Mathematics doi: 10.3390/math12081188

Authors: Andreas D. Demou Nikos Savva

This work presents a novel approach for the study of the movement of droplets on inclined surfaces under the influence of gravity and chemical heterogeneities. The developed numerical methodology uses data-driven modeling to extend the applicability limits of an analytically derived reduced-order model for the contact line velocity. More specifically, while the reduced-order model is able to capture the effects of the chemical heterogeneities to a satisfactory degree, it does not account for gravity. To alleviate this shortcoming, datasets generated from direct numerical simulations are used to train a data-driven model for the contact line velocity, which is based on the Fourier neural operator and corrects the reduced-order model predictions to match the reference solutions. This hybrid surrogate model, which comprises of both analytical and data-driven components, is then integrated in time to simulate the droplet movement, offering a speedup of five orders of magnitude compared to direct numerical simulations. The performance of this hybrid model is quantified and assessed in different wetting scenarios, by considering various inclination angles and values for the Bond number, demonstrating the accuracy of the predictions as long as the adopted parameters lie within the ranges considered in the training dataset.

]]>Mathematics doi: 10.3390/math12081187

Authors: Shiying Tu Jiehu Huang Huailong Mu Juan Lu Ying Li

Stock market performance is one key indicator of the economic condition of a country, and stock price forecasting is important for investments and financial risk management. However, the inherent nonlinearity and complexity in stock price movements imply that simple conventional modeling techniques are not adequate for stock price forecasting. In this paper, we present a hybrid model (ARIMA + GPRC) which combines the autoregressive integrated moving average (ARIMA) model and Gaussian process regression (GPR) with a combined covariance function (GPRC). The proposed hybrid model can account for both the linearity and nonlinearity in stock price movements. Based on daily data on three stocks listed on the Shanghai Stock Exchange (SSE), it is found that GPRC outperforms GPR with a single covariance function. Further, the proposed hybrid model is compared with the ARIMA model, artificial neural network (ANN), and GPRC model. Based on the forecasting trend and the statistical performance of the four models, the ARIMA + GPRC model is found to be the dominant model for stock price forecasting and can significantly improve forecasting performance.

]]>Mathematics doi: 10.3390/math12081186

Authors: Ronghua Li Mingshuo Zhao Haopeng Xue Xinyu Li Yuan Deng

Aiming at the nonlinear radiometric differences between multi-source sensor images and coherent spot noise and other factors that lead to alignment difficulties, the registration method of gradient weakly sensitive multi-source sensor images is proposed, which does not need to extract the image gradient in the whole process and has rotational invariance. In the feature point detection stage, the maximum moment map is obtained by using the phase consistency transform to replace the gradient edge map for chunked Harris feature point detection, thus increasing the number of repeated feature points in the heterogeneous image. To have rotational invariance of the subsequent descriptors, a method to determine the main phase angle is proposed. The phase angle of the region near the feature point is counted, and the parabolic interpolation method is used to estimate the more accurate main phase angle under the determined interval. In the feature description stage, the Log-Gabor convolution sequence is used to construct the index map with the maximum phase amplitude, the heterogeneous image is converted to an isomorphic image, and the isomorphic image of the region around the feature point is rotated by using the main phase angle, which is in turn used to construct the feature vector with the feature point as the center by the quadratic interpolation method. In the feature matching stage, feature matching is performed by using the sum of squares of Euclidean distances as a similarity metric. Finally, after qualitative and quantitative experiments of six groups of five pairs of different multi-source sensor image alignment correct matching rates, root mean square errors, and the number of correctly matched points statistics, this algorithm is verified to have the advantage of robust accuracy compared with the current algorithms.

]]>Mathematics doi: 10.3390/math12081185

Authors: Han Miao Qingbing Sang

No reference image quality assessment is a technique that uses computers to simulate the human visual system and automatically evaluate the perceived quality of images. In recent years, with the widespread success of deep learning in the field of computer vision, many end-to-end image quality assessment algorithms based on deep learning have emerged. However, unlike other computer vision tasks that focus on image content, an excellent image quality assessment model should simultaneously consider distortions in the image and comprehensively evaluate their relationships. Motivated by this, we propose a Multi-module Collaborative Model for Image Quality Assessment (McmIQA). The image quality assessment is divided into three subtasks: distortion perception, content recognition, and correlation mapping. And specific modules are constructed for each subtask: the distortion perception module, the content recognition module, and the correlation mapping module. Specifically, we apply two contrastive learning frameworks on two constructed datasets to train the distortion perception module and the content recognition module to extract two types of features from the image. Subsequently, using these extracted features as input, we employ a ranking loss to train the correlation mapping module to predict image quality on image quality assessment datasets. Extensive experiments conducted on seven relevant datasets demonstrated that the proposed method achieves state-of-the-art performance in both synthetic distortion and natural distortion image quality assessment tasks.

]]>Mathematics doi: 10.3390/math12081183

Authors: Ruzakhon Kazimirova Gafurjan Ibragimov Bruno Antonio Pansera Abdulla Ibragimov

In the Hilbert space l2, a differential evasion game involving multiple pursuers is considered. Integral constraints are imposed on player control functions. The pursuers are tasked with bringing the state of a system back to the origin of l2, while the evader simultaneously tries to avoid it. It is assumed that the energy of the evader is greater than the total energy of the pursuers. In this paper, we contribute to the solution of the differential evasion game with multiple pursuers by building an exact strategy for the evader.

]]>Mathematics doi: 10.3390/math12081184

Authors: Ze-Ping Wang Li-Hua Qin

f-biharmonic maps are generalizations of harmonic maps and biharmonic maps. In this paper, we give some descriptions of f-biharmonic curves in a space form. We also obtain a complete classification of proper f-biharmonic isometric immersions of a developable surface in R3 by proving that a proper f-biharmonic developable surface exists only in the case where the surface is a cylinder. Based on this, we show that a proper biharmonic conformal immersion of a developable surface into R3 exists only in the case when the surface is a cylinder. Riemannian submersions can be viewed as a dual notion of isometric immersions (i.e., submanifolds). We also study f-biharmonicity of Riemannian submersions from 3-manifolds by using the integrability data. Examples are given of proper f-biharmonic Riemannian submersions and f-biharmonic surfaces and curves.

]]>Mathematics doi: 10.3390/math12081182

Authors: Xiangshuo Liu Lijun Zhang Mingji Zhang

We examine the qualitative properties of ionic flows through ion channels via a quasi-one-dimensional Poisson&ndash;Nernst&ndash;Planck model under relaxed neutral boundary conditions. Bikerman&rsquo;s local hard-sphere potential is included in the model to account for finite ion size effects. Our main interest is to examine the boundary layer effects (due to the relaxation of electroneutrality boundary conditions) on both individual fluxes and current&ndash;voltage relations systematically. Critical values of potentials are identified that play significant roles in studying internal dynamics of ionic flows. It turns out that the finite ion size can either enhance or reduce the ionic flow under different nonlinear interplays between the physical parameters in the system, particularly, boundary concentrations, boundary potentials, boundary layers, and finite ion sizes. Much more rich dynamics of ionic flows through membrane channels is observed.

]]>Mathematics doi: 10.3390/math12081181

Authors: Tianjun Su Linhai Wu Jingxiang Zhang

This study develops a tripartite evolutionary game dynamic model with a time delay effect to analyze the interactions among food enterprise, government regulatory, and food inspection agencies in managing food safety risks. This model enables government regulatory agencies to more accurately assess and predict food safety risks, thereby implementing more effective preventative measures, ensuring the maximization of policy effectiveness and reducing food safety incidents. The results emphasize the significance of recent company performance by showing that regulatory and inspection entities&rsquo; strategic decisions are significantly impacted by delay effects from food companies. This study also shows that negative self-feedback intensity drives food enterprises to develop safer products and encourages tighter government oversight. Recommendations include improving consumer reporting channels, changing government incentives and penalties, allocating resources efficiently, and advancing information technology to decrease the effects of time delays and improve food safety management. Governments can improve food safety regulation by using strategic insights from numerical simulations.

]]>Mathematics doi: 10.3390/math12081180

Authors: Yiquan Guo Bowen Zhang Xiaomao Fan Xiaole Shen Xiaojiang Peng

Electroencephalogram (EEG) is the most preferred and credible source for emotion recognition, where long-short range features and a multichannel relationship are crucial for performance because numerous physiological components function at various time scales and on different channels. We propose a cascade scale-aware adaptive graph convolutional network and cross-EEG transformer (SAG-CET) to explore the comprehensive interaction between multiscale and multichannel EEG signals with two novel ideas. First, to model the relationship of multichannel EEG signals and enhance signal representation ability, the multiscale EEG signals are fed into a scale-aware adaptive graph convolutional network (SAG) before the CET model. Second, the cross-EEG transformer (CET), is used to explicitly capture multiscale features as well as their correlations. The CET consists of two self-attention encoders for gathering features from long-short time series and a cross-attention module to integrate multiscale class tokens. Our experiments show that CET significantly outperforms a vanilla unitary transformer, and the SAG module brings visible gains. Our methods also outperform state-of-the-art methods in subject-dependent tasks with 98.89%/98.92% in accuracy for valence/arousal on DEAP and 99.08%/99.21% on DREAMER.

]]>Mathematics doi: 10.3390/math12081179

Authors: Jiayun He Lei Yang Jiajun Zhan

In this paper, a family of temporal high-order accurate numerical schemes for the Landau&ndash;Lifshitz&ndash;Gilbert (LLG) equation is proposed. The proposed schemes are developed utilizing the Gauss&ndash;Legendre quadrature method, enabling them to achieve arbitrary high-order time discretization. Furthermore, the geometrical properties of the LLG equation, such as the preservation of constant magnetization magnitude and the Lyapunov structure, are investigated based on the proposed discrete schemes. It is demonstrated that the magnetization magnitude remains constant with an error of (2p+3) order in time when utilizing a (2p+2)th-order discrete scheme. Additionally, the preservation of the Lyapunov structure is achieved with a second-order error in the temporal step size. Numerical experiments and simulations effectively verify the performance of our proposed algorithm and validate our theoretical analysis.

]]>Mathematics doi: 10.3390/math12081178

Authors: Hang Xu Chaohui Huang Jianbing Lin Min Lin Huahui Zhang Rongbin Xu

Evolutionary algorithms have been widely applied for solving multi-objective optimization problems, while the feature selection in classification can also be treated as a discrete bi-objective optimization problem if attempting to minimize both the classification error and the ratio of selected features. However, traditional multi-objective evolutionary algorithms (MOEAs) may have drawbacks for tackling large-scale feature selection, due to the curse of dimensionality in the decision space. Therefore, in this paper, we concentrated on designing an multi-task decomposition-based evolutionary algorithm (abbreviated as MTDEA), especially for handling high-dimensional bi-objective feature selection in classification. To be more specific, multiple subpopulations related to different evolutionary tasks are separately initialized and then adaptively merged into a single integrated population during the evolution. Moreover, the ideal points for these multi-task subpopulations are dynamically adjusted every generation, in order to achieve different search preferences and evolutionary directions. In the experiments, the proposed MTDEA was compared with seven state-of-the-art MOEAs on 20 high-dimensional classification datasets in terms of three performance indicators, along with using comprehensive Wilcoxon and Friedman tests. It was found that the MTDEA performed the best on most datasets, with a significantly better search ability and promising efficiency.

]]>Mathematics doi: 10.3390/math12081177

Authors: Michel Nguiffo Boyom Stephane Puechmorel

The gauge equation is a generalization of the conjugacy relation for the Koszul connection to bundle morphisms that are not isomorphisms. The existence of nontrivial solution to this equation, especially when duality is imposed upon related connections, provides important information about the geometry of the manifolds under consideration. In this article, we use the gauge equation to introduce spectral sequences that are further specialized to Hessian structures.

