Mathematics

22 pages, 7646 KiB

Open AccessArticle

A Study on Effects of Species with the Adaptive Sex-Ratio on Bio-Community Based on Mechanism Analysis and ODE

by Haoyu Wang, Xiaoyuan Wan, Junyao Hou, Jing Lian and Yuzhao Wang

Mathematics 2024, 12(14), 2298; https://doi.org/10.3390/math12142298 - 22 Jul 2024

Viewed by 476

The species of the adaptive male–female sex ratio has different effects on the bio-community. This paper is aimed at figuring out these effects through mechanism analysis and Ordinary Differential Equation (ODE). Hence, the ODE environmental model is created by combining the Lotka–Volterra model, [...] Read more.

The species of the adaptive male–female sex ratio has different effects on the bio-community. This paper is aimed at figuring out these effects through mechanism analysis and Ordinary Differential Equation (ODE). Hence, the ODE environmental model is created by combining the Lotka–Volterra model, the interspecific model, and other external factors. The stability is used to characterize these effects. According to this model, effects on bio-community stability under different male–female sex ratios are roughly observed. By innovatively considering different living environments during the species’ lifecycle, the ODE environmental model is optimized, and the effects of different male–female sex ratios on the bio-community are further analyzed by phase-track maps and relative standard deviation. It is found that there are different findings and features in resource-rich and resource-scarce living environments during the lifecycle. Meanwhile, bio-communities in these two types of environments are in a stable state based on different male–female sex ratios. Based on these findings, directive opinions can be used to manage and help relevant bio-communities. Full article

(This article belongs to the Special Issue Computational Methods for Biological Modeling and Simulation)

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16 pages, 421 KiB

Open AccessArticle

The Event-Triggered Resilient Control of Discrete-Time Nonlinear Semi-Markov Jump Systems Based on Incremental Quadratic Constraints

by Shuguang Liu, Yueyuan Zhang and Yuan Sun

Mathematics 2024, 12(14), 2297; https://doi.org/10.3390/math12142297 - 22 Jul 2024

Viewed by 337

Abstract

This paper explores resilient control problems for discrete-time nonlinear semi-Markov jump systems characterized by incremental quadratic constraints. Considering the system’s uncertainties and external environmental factors, mode-dependent resilient controllers are developed to ensure the system’s mean-square stability. A proposed event-triggering mechanism is suggested to [...] Read more.

This paper explores resilient control problems for discrete-time nonlinear semi-Markov jump systems characterized by incremental quadratic constraints. Considering the system’s uncertainties and external environmental factors, mode-dependent resilient controllers are developed to ensure the system’s mean-square stability. A proposed event-triggering mechanism is suggested to alleviate the communication burden within the system. Additionally, the system’s nonlinearity is characterized by using incremental quadratic constraints to derive a less conservative feasible solution. Sufficient conditions for the system’s mean-square stability are established by employing the Lyapunov stability theory. Finally, a numerical simulation example is given to prove the conclusion’s validity. Full article

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

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25 pages, 5896 KiB

Open AccessArticle

A Student Performance Prediction Model Based on Hierarchical Belief Rule Base with Interpretability

by Minjie Liang, Guohui Zhou, Wei He, Haobing Chen and Jidong Qian

Mathematics 2024, 12(14), 2296; https://doi.org/10.3390/math12142296 - 22 Jul 2024

Viewed by 363

Abstract

Predicting student performance in the future is a crucial behavior prediction problem in education. By predicting student performance, educational experts can provide individualized instruction, optimize the allocation of resources, and develop educational strategies. If the prediction results are unreliable, it is difficult to [...] Read more.

Predicting student performance in the future is a crucial behavior prediction problem in education. By predicting student performance, educational experts can provide individualized instruction, optimize the allocation of resources, and develop educational strategies. If the prediction results are unreliable, it is difficult to earn the trust of educational experts. Therefore, prediction methods need to satisfy the requirement of interpretability. For this reason, the prediction model is constructed in this paper using belief rule base (BRB). BRB not only combines expert knowledge, but also has good interpretability. There are two problems in applying BRB to student performance prediction: first, in the modeling process, the system is too complex due to the large number of indicators involved. Secondly, the interpretability of the model can be compromised during the optimization process. To overcome these challenges, this paper introduces a hierarchical belief rule base with interpretability (HBRB-I) for student performance prediction. First, it analyzes how the HBRB-I model achieves interpretability. Then, an attribute grouping method is proposed to construct a hierarchical structure by reasonably organizing the indicators, so as to effectively reduce the complexity of the model. Finally, an objective function considering interpretability is designed and the projected covariance matrix adaptive evolution strategy (P-CMA-ES) optimization algorithm is improved. The aim is to ensure that the model remains interpretable after optimization. By conducting experiments on the student performance dataset, it is demonstrated that the proposed model performs well in terms of both accuracy and interpretability. Full article

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19 pages, 288 KiB

Open AccessArticle

Best Proximity Point Results for Fuzzy Proximal Quasi Contractions with Applications

by Muzammil Ali and Basit Ali

Mathematics 2024, 12(14), 2295; https://doi.org/10.3390/math12142295 - 22 Jul 2024

Viewed by 348

Abstract

In this work, we introduce a new type of multivalued fuzzy proximal quasi-contraction. These are generalized contractions which are a hybrid of

H

-contractive mappings and quasi-contractions. Furthermore, we establish the best proximity point results for newly introduced fuzzy contractions in the context [...] Read more.

