Mathematics

19 pages, 4443 KiB

Open AccessArticle

Multimodal Image Translation Algorithm Based on Singular Squeeze-and-Excitation Network

by Hangyao Tu, Zheng Wang and Yanwei Zhao

Mathematics 2025, 13(1), 177; https://doi.org/10.3390/math13010177 - 6 Jan 2025

Viewed by 1228

Image-to-image translation methods have advanced from focusing on image-level info to incorporating pixel-level and instance-level details. However, with feature-level constraint, deviation occurs when the network overemphasizes convolutional features, neglecting traditional image feature extraction. To address this, we proposed the multimodal image translation algorithm [...] Read more.

Image-to-image translation methods have advanced from focusing on image-level info to incorporating pixel-level and instance-level details. However, with feature-level constraint, deviation occurs when the network overemphasizes convolutional features, neglecting traditional image feature extraction. To address this, we proposed the multimodal image translation algorithm MASSE based on a Singular Squeeze-and-Excitation Network, combining GANs and SENet. It utilizes SVD features to assist the SENet in managing the scaling degree. The SENet employs SVD to extract features and enhance the Excitation operation to obtain new channel attention weights and form attention feature maps. Then, image content features are refined by combining convolutional and attention feature maps, and style features are obtained by the style generator. Finally, content and style features are combined to generate new style images. Ablation experiments showed the optimal SVD parameter is 128, producing the best translation results. According to FID, MASSE outperforms current methods in generating diverse images. Full article

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17 pages, 3986 KiB

Open AccessArticle

Efficient Image Inpainting for Handwritten Text Removal Using CycleGAN Framework

by Somanka Maiti, Shabari Nath Panuganti, Gaurav Bhatnagar and Jonathan Wu

Mathematics 2025, 13(1), 176; https://doi.org/10.3390/math13010176 - 6 Jan 2025

Viewed by 1185

Abstract

With the recent rise in the development of deep learning techniques, image inpainting—the process of restoring missing or corrupted regions in images—has witnessed significant advancements. Although state-of-the-art models are effective, they often fail to inpaint complex missing areas, especially when handwritten occlusions are [...] Read more.

With the recent rise in the development of deep learning techniques, image inpainting—the process of restoring missing or corrupted regions in images—has witnessed significant advancements. Although state-of-the-art models are effective, they often fail to inpaint complex missing areas, especially when handwritten occlusions are present in the image. To address this issue, an image inpainting model based on a residual CycleGAN is proposed. The generator takes as input the image occluded by handwritten missing patches and generates a restored image, which the discriminator then compares with the original ground truth image to determine whether it is real or fake. An adversarial trade-off between the generator and discriminator motivates the model to improve its training and produce a superior reconstructed image. Extensive experiments and analyses confirm that the proposed method generates inpainted images with superior visual quality and outperforms state-of-the-art deep learning approaches. Full article

(This article belongs to the Special Issue New Trends in Computer Vision, Pattern Recognition and Machine Learning)

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3 pages, 121 KiB

Open AccessEditorial

Special Issue: “Optimization Algorithms: Theory and Applications”

by Frank Werner

Mathematics 2025, 13(1), 175; https://doi.org/10.3390/math13010175 - 6 Jan 2025

Viewed by 949

Abstract

This Special Issue of the journal Mathematics was dedicated to compiling new results in the area of optimization algorithms, and both theoretical works and practical applications have been searched [...] Full article

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

39 pages, 5106 KiB

Open AccessArticle

Mathematical Modelling and Optimisation of Operating Parameters for Enhanced Energy Generation in Gas Turbine Power Plant with Intercooler

by Anthony O. Onokwai, Udochukwu B. Akuru and Dawood A. Desai

Mathematics 2025, 13(1), 174; https://doi.org/10.3390/math13010174 - 6 Jan 2025

Viewed by 1830

Abstract

This study developed an optimal model for gas turbine power plants (GTPPs) with intercoolers, focusing on the challenges related to power output, thermal efficiency and specific fuel consumption. The study combined response surface methodology (RSM) and central composite design (CCD) with advanced metaheuristic [...] Read more.

This study developed an optimal model for gas turbine power plants (GTPPs) with intercoolers, focusing on the challenges related to power output, thermal efficiency and specific fuel consumption. The study combined response surface methodology (RSM) and central composite design (CCD) with advanced metaheuristic algorithms, including ANFIS, ANFIS PSO and ANFIS GA, to model nonlinear interactions of key parameters, including the pressure ratio, ambient temperature, turbine inlet temperature and the effectiveness of the intercooler. Optimal values of thermal efficiency (47.8%), power output (165 MW) and specific fuel consumption (0.16 kg/kWh) were attained under conditions of a pressure ratio of 25, an ambient temperature 293 K, a turbine inlet temperature of 1550 K and 95% intercooler effectiveness. The RSM, being the initial model, was able to predict but lacked precision when compared with the nonlinear influences that were modelled by ANFIS PSO and ANFIS GA, with power output, thermal efficiency and specific fuel consumption (sfc) having corresponding R² values of 0.979, 0.987 and 0.972. The study demonstrated the potential of extending metaheuristic algorithms to provide sustainable solutions to energy system problems and reduced emissions through gas turbine power plant (GTPP) optimisation. Full article

(This article belongs to the Special Issue Mathematical Modelling and Numerical Analysis in Electrical Engineering, 2nd Edition)

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17 pages, 2587 KiB

Open AccessArticle

A Multi-Robot Collaborative Exploration Method Based on Deep Reinforcement Learning and Knowledge Distillation

by Rui Wang, Ming Lyu and Jie Zhang

Mathematics 2025, 13(1), 173; https://doi.org/10.3390/math13010173 - 6 Jan 2025

Viewed by 1366

Abstract

Multi-robot collaborative autonomous exploration in communication-constrained scenarios is essential in areas such as search and rescue. During the exploration process, the robot teams must minimize the occurrence of redundant scanning of the environment. To this end, we propose to view the robot team [...] Read more.

