Mathematics

24 pages, 10562 KiB

Open AccessArticle

An Exponentially Delayed Feedback Chaotic Model Resistant to Dynamic Degradation and Its Application

by Bocheng Liu, Jian Song, Niande Jiang and Zhuo Wang

Mathematics 2025, 13(14), 2324; https://doi.org/10.3390/math13142324 - 21 Jul 2025

Viewed by 327

In this paper, an exponential delay feedback method is proposed to improve the performance of the digital chaotic maps against their dynamical degradation. In this paper, the performance of the scheme is verified using one-dimensional linear, exponential, and nonlinear exponential, Logistic, and Chebyshev [...] Read more.

In this paper, an exponential delay feedback method is proposed to improve the performance of the digital chaotic maps against their dynamical degradation. In this paper, the performance of the scheme is verified using one-dimensional linear, exponential, and nonlinear exponential, Logistic, and Chebyshev maps, and numerical analyses show that the period during which the chaotic sequence enters the cycle is considerably prolonged, and the correlation performance is improved. At the same time, in order to verify the practicality of the method, an image encryption algorithm is designed, and its security analysis results show that the algorithm has a high level of security and can compete with other encryption schemes. Therefore, the exponential delay feedback method can effectively improve the dynamics degradation of a digital chaotic map. Full article

(This article belongs to the Special Issue Chaos-Based Secure Communication and Cryptography, 2nd Edition)

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24 pages, 6464 KiB

Open AccessArticle

A Hybrid Model for Carbon Price Forecasting Based on Secondary Decomposition and Weight Optimization

by Yongfa Chen, Yingjie Zhu, Jie Wang and Meng Li

Mathematics 2025, 13(14), 2323; https://doi.org/10.3390/math13142323 - 21 Jul 2025

Viewed by 232

Abstract

Accurate carbon price forecasting is essential for market stability, risk management, and policy-making. To address the nonlinear, non-stationary, and multiscale nature of carbon prices, this paper proposes a forecasting framework integrating secondary decomposition, two-stage feature selection, and dynamic ensemble learning. Firstly, the original [...] Read more.

Accurate carbon price forecasting is essential for market stability, risk management, and policy-making. To address the nonlinear, non-stationary, and multiscale nature of carbon prices, this paper proposes a forecasting framework integrating secondary decomposition, two-stage feature selection, and dynamic ensemble learning. Firstly, the original price series is decomposed into intrinsic mode functions (IMFs), using complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). The IMFs are then grouped into low- and high-frequency components based on multiscale entropy (MSE) and K-Means clustering. To further alleviate mode mixing in the high-frequency components, an improved variational mode decomposition (VMD) optimized by particle swarm optimization (PSO) is applied for secondary decomposition. Secondly, a two-stage feature-selection method is employed, in which the partial autocorrelation function (PACF) is used to select relevant lagged features, while the maximal information coefficient (MIC) is applied to identify key variables from both historical and external data. Finally, this paper introduces a dynamic integration module based on sliding windows and sequential least squares programming (SLSQP), which can not only adaptively adjust the weights of four base learners but can also effectively leverage the complementary advantages of each model and track the dynamic trends of carbon prices. The empirical results of the carbon markets in Hubei and Guangdong indicate that the proposed method outperforms the benchmark model in terms of prediction accuracy and robustness, and the method has been tested by Diebold Mariano (DM). The main contributions are the improved feature-extraction process and the innovative use of a sliding window-based SLSQP method for dynamic ensemble weight optimization. Full article

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35 pages, 7934 KiB

Open AccessArticle

Analyzing Diagnostic Reasoning of Vision–Language Models via Zero-Shot Chain-of-Thought Prompting in Medical Visual Question Answering

by Fatema Tuj Johora Faria, Laith H. Baniata, Ahyoung Choi and Sangwoo Kang

Mathematics 2025, 13(14), 2322; https://doi.org/10.3390/math13142322 - 21 Jul 2025

Viewed by 463

Abstract

Medical Visual Question Answering (MedVQA) lies at the intersection of computer vision, natural language processing, and clinical decision-making, aiming to generate accurate responses from medical images paired with complex inquiries. Despite recent advances in vision–language models (VLMs), their use in healthcare remains limited [...] Read more.

Medical Visual Question Answering (MedVQA) lies at the intersection of computer vision, natural language processing, and clinical decision-making, aiming to generate accurate responses from medical images paired with complex inquiries. Despite recent advances in vision–language models (VLMs), their use in healthcare remains limited by a lack of interpretability and a tendency to produce direct, unexplainable outputs. This opacity undermines their reliability in medical settings, where transparency and justification are critically important. To address this limitation, we propose a zero-shot chain-of-thought prompting framework that guides VLMs to perform multi-step reasoning before arriving at an answer. By encouraging the model to break down the problem, analyze both visual and contextual cues, and construct a stepwise explanation, the approach makes the reasoning process explicit and clinically meaningful. We evaluate the framework on the PMC-VQA benchmark, which includes authentic radiological images and expert-level prompts. In a comparative analysis of three leading VLMs, Gemini 2.5 Pro achieved the highest accuracy (72.48%), followed by Claude 3.5 Sonnet (69.00%) and GPT-4o Mini (67.33%). The results demonstrate that chain-of-thought prompting significantly improves both reasoning transparency and performance in MedVQA tasks. Full article

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

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14 pages, 275 KiB

Open AccessArticle

New Identities and Equation Solutions Involving k-Oresme and k-Oresme–Lucas Sequences

by Bahar Demirtürk

Mathematics 2025, 13(14), 2321; https://doi.org/10.3390/math13142321 - 21 Jul 2025

Viewed by 181

Abstract

Number sequences are among the research areas of interest in both number theory and linear algebra. In particular, the study of matrix representations of recursive sequences is important in revealing the structural properties of these sequences. In this study, the relationships between the [...] Read more.