]]>Mathematics doi: 10.3390/math12081176

Authors: Ebrahim Zareimani Reza Parvaz

The secure transmission of information is one of the most important topics in the field of information technology. Considering that images contain important visual information, it is crucial to create a safe platform for image transfer. One commonly employed tool to enhance the complexity and randomness in image encryption methods is the chaos system. The logistic and sine maps are utilized in encryption algorithms but these systems have some weaknesses, notably chaotic behavior in a confined area. In this study, to address these weaknesses, a hybrid system based on the Atangana&ndash;Baleanu fractional derivative is proposed. The various tests employed to evaluate the behavior of the new system, including the NIST test, histogram analysis, Lyapunov exponent calculation, and bifurcation diagram, demonstrate the efficiency of the proposed system. Furthermore, in comparison to the logistic and sine maps, the proposed hybrid exhibits chaotic behavior over a broader range. This system is utilized to establish a secure environment for the transmission of multiple images within an encryption algorithm, subsequently concealing them within a meaningful image. Various tools employed to assess the security of the proposed algorithm, including histogram analysis, NPCR, UACI, and correlation values, indicate that the proposed hybrid system has application value in encryption.

]]>Mathematics doi: 10.3390/math12081175

Authors: Jilin Zhang Yanling Chen Shuaifeng Zhang Yang Zhang

This paper proposes a graph residual gated recurrent network subway passenger flow prediction model considering the flat-peak characteristics, which firstly proposes the use of an adaptive density clustering method, which is capable of dynamically dividing the flat-peak time period of subway passenger flow. Secondly, this paper proposes graph residual gated recurrent network, which uses a graph convolutional network fused with a residual network and combined with a gated recurrent network, to simultaneously learn the temporal and spatial characteristics of passenger flow. Finally, this paper proposes to use the spatial attention mechanism to learn the spatial features around the subway stations, construct the spatial local feature components, and fully learn the spatial features around the stations to realize the local quantization of the spatial features around the subway stations. The experimental results show that the graph residual gated recurrent network considering the flat-peak characteristics can effectively improve the prediction performance of the model, and the method proposed in this paper has the highest prediction accuracy when compared with the traditional prediction model.

]]>Mathematics doi: 10.3390/math12081174

Authors: Chenhua Xu Wenjie Zhang Dan Liu Jian Cen Jianbin Xiong Guojuan Luo

In the abnormal situation of an aluminum electrolysis cell, the setting of cell voltage is mainly based on manual experience. To obtain a smaller cell voltage and optimize the operating parameters, a multi-objective optimization method for cell voltage based on a comprehensive index evaluation model is proposed. Firstly, a comprehensive judgment model of the cell state based on the energy balance, material balance, and stability of the aluminum electrolysis process is established. Secondly, a fuzzy neural network (FNN) based on the autoregressive moving average (ARMA) model is designed to establish the cell-state prediction model in order to finish the real-time monitoring of the process. Thirdly, the optimization goal of the process is summarized as having been met when the difference between the average cell voltage and the target value reaches the minimum, and the condition of the cell is excellent. And then, the optimization setting model of cell voltage is established under the constraints of the production and operation requirements. Finally, a multi-objective antlion optimization algorithm (MOALO) is used to solve the above model and find a group of optimized values of the electrolysis cell, which is used to realize the optimization control of the cell state. By using actual production data, the above method is validated to be effective. Moreover, optimized operating parameters are used to verify the prediction model of cell voltage, and the cell state is just excellent. The method is also applied to realize the optimization control of the process. It is of guiding significance for stabilizing the electrolytic aluminum production and achieving energy saving and consumption reduction.

]]>Mathematics doi: 10.3390/math12081173

Authors: Dário Ferreira Sandra S. Ferreira

This paper presents an approach for the study of probabilistic outcomes in experiments with multiple possible results. An approach to obtain confidence ellipsoids for the vector of probabilities, which represents the likelihood of specific results, for both discrete and continuous discriminant analysis, is presented. The obtention of optimal allocation rules, in order to reduce the allocation costs is investigated. In the context of discrete discriminant analysis, the approach focuses on assigning elements to specific groups in an optimal way. Whereas in the continuous case, the approach involves determining the regions where each action is the optimal choice. The effectiveness of the proposed approach is examined with two numerical applications. One of them uses real data, while the other one uses simulated data.

]]>Mathematics doi: 10.3390/math12081172

Authors: Saidat Fehintola Olaniran Oyebayo Ridwan Olaniran Jeza Allohibi Abdulmajeed Atiah Alharbi Mohd Tahir Ismail

Asymptotic theories for fractional cointegrations have been extensively studied in the context of time series data, with numerous empirical studies and tests having been developed. However, most previously developed testing procedures for fractional cointegration are primarily designed for time series data. This paper proposes a generalized residual-based test for fractionally cointegrated panels with fixed effects. The test&rsquo;s development is based on a bivariate panel series with the regressor assumed to be fixed across cross-sectional units. The proposed test procedure accommodates any integration order between [0,1], and it is asymptotically normal under the null hypothesis. Monte Carlo experiments demonstrate that the test exhibits better size and power compared to a similar residual-based test across varying sample sizes.

]]>Mathematics doi: 10.3390/math12081171

Authors: Fangfang Li Yansheng Ma

This paper deals with a phase transition model with polarization which describes the thermodynamic, electromagnetic, and polarization properties of ferromagnetic&ndash;ferroelectric materials. The existence of the global weak solution for the phase transition equations with polarization is rigorously established through the viscosity vanishing argument.

]]>Mathematics doi: 10.3390/math12081170

Authors: Hassan Y. Alfifi Saad M. Almuaddi

This paper investigates the effect of a gene expression time delay on the Brusselator model with reaction and diffusion terms in one dimension. We obtain ODE systems analytically by using the Galerkin method. We determine a condition that assists in showing the existence of theoretical results. Full maps of the Hopf bifurcation regions of the stability analysis are studied numerically and theoretically. The influences of two different sources of diffusion coefficients and gene expression time delay parameters on the bifurcation diagram are examined and plotted. In addition, the effect of delay and diffusion values on all other free parameters in this system is shown. They can significantly affect the stability regions for both control parameter concentrations through the reaction process. As a result, as the gene expression time delay increases, both control concentration values increase, while the Hopf points for both diffusion coefficient parameters decrease. These values can impact solutions in the bifurcation regions, causing the region of instability to grow. In addition, the Hopf bifurcation points for the diffusive and non-diffusive cases as well as delay and non-delay cases are studied for both control parameter concentrations. Finally, various examples and bifurcation diagrams, periodic oscillations, and 2D phase planes are provided. There is close agreement between the theoretical and numerical solutions in all cases.

]]>Mathematics doi: 10.3390/math12081169

Authors: Inna Stepanova Igor Kolotov Dmitry Lukyanenko Alexey Shchepetilov

This paper considers the problem of the uniqueness of the solution to the coefficient inverse problem for the system of equations of magneto-hydrodynamics, the solution to which allows more accurately describing the processes of generating the magnetic field of planets with a magneto-hydrodynamic dynamo. The conditions under which it is possible to determine three components of the magnetic induction vector and the magnetic field diffusion coefficient are determined.

]]>Mathematics doi: 10.3390/math12081168

Authors: Haiyang Zhang Chenglin Wen

The cubature Kalman filter (CKF) cannot accurately estimate the nonlinear model, and these errors will have an impact on the accuracy. In order to improve the filtering performance of the CKF, this paper proposes a new CKF method to improve the estimation accuracy by using the statistical characteristics of rounding error, establishes a higher-order extended cubature Kalman filter (RHCKF) for joint estimation of sigma sampling points and random variables of rounding error, and gives a solution method considering the rounding error of multi-level approximation of the original function in the undermeasured dimension. Finally, numerical simulations show that the RHCKF has a better estimation effect than the CKF, and that the filtering accuracy is improved by using the information of the higher-order rounding error, which also proves the effectiveness of the method.

]]>Mathematics doi: 10.3390/math12081167

Authors: Jelena Tašić Zsófia Nagy-Perjési Márta Takács

In this paper, we present a multilevel fuzzy inference model for predicting the risk of type 2 diabetes. We have designed a system for predicting this risk by taking into account various factors such as physical, behavioral, and environmental parameters related to the investigated patient and thus facilitate experts to diagnose the risk of diabetes. The important risk parameters of type 2 diabetes are identified based on the literature and the recommendations of experts. The parameters are scaled and fuzzified on their own universe and, based on the experts&rsquo; recommendation, fuzzy inference subsystems are created with 3&ndash;4 related risk parameters to calculate the risk level. These sub-systems are then arranged into Mamdani-type inference systems so that the system calculates an aggregated risk level. The overview of the large number of diverse types of risk factors, which may be difficult for specialists and doctors, is facilitated by the proposed system.

]]>Mathematics doi: 10.3390/math12081166

Authors: Yiqin Lin

In this paper, we consider the numerical solution of large-scale discrete-time projected Lyapunov equations. We provide some reasonable extensions of the most frequently used low-rank iterative methods for linear matrix equations, such as the low-rank Smith method and the low-rank alternating-direction implicit (ADI) method. We also consider how to reduce complex arithmetic operations and storage when shift parameters are complex and propose a partially real version of the low-rank ADI method. Through two standard numerical examples from discrete-time descriptor systems, we will show that the proposed low-rank alternating-direction implicit method is efficient.

]]>Mathematics doi: 10.3390/math12081165

Authors: Christos E. Kountzakis Damiano Rossello

The aim of this paper is to provide a dual representation of convex and coherent risk measures in partially ordered linear spaces with respect to the algebraic dual space. An algebraic robust representation is deduced by weak separation of convex sets by functionals, which are assumed to be only linear; thus, our framework does not require any topological structure of the underlying spaces, and our robust representations are found without any continuity requirement for the risk measures. We also use such extensions to the representation of acceptability indices.

]]>Mathematics doi: 10.3390/math12081164

Authors: Walter Peter Vispoel Hyeryung Lee Tingting Chen

We illustrate how structural equation models (SEMs) can be used to assess the reliability and generalizability of composite and subscale scores, proportions of multiple sources of measurement error, and subscale added value within multivariate designs using data from a popular inventory measuring hierarchically structured personality traits. We compare these techniques between standard SEMs representing congeneric relations between indicators and underlying factors versus SEM-based generalizability theory (GT) designs with simplified essential tau-equivalent constraints. Results strongly emphasized the importance of accounting for multiple sources of measurement error in both contexts and revealed that, in most but not all instances, congeneric designs yielded higher score accuracy, lower proportions of measurement error, greater average subscale score viability, stronger model fits, and differing magnitudes of disattenuated subscale intercorrelations. Extending the congeneric analyses to the item level further highlighted consistent weaknesses in the psychometric properties of negatively versus positively keyed items. Collectively, these findings demonstrate the practical value and advantages of applying GT-based principles to congeneric SEMs that are much more commonly encountered in the research literature and more directly linked to the specific measures being analyzed. We also provide prophecy formulas to estimate reliability and generalizability coefficients, proportions of individual sources of measurement error, and subscale added-value indices for changes made to measurement procedures and offer guidelines and examples for running all illustrated analyses using the lavaan (Version 0.6-17) and semTools (Version 0.5-6) packages in R. The methods described for the analyzed designs are applicable to any objectively or subjectively scored assessments for which both composite and subcomponent scores are reported.

]]>Mathematics doi: 10.3390/math12081161

Authors: Kirill D. Cherednichenko Yulia Yu. Ershova Alexander V. Kiselev

Norm-resolvent convergence with an order-sharp error estimate is established for Neumann Laplacians on thin domains in Rd,&nbsp;d&ge;2, converging to metric graphs in the limit of vanishing thickness parameter in the &ldquo;resonant&rdquo; case. The vertex matching conditions of the limiting quantum graph are revealed as being closely related to those of the &delta;&prime; type.

]]>Mathematics doi: 10.3390/math12081163

Authors: Tzu-Hsin Liu Kuo-Ching Chiou Chih-Ming Chen Fu-Min Chang

This work investigates a two-way communication retrial queue with synchronous working vacation and a constant retrial policy. During the idle time, a server makes an outgoing call after a random length. The service time of the incoming call and outgoing call obeys exponential distribution with different rates. If the incoming call finds all servers to be unavailable, it may or may not enter orbit. All servers immediately go on vacation simultaneously as soon as they find an empty system after the service finishes. During vacation, the servers can provide a service to those incoming calls, but this is at a lower-speed rate. The stationary probability distribution and the ergodic condition are obtained utilizing the matrix geometric technique. Some system characteristics are developed. Using MATLAB software, the variation in average orbit length, idle ratio, and the average number of servers in different server states is plotted for different values of the incoming/outgoing call rate and retrial rate. We further propose a multi-objective optimization model from which the optimal rate of outgoing calls and optimal vacation rate are explicitly obtained.