Multi-robot collaborative autonomous exploration in communication-constrained scenarios is essential in areas such as search and rescue. During the exploration process, the robot teams must minimize the occurrence of redundant scanning of the environment. To this end, we propose to view the robot team as an agent and obtain a policy network that can be centrally executed by training with an improved SAC deep reinforcement learning algorithm. In addition, we transform the obtained policy network into distributed networks that can be adapted to communication-constrained scenarios using knowledge distillation. Our proposed method offers an innovative solution to the decision-making problem for multiple robots. We conducted experiments on our proposed method within simulated environments. The experimental results show the adaptability of our proposed method to various sizes of environments and its superior performance compared to the current mainstream methods. Full article

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21 pages, 6954 KiB

Open AccessArticle

Disturbance Observer-Based Dynamic Surface Control for Servomechanisms with Prescribed Tracking Performance

by Xingfa Zhao, Wenhe Liao, Tingting Liu, Dongyang Zhang and Yumin Tao

Mathematics 2025, 13(1), 172; https://doi.org/10.3390/math13010172 - 6 Jan 2025

Viewed by 654

Abstract

The critical design challenge for a class of servomechanisms is to reject unknown dynamics (including internal uncertainties and external disturbances) and achieve the prescribed performance of the tracking error. To get rid of the influence of unknown dynamics, an extended state observer (ESO) [...] Read more.

The critical design challenge for a class of servomechanisms is to reject unknown dynamics (including internal uncertainties and external disturbances) and achieve the prescribed performance of the tracking error. To get rid of the influence of unknown dynamics, an extended state observer (ESO) is employed to estimate system states and total unknown dynamics and does not require a priori information of the known dynamic. Meanwhile, an improved prescribed performance function is presented to guarantee the transient performance of the tracking error (e.g., the overshoot, convergence rate, and the steady state error). Consequently, a modified dynamic surface control strategy is designed based on the estimations of the ESO and error constraints. The stability of the proposed control strategy is demonstrated using Lyapunov theory. Finally, some simulation results based on a turntable servomechanism show that the proposed method is effective, and it has a better control effect and stronger anti-disturbance ability compared with the traditional control method. Full article

(This article belongs to the Section C2: Dynamical Systems)

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20 pages, 798 KiB

Open AccessArticle

Modeling the Tripodal Mobile Market Using Response Functions Instead of Payoff Maximization

by Aynur Ali, Atanas Ilchev, Vanya Ivanova, Hristina Kulina, Polina Yaneva and Boyan Zlatanov

Mathematics 2025, 13(1), 171; https://doi.org/10.3390/math13010171 - 6 Jan 2025

Viewed by 603

Abstract

We investigate the dynamics of tripodal markets using the response functions, which is a continuation of recent research in the field. Instead of investigating the optimization problem of finding the levels of production that maximize the payoff functions of the participants in an [...] Read more.

We investigate the dynamics of tripodal markets using the response functions, which is a continuation of recent research in the field. Instead of investigating the optimization problem of finding the levels of production that maximize the payoff functions of the participants in an oligopolistic market, based on the available statistical data on market presence, we construct a model of the reaction of the participants. This approach allows, in the absence of information about the cost functions of producers and the demand and utility functions of consumers, to construct a model that is statistically reliable and answers the questions about the levels at which the market has reached equilibrium and whether it is sustainable. On the other hand, any external impact, such as changes in the regulations or the behavior of small market participants, is implicitly included in the response functions. The additional analysis confirms that there are no dependencies, even of a nonlinear type, in the constructed models that are not included. Stability and equilibrium are investigated in the proposed models. The statistical performance measurements for the constructed models are calculated, and their credibility is tested. The models demonstrate high statistical performance and adequacy. Full article

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21 pages, 1357 KiB

Open AccessArticle

Stochastic Modeling of Adaptive Trait Evolution in Phylogenetics: A Polynomial Regression and Approximate Bayesian Computation Approach

by Dwueng-Chwuan Jhwueng and Chia-Hua Chang

Mathematics 2025, 13(1), 170; https://doi.org/10.3390/math13010170 - 6 Jan 2025

Cited by 1 | Viewed by 748

Abstract

In nature, closely related species often exhibit diverse characteristics, challenging simplistic line interpretations of trait evolution. For these species, the evolutionary dynamics of one trait may differ markedly from another, with some traits evolving at a slower pace and others rapidly diversifying. In [...] Read more.

In nature, closely related species often exhibit diverse characteristics, challenging simplistic line interpretations of trait evolution. For these species, the evolutionary dynamics of one trait may differ markedly from another, with some traits evolving at a slower pace and others rapidly diversifying. In light of this complexity and concerning the phenomenon of trait relationships that escape line measurement, we introduce a novel general adaptive optimal regression model, grounded on polynomial relationships. This approach seeks to capture intricate patterns in trait evolution by considering them as continuous stochastic variables along a phylogenetic tree. Using polynomial functions, the model offers a holistic and comprehensive description of the traits of the studied species, accounting for both decreasing and increasing trends over evolutionary time. We propose two sets of optimal adaptive evolutionary polynomial regression models of

k^{t h}

order, named the Ornstein–Uhlenbeck Brownian Motion Polynomial (

{OUBMP}_{k}

) model and Ornstein–Uhlenbeck Ornstein–Uhlenbeck Polynomial (

{OUOUP}_{k}

) model, respectively. Assume that the main trait value

y_{t}

is a random variable of the Ornstein–Uhlenbeck (OU) process and that its optimal adaptive value