In this work, we introduce a new type of multivalued fuzzy proximal quasi-contraction. These are generalized contractions which are a hybrid of

H

-contractive mappings and quasi-contractions. Furthermore, we establish the best proximity point results for newly introduced fuzzy contractions in the context of fuzzy b-metric spaces. Fuzzy b-metric spaces are more general than fuzzy metric spaces and are linked with the cosine distance, which is used in various contexts of artificial intelligence to measure the similarity between elements of a vector space. Full article

(This article belongs to the Special Issue New Advances in Fuzzy Metric Spaces, Soft Metric Spaces, and Other Related Structures, 2nd Edition)

14 pages, 543 KiB

Open AccessArticle

Eighth-Order Numerov-Type Methods Using Varying Step Length

by Obaid Alshammari, Sondess Ben Aoun, Mourad Kchaou, Theodore E. Simos, Charalampos Tsitouras and Houssem Jerbi

Mathematics 2024, 12(14), 2294; https://doi.org/10.3390/math12142294 - 22 Jul 2024

Viewed by 288

Abstract

This work explores a well-established eighth-algebraic-order numerical method belonging to the explicit Numerov-type family. To enhance its efficiency, we integrated a cost-effective algorithm for adjusting the step size. After each step, the algorithm either maintains the current step length, halves it, or doubles [...] Read more.

This work explores a well-established eighth-algebraic-order numerical method belonging to the explicit Numerov-type family. To enhance its efficiency, we integrated a cost-effective algorithm for adjusting the step size. After each step, the algorithm either maintains the current step length, halves it, or doubles it. Any off-step points required by this technique are calculated using a local interpolation function. Numerical tests involving diverse problems demonstrate the significant efficiency improvements achieved through this approach. The method is particularly effective for solving differential equations with oscillatory behavior, showcasing its ability to maintain high accuracy with fewer function evaluations. This advancement is crucial for applications requiring precise solutions over long intervals, such as in physics and engineering. Additionally, the paper provides a comprehensive MATLAB-R2018a implementation, facilitating ease of use and further research in the field. By addressing both computational efficiency and accuracy, this study contributes a valuable tool for the numerical analysis community. Full article

(This article belongs to the Section Engineering Mathematics)

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24 pages, 378 KiB

Open AccessArticle

Optimal Solutions for a Class of Impulsive Differential Problems with Feedback Controls and Volterra-Type Distributed Delay: A Topological Approach

by Paola Rubbioni

Mathematics 2024, 12(14), 2293; https://doi.org/10.3390/math12142293 - 22 Jul 2024

Viewed by 333

Abstract

In this paper, the existence of optimal solutions for problems governed by differential equations involving feedback controls is established for when the problem must account for a Volterra-type distributed delay and is subject to the action of impulsive external forces. The problem is [...] Read more.

In this paper, the existence of optimal solutions for problems governed by differential equations involving feedback controls is established for when the problem must account for a Volterra-type distributed delay and is subject to the action of impulsive external forces. The problem is reformulated within the class of impulsive semilinear integro-differential inclusions in Banach spaces and is studied by using topological methods and multivalued analysis. The paper concludes with an application to a population dynamics model. Full article

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

5 pages, 149 KiB

Open AccessEditorial

Preface to the Special Issue “Mathematical Modelling and Optimization of Service Supply Chain”

by Yong He

Mathematics 2024, 12(14), 2292; https://doi.org/10.3390/math12142292 - 22 Jul 2024

Viewed by 386

Abstract

In recent years, as the world economy has grown, increasingly, service-oriented systems play a more significant role in the supply chain [...] Full article

(This article belongs to the Special Issue Mathematical Modelling and Optimization of Service Supply Chain)

16 pages, 572 KiB

Open AccessArticle

Limit Theorems for Spectra of Circulant Block Matrices with Large Random Blocks

by Alexander Tikhomirov, Sabina Gulyaeva and Dmitry Timushev

Mathematics 2024, 12(14), 2291; https://doi.org/10.3390/math12142291 - 22 Jul 2024

Viewed by 329

Abstract

This paper investigates the spectral properties of block circulant matrices with high-order symmetric (or Hermitian) blocks. We analyze cases with dependent or sparse independent entries within these blocks. Additionally, we analyze the distribution of singular values for the product of independent circulant matrices [...] Read more.

This paper investigates the spectral properties of block circulant matrices with high-order symmetric (or Hermitian) blocks. We analyze cases with dependent or sparse independent entries within these blocks. Additionally, we analyze the distribution of singular values for the product of independent circulant matrices with non-Hermitian blocks. Full article

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23 pages, 15233 KiB

Open AccessArticle

The Application of the Piecewise Linear Method for Non-Linear Programming Problems in Ride-Hailing Assignment Based on Service Level, Driver Workload, and Fuel Consumption

by Tubagus Robbi Megantara, Sudradjat Supian, Diah Chaerani and Abdul Talib Bon

Mathematics 2024, 12(14), 2290; https://doi.org/10.3390/math12142290 - 22 Jul 2024

Viewed by 361

Abstract

Ride-hailing services have grown rapidly, presenting challenges such as increased traffic congestion, inefficient driver workload distribution, and environmental concerns like higher fuel consumption and emissions. This study develops a non-linear ride-hailing assignment model addressing these issues by considering service level, driver workload, and [...] Read more.

