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Mathematics
Volume 13
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Mathematics, Volume 13, Issue 2 (January-2 2025) – 149 articles

Cover Story (view full-size image): Accurate crude oil price forecasting is crucial due to oil's critical role in the global economy. In this study, we introduce a Crude Oil-driven Conditional Generative Adversarial Network (CO-CGAN) framework for forecasting, integrating advanced techniques into a unified, mathematically rigorous approach. The model enhances prediction accuracy by combining Generative Adversarial Networks (GANs) with market sentiment analysis and a Lévy jump-diffusion process, capturing both continuous fluctuations and discrete jumps in price dynamics. Lévy parameters are calibrated using a neural network, while the Grey Wolf Optimizer (GWO) efficiently tunes hyperparameters, ensuring robust performance in addressing market volatility and non-linear price behavior. View this paper
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17 pages, 1341 KiB  
Article
Two-Party Quantum Private Comparison Protocol for Direct Secret Comparison
by Min Hou and Yue Wu
Mathematics 2025, 13(2), 326; https://doi.org/10.3390/math13020326 - 20 Jan 2025
Viewed by 449
Abstract
In this paper, we leverage the properties of the swap test to evaluate the similarity of two qubits and propose a two-party quantum private comparison (QPC) protocol involving a semi-trusted third party (TP). The TP facilitates the comparison between participants without accessing their [...] Read more.
In this paper, we leverage the properties of the swap test to evaluate the similarity of two qubits and propose a two-party quantum private comparison (QPC) protocol involving a semi-trusted third party (TP). The TP facilitates the comparison between participants without accessing their private information, other than the final comparison results. Our protocol encodes participants’ secret integers directly into the amplitudes of single-photon states and introduces a novel method for secret-to-secret comparison rather than the traditional bit-to-bit comparison, resulting in improved scalability. To ensure security, the encoded single-photon states are concealed using rotation operations. The comparison results are derived through the implementation of the swap test. A simulation on the IBM Quantum Platform demonstrates the protocol’s feasibility, and a security analysis confirms its robustness against potential eavesdropping and participant attacks. Compared with existing QPC protocols that employ bit-to-bit comparison methods, our approach offers improved practicality and scalability. Specifically, it integrates single-photon states, rotation operations, and the swap test as key components for direct secret comparison, facilitating easier implementation with quantum technology. Full article
(This article belongs to the Section E4: Mathematical Physics)
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34 pages, 423 KiB  
Review
Topology Unveiled: A New Horizon for Economic and Financial Modeling
by Yicheng Wei, Junzo Watada and Zijin Wang
Mathematics 2025, 13(2), 325; https://doi.org/10.3390/math13020325 - 20 Jan 2025
Viewed by 534
Abstract
Sinceits introduction in the 19th century to address geometric problems, topology as a methodology has undergone a series of evolutions, encompassing branches of geometric topology, point-set topology (analytic topology), algebraic topology, and differential topology, gradually permeating into various interdisciplinary applied fields. Starting from [...] Read more.
Sinceits introduction in the 19th century to address geometric problems, topology as a methodology has undergone a series of evolutions, encompassing branches of geometric topology, point-set topology (analytic topology), algebraic topology, and differential topology, gradually permeating into various interdisciplinary applied fields. Starting from disciplines with typical geometric characteristics such as geography, physics, biology, and computer science, topology has found its way to economic fields in the 20th century. Given that the introduction of topology to economics is relatively new and presents features of being fragmented and non-systematic, this review aimed to provide scholars with a systematic evolution map to refine the characteristics of topology as a methodology applied in economics and finance, thereby aiding future potential interdisciplinary developments in these fields. By collecting abundant literature indexed in SCOPUS/WoS and other famous databases, with a qualitative analysis to classify and summarize it, we found that topological methods were introduced to modern economics when dealing with dynamic optimization, functional analysis, and convex programming problems, including famous applications such as uncovering equilibrium with fixed-point theorems in Walrasian economics. Topology can help uncover and refine the topological properties of these function space transformations, thus finding unchangeable features. Meanwhile, in contemporary economics, topology is being used for high-dimension reduction, complex network construction, and structural data mining, combined with techniques of machine learning, and applied to high-dimensional time series and structure analysis in financial markets. The most famous practical applications include the use of topological data analysis (TDA) and topological machine learning (TML) for different applied problems. Full article
19 pages, 333 KiB  
Article
Bi-Fuzzy S-Approximation Spaces
by Ronghai Wang, Xiaojie Xie and Huilai Zhi
Mathematics 2025, 13(2), 324; https://doi.org/10.3390/math13020324 - 20 Jan 2025
Viewed by 349
Abstract
The S-approximation spaces are significant extension of the rough set model and have been widely applied in intelligent decision-making. However, traditional S-approximation spaces are limited to two crisp universes, whereas bi-fuzzy universes (i.e., two distinct fuzzy domains) are more prevalent in practical applications. [...] Read more.
The S-approximation spaces are significant extension of the rough set model and have been widely applied in intelligent decision-making. However, traditional S-approximation spaces are limited to two crisp universes, whereas bi-fuzzy universes (i.e., two distinct fuzzy domains) are more prevalent in practical applications. To bridge this gap, this study introduces the bi-fuzzy S-approximation spaces (BFS approximation spaces) as an advancement of knowledge space theory’s fuzzy extension. Upper and lower approximation operators are formally defined, and the properties of BFS approximation spaces under various operations, such as complement, intersection and union are systematically explored. Special attention is given to a significant form of these operators, under which the monotonicity and complementary compatibility of BFS approximation spaces are rigorously analyzed. These results not only extend the theoretical framework of S-approximation spaces but also pave the way for further exploration of fuzzy extensions within knowledge space theory. Full article
(This article belongs to the Special Issue Fuzzy Convex Structures and Some Related Topics, 2nd Edition)
15 pages, 273 KiB  
Article
Density Formula in Malliavin Calculus by Using Stein’s Method and Diffusions
by Hyun-Suk Park
Mathematics 2025, 13(2), 323; https://doi.org/10.3390/math13020323 - 20 Jan 2025
Viewed by 428
Abstract
Let G be a random variable of functionals of an isonormal Gaussian process X defined on some probability space. Studies have been conducted to determine the exact form of the density function of the random variable G. In this paper, unlike previous [...] Read more.
