Mathematics

31 pages, 6941 KiB

Open AccessArticle

A Heuristic Approach for Last-Mile Delivery with Consistent Considerations and Minimum Service for a Supply Chain

by Esteban Santana Contreras, John Willmer Escobar and Rodrigo Linfati

Mathematics 2025, 13(10), 1553; https://doi.org/10.3390/math13101553 (registering DOI) - 8 May 2025

This paper considers the problem of consistent routing with minimum service (ConVRPms). ConVRPms aims to determine the minimum cost routes for each day of a planning horizon. In particular, the goal is to satisfy all individual demands and serve every customer via a [...] Read more.

This paper considers the problem of consistent routing with minimum service (ConVRPms). ConVRPms aims to determine the minimum cost routes for each day of a planning horizon. In particular, the goal is to satisfy all individual demands and serve every customer via a single driver, with times that do not differ by more than

L

time units. There is a fleet of homogeneous vehicles that start from a single depot. In this paper, a heuristic algorithm for ConVRPms is proposed. The algorithm is based on classical constructive heuristics and the tabu search metaheuristic. The proposed algorithm has been tested on benchmark instances from the literature. The experimental results show that the proposed approach produces high-quality solutions within computing times considerably less than those observed with CPLEX. The proposed algorithm can optimally solve instances with 20 customers and a planning horizon of three days, producing more economical solutions in some of the larger instances and those requiring hourly consistency (

L = 1 h

). Full article

(This article belongs to the Special Issue Advances in Operations Research for Logistic and Operations Management of Supply Chain Management)

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11 pages, 437 KiB

Open AccessFeature PaperArticle

A Multi-Period Optimization Framework for Portfolio Selection Using Interval Analysis

by Florentin Șerban

Mathematics 2025, 13(10), 1552; https://doi.org/10.3390/math13101552 - 8 May 2025

Abstract

This paper presents a robust multi-period portfolio optimization framework that integrates interval analysis, entropy-based diversification, and downside risk control. In contrast to classical models relying on precise probabilistic assumptions, our approach captures uncertainty through interval-valued parameters for asset returns, risk, and liquidity—particularly suitable [...] Read more.

This paper presents a robust multi-period portfolio optimization framework that integrates interval analysis, entropy-based diversification, and downside risk control. In contrast to classical models relying on precise probabilistic assumptions, our approach captures uncertainty through interval-valued parameters for asset returns, risk, and liquidity—particularly suitable for volatile markets such as cryptocurrencies. The model seeks to maximize terminal portfolio wealth over a finite investment horizon while ensuring compliance with return, risk, liquidity, and diversification constraints at each rebalancing stage. Risk is modeled using semi-absolute deviation, which better reflects investor sensitivity to downside outcomes than variance-based measures, and diversification is promoted through Shannon entropy to prevent excessive concentration. A nonlinear multi-objective formulation ensures computational tractability while preserving decision realism. To illustrate the practical applicability of the proposed framework, a simulated case study is conducted on four major cryptocurrencies—Bitcoin (BTC), Ethereum (ETH), Solana (SOL), and Binance Coin (BNB). The model evaluates three strategic profiles based on investor risk attitude: pessimistic (lower return bounds and upper risk bounds), optimistic (upper return bounds and lower risk bounds), and mixed (average values). The resulting final terminal wealth intervals are [1085.32, 1163.77] for the pessimistic strategy, [1123.89, 1245.16] for the mixed strategy, and [1167.42, 1323.55] for the optimistic strategy. These results demonstrate the model’s adaptability to different investor preferences and its empirical relevance in managing uncertainty under real-world volatility conditions. Full article

(This article belongs to the Section E: Applied Mathematics)

27 pages, 2484 KiB

Open AccessArticle

Hybrid LSTM–Transformer Architecture with Multi-Scale Feature Fusion for High-Accuracy Gold Futures Price Forecasting

by Yali Zhao, Yingying Guo and Xuecheng Wang

Mathematics 2025, 13(10), 1551; https://doi.org/10.3390/math13101551 - 8 May 2025

Abstract

Amidst global economic fluctuations and escalating geopolitical risks, gold futures, as a pivotal safe-haven asset, demonstrate price dynamics that directly impact investor decision-making and risk mitigation effectiveness. Traditional forecasting models face significant limitations in capturing long-term trends, addressing abrupt volatility, and mitigating multi-source [...] Read more.

