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Mathematics
Volume 12
Issue 17
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Mathematics, Volume 12, Issue 17 (September-1 2024) – 193 articles

Cover Story (view full-size image): We propose a pricing formula for a defaultable zero-coupon bond with imperfect information under a regime switching model using a structural form of credit risk modelling. This paper provides explicit representations of risky debt under regime switching with a constant interest rate and risky debt under regime switching with a regime switching interest rate. While the value of the firm’s equity is observed continuously, we assume that the total value of the firm is only observed at discrete times, such as the dates of the release of the firm’s annual reports, or quarterly reports. This uncertainty about the true value of the firm results in credit spreads that do not approach zero as the debt approaches maturity, which is a problem with many structural models. View this paper
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16 pages, 366 KiB  
Article
A Method for Transforming Non-Convex Optimization Problem to Distributed Form
by Oleg O. Khamisov, Oleg V. Khamisov, Todor D. Ganchev and Eugene S. Semenkin
Mathematics 2024, 12(17), 2796; https://doi.org/10.3390/math12172796 - 9 Sep 2024
Viewed by 805
Abstract
We propose a novel distributed method for non-convex optimization problems with coupling equality and inequality constraints. This method transforms the optimization problem into a specific form to allow distributed implementation of modified gradient descent and Newton’s methods so that they operate as if [...] Read more.
We propose a novel distributed method for non-convex optimization problems with coupling equality and inequality constraints. This method transforms the optimization problem into a specific form to allow distributed implementation of modified gradient descent and Newton’s methods so that they operate as if they were distributed. We demonstrate that for the proposed distributed method: (i) communications are significantly less time-consuming than oracle calls, (ii) its convergence rate is equivalent to the convergence of Newton’s method concerning oracle calls, and (iii) for the cases when oracle calls are more expensive than communication between agents, the transition from a centralized to a distributed paradigm does not significantly affect computational time. The proposed method is applicable when the objective function is twice differentiable and constraints are differentiable, which holds for a wide range of machine learning methods and optimization setups. Full article
(This article belongs to the Special Issue Applied and Computational Mathematics for Digital Environments, 2nd Edition)
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22 pages, 1531 KiB  
Article
Quantitative and Qualitative Analysis of Aircraft Round-Trip Times Using Phase Type Distributions
by Srinivas R. Chakravarthy
Mathematics 2024, 12(17), 2795; https://doi.org/10.3390/math12172795 - 9 Sep 2024
Viewed by 521
Abstract
One of the major issues facing commercial airlines is the time that it takes to board passengers. Further, most airlines wish to increase the number of trips that an aircraft can make between two or more cities. Thus, reducing the overall boarding times [...] Read more.
One of the major issues facing commercial airlines is the time that it takes to board passengers. Further, most airlines wish to increase the number of trips that an aircraft can make between two or more cities. Thus, reducing the overall boarding times by a few minutes will have a significant impact on the number of trips made by an aircraft, as well as enabling improvements in key measures such as the median and 75th and 95th percentiles. Looking at such measures other than the mean is critical as it is well known that the mean can under- or overestimate the performance of any model. While there is considerable literature on the study of strategies to decrease boarding times, the same cannot be said about the study of the boarding time given a particular strategy for boarding. Thus, the focus of this paper is to study analytically (using suitable stochastic models) and numerically the impact of reducing the average time on the key measures to help the system to plan accordingly. This is achieved using a well-known probability distribution, namely the phase type distribution, to model various events involved in the boarding process. Illustrative numerical results show a reduction in the percentile values when the average boarding times are decreased. Understanding the percentiles of the boarding times, as opposed to relying only on the average boarding times, will help management to adopt a better boarding strategy that in turn will lead to an increase in the number of trips that an aircraft can make. Full article
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36 pages, 18802 KiB  
Article
A Novel Hybrid Model (EMD-TI-LSTM) for Enhanced Financial Forecasting with Machine Learning
by Olcay Ozupek, Reyat Yilmaz, Bita Ghasemkhani, Derya Birant and Recep Alp Kut
Mathematics 2024, 12(17), 2794; https://doi.org/10.3390/math12172794 - 9 Sep 2024
Viewed by 2185
Abstract
Financial forecasting involves predicting the future financial states and performance of companies and investors. Recent technological advancements have demonstrated that machine learning-based models can outperform traditional financial forecasting techniques. In particular, hybrid approaches that integrate diverse methods to leverage their strengths have yielded [...] Read more.
Financial forecasting involves predicting the future financial states and performance of companies and investors. Recent technological advancements have demonstrated that machine learning-based models can outperform traditional financial forecasting techniques. In particular, hybrid approaches that integrate diverse methods to leverage their strengths have yielded superior results in financial prediction. This study introduces a novel hybrid model, entitled EMD-TI-LSTM, consisting of empirical mode decomposition (EMD), technical indicators (TI), and long short-term memory (LSTM). The proposed model delivered more accurate predictions than those generated by the conventional LSTM approach on the same well-known financial datasets, achieving average enhancements of 39.56%, 36.86%, and 39.90% based on the MAPE, RMSE, and MAE metrics, respectively. Furthermore, the results show that the proposed model has a lower average MAPE rate of 42.91% compared to its state-of-the-art counterparts. These findings highlight the potential of hybrid models and mathematical innovations to advance the field of financial forecasting. Full article
(This article belongs to the Special Issue Machine Learning and Finance)
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15 pages, 500 KiB  
Article
Reduction in Optimal Time in Systems with Input Redundancy
by Zhongxing Peng, Gengzhong Zheng and Wei Huang
Mathematics 2024, 12(17), 2793; https://doi.org/10.3390/math12172793 - 9 Sep 2024
Viewed by 508
Abstract
This paper discusses a reduction in the optimal time due to the presence of input redundancy in time-optimal control problems. By introducing a non-idle channel to represent an active input channel, we establish the necessary and sufficient conditions that ensure a strict reduction [...] Read more.