Let G be a random variable of functionals of an isonormal Gaussian process X defined on some probability space. Studies have been conducted to determine the exact form of the density function of the random variable G. In this paper, unlike previous studies, we will use the Stein’s method for invariant measures of diffusions to obtain the density formula of G. By comparing the density function obtained in this paper with that of the diffusion invariant measure, we find that the diffusion coefficient of an Itô diffusion with an invariant measure having a density can be expressed as in terms of operators in Malliavin calculus. Full article
(This article belongs to the Special Issue Differential Equations and Stochastic Processes: Trends and Challenges)
26 pages, 20364 KiB  
Article
Seasonal Mathematical Model of Salmonellosis Transmission and the Role of Contaminated Environments and Food Products
by Mohammed H. Alharbi, Fawaz K. Alalhareth and Mahmoud A. Ibrahim
Mathematics 2025, 13(2), 322; https://doi.org/10.3390/math13020322 - 20 Jan 2025
Viewed by 562
Abstract
Salmonellosis continues to be a global public health priority in which humans, livestock, and the contaminated environment interact with food to create complex interactions. Here, a new non-autonomous model is proposed to capture seasonal dynamics of Salmonella typhimurium transmission with key compartments that [...] Read more.
Salmonellosis continues to be a global public health priority in which humans, livestock, and the contaminated environment interact with food to create complex interactions. Here, a new non-autonomous model is proposed to capture seasonal dynamics of Salmonella typhimurium transmission with key compartments that include humans, cattle, and bacteria in environmental and food sources. The model explores how bacterial growth, shedding, and ingestion rates, along with contamination pathways, determine disease dynamics. Some analytical derivations of the basic reproduction number (R0) and threshold conditions for disease persistence or extinction are derived by using the spectral radius of a linear operator associated with the monodromy matrix. Parameter estimation for the model was accomplished with the aid of Latin hypercube sampling and least squares methods on Salmonella outbreak data from Saudi Arabia ranging from 2018 to 2021. The model was able to conduct an analysis based on the estimated 0.606 value of R0, and this meant that the model was able to fit reasonably well for both the cumulative and the new individual case data, which in turn, suggests the disease is curable. Predictions indicate a gradual decline in the number of new cases, with stabilization anticipated at approximately 40,000 cumulative cases. Further simulations examined the dynamics of disease extinction and persistence based on R0. When R0 is less than 1, the disease-free equilibrium is stable, resulting in the extinction of the disease. Conversely, when R0 exceeds 1, the disease persists, exhibiting endemic characteristics with recurrent outbreaks. Sensitivity analysis identified several parameters as having a significant impact on the model’s outcomes, specifically mortality and infection rates, along with decay rates. These findings highlight the critical importance of precise parameter estimation in understanding and controlling the transmission dynamics of Salmonella. Sensitivity indices and contour plots were employed to assess the impact of various parameters on the basic reproduction number and provide insights into the factors most influencing disease transmission. Full article
(This article belongs to the Special Issue Dynamics and Differential Equations in Mathematical Biology)
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12 pages, 231 KiB  
Article
Polynomial Identities for Binomial Sums of Harmonic Numbers of Higher Order
by Takao Komatsu and B. Sury
Mathematics 2025, 13(2), 321; https://doi.org/10.3390/math13020321 - 20 Jan 2025
Viewed by 407
Abstract
We study the formulas for binomial sums of harmonic numbers of higher order [...] Read more.
We study the formulas for binomial sums of harmonic numbers of higher order ∑k=0nHk(r)nk(1−q)kqn−k=Hn(r)−∑j=1nDr(n,j)qjj. Recently, Mneimneh proved that D1(n,j)=1. In this paper, we find several different expressions of Dr(n,j) for r≥1. Full article
20 pages, 307 KiB  
Article
The Gyrokinetic Limit for the Two-Dimensional Vlasov–Yukawa System with a Point Charge
by Xianghong Hu and Xianwen Zhang
Mathematics 2025, 13(2), 320; https://doi.org/10.3390/math13020320 - 20 Jan 2025
Viewed by 383
Abstract
In this article, we study the asymptotic behavior of the two-dimensional Vlasov–Yukawa system with a point charge under a large external magnetic field. When the intensity of the magnetic field tends to infinity, we show that the kinetic system converges to the measure-valued [...] Read more.
In this article, we study the asymptotic behavior of the two-dimensional Vlasov–Yukawa system with a point charge under a large external magnetic field. When the intensity of the magnetic field tends to infinity, we show that the kinetic system converges to the measure-valued Euler equation with a defect measure, which extends the results of Miot to the case of the Vlasov–Yukawa system. And compared with the Miot’s work, an important improvement is that our results do not require compact support conditions for spatial variables or uniform bound conditions for second-order spatial moments. In addition, the extra small condition for initial data is also not required. Full article
17 pages, 332 KiB  
Article
Finite and Infinte Time Blow Up of Solutions to Wave Equations with Combined Logarithmic and Power-Type Nonlinearities
by Milena Dimova, Natalia Kolkovska and Nikolai Kutev
Mathematics 2025, 13(2), 319; https://doi.org/10.3390/math13020319 - 20 Jan 2025
Viewed by 428
Abstract
In this paper, we investigate the global behavior of the weak solutions to the initial boundary value problem for the nonlinear wave equation in a bounded domain. The nonlinearity includes a logarithmic term and several power-type terms with nonnegative variable coefficients. Two new [...] Read more.