Amidst global economic fluctuations and escalating geopolitical risks, gold futures, as a pivotal safe-haven asset, demonstrate price dynamics that directly impact investor decision-making and risk mitigation effectiveness. Traditional forecasting models face significant limitations in capturing long-term trends, addressing abrupt volatility, and mitigating multi-source noise within complex market environments characterized by nonlinear interactions and extreme events. Current research predominantly focuses on single-model approaches (e.g., ARIMA or standalone neural networks), inadequately addressing the synergistic effects of multimodal market signals (e.g., cross-market index linkages, exchange rate fluctuations, and policy shifts) and lacking the systematic validation of model robustness under extreme events. Furthermore, feature selection often relies on empirical assumptions, failing to uncover non-explicit correlations between market factors and gold futures prices. A review of the global literature reveals three critical gaps: (1) the insufficient integration of temporal dependency and global attention mechanisms, leading to imbalanced predictions of long-term trends and short-term volatility; (2) the neglect of dynamic coupling effects among cross-market risk factors, such as energy ETF-metal market spillovers; and (3) the absence of hybrid architectures tailored for high-frequency noise environments, limiting predictive utility for decision support. This study proposes a three-stage LSTM–Transformer–XGBoost fusion framework. Firstly, XGBoost-based feature importance ranking identifies six key drivers from thirty-six candidate indicators: the NASDAQ Index, S&P 500 closing price, silver futures, USD/CNY exchange rate, China’s 1-year Treasury yield, and Guotai Zhongzheng Coal ETF. Second, a dual-channel deep learning architecture integrates LSTM for long-term temporal memory and Transformer with multi-head self-attention to decode implicit relationships in unstructured signals (e.g., market sentiment and climate policies). Third, rolling-window forecasting is conducted using daily gold futures prices from the Shanghai Futures Exchange (2015–2025). Key innovations include the following: (1) a bidirectional LSTM–Transformer interaction architecture employing cross-attention mechanisms to dynamically couple global market context with local temporal features, surpassing traditional linear combinations; (2) a Dynamic Hierarchical Partition Framework (DHPF) that stratifies data into four dimensions (price trends, volatility, external correlations, and event shocks) to address multi-driver complexity; (3) a dual-loop adaptive mechanism enabling endogenous parameter updates and exogenous environmental perception to minimize prediction error volatility. This research proposes innovative cross-modal fusion frameworks for gold futures forecasting, providing financial institutions with robust quantitative tools to enhance asset allocation optimization and strengthen risk hedging strategies. It also provides an interpretable hybrid framework for derivative pricing intelligence. Future applications could leverage high-frequency data sharing and cross-market risk contagion models to enhance China’s influence in global gold pricing governance. Full article

(This article belongs to the Special Issue Complex Process Modeling and Control Based on AI Technology)

20 pages, 433 KiB

Open AccessArticle

Dynamics of an Impulsive Predator–Prey Model with a Seasonally Mass Migrating Prey Population

by Yunpeng Xiao and Jianjun Jiao

Mathematics 2025, 13(10), 1550; https://doi.org/10.3390/math13101550 - 8 May 2025

Abstract

Seasonality is a complex force in nature that affects multiple processes in wild animal populations. Animal mass migration refers to the migration of a large number of animals from a certain distance due to breeding, foraging, climate change or other reasons. In this [...] Read more.

Seasonality is a complex force in nature that affects multiple processes in wild animal populations. Animal mass migration refers to the migration of a large number of animals from a certain distance due to breeding, foraging, climate change or other reasons. In this work, an impulsive predator–prey model with a seasonally mass migrating prey population is constructed. The predator–extinction boundary periodic solution of system (3) is proved to be globally asymptotically stable. System (3) is also proved to be permanent. Our results provide a theoretical reference for biodiversity protection management. Full article

(This article belongs to the Section E3: Mathematical Biology)

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17 pages, 287 KiB

Open AccessFeature PaperArticle

T-Eigenvalues of Third-Order Quaternion Tensors

by Zhuo-Heng He, Mei-Ling Deng and Shao-Wen Yu

Mathematics 2025, 13(10), 1549; https://doi.org/10.3390/math13101549 - 8 May 2025

Abstract

In this paper, theories, algorithms and properties of eigenvalues of quaternion tensors via the t-product termed T-eigenvalues are explored. Firstly, we define the T-eigenvalue of quaternion tensors and provide an algorithm to compute the right T-eigenvalues and the corresponding T-eigentensors, along with an [...] Read more.