Number sequences are among the research areas of interest in both number theory and linear algebra. In particular, the study of matrix representations of recursive sequences is important in revealing the structural properties of these sequences. In this study, the relationships between the elements of the k-Fibonacci and k-Oresme sequences were analyzed using matrix algebra through matrix structures created by connecting the characteristic equations and roots of these sequences. In this context, using the properties of these matrices, the identities

A_{n}^{2} - A_{n + 1} A_{n - 1} = k^{- 2 n}

,

A_{n}^{2} - A_{n} A_{n - 1} + \frac{1}{k^{2}} A_{n - 1}^{2} = k^{- 2 n}

, and

B_{n}^{2} - B_{n} B_{n - 1} + \frac{1}{k^{2}} B_{n - 1}^{2} = - (k^{2} - 4) k^{- 2 n}

, and some generalizations such as

B_{n + m}^{2} - (k^{2} - 4) A_{n - t} B_{n + m} A_{t + m} - (k^{2} - 4) k^{2 t - 2 n} A_{t + m}^{2} = k^{- 2 m - 2 t} B_{n - t}^{2}

,

A_{t + m}^{2} - B_{t - n} A_{n + m} A_{t + m} + k^{2 n - 2 t} A_{n + m}^{2} = k^{- 2 n - 2 m} A_{t - n}^{2}

, and more were derived, where

m, n, t \in ℤ

and

t \neq n

. In addition to this, the solution pairs of the algebraic equations

x^{2} - B_{p} x y + k^{- 2 p} y^{2} = k^{- 2 q} A_{p}^{2}

,

x^{2} - (k^{2} - 4) A_{p} x y - (k^{2} - 4) k^{- 2 p} y^{2} = k^{- 2 q} B_{p}^{2}

, and

x^{2} - B_{p} x y + k^{- 2 p} y^{2} = - (k^{2} - 4) k^{- 2 q} A_{p}^{2}

are presented, where

A_{p}

and

B_{p}

are k-Oresme and k-Oresme–Lucas numbers, respectively. Full article

(This article belongs to the Section A: Algebra and Logic)

21 pages, 1061 KiB

Open AccessFeature PaperArticle

Local Streamline Pattern and Topological Index of an Isotropic Point in a 2D Velocity Field

by Jian Gao, Rong Wang, Hongping Ma and Wennan Zou

Mathematics 2025, 13(14), 2320; https://doi.org/10.3390/math13142320 - 21 Jul 2025

Viewed by 133

Abstract

In fluid mechanics, most studies on flow structure analysis are simply based on the velocity gradient, which only involves the linear part of the velocity field and does not focus on the isotropic point. In this paper, we are concerned with a general [...] Read more.

In fluid mechanics, most studies on flow structure analysis are simply based on the velocity gradient, which only involves the linear part of the velocity field and does not focus on the isotropic point. In this paper, we are concerned with a general polynomial velocity field with a nonzero linear part and study its streamline pattern around an isotropic point, i.e., the local streamline pattern (LSP). A complete classification of LSPs in two-dimensional (2D) velocity fields is established. By proposing a novel formulation of qualitative equivalence, namely, the invariance under spatiotemporal transformations, we first introduce the quasi-real Schur form to classify the linear part of velocity fields. Then, for a nonlinear velocity field, the topological type of its LSP is either completely determined by the linear part when the determinant of the velocity gradient at the isotropic point is nonzero or controlled by both linear and nonlinear parts when the determinant of the velocity gradient vanishes at the isotropic point. Four new topological types of LSPs through detailed sector analysis are identified. Finally, we propose a direct method for calculating the index of the isotropic point, which also serves as a fundamental topological property of LSPs. These results do challenge the conventional linear analysis paradigm that simply neglects the contribution of the nonlinear part of the velocity field to the streamline pattern. Full article

(This article belongs to the Section E4: Mathematical Physics)

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13 pages, 272 KiB

Open AccessFeature PaperArticle

Asymptotic Behavior of the Bayes Estimator of a Regression Curve

by Agustín G. Nogales

Mathematics 2025, 13(14), 2319; https://doi.org/10.3390/math13142319 - 21 Jul 2025

Viewed by 104

Abstract

In this work, we prove the convergence to 0 in both

L^{1}

and

L^{2}

of the Bayes estimator of a regression curve (i.e., the conditional expectation of the response variable given the regressor). The strong consistency of the estimator is also [...] Read more.

In this work, we prove the convergence to 0 in both

L^{1}

and

L^{2}

of the Bayes estimator of a regression curve (i.e., the conditional expectation of the response variable given the regressor). The strong consistency of the estimator is also derived. The Bayes estimator of a regression curve is the regression curve with respect to the posterior predictive distribution. The result is general enough to cover discrete and continuous cases, parametric or nonparametric, and no specific supposition is made about the prior distribution. Some examples, two of them of a nonparametric nature, are given to illustrate the main result; one of the nonparametric examples exhibits a situation where the estimation of the regression curve has an optimal solution, although the problem of estimating the density is meaningless. An important role in the demonstration of these results is the establishment of a probability space as an adequate framework to address the problem of estimating regression curves from the Bayesian point of view, putting at our disposal powerful probabilistic tools in that endeavor. Full article

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

20 pages, 1823 KiB

Open AccessArticle

Smooth UAV Path Planning Based on Composite-Energy-Minimizing Bézier Curves

by Huanxin Cao, Zhanhe Du, Gang Hu, Yi Xu and Lanlan Zheng

Mathematics 2025, 13(14), 2318; https://doi.org/10.3390/math13142318 - 21 Jul 2025

Viewed by 215

Abstract

Path smoothing is an important part of UAV (Unmanned Aerial Vehicle) path planning, because the smoothness of the planned path is related to the flight safety and stability of UAVs. In existing smooth UAV path planning methods, different characteristics of a path curve [...] Read more.

Path smoothing is an important part of UAV (Unmanned Aerial Vehicle) path planning, because the smoothness of the planned path is related to the flight safety and stability of UAVs. In existing smooth UAV path planning methods, different characteristics of a path curve are not considered comprehensively, and the optimization functions established based on the arc length or curvature of the path curve are complex, resulting in low efficiency and quality of path smoothing. To balance the arc length and smoothness of UAV paths, this paper proposes to use energy-minimizing Bézier curves based on composite energy for smooth UAV path planning. In order to simplify the calculation, a kind of approximate stretching energy and bending energy are used to control the arc length and smoothness, respectively, of the path, by which the optimal path can be directly obtained by solving a linear system. Experimental validation in multiple scenarios demonstrates the methodology’s effectiveness and real-time computational viability, where the planned paths by this method have the characteristics of curvature continuity, good smoothness, and short arc length. What is more, in many cases, compared to path smoothing methods based solely on bending energy optimization, the proposed method can generate paths with a smaller maximum curvature, which is more conducive to the safe and stable flight of UAVs. Furthermore, the design of collision-free smooth path for UAVs based on the piecewise energy-minimizing Bézier curve is studied. The new method is simple and efficient, which can help to improve UAV path planning efficiency and thus improve UAV reaction speed and obstacle avoidance ability. Full article

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

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12 pages, 1622 KiB

Open AccessArticle

Symmetry and Quantum Calculus in Defining New Classes of Analytic Functions

by Fuad Alsarari, Abdulbasit Darem, Muflih Alhazmi and Alaa Awad Alzulaibani

Mathematics 2025, 13(14), 2317; https://doi.org/10.3390/math13142317 - 21 Jul 2025

Viewed by 115

Abstract

This paper introduces a novel class of analytic functions that integrates q-calculus, Janowski-type functions, and (a, b)-symmetrical functions. By exploring convolution operations and quantum calculus, we establish essential convolution conditions that lay the groundwork for subsequent research. Building on [...] Read more.

