer operates an online channel, and the retailer operates an offline channel. More specifically, Stackelberg game models are developed for both manufacturer-led and retailer-led scenarios to analyze the impact of different power structures on the pricing decisions, information misreporting behavior, and the profits of both individual members and the overall supply chain. The main findings are as follows: (1) The power structure exerts a pivotal influence on the misinformation strategies adopted by supply chain members. (2) As the retailer’s misinformation factor increases, the wholesale price decreases, whereas the traditional retail price rises. (3) The profit advantage from dominance is counteracted by misreporting, and the extent of this effect depends on cross-price sensitivity. (4) Followers often resort to information misreporting to maximize their own profits, a strategy that benefits the misreporting party individually yet undermines the total supply chain profit. Full article

(This article belongs to the Special Issue Mathematical Modelling and Optimization for Sustainable Operations Management, 2nd Edition)

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21 pages, 2695 KB

Open AccessArticle

Ship Spare Parts Optimization Model Based on Ideal Point Method and Improved Ant Colony Algorithm

by Tianyu Ma, Huiling Sun, Rui Qi and Xiangjun Li

Mathematics 2025, 13(23), 3862; https://doi.org/10.3390/math13233862 - 2 Dec 2025

Viewed by 259

Abstract

This study proposes an optimization approach for ship spare parts allocation by integrating the ideal point method (IPM) with an improved ant colony algorithm. The traditional R/C (Reliability–Cost Ratio) model is constrained by single-objective formulations that fail to reconcile cost efficiency with system [...] Read more.

This study proposes an optimization approach for ship spare parts allocation by integrating the ideal point method (IPM) with an improved ant colony algorithm. The traditional R/C (Reliability–Cost Ratio) model is constrained by single-objective formulations that fail to reconcile cost efficiency with system reliability, often producing the paradoxical result that fewer spare parts correspond to higher reliability. To address this limitation, a multi-objective model was constructed for reliability–cost optimization, while the enhanced ant colony algorithm identifies optimal spare part configurations that achieve balanced trade-offs. Nine representative scenarios were analyzed, with simulation outcomes compared between the IPM and R/C model approaches. Sensitivity analyses of critical parameters were conducted, and the effectiveness of both approaches was evaluated. The results demonstrate that the IPM consistently achieves higher reliability, particularly under stringent reliability requirements and tighter spare parts constraints. The findings provide a robust analytical foundation for evidence-based decision-making in ship equipment support. Full article

(This article belongs to the Special Issue Optimization Theory, Algorithms and Applications)

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Mathematics, Volume 13, Issue 23 (December-1 2025) – 158 articles

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