In this paper, theories, algorithms and properties of eigenvalues of quaternion tensors via the t-product termed T-eigenvalues are explored. Firstly, we define the T-eigenvalue of quaternion tensors and provide an algorithm to compute the right T-eigenvalues and the corresponding T-eigentensors, along with an example to illustrate the efficiency of our algorithm by comparing it with other methods. We then study some inequalities related to the right T-eigenvalues of Hermitian quaternion tensors, providing upper and lower bounds for the right T-eigenvalues of the sum of a pair of Hermitian tensors. We further generalize the Weyl theorem from matrices to quaternion third-order tensors. Additionally, we explore estimations related to right T-eigenvalues, extending the

G e r \overset{ˇ}{s} g o r i n

theorem for matrices to quaternion third-order tensors. Full article

(This article belongs to the Section E: Applied Mathematics)

34 pages, 7854 KiB

Open AccessArticle

Transformer and Convolutional Neural Network: A Hybrid Model for Multimodal Data in Multiclass Classification of Alzheimer’s Disease

by Abdulaziz Alorf

Mathematics 2025, 13(10), 1548; https://doi.org/10.3390/math13101548 - 8 May 2025

Abstract

Alzheimer’s disease (AD) is a form of dementia that progressively impairs a person’s mental abilities. Current classification methods for the six AD stages perform poorly in multiclass classification and are computationally expensive, which hinders their clinical use. An efficient, low-computational model for accurate [...] Read more.

Alzheimer’s disease (AD) is a form of dementia that progressively impairs a person’s mental abilities. Current classification methods for the six AD stages perform poorly in multiclass classification and are computationally expensive, which hinders their clinical use. An efficient, low-computational model for accurate multiclass classification across all AD stages is needed that can integrate both local and global feature extraction. This study uses rs-fMRI, clinical data, and transformer-based models to classify six AD stages. The proposed network is a hybrid of two architectures, namely a transformer and a convolutional neural network (CNN). The model addresses multiclass classification by examining the brain’s functional connectivity networks based on rs-fMRI data and clinical data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI). The proposed architecture leverages CNNs for local feature extraction and transformers for global context; this method employs the contextual attention power of transformers to improve the multiclass classification accuracy of AD. The k-fold cross-validation method was employed to evaluate the performance of the proposed model. For the multiclass classification of six stages, the average accuracy of the model was 96%. For binary classification, accuracies were 98.96% (AD vs. MCI), 99.65% (AD vs. CN), 98.44% (AD vs. LMCI), 96.88% (AD vs. EMCI), and 98.36% (AD vs. SMC). These results highlight the potential of the proposed network in achieving high accuracy for both binary and multistage AD classification with limited computational resources. The proposed method was also compared to benchmark algorithms and outperformed them; it was substantially less computationally expensive while maintaining its accuracy. Full article

(This article belongs to the Special Issue Mathematical Modeling and Analysis in Biology and Medicine, 3rd Edition)

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26 pages, 5428 KiB

Open AccessArticle

Multi-Subject Decision-Making Analysis in the Public Opinion of Emergencies: From an Evolutionary Game Perspective

by Chen Guo and Yinghua Song

Mathematics 2025, 13(10), 1547; https://doi.org/10.3390/math13101547 - 8 May 2025

Abstract

This study employs evolutionary game theory to analyze the tripartite interaction among government regulators, media publishers, and self-media participants in emergency public opinion management. We establish an evolutionary game model incorporating strategic motivations and key influencing factors; then, we validate the model through [...] Read more.