θ_{t}^{y}

has a polynomial relationship with other traits

x_{t}

for statistical modeling, where

x_{t}

can be a random variable of Brownian motion (BM) or OU process. As analytical representations for the likelihood of the models are not feasible, we implement an approximate Bayesian computation (ABC) technique to assess the performance through simulation. We also plan to apply models to the empirical study using the two datasets: the longevity vs. fecundity in the Mediterranean nekton group, and the trophic niche breadth vs. body mass in carnivores in a European forest region. Full article

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

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11 pages, 302 KiB

Open AccessArticle

The Half-Space Sommerfeld Problem of a Horizontal Dipole for Magnetic Media

by Seil Sautbekov and Merey Sautbekova

Mathematics 2025, 13(1), 169; https://doi.org/10.3390/math13010169 - 6 Jan 2025

Viewed by 716

Abstract

A Hertz radiator’s Sommerfeld boundary value problem is considered for the case when its electric moment is directed horizontally relative to the plane interface between two media with different values of magnetic permeability. An integral representation of the exact expression for the Hertz [...] Read more.

A Hertz radiator’s Sommerfeld boundary value problem is considered for the case when its electric moment is directed horizontally relative to the plane interface between two media with different values of magnetic permeability. An integral representation of the exact expression for the Hertz potential, which generalizes the classical solution for non-magnetic media, both in cylindrical and spherical coordinate systems, is obtained. The corresponding expressions for the scattered wave fields are given in the form of Sommerfeld integrals. It is shown that the potential components can be represented as the sum of an infinite series in powers of the Green function. Full article

(This article belongs to the Special Issue Computational Methods in Electromagnetics)

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18 pages, 461 KiB

Open AccessArticle

Machine Learning vs. Econometric Models to Forecast Inflation Rate in Romania? The Role of Sentiment Analysis

by Mihaela Simionescu

Mathematics 2025, 13(1), 168; https://doi.org/10.3390/math13010168 - 6 Jan 2025

Viewed by 1850

Abstract

Given the high inflationary pressure in Romania, the aim of this paper is to demonstrate the potential of autoregressive distributed lag (ARDL) models incorporating sentiment analysis to provide better inflation forecasts compared to machine learning (ML) techniques. Sentiment analysis based on National Bank [...] Read more.

Given the high inflationary pressure in Romania, the aim of this paper is to demonstrate the potential of autoregressive distributed lag (ARDL) models incorporating sentiment analysis to provide better inflation forecasts compared to machine learning (ML) techniques. Sentiment analysis based on National Bank of Romania reports on quarterly inflation may provide valuable inputs for econometric models. The ARDL model, utilizing inflation and sentiment index data from the previous period, outperformed the proposed seasonal autoregressive integrated moving average (SARIMA) model and the ML techniques (support vector machine and artificial neural networks). The forecasts based on the ARDL model predicted correctly all the changes in inflation, while accuracy measures (mean error, mean absolute error, root squared mean error) in the short-run 2023: Q1–2024: Q3 indicated the most accurate predictions. The more accurate forecasts are essential for national banks, companies, policymakers, and households. Full article

(This article belongs to the Special Issue Advanced Statistical Applications in Financial Econometrics)

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13 pages, 1675 KiB

Open AccessFeature PaperArticle

Genotype-Structured Modeling of Variant Emergence and Its Impact on Virus Infection

by Anass Bouchnita

Mathematics 2025, 13(1), 167; https://doi.org/10.3390/math13010167 - 6 Jan 2025

Viewed by 935

Abstract

Variant emergence continues to pose a threat to global public health, despite the large-scale campaigns of immunization worldwide. In this paper, we present a genotype-structured model of viral infectious and evolutionary dynamics. We calibrate the model using the available estimates for SARS-CoV-2 infection [...] Read more.

Variant emergence continues to pose a threat to global public health, despite the large-scale campaigns of immunization worldwide. In this paper, we present a genotype-structured model of viral infectious and evolutionary dynamics. We calibrate the model using the available estimates for SARS-CoV-2 infection parameters and use it to study the conditions leading to the emergence of immune escaping variants. In particular, we show that the emergence of highly replicating or immune escaping variants could extend the duration of the infection, while the emergence of variants that are both highly replicating and immune escaping could provoke a rebound of the infection. Then, we show that the high frequency of mutation increases the chances of variant emergence, which promotes virus persistence. Further, simulations suggest that weak neutralization by antibodies could exert a selective pressure that favors the development of aggressive variants. These results can help public health officials identify and isolate the patients from where new variants emerge, which would make genomic surveillance efforts more efficient. Full article

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

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21 pages, 3818 KiB

Open AccessArticle

EEG-Based Emotion Recognition with Combined Fuzzy Inference via Integrating Weighted Fuzzy Rule Inference and Interpolation

by Fangyi Li, Fusheng Yu, Liang Shen, Hexi Li, Xiaonan Yang and Qiang Shen

Mathematics 2025, 13(1), 166; https://doi.org/10.3390/math13010166 - 5 Jan 2025

Cited by 3 | Viewed by 1184

Abstract

Emotions play a significant role in shaping psychological activities, behaviour, and interpersonal communication. Reflecting this importance, automated emotion classification has become a vital research area in artificial intelligence. Electroencephalogram (EEG)-based emotion recognition is particularly promising due to its high temporal resolution and resistance [...] Read more.

