Mathematics

26 pages, 1269 KB

Open AccessArticle

Fair Transmission Expansion Cost Allocation for Renewable Energy Resource Interconnection Based on Stochastic Cooperative Game Theory

by Youngjun Go, Wonseok Choi, Minsung Kim, Jin-Ho Chung, Hyeonjin Kim and Duehee Lee

Mathematics 2025, 13(24), 3898; https://doi.org/10.3390/math13243898 (registering DOI) - 5 Dec 2025

Abstract

We propose a fair transmission expansion cost allocation (CA) algorithm and a fair process to build alternative transmission expansion plans. We define fairness such that each participant’s payment does not exceed its own benefit and the total payment equals the total TEP cost. [...] Read more.

We propose a fair transmission expansion cost allocation (CA) algorithm and a fair process to build alternative transmission expansion plans. We define fairness such that each participant’s payment does not exceed its own benefit and the total payment equals the total TEP cost. In our framework, excessive payments over generator benefits are minimized. Owners of renewable energy resources (RES)s can choose the point of interconnection via the CA algorithm; owners in the same interconnection queue may form an intermediate coalition to persuade owners of expensive bottleneck plans to change at reduced allocation cost. Fairness is implemented using stochastic cooperative game theory (SCGT); the fair CA is obtained by recursively minimizing the largest unfairness, which is the difference between payments and benefits, through coalitions. Benefits consider transmission usage, transmission-induced gains, and the variability of RESs and demand. We design spatially and temporally correlated RESs and demand scenarios using Gibbs sampling specialized for long-term interconnection studies, validate plausibility against a benchmark from the Global Probabilistic Mid-term Load Forecasting Competition 2017, and verify fairness by showing that entities with greater benefits pay larger costs. Full article

(This article belongs to the Topic Advances in Planning, Operation, Control/Protection, and Market of New Power Energy System)

34 pages, 1252 KB

Open AccessArticle

Pricing Optimization for High-Speed Railway Considering Hybrid Choice Behavior of Heterogeneous Passengers Under Stochastic Demand

by Yu Wang and Zhendong Wang

Mathematics 2025, 13(24), 3897; https://doi.org/10.3390/math13243897 (registering DOI) - 5 Dec 2025

Abstract

Passenger heterogeneity in loyalty fundamentally influences their choice behaviors, and is pivotal to railway differentiated pricing. Thus, travelers are categorized into loyal passengers and non-loyal passengers. According to the generalized cost minimization, we identify a train priority sequence reflecting consistent preferences of loyal [...] Read more.

Passenger heterogeneity in loyalty fundamentally influences their choice behaviors, and is pivotal to railway differentiated pricing. Thus, travelers are categorized into loyal passengers and non-loyal passengers. According to the generalized cost minimization, we identify a train priority sequence reflecting consistent preferences of loyal passengers and establish a train selection probability model based on stochastic preferences of non-loyal passengers. Then, a hybrid choice model resulting from the distinct decision-making processes of these two passenger categories is formulated. A nonlinear pricing optimization model in the scenario of multiple train categories with multiple trains is established. An improved Particle Swarm Optimization algorithm based on the Sampling Fitness Strategy (SFS-PSO) is proposed to improve the solution accuracy. The SFS-PSO enhances the search diversity for the personal historical best positions and global best position without expanding the size of the particle swarm as much as possible. The case analysis demonstrates that the proposed pricing optimization approach can increase the expected revenue by 1.7%, validating the rationality of considering the hybrid choice behavior of passenger loyalty heterogeneity for the railway pricing optimization problem. Meanwhile, the case results highlighted the significant impact of the proportion of loyal passengers on revenue improvement. Full article

(This article belongs to the Special Issue Fusion of Evolutionary Computation and Multidisciplinary Innovations for Emerging Optimization Challenges)

31 pages, 5905 KB

Open AccessArticle

Very Flexible Weibull Reliability Modeling for Shock Environments Using Unified Censoring Plans

by Ahmed Elshahhat and Eslam Abdelhakim Seyam

Mathematics 2025, 13(24), 3896; https://doi.org/10.3390/math13243896 (registering DOI) - 5 Dec 2025

Abstract

The very flexible Weibull (VF-W) distribution is formulated by expressing its cumulative risk function as a logarithmic composite of auxiliary cumulative risks, making the model particularly well-suited for modeling heterogeneous life behaviors. This model admits a remarkably flexible hazard structure, capable of generating [...] Read more.