This paper introduces a novel class of analytic functions that integrates q-calculus, Janowski-type functions, and (a, b)-symmetrical functions. By exploring convolution operations and quantum calculus, we establish essential convolution conditions that lay the groundwork for subsequent research. Building on a new conceptual framework, we also define analogous neighborhoods for the classes

{\bar{F}}_{q}^{a, b} (F, H)

and investigate related neighborhood properties. These developments provide a deeper understanding of the structural and analytical behavior of these functions, opening up avenues for future study. Full article

(This article belongs to the Special Issue Geometric Function Theory and Applications―Festschrift for Grigore-Stefan Salagean's 75th Birthday)

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18 pages, 3004 KiB

Open AccessArticle

A Spatiotemporal Convolutional Neural Network Model Based on Dual Attention Mechanism for Passenger Flow Prediction

by Jinlong Li, Haoran Chen, Qiuzi Lu, Xi Wang, Haifeng Song and Lunming Qin

Mathematics 2025, 13(14), 2316; https://doi.org/10.3390/math13142316 - 21 Jul 2025

Viewed by 237

Abstract

Establishing a high-precision passenger flow prediction model is a critical and complex task for the optimization of urban rail transit systems. With the development of artificial intelligence technology, the data-driven technology has been widely studied in the intelligent transportation system. In this study, [...] Read more.

Establishing a high-precision passenger flow prediction model is a critical and complex task for the optimization of urban rail transit systems. With the development of artificial intelligence technology, the data-driven technology has been widely studied in the intelligent transportation system. In this study, a neural network model based on the data-driven technology is established for the prediction of passenger flow in multiple urban rail transit stations to enable smart perception for optimizing urban railway transportation. The integration of network units with different specialities in the proposed model allows the network to capture passenger flow data, temporal correlation, spatial correlation, and spatiotemporal correlation with the dual attention mechanism, further improving the prediction accuracy. Experiments based on the actual passenger flow data of Beijing Metro Line 13 are conducted to compare the prediction performance of the proposed data-driven model with the other baseline models. The experimental results demonstrate that the proposed prediction model achieves lower MAE and RMSE in passenger flow prediction, and its fitted curve more closely aligns with the actual passenger flow data. This demonstrates the model’s practical potential to enhance intelligent transportation system management through more accurate passenger flow forecasting. Full article

(This article belongs to the Special Issue Advances in Perception, Control and Optimization Methods in Intelligent Transportation Systems)

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23 pages, 2543 KiB

Open AccessArticle

Beyond Standard Losses: Redefining Text-to-SQL with Task-Specific Optimization

by Iker Azurmendi, Ekaitz Zulueta, Gustavo García, Nekane Uriarte-Arrazola and Jose Manuel Lopez-Guede

Mathematics 2025, 13(14), 2315; https://doi.org/10.3390/math13142315 - 20 Jul 2025

Viewed by 355

Abstract

In recent years, large language models (LLMs) have shown an impressive ability in translating text to SQL queries. However, in real-world applications, standard loss functions frequently fail to capture the complexity of queries adequately. Therefore, in this study, a dynamic loss function is [...] Read more.

In recent years, large language models (LLMs) have shown an impressive ability in translating text to SQL queries. However, in real-world applications, standard loss functions frequently fail to capture the complexity of queries adequately. Therefore, in this study, a dynamic loss function is proposed, which assigns different weights to specific groups of tokens, such as SQL keywords or table names. The objective is to guide the model during training to facilitate the mastery of more fundamental concepts within the SQL. Our custom loss function is composed of four components: cross-entropy with sequence matching loss, focal loss, F-beta loss, and contrastive sequence loss. During the training process, the weights of each component of the loss function are dynamically adjusted to prioritize different aspects of query generation at the appropriate stage. This approach avoids computationally expensive approaches such as SQL validation or detokenization, which improves the efficiency of the learning process compared to alternative methods. We empirically tested this method on several open source LLMs with less than 2 billion parameters, using a customized real vehicle diagnostic dataset. The findings demonstrate that the employment of our dynamic loss function can enhance SQL execution accuracy by up to 20% in comparison with standard cross-entropy loss. It has been demonstrated that customized loss functions for specific tasks can improve the efficiency of LLMs without extending the model or acquiring additional labelled data. The proposed technique is also scalable and adaptable to new domains or more complex weighting schemes, highlighting the importance of custom design of loss functions in real world applications. Full article

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22 pages, 2893 KiB

Open AccessArticle

Research on the Cable Force Optimization of the Precise Closure of Steel Truss Arch Bridges Based on Stress-Free State Control

by Ningbo Wang, Qian Wei, Zhugang Chang, Bei Liu, Zhihao Fan and Chengshuo Han

Mathematics 2025, 13(14), 2314; https://doi.org/10.3390/math13142314 - 20 Jul 2025

Viewed by 192

Abstract

During the construction of large-span steel truss arch bridges, challenges such as complex control calculations, frequent adjustments of the cantilever structure, and deviations in the closure state often arise in the process of the assembly and closure of arch ribs. Based on the [...] Read more.