In this paper, we investigate the global behavior of the weak solutions to the initial boundary value problem for the nonlinear wave equation in a bounded domain. The nonlinearity includes a logarithmic term and several power-type terms with nonnegative variable coefficients. Two new necessary and sufficient conditions for blow up of the weak solutions are established. The first one addresses the blow up of the global weak solutions at infinity. The second necessary and sufficient condition is obtained in the case of strong superlinearity and concerns blow up of the weak solutions for a finite time. Additionally, we derive new sufficient conditions on the initial data that guarantee blow up for either finite or infinite time. A comparison with previous results is also given. Full article
13 pages, 352 KiB  
Article
A Robust Hermitian and Skew-Hermitian Based Multiplicative Splitting Iterative Method for the Continuous Sylvester Equation
by Mohammad Khorsand Zak and Abbas Abbaszadeh Shahri
Mathematics 2025, 13(2), 318; https://doi.org/10.3390/math13020318 - 20 Jan 2025
Viewed by 539
Abstract
For solving the continuous Sylvester equation, a class of Hermitian and skew-Hermitian based multiplicative splitting iteration methods is presented. We consider two symmetric positive definite splittings for each coefficient matrix of the continuous Sylvester equations, and it can be equivalently written as two [...] Read more.
For solving the continuous Sylvester equation, a class of Hermitian and skew-Hermitian based multiplicative splitting iteration methods is presented. We consider two symmetric positive definite splittings for each coefficient matrix of the continuous Sylvester equations, and it can be equivalently written as two multiplicative splitting matrix equations. When both coefficient matrices in the continuous Sylvester equation are (non-symmetric) positive semi-definite, and at least one of them is positive definite, we can choose Hermitian and skew-Hermitian (HS) splittings of matrices A and B in the first equation, and the splitting of the Jacobi iterations for matrices A and B in the second equation in the multiplicative splitting iteration method. Convergence conditions of this method are studied in depth, and numerical experiments show the efficiency of this method. Moreover, by numerical computation, we show that multiplicative splitting can be used as a splitting preconditioner and induce accurate, robust and effective preconditioned Krylov subspace iteration methods for solving the continuous Sylvester equation. Full article
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23 pages, 1537 KiB  
Article
CR-Selfdual Cubic Curves
by Mircea Crasmareanu, Cristina-Liliana Pripoae and Gabriel-Teodor Pripoae
Mathematics 2025, 13(2), 317; https://doi.org/10.3390/math13020317 - 19 Jan 2025
Viewed by 350
Abstract
We introduce a special class of cubic curves whose defining parameter satisfies a linear or quadratic equation provided by the values of a cross ratio. There are only seven such cubics and several properties of the real cubics in this class (some of [...] Read more.
We introduce a special class of cubic curves whose defining parameter satisfies a linear or quadratic equation provided by the values of a cross ratio. There are only seven such cubics and several properties of the real cubics in this class (some of them being elliptic curves) are discussed. Using the Möbius transformation, we extend this self-duality and obtain new families of remarkable complex cubics. In addition, we study (from the differential geometric viewpoint) the surface parameterized by all real cubic curves and we derive its curvature functions. As a by-product, we find a new classification of real Möbius transformations and some estimates for the number of vertices of real cubic curves. Full article
(This article belongs to the Special Issue Differential Geometric Structures and Their Applications)
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26 pages, 3274 KiB  
Article
Bulk Low-Inertia Power Systems Adaptive Fault Type Classification Method Based on Machine Learning and Phasor Measurement Units Data
by Mihail Senyuk, Svetlana Beryozkina, Inga Zicmane, Murodbek Safaraliev, Viktor Klassen and Firuz Kamalov
Mathematics 2025, 13(2), 316; https://doi.org/10.3390/math13020316 - 19 Jan 2025
Viewed by 538
Abstract
This research focuses on developing and testing a method for classifying disturbances in power systems using machine learning algorithms and phasor measurement unit (PMU) data. To enhance the speed and accuracy of disturbance classification, we employ a range of ensemble machine learning techniques, [...] Read more.
This research focuses on developing and testing a method for classifying disturbances in power systems using machine learning algorithms and phasor measurement unit (PMU) data. To enhance the speed and accuracy of disturbance classification, we employ a range of ensemble machine learning techniques, including Random forest, AdaBoost, Extreme gradient boosting (XGBoost), and LightGBM. The classification method was evaluated using both synthetic data, generated from transient simulations of the IEEE24 test system, and real-world data from actual transient events in power systems. Among the algorithms tested, XGBoost achieved the highest classification accuracy, with 96.8% for synthetic data and 85.2% for physical data. Additionally, this study investigates the impact of data sampling frequency and calculation window size on classification performance. Through numerical experiments, we found that increasing the signal sampling rate beyond 5 kHz and extending the calculation window beyond 5 ms did not significantly improve classification accuracy. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods for Mechanics and Engineering)
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18 pages, 299 KiB  
Article
Improving the Accuracy of the Pencil of Function Method Increasing Its Matrix Polynomial Degree
by Raul H. Barroso and Alfonso J. Zozaya Sahad
Mathematics 2025, 13(2), 315; https://doi.org/10.3390/math13020315 - 19 Jan 2025
Viewed by 396
Abstract
The estimation of complex natural frequencies in linear systems through their transient response analysis is a common practice in engineering and applied physics. In this context, the conventional Generalized Pencil of Function (GPOF) method that employs a matrix pencil of degree one, utilizing [...] Read more.