]]>Mathematics doi: 10.3390/math12081162

Authors: Xiuchun Lin Renguang Chen Chen Feng Zhide Chen Xu Yang Hui Cui

Functional Movement Screening (FMS) is a movement pattern quality assessment system used to assess basic movement capabilities such as flexibility, stability, and pliability. Movement impairments and abnormal postures can be identified through peculiar movements and postures of the body. The reliability, validity, and accuracy of functional movement screening are difficult to test due to the subjective nature of the assessment. In this sense, this paper presents an automatic evaluation method for functional movement screening based on a dual-stream network and feature fusion. First, the RAFT algorithm is used to estimate the optical flow of a video, generating a set of optical flow images to represent the motion between consecutive frames. By inputting optical flow images and original video frames separately into the I3D model, it can better capture spatiotemporal features compared to the single-stream method. Meanwhile, this paper introduces a simple but effective attention fusion method that combines features extracted from optical flow with the original frames, enabling the network to focus on the most relevant parts of the input data, thereby improving prediction accuracy. The prediction of the four categories of FMS results was performed. It produced better correlation results compared to other more complex fusion protocols, with an accuracy improvement of 3% over the best-performing fusion method. Tests on public datasets showed that the evaluation metrics of the method proposed in this paper were the most advanced, with an accuracy improvement of approximately 4% compared to the currently superior methods. The use of deep learning methods makes it more objective and reliable to identify human movement impairments and abnormal postures.

]]>Mathematics doi: 10.3390/math12081160

Authors: Yude Fu Jing Zhu Xiang Li Xu Han Wenhui Tan Qizi Huangpeng Xiaojun Duan

This study investigates coordinated behaviors and the underlying collective intelligence in biological groups, particularly those led by informed leaders. By establishing new convergence condition based on experiments involving real biological groups, this research introduces the concept of a volitional term and heterogeneous networks, constructing a coupled-force Cucker&ndash;Smale model with informed leaders. Incorporating informed leaders into the leader-follower group model enables a more accurate representation of biological group behaviors. The paper then extracts the Flock Leadership Hierarchy Network (FLH), a model reflecting real biological interactions. Employing time slicing and rolling time windows, the study methodically analyzes group behavior stages, using volatility and convergence time as metrics to examine the relationship between group consistency and interactions. Comparative experiments show the FLH network&rsquo;s superior performance. The Kolmogorov-Smirnov test demonstrates that the FLH network conforms to a power-law distribution, a prevalent law in nature. This result further illuminates the crucial role that power-law distribution plays in the evolutionary processes of biological communities. This study offers new perspectives on the evolution of biological groups, contributing to our understanding of the behaviors of both natural and artificial systems, such as animal migration and autonomous drone operations.

]]>Mathematics doi: 10.3390/math12081159

Authors: Hashem Althagafi Ahmed Ghezal

This paper aims to derive analytical expressions for solutions of fractional bidimensional systems of difference equations with higher-order terms under specific parametric conditions. Additionally, formulations of solutions for one-dimensional equations derived from these systems are explored. Furthermore, rigorous proof is provided for the local stability of the unique positive equilibrium point of the proposed systems. The theoretical findings are validated through numerical examples using MATLAB, facilitating graphical illustrations of the results.

]]>Mathematics doi: 10.3390/math12081158

Authors: Ruixiao Wang Yanxin Hu Zhiyu Chen Jianwei Guo Gang Liu

Currently, self-supervised learning has shown effectiveness in solving data labeling issues. Its success mainly depends on having access to large, high-quality datasets with diverse features. It also relies on utilizing the spatial, temporal, and semantic structures present in the data. However, domains such as finance, healthcare, and insurance primarily utilize tabular data formats. This presents challenges for traditional data augmentation methods aimed at improving data quality. Furthermore, the privacy-sensitive nature of these domains complicates the acquisition of the extensive, high-quality datasets necessary for training effective self-supervised models. To tackle these challenges, our proposal introduces a novel framework that combines self-supervised learning with Federated Learning (FL). This approach aims to solve the problem of data-distributed training while ensuring training quality. Our framework improves upon the conventional self-supervised learning data augmentation paradigm by incorporating data labeling through the segmentation of data into subsets. Our framework adds noise by splitting subsets of data and can achieve the same level of centralized learning in a distributed environment. Moreover, we conduct experiments on various public tabular datasets to evaluate our approach. The experimental results showcase the effectiveness and generalizability of our proposed method in scenarios involving unlabeled data and distributed settings.

]]>Mathematics doi: 10.3390/math12081157

Authors: Alina Elena Ionașcu Shankha Shubhra Goswami Alexandra Dănilă Maria-Gabriela Horga Corina Barbu Şerban-Comǎnescu Adrian

This study presents an in-depth analysis of the selection process for primary sectors impacting the economic activity in Romania, employing an interval-valued fuzzy (IVF) approach combined with multi-criteria decision-making (MCDM) methodologies. This research aims to identify eight key criteria influencing the selection of Romanian primary sectors, including technology adaptation, infrastructure development and investment, gross domestic product (GDP), sustainability, employment generation, market demand, risk management and government policies. The current analysis evaluates eight primary sector performances against these eight criteria through the application of three MCDM methods, namely, Simple Additive Weighting (SAW), Weighted Product Model (WPM), and Weighted Aggregated Sum Product Assessment (WASPAS). Ten economic experts comprising a committee have been invited to provide their views on the criteria&rsquo;s importance and the alternatives&rsquo; performance. Based on the decision-maker&rsquo;s qualitative judgement, GDP acquires the highest weightage, followed by environmental impact and sustainability, thus indicating the most critical factors among the group. The IVF-MCDM hybrid model indicates the energy sector as Romanian primary sector with the most potential, followed by the agriculture and forestry sector among the list of eight alternatives. It also explores the robustness of results by considering sensitivity analysis and the potential impacts of political and international factors, such as pandemics or armed conflicts, on sector selection. The findings indicate consistency in sector rankings across the different methodologies employed, underscoring the importance of methodological choice and criteria weighting. Additionally, this study sheds light on the potential influence of political and international dynamics on sector prioritization, emphasizing the need for comprehensive decision-making frameworks in economic planning processes.

]]>Mathematics doi: 10.3390/math12081156

Authors: Can Kızılateş Wei-Shih Du Nazlıhan Terzioğlu

This paper presents a comprehensive survey of the generalization of hybrid numbers and hybrid polynomials, particularly in the fields of mathematics and physics. In this paper, by using higher-order generalized Fibonacci polynomials, we introduce higher-order generalized Fibonacci hybrid polynomials called higher-order generalized Fibonacci hybrinomials. We obtain some special cases and algebraic properties of the higher-order generalized Fibonacci hybrinomials, such as the recurrence relation, generating function, exponential generating function, Binet formula, Vajda&rsquo;s identity, Catalan&rsquo;s identity, Cassini&rsquo;s identity and d&rsquo;Ocagne&rsquo;s identity. We also present three different matrices whose components are higher-order generalized Fibonacci hybrinomials, higher-order generalized Fibonacci polynomials and Lucas polynomials. By using these matrices, we obtain some identities related to these newly established hybrinomials.

]]>Mathematics doi: 10.3390/math12081155

Authors: Mogeeb A. A. Mosleh Adel Assiri Abdu H. Gumaei Bader Fahad Alkhamees Manal Al-Qahtani

Sign language is widely used to facilitate the communication process between deaf people and their surrounding environment. Sign language, like most other languages, is considered a complex language which cannot be mastered easily. Thus, technology can be used as an assistive tool to solve the difficulties and challenges that deaf people face during interactions with society. In this study, an automatic bidirectional translation framework for Arabic Sign Language (ArSL) is designed to assist both deaf and ordinary people to communicate and express themselves easily. Two main modules were intended to translate Arabic sign images into text by utilizing different transfer learning models and to translate the input text into Arabic sign images. A prototype was implemented based on the proposed framework by using several pre-trained convolutional neural network (CNN)-based deep learning models, including the DenseNet121, ResNet152, MobileNetV2, Xception, InceptionV3, NASNetLarge, VGG19, and VGG16 models. A fuzzy string matching score method, as a novel concept, was employed to translate the input text from ordinary people into appropriate sign language images. The dataset was constructed with specific criteria to obtain 7030 images for 14 classes captured from both deaf and ordinary people locally. The prototype was developed to conduct the experiments on the collected ArSL dataset using the utilized CNN deep learning models. The experimental results were evaluated using standard measurement metrics such as accuracy, precision, recall, and F1-score. The performance and efficiency of the ArSL prototype were assessed using a test set of an 80:20 splitting procedure, obtaining accuracy results from the highest to the lowest rates with average classification time in seconds for each utilized model, including (VGG16, 98.65%, 72.5), (MobileNetV2, 98.51%, 100.19), (VGG19, 98.22%, 77.16), (DenseNet121, 98.15%, 80.44), (Xception, 96.44%, 72.54), (NASNetLarge, 96.23%, 84.96), (InceptionV3, 94.31%, 76.98), and (ResNet152, 47.23%, 98.51). The fuzzy matching score is mathematically validated by computing the distance between the input and associative dictionary words. The study results showed the prototype&rsquo;s ability to successfully translate Arabic sign images into Arabic text and vice versa, with the highest accuracy. This study proves the ability to develop a robust and efficient real-time bidirectional ArSL translation system using deep learning models and the fuzzy string matching score method.

]]>Mathematics doi: 10.3390/math12081153

Authors: Zhongyuan Che Chong Peng

Low-alloy steel is widely employed in the aviation industry for its exceptional mechanical properties. These materials are frequently used in critical structural components such as aircraft landing gear and engine mounts, where a high strength-to-weight ratio is crucial for optimal performance. However, the mechanical properties of low-alloy steel are influenced by various components and their compositions, making identification and prediction challenging. Accurately predicting these mechanical properties can significantly reduce the development time of new alloy steel, lower production costs, and offer valuable insights for design analysis. support vector regression (SVR) is known for its superior learning and generalization capabilities. However, optimizing SVR performance can be challenging due to the significant impact of the penalty factor and kernel parameters. To address this issue, a hybrid method called SMA-SVR is proposed, which combines the Slime Mould Algorithm (SMA) with SVR. This hybrid approach aims to efficiently and accurately predict two crucial mechanical parameters of low-alloy steel: tensile strength and 0.2% proof stress. Detailed descriptions of the modeling processes and principles that are involved in the hybrid method are provided. Furthermore, three other popular hybrid models for comparison are introduced. To evaluate the performance of these models, four statistical measures are utilized: Mean Absolute Error, Root Mean Square Error, R-Squared, and computational time. Using data from the NIMS database and from material tests conducted on a universal testing machine, experiments were carried out to compare the performance of these models. The results indicate that SMA-SVR outperforms the other methods in terms of accuracy and computational efficiency.

]]>Mathematics doi: 10.3390/math12081154

Authors: Vishal Gupta Aanchal Gondhi Rahul Shukla

This paper establishes a new type of space, modified intuitionistic fuzzy soft metric space (MIFSMS). Basic properties and topological structures are defined in the setting of this new notion with valid examples. Moreover, we have given some new results along with suitable examples to show their validity. An application for finding the solution of an integral equation is also given by utilizing our newly developed results.

]]>Mathematics doi: 10.3390/math12081152

Authors: Sutida Patlertsin Suchada Pongprasert Thitarie Rungratgasame

Leibniz algebras are generalizations of Lie algebras. Similar to Lie algebras, inner derivations play a crucial role in characterizing complete Leibniz algebras. In this work, we demonstrate that the algebra of inner derivations of a Leibniz algebra can be decomposed into the sum of the algebra of left multiplications and a certain ideal. Furthermore, we show that the quotient of the algebra of derivations of the Leibniz algebra by this ideal yields a complete Lie algebra. Our results independently establish that any derivation of a semisimple Leibniz algebra can be expressed as a combination of three derivations. Additionally, we compare the properties of the algebra of inner derivations of Leibniz algebras with the algebra of central derivations.