During the construction of large-span steel truss arch bridges, challenges such as complex control calculations, frequent adjustments of the cantilever structure, and deviations in the closure state often arise in the process of the assembly and closure of arch ribs. Based on the stress-free state control theory, this paper proposes a precise assembly control method for steel truss arch bridges, which takes the minimization of structural deformation energy and the maintenance of the stress-free dimensions of the closure wedge as the control objectives. By establishing a mathematical relationship between temporary buckle cables and the spatial position of the closure section, as well as adopting the influence matrix method and the quadprog function to determine the optimal parameters of temporary buckle cables (i.e., size, position, and orientation) conforming to actual construction constraints, the automatic approaching of bridge alignment to the target alignment can be achieved. Combined with the practical engineering case of Muping Xiangjiang River Bridge, a numerical calculation study of the precise assembly and closure of steel truss arch bridges was conducted. The calculated results demonstrate that, under the specified construction scheme, the proposed method can determine the optimal combination for temporary buckle cable tension. Considering the actual construction risk and the economic cost, the precise matching of closure joints can be achieved by selectively trimming the size of the closure wedge by a minimal amount. The calculated maximum stress of the structural rods in the construction process is 42% of the allowable value of steel, verifying the feasibility and practicality of the proposed method. The precise assembly method of steel truss arch bridges based on stress-free state control can significantly provide guidance and reference for the design and construction of bridges of this type. Full article

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19 pages, 1356 KiB

Open AccessArticle

Using Transformers and Reinforcement Learning for the Team Orienteering Problem Under Dynamic Conditions

by Antoni Guerrero, Marc Escoto, Majsa Ammouriova, Yangchongyi Men and Angel A. Juan

Mathematics 2025, 13(14), 2313; https://doi.org/10.3390/math13142313 - 20 Jul 2025

Viewed by 259

Abstract

This paper presents a reinforcement learning (RL) approach for solving the team orienteering problem under both deterministic and dynamic travel time conditions. The proposed method builds on the transformer architecture and is trained to construct routes that adapt to real-time variations, such as [...] Read more.

This paper presents a reinforcement learning (RL) approach for solving the team orienteering problem under both deterministic and dynamic travel time conditions. The proposed method builds on the transformer architecture and is trained to construct routes that adapt to real-time variations, such as traffic and environmental changes. A key contribution of this work is the model’s ability to generalize across problem instances with varying numbers of nodes and vehicles, eliminating the need for retraining when problem size changes. To assess performance, a comprehensive set of experiments involving 27,000 synthetic instances is conducted, comparing the RL model with a variable neighborhood search metaheuristic. The results indicate that the RL model achieves competitive solution quality while requiring significantly less computational time. Moreover, the RL approach consistently produces feasible solutions across all dynamic instances, demonstrating strong robustness in meeting time constraints. These findings suggest that learning-based methods can offer efficient, scalable, and adaptable solutions for routing problems in dynamic and uncertain environments. Full article

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

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25 pages, 14579 KiB

Open AccessFeature PaperArticle

A Hybrid Path Planning Framework Integrating Deep Reinforcement Learning and Variable-Direction Potential Fields

by Yunfei Bi and Xi Fang

Mathematics 2025, 13(14), 2312; https://doi.org/10.3390/math13142312 - 20 Jul 2025

Viewed by 340

Abstract

To address the local optimality in path planning for logistics robots using APF (artificial potential field) and the stagnation problem when encountering trap obstacles, this paper proposes VDPF (variable-direction potential field) combined with RL (reinforcement learning) to effectively solve these problems. First, based [...] Read more.

To address the local optimality in path planning for logistics robots using APF (artificial potential field) and the stagnation problem when encountering trap obstacles, this paper proposes VDPF (variable-direction potential field) combined with RL (reinforcement learning) to effectively solve these problems. First, based on obstacle distribution, an obstacle classification algorithm is designed, enabling the robot to select appropriate obstacle avoidance strategies according to obstacle types. Second, the attractive force and repulsive force in APF are separated, and the direction of the repulsive force is modified to break the local optimum, allowing the robot to focus on handling current obstacle avoidance tasks. Finally, the improved APF is integrated with the TD3 (Twin Delayed Deep Deterministic Policy Gradient) algorithm, and a weight factor is introduced to adjust the robot’s acting forces. By sacrificing a certain level of safety for a larger exploration space, the robot is guided to escape from local optima and trap regions. Experimental results show that the improved algorithm effectively mitigates the trajectory oscillation of the robot and can efficiently solve the problems of local optimum and trap obstacles in the APF method. Compared with the algorithm APF-TD3 in scenarios with five obstacles, the proposed algorithm reduces the GS (Global Safety) by 8.6% and shortens the length by 8.3%. In 10 obstacle scenarios, the proposed algorithm reduces the GS by 29.8% and shortens the length by 9.7%. Full article

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16 pages, 1531 KiB

Open AccessArticle

Intelligent HVAC Control: Comparative Simulation of Reinforcement Learning and PID Strategies for Energy Efficiency and Comfort Optimization

by Atef Gharbi, Mohamed Ayari, Nasser Albalawi, Yamen El Touati and Zeineb Klai

Mathematics 2025, 13(14), 2311; https://doi.org/10.3390/math13142311 - 19 Jul 2025

Viewed by 401

Abstract

This study presents a new comparative analysis of the cognitive control methods of HVAC systems that assess reinforcement learning (RL) and traditional proportional-integral-derivative (PID) control. Through extensive simulations in various building environments, we have shown that while the PID controller provides stability under [...] Read more.

This study presents a new comparative analysis of the cognitive control methods of HVAC systems that assess reinforcement learning (RL) and traditional proportional-integral-derivative (PID) control. Through extensive simulations in various building environments, we have shown that while the PID controller provides stability under predictable conditions, the RL-based control can improve energy efficiency and thermal comfort in dynamic environments by constantly adapting to environmental changes. Our framework integrates real-time sensor data with a scalable RL architecture, allowing autonomous optimization without the need for a precise system model. Key findings show that RL largely outperforms PID during disturbances such as occupancy increases and weather fluctuations, and that the preferably optimal solution balances energy savings and comfort. The study provides practical insight into the implementation of adaptive HVAC control and outlines the potential of RL to transform building energy management despite its higher computational requirements. Full article

(This article belongs to the Special Issue Control Theory and Applications, 2nd Edition)

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18 pages, 425 KiB

Open AccessArticle

Stability of Stochastic Delayed Recurrent Neural Networks

by Hongying Xiao, Mingming Xu, Yuanyuan Zhang and Shengquan Weng

Mathematics 2025, 13(14), 2310; https://doi.org/10.3390/math13142310 - 19 Jul 2025

Viewed by 141

Abstract

This paper addresses the stability of stochastic delayed recurrent neural networks (SDRNNs), identifying challenges in existing scalar methods, which suffer from strong assumptions and limited applicability. Three key innovations are introduced: (1) weakening noise perturbation conditions by extending diagonal matrix assumptions to non-negative [...] Read more.