The very flexible Weibull (VF-W) distribution is formulated by expressing its cumulative risk function as a logarithmic composite of auxiliary cumulative risks, making the model particularly well-suited for modeling heterogeneous life behaviors. This model admits a remarkably flexible hazard structure, capable of generating monotone increasing, unimodal (increase-then-decrease), and multi-turning-point shapes, thereby capturing complex failure behaviors far beyond those allowed by the classical Weibull distribution. This paper presents a comprehensive inferential study of the VF-W model through the unified progressive hybrid (UPH) censoring framework for modeling shock-type lifetime data. The UPH scheme integrates the advantages of Type-II, generalized hybrid, and progressive hybrid censoring mechanisms into a unified structure that ensures efficiency and adaptability in reliability testing. Classical inference is developed through maximum likelihood estimation with asymptotic interval construction, while Bayesian inference is performed using independent gamma priors and a Markov iterative algorithm. Extensive Monte Carlo experiments are conducted to evaluate the finite-sample performance of both approaches under various censoring intensities, revealing that the Bayesian MCMC-based estimators and their highest posterior density intervals provide superior precision, coverage, and robustness. The proposed VF-W model using UPH-based strategy is further validated through the analysis of a real shocks dataset, where it demonstrates a comparative performance improvement over existing models. The VF-W model exhibits stable parameter estimation under diverse censoring levels, indicating robustness in incomplete-data scenarios. Furthermore, the model maintains analytical tractability, offering closed-form expressions for key reliability measures, which facilitates practical implementation in different scenarios. The results confirm the VFW model’s strong potential as a unifying and computationally stable tool for reliability modeling, particularly in complex engineering and physical systems operating under stochastic shock environments. Full article

(This article belongs to the Special Issue Reliability Analysis and Statistical Computing)

17 pages, 728 KB

Open AccessArticle

Multi-Aspect Sentiment Analysis of Arabic Café Reviews Using Machine and Deep Learning Approaches

by Hmood Al-Dossari and Munerah Altalasi

Mathematics 2025, 13(24), 3895; https://doi.org/10.3390/math13243895 (registering DOI) - 5 Dec 2025

Abstract

Online reviews on platforms such as Google Maps strongly influence consumer decisions. However, aggregated ratings mask nuanced opinions about specific aspects such as food, drinks, service, lounge, and price. This study presents a multi-aspect sentiment analysis framework for Arabic café reviews. Specifically, we [...] Read more.

Online reviews on platforms such as Google Maps strongly influence consumer decisions. However, aggregated ratings mask nuanced opinions about specific aspects such as food, drinks, service, lounge, and price. This study presents a multi-aspect sentiment analysis framework for Arabic café reviews. Specifically, we combine machine learning (Linear SVC, Naïve Bayes, Logistic Regression, Decision Tree, Random Forest) and a Convolutional Neural Network (CNN) to perform aspect identification and sentiment classification. A rigorous preprocessing and feature-engineering with TF-IDF and n-gram was implemented and statistically validated through bootstrap confidence intervals and Friedman–Nemenyi significance tests. Experimental results demonstrate that Linear SVC with optimized TF-IDF tri-grams achieved a macro-F1 of 0.89 for aspect identification and 0.71 for sentiment classification. Meanwhile, the CNN model yielded a comparable F1 of 0.89 for aspect identification and a higher 0.76 for sentiment classification. The findings highlight that effective feature representation and model selection can substantially improve Arabic opinion mining. The proposed framework provides a reliable foundation for analyzing Arabic user feedback on location-based platforms and supports more interpretable and data-driven business insights. These insights are essential to enhance personalized recommendations and business intelligence in the hospitality sector. Full article

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

22 pages, 359 KB

Open AccessFeature PaperArticle

Associative Ternary Algebras and Ternary Lie Algebras at Cube Roots of Unity

by Anti Maria Aader, Viktor Abramov and Olga Liivapuu

Mathematics 2025, 13(24), 3894; https://doi.org/10.3390/math13243894 (registering DOI) - 5 Dec 2025

Abstract

We propose an approach to extend the concept of a Lie algebra to ternary structures based on

ω

-symmetry, where

ω

is a primitive cube root of unity. We give a definition of a corresponding structure, called a ternary Lie algebra at cube [...] Read more.

We propose an approach to extend the concept of a Lie algebra to ternary structures based on

ω

-symmetry, where

ω

is a primitive cube root of unity. We give a definition of a corresponding structure, called a ternary Lie algebra at cube roots of unity, or a ternary

ω

-Lie algebra. A method for constructing ternary associative algebras has been developed. For ternary algebras, the notions of the ternary

ω

-associator and the ternary

ω

-commutator are introduced. It is shown that if a ternary algebra possesses the property of associativity of the first or second kind, then the ternary

ω

-commutator on this algebra determines the structure of a ternary

ω

-Lie algebra. Ternary algebras of cubic matrices with associative ternary multiplication of the second kind are considered. The structure of the 8-dimensional ternary

ω

-Lie algebra of cubic matrices of the second order is studied, and all its subalgebras of dimensions 2 and 3 are determined. Full article

(This article belongs to the Special Issue Advances in Algebraic Structures: Representation Theory and Lie Groups)

13 pages, 729 KB

Open AccessArticle

A Single-Neuron-per-Class Readout for Image-Encoded Sensor Time Series

by David Bernal-Casas and Jaime Gallego

Mathematics 2025, 13(24), 3893; https://doi.org/10.3390/math13243893 (registering DOI) - 5 Dec 2025

Abstract

We introduce an ultra-compact, single-neuron-per-class end-to-end readout for binary classification of noisy, image-encoded sensor time series. The approach compares a linear single-unit perceptron (E2E-MLP-1) with a resonate-and-fire (RAF) neuron (E2E-RAF-1), which merges feature selection and decision-making in a single block. Beyond empirical evaluation, [...] Read more.