This study employs evolutionary game theory to analyze the tripartite interaction among government regulators, media publishers, and self-media participants in emergency public opinion management. We establish an evolutionary game model incorporating strategic motivations and key influencing factors; then, we validate the model through systematic simulations. Key findings demonstrate the following: ① the system exhibits dual stable equilibria: regulated equilibrium and autonomous equilibrium. ② Sensitivity analysis identifies critical dynamics: ① self-media behavior is primarily driven by penalty avoidance (

g_{3}

) and losses (

w_{2}

); ② media participation hinges on revenue incentives (

m_{2}

) versus regulatory burdens (

k

); ③ government intervention efficacy diminishes on emergencies when resistance (

v_{1}

+

v_{3}

) exceeds control benefits. The study reveals that effective governance requires the following: ① adaptive parameter tuning of punishment–reward mechanisms; ② dynamic coordination between information control and market incentives. This framework advances emergency management by quantifying how micro-level interactions shape macro-level opinion evolution, providing actionable insights for balancing stability and information freedom in digital governance. Full article

(This article belongs to the Special Issue Mathematical Modelling in Decision Making Analysis)

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22 pages, 398 KiB

Open AccessArticle

High-Dimensional Modeling of Huanglongbing Dynamics with Time-Varying Impulsive Control

by Feiping Xie, Youquan Luo, Yan Zhang and Shujing Gao

Mathematics 2025, 13(10), 1546; https://doi.org/10.3390/math13101546 - 8 May 2025

Abstract

This study develops a high-dimensional impulsive differential equation model to analyze Huanglongbing (HLB) transmission dynamics, incorporating seasonal fluctuations in vector psyllid populations and multi-pronged control measures: (1) periodic removal of infected/dead citrus trees to eliminate pathogen reservoirs and (2) non-uniform pesticide applications timed [...] Read more.

This study develops a high-dimensional impulsive differential equation model to analyze Huanglongbing (HLB) transmission dynamics, incorporating seasonal fluctuations in vector psyllid populations and multi-pronged control measures: (1) periodic removal of infected/dead citrus trees to eliminate pathogen reservoirs and (2) non-uniform pesticide applications timed to disrupt psyllid life cycles. The model analytically derives the basic reproduction number (

R_{0}

) and proves the existence of a unique disease-free periodic solution. Theoretical analysis reveals a threshold-dependent stability: when

R_{0} < 1

, the disease-free solution is globally asymptotically stable, ensuring pathogen extinction; when

R_{0} > 1

, the system becomes uniformly persistent, indicating endemic HLB. Numerical simulations validate these findings and demonstrate that integrated interventions, combining psyllid population control and removal of infected plants, can significantly suppress HLB spread. The results provide a mathematical framework for optimizing intervention timing and intensity, offering actionable strategies for citrus growers. Full article

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32 pages, 848 KiB

Open AccessArticle

Differentiated Advertising, Heterogeneous Consumers and Suitable Design of Platform Merchant

by Xuefeng Zhang, Ji Luo and Xiao Liu

Mathematics 2025, 13(10), 1545; https://doi.org/10.3390/math13101545 - 8 May 2025

Abstract

The limited endowment of initial traffic creates fierce competition among merchants for securing scarce resources in e-commerce platforms. Optimal pricing mechanisms are imperative to maximize transaction volumes and attract sustained traffic support from platforms. This study investigates merchant pricing mechanisms under two advertising [...] Read more.

The limited endowment of initial traffic creates fierce competition among merchants for securing scarce resources in e-commerce platforms. Optimal pricing mechanisms are imperative to maximize transaction volumes and attract sustained traffic support from platforms. This study investigates merchant pricing mechanisms under two advertising strategies—broadband advertising and targeted advertising—by constructing differentiated pricing models that account for consumer preference heterogeneity. The findings reveal that, in most cases where merchants prioritize profit maximization, targeted advertising-driven pricing mechanisms outperform broadband advertising strategies. However, when merchants prioritize early-stage sales volume, broadband advertising proves to be more advantageous. Furthermore, the study shows that merchant pricing strategies evolve over their lifecycle, transitioning from offering lower prices to high-type consumers toward progressively higher prices, thus validating the underlying mechanism of “big data price discrimination” (the phenomenon of “killing loyal customers”). Additionally, this research emphasizes the importance of accurately understanding consumer preferences, as the sensitivity differential between price and advertising responses plays a crucial moderating role. When the sensitivity gap becomes excessively large, the price differential in differentiated pricing mechanisms should be proportionally reduced to maintain effectiveness. In conclusion, by integrating consumer utility, merchant profit, and platform incentives, pricing mechanisms based on targeted advertising exhibit superior capabilities in screening consumer information. When combined with advertising effectiveness and consumer preference heterogeneity, these mechanisms represent a relatively optimal strategy. However, this conclusion holds only when the proportion of high-type consumers in the market is moderate, not excessively low. This study contributes to the literature by providing a comprehensive framework for merchants to select appropriate pricing strategies under varying advertising environments and consumer structures. Full article