This paper addresses the stability of stochastic delayed recurrent neural networks (SDRNNs), identifying challenges in existing scalar methods, which suffer from strong assumptions and limited applicability. Three key innovations are introduced: (1) weakening noise perturbation conditions by extending diagonal matrix assumptions to non-negative definite matrices; (2) establishing criteria for both mean-square exponential stability and almost sure exponential stability in the absence of input; (3) directly handling complex structures like time-varying delays through matrix analysis. Compared with prior studies, this approach yields broader stability conclusions under weaker conditions, with numerical simulations validating the theoretical effectiveness. Full article

(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications in Science and Engineering, 4th Edition)

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51 pages, 7255 KiB

Open AccessFeature PaperArticle

Existence and Phase Structure of Random Inverse Limit Measures

by B. J. K. Kleijn

Mathematics 2025, 13(14), 2309; https://doi.org/10.3390/math13142309 - 19 Jul 2025

Viewed by 106

Abstract

Analogous to Kolmogorov’s theorem for the existence of stochastic processes describing random functions, we consider theorems for the existence of stochastic processes describing random measures as limits of inverse measure systems. Specifically, given a coherent inverse system of random (bounded/signed/positive/probability) histograms on refining [...] Read more.

Analogous to Kolmogorov’s theorem for the existence of stochastic processes describing random functions, we consider theorems for the existence of stochastic processes describing random measures as limits of inverse measure systems. Specifically, given a coherent inverse system of random (bounded/signed/positive/probability) histograms on refining partitions, we study conditions for the existence and uniqueness of a corresponding random inverse limit, a Radon probability measure on the space of (bounded/signed/positive/probability) measures. Depending on the topology (vague/tight/weak/total-variational) and Kingman’s notion of complete randomness, the limiting random measure is in one of four phases, distinguished by their degrees of concentration (support/domination/discreteness). The results are applied in the well-known Dirichlet and Polya tree families of random probability measures and a new Gaussian family of signed inverse limit measures. In these three families, examples of all four phases occur, and we describe the corresponding conditions of defining parameters. Full article

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

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13 pages, 1922 KiB

Open AccessFeature PaperArticle

On an Ambrosetti-Prodi Type Problem with Applications in Modeling Real Phenomena

by Irina Meghea

Mathematics 2025, 13(14), 2308; https://doi.org/10.3390/math13142308 - 19 Jul 2025

Viewed by 122

Abstract

This work presents a solving method for problems of Ambrosetti-Prodi type involving p-Laplacian and p-pseudo-Laplacian operators by using adequate variational methods. A variant of the mountain pass theorem, together with a kind of Palais-Smale condition, is involved in order to obtain [...] Read more.

This work presents a solving method for problems of Ambrosetti-Prodi type involving p-Laplacian and p-pseudo-Laplacian operators by using adequate variational methods. A variant of the mountain pass theorem, together with a kind of Palais-Smale condition, is involved in order to obtain and characterize solutions for some mathematical physics issues. Applications of these results for solving some physical chemical problems evolved from the need to model real phenomena are displayed. Solutions for Dirichlet problems containing these two operators applied for modeling critical micellar concentration, as well as the volume fraction of liquid mixtures, have been drawn. Full article

(This article belongs to the Special Issue Applications of Partial Differential Equations in Mathematical Physics, 2nd Edition)

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14 pages, 370 KiB

Open AccessArticle

Stabilization of Stochastic Dynamic Systems with Markov Parameters and Concentration Point

by Taras Lukashiv, Igor V. Malyk, Venkata P. Satagopam and Petr V. Nazarov

Mathematics 2025, 13(14), 2307; https://doi.org/10.3390/math13142307 - 19 Jul 2025

Viewed by 211

Abstract

This paper addresses the problem of optimal stabilization for stochastic dynamical systems characterized by Markov switches and concentration points of jumps, which is a scenario not adequately covered by classical stability conditions. Unlike traditional approaches requiring a strictly positive minimal interval between jumps, [...] Read more.

This paper addresses the problem of optimal stabilization for stochastic dynamical systems characterized by Markov switches and concentration points of jumps, which is a scenario not adequately covered by classical stability conditions. Unlike traditional approaches requiring a strictly positive minimal interval between jumps, we allow jump moments to accumulate at a finite point. Utilizing Lyapunov function methods, we derive sufficient conditions for exponential stability in the mean square and asymptotic stability in probability. We provide explicit constructions of Lyapunov functions adapted to scenarios with jump concentration points and develop conditions under which these functions ensure system stability. For linear stochastic differential equations, the stabilization problem is further simplified to solving a system of Riccati-type matrix equations. This work provides essential theoretical foundations and practical methodologies for stabilizing complex stochastic systems that feature concentration points, expanding the applicability of optimal control theory. Full article

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25 pages, 11175 KiB

Open AccessArticle

AI-Enabled Condition Monitoring Framework for Autonomous Pavement-Sweeping Robots

by Sathian Pookkuttath, Aung Kyaw Zin, Akhil Jayadeep, M. A. Viraj J. Muthugala and Mohan Rajesh Elara

Mathematics 2025, 13(14), 2306; https://doi.org/10.3390/math13142306 - 18 Jul 2025

Viewed by 203

Abstract

The demand for large-scale, heavy-duty autonomous pavement-sweeping robots is rising due to urban growth, hygiene needs, and labor shortages. Ensuring their health and safe operation in dynamic outdoor environments is vital, as terrain unevenness and slope gradients can accelerate wear, increase maintenance costs, [...] Read more.

The demand for large-scale, heavy-duty autonomous pavement-sweeping robots is rising due to urban growth, hygiene needs, and labor shortages. Ensuring their health and safe operation in dynamic outdoor environments is vital, as terrain unevenness and slope gradients can accelerate wear, increase maintenance costs, and pose safety risks. This study introduces an AI-driven condition monitoring (CM) framework designed to detect terrain unevenness and slope gradients in real time, distinguishing between safe and unsafe conditions. As system vibration levels and energy consumption vary with terrain unevenness and slope gradients, vibration and current data are collected for five CM classes identified: safe, moderately safe terrain, moderately safe slope, unsafe terrain, and unsafe slope. A simple-structured one-dimensional convolutional neural network (1D CNN) model is developed for fast and accurate prediction of the safe to unsafe classes for real-time application. An in-house developed large-scale autonomous pavement-sweeping robot, PANTHERA 2.0, is used for data collection and real-time experiments. The training dataset is generated by extracting representative vibration and heterogeneous slope data using three types of interoceptive sensors mounted in different zones of the robot. These sensors complement each other to enable accurate class prediction. The dataset includes angular velocity data from an IMU, vibration acceleration data from three vibration sensors, and current consumption data from three current sensors attached to the key motors. A CM-map framework is developed for real-time monitoring of the robot by fusing the predicted anomalous classes onto a 3D occupancy map of the workspace. The performance of the trained CM framework is evaluated through offline and real-time field trials using statistical measurement metrics, achieving an average class prediction accuracy of 92% and 90.8%, respectively. This demonstrates that the proposed CM framework enables maintenance teams to take timely and appropriate actions, including the adoption of suitable maintenance strategies. Full article