This paper discusses a reduction in the optimal time due to the presence of input redundancy in time-optimal control problems. By introducing a non-idle channel to represent an active input channel, we establish the necessary and sufficient conditions that ensure a strict reduction in the optimal time for affine nonlinear systems. In cases of identical input redundancy, its impact varies according to the type of input constraint, and certain types may not lead to a reduction in the optimal time. Ultimately, in linear time-invariant (LTI) systems, the extent of the optimal time reduction depends on the system’s controllability. Full article
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13 pages, 1017 KiB  
Article
Hybrid Fuzzy Method for Performance Evaluation of City Construction
by Chun-Ming Yang, Chang-Hsien Hsu, Tian Chen and Shiyao Li
Mathematics 2024, 12(17), 2792; https://doi.org/10.3390/math12172792 - 9 Sep 2024
Viewed by 613
Abstract
Evaluating the performance of city construction not only helps optimize city functions and improve city quality, but it also contributes to the development of sustainable cities. However, most of the scoring rules for evaluating the performance of city construction are overly cumbersome and [...] Read more.
Evaluating the performance of city construction not only helps optimize city functions and improve city quality, but it also contributes to the development of sustainable cities. However, most of the scoring rules for evaluating the performance of city construction are overly cumbersome and demand very high data integrity. Moreover, the properties, change scale, and scope of different evaluation indicators of city construction often lead to uncertain and ambiguous results. In this study, a hybrid fuzzy method is proposed to conduct the performance evaluation of city construction in two phases. Firstly, a city performance index (CPI) was developed by combining the means and standard deviations of indicators of city construction to address the volatility of historical statistical data as well as different types of data. Considering the sampling errors in data analysis, the parameter estimation method was used to derive the 100% × (1 − α) confidence interval of the CPI. Buckley’s fuzzy approach was then adopted to extend the statistical estimators from the CPI into fuzzy estimators, after which a fuzzy CPI was proposed. To identify the specific improvement directions for city construction, the fuzzy axiom design (fuzzy AD) method was applied to explore the relationship between the targets set by city managers and actual performance. Finally, an example of six cities in China is provided to illustrate the effectiveness and practicality of the proposed method. The results show that the performance of Chongqing on several evaluation indicators is lower than that of other cities. The proposed method takes into account the issues of uniformity and diversity in the performance evaluation of city construction. It can enable a quantitative assessment of the city construction level in all cities and provide theoretical support and a decision-making basis for relevant government departments to optimize city construction planning and scientifically formulate city construction policies. Full article
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Numbers, Fuzzy Modeling, and Their Applications in Management and Engineering, 2nd Edition)
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14 pages, 505 KiB  
Article
Few-Shot Learning Sensitive Recognition Method Based on Prototypical Network
by Guoquan Yuan, Xinjian Zhao, Liu Li, Song Zhang and Shanming Wei
Mathematics 2024, 12(17), 2791; https://doi.org/10.3390/math12172791 - 9 Sep 2024
Viewed by 626
Abstract
Traditional machine learning-based entity extraction methods rely heavily on feature engineering by experts, and the generalization ability of the model is poor. Prototype networks, on the other hand, can effectively use a small amount of labeled data to train models while using category [...] Read more.
Traditional machine learning-based entity extraction methods rely heavily on feature engineering by experts, and the generalization ability of the model is poor. Prototype networks, on the other hand, can effectively use a small amount of labeled data to train models while using category prototypes to enhance the generalization ability of the models. Therefore, this paper proposes a prototype network-based named entity recognition (NER) method, namely the FSPN-NER model, to solve the problem of difficult recognition of sensitive data in data-sparse text. The model utilizes the positional coding model (PCM) to pre-train the data and perform feature extraction, then computes the prototype vectors to achieve entity matching, and finally introduces a boundary detection module to enhance the performance of the prototype network in the named entity recognition task. The model in this paper is compared with LSTM, BiLSTM, CRF, Transformer and their combination models, and the experimental results on the test dataset show that the model outperforms the comparative models with an accuracy of 84.8%, a recall of 85.8% and an F1 value of 0.853. Full article
(This article belongs to the Special Issue Data Mining and Machine Learning in the Era of Big Knowledge and Large Models)
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46 pages, 27418 KiB  
Article
Enhanced Parameter Estimation of DENsity CLUstEring (DENCLUE) Using Differential Evolution
by Omer Ajmal, Shahzad Mumtaz, Humaira Arshad, Abdullah Soomro, Tariq Hussain, Razaz Waheeb Attar and Ahmed Alhomoud
Mathematics 2024, 12(17), 2790; https://doi.org/10.3390/math12172790 - 9 Sep 2024
Cited by 1 | Viewed by 722
Abstract
The task of finding natural groupings within a dataset exploiting proximity of samples is known as clustering, an unsupervised learning approach. Density-based clustering algorithms, which identify arbitrarily shaped clusters using spatial dimensions and neighbourhood aspects, are sensitive to the selection of parameters. For [...] Read more.
The task of finding natural groupings within a dataset exploiting proximity of samples is known as clustering, an unsupervised learning approach. Density-based clustering algorithms, which identify arbitrarily shaped clusters using spatial dimensions and neighbourhood aspects, are sensitive to the selection of parameters. For instance, DENsity CLUstEring (DENCLUE)—a density-based clustering algorithm—requires a trial-and-error approach to find suitable parameters for optimal clusters. Earlier attempts to automate the parameter estimation of DENCLUE have been highly dependent either on the choice of prior data distribution (which could vary across datasets) or by fixing one parameter (which might not be optimal) and learning other parameters. This article addresses this challenge by learning the parameters of DENCLUE through the differential evolution optimisation technique without prior data distribution assumptions. Experimental evaluation of the proposed approach demonstrated consistent performance across datasets (synthetic and real datasets) containing clusters of arbitrary shapes. The clustering performance was evaluated using clustering validation metrics (e.g., Silhouette Score, Davies–Bouldin Index and Adjusted Rand Index) as well as qualitative visual analysis when compared with other density-based clustering algorithms, such as DPC, which is based on weighted local density sequences and nearest neighbour assignments (DPCSA) and Variable KDE-based DENCLUE (VDENCLUE). Full article
(This article belongs to the Special Issue Computational Methods and Application in Machine Learning, 2nd Edition)
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23 pages, 1677 KiB  
Article
Design and Comparison of Fractional-Order Controllers in Flotation Cell Banks and Flotation Columns Used in Copper Extraction Processes
by Manuel A. Duarte-Mermoud, Abdiel Ricaldi-Morales, Juan Carlos Travieso-Torres and Rafael Castro-Linares
Mathematics 2024, 12(17), 2789; https://doi.org/10.3390/math12172789 - 9 Sep 2024
Viewed by 624
Abstract
This work explores efficiency improvements in the copper flotation stage, a complex nonlinear, multivariable process subject to numerous perturbations. The primary objective is to design a fractional-order PID (FOPID) control strategy and a fractional-order model reference adaptive control (FOMRAC) system. The parameters for [...] Read more.