Emotions play a significant role in shaping psychological activities, behaviour, and interpersonal communication. Reflecting this importance, automated emotion classification has become a vital research area in artificial intelligence. Electroencephalogram (EEG)-based emotion recognition is particularly promising due to its high temporal resolution and resistance to manipulation. This study introduces an advanced fuzzy inference algorithm for EEG data-driven emotion recognition, effectively addressing the ambiguity of emotional states. By combining adaptive fuzzy rule generation, feature evaluation, and weighted fuzzy rule interpolation, the proposed approach achieves accurate emotion classification while handling incomplete knowledge. Experimental results demonstrate that the integrated fuzzy system outperforms state-of-the-art techniques, offering improved recognition accuracy and robustness under uncertainty. Full article

(This article belongs to the Special Issue The Recent Advances in Computational Intelligence)

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22 pages, 26214 KiB

Open AccessArticle

SwinInsSeg: An Improved SOLOv2 Model Using the Swin Transformer and a Multi-Kernel Attention Module for Ship Instance Segmentation

by Rabi Sharma, Muhammad Saqib, Chin-Teng Lin and Michael Blumenstein

Mathematics 2025, 13(1), 165; https://doi.org/10.3390/math13010165 - 5 Jan 2025

Viewed by 1075

Abstract

Maritime surveillance is essential for ensuring security in the complex marine environment. The study presents SwinInsSeg, an instance segmentation model that combines the Swin transformer and a lightweight MKA module to segment ships accurately and efficiently in maritime surveillance. Current models have limitations [...] Read more.

Maritime surveillance is essential for ensuring security in the complex marine environment. The study presents SwinInsSeg, an instance segmentation model that combines the Swin transformer and a lightweight MKA module to segment ships accurately and efficiently in maritime surveillance. Current models have limitations in segmenting multiscale ships and achieving accurate segmentation boundaries. SwinInsSeg addresses these limitations by identifying ships of various sizes and capturing finer details, including both small and large ships, through the MKA module, which emphasizes important information at different processing stages. Performance evaluations on the MariBoats and ShipInsSeg datasets show that SwinInsSeg outperforms YOLACT, SOLO, and SOLOv2, achieving mask average precision scores of 50.6% and 52.0%, respectively. These results demonstrate SwinInsSeg’s superior capability in segmenting ship instances with improved accuracy. Full article

(This article belongs to the Special Issue New Advances and Applications in Image Processing and Computer Vision)

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16 pages, 298 KiB

Open AccessArticle

New Perspectives on Generalised Lacunary Statistical Convergence of Multiset Sequences

by María C. Listán-García, Ömer Kişi and Mehmet Gürdal

Mathematics 2025, 13(1), 164; https://doi.org/10.3390/math13010164 - 5 Jan 2025

Viewed by 813

Abstract

This paper explores the concepts of

J

-lacunary statistical limit points,

J

-lacunary statistical cluster points, and

J

-lacunary statistical Cauchy multiset sequences. Building upon previous work in the field, we investigate the relationships between

J

-lacunary statistical convergence and

J^{*}

-lacunary [...] Read more.

This paper explores the concepts of

J

-lacunary statistical limit points,

J

-lacunary statistical cluster points, and

J

-lacunary statistical Cauchy multiset sequences. Building upon previous work in the field, we investigate the relationships between

J

-lacunary statistical convergence and

J^{*}

-lacunary statistical convergence in multiset sequences. The findings contribute to a deeper understanding of the convergence behaviour of multiset sequences and provide new insights into the application of ideal convergence in this context. Full article

(This article belongs to the Section C1: Difference and Differential Equations)

13 pages, 284 KiB

Open AccessArticle

Generalized Weak Contractions Involving a Pair of Auxiliary Functions via Locally Transitive Binary Relations and Applications to Boundary Value Problems

by Nidal H. E. Eljaneid, Esmail Alshaban, Adel Alatawi, Montaser Saudi Ali, Saud S. Alsharari and Faizan Ahmad Khan

Mathematics 2025, 13(1), 163; https://doi.org/10.3390/math13010163 - 5 Jan 2025

Viewed by 755

Abstract

The intent of this paper was to investigate the fixed-point results under relation-theoretic generalized weak contractivity condition employing a pair of auxiliary functions

ϕ

and

ψ

verifying appropriate properties. In proving our outcomes, we observed that the partial-ordered relation (even, transitive relation) adopted [...] Read more.

The intent of this paper was to investigate the fixed-point results under relation-theoretic generalized weak contractivity condition employing a pair of auxiliary functions

ϕ

and

ψ

verifying appropriate properties. In proving our outcomes, we observed that the partial-ordered relation (even, transitive relation) adopted by earlier authors can be weakened to the extent of a locally

ϝ

-transitive binary relation. The findings proved herewith generalize, extend, improve, and unify a number of existing outcomes. To validate of our findings, we offer a number of illustrative examples. Our outcomes assist us to figure out the existence and uniqueness of solutions to a boundary value problem. Full article

(This article belongs to the Special Issue Advances in Nonlinear Analysis, Analytic Number Theory, and Mathematical Inequalities)

29 pages, 759 KiB

Open AccessArticle

Linearized Harmonic Balance Method for Seeking the Periodic Vibrations of Second- and Third-Order Nonlinear Oscillators

by Chein-Shan Liu, Chung-Lun Kuo and Chih-Wen Chang

Mathematics 2025, 13(1), 162; https://doi.org/10.3390/math13010162 - 5 Jan 2025

Cited by 2 | Viewed by 928

Abstract

To solve the nonlinear vibration problems of second- and third-order nonlinear oscillators, a modified harmonic balance method (HBM) is developed in this paper. In the linearized technique, we decompose the nonlinear terms of the governing equation on two sides via a constant weight [...] Read more.