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23 pages, 114840 KiB

Open AccessArticle

AIF: Infrared and Visible Image Fusion Based on Ascending–Descending Mechanism and Illumination Perception Subnetwork

by Ying Liu, Xinyue Mi, Zhaofu Liu and Yu Yao

Mathematics 2025, 13(10), 1544; https://doi.org/10.3390/math13101544 - 8 May 2025

Abstract

The purpose of infrared and visible image fusion is to generate a composite image that can contain both the thermal radiation profile information of the infrared image and the texture details of the visible image. This kind of composite image can be used [...] Read more.

The purpose of infrared and visible image fusion is to generate a composite image that can contain both the thermal radiation profile information of the infrared image and the texture details of the visible image. This kind of composite image can be used to detect targets under various lighting conditions and offer high scene spatial resolution. However, the existing image fusion algorithms rarely consider light factor in the modeling process. The study presents a novel image fusion approach (AIF) that can adaptively fuse infrared and visible images under various lighting conditions. Specifically, the infrared image and the visible image are extracted by the AdC feature extractor, respectively, and both of them are adaptively fused under the guidance of the illumination perception subnetwork. The image fusion model is trained in an unsupervised manner with a customized loss function. The AdC feature extractor adopts an ascending–descending feature extraction mechanism to organize convolutional layers and combines these convolutional layers with cross-modal interactive differential modules to achieve the effective extraction of hierarchical complementary and differential information. The illumination perception subnetwork obtains the scene lighting condition based on the visible image, which determines the contribution weights of the visible image and the infrared image in the composite image. The customized loss function consists of illumination loss, gradient loss, and intensity loss. It is more targeted and can effectively improve the fusion effect of visible images and infrared images under different lighting conditions. Ablation experiments demonstrate the effectiveness of the loss function. We compare our method with nine other methods on public datasets, including four traditional methods and five deep-learning-based methods. Qualitative and quantitative experiments show that our method performs better in terms of indicators such as SD, and the fused image has more prominent contour information and richer detail information. Full article

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17 pages, 279 KiB

Open AccessArticle

CL-Transformation on 3-Dimensional Quasi Sasakian Manifolds and Their Ricci Soliton

by Rajesh Kumar, Lalnunenga Colney and Dalal Alhwikem

Mathematics 2025, 13(10), 1543; https://doi.org/10.3390/math13101543 - 8 May 2025

Abstract

This paper explores the geometry of 3-dimensional quasi Sasakian manifolds under CL-transformations. We construct both infinitesimal and

C L

-transformation and demonstrate that the former does not necessarily yield projective killing vector fields. A novel invariant tensor, termed the

C L

-curvature [...] Read more.

This paper explores the geometry of 3-dimensional quasi Sasakian manifolds under CL-transformations. We construct both infinitesimal and

C L

-transformation and demonstrate that the former does not necessarily yield projective killing vector fields. A novel invariant tensor, termed the

C L

-curvature tensor, is introduced and shown to remain invariant under

C L

-transformations. Utilizing this tensor, we characterize

C L

-flat,

C L

-symmetric,

C L

-

φ

symmetric and

C L

-

φ

recurrent structures on such manifolds by mean of differential equations. Furthermore, we investigate conditions under which a Ricci soliton exists on a CL-transformed quasi Sasakian manifold, revealing that under flat curvature, the structure becomes Einstein. These findings contribute to the understanding of curvature dynamics and soliton theory within the context of contact metric geometry. Full article

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

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, 438 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

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

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

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

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

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

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

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

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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