This work explores efficiency improvements in the copper flotation stage, a complex nonlinear, multivariable process subject to numerous perturbations. The primary objective is to design a fractional-order PID (FOPID) control strategy and a fractional-order model reference adaptive control (FOMRAC) system. The parameters for these controllers are optimized using the particle swarm optimization (PSO) algorithm with an objective function tailored to the control goals. This study employs models of both a bank series of five flotation cells and a flotation column. Their performance results are compared against traditional controllers, such as an integer-order PID and MRAC. The findings reveal that fractional-order controllers offer notable advantages over their integer-order counterparts, showing improved performance metrics with minimal changes to the existing control framework. This research highlights the effectiveness of fractional control in enhancing flotation processes and introduces a novel application of fractional control techniques in this area. Full article
(This article belongs to the Special Issue Theory, Modeling and Applications of Fractional-Order Systems)
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26 pages, 3243 KiB  
Article
A Novel Brillouin and Langevin Functions Dynamic Model for Two Conflicting Social Groups: Study of R&D Processes
by Ekaterina V. Orlova
Mathematics 2024, 12(17), 2788; https://doi.org/10.3390/math12172788 - 9 Sep 2024
Viewed by 522
Abstract
We consider a two-group social conflict under the corporates’ research and development (R&D) business processes. Conflict participants are divided into two groups depending on their attitude to new ideas, technologies, and behavioral style for R&D creative problems—innovators and adapters. We reveal the contradiction [...] Read more.
We consider a two-group social conflict under the corporates’ research and development (R&D) business processes. Conflict participants are divided into two groups depending on their attitude to new ideas, technologies, and behavioral style for R&D creative problems—innovators and adapters. We reveal the contradiction that arises between the need to include both types of employees in one project team and their objectively antagonistic positions regarding the methods and approaches to R&D processes. The proposed research methodology is based on a modern post-non-classical paradigm formed on the principles of coherence, interdisciplinarity, openness, and nonlinearity, as well as a sociophysical approach to the social conflicts modeling. We use the general theories of magnetism, paramagnetism, and functions of P. Langevin and L. Brillouin to describe the dynamics of group participants’ preferences regarding the style of conflict behavior. The analogy of paramagnetism, consisting in the orienting effect of the magnetic field, is used to describe social groups interactions that have not only their own interests, but are also influenced by the opinions of opposite social groups. A two-dimensional, four-parameter map represents the dynamics of group conflict. Modeling results show that regardless of the initial states and with certain parameters of intra-group and intergroup interactions, the trajectories eventually converge to an attractor (limit cycle) in a two-dimensional space. No non-periodic or chaotic modes are identified in the two-group conflict, which determines the controllability of the described conflict. The results of the simulation experiments are used as decision support and contradictions resolution aimed at forming the required modes of the corporates’ research and development business processes and ensuring the group participants’ cohesion and depolarization. The results of testing the model at an industrial enterprise are presented. Full article
(This article belongs to the Special Issue Study on Convergence of Nonlinear Dynamical Systems)
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23 pages, 2176 KiB  
Article
Robust Liu Estimator Used to Combat Some Challenges in Partially Linear Regression Model by Improving LTS Algorithm Using Semidefinite Programming
by Waleed B. Altukhaes, Mahdi Roozbeh and Nur A. Mohamed
Mathematics 2024, 12(17), 2787; https://doi.org/10.3390/math12172787 - 9 Sep 2024
Cited by 2 | Viewed by 532
Abstract
Outliers are a common problem in applied statistics, together with multicollinearity. In this paper, robust Liu estimators are introduced into a partially linear model to combat the presence of multicollinearity and outlier challenges when the error terms are not independent and some linear [...] Read more.
Outliers are a common problem in applied statistics, together with multicollinearity. In this paper, robust Liu estimators are introduced into a partially linear model to combat the presence of multicollinearity and outlier challenges when the error terms are not independent and some linear constraints are assumed to hold in the parameter space. The Liu estimator is used to address the multicollinearity, while robust methods are used to handle the outlier problem. In the literature on the Liu methodology, obtaining the best value for the biased parameter plays an important role in model prediction and is still an unsolved problem. In this regard, some robust estimators of the biased parameter are proposed based on the least trimmed squares (LTS) technique and its extensions using a semidefinite programming approach. Based on a set of observations with a sample size of n, and the integer trimming parameter h ≤ n, the LTS estimator computes the hyperplane that minimizes the sum of the lowest h squared residuals. Even though the LTS estimator is statistically more effective than the widely used least median squares (LMS) estimate, it is less complicated computationally than LMS. It is shown that the proposed robust extended Liu estimators perform better than classical estimators. As part of our proposal, using Monte Carlo simulation schemes and a real data example, the performance of robust Liu estimators is compared with that of classical ones in restricted partially linear models. Full article
(This article belongs to the Special Issue Nonparametric Regression Models: Theory and Applications)
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13 pages, 273 KiB  
Article
Some Fractional Integral and Derivative Formulas Revisited
by Juan Luis González-Santander and Francesco Mainardi
Mathematics 2024, 12(17), 2786; https://doi.org/10.3390/math12172786 - 9 Sep 2024
Viewed by 546
Abstract
In the most common literature about fractional calculus, we find that Dtαaft=It−αaft is assumed implicitly in the tables of fractional integrals and derivatives. However, this is not straightforward from the [...] Read more.