Ride-hailing services have grown rapidly, presenting challenges such as increased traffic congestion, inefficient driver workload distribution, and environmental concerns like higher fuel consumption and emissions. This study develops a non-linear ride-hailing assignment model addressing these issues by considering service level, driver workload, and fuel consumption. A piecewise linear method was employed to handle a non-linear programming model, and the method was modified to function autonomously without operator intervention. The model’s performance was evaluated using a publicly accessible dataset of taxi trips in Manhattan, focusing on indicators such as passenger waiting time, driver workload distribution, and fuel consumption. Numerical simulations demonstrated significant improvements: a 15% reduction in average passenger waiting time, a 20% improvement in balancing driver workloads, and a 10% decrease in overall fuel consumption, contributing to reduced emissions and environmental impact. The modified piecewise linear method proved effective in optimizing ride-hailing assignments, providing a more efficient and sustainable solution. The model also showed robustness in handling large datasets, ensuring scalability and applicability to various urban settings. These findings highlight the model’s potential to enhance operational efficiency and promote sustainability in ride-hailing services. By integrating considerations for service level, driver workload, and fuel consumption, the model offers a holistic approach to addressing the key challenges faced by the ride-hailing industry. This study provides valuable insights for future ride-hailing development and implementations of ride-hailing systems, promoting practices that are both efficient and environmentally friendly. Full article

(This article belongs to the Section Computational and Applied Mathematics)

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19 pages, 1714 KiB

Open AccessArticle

Bayesian Estimation of the Semiparametric Spatial Lag Model

by Kunming Li and Liting Fang

Mathematics 2024, 12(14), 2289; https://doi.org/10.3390/math12142289 - 22 Jul 2024

Viewed by 295

Abstract

This paper proposes a semiparametric spatial lag model and develops a Bayesian estimation method for this model. In the estimation of the model, the paper combines Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm, random walk Metropolis sampler, and Gibbs sampling techniques to [...] Read more.

This paper proposes a semiparametric spatial lag model and develops a Bayesian estimation method for this model. In the estimation of the model, the paper combines Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm, random walk Metropolis sampler, and Gibbs sampling techniques to sample all the parameters. The paper conducts numerical simulations to validate the proposed Bayesian estimation theory using a numerical example. The simulation results demonstrate satisfactory estimation performance of the parameter part and the fitting performance of the nonparametric function under different spatial weight matrix settings. Furthermore, the paper applies the constructed model and its estimation method to an empirical study on the relationship between economic growth and carbon emissions in China, illustrating the practical application value of the theoretical results. Full article

(This article belongs to the Section Probability and Statistics)

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32 pages, 11808 KiB

Open AccessArticle

A Multi-Objective Non-Dominated Sorting Gravitational Search Algorithm for Assembly Flow-Shop Scheduling of Marine Prefabricated Cabins

by Ruipu Dong, Jinghua Li, Dening Song, Boxin Yang and Lei Zhou

Mathematics 2024, 12(14), 2288; https://doi.org/10.3390/math12142288 - 22 Jul 2024

Viewed by 340

Abstract

Prefabricated cabin modular units (PMCUs) are a widespread type of intermediate products used during ship or offshore platform construction. This paper focuses on the scheduling problem of PMCU assembly flow shops, which is summarized as a multi-objective, fuzzy-blocking hybrid flow-shop-scheduling problem based on [...] Read more.

Prefabricated cabin modular units (PMCUs) are a widespread type of intermediate products used during ship or offshore platform construction. This paper focuses on the scheduling problem of PMCU assembly flow shops, which is summarized as a multi-objective, fuzzy-blocking hybrid flow-shop-scheduling problem based on learning and fatigue effects (FB-HFSP-LF) to minimize the maximum fuzzy makespan and maximize the average fuzzy due-date agreement index. This paper proposes a multi-objective non-dominated sorting gravitational search algorithm (MONSGSA) to solve it. In the proposed MONSGSA, the ranked-order value is used to convert continuous solutions to discrete solutions. Multi-dimensional Latin hypercube sampling is used to enhance initial population diversity. Setting up an external archive to maintain non-dominated solutions while introducing an adaptive inertia factor and a trap avoidance operator to guide individual positional updates. The results of multiple sets of experiments show that Pareto solutions of MONSGSA have better distribution and convergence compared to other competitors. Finally, the instance of PMCU manufacturer is used for validation, and the results show that MONSGSA has better applicability to practical problems. Full article

(This article belongs to the Special Issue Mathematical Programming, Optimization and Operations Research)

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11 pages, 2987 KiB

Open AccessArticle

On the Selection of Weights for Difference Schemes to Approximate Systems of Differential Equations

by Viktor Kadrov, Mikhail Malykh and Alexander Zorin

Mathematics 2024, 12(14), 2287; https://doi.org/10.3390/math12142287 - 22 Jul 2024

Viewed by 334

Abstract

We consider the problem of determining the weights of difference schemes whose form is specified by a particular symbolic expression. The order of approximation of the differential equation is equal to a given number. To solve it, it was propose to proceed from [...] Read more.

We consider the problem of determining the weights of difference schemes whose form is specified by a particular symbolic expression. The order of approximation of the differential equation is equal to a given number. To solve it, it was propose to proceed from considering systems of differential equations of a general form to one scalar equation. This method provides us with some values for the weights, which we propose to test using Richardson’s method. The method was shown to work in the case of low-order schemes. However, when transitioning from the scalar problem to the vector and nonlinear problems, the reduction of the order of the scheme, whose weights are selected for the scalar problem, occurs in different families of schemes. This was first discovered when studying the Shanks scheme, which belongs to the family of explicit Runge–Kutta schemes. This does not deteriorate the proposed strategy itself concerning the simplification of the weight-determination problem, which should include a clause on mandatory testing of the order using the Richardson method. Full article

(This article belongs to the Section Dynamical Systems)

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12 pages, 229 KiB

Open AccessArticle

Characterizations of Commutativity of Prime Ring with Involution by Generalized Derivations

by Mingxing Sui and Quanyuan Chen

Mathematics 2024, 12(14), 2286; https://doi.org/10.3390/math12142286 - 22 Jul 2024

Viewed by 295

Abstract

In the paper, we investigate the commutativity of a two-torsion free prime ring

R

provided with generalized derivations, and some well-known results that characterize the commutativity of prime rings through generalized derivations have been generalized. Moreover, we provide some examples to testify that [...] Read more.