]]>Mathematics doi: 10.3390/math12081151

Authors: Teddy Lazebnik Svetlana Bunimovich-Mendrazitsky

In this paper, we propose a novel, highly accurate numerical algorithm for matrix exponentials (MEs). The algorithm is based on approximating Putzer&rsquo;s algorithm by analytically solving the ordinary differential equation (ODE)-based coefficients and approximating them. We show that the algorithm outperforms other ME algorithms for stiff matrices for several matrix sizes while keeping the computation and memory consumption asymptotically similar to these algorithms. In addition, we propose a numerical-error- and complexity-optimized decision tree model for efficient ME computation based on machine learning and genetic programming methods. We show that, while there is not one ME algorithm that outperforms the others, one can find a good algorithm for any given matrix according to its properties.

]]>Mathematics doi: 10.3390/math12081150

Authors: Vladimir Mazalov Vladimir Yashin

The problem of dividing a pie between two persons is considered. An arbitration procedure for dividing the pie is proposed, in which the arbitrator is a random number generator. In this procedure, the arbitrator makes an offer to the players at each step, and the players can either accept or reject the arbitrator&rsquo;s offer. If there is no consensus, negotiations move on to the next step. At the same time, the arbitrator punishes the rejecting player by reducing the amount of the resource in favor of the consenting player. A subgame perfect equilibrium is found in the process.

]]>Mathematics doi: 10.3390/math12081149

Authors: Chitaranjan Mahapatra Inna Samuilik

We developed a mathematical model to simulate the dynamics of background synaptic noise in non-neuronal cells. By employing the stochastic Ornstein&ndash;Uhlenbeck process, we represented excitatory synaptic conductance and integrated it into a whole-cell model to generate spontaneous and evoke cellular electrical activities. This single-cell model encompasses numerous biophysically detailed ion channels, depicted by a set of ordinary differential equations in Hodgkin&ndash;Huxley and Markov formalisms. Consequently, this approach effectively induced irregular spontaneous depolarizations (SDs) and spontaneous action potentials (sAPs), resembling electrical activity observed in vitro. The input resistance decreased significantly, while the firing rate of spontaneous action potentials increased. Moreover, alterations in the ability to reach the action potential threshold were observed. Background synaptic activity can modify the input/output characteristics of non-neuronal excitatory cells. Hence, suppressing these baseline activities could aid in identifying new pharmaceutical targets for various clinical diseases.

]]>Mathematics doi: 10.3390/math12081148

Authors: Ping Xie Xiangrui Gao Fan Li Ling Xing Yu Zhang Hanxiao Sun

Federated learning has become a prevalent distributed training paradigm, in which local devices collaboratively train learning models without exchanging local data. One of the most dominant frameworks of federated learning (FL) is FedAvg, since it is efficient and simple to implement; here, the first-order information is generally utilized to train the parameters of learning models. In practice, however, the gradient information may be unavailable or infeasible in some applications, such as federated black-box optimization problems. To solve the issue, we propose an innovative zeroth-order adaptive federated learning algorithm without using the gradient information, referred to as ZO-AdaFL, which integrates the zeroth-order optimization algorithm into the adaptive gradient method. Moreover, we also rigorously analyze the convergence behavior of ZO-AdaFL in a non-convex setting, i.e., where ZO-AdaFL achieves convergence to a region close to a stationary point at a speed of O(1/T) (T represents the total iteration number). Finally, to verify the performance of ZO-AdaFL, simulation experiments are performed using the MNIST and FMNIST datasets. Our experimental findings demonstrate that ZO-AdaFL outperforms other state-of-the-art zeroth-order FL approaches in terms of both effectiveness and efficiency.

]]>Mathematics doi: 10.3390/math12081147

Authors: Zakaria Houta Thomas Huguet Nicolas Lebbe Frédéric Messine

Topology optimization is currently enjoying renewed interest thanks to the recent development of 3D printing techniques, which offer the possibility of producing these new complex designs. One of the difficulties encountered in manufacturing topologically optimized magnetostatic structures is that they are not necessarily mechanically stable. In order to take this mechanical constraint into account, we have developed a SIMP-based topology optimization algorithm which relies on numerical simulations of both the mechanical deformation and the magnetostatic behavior of the structure. Two variants are described in this paper, respectively taking into account the compliance or the von Mises constraint. By comparing the designs obtained with those from magnetostatic optimization alone, our approach proves effective in obtaining efficient and robust designs.

]]>Mathematics doi: 10.3390/math12081146

Authors: Jiashun Huang Dengguo Xu Yahui Li Yan Ma

This paper proposes an optimal tracking control scheme through adaptive dynamic programming (ADP) for a class of partially unknown discrete-time (DT) nonlinear systems based on a radial basis function neural network (RBF-NN). In order to acquire the unknown system dynamics, we use two RBF-NNs; the first one is used to construct the identifier, and the other one is used to directly approximate the steady-state control input, where a novel adaptive law is proposed to update neural network weights. The optimal feedback control and the cost function are derived via feedforward neural network approximation, and a means of regulating the tracking error is proposed. The critic network and the actor network were trained online to obtain the solution of the associated Hamilton&ndash;Jacobi&ndash;Bellman (HJB) equation within the ADP framework. Simulations were carried out to verify the effectiveness of the optimal tracking control technique using the neural networks.

]]>Mathematics doi: 10.3390/math12081145

Authors: Dongdong Gao Jianli Li

In this paper, we study the existence, uniqueness and Hyers&ndash;Ulam stability of a class of fractional stochastic pantograph equations with random impulses. Firstly, we establish sufficient conditions to ensure the existence of solutions for the considered equations by applying Schaefer&rsquo;s fixed point theorem under relaxed linear growth conditions. Secondly, we prove the solution for the considered equations is Hyers&ndash;Ulam stable via Gronwall&rsquo;s inequality. Moreover, the previous literature will be significantly generalized in our paper. Finally, an example is given to explain the efficiency of the obtained results.

]]>Mathematics doi: 10.3390/math12081144

Authors: Péter Mogyorósi Sándor Szénási Edit Laufer

It is necessary to extensively investigate the causes of road accidents with the utmost precision to harness future technological advancements, such as autonomous driving and intelligent accident prevention systems. Nevertheless, since most accidents are attributed to simple human errors, unraveling the complex root-cause factors poses a considerable challenge. This is where fuzzy logic can offer a potential solution: it is essential to understand even seemingly straightforward errors, such as speeding, to identify external factors that could play a pivotal role in future accident prevention. A more in-depth examination and comprehension of elements like road curvature, slope, and their correlation with accidents are necessary. Additionally, it is crucial to explore how the frequency of accidents on specific road segments varies under diverse weather conditions. This article analyzes which curves can be considered more dangerous and the factors that render them risky. The fuzzy model presented in this article is primarily capable of estimating the risk of a given road segment based on its curvature characteristics. The model results presented in the article indicate that sections of the road can become more risky due to multiple curves and curves with a radius of less than 80 m. The model assesses risk based on the physical characteristics of road segments, primarily the curvature radius, while, typically, other road risk assessment models rely on traffic volume and accident counts.

]]>Mathematics doi: 10.3390/math12081143

Authors: Jie Wu Yujie Huang

In this paper, we consider the following two-dimensional chemotaxis system of attraction&ndash;repulsion with indirect signal production &#120597;tu=&Delta;u&minus;&nabla;&middot;&chi;1u&nabla;v1+&nabla;&middot;(&chi;2u&nabla;v2),x&isin;R2,t&gt;0,0=&Delta;vj&minus;&lambda;jvj+w,x&isin;R2,t&gt;0,(j=1,2),&#120597;tw+&delta;w=u,x&isin;R2,t&gt;0,u(0,x)=u0(x),w(0,x)=w0(x),x&isin;R2, where the parameters &chi;i&ge;0,&nbsp;&lambda;i&gt;0(i=1,2) and non-negative initial data (u0(x),w0(x))&isin;L1(R2)&cap;L&infin;(R2). We prove the global bounded solution exists when the attraction is more dominant than the repulsion in the case of &chi;1&ge;&chi;2. At the same time, we propose that when the radial solution satisfies &chi;1&minus;&chi;2&le;2&pi;&delta;&#8741;u0&#8741;L1(R2)+&#8741;w0&#8741;L1(R2), the global solution is bounded. During the proof process, we found that adding indirect signals can constrict the blow-up of the global solution.

]]>Mathematics doi: 10.3390/math12081142

Authors: Fehaid Salem Alshammari

Consideration is given to a reaction&ndash;diffusion free boundary value problem with one or two turning points arising in oil price modeling. First, an exact (analytical) solution to the reduced problem (i.e., no diffusion term) was obtained for some given parameters. The space&ndash;time Chebyshev pseudospectral and superconsistent Chebyshev collocation method is proposed for both reaction diffusion (RDFBP) and reduced free boundary value problem. Error bounds on the discrete L2&ndash;norm and Sobolev norm (Hp) are presented. Adaptively graded intervals were introduced and used according to the value of turning points to avoid the twin boundary layers phenomena. Excellent convergent (spectrally) and stable results for some special turning points were obtained for both reduced and RDFBP equations on an adaptively graded interval and this has been documented for the first time.

]]>Mathematics doi: 10.3390/math12081141

Authors: Dimitris Tsintsaris Milan Tsompanoglou Evangelos Ioannidis

In this paper we offer a comprehensive review of Sociophysics, focusing on relevant models as well as selected applications in social trading, behavioral finance and business. We discuss three key aspects of social diffusion dynamics, namely Opinion Dynamics (OD), Group Decision-Making (GDM) and Knowledge Dynamics (KD). In the OD case, we highlight special classes of social agents, such as informed agents, contrarians and extremists. As regards GDM, we present state-of-the-art models on various kinds of decision-making processes. In the KD case, we discuss processes of knowledge diffusion and creation via the presence of self-innovating agents. The primary question we wish to address is: to what extent does Sociophysics correspond to social reality? For that purpose, for each social diffusion model category, we present notable Sociophysics applications for real-world socioeconomic phenomena and, additionally, we provide a much-needed critique of the existing Sociophysics literature, so as to raise awareness of certain issues that currently undermine the effective application of Sociophysics, mainly in terms of modelling assumptions and mathematical formulation, on the investigation of key social processes.

]]>Mathematics doi: 10.3390/math12081140

Authors: Arkadiusz Jadczyk

We geometrically derive the explicit form of the unitary representation of the Poincar&eacute; group for vector-valued wave functions and use it to apply speed-of-light boosts to a simple polarization basis to end up with a Hawton&ndash;Baylis photon position operator with commuting components. We give explicit formulas for other photon boost eigenmodes. We investigate the underlying affine connections on the light cone in momentum space and find that while the Pryce connection is metric semi-symmetric, the flat Hawton&ndash;Baylis connection is not semi-symmetric. Finally, we discuss the localizability of photon states on closed loops and show that photon states on the circle, both unnormalized improper states and finite-norm wave packet smeared-over washer-like regions are strictly localized not only with respect to Hawton&ndash;Baylis operators with commuting components but also with respect to the noncommutative Jauch&ndash;Piron&ndash;Amrein POV measure.

]]>Mathematics doi: 10.3390/math12081139

Authors: Chenchen Peng Haiyi Yang Anqing Yang Ling Ren

This article designs an observer for the joint estimation of the state and the unknown input for a class of nonlinear fractional-order systems (FOSs) such that one portion satisfies the Lipschitz condition and the other does not necessarily satisfy such a condition. Firstly, by reconstructing system dynamics, the observer design is transformed equivalently into the tracking problem between the original nonlinear FOSs and the designed observer. Secondly, the parameterized matrices of the desired observer are derived by use of the property of the generalized inverse matrices and the linear matrix inequality (LMI) technique combined with the Schur complement lemma. Moreover, an algorithm is presented to determine the desired observer for the nonlinear FOSs effectively. Finally, a numerical example is reported to verify the correctness and efficiency of the proposed algorithm.

]]>Mathematics doi: 10.3390/math12081138

Authors: Hongbo Chen Zhenwei Ma Jinbo Wang Linfeng Su

Additional Notes on Article [...]