The estimation of complex natural frequencies in linear systems through their transient response analysis is a common practice in engineering and applied physics. In this context, the conventional Generalized Pencil of Function (GPOF) method that employs a matrix pencil of degree one, utilizing singular value decomposition (SVD) filtering, has emerged as a prominent strategy to carry out a complex natural frequency estimation. However, some modern engineering applications increasingly demand higher accuracy estimation. In this context, some intrinsic properties of Hankel matrices and exponential functions are utilized in this paper in order to develop a modified GPOF method which employs a matrix pencil of degree greater than one. Under conditions of low noise in the transient response, our method significantly enhances accuracy compared to the conventional GPOF approach. This improvement is especially valuable for applications involving closely spaced complex natural frequencies, where a precise estimation is crucial. Full article
(This article belongs to the Section E: Applied Mathematics)
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19 pages, 3164 KiB  
Article
Application of Real-Coded Genetic Algorithm–PID Cascade Speed Controller to Marine Gas Turbine Engine Based on Sensitivity Function Analysis
by Yunhyung Lee, Kitak Ryu, Gunbaek So, Jaesung Kwon and Jongkap Ahn
Mathematics 2025, 13(2), 314; https://doi.org/10.3390/math13020314 - 19 Jan 2025
Viewed by 424
Abstract
Gas turbine engines at sea, characterized by nonlinear behavior and parameter variations due to dynamic marine environments, pose challenges for precise speed control. The focus of this study was a COGAG system with four LM-2500 gas turbines. A third-order model with time delay [...] Read more.
Gas turbine engines at sea, characterized by nonlinear behavior and parameter variations due to dynamic marine environments, pose challenges for precise speed control. The focus of this study was a COGAG system with four LM-2500 gas turbines. A third-order model with time delay was derived at three operating points using commissioning data to capture the engines’ inherent characteristics. The cascade controller design employs a real-coded genetic algorithm–PID (R-PID) controller, optimizing PID parameters for each model. Simulations revealed that the R-PID controllers, optimized for robustness, show Nyquist path stability, maintaining the furthest distance from the critical point (−1, j0). The smallest sensitivity function Ms (maximum sensitivity) values and minimal changes in Ms for uncertain plants confirm robustness against uncertainties. Comparing transient responses, the R-PID controller outperforms traditional methods like IMC and Sadeghi in total variation in control input, settling time, overshoot, and ITAE, despite a slightly slower rise time. However, controllers designed for specific operating points show decreased performance when applied beyond those points, with increased rise time, settling time, and overshoot, highlighting the need for operating-point-specific designs to ensure optimal performance. This research underscores the importance of tailored controller design for effective gas turbine engine management in marine applications. Full article
(This article belongs to the Special Issue Dynamic Modeling and Simulation for Control Systems, 3rd Edition)
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16 pages, 494 KiB  
Article
An Upper Bound for Locating Strings with High Probability Within Consecutive Bits of Pi
by Víctor Manuel Silva-García, Manuel Alejandro Cardona-López and Rolando Flores-Carapia
Mathematics 2025, 13(2), 313; https://doi.org/10.3390/math13020313 - 19 Jan 2025
Viewed by 378
Abstract
Numerous studies on the number pi (π) explore its properties, including normality and applicability. This research, grounded in two hypotheses, proposes and proves a theorem that employs a Bernoulli experiment to demonstrate the high probability of encountering any finite bit string [...] Read more.
Numerous studies on the number pi (π) explore its properties, including normality and applicability. This research, grounded in two hypotheses, proposes and proves a theorem that employs a Bernoulli experiment to demonstrate the high probability of encountering any finite bit string within a sequence of consecutive bits in the decimal part of π. This aligns with findings related to its normality. To support the hypotheses, we present experimental evidence about the equiprobable and independent properties of bits of π, analyzing their distribution, and measuring correlations between bit strings. Additionally, from a cryptographic perspective, we evaluate the chaotic properties of two images generated using bits of π. These properties are evaluated similarly to those of encrypted images, using measures of correlation and entropy, along with two hypothesis tests to confirm the uniform distribution of bits and the absence of periodic patterns. Unlike previous works that solely examine the presence of sequences, this study provides, as a corollary, a formula to calculate an upper bound N. This bound represents the length of the sequence from π required to ensure the location of any n-bit string at least once, with an adjustable probability p that can be set arbitrarily close to one. To validate the formula, we identify sequences of up to n= 40 consecutive zeros and ones within the first N bits of π. This work has potential applications in Cryptography that use the number π for random sequence generation, offering insights into the number of bits of π required to ensure good randomness properties. Full article
(This article belongs to the Special Issue Advances in Computational Statistics, Design of Experiments, and Its Applications)
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23 pages, 1651 KiB  
Article
Analysis and Control of Rumor Propagation Model Considering Multiple Waiting Phases
by Hai Wu, Xin Yan, Shengxiang Gao, Zhongying Deng and Haiyang Chi
Mathematics 2025, 13(2), 312; https://doi.org/10.3390/math13020312 - 19 Jan 2025
Viewed by 618
Abstract
Rumors pose serious harm to society and exhibit a certain degree of repetitiveness. Existing rumor propagation models often have simple rules and neglect the repetitiveness of rumors. Therefore, we propose a new SCWIR rumor propagation model (susceptible, commented, waited, infected, recovered) by introducing [...] Read more.