In the paper, we investigate the commutativity of a two-torsion free prime ring

R

provided with generalized derivations, and some well-known results that characterize the commutativity of prime rings through generalized derivations have been generalized. Moreover, we provide some examples to testify that the assumed restriction in our theorems cannot be omitted. Full article

(This article belongs to the Special Issue New Advances in Algebra, Ring Theory and Homological Algebra, 2nd Edition)

17 pages, 1696 KiB

Open AccessArticle

A Multiobjective Optimization Algorithm for Fluid Catalytic Cracking Process with Constraints and Dynamic Environments

by Guanzhi Liu, Xinfu Pang and Jishen Wan

Mathematics 2024, 12(14), 2285; https://doi.org/10.3390/math12142285 - 22 Jul 2024

Viewed by 325

Abstract

The optimization problems in a fluid catalytic cracking process with dynamic constraints and conflicting objectives are challenging due to the complicated constraints and dynamic environments. The decision variables need to be reoptimized to obtain the best objectives when dynamic environments arise. To solve [...] Read more.

The optimization problems in a fluid catalytic cracking process with dynamic constraints and conflicting objectives are challenging due to the complicated constraints and dynamic environments. The decision variables need to be reoptimized to obtain the best objectives when dynamic environments arise. To solve these problems, we established a mathematical model and proposed a dynamic constrained multiobjective optimization evolution algorithm for the fluid catalytic cracking process. In this algorithm, we design an offspring generation strategy based on minimax solutions, which can explore more feasible regions and converge quickly. Additionally, a dynamic response strategy based on population feasibility is proposed to improve the feasible and infeasible solutions by different perturbations, respectively. To verify the effectiveness of the algorithm, we test the algorithm on ten instances based on the hypervolume metric. Experimental results show that the proposed algorithm is highly competitive with several state-of-the-art competitors. Full article

(This article belongs to the Section Fuzzy Sets, Systems and Decision Making)

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16 pages, 2416 KiB

Open AccessArticle

Enhanced Attention Res-Unet for Segmentation of Knee Bones

by Daniel Aibinder, Matan Weisberg, Anna Ghidotti and Miri Weiss Cohen

Mathematics 2024, 12(14), 2284; https://doi.org/10.3390/math12142284 - 22 Jul 2024

Viewed by 293

Abstract

The objective of this study was to develop a U-net capable of generating highly accurate 3D models of knee bones, in particular the femur. As part of the approach, a U-net was designed, trained, and validated. In order to achieve these goals, a [...] Read more.

The objective of this study was to develop a U-net capable of generating highly accurate 3D models of knee bones, in particular the femur. As part of the approach, a U-net was designed, trained, and validated. In order to achieve these goals, a novel architecture was proposed, including an architecture that reduces encoder parameters and incorporates transfer learning, in order to enhance the attention U-net. Additionally, an extra depth layer was added to extract more salient information. Moreover, the model includes a classifier unit to reduce false positives, as well as a Tversky focal loss function, which is an innovative loss function. The proposed architecture achieved a Dice coefficient of 98.05. By using these enhanced tools, clinicians can visualize and analyze knee structures more accurately, improve surgical intervention effectiveness, and improve patient care quality overall. Full article

(This article belongs to the Special Issue Mathematical Modelling and Machine Learning Methods for Bioinformatics and Data Science Applications, 2nd Edition)

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35 pages, 4711 KiB

Open AccessArticle

Multi-Objective Optimization of Resilient, Sustainable, and Safe Urban Bus Routes for Tourism Promotion Using a Hybrid Reinforcement Learning Algorithm

by Keartisak Sriprateep, Rapeepan Pitakaso, Surajet Khonjun, Thanatkij Srichok, Peerawat Luesak, Sarayut Gonwirat, Chutchai Kaewta, Monika Kosacka-Olejnik and Prem Enkvetchakul

Mathematics 2024, 12(14), 2283; https://doi.org/10.3390/math12142283 - 22 Jul 2024

Viewed by 549

Abstract

Urban transportation systems in tourism-centric cities face challenges from rapid urbanization and population growth. Efficient, resilient, and sustainable bus route optimization is essential to ensure reliable service, minimize environmental impact, and maintain safety standards. This study presents a novel Hybrid Reinforcement Learning-Variable Neighborhood [...] Read more.