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19 pages, 2954 KiB

Open AccessArticle

Maximum Power Extraction of Photovoltaic Systems Using Dynamic Sliding Mode Control and Sliding Observer

by Ali Karami-Mollaee and Oscar Barambones

Mathematics 2025, 13(14), 2305; https://doi.org/10.3390/math13142305 - 18 Jul 2025

Viewed by 166

Abstract

In this paper, a robust optimized controller is implemented in the photovoltaic generator system (PVGS). The PVGS is composed of individual photovoltaic (PV) cells, which convert solar energy to electrical energy. To optimize the efficiency of the PVGS under variable solar irradiance and [...] Read more.

In this paper, a robust optimized controller is implemented in the photovoltaic generator system (PVGS). The PVGS is composed of individual photovoltaic (PV) cells, which convert solar energy to electrical energy. To optimize the efficiency of the PVGS under variable solar irradiance and temperatures, a maximum power point tracking (MPPT) controller is necessary. Additionally, the PVGS output voltage is typically low for many applications. To achieve the MPPT and to gain the output voltage, an increasing boost converter (IBC) is employed. Then, two issues should be considered in MPPT. At first, a smooth control signal for adjusting the duty cycle of the IBC is important. Another critical issue is the PVGS and IBC unknown sections, i.e., the total system uncertainty. Therefore, to address the system uncertainties and to regulate the smooth duty cycle of the converter, a robust dynamic sliding mode control (DSMC) is proposed. In DSMC, a low-pass integrator is placed before the system to suppress chattering and to produce a smooth actuator signal. However, this integrator increases the system states, and hence, a sliding mode observer (SMO) is proposed to estimate this additional state. The stability of the proposed control scheme is demonstrated using the Lyapunov theory. Finally, to demonstrate the effectiveness of the proposed method and provide a reliable comparison, conventional sliding mode control (CSMC) with the same proposed SMO is also implemented. Full article

(This article belongs to the Special Issue Applied Mathematics and Intelligent Control in Electrical Engineering)

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21 pages, 2143 KiB

Open AccessFeature PaperArticle

Physically Informed Synthetic Data Generation and U-Net Generative Adversarial Network for Palimpsest Reconstruction

by Jose L. Salmeron and Eva Fernandez-Palop

Mathematics 2025, 13(14), 2304; https://doi.org/10.3390/math13142304 - 18 Jul 2025

Viewed by 187

Abstract

This paper introduces a novel adversarial learning framework for reconstructing hidden layers in historical palimpsests. Recovering text hidden in historical palimpsests is complicated by various artifacts, such as ink diffusion, degradation of the writing substrate, and interference between overlapping layers. To address these [...] Read more.

This paper introduces a novel adversarial learning framework for reconstructing hidden layers in historical palimpsests. Recovering text hidden in historical palimpsests is complicated by various artifacts, such as ink diffusion, degradation of the writing substrate, and interference between overlapping layers. To address these challenges, the authors of this paper combine a synthetic data generator grounded in physical modeling with three generative architectures: a baseline VAE, an improved variant with stronger regularization, and a U-Net-based GAN that incorporates residual pathways and a mixed loss strategy. The synthetic data engine aims to emulate key degradation effects—such as ink bleeding, the irregularity of parchment fibers, and multispectral layer interactions—using stochastic approximations of underlying physical processes. The quantitative results suggest that the U-Net-based GAN architecture outperforms the VAE-based models by a notable margin, particularly in scenarios with heavy degradation or overlapping ink layers. By relying on synthetic training data, the proposed method facilitates the non-invasive recovery of lost text in culturally important documents, and does so without requiring costly or specialized imaging setups. Full article

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

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23 pages, 20932 KiB

Open AccessArticle

Robust Small-Object Detection in Aerial Surveillance via Integrated Multi-Scale Probabilistic Framework

by Youyou Li, Yuxiang Fang, Shixiong Zhou, Yicheng Zhang and Nuno Antunes Ribeiro

Mathematics 2025, 13(14), 2303; https://doi.org/10.3390/math13142303 - 18 Jul 2025

Viewed by 245

Abstract

Accurate and efficient object detection is essential for aerial airport surveillance, playing a critical role in aviation safety and the advancement of autonomous operations. Although recent deep learning approaches have achieved notable progress, significant challenges persist, including severe object occlusion, extreme scale variation, [...] Read more.

Accurate and efficient object detection is essential for aerial airport surveillance, playing a critical role in aviation safety and the advancement of autonomous operations. Although recent deep learning approaches have achieved notable progress, significant challenges persist, including severe object occlusion, extreme scale variation, dense panoramic clutter, and the detection of very small targets. In this study, we introduce a novel and unified detection framework designed to address these issues comprehensively. Our method integrates a Normalized Gaussian Wasserstein Distance loss for precise probabilistic bounding box regression, Dilation-wise Residual modules for improved multi-scale feature extraction, a Hierarchical Screening Feature Pyramid Network for effective hierarchical feature fusion, and DualConv modules for lightweight yet robust feature representation. Extensive experiments conducted on two public airport surveillance datasets, ASS1 and ASS2, demonstrate that our approach yields substantial improvements in detection accuracy. Specifically, the proposed method achieves an improvement of up to 14.6 percentage points in mean Average Precision (mAP@0.5) compared to state-of-the-art YOLO variants, with particularly notable gains in challenging small-object categories such as personnel detection. These results highlight the effectiveness and practical value of the proposed framework in advancing aviation safety and operational autonomy in airport environments. Full article

(This article belongs to the Special Issue Artificial Intelligence and Optimization in Aircraft Design and Unmanned Aerial Vehicles, 2nd Edition)

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Graphical abstract

15 pages, 656 KiB

Open AccessArticle

Green Technology Game and Data-Driven Parameter Identification in the Digital Economy

by Xiaofeng Li and Qun Zhao

Mathematics 2025, 13(14), 2302; https://doi.org/10.3390/math13142302 - 18 Jul 2025

Viewed by 159

Abstract

The digital economy presents multiple challenges to the promotion of green technologies, including behavioral uncertainty among firms, heterogeneous technological choices, and disparities in policy incentive strength. This study develops a tripartite evolutionary game model encompassing government, production enterprises, and technology suppliers to systematically [...] Read more.