]]>Mathematics doi: 10.3390/math12081136

Authors: Amadeo Hernández Rosa María Ortega-Mendoza Esaú Villatoro-Tello César Joel Camacho-Bello Obed Pérez-Cortés

Human&ndash;robot interaction is becoming increasingly common to perform useful tasks in everyday life. From the human&ndash;machine communication perspective, achieving effective interaction in natural language is one challenge. To address it, natural language processing strategies have recently been used, commonly following a supervised machine learning framework. In this context, most approaches rely on the use of linguistic resources (e.g., taggers or embeddings), including training corpora. Unfortunately, such resources are scarce for some languages in specific domains, increasing the complexity of solution approaches. Motivated by these challenges, this paper explores deep learning methods for understanding natural language commands emitted to service robots that guide their movements in low-resource scenarios, defined by the use of Spanish and Nahuatl languages, for which linguistic resources are scarcely unavailable for this specific task. Particularly, we applied natural language understanding (NLU) techniques using deep neural networks and transformers-based models. As part of the research methodology, we introduced a labeled dataset of movement commands in the mentioned languages. The results show that models based on transformers work well to recognize commands (intent classification task) and their parameters (e.g., quantities and movement units) in Spanish, achieving a performance of 98.70% (accuracy) and 96.96% (F1) for the intent classification and slot-filling tasks, respectively). In Nahuatl, the best performance obtained was 93.5% (accuracy) and 88.57% (F1) in these tasks, respectively. In general, this study shows that robot movements can be guided in natural language through machine learning models using neural models and cross-lingual transfer strategies, even in low-resource scenarios.

]]>Mathematics doi: 10.3390/math12081137

Authors: Xiaoou Li Yingqin Zhu

This paper presents a novel data-driven approach for enhancing time series forecasting accuracy when faced with missing data. Our proposed method integrates an Echo State Network (ESN) with ARIMA (Autoregressive Integrated Moving Average) modeling, frequency decomposition, and online transfer learning. This combination specifically addresses the challenges missing data introduce in time series prediction. By using the strengths of each technique, our framework offers a robust solution for handling missing data and achieving superior forecasting accuracy in real-world applications. We demonstrate the effectiveness of the proposed model through a wind speed prediction case study. Compared to the existing methods, our approach achieves significant improvement in prediction accuracy, paving the way for more reliable decisionmaking in wind energy operations and management.

]]>Mathematics doi: 10.3390/math12081135

Authors: Lu Lu Sujit Ghosh

Conditional copulas are useful tools for modeling the dependence between multiple response variables that may vary with a given set of predictor variables. Conditional dependence measures such as conditional Kendall&rsquo;s tau and Spearman&rsquo;s rho that can be expressed as functionals of the conditional copula are often used to evaluate the strength of dependence conditioning on the covariates. In general, semiparametric estimation methods of conditional copulas rely on an assumed parametric copula family where the copula parameter is assumed to be a function of the covariates. The functional relationship can be estimated nonparametrically using different techniques, but it is required to choose an appropriate copula model from various candidate families. In this paper, by employing the empirical checkerboard Bernstein copula (ECBC) estimator, we propose a fully nonparametric approach for estimating conditional copulas, which does not require any selection of parametric copula models. Closed-form estimates of the conditional dependence measures are derived directly from the proposed ECBC-based conditional copula estimator. We provide the large-sample consistency of the proposed estimator as well as the estimates of conditional dependence measures. The finite-sample performance of the proposed estimator and comparison with semiparametric methods are investigated through simulation studies. An application to real case studies is also provided.

]]>Mathematics doi: 10.3390/math12081134

Authors: Mostafa Sadeghian Asif Jamil Arvydas Palevicius Giedrius Janusas Vytenis Naginevicius

In this context, the nonlinear bending investigation of a sector nanoplate on the elastic foundation is carried out with the aid of the nonlocal strain gradient theory. The governing relations of the graphene plate are derived based on the higher-order shear deformation theory (HSDT) and considering von Karman nonlinear strains. Contrary to the first shear deformation theory (FSDT), HSDT offers an acceptable distribution for shear stress along the thickness and removes the defects of FSDT by presenting acceptable precision without a shear correction parameter. Since the governing equations are two-dimensional and partial differential, the extended Kantorovich method (EKM) and differential quadrature (DQM) have been used to solve the equations. Furthermore, the numeric outcomes were compared with a reference, which shows good harmony between them. Eventually, the effects of small-scale parameters, load, boundary conditions, geometric dimensions, and elastic foundations are studied on maximum nondimensional deflection. It can be concluded that small-scale parameters influence the deflection of the sector nanoplate significantly.

]]>Mathematics doi: 10.3390/math12081133

Authors: Guruprakash Jayabalasamy Cyril Pujol Krithika Latha Bhaskaran

Blockchain technology, serving as the backbone for decentralized systems, facilitates secure and transparent transactional data storage across a distributed network of nodes. Blockchain platforms rely on distributed ledgers to enable secure peer-to-peer transactions without central oversight. As these systems grow in complexity, analyzing their topological structure and vulnerabilities requires robust mathematical frameworks. This paper explores applications of graph theory for modeling blockchain networks to evaluate decentralization, security, privacy, scalability and NFT Mapping. We use graph metrics like degree distribution and betweenness centrality to quantify node connectivity, identify network bottlenecks, trace asset flows and detect communities. Attack vectors are assessed by simulating adversarial scenarios within graph models of blockchain systems. Overall, translating blockchain ecosystems into graph representations allows comprehensive analytical insights to guide the development of efficient, resilient decentralized infrastructures.

]]>Mathematics doi: 10.3390/math12081132

Authors: Zhifu Jia Cunlin Li

This paper describes a kind of linear quadratic uncertain stochastic hybrid differential game system grounded in the framework of subadditive measures, in which the system dynamics are described by a hybrid differential equation with Wiener&ndash;Liu noise and the performance index function is quadratic. Firstly, we introduce the concept of hybrid differential games and establish the Max&ndash;Min Lemma for the two-player zero-sum game scenario. Next, we discuss the analysis of saddle-point equilibrium strategies for linear quadratic hybrid differential games, addressing both finite and infinite time horizons. Through the incorporation of a generalized Riccati differential equation (GRDE) and guided by the principles of the It&ocirc;&ndash;Liu formula, we prove that that solving the GRDE is crucial and serves as both a sufficient and necessary precondition for identifying equilibrium strategies within a finite horizon. In addition, we also acquire the explicit formulations of equilibrium strategies in closed forms, alongside determining the optimal values of the cost function. Through the adoption of a generalized Riccati equation (GRE) and applying a similar approach to that used for the finite horizon case, we establish that the ability to solve the GRE constitutes a sufficient criterion for the emergence of equilibrium strategies in scenarios extending over an infinite horizon. Moreover, we explore the dynamics of a resource extraction problem within a finite horizon and separately delve into an H&infin; control problem applicable to an infinite horizon. Finally, we present the conclusions.

]]>Mathematics doi: 10.3390/math12081131

Authors: Shaomin Wang Cunji Yang Guozhi Cha

In this paper, we study the variational principle and the existence of periodic solutions for a new class of second-order ordinary p-Laplacian systems. The variational principle is given by making use of two methods. We obtain three existence theorems of periodic solutions to this problem on various sufficient conditions on the potential function F(t,x) or nonlinearity &nabla;F(t,x). Four examples are presented to illustrate the feasibility and effectiveness of our results.

]]>Mathematics doi: 10.3390/math12081130

Authors: Enrique Duarte Juan Ramón García Rozas Hanane Ouberka Luis Oyonarte

Recently, Gorenstein dimensions relative to a semidualizing module have been the subject of numerous studies with interesting extensions of the classical homological dimensions. Although all these studies share the same direction, a common basis, and similar final goals, there is no common framework encompassing them as parts of a whole, progressing, on different fronts, towards the same end. We provide this general and global framework in the context of abelian categories, standardizing terminology and notation: we establish a general context by defining Gorenstein categories relative to two classes of objects ((X,Y)-Gorenstein categories, denoted G(X,Y)), and carry out a study of the homological dimensions associated with them. We prove, under some mild standard conditions, the corresponding version of the Comparison Lemma that ensures the consistency of a homological-dimension theory. We show that Ext functors can be used as tools to compute these G(X,Y)-dimensions, and we compare the dimensions obtained using the classes G(X) with those computed using G(X,Y). We also initiate a research of the global dimensions obtained with these classes G(X,Y) and find conditions for them to be finite. Finally, we show that these classes of Gorenstein objects are closely and interestingly related to the Foxby classes induced by a pair of functors. Namely, we prove that the Auslander and Bass classes are indeed G(X,Y) categories for some specific classes X and Y.

]]>Mathematics doi: 10.3390/math12081129

Authors: Paulius Drungilas Jonas Jankauskas Grintas Junevičius

Let n&gt;m be positive integers. Polynomials of the form zn&plusmn;zm&plusmn;1 are called Borwein trinomials. Using an old result of Bohl, we derive explicit formulas for the number of roots of a Borwein trinomial inside the unit circle |z|&lt;1. Based on this, we determine all Borwein trinomials that have a complex Pisot number as a root. There are exactly 29 such trinomials.

]]>Mathematics doi: 10.3390/math12081128

Authors: M. N. Abu_Shugair A. A. Abdallah S. E. Abbas E. El-Sanowsy Ismail Ibedou

In this paper, we introduce the notion of p,q-fuzzy local function and DF-ideal topological space. Also, we introduce the concepts DFU-&eth;-continuous and DFL-&eth;-continuous, almost &eth;-continuous, weakly &eth;-continuous and almost weakly &eth;-continuous multifunctions. Several properties and characterizations of the introduced multifunctions and types of continuity are established. Some examples are given to explain the correct implications between these notions.

]]>Mathematics doi: 10.3390/math12081125

Authors: Xiaoman Yang Xin Zhou

Based on the definitions of fuzzy associative algebras and fuzzy ideals, it is proven that the intersections of fuzzy subalgebras are fuzzy subalgebras, and the intersections of fuzzy ideals are fuzzy ideals. Moreover, we prove that the kernels of fuzzy homomorphisms are fuzzy ideals. Using fuzzy ideals, the quotient structures of fuzzy associative algebras are constructed, their corresponding properties are discussed, and their homomorphism theorems are proven.

]]>Mathematics doi: 10.3390/math12081127

Authors: Peng Zhang Zifan Ma Zeyuan Ren Hongxiang Wang Chuankai Zhang Qing Wan Dongxue Sun

With the continuous deepening of educational reform, a large number of educational policies, programs, and research reports have emerged, bringing a heavy burden of information processing and management to educators. Traditional manual classification and archiving methods are inefficient and susceptible to subjective factors. Therefore, an automated method is needed to quickly and accurately classify and archive documents into their respective categories. Based on this, this paper proposes a design of an automatic document classification system for educational reform based on the Naive Bayes algorithm to address the challenges of document management in the education field. Firstly, the relevant literature and document data in the field of educational reform are collected and organized to establish an annotated dataset for model detection. Secondly, the raw data are preprocessed by cleaning and transforming the original text data to make them more suitable for input into machine learning algorithms. Thirdly, various algorithms are trained and selected to determine the best algorithm for classifying educational reform documents. Finally, based on the determined algorithm, a corresponding classification software is designed to automatically classify and archive educational reform documents for analysis. Through experimental evaluation and result analysis, this research demonstrates the effectiveness and accuracy of the education reform document automatic classification system based on the Naive Bayes algorithm. This method can efficiently classify a large number of documents into their respective categories quickly and accurately, thereby improving the efficiency of educators and their information management capabilities. In the future, further exploration of feature extraction methods and machine learning algorithms can be conducted to optimize the classification performance and apply this method to practical management and decision-making in the education field.

]]>Mathematics doi: 10.3390/math12081126

Authors: Eleonora Muzzupappa

This study examines the impact of the Basel Accords on competition within the UK banking sector, considering variations based on bank size. The Basel Accords, designed to enhance financial stability, introduce provisions that may affect competition dynamics. Empirical analysis reveals divergent outcomes: large banks tend towards monopolization, while other banks shift towards a more competitive environment. Large banks benefit from regulatory barriers and technological advancements, while other banks face challenges from increased compliance costs. These findings highlight the complex relationship between regulation and competition in banking, emphasizing the need for balanced regulations that promote stability while fostering healthy competition.