In the most common literature about fractional calculus, we find that Dtαaft=It−αaft is assumed implicitly in the tables of fractional integrals and derivatives. However, this is not straightforward from the definitions of Itαaft and Dtαaft. In this sense, we prove that Dt0ft=It−α0ft is true for ft=tν−1logt, and ft=eλt, despite the fact that these derivations are highly non-trivial. Moreover, the corresponding formulas for Dtα−∞t−δ and Itα−∞t−δ found in the literature are incorrect; thus, we derive the correct ones, proving in turn that Dtα−∞t−δ=It−α−∞t−δ holds true. Full article
(This article belongs to the Topic Fractional Calculus: Theory and Applications, 2nd Edition)
22 pages, 357 KiB  
Article
Accelerating the Speed of Convergence for High-Order Methods to Solve Equations
by Ramandeep Behl, Ioannis K. Argyros and Sattam Alharbi
Mathematics 2024, 12(17), 2785; https://doi.org/10.3390/math12172785 - 9 Sep 2024
Viewed by 466
Abstract
This article introduces a multistep method for developing sequences that solve Banach space-valued equations. It provides error estimates, a radius of convergence, and uniqueness results. Our approach improves the applicability of the recommended method and addresses challenges in applied science. The theoretical advancements [...] Read more.
This article introduces a multistep method for developing sequences that solve Banach space-valued equations. It provides error estimates, a radius of convergence, and uniqueness results. Our approach improves the applicability of the recommended method and addresses challenges in applied science. The theoretical advancements are supported by comprehensive computational results, demonstrating the practical applicability and robustness of the earlier method. We ensure more reliable and precise solutions to Banach space-valued equations by providing computable error estimates and a clear radius of convergence for the considered method. We conclude that our work significantly improves the practical utility of multistep methods, offering a rigorous and computable approach to solving complex equations in Banach spaces, with strong theoretical and computational results. Full article
(This article belongs to the Special Issue New Trends and Developments in Numerical Analysis: 2nd Edition)
10 pages, 725 KiB  
Article
Coarse-Gridded Simulation of the Nonlinear Schrödinger Equation with Machine Learning
by Benjamin F. Akers and Kristina O. F. Williams
Mathematics 2024, 12(17), 2784; https://doi.org/10.3390/math12172784 - 9 Sep 2024
Viewed by 547
Abstract
A numerical method for evolving the nonlinear Schrödinger equation on a coarse spatial grid is developed. This trains a neural network to generate the optimal stencil weights to discretize the second derivative of solutions to the nonlinear Schrödinger equation. The neural network is [...] Read more.
A numerical method for evolving the nonlinear Schrödinger equation on a coarse spatial grid is developed. This trains a neural network to generate the optimal stencil weights to discretize the second derivative of solutions to the nonlinear Schrödinger equation. The neural network is embedded in a symmetric matrix to control the scheme’s eigenvalues, ensuring stability. The machine-learned method can outperform both its parent finite difference method and a Fourier spectral method. The trained scheme has the same asymptotic operation cost as its parent finite difference method after training. Unlike traditional methods, the performance depends on how close the initial data are to the training set. Full article
(This article belongs to the Special Issue Numerical Analysis in Computational Mathematics)
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14 pages, 1181 KiB  
Article
Prediction of Wind Turbine Gearbox Oil Temperature Based on Stochastic Differential Equation Modeling
by Hongsheng Su, Zonghao Ding and Xingsheng Wang
Mathematics 2024, 12(17), 2783; https://doi.org/10.3390/math12172783 - 9 Sep 2024
Viewed by 517
Abstract
Aiming at the problem of high failure rate and inconvenient maintenance of wind turbine gearboxes, this paper establishes a stochastic differential equation model that can be used to fit the change of gearbox oil temperature and adopts an iterative computational method and Markov-based [...] Read more.
Aiming at the problem of high failure rate and inconvenient maintenance of wind turbine gearboxes, this paper establishes a stochastic differential equation model that can be used to fit the change of gearbox oil temperature and adopts an iterative computational method and Markov-based modified optimization to fit the prediction sequence in order to realize the accurate prediction of gearbox oil temperature. The model divides the oil temperature change of the gearbox into two parts, internal aging and external random perturbation, adopts the approximation theorem to establish the internal aging model, and uses Brownian motion to simulate the external random perturbation. The model parameters were calculated by the Newton–Raphson iterative method based on the gearbox oil temperature monitoring data. Iterative calculations and Markov-based corrections were performed on the model prediction data. The gearbox oil temperature variations were simulated in MATLAB, and the fitting and testing errors were calculated before and after the iterations. By comparing the fitting and testing errors with the ordinary differential equations and the stochastic differential equations before iteration, the iterated model can better reflect the gear oil temperature trend and predict the oil temperature at a specific time. The accuracy of the iterated model in terms of fitting and prediction is important for the development of preventive maintenance. Full article
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18 pages, 10325 KiB  
Article
Research on the Detection of Steel Plate Defects Based on SimAM and Twin-NMF Transfer
by Yongqiang Zou, Guanghui Zhang and Yugang Fan
Mathematics 2024, 12(17), 2782; https://doi.org/10.3390/math12172782 - 8 Sep 2024
Cited by 1 | Viewed by 939
Abstract
Pulsed eddy current thermography can detect surface or subsurface defects in steel, but in the process of combining deep learning, it is expensive and inefficient to build a complete sample of defects due to the complexity of the actual industrial environment. Consequently, this [...] Read more.