The digital economy presents multiple challenges to the promotion of green technologies, including behavioral uncertainty among firms, heterogeneous technological choices, and disparities in policy incentive strength. This study develops a tripartite evolutionary game model encompassing government, production enterprises, and technology suppliers to systematically explore the strategic evolution mechanisms underlying green technology adoption. A three-dimensional nonlinear dynamic system is constructed using replicator dynamics, and the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is applied to identify key cost and benefit parameters for firms. Simulation results exhibit a strong match between the estimated parameters and simulated data, highlighting the model’s identifiability and explanatory capacity. In addition, the stability of eight pure strategy equilibrium points is examined through Jacobian analysis, revealing the evolutionary trajectories and local stability features across various strategic configurations. These findings offer theoretical guidance for optimizing green policy design and identifying behavioral pathways, while establishing a foundation for data-driven modeling of dynamic evolutionary processes. Full article

(This article belongs to the Special Issue Dynamic Analysis and Decision-Making in Complex Networks)

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18 pages, 608 KiB

Open AccessArticle

The Geometric Characterizations of the Ramanujan-Type Entire Function

by Khaled Mehrez and Abdulaziz Alenazi

Mathematics 2025, 13(14), 2301; https://doi.org/10.3390/math13142301 - 18 Jul 2025

Viewed by 200

Abstract

In the present paper, we present certain geometric properties, such as starlikeness, convexity of order

η (0 \leq η < 1)

, and close-to-convexity, in an open unit disk of the normalized form of Ramanujan-type entire functions. As a consequence, a [...] Read more.

In the present paper, we present certain geometric properties, such as starlikeness, convexity of order

η (0 \leq η < 1)

, and close-to-convexity, in an open unit disk of the normalized form of Ramanujan-type entire functions. As a consequence, a specific range of parameters is derived such that this function belongs to Hardy spaces

H^{\infty}

and

H^{r} .

Finally, as an application, we present the monotonicity property of the Ramanujan-type entire function using the method of subordination factor sequences. Full article

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

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29 pages, 6397 KiB

Open AccessArticle

A Hybrid GAS-ATT-LSTM Architecture for Predicting Non-Stationary Financial Time Series

by Kevin Astudillo, Miguel Flores, Mateo Soliz, Guillermo Ferreira and José Varela-Aldás

Mathematics 2025, 13(14), 2300; https://doi.org/10.3390/math13142300 - 18 Jul 2025

Viewed by 314

Abstract

This study proposes a hybrid approach to analyze and forecast non-stationary financial time series by combining statistical models with deep neural networks. A model is introduced that integrates three key components: the Generalized Autoregressive Score (GAS) model, which captures volatility dynamics; an attention [...] Read more.

This study proposes a hybrid approach to analyze and forecast non-stationary financial time series by combining statistical models with deep neural networks. A model is introduced that integrates three key components: the Generalized Autoregressive Score (GAS) model, which captures volatility dynamics; an attention mechanism (ATT), which identifies the most relevant features within the sequence; and a Long Short-Term Memory (LSTM) neural network, which receives the outputs of the previous modules to generate price forecasts. This architecture is referred to as GAS-ATT-LSTM. Both unidirectional and bidirectional variants were evaluated using real financial data from the Nasdaq Composite Index, Invesco QQQ Trust, ProShares UltraPro QQQ, Bitcoin, and gold and silver futures. The proposed model’s performance was compared against five benchmark architectures: LSTM Bidirectional, GARCH-LSTM Bidirectional, ATT-LSTM, GAS-LSTM, and GAS-LSTM Bidirectional, under sliding windows of 3, 5, and 7 days. The results show that GAS-ATT-LSTM, particularly in its bidirectional form, consistently outperforms the benchmark models across most assets and forecasting horizons. It stands out for its adaptability to varying volatility levels and temporal structures, achieving significant improvements in both accuracy and stability. These findings confirm the effectiveness of the proposed hybrid model as a robust tool for forecasting complex financial time series. Full article

(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Economics, Econometrics, and Financial Management)

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22 pages, 487 KiB

Open AccessArticle

Fuzzy Hypothesis Testing for Radar Detection: A Statistical Approach for Reducing False Alarm and Miss Probabilities

by Ahmed K. Elsherif, Hanan Haj Ahmad, Mohamed Aboshady and Basma Mostafa

Mathematics 2025, 13(14), 2299; https://doi.org/10.3390/math13142299 - 17 Jul 2025

Viewed by 232

Abstract

This paper addresses a fundamental challenge in statistical radar detection systems: optimizing the trade-off between the probability of a false alarm (

P_{F A}

) and the probability of a miss (

P_{M}

). These two metrics are inversely related and [...] Read more.

This paper addresses a fundamental challenge in statistical radar detection systems: optimizing the trade-off between the probability of a false alarm (

P_{F A}

) and the probability of a miss (

P_{M}

). These two metrics are inversely related and critical for performance evaluation. Traditional detection approaches often enhance one aspect at the expense of the other, limiting their practical applicability. To overcome this limitation, a fuzzy hypothesis testing framework is introduced that improves decision making under uncertainty by incorporating both crisp and fuzzy data representations. The methodology is divided into three phases. In the first phase, we reduce the probability of false alarm

P_{F A}

while maintaining a constant probability of miss

P_{M}

using crisp data characterized by deterministic values and classical statistical thresholds. In the second phase, the inverse scenario is considered: minimizing

P_{M}

while keeping

P_{F A}

fixed. This is achieved through parameter tuning and refined threshold calibration. In the third phase, a strategy is developed to simultaneously enhance both

P_{F A}

and

P_{M}

, despite their inverse correlation, by adopting adaptive decision rules. To further strengthen system adaptability, fuzzy data are introduced, which effectively model imprecision and ambiguity. This enhances robustness, particularly in scenarios where rapid and accurate classification is essential. The proposed methods are validated through both real and synthetic simulations of radar measurements, demonstrating their ability to enhance detection reliability across diverse conditions. The findings confirm the applicability of fuzzy hypothesis testing for modern radar systems in both civilian and military contexts, providing a statistically sound and operationally applicable approach for reducing detection errors and optimizing system performance. Full article

(This article belongs to the Special Issue New Advance in Applied Probability and Statistical Inference)

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32 pages, 2992 KiB

Open AccessArticle

An Inter-Regional Lateral Transshipment Model to Massive Relief Supplies with Deprivation Costs

by Shuanglin Li, Na Zhang and Jin Qin

Mathematics 2025, 13(14), 2298; https://doi.org/10.3390/math13142298 - 17 Jul 2025

Viewed by 312

Abstract

Massive relief supplies inter-regional lateral transshipment (MRSIRLT) can significantly enhance the efficiency of disaster response, meet the needs of affected areas (AAs), and reduce deprivation costs. This paper develops an integrated allocation and intermodality optimization model (AIOM) to address the MRSIRLT challenge. A [...] Read more.