We introduce an ultra-compact, single-neuron-per-class end-to-end readout for binary classification of noisy, image-encoded sensor time series. The approach compares a linear single-unit perceptron (E2E-MLP-1) with a resonate-and-fire (RAF) neuron (E2E-RAF-1), which merges feature selection and decision-making in a single block. Beyond empirical evaluation, we provide a mathematical analysis of the RAF readout: starting from its subthreshold ordinary differential equation, we derive the transfer function

H (j ω)

, characterize the frequency response, and relate the output signal-to-noise ratio (SNR) to

{| H (j ω) |}^{2}

and the noise power spectral density

S_{n} (ω) \propto ω^{α}

(brown, pink, and blue noise). We present a stable discrete-time implementation compatible with surrogate gradient training and discuss the associated stability constraints. As a case study, we classify walk-in-place (WIP) in a virtual reality (VR) environment, a vision-based motion encoding (72 × 56 grayscale) derived from 3D trajectories, comprising 44,084 samples from 15 participants. On clean data, both single-neuron-per-class models approach ceiling accuracy. At the same time, under colored noise, the RAF readout yields consistent gains (typically +5–8% absolute accuracy at medium/high perturbations), indicative of intrinsic band-selective filtering induced by resonance. With ∼8 k parameters and sub-2 ms inference on commodity graphical processing units (GPUs), the RAF readout provides a mathematically grounded, robust, and efficient alternative for stochastic signal processing across domains, with virtual reality locomotion used here as an illustrative validation. Full article

(This article belongs to the Special Issue Computer Vision, Image Processing Technologies and Machine Learning)

► Show Figures

Figure 1

33 pages, 1704 KB

Open AccessArticle

AGF-HAM: Adaptive Gated Fusion Hierarchical Attention Model for Explainable Sentiment Analysis

by Mahander Kumar, Lal Khan, Mohammad Zubair Khan and Amel Ali Alhussan

Mathematics 2025, 13(24), 3892; https://doi.org/10.3390/math13243892 (registering DOI) - 5 Dec 2025

Abstract

The rapid growth of user-generated content in the digital space has increased the necessity of properly and interpretively analyzing sentiment and emotion systems. This research paper presents a new hybrid model, HAM (Hybrid Attention-based Model), a Transformer-based contextual embedding model combined with deep [...] Read more.

The rapid growth of user-generated content in the digital space has increased the necessity of properly and interpretively analyzing sentiment and emotion systems. This research paper presents a new hybrid model, HAM (Hybrid Attention-based Model), a Transformer-based contextual embedding model combined with deep sequential modeling and multi-layer explainability. The suggested framework integrates the BERT/RoBERTa encoders, Bidirectional LSTM, and Graph Attention that can be used to embrace semantic and aspect-level sentiment correlation. Additionally, an enhanced Explainability Module, including Attention Heatmaps, Aspect-Level Interpretations, and SHAP/Integrated Gradients analysis, contributes to the increased model transparency and interpretive reliability. Four benchmark datasets, namely GoEmotions-1, GoEmotions-2, GoEmotions-3, and Amazon Cell Phones and Accessories Reviews, were experimented on in order to have a strong cross-domain assessment. The 28 emotion words of GoEmotions were merged into five sentiment-oriented classes to harmonize the dissimilarity in the emotional granularities to fit the schema of the Amazon dataset. The proposed HAM model had a highest accuracy of 96.4% and F1-score of 94.9%, which was significantly higher than the state-of-the-art baselines like BERT (89.8%), RoBERTa (91.7%), and RoBERTa+BiLSTM (92.5%). These findings support the idea that HAM is a better solution to finer-grained emotional details and is still interpretable as a vital move towards creating open, exposible, and domain-tailored sentiment intelligence systems. Future endeavors will aim at expanding this architecture to multimodal fusion, cross-lingual adaptability, and federated learning systems to increase the scalability, generalization, and ethical application of AI. Full article

(This article belongs to the Section E1: Mathematics and Computer Science)

► Show Figures

Figure 1

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

Abstract

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)

► Show Figures

Figure 1

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

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

► Show Figures

Figure 1

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

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)

► Show Figures

Figure 1

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

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)

► Show Figures

Figure 1

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

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

► Show Figures

Figure 1

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

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)

► Show Figures

Figure 1

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

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)

► Show Figures

Figure 1

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

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)

► Show Figures

Figure 1

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

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)

► Show Figures

Figure 1

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

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)

► Show Figures

Figure 1

18 pages, 814 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

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)

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

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)

Journal Description

Mathematics

Latest Articles

Journal Menu

Journal Browser

Highly Accessed Articles

Latest Books

E-Mail Alert

News

Topics

Conferences

Special Issues

Topical Collections

Further Information

Guidelines

MDPI Initiatives

Follow MDPI