Pulsed eddy current thermography can detect surface or subsurface defects in steel, but in the process of combining deep learning, it is expensive and inefficient to build a complete sample of defects due to the complexity of the actual industrial environment. Consequently, this study proposes a transfer learning method based on Twin-NMF and combines it with the SimAM attention mechanism to enhance the detection accuracy of the target domain task. First, to address the domain differences between the target domain task and the source domain samples, this study introduces a Twin-NMF transfer method. This approach reconstructs the feature space of both the source and target domains using twin non-negative matrix factorization and employs cosine similarity to measure the correlation between the features of these two domains. Secondly, this study integrates a parameter-free SimAM into the neck of the YOLOv8 model to enhance its capabilities in extracting and classifying steel surface defects, as well as to alleviate the precision collapse phenomenon associated with multi-scale defect recognition. The experimental results show that the proposed Twin-NMF model with SimAM improves the detection accuracy of steel surface defects. Taking NEU-DET and GC10-DET as source domains, respectively, in the ECTI dataset, [email protected] reaches 99.3% and 99.2%, and the detection accuracy reaches 98% and 98.5%. Full article
(This article belongs to the Section Engineering Mathematics)
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14 pages, 2684 KiB  
Article
A Scheme for Generating Millimeter Wave Signals through 32-Tupling Frequency Multiplication without Filtering Using Eight Mach-Zehnder Modulators
by Xiangqing Wang, Lei Ren, Xiaokun Yang and Dongfei Wang
Mathematics 2024, 12(17), 2781; https://doi.org/10.3390/math12172781 - 8 Sep 2024
Viewed by 767
Abstract
In this paper, a filterless 32-tupling millimeter wave generation scheme based on eight MZMs is proposed. The system has an upper and lower parallel two-branch structure. The upper branch consists of two subsystems Sub-A and Sub-B in cascade, each subsystem contains four MZMs, [...] Read more.
In this paper, a filterless 32-tupling millimeter wave generation scheme based on eight MZMs is proposed. The system has an upper and lower parallel two-branch structure. The upper branch consists of two subsystems Sub-A and Sub-B in cascade, each subsystem contains four MZMs, and the MZMs are all operating at maximum transfer point (MATP). Sub-A mainly generates ±8th order optical sideband signal as the incident light signal of Sub-B. After modulation of Sub−B, the output signal is mainly ±16th order optical sideband signal containing the central optical carrier component. The optical attenuator (OATT) and optical phase shifter (OPS) of the lower branch are used to regulate the phase and amplitude of the optical carrier. The upper and lower branches are coupled, and the central optical carrier component is superimposed and cancelled so only the ±16th order optical sideband signal is retained. Finally, the 32-tupling frequency millimeter is generated by the photodiode (PD) receiver after photoelectric detection which receives and generates a 32-tupling frequency millimeter wave signal. The simulation results show that the 160 GHz millimeter wave signal can be obtained by driving the MZM with a 5 GHz RF signal, and the optical sideband suppression ratio (OSSR) and the RF sideband suppression ratio (RFSSR) are 52.6 dB and 44.75 dB, respectively. Theoretical analysis and simulation experiments are carried out for the proposed scheme which proves the feasibility of the scheme. Full article
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11 pages, 547 KiB  
Article
GaitAE: A Cognitive Model-Based Autoencoding Technique for Gait Recognition
by Rui Li, Huakang Li, Yidan Qiu, Jinchang Ren, Wing W. Y. Ng and Huimin Zhao
Mathematics 2024, 12(17), 2780; https://doi.org/10.3390/math12172780 - 8 Sep 2024
Viewed by 855
Abstract
Gait recognition is a long-distance biometric technique with significant potential for applications in crime prevention, forensic identification, and criminal investigations. Existing gait recognition methods typically introduce specific feature refinement modules on designated models, leading to increased parameter volume and computational complexity while lacking [...] Read more.
Gait recognition is a long-distance biometric technique with significant potential for applications in crime prevention, forensic identification, and criminal investigations. Existing gait recognition methods typically introduce specific feature refinement modules on designated models, leading to increased parameter volume and computational complexity while lacking flexibility. In response to this challenge, we propose a novel framework called GaitAE. GaitAE efficiently learns gait representations from large datasets and reconstructs gait sequences through an autoencoder mechanism, thereby enhancing recognition accuracy and robustness. In addition, we introduce a horizontal occlusion restriction (HOR) strategy, which introduces horizontal blocks to the original input sequences at random positions during training to minimize the impact of confounding factors on recognition performance. The experimental results demonstrate that our method achieves high accuracy and is effective when applied to existing gait recognition techniques. Full article
(This article belongs to the Special Issue Mathematical Methods for Pattern Recognition)
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25 pages, 9008 KiB  
Article
Dynamic Niches-Based Hybrid Breeding Optimization Algorithm for Solving Multi-Modal Optimization Problem
by Ting Cai, Ziteng Qiao, Zhiwei Ye, Hu Pan, Mingwei Wang, Wen Zhou, Qiyi He, Peng Zhang and Wanfang Bai
Mathematics 2024, 12(17), 2779; https://doi.org/10.3390/math12172779 - 8 Sep 2024
Viewed by 824
Abstract
Some problems exist in classical optimization algorithms to solve multi-modal optimization problems and other complex systems. A Dynamic Niches-based Improved Hybrid Breeding Optimization (DNIHBO) algorithm is proposed to address the multi-modal optimization problem in the paper. By dynamically adjusting the niche scale, it [...] Read more.
Some problems exist in classical optimization algorithms to solve multi-modal optimization problems and other complex systems. A Dynamic Niches-based Improved Hybrid Breeding Optimization (DNIHBO) algorithm is proposed to address the multi-modal optimization problem in the paper. By dynamically adjusting the niche scale, it effectively addresses the issue of niche parameter sensitivity. The structure of the algorithm includes three distinct groups: maintainer, restorer, and sterile lines for updating operations. However, the maintainer individuals often stagnate, leading to the risk of the local optima. To overcome this, neighborhood search and elite mutation strategies are incorporated, enhancing the balance between exploration and exploitation. To further improve individual utilization within niches, a niche restart strategy is introduced, ensuring sustained population diversity. The efficacy of DNIHBO is validated through simulations on 16 multi-modal test functions, followed by comparative analyses with various multi-modal optimization algorithms. The results convincingly demonstrate that DNIHBO not only effectively locates multiple global optima but also consistently outperforms other algorithms on test functions. These findings underscore the superiority of DNIHBO as a high-performing solution for multi-modal optimization. Full article
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23 pages, 644 KiB  
Article
Variable Selection in Semi-Functional Partially Linear Regression Models with Time Series Data
by Shuyu Meng and Zhensheng Huang
Mathematics 2024, 12(17), 2778; https://doi.org/10.3390/math12172778 - 8 Sep 2024
Viewed by 704
Abstract
This article investigates a variable selection method in semi-functional partially linear regression (SFPLR) models for strong α-mixing functional time series data. We construct penalized least squares estimators for unknown parameters and unknown link functions in our models. Under some regularity assumptions, we [...] Read more.