To solve the nonlinear vibration problems of second- and third-order nonlinear oscillators, a modified harmonic balance method (HBM) is developed in this paper. In the linearized technique, we decompose the nonlinear terms of the governing equation on two sides via a constant weight factor; then, they are linearized with respect to a fundamental periodic function satisfying the specified initial conditions. The periodicity of nonlinear oscillation is reflected in the Mathieu-type ordinary differential equation (ODE) with periodic forcing terms appeared on the right-hand side. In each iteration of the linearized harmonic balance method (LHBM), we simply solve a small-size linear system to determine the Fourier coefficients and the vibration frequency. Because the algebraic manipulations required for the LHBM are quite saving, it converges fast with a few iterations. For the Duffing oscillator, a frequency–amplitude formula is derived in closed form, which improves the accuracy of frequency by about three orders compared to that obtained by the Hamiltonian-based frequency–amplitude formula. To reduce the computational cost of analytically solving the third-order nonlinear jerk equations, the LHBM invoking a linearization technique results in the Mathieu-type ODE again, of which the harmonic balance equations are easily deduced and solved. The LHBM can achieve quite accurate periodic solutions, whose accuracy is assessed by using the fourth-order Runge–Kutta numerical integration method. The optimal value of weight factor is chosen such that the absolute error of the periodic solution is minimized. Full article

(This article belongs to the Special Issue Computational Mathematics: Advanced Methods and Applications)

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14 pages, 317 KiB

Open AccessArticle

Sequential Confidence Intervals for Comparing Two Proportions with Applications in A/B Testing

by Jun Hu, Lijia Zheng and Ibtihal Alanazi

Mathematics 2025, 13(1), 161; https://doi.org/10.3390/math13010161 - 5 Jan 2025

Viewed by 620

Abstract

This article addresses the use of fixed-width confidence intervals (FWCIs) for comparing two independent Bernoulli populations in A/B testing scenarios. Two sequential estimation procedures are proposed: one for estimating the difference in log probabilities of success and the other for log odds ratios. [...] Read more.

This article addresses the use of fixed-width confidence intervals (FWCIs) for comparing two independent Bernoulli populations in A/B testing scenarios. Two sequential estimation procedures are proposed: one for estimating the difference in log probabilities of success and the other for log odds ratios. Both methods showcase great efficiency, as established via theoretical analysis and Monte Carlo simulations. The practical utility of these methods is demonstrated through two real-world applications: analyzing retention rates in mobile game Cookie Cats and evaluating the effectiveness of online advertising. Full article

(This article belongs to the Special Issue Sequential Sampling Methods for Statistical Inference)

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16 pages, 4019 KiB

Open AccessArticle

Arouse-Net: Enhancing Glioblastoma Segmentation in Multi-Parametric MRI with a Custom 3D Convolutional Neural Network and Attention Mechanism

by Haiyang Li, Xiaozhi Qi, Ying Hu and Jianwei Zhang

Mathematics 2025, 13(1), 160; https://doi.org/10.3390/math13010160 - 4 Jan 2025

Cited by 1 | Viewed by 907

Abstract

Glioblastoma, a highly aggressive brain tumor, is challenging to diagnose and treat due to its variable appearance and invasiveness. Traditional segmentation methods are often limited by inter-observer variability and the lack of annotated datasets. Addressing these challenges, this study introduces Arouse-Net, a 3D [...] Read more.

Glioblastoma, a highly aggressive brain tumor, is challenging to diagnose and treat due to its variable appearance and invasiveness. Traditional segmentation methods are often limited by inter-observer variability and the lack of annotated datasets. Addressing these challenges, this study introduces Arouse-Net, a 3D convolutional neural network that enhances feature extraction through dilated convolutions, improving tumor margin delineation. Our approach includes an attention mechanism to focus on edge features, essential for precise glioblastoma segmentation. The model’s performance is benchmarked against the state-of-the-art BRATS test dataset, demonstrating superior results with an over eight times faster processing speed. The integration of multi-modal MRI data and the novel evaluation protocol developed for this study offer a robust framework for medical image segmentation, particularly useful for clinical scenarios where annotated datasets are limited. The findings of this research not only advance the field of medical image analysis but also provide a foundation for future work in the development of automated segmentation tools for brain tumors. Full article

(This article belongs to the Special Issue Robust Perception and Control in Prognostic Systems)

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18 pages, 300 KiB

Open AccessArticle

Magnetic Curves in Homothetic s-th Sasakian Manifolds

by Şaban Güvenç and Cihan Özgür

Mathematics 2025, 13(1), 159; https://doi.org/10.3390/math13010159 - 4 Jan 2025

Viewed by 553

Abstract

We investigate normal magnetic curves in

(2 n + s)

-dimensional homothetic s-th Sasakian manifolds as a generalization of S-manifolds. We show that a curve

γ

is a normal magnetic curve in a homothetic s-th Sasakian manifold if [...] Read more.

We investigate normal magnetic curves in

(2 n + s)

-dimensional homothetic s-th Sasakian manifolds as a generalization of S-manifolds. We show that a curve

γ

is a normal magnetic curve in a homothetic s-th Sasakian manifold if and only if its osculating order satisfies

r \leq 3

and it belongs to a family of

θ_{i}

-slant helices. Additionally, we construct a homothetic s-th Sasakian manifold using generalized D-homothetic transformations and present the parametric equations of normal magnetic curves in this manifold. Full article

(This article belongs to the Special Issue Differentiable Manifolds and Geometric Structures)

25 pages, 1043 KiB

Open AccessArticle

AdaMoR-DDMOEA: Adaptive Model Selection with a Reliable Individual-Based Model Management Framework for Offline Data-Driven Multi-Objective Optimization

by Subhadip Pramanik, Abdalla Alameen, Hitesh Mohapatra, Debanjan Pathak and Adrijit Goswami

Mathematics 2025, 13(1), 158; https://doi.org/10.3390/math13010158 - 3 Jan 2025

Cited by 1 | Viewed by 1020

Abstract

Many real-world expensive industrial and engineering multi-objective optimization problems (MOPs) are driven by historical, experimental, or simulation data. In such scenarios, due to the expensive cost and time required, we are only left with a small amount of labeled data to perform the [...] Read more.