Rumors pose serious harm to society and exhibit a certain degree of repetitiveness. Existing rumor propagation models often have simple rules and neglect the repetitiveness of rumors. Therefore, we propose a new SCWIR rumor propagation model (susceptible, commented, waited, infected, recovered) by introducing the user’s repeated waiting behavior to simulate the potential for rumors to lie dormant and spread opportunistically. First, we present the dynamic equations of the model, then introduce three influencing factors to improve the model. Next, by solving for the equilibrium points and the basic reproduction number, we discuss the local and global stability of the rumor-free/rumor equilibrium points. Finally, we perform numerical simulations to analyze the effects of different factors on rumor propagation. The results show that the introduction of the multiple waiting mechanism helps simulate the repetitiveness of rumor propagation. Among the rumor suppression strategies, the effectiveness, from highest to lowest, is as follows: government intervention, information dissemination and popularization, and accelerated rumor value decay, with government intervention playing a decisive role. Information dissemination can reduce the intensity of rumors at the source. Full article
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18 pages, 316 KiB  
Article
Uniqueness of Positive Solutions to Non-Local Problems of Brézis–Oswald Type Involving Hardy Potentials
by Yun-Ho Kim
Mathematics 2025, 13(2), 311; https://doi.org/10.3390/math13020311 - 18 Jan 2025
Viewed by 560
Abstract
The aim of this paper is to demonstrate the existence of a unique positive solution to non-local fractional p-Laplacian equations of the Brézis–Oswald type involving Hardy potentials. The main feature of this paper is solving the difficulty that arises in the presence [...] Read more.
The aim of this paper is to demonstrate the existence of a unique positive solution to non-local fractional p-Laplacian equations of the Brézis–Oswald type involving Hardy potentials. The main feature of this paper is solving the difficulty that arises in the presence of a singular coefficient and in the lack of the semicontinuity property of an energy functional associated with the relevant problem. The main tool for overcoming this difficulty is the concentration–compactness principle in fractional Sobolev spaces. Also, the uniqueness result of the Brézis–Oswald type is obtained by exploiting the discrete Picone inequality. Full article
(This article belongs to the Section C1: Difference and Differential Equations)
26 pages, 3631 KiB  
Article
Ordinal Random Tree with Rank-Oriented Feature Selection (ORT-ROFS): A Novel Approach for the Prediction of Road Traffic Accident Severity
by Bita Ghasemkhani, Kadriye Filiz Balbal, Kokten Ulas Birant and Derya Birant
Mathematics 2025, 13(2), 310; https://doi.org/10.3390/math13020310 - 18 Jan 2025
Viewed by 522
Abstract
Road traffic accident severity prediction is crucial for implementing effective safety measures and proactive traffic management strategies. Existing methods often treat this as a nominal classification problem and use traditional feature selection techniques. However, ordinal classification methods that account for the ordered nature [...] Read more.
Road traffic accident severity prediction is crucial for implementing effective safety measures and proactive traffic management strategies. Existing methods often treat this as a nominal classification problem and use traditional feature selection techniques. However, ordinal classification methods that account for the ordered nature of accident severity (e.g., slight < serious < fatal injuries) in feature selection still need to be investigated thoroughly. In this study, we propose a novel approach, the Ordinal Random Tree with Rank-Oriented Feature Selection (ORT-ROFS), which utilizes the inherent ordering of class labels both in the feature selection and prediction stages for accident severity classification. The proposed approach enhances the model performance by separately determining feature importance based on severity levels. The experiments demonstrated the effectiveness of ORT-ROFS with an accuracy of 87.19%. According to the results, the proposed method improved prediction accuracy by 10.81% over state-of-the-art studies on average on different train–test split ratios. In addition, it achieved an average improvement of 4.58% in accuracy over traditional methods. These findings suggest that ORT-ROFS is a promising approach for accurate accident severity prediction, supporting road safety planning and intervention strategies. Full article
(This article belongs to the Special Issue Applications of Advanced Machine Learning and Intelligent Data Analysis)
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23 pages, 454 KiB  
Article
New Simplification Rules for Databases with Positive and Negative Attributes
by Domingo López-Rodríguez, Manuel Ojeda-Hernández and Carlos Bejines
Mathematics 2025, 13(2), 309; https://doi.org/10.3390/math13020309 - 18 Jan 2025
Viewed by 453
Abstract
In this paper, new logical equivalences are presented within the simplification logic with mixed attributes paradigm, which allow the obtention of bases of shorter, easier-to-read attribute implications. In addition to the theoretical results which show that the proposed equivalences indeed hold in simplification [...] Read more.
In this paper, new logical equivalences are presented within the simplification logic with mixed attributes paradigm, which allow the obtention of bases of shorter, easier-to-read attribute implications. In addition to the theoretical results which show that the proposed equivalences indeed hold in simplification logic with mixed attributes, experimental results which showcase the effectiveness of this method are also provided. Furthermore, the simplification method presented is iterative and gives sufficiently good results in only one or two iterations, therefore presenting itself as a reasonable procedure in time-sensitive experiments. Full article
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17 pages, 545 KiB  
Article
Enhancing Diversity and Convergence in MMOPs with a Gaussian Similarity-Based Evolutionary Algorithm
by Shizhao Wei and Da-Jung Cho
Mathematics 2025, 13(2), 308; https://doi.org/10.3390/math13020308 - 18 Jan 2025
Viewed by 383
Abstract
Multi-modal multi-objective optimization problems (MMOPs) are challenging due to multiple solutions sharing similar objective values. Existing algorithms for solving MMOPs typically evaluate the crowding in the decision space and objective space independently, leading to an imbalance in diversity between the two spaces. We [...] Read more.