This article investigates a variable selection method in semi-functional partially linear regression (SFPLR) models for strong α-mixing functional time series data. We construct penalized least squares estimators for unknown parameters and unknown link functions in our models. Under some regularity assumptions, we establish the asymptotic convergence rate and asymptotic distribution for the proposed estimators. Furthermore, we make a comparison of our variable selection method with the oracle method without variable selection in simulation studies and an electricity consumption data analysis. Simulation experiments and real data analysis results indicate that the variable selection method performs well at extracting the primary information and reducing dimensionality. Full article
(This article belongs to the Special Issue Advances in High-Dimensional Data Analysis and Applications)
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15 pages, 2704 KiB  
Article
An Improved YOLOv5 Model for Concrete Bubble Detection Based on Area K-Means and ECANet
by Wei Tian, Bazhou Li, Jingjing Cao, Feichao Di, Yang Li and Jun Liu
Mathematics 2024, 12(17), 2777; https://doi.org/10.3390/math12172777 - 8 Sep 2024
Viewed by 549
Abstract
The appearance quality of fair-faced concrete plays a crucial role in evaluating the engineering quality, as the abundance of small-area bubbles generated during construction diminishes the surface quality of concrete. However, existing methods are plagued by sluggish detection speed and inadequate accuracy. Therefore, [...] Read more.
The appearance quality of fair-faced concrete plays a crucial role in evaluating the engineering quality, as the abundance of small-area bubbles generated during construction diminishes the surface quality of concrete. However, existing methods are plagued by sluggish detection speed and inadequate accuracy. Therefore, this paper proposes an improved method based on YOLOv5 to rapidly and accurately detect small bubble defects on the surface of fair-faced concrete. Firstly, to address the issue of YOLOv5 in generating prior boxes for imbalanced samples, we divide the image preprocessing part into small-, medium-, and large-area intervals corresponding to the number of heads. Additionally, we propose an area-based k-means clustering approach specifically tailored for the anchor boxes within each of these intervals. Moreover, we adjust the number of prior boxes generated by k-means clustering according to the training loss function to adapt to bubbles of different sizes. Then, we introduce the ECA (Efficient Channel Attention) mechanism into the neck part of the model to effectively capture inter-channel interactions and enhance feature representation. Subsequently, we incorporate feature concatenation in the neck part to facilitate the fusion of low-level and high-level features, thereby improving the accuracy and generalization ability of the network. Finally, we construct our own dataset containing 980 images of two classes: cement and bubbles. Comparative experiments are conducted on our dataset using YOLOv5s, YOLOv6s, YOLOxs, and our method. Experimental results demonstrate that the proposed method achieves the highest detection accuracy in terms of mAP0.5, mAP0.75, and mAP0.5:0.95. Compared to YOLOv5s, our method achieves a 7.1% improvement in mAP0.5, a 3.7% improvement in mAP0.75, and a 4.5% improvement in mAP0.5:0.95. Full article
(This article belongs to the Special Issue Application of Machine Learning and Data Mining, 2nd Edition)
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27 pages, 5783 KiB  
Article
The Contagion of Debt Default Risk in Energy Enterprises Considering Carbon Price Fluctuations
by Lei Wang, Xuan Jiang, Tingqiang Chen and Ruirui Zhu
Mathematics 2024, 12(17), 2776; https://doi.org/10.3390/math12172776 - 8 Sep 2024
Viewed by 468
Abstract
Under the constraints of low-carbon transformation goals, energy enterprises have significantly increased their debt default risk levels due to carbon price fluctuations. This article first analyzes the contagion mechanism of debt default risk among energy enterprises, and based on this, constructs a debt [...] Read more.
Under the constraints of low-carbon transformation goals, energy enterprises have significantly increased their debt default risk levels due to carbon price fluctuations. This article first analyzes the contagion mechanism of debt default risk among energy enterprises, and based on this, constructs a debt default risk contagion model among energy enterprises considering carbon price fluctuations, and then simulates and analyzes the evolution characteristics of debt default risk contagion among energy enterprises. The research results indicate that: (1) As the proportion of carbon emission cost increment and investor sentiment index increase, the stability of the debt network of energy enterprises strengthens. As the ratio of commercial credit among energy enterprises and influence of energy enterprises increase, the impact of debt risk gradually intensifies. (2) The investor sentiment index has a strengthening effect on the influence of energy enterprises, the proportion of commercial credit among energy enterprises, and the proportion of carbon emission cost increment. The commercial credit ratio between energy enterprises and its influence has a mutually reinforcing effect. (3) The investor sentiment index has suppressed debt default risk for various energy enterprises. The joint risk suppression effect of the proportion of carbon emission cost increment and the influence of energy enterprises in petroleum and petrochemical enterprises is more prominent. The joint risk constraint ability between the proportion of carbon emission cost increment and investor sentiment index in coal enterprises is stronger. Full article
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18 pages, 4315 KiB  
Article
Synchronization of Bidirectionally Coupled Fractional-Order Chaotic Systems with Unknown Time-Varying Parameter Disturbance in Different Dimensions
by Chunli Zhang, Yangjie Gao, Junliang Yao and Fucai Qian
Mathematics 2024, 12(17), 2775; https://doi.org/10.3390/math12172775 - 8 Sep 2024
Viewed by 637
Abstract
In this article, the synchronization of bidirectionally coupled fractional-order chaotic systems with unknown time-varying parameter disturbance in different dimensions is investigated. The scale matrices are designed to address the problem of the synchronization for fractional-order chaotic systems across two different dimensions. Congelation of [...] Read more.