Massive relief supplies inter-regional lateral transshipment (MRSIRLT) can significantly enhance the efficiency of disaster response, meet the needs of affected areas (AAs), and reduce deprivation costs. This paper develops an integrated allocation and intermodality optimization model (AIOM) to address the MRSIRLT challenge. A phased interactive framework incorporating adaptive differential evolution (JADE) and improved adaptive large neighborhood search (IALNS) is designed. Specifically, JADE is employed in the first stage to allocate the volume of massive relief supplies, aiming to minimize deprivation costs, while IALNS optimizes intermodal routing in the second stage to minimize the weighted sum of transportation time and cost. A case study based on a typhoon disaster in the Chinese region of Bohai Rim demonstrates and verifies the effectiveness and applicability of the proposed model and algorithm. The results and sensitivity analysis indicate that reducing loading and unloading times and improving transshipment efficiency can effectively decrease transfer time. Additionally, the weights assigned to total transfer time and costs can be balanced depending on demand satisfaction levels. Full article

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12 pages, 276 KiB

Open AccessArticle

A Note on Rigidity and Vanishing Theorems for Translating Solitons

by Jiji Peng and Guangwen Zhao

Mathematics 2025, 13(14), 2297; https://doi.org/10.3390/math13142297 - 17 Jul 2025

Viewed by 127

Abstract

In this short note, we focus on complete translating solitons with a bounded

L_{f}^{n}

-norm of the second fundamental form and obtain two results. First, based on a Sobolev-type inequality and a Simons-type inequality, we establish a rigidity theorem of complete [...] Read more.

In this short note, we focus on complete translating solitons with a bounded

L_{f}^{n}

-norm of the second fundamental form and obtain two results. First, based on a Sobolev-type inequality and a Simons-type inequality, we establish a rigidity theorem of complete translating solitons. Second, based on the same Sobolev-type inequality and a Bochner-type inequality, a vanishing theorem regarding

L_{f}^{p}

weighted harmonic 1-forms is proved. Full article

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40 pages, 4846 KiB

Open AccessArticle

Comparative Analysis of Some Methods and Algorithms for Traffic Optimization in Urban Environments Based on Maximum Flow and Deep Reinforcement Learning

by Silvia Baeva, Nikolay Hinov and Plamen Nakov

Mathematics 2025, 13(14), 2296; https://doi.org/10.3390/math13142296 - 17 Jul 2025

Viewed by 216

Abstract

This paper presents a comparative analysis between classical maximum flow algorithms and modern deep Reinforcement Learning (RL) algorithms applied to traffic optimization in urban environments. Through SUMO simulations and statistical tests, algorithms such as Ford–Fulkerson, Edmonds–Karp, Dinitz, Preflow–Push, Boykov–Kolmogorov and Double [...] Read more.

This paper presents a comparative analysis between classical maximum flow algorithms and modern deep Reinforcement Learning (RL) algorithms applied to traffic optimization in urban environments. Through SUMO simulations and statistical tests, algorithms such as Ford–Fulkerson, Edmonds–Karp, Dinitz, Preflow–Push, Boykov–Kolmogorov and Double

D Q N

are compared. Their efficiency and stability are evaluated in terms of metrics such as cumulative vehicle dispersion and the ratio of waiting time to vehicle number. The results show that classical algorithms such as Edmonds–Karp and Dinitz perform stably under deterministic conditions, while Double

D Q N

suffers from high variation. Recommendations are made regarding the selection of an appropriate algorithm based on the characteristics of the environment, and opportunities for improvement using DRL techniques such as PPO and A2C are indicated. Full article

(This article belongs to the Special Issue Mathematical Applications in Digitalization, Electrification, and Sustainable Development)

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20 pages, 523 KiB

Open AccessArticle

Improved Probability-Weighted Moments and Two-Stage Order Statistics Methods of Generalized Extreme Value Distribution

by Autcha Araveeporn

Mathematics 2025, 13(14), 2295; https://doi.org/10.3390/math13142295 - 17 Jul 2025

Viewed by 216

Abstract

This study evaluates six parameter estimation methods for the generalized extreme value (GEV) distribution: maximum likelihood estimation (MLE), two probability-weighted moments (PWM-UE and PWM-PP), and three robust two-stage order statistics estimators (TSOS-ME, TSOS-LMS, and TSOS-LTS). Their performance was assessed using simulation experiments under [...] Read more.

This study evaluates six parameter estimation methods for the generalized extreme value (GEV) distribution: maximum likelihood estimation (MLE), two probability-weighted moments (PWM-UE and PWM-PP), and three robust two-stage order statistics estimators (TSOS-ME, TSOS-LMS, and TSOS-LTS). Their performance was assessed using simulation experiments under varying tail behaviors, represented by three types of GEV distributions: Weibull (short-tailed), Gumbel (light-tailed), and Fréchet (heavy-tailed) distributions, based on the mean squared error (MSE) and mean absolute percentage error (MAPE). The results showed that TSOS-LTS consistently achieved the lowest MSE and MAPE, indicating high robustness and forecasting accuracy, particularly for short-tailed distributions. Notably, PWM-PP performed well for the light-tailed distribution, providing accurate and efficient estimates in this specific setting. For heavy-tailed distributions, TSOS-LTS exhibited superior estimation accuracy, while PWM-PP showed a better predictive performance in terms of MAPE. The methods were further applied to real-world monthly maximum PM2.5 data from three air quality stations in Bangkok. TSOS-LTS again demonstrated superior performance, especially at Thon Buri station. This research highlights the importance of tailoring estimation techniques to the distribution’s tail behavior and supports the use of robust approaches for modeling environmental extremes. Full article

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

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Mathematics, Volume 13, Issue 14 (July-2 2025) – 107 articles

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