Multi-modal multi-objective optimization problems (MMOPs) are challenging due to multiple solutions sharing similar objective values. Existing algorithms for solving MMOPs typically evaluate the crowding in the decision space and objective space independently, leading to an imbalance in diversity between the two spaces. We introduce a mechanism that balances diversity in both the decision and objective spaces, aiming to enhance diversity while maintaining convergence in both spaces. We propose a multi-modal multi-objective evolutionary algorithm (MMEA) that selects qualified solutions based on Gaussian similarity. Gaussian similarity assesses the closeness of solution pairs and serves as the diversity fitness criterion for the algorithm. We conducted experiments on 28 benchmark problems and compared MMEA-GS with five state-of-the-art approaches. The results demonstrate that MMEA-GS effectively addresses most MMOPs, achieving higher diversity and convergence. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
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16 pages, 1468 KiB  
Article
Probabilistic Forecasting of Crude Oil Prices Using Conditional Generative Adversarial Network Model with Lévy Process
by Mohammed Alruqimi and Luca Di Persio
Mathematics 2025, 13(2), 307; https://doi.org/10.3390/math13020307 - 18 Jan 2025
Viewed by 620
Abstract
Accurate crude oil price forecasting is essential, considering oil’s critical role in the global economy. However, the crude oil market is significantly influenced by external, transient events, posing challenges in capturing price fluctuations’ complex dynamics and uncertainties. Traditional time series forecasting models, such [...] Read more.
Accurate crude oil price forecasting is essential, considering oil’s critical role in the global economy. However, the crude oil market is significantly influenced by external, transient events, posing challenges in capturing price fluctuations’ complex dynamics and uncertainties. Traditional time series forecasting models, such as ARIMA and LSTM, often rely on assumptions regarding data structure, limiting their flexibility to estimate volatility or account for external shocks effectively. Recent research highlights Generative Adversarial Networks (GANs) as a promising alternative approach for capturing intricate patterns in time series data, leveraging the adversarial learning framework. This paper introduces a Crude Oil-Driven Conditional GAN (CO-CGAN), a hybrid model for enhancing crude oil price forecasting by combining advanced AI frameworks (GANs), oil market sentiment analysis, and stochastic jump-diffusion models. By employing conditional supervised training, the inherent structure of the data distribution is preserved, thereby enabling more accurate and reliable probabilistic price forecasts. Additionally, the CO-CGAN integrates a Lévy process and sentiment features to better account for uncertainties and price shocks in the crude oil market. Experimental evaluations on two real-world oil price datasets demonstrate the superior performance of the proposed model, achieving a Mean Squared Error (MSE) of 0.000054 and outperforming benchmark models. Full article
(This article belongs to the Special Issue Statistical Data Modeling and Machine Learning with Applications, 3rd Edition)
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27 pages, 414 KiB  
Article
Backward Anticipated Social Optima: Input Constraints and Partial Information
by Shujun Wang
Mathematics 2025, 13(2), 306; https://doi.org/10.3390/math13020306 - 18 Jan 2025
Viewed by 408
Abstract
A class of stochastic linear-quadratic (LQ) dynamic optimization problems involving a large population is investigated in this work. Here, the agents cooperate with each other to minimize certain social costs. Furthermore, differently from the classic social optima literature, the dynamics in this framework [...] Read more.
A class of stochastic linear-quadratic (LQ) dynamic optimization problems involving a large population is investigated in this work. Here, the agents cooperate with each other to minimize certain social costs. Furthermore, differently from the classic social optima literature, the dynamics in this framework are driven by anticipated backward stochastic differential equations (ABSDE) in which the terminal instead of the initial condition is specified and the anticipated terms are involved. The individual admissible controls are constrained in closed convex subsets, and the common noise is considered. As a result, the related social cost is represented by a recursive functional in which the initial state is involved. By virtue of the so-called anticipated person-by-person optimality principle, a decentralized strategy can be derived. This is based on a class of new consistency condition systems, which are mean-field-type anticipated forward-backward stochastic differential delay equations (AFBSDDEs). The well-posedness of such a consistency condition system is obtained through a discounting decoupling method. Finally, the corresponding asymptotic social optimality is proved. Full article
(This article belongs to the Special Issue Stochastic Optimal Control, Game Theory, and Related Applications)
10 pages, 221 KiB  
Article
Linear Jointly Disjointness-Preserving Maps Between Rectangular Matrix Spaces
by Ru-Jheng Li, Yu-Ju Lin, Ming-Cheng Tsai and Ya-Shu Wang
Mathematics 2025, 13(2), 305; https://doi.org/10.3390/math13020305 - 18 Jan 2025
Viewed by 390
Abstract
This paper studies pairs of linear maps that preserve the disjointness of matrices in rectangular matrix spaces. We present a complete characterization of all pairs of bijective linear maps that jointly preserve disjointness. Additionally, we apply these results to study maps that preserve [...] Read more.
This paper studies pairs of linear maps that preserve the disjointness of matrices in rectangular matrix spaces. We present a complete characterization of all pairs of bijective linear maps that jointly preserve disjointness. Additionally, we apply these results to study maps that preserve specific matrix properties, such as the double-zero product property. Full article
(This article belongs to the Special Issue Advances in Intelligent Computing, Machine Learning and Pattern Recognition)
22 pages, 3406 KiB  
Article
Design of a Multi-Layer Symmetric Encryption System Using Reversible Cellular Automata
by George Cosmin Stănică and Petre Anghelescu
Mathematics 2025, 13(2), 304; https://doi.org/10.3390/math13020304 - 18 Jan 2025
Viewed by 490
Abstract
The increasing demand for secure and efficient encryption algorithms has intensified the exploration of alternative cryptographic solutions, including biologically inspired systems like cellular automata. This study presents a symmetric block encryption design based on multiple reversible cellular automata (RCAs) that can assure both [...] Read more.