In this article, the synchronization of bidirectionally coupled fractional-order chaotic systems with unknown time-varying parameter disturbance in different dimensions is investigated. The scale matrices are designed to address the problem of the synchronization for fractional-order chaotic systems across two different dimensions. Congelation of variables is used to deal with the unknown time-varying parameter disturbance. Based on Lyapunov’s stability theorem, the synchronization controllers in different dimensions are obtained. At the same time, adaptive laws of the unknown disturbance can be designed. Benefiting from the proposed methods, we verify all the synchronization errors can converge to zero as time approaches infinity, regardless of whether in n-D or m-D synchronization, simultaneously ensuring that both control and estimation signals are bounded. Finally, simulation studies based on fractional-order financial systems are carried out to validate the effectiveness of the proposed synchronization method. Full article
(This article belongs to the Special Issue Chaotic Systems and Their Applications, 2nd Edition)
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30 pages, 4873 KiB  
Article
An Evolutionary Game-Based Regulatory Path for Algorithmic Price Discrimination in E-Commerce Platforms
by Yan Guo, Jiajun Lin and Weiqing Zhuang
Mathematics 2024, 12(17), 2774; https://doi.org/10.3390/math12172774 - 7 Sep 2024
Viewed by 898
Abstract
With the advent of big data, the swift advancement of diverse algorithmic technologies has enhanced the transaction efficiency of the e-commerce business. Nevertheless, it is crucial to acknowledge that e-commerce platforms might employ algorithmic technology to enforce differential pricing for various consumers with [...] Read more.
With the advent of big data, the swift advancement of diverse algorithmic technologies has enhanced the transaction efficiency of the e-commerce business. Nevertheless, it is crucial to acknowledge that e-commerce platforms might employ algorithmic technology to enforce differential pricing for various consumers with the aim of maximizing profits, thus infringing upon the lawful rights and interests of consumers. This paper focuses on the algorithmic price discrimination commonly observed on e-commerce platforms. To effectively regulate this behavior, the paper utilizes evolutionary game theory (EGT) to analyze the strategies employed by e-commerce platforms, consumers, and market regulators to achieve stability. This research employs a real-life situation and utilizes parametric simulation to visualize and analyze the process and outcomes of the three-party evolutionary game. The results demonstrate the credibility and feasibility of the article’s findings. Based on our research, we have reached the following findings: During the process of evolution, the strategic decisions made by the game participants from the three parties will mutually impact each other, and various elements exert varying degrees of influence on the strategic choices made by the game participants from each party. Collaborative governance can enable consumers and market regulators to regulate the discriminatory pricing behavior of e-commerce platforms effectively. This article offers valuable insights into the governance of violations in the e-commerce sector based on robust data and model research. Full article
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29 pages, 4359 KiB  
Article
FMEA-TSTM-NNGA: A Novel Optimization Framework Integrating Failure Mode and Effect Analysis, the Taguchi Method, a Neural Network, and a Genetic Algorithm for Improving the Resistance in Dynamic Random Access Memory Components
by Chia-Ming Lin and Shang-Liang Chen
Mathematics 2024, 12(17), 2773; https://doi.org/10.3390/math12172773 - 7 Sep 2024
Viewed by 763
Abstract
Dynamic random access memory (DRAM) serves as a critical component in medical equipment. Given the exacting standards demanded by medical equipment products, manufacturers face pressure to improve their product quality. The electrical characteristics of these products are based on the resistance value of [...] Read more.
Dynamic random access memory (DRAM) serves as a critical component in medical equipment. Given the exacting standards demanded by medical equipment products, manufacturers face pressure to improve their product quality. The electrical characteristics of these products are based on the resistance value of the DRAM components. Hence, the purpose of this study is to optimize the resistance value of DRAM components in medical equipment. We proposed a novel FMEA-TSTM-NNGA framework that integrates failure mode and effect analysis (FMEA), the two-stage Taguchi method (TSTM), neural networks (NN), and genetic algorithms (GA) to optimize the manufacturing process. Moreover, the proposed FMEA-TSTM-NNGA framework achieved a substantial reduction in experimental trials, cutting the required number by a factor of 85.3 when compared to the grid search method. Our framework successfully identified optimal manufacturing condition settings for the resistance values of DRAM components: Depo time = 27 s, Depo O2 flow = 151 sccm, ARC-LTO etch time = 43 s, ARC-LTO etch pressure = 97 mTorr, Ox-SiCO etch time = 91 s, Ox-SiCO gas ratio = 22%, and Polish time = 84 s. The results helped the case company improve the resistance value of DRAM components from 191.1 × 10−3 Ohm to 176.84 × 10−3 Ohm, which is closer to the target value of 176.5 × 10−3 Ohm. The proposed FMEA-TSTM-NNGA framework is designed to operate efficiently on resource-constrained, facilitating real-time adjustments to production attributes. This capability enables DRAM manufacturers to swiftly optimize product quality. Full article
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17 pages, 6367 KiB  
Article
The Discovery of Truncated M-Fractional Exact Solitons and a Qualitative Analysis of the Generalized Bretherton Model
by Haitham Qawaqneh, Khalil Hadi Hakami, Ali Altalbe and Mustafa Bayram
Mathematics 2024, 12(17), 2772; https://doi.org/10.3390/math12172772 - 7 Sep 2024
Viewed by 551
Abstract
This paper is concerned with the novel exact solitons for the truncated M-fractional (1+1)-dimensional nonlinear generalized Bretherton model with arbitrary constants. This model is used to explain the resonant nonlinear interaction between the waves in different phenomena, including fluid dynamics, plasma physics, ocean [...] Read more.