Urban transportation systems in tourism-centric cities face challenges from rapid urbanization and population growth. Efficient, resilient, and sustainable bus route optimization is essential to ensure reliable service, minimize environmental impact, and maintain safety standards. This study presents a novel Hybrid Reinforcement Learning-Variable Neighborhood Strategy Adaptive Search (H-RL-VaNSAS) algorithm for multi-objective urban bus route optimization. Our mathematical model maximizes resilience, sustainability, tourist satisfaction, and accessibility while minimizing total travel distance. H-RL-VaNSAS is evaluated against leading optimization methods, including the Crested Porcupine Optimizer (CPO), Krill Herd Algorithm (KHA), and Salp Swarm Algorithm (SSA). Using metrics such as Hypervolume and the Average Ratio of Pareto Optimal Solutions, H-RL-VaNSAS demonstrates superior performance. Specifically, H-RL-VaNSAS achieved the highest resilience index (550), sustainability index (370), safety score (480), tourist preferences score (300), and accessibility score (2300), while minimizing total travel distance to 950 km. Compared to other methods, H-RL-VaNSAS improved resilience by 12.24–17.02%, sustainability by 5.71–12.12%, safety by 4.35–9.09%, tourist preferences by 7.14–13.21%, accessibility by 4.55–9.52%, and reduced travel distance by 9.52–17.39%. This research offers a framework for designing efficient, resilient, and sustainable public transit systems that align with urban planning and transportation goals. The integration of reinforcement learning with VaNSAS significantly enhances optimization capabilities, providing a valuable tool for mathematical and urban transportation research communities. Full article

(This article belongs to the Special Issue Planning and Scheduling in City Logistics Optimization)

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21 pages, 3753 KiB

Open AccessArticle

Laplace-Logistic Unit Distribution with Application in Dynamic and Regression Analysis

by Vladica S. Stojanović, Tanja Jovanović Spasojević and Mihailo Jovanović

Mathematics 2024, 12(14), 2282; https://doi.org/10.3390/math12142282 - 22 Jul 2024

Viewed by 413

Abstract

This manuscript presents a new two-parameter unit stochastic distribution, obtained by transforming the Laplace distribution, using a generalized logistic map, into a unit interval. The distribution thus obtained is named the Laplace-logistic unit (abbreviated LLU) distribution, and its basic stochastic properties are examined [...] Read more.

This manuscript presents a new two-parameter unit stochastic distribution, obtained by transforming the Laplace distribution, using a generalized logistic map, into a unit interval. The distribution thus obtained is named the Laplace-logistic unit (abbreviated LLU) distribution, and its basic stochastic properties are examined in detail. Also, the procedure for estimating parameters based on quantiles is provided, along with the asymptotic properties of the obtained estimates and the appropriate numerical simulation study. Finally, the application of the LLU distribution in dynamic and regression analysis of real-world data with accentuated “peaks” and “fat” tails is also discussed. Full article

(This article belongs to the Special Issue Advanced Statistical Application for Realistic Problems)

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12 pages, 288 KiB

Open AccessArticle

A Maslov-Type Index in Dimension 2

by Qiyu Zhong and Hai-Long Her

Mathematics 2024, 12(14), 2281; https://doi.org/10.3390/math12142281 - 22 Jul 2024

Viewed by 290

Abstract

In this article, we define an index of the Maslov type for paths of

2 \times 2

orthogonal symplectic matrices. The starting point is an arbitrary

2 \times 2

orthogonal symplectic matrix rather than the identity matrix. We use this index to explain [...] Read more.

In this article, we define an index of the Maslov type for paths of

2 \times 2

orthogonal symplectic matrices. The starting point is an arbitrary

2 \times 2

orthogonal symplectic matrix rather than the identity matrix. We use this index to explain the geometric intersection number of a pair of Lagrangian paths and compare it with the Cappell–Lee–Miller index. Full article

(This article belongs to the Section Mathematical Physics)

18 pages, 4914 KiB

Open AccessArticle

Seismic Response Prediction of Rigid Rocking Structures Using Explainable LightGBM Models

by Ioannis Karampinis, Kosmas E. Bantilas, Ioannis E. Kavvadias, Lazaros Iliadis and Anaxagoras Elenas

Mathematics 2024, 12(14), 2280; https://doi.org/10.3390/math12142280 - 21 Jul 2024

Viewed by 547

Abstract

This study emphasizes the explainability of machine learning (ML) models in predicting the seismic response of rigid rocking structures, specifically using the LightGBM algorithm. By employing SHapley Additive exPlanations (SHAP), partial dependence plots (PDP), and accumulated local effects (ALE), a comprehensive feature importance [...] Read more.

This study emphasizes the explainability of machine learning (ML) models in predicting the seismic response of rigid rocking structures, specifically using the LightGBM algorithm. By employing SHapley Additive exPlanations (SHAP), partial dependence plots (PDP), and accumulated local effects (ALE), a comprehensive feature importance analysis has been performed. This revealed that ground motion parameters, particularly peak ground acceleration (PGA), are critical for predicting small rotations, while structural parameters like slenderness and frequency are more significant for larger rotations. Utilizing an extensive dataset generated from nonlinear time history analyses, the trained LightGBM model demonstrated high accuracy in estimating the maximum rotation angle of rigid blocks under natural ground motions. The study also examined the sensitivity of model performance to lower bound thresholds of the target variable, revealing that reduced feature sets can maintain predictive performance effectively. These findings advance ML-based modeling of seismic rocking responses, providing interpretable and accurate models that enhance our understanding of rocking structures’ dynamic behavior, which is crucial for designing resilient structures and improving seismic risk assessments. Future research will focus on incorporating additional parameters and exploring advanced ML techniques to further refine these models. Full article

(This article belongs to the Special Issue Application of Advanced Computing and Artificial Intelligence in Engineering and Science, 2nd Edition)

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18 pages, 1826 KiB

Open AccessArticle

Learning a Context-Aware Environmental Residual Correlation Filter via Deep Convolution Features for Visual Object Tracking

by Sachin Sakthi Kuppusami Sakthivel, Sathishkumar Moorthy, Sathiyamoorthi Arthanari, Jae Hoon Jeong and Young Hoon Joo

Mathematics 2024, 12(14), 2279; https://doi.org/10.3390/math12142279 - 21 Jul 2024

Viewed by 450

Abstract

Visual tracking has become widespread in swarm robots for intelligent video surveillance, navigation, and autonomous vehicles due to the development of machine learning algorithms. Discriminative correlation filter (DCF)-based trackers have gained increasing attention owing to their efficiency. This study proposes “context-aware environmental residual [...] Read more.