The increasing demand for secure and efficient encryption algorithms has intensified the exploration of alternative cryptographic solutions, including biologically inspired systems like cellular automata. This study presents a symmetric block encryption design based on multiple reversible cellular automata (RCAs) that can assure both computational efficiency and reliable restoration of original data. The encryption key, with a length of 224 bits, is composed of specific rules used by the four distinct RCAs: three with radius-2 neighborhoods and one with a radius-3 neighborhood. By dividing plaintext into 128-bit blocks, the algorithm performs iterative transformations over multiple rounds. Each round includes forward or backward evolution steps, along with dynamically computed shift values and reversible transformations to securely encrypt or decrypt data. The encryption process concludes with an additional layer of security by encrypting the final RCA configurations, further protecting against potential attacks on the encrypted data. Additionally, the 224-bit key length provides robust resistance against brute force attacks. Testing and analysis were performed using a custom-developed software (version 1.0) application, which helped demonstrate the algorithm’s robustness, encryption accuracy, and ability to maintain data integrity. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
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14 pages, 1044 KiB  
Article
Accurate Computations with Generalized Pascal k-Eliminated Functional Matrices
by Jorge Delgado, Héctor Orera and Juan Manuel Peña
Mathematics 2025, 13(2), 303; https://doi.org/10.3390/math13020303 - 18 Jan 2025
Viewed by 380
Abstract
This paper presents an accurate method to obtain the bidiagonal decomposition of some generalized Pascal matrices, including Pascal k-eliminated functional matrices and Pascal symmetric functional matrices. Sufficient conditions to assure that these matrices are either totally positive or inverse of totally positive [...] Read more.
This paper presents an accurate method to obtain the bidiagonal decomposition of some generalized Pascal matrices, including Pascal k-eliminated functional matrices and Pascal symmetric functional matrices. Sufficient conditions to assure that these matrices are either totally positive or inverse of totally positive matrices are provided. In these cases, the presented method can be used to compute their eigenvalues, singular values and inverses with high relative accuracy. Numerical examples illustrate the high accuracy of our approach. Full article
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17 pages, 3763 KiB  
Article
Graph-Based Feature Crossing to Enhance Recommender Systems
by Congyu Cai, Hong Chen, Yunxuan Liu, Daoquan Chen, Xiuze Zhou and Yuanguo Lin
Mathematics 2025, 13(2), 302; https://doi.org/10.3390/math13020302 - 18 Jan 2025
Viewed by 515
Abstract
In recommendation tasks, most existing models that learn users’ preferences from user–item interactions ignore the relationships between items. Additionally, ensuring that the crossed features capture both global graph structures and local context is non-trivial, requiring innovative techniques for multi-scale representation learning. To overcome [...] Read more.
In recommendation tasks, most existing models that learn users’ preferences from user–item interactions ignore the relationships between items. Additionally, ensuring that the crossed features capture both global graph structures and local context is non-trivial, requiring innovative techniques for multi-scale representation learning. To overcome these difficulties, we develop a novel neural network, CoGraph, which uses a graph to build the relations between items. The item co-occurrence pattern assumes that certain items consistently appear in pairs in users’ viewing or consumption logs. First, to learn relationships between items, a graph whose distance is measured by Normalised Point-Wise Mutual Information (NPMI) is applied to link items for the co-occurrence pattern. Then, to learn as many useful features as possible for higher recommendation quality, a Convolutional Neural Network (CNN) and the Transformer model are used to parallelly learn local and global feature interactions. Finally, a series of comprehensive experiments were conducted on several public data sets to show the performance of our model. It provides valuable insights into the capability of our model in recommendation tasks and offers a viable pathway for the public data operation. Full article
(This article belongs to the Special Issue Advanced Research in Data-Centric AI)
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28 pages, 3246 KiB  
Article
Identification of Industrial Occupational Safety Risks and Selection of Optimum Intervention Strategies: Fuzzy MCDM Approach
by Gülay Demir, Mouhamed Bayane Bouraima, Ibrahim Badi, Željko Stević and Dillip Kumar Das
Mathematics 2025, 13(2), 301; https://doi.org/10.3390/math13020301 - 17 Jan 2025
Viewed by 607
Abstract
Over 1.1 million deaths occur annually from workplace injuries and diseases, with higher risks in developing countries. Occupational safety studies commonly use quantitative or qualitative methods, but these often fail to address uncertainty. This research targets the Libyan Steel Company (LISCO), aiming to [...] Read more.
Over 1.1 million deaths occur annually from workplace injuries and diseases, with higher risks in developing countries. Occupational safety studies commonly use quantitative or qualitative methods, but these often fail to address uncertainty. This research targets the Libyan Steel Company (LISCO), aiming to analyze safety risks and develop a structured approach to identify optimal risk mitigation strategies. To this end, the Fuzzy Weights by ENvelope and SLOpe (F-WENSLO) method was chosen to determine the weights of three main safety risks and a total of 18 sub-risks belonging to them, and the fuzzy Bonferroni mean aggregation operator is applied to synthesize expert opinions. The Fuzzy Alternative Ranking Technique based on Adaptive Standardized Intervals (F-ARTASI) method was used to identify and rank the most appropriate safety interventions. While the primary risks identified under the main criteria and sub-criteria are occupational diseases and noise-induced diseases, with weights of 0.4737 and 0.1313, respectively, the intervention strategy deemed most effective for enhancing occupational safety is behavioral safety programs, which hold a weight of 11.0341. The sensitivity test of the analysis results reveals that although the criteria weights and the parameters used in the analysis vary under various scenarios, the ranking of the alternatives remains consistent. Since the general ranking of the alternatives is the same in other methods, decision makers will reach similar results no matter which method they use. This shows that a flexible and reliable decision-making approach is adopted in the process of optimizing occupational safety risks. This research emphasizes the critical importance of prioritizing occupational diseases and natural hazards in the formulation of occupational safety strategies and thus aims to contribute to the protection of workers in industrial plants such as LISCO. Full article
(This article belongs to the Special Issue Soft Computing and Fuzzy Mathematics: New Advances and Applications)
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26 pages, 1259 KiB  
Article
A Collocation Approach for the Nonlinear Fifth-Order KdV Equations Using Certain Shifted Horadam Polynomials
by Waleed Mohamed Abd-Elhameed, Omar Mazen Alqubori and Ahmed Gamal Atta
Mathematics 2025, 13(2), 300; https://doi.org/10.3390/math13020300 - 17 Jan 2025
Viewed by 417
Abstract
This paper proposes a numerical algorithm for the nonlinear fifth-order Korteweg–de Vries equations. This class of equations is known for its significance in modeling various complex wave phenomena in physics and engineering. The approximate solutions are expressed in terms of certain shifted Horadam [...] Read more.