]]>Mathematics doi: 10.3390/math12081124

Authors: Yuqi Yang Shanshan Yu Baicheng Pan Chenglu Li Man-Fai Leung

In recent years, community detection has received increasing interest. In network analysis, community detection refers to the identification of tightly connected subsets of nodes, which are called &ldquo;communities&rdquo; or &ldquo;groups&rdquo;, in the network. Non-negative matrix factorization models are often used to solve the problem. Orthogonal non-negative matrix tri-factorization (ONMTF) exhibits significant potential as an approach for community detection within multiplex networks. This paper explores the application of ONMTF in multiplex networks, aiming to detect both shared and exclusive communities simultaneously. The model decomposes each layer within the multiplex network into two low-rank matrices. One matrix corresponds to shared communities across all layers, and the other to unique communities within each layer. Additionally, graph regularization and the diversity of private communities are taken into account in the algorithm. The Hilbert Schmidt Independence Criterion (HSIC) is used to constrain the independence of private communities. The results prove that ONMTF effectively addresses community detection in multiplex networks. It also offers strong interpretability and feature extraction capabilities. Therefore, it is an advanced method for community detection in multiplex networks.

]]>Mathematics doi: 10.3390/math12081123

Authors: Wenjie Bi Bing Wang Haiying Liu

This study investigates personalized pricing with demand learning. We first encode consumer-personalized feature information into high-dimensional vectors, then establish the relationship between this feature vector and product demand using a logit model, and finally learn demand parameters through historical transaction data. To address the balance between learning and revenue, we introduce the Thompson Sampling algorithm. Considering the difficulty of Bayesian inference in Thompson Sampling owing to high-dimensional feature vectors, we improve the basic Thompson Sampling by approximating the likelihood function of the logit model with the P&oacute;lya-Gamma (PG) distribution and by proposing a Thompson Sampling algorithm based on the PG distribution. To validate the proposed algorithm&rsquo;s effectiveness, we conduct experiments using both simulated data and real loan data provided by the Columbia University Revenue Management Center. The study results demonstrate that the Thompson Sampling algorithm based on the PG distribution proposed outperforms traditional Laplace approximation methods regarding convergence speed and regret value in both real and simulated data experiments. The real-time personalized pricing algorithm developed here not only enriches the theoretical research of personalized dynamic pricing, but also provides a theoretical basis and guidance for enterprises to implement personalized pricing.

]]>Mathematics doi: 10.3390/math12071122

Authors: Salma Aljawi Kais Feki Zakaria Taki

We investigate a novel operator seminorm, QA,m&lambda;,f, for an A-bounded operator Q, where A is a positive operator on a complex Hilbert space (K,&#10216;&middot;,&middot;&#10217;). This seminorm is defined using a continuous increasing and bijective function f:R+&#10230;R+ and an interpolational path m&lambda; of the symmetric mean m. Specifically, QA,m&lambda;,f=supf&minus;1fQy,yAm&lambda;fQyA:y&isin;K,yA=1, where f&minus;1 represents the reciprocal function of f, and &#10216;&middot;,&middot;&#10217;A and &middot;A denote the semi-inner product and seminorm, respectively, induced by A on K. We explore various bounds and relationships associated with this new concept, establishing connections with existing literature.

]]>Mathematics doi: 10.3390/math12071121

Authors: Tao Liu Stanford Shateyi

An effective strategy to enhance the convergence order of nodal approximations in interpolation or PDE problems is to increase the size of the stencil, albeit at the cost of increased computational burden. In this study, our goal is to improve the convergence orders for approximating the first and second derivatives of sufficiently differentiable functions using the radial basis function-generated Hermite finite-difference (RBF-HFD) scheme. By utilizing only three equally spaced points in 1D, we are able to boost the convergence rate to four. Extensive tests have been conducted to demonstrate the effectiveness of the proposed theoretical weighting coefficients in solving interpolation and PDE problems.

]]>Mathematics doi: 10.3390/math12071120

Authors: Ruwen Zhao Chuanpei Xu Zhibin Zhu Wei Mo

Real-time electrical impedance tomography (EIT) data sharing is becoming increasingly necessary, due to the extensive use of EIT technology in various sectors, including material analysis, biomedicine, and industrial process monitoring. The prevalence of portable EIT equipment and remote imaging technology has led to a predominance of centralized storage, Internet protocol transmission, and certificates from certificate authorities (CA) in telemedicine data. This has resulted in compromised data security, network communication delays, high CA maintenance costs, increased risks of medical data privacy breaches, and low security. Therefore, this paper offers a consortia blockchain-based method for exchanging EIT data that addresses security and integrity concerns during data storage and exchange, while maintaining transparency and traceability. Proprietary re-encryption techniques are employed to guarantee traceability when exchanging anonymous data, enabling precise control over data access. This scheme serves to protect both data and identity privacy, as well as to trace the actual identity of potential malicious users, while also thwarting any coordinated efforts between partially trusted parties and data requesters seeking unauthorized access to confidential information. Additionally, a combination of blockchain and InterPlanetary File System (IPFS) distributed storage technology is utilized to ease the burden of EIT data storage. The feasibility and effectiveness of the proposed solution were validated through a series of experiments, demonstrating its ability to effectively prevent data tampering and misuse, reduce data management costs, and enhance the efficiency and quality of data sharing.

]]>Mathematics doi: 10.3390/math12071119

Authors: Daijun Ding Genan Dai Cheng Peng Xiaojiang Peng Bowen Zhang Hu Huang

Investigating public attitudes on social media is crucial for opinion mining systems. Stance detection aims to predict the attitude towards a specific target expressed in a text. However, effective neural stance detectors require substantial training data, which are challenging to curate due to the dynamic nature of social media. Moreover, deep neural networks (DNNs) lack explainability, rendering them unsuitable for scenarios requiring explanations. We propose a distantly supervised explainable stance detection framework (DS-ESD), comprising an instruction-based chain-of-thought (CoT) method, a generative network, and a transformer-based stance predictor. The CoT method employs prompt templates to extract stance detection explanations from a very large language model (VLLM). The generative network learns the input-explanation mapping, and a transformer-based stance classifier is trained with VLLM-annotated stance labels, implementing distant supervision. We propose a label rectification strategy to mitigate the impact of erroneous labels. Experiments on three benchmark datasets showed that our model outperformed the compared methods, validating its efficacy in stance detection tasks. This research contributes to the advancement of explainable stance detection frameworks, leveraging distant supervision and label rectification strategies to enhance performance and interpretability.

]]>Mathematics doi: 10.3390/math12071118

Authors: Tianyi Wang Luxin Zhang Zhihua Chen

Dynamic surface control (DSC) is a recognized nonlinear control approach for high-order systems. However, as the complexity of the system increases and the first-order filter (FOF) is introduced, there exists a singularity problem, i.e., the control input will reach infinity. This limits the application of the DSC algorithm to a class of real-world systems with complex dynamics. To address the problem of singularity, we present a novel DSC approach called nonsingular dynamic surface control (NDSC), which completely avoids the singularity problem and significantly improves the overall control performance. NDSC includes a nonsingular hypersurface, which is constructed by the error between system states and virtual control inputs. Then the nonsingular hypersurface will be applied to derive the corresponding control law with the aid of the DSC approach to ensure the output of the system can track arbitrary desired trajectories. NDSC has the following novel features: (1) finite time asymptotic stabilization can be guaranteed; (2) the performance of NDSC is insensitive to the FOF&rsquo;s parameter variation once the maximum tracking error of FOF is bounded, which significantly reduces reliance on the control sampling frequency. We thoroughly evaluate the proposed NDSC algorithm in an unmanned aerial vehicle (UAV) system with an underactuated nature. Finally, the simulation results illustrate and highlight the effectiveness and superiority of the proposed control algorithm.

]]>Mathematics doi: 10.3390/math12071117

Authors: Evariste Sanchez-Palencia M. A. Aziz-Alaoui

We give a series of numerical examples of competitive evolution in the predation system, showing in some cases how the choice is made to increase the efficiency of the predation mechanism (or other significant parameters) to the detriment of populations (both of prey and predators). We then develop the mathematical theory that enables us to understand the causality involved, and we identify a trend towards the emergence of the functional predation mechanism as such (and not of populations of the species involved). The realization of this trend only takes place when the conditions for it are offered by the hazards proposed to successive competitive choices. The logical structure of this trend is similar to that of the &ldquo;tendency of rate of profit to fall&rdquo; in certain economic models.

]]>Mathematics doi: 10.3390/math12071116

Authors: Hongbing Chen Fengling Jia

A critical function of polymeric matrices in biological systems is to exert selective control over the transport of thousands of nanoparticulate species. Utilizing &ldquo;third-party&rdquo; molecular anchors to crosslink nanoparticulates to the matrix is an effective strategy, and a trapped nanoparticulate formed a desired complex MAP that is necessary to keep the nanoparticulate immobilized at any given time. In this paper, the global solution and stability of a parabolic&ndash;ordinary-parabolic haptotaxis system to complex MAP are studied. First, the existence of a local classical solution to system (4) has been observed using fixed point argument and parabolic Schauder estimates. Furthermore, some a priori estimates that can raise the regularity estimate of the solution for the relatively complicated first equation of system (3) from L&rho; to L2&rho; (&rho;&ge;1) are given; then, the local classic solution can thus extend to the global classic solution when the space dimension N&le;3. Lastly, by using various analytical methods, a threshold value &xi;00(&xi;00&lt;0) is found, such that positive constant steady state (u&lowast;,v&lowast;,w&lowast;) becomes unstable when &xi;&lt;&xi;00. Our results show that the haptotaxis plays a crucial role in determining the stability to the model (3), that is, it can have a destabilizing effect.

]]>Mathematics doi: 10.3390/math12071115

Authors: Hongri Cong Bo Wang Zhe Wang

Optimization, particularly constrained optimization problems (COPs), is fundamental in engineering, influencing various sectors with its critical role in enhancing design efficiency, reducing experimental costs, and shortening testing cycles. This study explores the challenges inherent in COPs, with a focus on developing efficient solution methodologies under stringent constraints. Surrogate models, especially Gaussian Process Regression (GPR), are pivotal in our approach, enabling the approximation of complex systems with reduced computational demand. We evaluate the efficacy of the Efficient Global Optimization (EGO) algorithm, which synergizes GPR with the Expected Improvement (EI) function, and further extend this framework to Constrained Expected Improvement (CEI) and our novel methodology Constrained Expected Prediction Error (CEPE). We demonstrate the effectiveness of these methodologies by numerical benchmark simulations and the real-world application of optimizing a Three-Bar Truss Design. In essence, the innovative CEPE approach promises a potent balance between solution accuracy and computational prowess, offering significant potential in the broader engineering field.

]]>Mathematics doi: 10.3390/math12071114

Authors: Junjun Jiao Ruijie Guan

For a common type of mixture distribution, namely the mixture normal distribution, existing methods for constructing its tolerance interval are unsatisfactory for cases of small sample size and large content. In this study, we propose a method to construct a tolerance interval for the mixture normal distribution based on the generalized extreme value theory. The proposed method is implemented on simulated as well as real-life datasets and its performance is compared with the existing methods.

]]>Mathematics doi: 10.3390/math12071113

Authors: Iman Bahmani Jafarloo Cristiano Bocci Elena Guardo

In this paper, we generalize and study the concept of Hadamard product of ideals of projective varieties to the case of monomial ideals. We have a research direction similar to the one of the join of monomial ideals contained in a paper of Sturmfels and Sullivant. In the second part of the paper, we give a brief tutorial on the Hadamard.m2 package of Macaulay2.

]]>Mathematics doi: 10.3390/math12071112

Authors: Ali M. Jasim Basil H. Jasim Florin-Constantin Baiceanu Bogdan-Constantin Neagu

In the original publication [...]