Visual tracking has become widespread in swarm robots for intelligent video surveillance, navigation, and autonomous vehicles due to the development of machine learning algorithms. Discriminative correlation filter (DCF)-based trackers have gained increasing attention owing to their efficiency. This study proposes “context-aware environmental residual correlation filter tracking via deep convolution features (CAERDCF)” to enhance the performance of the tracker under ambiguous environmental changes. The objective is to address the challenges posed by intensive environment variations that confound DCF-based trackers, resulting in undesirable tracking drift. We present a selective spatial regularizer in the DCF to suppress boundary effects and use the target’s context information to improve tracking performance. Specifically, a regularization term comprehends the environmental residual among video sequences, enhancing the filter’s discrimination and robustness in unpredictable tracking conditions. Additionally, we propose an efficient method for acquiring environmental data using the current observation without additional computation. A multi-feature integration method is also introduced to enhance the target’s presence by combining multiple metrics. We demonstrate the efficiency and feasibility of our proposed CAERDCF approach by comparing it with existing methods using the OTB2015, TempleColor128, UAV123, LASOT, and GOT10K benchmark datasets. Specifically, our method increased the precision score by 12.9% in OTB2015 and 16.1% in TempleColor128 compared to BACF. Full article

(This article belongs to the Special Issue Advanced Computational Intelligence)

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21 pages, 4569 KiB

Open AccessArticle

Pairwise-Constraint-Guided Multi-View Feature Selection by Joint Sparse Regularization and Similarity Learning

by Jinxi Li and Hong Tao

Mathematics 2024, 12(14), 2278; https://doi.org/10.3390/math12142278 - 21 Jul 2024

Viewed by 351

Abstract

Feature selection is a basic and important step in real applications, such as face recognition and image segmentation. In this paper, we propose a new weakly supervised multi-view feature selection method by utilizing pairwise constraints, i.e., the pairwise constraint-guided multi-view f [...] Read more.

Feature selection is a basic and important step in real applications, such as face recognition and image segmentation. In this paper, we propose a new weakly supervised multi-view feature selection method by utilizing pairwise constraints, i.e., the pairwise constraint-guided multi-view feature selection (PCFS for short) method. In this method, linear projections of all views and a consistent similarity graph with pairwise constraints are jointly optimized to learning discriminative projections. Meanwhile, the

l_{2, 0}

-norm-based row sparsity constraint is imposed on the concatenation of projections for discriminative feature selection. Then, an iterative algorithm with theoretically guaranteed convergence is developed for the optimization of PCFS. The performance of the proposed PCFS method was evaluated by comprehensive experiments on six benchmark datasets and applications on cancer clustering. The experimental results demonstrate that PCFS exhibited competitive performance in feature selection in comparison with related models. Full article

(This article belongs to the Special Issue Applications of Artificial Intelligence, Machine Learning and Data Science)

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26 pages, 2261 KiB

Open AccessArticle

Learning from Feature and Global Topologies: Adaptive Multi-View Parallel Graph Contrastive Learning

by Yumeng Song, Xiaohua Li, Fangfang Li and Ge Yu

Mathematics 2024, 12(14), 2277; https://doi.org/10.3390/math12142277 - 21 Jul 2024

Viewed by 469

Abstract

To address the limitations of existing graph contrastive learning methods, which fail to adaptively integrate feature and topological information and struggle to efficiently capture multi-hop information, we propose an adaptive multi-view parallel graph contrastive learning framework (AMPGCL). It is an unsupervised graph representation [...] Read more.

To address the limitations of existing graph contrastive learning methods, which fail to adaptively integrate feature and topological information and struggle to efficiently capture multi-hop information, we propose an adaptive multi-view parallel graph contrastive learning framework (AMPGCL). It is an unsupervised graph representation learning method designed to generate task-agnostic node embeddings. AMPGCL constructs and encodes feature and topological views to mine feature and global topological information. To encode global topological information, we introduce an H-Transformer to decouple multi-hop neighbor aggregations, capturing global topology from node subgraphs. AMPGCL learns embedding consistency among feature, topology, and original graph encodings through a multi-view contrastive loss, generating semantically rich embeddings while avoiding information redundancy. Experiments on nine real datasets demonstrate that AMPGCL consistently outperforms thirteen state-of-the-art graph representation learning models in classification accuracy, whether in homophilous or non-homophilous graphs. Full article

(This article belongs to the Special Issue Mathematical Modeling for Parallel and Distributed Processing, 2nd Edition)

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17 pages, 522 KiB

Open AccessReview

From Classical to Modern Nonlinear Central Limit Theorems

by Vladimir V. Ulyanov

Mathematics 2024, 12(14), 2276; https://doi.org/10.3390/math12142276 - 21 Jul 2024

Viewed by 271

Abstract

In 1733, de Moivre, investigating the limit distribution of the binomial distribution, was the first to discover the existence of the normal distribution and the central limit theorem (CLT). In this review article, we briefly recall the history of classical CLT and martingale [...] Read more.