This paper proposes a numerical algorithm for the nonlinear fifth-order Korteweg–de Vries equations. This class of equations is known for its significance in modeling various complex wave phenomena in physics and engineering. The approximate solutions are expressed in terms of certain shifted Horadam polynomials. A theoretical background for these polynomials is first introduced. The derivatives of these polynomials and their operational metrics of derivatives are established to tackle the problem using the typical collocation method to transform the nonlinear fifth-order Korteweg–de Vries equation governed by its underlying conditions into a system of nonlinear algebraic equations, thereby obtaining the approximate solutions. This paper also includes a rigorous convergence analysis of the proposed shifted Horadam expansion. To validate the proposed method, we present several numerical examples illustrating its accuracy and effectiveness. Full article
(This article belongs to the Special Issue Exact Solutions and Numerical Solutions of Differential Equations)
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11 pages, 974 KiB  
Article
Improved Sampled-Data Consensus Control for Multi-Agent Systems via Delay-Incorporating Looped-Functional
by Khanh Hieu Nguyen and Sung Hyun Kim
Mathematics 2025, 13(2), 299; https://doi.org/10.3390/math13020299 - 17 Jan 2025
Viewed by 425
Abstract
This paper addresses the problem of achieving consensus control for homogeneous multi-agent systems (MASs) under aperiodic sampled data and communication delays. By incorporating additional delay information, this paper introduces two novel delay-incorporating integral terms, an enhanced two-sided looped functional, and a novel discontinuous [...] Read more.
This paper addresses the problem of achieving consensus control for homogeneous multi-agent systems (MASs) under aperiodic sampled data and communication delays. By incorporating additional delay information, this paper introduces two novel delay-incorporating integral terms, an enhanced two-sided looped functional, and a novel discontinuous function to further exploit system state responses observed during sampling and data transmission. In addition, this paper introduces two additional zero equalities to derive less conservative stability and stabilization conditions. Based on these, sufficient conditions for guaranteeing consensus in MASs under this context are derived as linear matrix inequalities (LMIs). Finally, the effectiveness and superiority of the proposed method are validated through a numerical example. Full article
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10 pages, 1256 KiB  
Article
Coarse-Grained Column Agglomeration Parallel Algorithm for LU Factorization Using Multi-Threaded MATLAB
by Osama Sabir and Reza Alebrahim
Mathematics 2025, 13(2), 298; https://doi.org/10.3390/math13020298 - 17 Jan 2025
Viewed by 395
Abstract
MATLAB programing language is one of the most popular scientific computing tools, especially for solving linear algebra problems. LU factorization is an essential component for the direct solution of linear equations systems. This paper studied a coarse-grained column agglomeration parallel algorithm in MATLAB [...] Read more.
MATLAB programing language is one of the most popular scientific computing tools, especially for solving linear algebra problems. LU factorization is an essential component for the direct solution of linear equations systems. This paper studied a coarse-grained column agglomeration parallel algorithm in MATLAB to analyze the implementation performance among all the available computation resources. In this paper, we focus on parallelizing the LU decomposition without pivoting algorithm using Gaussian elimination under MATLAB R2020b platform. Numerical experiments were provided to demonstrate the efficiency of CPU parallelization. Performances of the present methods were assessed by comparing the speed and accuracy of different coarse-grained column agglomeration algorithms using different sizes of matrices. Different algorithms were implemented in a four-core Xeon E3-1220 v3 @ 3.10 GHz CPU with 16 GB RAM memory. Full article
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24 pages, 295 KiB  
Article
Estimation for Two Sensitive Variables Using Randomization Response Model Under Stratified Random Sampling
by Gi-Sung Lee, Ki-Hak Hong, Sung-Hwan Kim and Chang-Kyoon Son
Mathematics 2025, 13(2), 297; https://doi.org/10.3390/math13020297 - 17 Jan 2025
Viewed by 425
Abstract
When direct survey are about sensitive characteristics such as addiction to drugs, alcoholism, proneness to tax invasion and sexual violence, nonresponse bias and response bias become serious problems because people oftentimes do not wish to give true information. In this study, when the [...] Read more.
When direct survey are about sensitive characteristics such as addiction to drugs, alcoholism, proneness to tax invasion and sexual violence, nonresponse bias and response bias become serious problems because people oftentimes do not wish to give true information. In this study, when the population is composed of strata such as gender, region, age group, we consider the simple model and crossed model by applying stratified random sampling which can estimate not only the domain population proportion but also the whole population proportion for two sensitive attributes such as drug use and sexual violence in the same time. In addition, when the size of each population stratum is unknown in stratified random sampling, we propose the simple model and crossed model by using stratified double sampling method. In each proposed survey design, the sample allocation of each stratum is dealt with in consideration of proportional allocation and optimal one. We compare the efficiency between the simple model and the crossed model according to the proposed stratified random sampling design. Full article
(This article belongs to the Special Issue Statistical Theory and Application, 2nd Edition)
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