]]>Mathematics doi: 10.3390/math12071111

Authors: Jianhui Li Yan Liu Wanru Zhao Tianning Zhu

This paper introduces an application of the dandelion optimization (DO) algorithm in antenna arrays. This is the first time that the DO algorithm has been used for optimizing antenna arrays. For antenna array optimization, sidelobe level (SLL) and deep nulls are key technical indicators. A lower SLL can improve the signal-to-noise ratio and reduce the impact of clutter signals outside the main beam. Deep nulls need to be aligned with the direction of interference to eliminate the influence of interference sources. The combination of the two can effectively improve the anti-interference ability of the entire system. Therefore, antenna arrays with ultra-low sidelobes and ultra-deep nulls are currently hot in the field of antenna array design and are also some of the key technologies needed to achieve modern high-performance radar systems. As a new type of evolutionary algorithm inspired by nature, the DO algorithm is inspired by the wind propagation behavior of dandelions in nature. This algorithm iteratively updates the population from three stages of ascent, descent, and landing, ultimately finding the optimal position. It has good optimization ability in solving complex problems such as those involving nonlinearity, discreteness, and non-convexity, and the antenna array pattern synthesis optimization problem belongs to multivariate nonlinear problems. Therefore, the DO algorithm can be effectively applied in the field of antenna array optimization. In this work, we use the following method to obtain an optimized pattern of a linear array with the lowest sidelobe level (SLL), null placement in particular directions, and a lower notch in particular directions: by controlling the antenna array&rsquo;s element spacing and leaving the phase unchanged to optimize the current amplitudes and by controlling the excitation current and phase fixation of the antenna array and changing the element spacing. In the first and second examples, different algorithms are used to reduce the SLL of the antenna. In the first example, the DO algorithm reduces the SLL to &minus;33.37 dB, which is 2.67 dB, 2.67 dB, 3.77 dB, 2.74 dB, and 2.52 dB lower than five other algorithms. In the second example, the SLL optimized by the DO algorithm is &minus;42.56 dB, which is 5.04 dB and 1.48 dB lower than two other algorithms. In both examples, the DO algorithm reduces the SLL lower than other algorithms when the main lobe of the antenna is not significantly widened. Examples 3, 4, and 5 use the DO algorithm to optimize the amplitude of the current, generating deep nulls and deep notches in specific directions. In Example 3, the DO algorithm obtains a depth of nulls equal to &minus;187.6 dB, which is 66.7 dB and 44.3 dB lower than that of the flower pollination algorithm (FPA) and the chaotic colony predation algorithm (CCPA), respectively. In Example 4, the deep null obtained by the DO algorithm is as low as &minus;98.69 dB, which is 6.67 dB lower than the deep null obtained by the grey wolf optimization (GWO) algorithm. In Example 5, the deep notch obtained by the DO algorithm is as low as &minus;63.1 dB, which is 6.4 dB and 1.9 dB lower than the spider monkey optimization (SMO) algorithm and the grasshopper optimization algorithm (GOA), respectively. The data prove that the DO algorithm produces deeper nulls and notches than other algorithms. The last two examples involve reducing sidelobe levels and generating deep nulls by optimizing the spacing between elements. In Example 5, the SLL obtained using the DO algorithm is &minus;22.8766 dB, which is 0.1998 dB lower than the lowest SLL of &minus;22.6768 dB among other algorithms. In Example 6, the SLL obtained using the DO algorithm is &minus;20.1012 dB, and the null depth is &minus;125.1 dB, which is 1.592 dB lower than the SLL obtained by the cat swarm optimization (CSO) algorithm and 19.1 dB lower than the deep null obtained by the GWO algorithm, respectively. In summary, the results of six simulation experiments indicate that the DO algorithm has better optimization ability in linear array optimization than other evolutionary algorithms.

]]>Mathematics doi: 10.3390/math12071110

Authors: Peiyao Wang Shangwen Peng Yihao Cao Rongpei Zhang

This paper introduces a novel approach employing the fast cosine transform to tackle the 2-D and 3-D fractional nonlinear Schr&ouml;dinger equation (fNLSE). The fractional Laplace operator under homogeneous Neumann boundary conditions is first defined through spectral decomposition. The difference matrix Laplace operator is developed by the second-order central finite difference method. Then, we diagonalize the difference matrix based on the properties of Kronecker products. The time discretization employs the Crank&ndash;Nicolson method. The conservation of mass and energy is proved for the fully discrete scheme. The advantage of this method is the implementation of the Fast Discrete Cosine Transform (FDCT), which significantly improves computational efficiency. Finally, the accuracy and effectiveness of the method are verified through two-dimensional and three-dimensional numerical experiments, solitons in different dimensions are simulated, and the influence of fractional order on soliton evolution is obtained; that is, the smaller the alpha, the lower the soliton evolution.

]]>Mathematics doi: 10.3390/math12071109

Authors: Longlong He Ruiyu Pan Yafei Wang Jiani Gao Tianze Xu Naqi Zhang Yue Wu Xuhui Zhang

In the face of the increasing complexity of risk factors in the coal mining transportation system (CMTS) during the process of intelligent transformation, this study proposes a method for analyzing accidents in CMTS based on fault tree analysis (FTA) combined with Bayesian networks (BN) and preliminary hazard analysis (PHA). Firstly, the fault tree model of CMTS was transformed into a risk Bayesian network, and the inference results of the fault tree and Bayesian network were integrated to identify the key risk factors in the transportation system. Subsequently, based on the preliminary hazard analysis of these key risk factors, corresponding rectification measures and a risk control system construction plan are proposed. Finally, a case study was carried out on the X coal mine as a pilot mine to verify the feasibility of the method. The application of this method effectively identifies and evaluates potential risk factors in CMTS, providing a scientific basis for accident prevention. This research holds significant importance for the safety management and decision making of coal mine enterprises during the process of intelligent transformation and is expected to provide strong support for enhancing the safety and reliability of CMTS.

]]>Mathematics doi: 10.3390/math12071108

Authors: Yihong Liu Yeguo Sun

Asymptotic synchronization requires continuous external control of the system, which is unrealistic considering the cost of control. Adaptive control methods have strong robustness to uncertainties such as disturbances and unknowns. On the other hand, for finite-time synchronization, if the initial value of the system is unknown, the synchronization time of the finite-time synchronization cannot be estimated. This paper explores the finite-time adaptive synchronization (FTAS) and fixed-time synchronization (FDTS) of fractional-order memristive cellular neural networks (FMCNNs) with time-varying delays (TVD). Utilizing the properties and principles of fractional order, we introduce a novel lemma. Based on this lemma and various analysis techniques, we establish new criteria to guarantee FTAS and FDTS of FMCNNs with TVD through the implementation of a delay-dependent feedback controller and fractional-order adaptive controller. Additionally, we estimate the upper bound of the synchronization setting time. Finally, numerical simulations are conducted to confirm the validity of the finite-time and fixed-time stability theorems.

]]>Mathematics doi: 10.3390/math12071106

Authors: Zuoxun Hou Ruichen Yuan Zihao Wang Xiaorui Wei Chujian Ren Jiale Zhou Xiaolei Qu

Breast cancer is a global health concern, emphasizing the need for early detection. However, current mammography struggles to effectively image dense breasts. Breast ultrasound can be an adjunctive method, but it is highly dependent on operator skill. Ultrasound computed tomography (USCT) reflection imaging provides high-quality 3D images, but often uses delay-and-sum (DAS) beamforming, which limits its image quality. This article proposes the integration of coherence-factor (CF) beamforming into ultrasound computed tomography (USCT) reflection imaging to enhance image quality. CF assesses the focus quality of beamforming by analyzing the signal coherence across different channels, assigning higher weights to high-quality focus points and thereby improving overall image quality. Numerical simulations and phantom experiments using our built USCT prototype were conducted to optimize the imaging parameters and assess and compare the image quality of CF and DAS beamforming. Numerical simulations demonstrated that CF beamforming can significantly enhance image quality. Phantom experiments with our prototype revealed that CF beamforming significantly improves image resolution (from 0.35 mm to 0.14 mm) and increases contrast ratio (from 24.54 dB to 63.28 dB). The integration of CF beamforming into USCT reflection imaging represents a substantial improvement in image quality, offering promise for enhanced breast cancer detection and imaging capabilities.

]]>Mathematics doi: 10.3390/math12071107

Authors: Zhihua Duan Chun Wang Wending Zhong

As user&ndash;item interaction information is typically limited, collaborative filtering (CF)-based recommender systems often suffer from the data sparsity issue. To address this issue, recent recommender systems have turned to graph neural networks (GNNs) due to their superior performance in capturing high-order relationships. Furthermore, some of these GNN-based recommendation models also attempt to incorporate other information. They either extract self-supervised signals to mitigate the data sparsity problem or employ social information to assist with learning better representations under a social recommendation setting. However, only a few methods can take full advantage of these different aspects of information. Based on some testing, we believe most of these methods are complex and redundantly designed, which may lead to sub-optimal results. In this paper, we propose SSGCL, which is a recommendation system model that utilizes both social information and self-supervised information. We design a GNN-based propagation strategy that integrates social information with interest information in a simple yet effective way to learn user&ndash;item representations for recommendations. In addition, a specially designed contrastive learning module is employed to take advantage of the self-supervised signals for a better user&ndash;item representation distribution. The contrastive learning module is jointly optimized with the recommendation module to benefit the final recommendation result. Experiments on several benchmark data sets demonstrate the significant improvement in performance achieved by our model when compared with baseline models.

]]>Mathematics doi: 10.3390/math12071105

Authors: Shaojun Wang Fei Wen Guoxing Wang Zepeng Li

A fall k-coloring of a graph G is a proper k-coloring of G such that each vertex has at least one neighbor in each of the other color classes. A graph G which has a fall k-coloring is equivalent to having a partition of the vertex set V(G) in k independent dominating sets. In this paper, we first prove that for any fall k-colorable graph G with order n, the number of edges of G is at least (n(k&minus;1)+r(k&minus;r))/2, where r&equiv;n(modk) and 0&le;r&le;k&minus;1, and the bound is tight. Then, we obtain that if G is k-colorable (k&ge;2) and the minimum degree of G is at least k&minus;2k&minus;1n, then G is fall k-colorable and this condition of minimum degree is the best possible. Moreover, we give a simple proof for an NP-hard result of determining whether a graph is fall k-colorable, where k&ge;3. Finally, we show that there exist an infinite family of fall k-colorable planar graphs for k&isin;{5,6}.

]]>Mathematics doi: 10.3390/math12071104

Authors: Yongsheng Rao Jianwei Su Behrouz Kheirfam

In this paper, a new full-Newton step feasible interior-point method for convex quadratic programming is presented and analyzed. The idea behind this method is to replace the complementarity condition with a non-negative weight vector and use the algebraic equivalent transformation for the obtained equation. Under the selection of appropriate parameters, the quadratic rate of convergence of the new algorithm is established. In addition, the iteration complexity of the algorithm is obtained. Finally, some numerical results are presented to demonstrate the practical performance of the proposed algorithm.

]]>Mathematics doi: 10.3390/math12071103

Authors: Awais Akhtar Rehan Ahmed Muhammad Haroon Yousaf Sergio A. Velastin

Motorbikes are an integral part of transportation in emerging countries, but unfortunately, motorbike users are also one the most vulnerable road users (VRUs) and are engaged in a large number of yearly accidents. So, motorbike detection is very important for proper traffic surveillance, road safety, and security. Most of the work related to bike detection has been carried out to improve accuracy. If this task is not performed in real-time then it loses practical significance, but little to none has been reported for its real-time implementation. In this work, we have looked at multiple real-time deployable cost-efficient solutions for motorbike detection using various state-of-the-art embedded edge devices. This paper discusses an investigation of a proposed methodology on five different embedded devices that include Jetson Nano, Jetson TX2, Jetson Xavier, Intel Compute Stick, and Coral Dev Board. Running the highly compute-intensive object detection model on edge devices (in real-time) is made possible by optimization. As a result, we have achieved inference rates on different devices that are twice as high as GPUs, with only a marginal drop in accuracy. Secondly, the baseline accuracy of motorbike detection has been improved by developing a custom network based on YoloV5 by introducing sparsity and depth reduction. Dataset augmentation has been applied at both image and object levels to enhance robustness of detection. We have achieved 99% accuracy as compared to the previously reported 97% accuracy, with better FPS. Additionally, we have provided a performance comparison of motorbike detection on the different embedded edge devices, for practical implementation.

]]>Mathematics doi: 10.3390/math12071102

Authors: Cristina E. Hretcanu

The present editorial contains 11 research articles, published in the Special Issue entitled &ldquo;Submanifolds in metric manifolds&rdquo; of the MDPI mathematics journal, which cover a wide range of topics from differential geometry in relation to the theory and applications of the structure induced on submanifolds by the structure defined on various ambient manifolds [...]