In 1733, de Moivre, investigating the limit distribution of the binomial distribution, was the first to discover the existence of the normal distribution and the central limit theorem (CLT). In this review article, we briefly recall the history of classical CLT and martingale CLT, and introduce new directions of CLT, namely Peng’s nonlinear CLT and Chen–Epstein’s nonlinear CLT, as well as Chen–Epstein’s nonlinear normal distribution function. Full article

(This article belongs to the Special Issue New Trends in Stochastic Processes, Probability and Statistics)

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17 pages, 2617 KiB

Open AccessArticle

Numerical Investigation of Nucleotides’ Interaction Considering Changes Caused by Liquid Influences

by Raimondas Jasevičius

Mathematics 2024, 12(14), 2275; https://doi.org/10.3390/math12142275 - 21 Jul 2024

Viewed by 421

Abstract

This work is devoted to the interaction of nucleotides. The goal of this study is to learn or try to learn how the interaction between nucleotides with exposure to a liquid takes place. Will the interacting forces of the nucleotides be sufficient to [...] Read more.

This work is devoted to the interaction of nucleotides. The goal of this study is to learn or try to learn how the interaction between nucleotides with exposure to a liquid takes place. Will the interacting forces of the nucleotides be sufficient to approach the incision? A numerical imitation of the interaction is conducted using the discrete element method and a Gears predictor–corrector as part of the integrated scheme. In this work, the results reflect the dynamics of nucleotides: velocity, displacement, and force graphs are presented with and without the effect of the liquid. During changes caused by the influence of a liquid, the nucleotide interaction transforms and passes three stages: a full stop, one similar to viscous damping, and one similar to non-dissipative behaviors. The main contribution of this work is a better understanding of the behavior of infinitely small objects that would be difficult to observe in vivo. The changing influence of a liquid can transform into certain effects. As a result, a model is provided, which can be based on the results of well-known physical experiments (DNA unzipping) for modeling nucleotide interactions. Full article

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11 pages, 248 KiB

Open AccessArticle

Stability and Instability of an Apollonius-Type Functional Equation

by Ponmana Selvan Arumugam, Won-Gil Park and Jaiok Roh

Mathematics 2024, 12(14), 2274; https://doi.org/10.3390/math12142274 - 21 Jul 2024

Viewed by 294

Abstract

For the inner product space, we have Appolonius’ identity. From this identity, Park and Th. M. Rassias induced and investigated the quadratic functional equation of the Apollonius type. And Park and Th. M. Rassias first introduced an Apollonius-type additive functional equation. In this [...] Read more.

For the inner product space, we have Appolonius’ identity. From this identity, Park and Th. M. Rassias induced and investigated the quadratic functional equation of the Apollonius type. And Park and Th. M. Rassias first introduced an Apollonius-type additive functional equation. In this work, we investigate an Apollonius-type additive functional equation in 2-normed spaces. We first investigate the stability of an Apollonius-type additive functional equation in 2-Banach spaces by using Hyers’ direct method. Then, we consider the instability of an Apollonius-type additive functional equation in 2-Banach spaces. Full article

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

14 pages, 322 KiB

Open AccessArticle

Coefficient Functionals of Sakaguchi-Type Starlike Functions Involving Caputo-Type Fractional Derivatives Subordinated to the Three-Leaf Function

by Kholood M. Alsager, Sheza M. El-Deeb, Gangadharan Murugusundaramoorthy and Daniel Breaz

Mathematics 2024, 12(14), 2273; https://doi.org/10.3390/math12142273 - 20 Jul 2024

Viewed by 376

Abstract

A challenging part of studying geometric function theory is figuring out the sharp boundaries for coefficient-related problems that crop up in the Taylor–Maclaurin series of univalent functions. Using Caputo-type fractional derivatives to define the families of Sakaguchi-type starlike functions with respect to symmetric [...] Read more.

A challenging part of studying geometric function theory is figuring out the sharp boundaries for coefficient-related problems that crop up in the Taylor–Maclaurin series of univalent functions. Using Caputo-type fractional derivatives to define the families of Sakaguchi-type starlike functions with respect to symmetric points, this article aims to investigate the first three initial coefficient estimates, the bounds for various problems such as Fekete–Szegő inequality, and the Zalcman inequalities, by subordinating to the function of the three leaves domain. Fekete–Szegő-type inequalities and initial coefficients for functions of the form

H^{- 1}

and

\frac{ζ}{H (ζ)}

and

\frac{1}{2} log (\frac{H (ζ)}{ζ})

connected to the three leaves functions are also discussed. Full article

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

33 pages, 5258 KiB

Open AccessArticle

Developing GA-FuL: A Generic Wide-Purpose Library for Computing with Geometric Algebra

by Ahmad Hosny Eid and Francisco G. Montoya

Mathematics 2024, 12(14), 2272; https://doi.org/10.3390/math12142272 - 20 Jul 2024

Viewed by 419

Abstract

The Geometric Algebra Fulcrum Library (GA-FuL) version 1.0 is introduced in this paper as a comprehensive computational library for geometric algebra (GA) and Clifford algebra (CA), in addition to other classical algebras. As a sophisticated software system, GA-FuL is useful for practical applications [...] Read more.