Many real-world expensive industrial and engineering multi-objective optimization problems (MOPs) are driven by historical, experimental, or simulation data. In such scenarios, due to the expensive cost and time required, we are only left with a small amount of labeled data to perform the optimization. These offline data-driven MOPs are usually solved by multi-objective evolutionary algorithms (MOEAs) with the help of surrogate models constructed from offline historical data. The key challenge in developing these data-driven MOEAs is that they have to replace multiple conflicting fitness functions by approximating these objective functions, which may produce cumulative approximation errors and misguide the search. In order to build a reliable surrogate model from a small amount of multi-output offline data and solve the DDMOPs, we have proposed an adaptive model selection method with a reliable individual-based model management-driven MOEA. The proposed algorithm dynamically selects between DNN and XGBoost by comparing their k-fold cross-validation MAE error, which can capture the true generalization ability of the surrogates on unseen data. Then, the selected surrogate is updated with a reliable individual selection strategy, where the individual who is closest, both in the decision and objective space, to the most preferred solution among labeled offline data is chosen. As a result, these two strategies guide the underlying MOEA to the Pareto optimal solutions. The empirical results of the ZDT and DTLZ benchmark test suite validate the use of the three state-of-the-art offline DDMOEAs, showing that our algorithm is able to achieve highly competitive results in terms of convergence and diversity for 2–3 objectives. Finally, our algorithm is applied to an offline data-driven multi-objective problem—transonic airfoil (RAE 2822) shape optimization—to validate its efficiency on real-world DDMOPs. Full article

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12 pages, 269 KiB

Open AccessArticle

Four Different Ulam-Type Stability for Implicit Second-Order Fractional Integro-Differential Equation with M-Point Boundary Conditions

by Ilhem Nasrallah, Rabiaa Aouafi and Said Kouachi

Mathematics 2025, 13(1), 157; https://doi.org/10.3390/math13010157 - 3 Jan 2025

Viewed by 637

Abstract

In this paper, we discuss the existence and uniqueness of a solution for the implicit two-order fractional integro-differential equation with m-point boundary conditions by applying the Banach fixed point theorem. Moreover, in the paper we establish the four different varieties of Ulam stability [...] Read more.

In this paper, we discuss the existence and uniqueness of a solution for the implicit two-order fractional integro-differential equation with m-point boundary conditions by applying the Banach fixed point theorem. Moreover, in the paper we establish the four different varieties of Ulam stability (Hyers–Ulam stability, generalized Hyers–Ulam stability, Hyers–Ulam-Rassias stability, and generalized Hyers–Ulam–Rassias stability) for the given problem. Full article

30 pages, 488 KiB

Open AccessFeature PaperArticle

Belyi Maps from Zeroes of Hypergeometric Polynomials

by Raimundas Vidunas

Mathematics 2025, 13(1), 156; https://doi.org/10.3390/math13010156 - 3 Jan 2025

Viewed by 614

Abstract

The evaluation of low-degree hypergeometric polynomials to zero defines algebraic hypersurfaces in the affine space of the free parameters and the argument of the hypergeometric function. This article investigates the algebraic surfaces defined by the hypergeometric equation [...] Read more.

The evaluation of low-degree hypergeometric polynomials to zero defines algebraic hypersurfaces in the affine space of the free parameters and the argument of the hypergeometric function. This article investigates the algebraic surfaces defined by the hypergeometric equation

{}_{2}F_{1} (- N, b; c; z) = 0

with

N = 3

or

N = 4

. As a captivating application, these surfaces parametrize certain families of genus 0 Belyi maps. Thereby, this article contributes to the systematic enumeration of Belyi maps. Full article

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16 pages, 1679 KiB

Open AccessArticle

Vibration Analysis of a Tetra-Layered FGM Cylindrical Shell Using Ring Support

by Asra Ayub, Naveed Hussain, Ahmad N. Al-Kenani and Madiha Ghamkhar

Mathematics 2025, 13(1), 155; https://doi.org/10.3390/math13010155 - 3 Jan 2025

Cited by 1 | Viewed by 639

Abstract

In the present study, the vibration characteristics of a cylindrical shell (CS) made up of four layers are investigated. The ring is placed in the axial direction of a four-layered functionally graded material (FGM) cylindrical shell. The layers are made of functionally graded [...] Read more.

In the present study, the vibration characteristics of a cylindrical shell (CS) made up of four layers are investigated. The ring is placed in the axial direction of a four-layered functionally graded material (FGM) cylindrical shell. The layers are made of functionally graded material (FGM). The materials used are stainless steel, aluminum, zirconia, and nickel. The frequency equations are derived by employing Sander’s shell theory and the Rayleigh–Ritz (RR) mathematical technique. Vibration characteristics of functionally graded materials have been investigated using polynomial volume fraction law for all FGM layers. The characteristic beam functions have been used to determine the axial model dependency. The natural frequencies are obtained with simply supported boundary conditions by using MATLAB software. Several analogical assessments of shell frequencies have also been conducted to confirm the accuracy and dependability of the current technique. Full article

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15 pages, 1079 KiB

Open AccessArticle

An Improved Hierarchical Optimization Framework for Walking Control of Underactuated Humanoid Robots Using Model Predictive Control and Whole Body Planner and Controller

by Yuanji Liu, Haiming Mou, Hao Jiang, Qingdu Li and Jianwei Zhang

Mathematics 2025, 13(1), 154; https://doi.org/10.3390/math13010154 - 3 Jan 2025

Viewed by 1128

Abstract

This paper addresses the fundamental challenge of achieving stable and efficient walking in a lightweight, underactuated humanoid robot that lacks an ankle roll degree of freedom. To tackle this relevant critical problem, we present a hierarchical optimization framework that combines model predictive control [...] Read more.