This paper is concerned with the novel exact solitons for the truncated M-fractional (1+1)-dimensional nonlinear generalized Bretherton model with arbitrary constants. This model is used to explain the resonant nonlinear interaction between the waves in different phenomena, including fluid dynamics, plasma physics, ocean waves, and many others. A series of exact solitons, including bright, dark, periodic, singular, singular–bright, singular–dark, and other solitons are obtained by applying the extended sinh-Gordon equation expansion (EShGEE) and the modified (G′/G2)-expansion techniques. A novel definition of fractional derivative provides solutions that are distinct from previous solutions. Mathematica software was used to obtain and verify the solutions. The solutions are shown through 2D, 3D, and density plots. A stability process was conducted to verify that the solutions are exact and accurate. Modulation instability was used to determine the steady-state results for the corresponding equation. Full article
(This article belongs to the Special Issue Analytical Approaches to Nonlinear Dynamical Systems and Applications II)
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20 pages, 382 KiB  
Review
Survey on Roman {2}-Domination
by Ahlam Almulhim, Bana Al Subaiei and Saiful Rahman Mondal
Mathematics 2024, 12(17), 2771; https://doi.org/10.3390/math12172771 - 7 Sep 2024
Viewed by 802
Abstract
The notion of Roman {2}-domination was introduced in 2016 as a variant of Roman domination, a concept inspired by a defending strategy used by the emperor Constantine (272–337 AD) to protect the Roman Empire. Since then, a considerable number of [...] Read more.
The notion of Roman {2}-domination was introduced in 2016 as a variant of Roman domination, a concept inspired by a defending strategy used by the emperor Constantine (272–337 AD) to protect the Roman Empire. Since then, a considerable number of papers on Roman {2}-domination and its variants have been published. In this paper, we survey published results on Roman {2}-domination as well as the main findings on Roman {2}-domination variants found in the literature. A list of open problems related to this notion and its variants are also given. Full article
22 pages, 496 KiB  
Article
Three-Layer Artificial Neural Network for Pricing Multi-Asset European Option
by Zhiqiang Zhou, Hongying Wu, Yuezhang Li, Caijuan Kang and You Wu
Mathematics 2024, 12(17), 2770; https://doi.org/10.3390/math12172770 - 7 Sep 2024
Viewed by 482
Abstract
This paper studies an artificial neural network (ANN) for multi-asset European options. Firstly, a simple three-layer ANN-3 is established with undetermined weights and bias. Secondly, the time–space discrete PDE of the multi-asset option is given and the corresponding discrete data are fed into [...] Read more.
This paper studies an artificial neural network (ANN) for multi-asset European options. Firstly, a simple three-layer ANN-3 is established with undetermined weights and bias. Secondly, the time–space discrete PDE of the multi-asset option is given and the corresponding discrete data are fed into the ANN-3. Then, using least squares error as the objective function, the weights and bias of ANN-3 are trained well. Numerical examples are carried out to confirm the stability, accuracy and efficiency. Experiments show the ANN’s relative error is about 0.8%. This method can be extended into multi-layer ANN-q(q>3) and extended into American options. Full article
(This article belongs to the Special Issue Computational Economics and Mathematical Modeling)
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18 pages, 10246 KiB  
Article
Hypergraph-Based Influence Maximization in Online Social Networks
by Chuangchuang Zhang, Wenlin Cheng, Fuliang Li and Xingwei Wang
Mathematics 2024, 12(17), 2769; https://doi.org/10.3390/math12172769 - 7 Sep 2024
Cited by 1 | Viewed by 635
Abstract
Influence maximization in online social networks is used to select a set of influential seed nodes to maximize the influence spread under a given diffusion model. However, most existing proposals have huge computational costs and only consider the dyadic influence relationship between two [...] Read more.
Influence maximization in online social networks is used to select a set of influential seed nodes to maximize the influence spread under a given diffusion model. However, most existing proposals have huge computational costs and only consider the dyadic influence relationship between two nodes, ignoring the higher-order influence relationships among multiple nodes. It limits the applicability and accuracy of existing influence diffusion models in real complex online social networks. To this end, in this paper, we present a novel information diffusion model by introducing hypergraph theory to determine the most influential nodes by jointly considering adjacent influence and higher-order influence relationships to improve diffusion efficiency. We mathematically formulate the influence maximization problem under higher-order influence relationships in online social networks. We further propose a hypergraph sampling greedy algorithm (HSGA) to effectively select the most influential seed nodes. In the HSGA, a random walk-based influence diffusion method and a Monte Carlo-based influence approximation method are devised to achieve fast approximation and calculation of node influences. We conduct simulation experiments on six real datasets for performance evaluations. Simulation results demonstrate the effectiveness and efficiency of the HSGA, and the HSGA has a lower computational cost and higher seed selection accuracy than comparison mechanisms. Full article
(This article belongs to the Special Issue Deep Representation Learning for Social Network Analysis)
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10 pages, 448 KiB  
Article
Random Generation Topology Coding Technique in Asymmetric Topology Encryption
by Jing Su and Bing Yao
Mathematics 2024, 12(17), 2768; https://doi.org/10.3390/math12172768 - 6 Sep 2024
Viewed by 748
Abstract
The security of traditional public key cryptography algorithms depends on the difficulty of the underlying mathematical problems. Asymmetric topological encryption is a graph-dependent encryption algorithm produced to resist attacks by quantum computers on these mathematical problems. The security of this encryption algorithm depends [...] Read more.
The security of traditional public key cryptography algorithms depends on the difficulty of the underlying mathematical problems. Asymmetric topological encryption is a graph-dependent encryption algorithm produced to resist attacks by quantum computers on these mathematical problems. The security of this encryption algorithm depends on two types of NP-complete problems: subgraph isomorphism and graph coloring. Topological coding technology refers to the technology of generating key strings or topology signature strings through topological coding graphs. We take odd-graceful labeling and set-ordered odd-graceful labeling as limiting functions, and propose two kinds of topological coding generation technique, which we call the random leaf-adding operation and randomly adding edge-removing operation. Through these two techniques, graphs of the same scale and larger scales can be generated with the same type of labeling so as to derive more number strings, expand the key space, and analyze the topology and property of the generated graphs. Full article
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11 pages, 453 KiB  
Article
On Polar Jacobi Polynomials
by Roberto S. Costas-Santos
Mathematics 2024, 12(17), 2767; https://doi.org/10.3390/math12172767 - 6 Sep 2024
Viewed by 438
Abstract
In the present work, we investigate certain algebraic and differential properties of the orthogonal polynomials with respect to a discrete–continuous Sobolev-type inner product defined in terms of the Jacobi measure. Full article
(This article belongs to the Special Issue Polynomials: Theory and Applications, 2nd Edition)
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