The Geometric Algebra Fulcrum Library (GA-FuL) version 1.0 is introduced in this paper as a comprehensive computational library for geometric algebra (GA) and Clifford algebra (CA), in addition to other classical algebras. As a sophisticated software system, GA-FuL is useful for practical applications requiring numerical or symbolic prototyping, optimized code generation, and geometric visualization. A comprehensive overview of the GA-FuL design is provided, including its core design intentions, data-driven programming characteristics, and extensible layered design. The library is capable of representing and manipulating sparse multivectors of any dimension, scalar kind, or metric signature, including conformal and projective geometric algebras. Several practical and illustrative use cases of the library are provided to highlight its potential for mathematical, scientific, and engineering applications. The metaprogramming code optimization capabilities of GA-FuL are found to be unique among other software systems. This allows for the automated production of highly efficient code, based on powerful geometric modeling formulations provided by geometric algebra. Full article

(This article belongs to the Section Algebra, Geometry and Topology)

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11 pages, 235 KiB

Open AccessArticle

Criteria of a Two-Weight, Weak-Type Inequality in Orlicz Classes for Maximal Functions Defined on Homogeneous Spaces

by Erxin Zhang

Mathematics 2024, 12(14), 2271; https://doi.org/10.3390/math12142271 - 20 Jul 2024

Viewed by 249

Abstract

In this study, some new necessary and sufficient conditions for a two-weight, weak-type maximal inequality of the form [...] Read more.

In this study, some new necessary and sufficient conditions for a two-weight, weak-type maximal inequality of the form

φ_{1} (λ) \int_{{x \in X : M f (x) > λ}} ϱ (x) d μ (x) \leq c \int_{X} φ_{2} (c | f (x) |) σ (x) d μ (x)

are obtained in Orlicz classes, where

M f

is a Hardy–Littlewood maximal function defined on homogeneous spaces and

ϱ

is a weight function. Full article

(This article belongs to the Special Issue Recent Trends in Convex Analysis and Mathematical Inequalities)

18 pages, 353 KiB

Open AccessArticle

On the Continuity Equation in Space–Time Algebra: Multivector Waves, Energy–Momentum Vectors, Diffusion, and a Derivation of Maxwell Equations

by Manuel Beato Vásquez and Melvin Arias Polanco

Mathematics 2024, 12(14), 2270; https://doi.org/10.3390/math12142270 - 20 Jul 2024

Viewed by 402

Abstract

Historically and to date, the continuity equation (C.E.) has served as a consistency criterion for the development of physical theories. In this paper, we study the C.E. employing the mathematical framework of space–time algebra (STA), showing how common equations in mathematical physics can [...] Read more.

Historically and to date, the continuity equation (C.E.) has served as a consistency criterion for the development of physical theories. In this paper, we study the C.E. employing the mathematical framework of space–time algebra (STA), showing how common equations in mathematical physics can be identified and derived from the C.E.’s structure. We show that, in STA, the nabla equation given by the geometric product between the vector derivative operator and a generalized multivector can be identified as a system of scalar and vectorial C.E.—and, thus, another form of the C.E. itself. Associated with this continuity system, decoupling conditions are determined, and a system of wave equations and the generalized analogous quantities to the energy–momentum vectors and the Lorentz force density (and their corresponding C.E.) are constructed. From the symmetry transformations that make the C.E. system’s structure invariant, a system with the structure of Maxwell’s field equations is derived. This indicates that a Maxwellian system can be derived not only from the nabla equation and the generalized continuity system as special cases, but also from the symmetries of the C.E. structure. Upon reduction to well-known simpler quantities, the results found are consistent with the usual STA treatment of electrodynamics and hydrodynamics. The diffusion equation is explored from the continuity system, where it is found that, for decoupled systems with constant or explicitly dependent diffusion coefficients, the absence of external vector sources implies a loss in the diffusion equation structure, transforming it into Helmholtz-like and wave equations. Full article

(This article belongs to the Special Issue Applications of Geometric Algebra)

23 pages, 2748 KiB

Open AccessArticle

Centroidous Method for Determining Objective Weights

by Irina Vinogradova-Zinkevič

Mathematics 2024, 12(14), 2269; https://doi.org/10.3390/math12142269 - 20 Jul 2024

Viewed by 306

Abstract

When using multi-criteria decision-making methods in applied problems, an important aspect is the determination of the criteria weights. These weights represent the degree of each criterion’s importance in a certain group. The process of determining weight coefficients from a dataset is described as [...] Read more.

When using multi-criteria decision-making methods in applied problems, an important aspect is the determination of the criteria weights. These weights represent the degree of each criterion’s importance in a certain group. The process of determining weight coefficients from a dataset is described as an objective weighting method. The dataset considered here contains quantitative data representing measurements of the alternatives being compared, according to a previously determined system of criteria. The purpose of this study is to suggest a new method for determining objective criteria weights and estimating the proximity of the studied criteria to the centres of their groups. It is assumed that the closer a criterion is to the centre of the group, the more accurately it describes the entire group. The accuracy of the description of the entire group’s priorities is interpreted as the importance, and the higher the value, the more significant the weight of the criterion. The Centroidous method suggested here evaluates the importance of each criterion in relation to the centre of the entire group of criteria. The stability of the Centroidous method is examined in relation to the measures of Euclidean, Manhattan, and Chebyshev distances. By slightly modifying the data in the original normalised data matrix by 5% and 10% 100 and 10,000 times, stability is examined. A comparative analysis of the proposed Centroidous method obtained from the entropy, CRITIC, standard deviation, mean, and MEREC methods was performed. Three sets of data were generated for the comparative study of the methods, as follows: the mean value for alternatives with weak and strong differences and criteria with linear dependence. Additionally, an actual dataset from mobile phones was also used for the comparison. Full article

(This article belongs to the Special Issue Mathematical Methods for Decision Making and Optimization)

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Mathematics, Volume 12, Issue 14 (July-2 2024) – 151 articles

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