This paper addresses the fundamental challenge of achieving stable and efficient walking in a lightweight, underactuated humanoid robot that lacks an ankle roll degree of freedom. To tackle this relevant critical problem, we present a hierarchical optimization framework that combines model predictive control (MPC) with a tailored whole body planner and controller (WBPC). At the high level, we employ a matrix exponential (ME)-based discretization of the MPC, ensuring numerical stability across a wide range of step sizes (5 to 100 ms), thereby reducing computational complexity without sacrificing control quality. At the low level, the WBPC is specifically designed to handle the unique kinematic constraints imposed by the missing ankle roll DOF, generating feasible joint trajectories for the swing foot phase. Meanwhile, a whole body control (WBC) strategy refines ground reaction forces and joint trajectories under full-body dynamics and contact wrench cone (CWC) constraints, guaranteeing physically realizable interactions with the environment. Finally, a position–velocity–torque (PVT) controller integrates feedforward torque commands with the desired trajectories for robust execution. Validated through walking experiments on the MuJoCo simulation platform using our custom-designed lightweight robot X02, this approach not only improves the numerical stability of MPC solutions, but also provides a scientifically sound and effective method for underactuated humanoid locomotion control. Full article

(This article belongs to the Special Issue Advanced Control of Complex Dynamical Systems and Robotics with Applications)

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11 pages, 540 KiB

Open AccessArticle

Iteratively Reweighted Least Squares Fiducial Interval for Variance in Unbalanced Variance Components Model

by Arisa Jiratampradab, Jiraphan Suntornchost and Thidaporn Supapakorn

Mathematics 2025, 13(1), 153; https://doi.org/10.3390/math13010153 - 3 Jan 2025

Viewed by 561

Abstract

The objective of this work is to propose the iteratively reweighted least squares concept to form a fiducial generalized pivotal quantity of the between-group variance component for the unbalanced variance components model. The fiducial generalized pivotal quantity is a subclass of the generalized [...] Read more.

The objective of this work is to propose the iteratively reweighted least squares concept to form a fiducial generalized pivotal quantity of the between-group variance component for the unbalanced variance components model. The fiducial generalized pivotal quantity is a subclass of the generalized pivotal quantity which is useful technique to deal with problem of nuisance parameters for finding interval estimator. This research provides the probability distribution and the properties of the statistics to lead the constructing of the confidence interval. The authors also prove the construction of the fiducial generalized pivotal quantity through iteratively reweighted least squares. The performance comparison for the new proposed method with other competing methods in the literature is studied through a simulation study. The results of the simulation study demonstrate that the proposed method is very satisfactory in terms of both the coverage probability and the average width of the confidence interval. Furthermore, the analysis of real data for patients of sickle cell disease also illustrates that the proposed method gives the smallest average width of the confidence interval. All these results confirm that the iteratively reweighted least squares fiducial generalized pivotal quantity confidence interval is recommended. Full article

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

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26 pages, 12514 KiB

Open AccessArticle

Reconstruction and Prediction of Chaotic Time Series with Missing Data: Leveraging Dynamical Correlations Between Variables

by Jingchan Lv, Hongcun Mao, Yu Wang and Zhihai Yao

Mathematics 2025, 13(1), 152; https://doi.org/10.3390/math13010152 - 3 Jan 2025

Cited by 1 | Viewed by 904

Abstract

Although data-driven machine learning methods have been successfully applied to predict complex nonlinear dynamics, forecasting future evolution based on incomplete past information remains a significant challenge. This paper proposes a novel data-driven approach that leverages the dynamical relationships among variables. By integrating Non-Stationary [...] Read more.

Although data-driven machine learning methods have been successfully applied to predict complex nonlinear dynamics, forecasting future evolution based on incomplete past information remains a significant challenge. This paper proposes a novel data-driven approach that leverages the dynamical relationships among variables. By integrating Non-Stationary Transformers with LightGBM, we construct a robust model where LightGBM builds a fitting function to capture and simulate the complex coupling relationships among variables in dynamically evolving chaotic systems. This approach enables the reconstruction of missing data, restoring sequence completeness and overcoming the limitations of existing chaotic time series prediction methods in handling missing data. We validate the proposed method by predicting the future evolution of variables with missing data in both dissipative and conservative chaotic systems. Experimental results demonstrate that the model maintains stability and effectiveness even with increasing missing rates, particularly in the range of 30% to 50%, where prediction errors remain relatively low. Furthermore, the feature importance extracted by the model aligns closely with the underlying dynamic characteristics of the chaotic system, enhancing the method’s interpretability and reliability. This research offers a practical and theoretically sound solution to the challenges of predicting chaotic systems with incomplete datasets. Full article

(This article belongs to the Special Issue Statistical Analysis and Data Science for Complex Data)

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18 pages, 607 KiB

Open AccessArticle

Deep Reinforcement Learning for Intraday Multireservoir Hydropower Management

by Rodrigo Castro-Freibott, Álvaro García-Sánchez, Francisco Espiga-Fernández and Guillermo González-Santander de la Cruz

Mathematics 2025, 13(1), 151; https://doi.org/10.3390/math13010151 - 3 Jan 2025

Viewed by 1148

Abstract

This study investigates the application of Reinforcement Learning (RL) to optimize intraday operations of hydropower reservoirs. Unlike previous approaches that focus on long-term planning with coarse temporal resolutions and discretized state-action spaces, we propose an RL framework tailored to the Hydropower Reservoirs Intraday [...] Read more.