]]>Mathematics doi: 10.3390/math12071101

Authors: C. D’Apice A. N. Dudin O. S. Dudina R. Manzo

We consider a multi-server queueing system with a visible queue and an arrival flow that is dynamically dependent on the system&rsquo;s rating. This rating reflects the level of customer satisfaction with the quality and price of the provided service. A higher rating implies a higher arrival rate, which motivates the service provider to increase the price of the service. A steady-state analysis of this system using the proposed mechanism for changing the rating and a threshold strategy for changing the price is performed. This is carried out via the consideration of a suitably constructed multidimensional Markov chain. The impact of the variation in the threshold defining the strategy for changing the price on the key performance indicators is numerically illustrated. The results can be used to make managerial decisions, leading to an increase in the effectiveness of system operations.

]]>Mathematics doi: 10.3390/math12071100

Authors: Zihao Chen Yuyang Li Cindy Long Yu

Implied volatility is known to have a string structure (smile curve) for a given time to maturity and can be captured by the B-spline. The parameters characterizing the curves can change over time, which complicates the modeling of the implied volatility surface. Although machine learning models could improve the in-sample fitting, they ignore the structure in common over time and might have poor prediction power. In response to these challenges, we propose a two-step procedure to model the dynamic implied volatility surface (IVS). In the first step, we construct the bivariate tensor-product B-spline (BTPB) basis to approximate cross-sectional structures, under which the surface can be represented by a vector of coefficients. In the second step, we allow for the time-dependent coefficients and model the dynamic coefficients with the tree-based method to provide more flexibility. We show that our approach has better performance than the traditional linear models (parametric models) and the tree-based machine learning methods (nonparametric models). The simulation study confirms that the tensor-product B-spline is able to capture the classical parametric model for IVS given different sample sizes and signal-to-noise ratios. The empirical study shows that our two-step approach outperforms the traditional parametric benchmark, nonparametric benchmark, and parametric benchmark with time-varying coefficients in predicting IVS for the S&amp;P 500 index options in the US market.

]]>Mathematics doi: 10.3390/math12071099

Authors: Sami Alabiad Alhanouf Ali Alhomaidhi Nawal A. Alsarori

The study of linear codes over local rings, particularly non-chain rings, imposes difficulties that differ from those encountered in codes over chain rings, and this stems from the fact that local non-chain rings are not principal ideal rings. In this paper, we present and successfully establish a new approach for linear codes of any finite length over local rings that are not necessarily chains. The main focus of this study is to produce generating characters, MacWilliams identities and generator matrices for codes over singleton local Frobenius rings of order 32. To do so, we first start by characterizing all singleton local rings of order 32 up to isomorphism. These rings happen to have strong connections to linear binary codes and Z4 codes, which play a significant role in coding theory.

]]>Mathematics doi: 10.3390/math12071097

Authors: Isabella Torcicollo Maria Vitiello

A nonlinear crime model is generalized by introducing self- and cross-diffusion terms. The effect of diffusion on the stability of non-negative constant steady states is applied. In particular, the cross-diffusion-driven instability, called Turing instability, is analyzed by linear stability analysis, and several Turing patterns driven by the cross-diffusion are studied through numerical investigations. When the Turing&ndash;Hopf conditions are satisfied, the type of instability highlighted in the ODE model persists in the PDE system, still showing an oscillatory behavior.

]]>Mathematics doi: 10.3390/math12071098

Authors: Shokofeh Zinodiny Saralees Nadarajah

Bayes minimax estimation is important because it provides a robust approach to statistical estimation that considers the worst-case scenario while incorporating prior knowledge. In this paper, Bayes minimax estimation of the mean matrix of a matrix variate normal distribution is considered under the quadratic loss function. A large class of (proper and generalized) Bayes minimax estimators of the mean matrix is presented. Two examples are given to illustrate the class of estimators, showing, among other things, that the class includes classes of estimators presented by Tsukuma.

]]>Mathematics doi: 10.3390/math12071096

Authors: Mohamed Mazen Mohamed M. A. El-Sheikh Samah Euat Tallah Gamal A. F. Ismail

In this paper, we discuss the oscillatory behavior of solutions of two general classes of nonlinear second-order differential equations. New criteria are obtained using Riccati transformations and the integral averaging techniques. The obtained results improve and generalize some recent criteria in the literature. Moreover, a traditional condition is relaxed. Three examples are given to justify the results.

]]>Mathematics doi: 10.3390/math12071095

Authors: Peter M. Mphekgwana Yehenew G. Kifle Chioneso S. Marange

The challenge of combining two unbiased estimators is a common occurrence in applied statistics, with significant implications across diverse fields such as manufacturing quality control, medical research, and the social sciences. Despite the widespread relevance of estimating the common population mean &mu;, this task is not without its challenges. A particularly intricate issue arises when the variations within populations are unknown or possibly unequal. Conventional approaches, like the two-sample t-test, fall short in addressing this problem as they assume equal variances among the two populations. When there exists prior information regarding population variances (&sigma;i2,i=1,2), with the consideration that &sigma;12 and &sigma;22 might be equal, a hypothesis test can be conducted: H0:&sigma;12=&sigma;22 versus H1:&sigma;12&ne;&sigma;22. The initial sample is utilized to test H0, and if we fail to reject H0, we gain confidence in incorporating our prior knowledge (after testing) to estimate the common mean &mu;. However, if H0 is rejected, indicating unequal population variances, the prior knowledge is discarded. In such cases, a second sample is obtained to compensate for the loss of prior knowledge. The estimation of the common mean &mu; is then carried out using either the Graybill&ndash;Deal estimator (GDE) or the maximum likelihood estimator (MLE). A noteworthy discovery is that the proposed preliminary testimators, denoted as &mu;^PT1 and &mu;^PT2, exhibit superior performance compared to the widely used unbiased estimators (GDE and MLE).

]]>Mathematics doi: 10.3390/math12071094

Authors: Longfei Jia Yuguo Hu Xianlong Tian Wenwei Luo Yanning Ye

In edge computing environments, limited storage and computational resources pose significant challenges to complex super-resolution network models. To address these challenges, we propose an agile super-resolution network via intelligent path selection (ASRN) that utilizes a policy network for dynamic path selection, thereby optimizing the inference process of super-resolution network models. Its primary objective is to substantially reduce the computational burden while maximally maintaining the super-resolution quality. To achieve this goal, a unique reward function is proposed to guide the policy network towards identifying optimal policies. The proposed ASRN not only streamlines the inference process but also significantly boosts inference speed on edge devices without compromising the quality of super-resolution images. Extensive experiments across multiple datasets confirm ASRN&rsquo;s remarkable ability to accelerate inference speeds while maintaining minimal performance degradation. Additionally, we explore the broad applicability and practical value of ASRN in various edge computing scenarios, indicating its widespread potential in this rapidly evolving domain.

]]>Mathematics doi: 10.3390/math12071092

Authors: Yingchun Jiang Ni Gao Haizhen Li

The nonuniform sampling and reconstruction of bandlimited random signals in the SAFT domain is discussed in the paper, where the nonuniform samples are obtained by randomly disturbing the uniform sampling. First, we prove that the concerned nonuniform problem is equivalent to the process of uniform sampling after a prefilter in the statistic sense. Then, an approximate reconstruction method based on sinc interpolation is proposed for the randomized nonuniform sampling of SAFT-bandlimited random signals. Finally, we offer the mean square error estimate for the corresponding approximate recovery approach. The results generalize the conclusions of nonuniform sampling of bandlimited random signals in the FrFT and LCT domains to the SAFT domain.

]]>Mathematics doi: 10.3390/math12071093

Authors: Raúl Montes-Pajuelo Ángel M. Rodríguez-Pérez Raúl López César A. Rodríguez

Exploring the realm of extreme weather events is indispensable for various engineering disciplines and plays a pivotal role in understanding climate change phenomena. In this study, we examine the ability of 10 probability distribution functions&mdash;including exponential, normal, two- and three-parameter log-normal, gamma, Gumbel, log-Gumbel, Pearson type III, log-Pearson type III, and SQRT-ET max distributions&mdash;to assess annual maximum 24 h rainfall series obtained over a long period (1972&ndash;2022) from three nearby meteorological stations. Goodness-of-fit analyses including Kolmogorov&ndash;Smirnov and chi-square tests reveal the inadequacy of exponential and normal distributions in capturing the complexity of the data sets. Subsequent frequency analysis and multi-criteria assessment enable us to discern optimal functions for various scenarios, including hydraulic engineering and sediment yield estimation. Notably, the log-Gumbel and three-parameter log-normal distributions exhibit superior performance for high return periods, while the Gumbel and three-parameter log-normal distributions excel for lower return periods. However, caution is advised regarding the overuse of log-Gumbel, due to its high sensitivity. Moreover, as our study considers the application of mathematical and statistical methods for the detection of extreme events, it also provides insights into climate change indicators, highlighting trends in the probability distribution of annual maximum 24 h rainfall. As a novelty in the field of functional analysis, the log-Gumbel distribution with a finite sample size is utilised for the assessment of extreme events, for which no previous work seems to have been conducted. These findings offer critical perspectives on extreme rainfall modelling and the impacts of climate change, enabling informed decision making for sustainable development and resilience.

]]>Mathematics doi: 10.3390/math12071091

Authors: Shan Feng Wenxian Xie Yufeng Nie

Finite Gaussian mixture models are powerful tools for modeling distributions of random phenomena and are widely used for clustering tasks. However, their interpretability and efficiency are often degraded by the impact of redundancy and noise, especially on high-dimensional datasets. In this work, we propose a generative graphical model for parsimonious modeling of the Gaussian mixtures and robust unsupervised learning. The model assumes that the data are generated independently and identically from a finite mixture of robust factor analyzers, where the features&rsquo; salience is adjusted by an active set of latent factors to allow a violation of the local independence assumption. For the model inference, we propose a structured variational Bayes inference framework to realize simultaneous clustering, model selection and outlier processing. Performance of the proposed algorithm is evaluated by conducting experiments on artificial and real-world datasets. Moreover, an application on the high-dimensional machine learning task of handwritten alphabet recognition is introduced.

]]>Mathematics doi: 10.3390/math12071090

Authors: Elena Corina Cipu Ruxandra Ioana Cipu Ştefania Maria Michnea

For decades, cancer has remained a persistent health challenge; this project represents a significant stride towards refining treatment approaches and prognostic insights. Proton beam therapy, a radiation therapy modality employing high-energy protons to target various malignancies while minimizing damage to adjacent healthy tissue, holds immense promise. This study analyzes the relationship between delivered radiation doses and patient outcomes, using various approximation functions and graphical representations for comparison. Statistical analysis is performed through the Monte Carlo method based on repeated sampling to estimate the variables of interest in this analysis, namely, the survival rates, financial implications, and medical effectiveness of proton beam therapy. To this end, open-source data from research centers that publish patient outcomes were utilized. The second study considered the estimation of pay gaps that can have long-lasting effects, leading to differences in retirement savings, wealth accumulation, and overall financial security. After finding a representative sample containing the relevant variables that contribute to pay gaps, such as gender, race, experience, education, and job role, MC modeling is used to simulate a range of possible pay gap estimates. Based on the Monte Carlo results, a sensitivity analysis is performed to identify which variables have the most significant impact on pay gaps.

]]>Mathematics doi: 10.3390/math12071089

Authors: Alberto Postiglione Mario Monteleone

The escalating intricacy of industrial systems necessitates strategies for augmenting the reliability and efficiency of industrial machinery to curtail downtime. In such a context, predictive maintenance (PdM) has surfaced as a pivotal strategy. The amalgamation of cyber-physical systems, IoT devices, and real-time data analytics, emblematic of Industry 4.0, proffers novel avenues to refine maintenance of production equipment from both technical and managerial standpoints, serving as a supportive technology to enhance the precision and efficacy of predictive maintenance. This paper presents an innovative approach that melds text mining techniques with the cyber-physical infrastructure of a manufacturing sector. The aim is to improve the precision and promptness of predictive maintenance within industrial settings. The text mining framework is designed to sift through extensive log files containing data on the status of operational parameters. These datasets encompass information generated by sensors or computed by the control system throughout the production process execution. The algorithm aids in forecasting potential equipment failures, thereby curtailing maintenance costs and fortifying overall system resilience. Furthermore, we substantiate the efficacy of our approach through a case study involving a real-world industrial machine. This research contributes to the progression of predictive maintenance strategies by leveraging the wealth of textual information available within industrial environments, ultimately bolstering equipment reliability and operational efficiency.

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