This study investigates the application of Reinforcement Learning (RL) to optimize intraday operations of hydropower reservoirs. Unlike previous approaches that focus on long-term planning with coarse temporal resolutions and discretized state-action spaces, we propose an RL framework tailored to the Hydropower Reservoirs Intraday Economic Optimization problem. This framework manages continuous state-action spaces while accounting for fine-grained temporal dynamics, including dam-to-turbine delays, gate movement constraints, and power group operations. Our methodology evaluates three distinct action space formulations (continuous, discrete, and adjustments) implemented using modern RL algorithms (A2C, PPO, and SAC). We compare them against both a greedy baseline and Mixed-Integer Linear Programming (MILP) solutions. Experiments on real-world data from a two-reservoir system and a simulated six-reservoir system demonstrate that while MILP achieves superior performance in the smaller system, its performance degrades significantly when scaled to six reservoirs. In contrast, RL agents, particularly those using discrete action spaces and trained with PPO, maintain consistent performance across both configurations, achieving considerable improvements with less than one second of execution time. These results suggest that RL offers a scalable alternative to traditional optimization methods for hydropower operations, particularly in scenarios requiring real-time decision making or involving larger systems. Full article

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

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20 pages, 3934 KiB

Open AccessArticle

An Importance Sampling Method for Generating Optimal Interpolation Points in Training Physics-Informed Neural Networks

by Hui Li, Yichi Zhang, Zhaoxiong Wu, Zhe Wang and Tong Wu

Mathematics 2025, 13(1), 150; https://doi.org/10.3390/math13010150 - 3 Jan 2025

Viewed by 913

Abstract

The application of machine learning and artificial intelligence to solve scientific challenges has significantly increased in recent years. A remarkable development is the use of Physics-Informed Neural Networks (PINNs) to solve Partial Differential Equations (PDEs) numerically. However, current PINN techniques often face problems [...] Read more.

The application of machine learning and artificial intelligence to solve scientific challenges has significantly increased in recent years. A remarkable development is the use of Physics-Informed Neural Networks (PINNs) to solve Partial Differential Equations (PDEs) numerically. However, current PINN techniques often face problems with accuracy and slow convergence. To address these problems, we propose an importance sampling method to generate optimal interpolation points during training. Experimental results demonstrate that our method achieves a 43% reduction in root mean square error compared to state-of-the-art methods when applied to the one-dimensional Korteweg–De Vries equation. Full article

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20 pages, 351 KiB

Open AccessFeature PaperArticle

Multilevel Constrained Bandits: A Hierarchical Upper Confidence Bound Approach with Safety Guarantees

by Ali Baheri

Mathematics 2025, 13(1), 149; https://doi.org/10.3390/math13010149 - 3 Jan 2025

Viewed by 1071

Abstract

The multi-armed bandit (MAB) problem is a foundational model for sequential decision-making under uncertainty. While MAB has proven valuable in applications such as clinical trials and online advertising, traditional formulations have limitations; specifically, they struggle to handle three key real-world scenarios: (1) when [...] Read more.

The multi-armed bandit (MAB) problem is a foundational model for sequential decision-making under uncertainty. While MAB has proven valuable in applications such as clinical trials and online advertising, traditional formulations have limitations; specifically, they struggle to handle three key real-world scenarios: (1) when decisions must follow a hierarchical structure (as in autonomous systems where high-level strategy guides low-level actions); (2) when there are constraints at multiple levels of decision-making (such as both system-wide and component-level resource limits); and (3) when available actions depend on previous choices or context. To address these challenges, we introduce the hierarchical constrained bandits (HCB) framework, which extends contextual bandits to incorporate both hierarchical decisions and multilevel constraints. We propose the HC-UCB (hierarchical constrained upper confidence bound) algorithm to solve the HCB problem. The algorithm uses confidence bounds within a hierarchical setting to balance exploration and exploitation while respecting constraints at all levels. Our theoretical analysis establishes that HC-UCB achieves sublinear regret, guarantees constraint satisfaction at all hierarchical levels, and is near-optimal in terms of achievable performance. Simple experimental results demonstrate the algorithm’s effectiveness in balancing reward maximization with constraint satisfaction. Full article

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11 pages, 232 KiB

Open AccessFeature PaperArticle

Exponential Growth and Properties of Solutions for a Forced System of Incompressible Navier–Stokes Equations in Sobolev–Gevrey Spaces

by José Luis Díaz Palencia

Mathematics 2025, 13(1), 148; https://doi.org/10.3390/math13010148 - 2 Jan 2025

Viewed by 615

Abstract

One problem of interest in the analysis of Navier–Stokes equations is concerned with the behavior of solutions for certain conditions in the forcing term or external force. In this work, we consider an external force of a maximum exponential growth, and we investigate [...] Read more.

One problem of interest in the analysis of Navier–Stokes equations is concerned with the behavior of solutions for certain conditions in the forcing term or external force. In this work, we consider an external force of a maximum exponential growth, and we investigate the local existence and uniqueness of solutions to the incompressible Navier–Stokes equations within the Sobolev–Gevrey space

H_{a, σ}^{1} (R^{3})

. Sobolev–Gevrey spaces are well suited for our purposes, as they provide high regularity and control over derivative growth, and this is particularly relevant for us, given the maximum exponential growth in the forcing term. Additionally, the structured bounds in Gevrey spaces help monitor potential solution blow-up by maintaining regularity, though they do not fully prevent or resolve global blow-up scenarios. Utilizing the Banach fixed-point theorem, we demonstrate that the nonlinear operator associated with the Navier–Stokes equations is locally Lipschitz continuous in

H_{a, σ}^{1} (R^{3})

. Through energy estimates and the application of Grönwall’s inequality, we establish that solutions exist, are unique, and also exhibit exponential growth in their Sobolev–Gevrey norms over time under certain assumptions in the forcing term. This analysis in intended to contribute in the understanding of the behavior of fluid flows with forcing terms in high-regularity function spaces. Full article

(This article belongs to the Section C2: Dynamical Systems)

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