Mathematics

14 pages, 322 KiB

Open AccessArticle

Some Results on Third-Order Differential Subordination and Differential Superordination for Analytic Functions Using a Fractional Differential Operator

by Faten Fakher Abdulnabi, Hiba F. Al-Janaby, Firas Ghanim and Alina Alb Lupaș

Mathematics 2023, 11(18), 4021; https://doi.org/10.3390/math11184021 - 21 Sep 2023

Cited by 4 | Viewed by 1235

Abstract

In this study, we explore the implications of a third-order differential subordination in the context of analytic functions associated with fractional differential operators. Our investigation involves the consideration of specific admissible classes of third-order differential functions. We also extend this exploration to establish [...] Read more.

In this study, we explore the implications of a third-order differential subordination in the context of analytic functions associated with fractional differential operators. Our investigation involves the consideration of specific admissible classes of third-order differential functions. We also extend this exploration to establish a dual principle, resulting in a sandwich-type outcome. We introduce these admissible function classes by employing the fractional derivative operator

{D_{z}^{α} S}_{N, S} ϑ (z)

and derive conditions on the normalized analytic function f that lead to sandwich-type subordination in combination with an appropriate fractional differential operator. Full article

(This article belongs to the Special Issue Current Topics in Geometric Function Theory)

28 pages, 786 KiB

Open AccessArticle

Optimal Consumption and Robust Portfolio Choice for the 3/2 and 4/2 Stochastic Volatility Models

by Yuyang Cheng and Marcos Escobar-Anel

Mathematics 2023, 11(18), 4020; https://doi.org/10.3390/math11184020 - 21 Sep 2023

Viewed by 1067

Abstract

This manuscript derives optimal consumption and investment strategies for risk-averse investors under the 4/2 stochastic volatility class of models. We work under an expected utility (EUT) framework and consider a Constant Relative Risk Aversion (CRRA) investor, who may also be ambiguity-averse. The corresponding [...] Read more.

This manuscript derives optimal consumption and investment strategies for risk-averse investors under the 4/2 stochastic volatility class of models. We work under an expected utility (EUT) framework and consider a Constant Relative Risk Aversion (CRRA) investor, who may also be ambiguity-averse. The corresponding Hamilton–Jacobi–Bellman (HJB) and HJB–Isaacs (HJBI) equations are solved in closed-form for a subset of the parametric space and under some restrictions on the portfolio setting, for complete markets. Conditions for proper changes of measure and well-defined solutions are provided. These are the first analytical solutions for the 4/2 stochastic volatility model and the embedded 3/2 model for the type of excess returns established in the literature. We numerically illustrate the differences between the 4/2 model and the embedded cases of the 1/2 model (Heston) as well as the 3/2 model under the same data, and for two main cases: risk-averse investor in a complete market with consumption, and ambiguity-averse investor in a complete market with no consumption. In general, the 4/2 and 1/2 models recommend similar levels of consumption and exposure, while the 3/2 leads to significantly different recommendations. Full article

(This article belongs to the Special Issue Recent Advances on Nonlinear Models in Mathematical Finance, 2nd Edition)

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16 pages, 2431 KiB

Open AccessArticle

A Comparative Study of Fuzzy Domination and Fuzzy Coloring in an Optimal Approach

by Annamalai Meenakshi, Adhimoolam Kannan, Miroslav Mahdal, Krishnasamy Karthik and Radek Guras

Mathematics 2023, 11(18), 4019; https://doi.org/10.3390/math11184019 - 21 Sep 2023

Cited by 1 | Viewed by 1588

Abstract

An optimal network refers to a computer or communication network designed, configured, and managed to maximize efficiency, performance, and effectiveness while minimizing cost and resource utilization. In a network design and management context, optimal typically implies achieving the best possible outcomes between various [...] Read more.

An optimal network refers to a computer or communication network designed, configured, and managed to maximize efficiency, performance, and effectiveness while minimizing cost and resource utilization. In a network design and management context, optimal typically implies achieving the best possible outcomes between various factors. This research investigated the use of fuzzy graph edge coloring for various fuzzy graph operations, and it focused on the efficacy and efficiency of the fuzzy network product using the minimal spanning tree and the chromatic index of the fuzzy network product. As a network made of nodes and vertices, measurement with vertices is a parameter for domination, and edge measurement is a parameter for edge coloring, so we used these two parameters in the algorithm. This paper aims to identify an optimal network that can be established using product outcomes. This study shows a way to find an optimal fuzzy network based on comparative optimal parameter domination and edge coloring, which can be elaborated with applications. An algorithm was generated using an optimal approach, which was subsequently implemented in the form of applications. Full article

(This article belongs to the Special Issue Fuzzy Optimization and Decision Making)

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31 pages, 556 KiB

Open AccessArticle

Change-Point Detection in the Volatility of Conditional Heteroscedastic Autoregressive Nonlinear Models

by Mohamed Salah Eddine Arrouch, Echarif Elharfaoui and Joseph Ngatchou-Wandji

Mathematics 2023, 11(18), 4018; https://doi.org/10.3390/math11184018 - 21 Sep 2023

Cited by 1 | Viewed by 1147

Abstract

This paper studies single change-point detection in the volatility of a class of parametric conditional heteroscedastic autoregressive nonlinear (CHARN) models. The conditional least-squares (CLS) estimators of the parameters are defined and are proved to be consistent. A Kolmogorov–Smirnov type-test for change-point detection is [...] Read more.

This paper studies single change-point detection in the volatility of a class of parametric conditional heteroscedastic autoregressive nonlinear (CHARN) models. The conditional least-squares (CLS) estimators of the parameters are defined and are proved to be consistent. A Kolmogorov–Smirnov type-test for change-point detection is constructed and its null distribution is provided. An estimator of the change-point location is defined. Its consistency and its limiting distribution are studied in detail. A simulation experiment is carried out to assess the performance of the results, which are compared to recent results and applied to two sets of real data. Full article

(This article belongs to the Special Issue Parametric and Nonparametric Statistics: From Theory to Applications)

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19 pages, 2840 KiB

Open AccessArticle

Mathematical Model to Predict Polyclonal T-Cell-Dependent Antibody Synthesis Responses

by Jagdish S. Thakur, Archana Thakur and Lawrence G. Lum

Mathematics 2023, 11(18), 4017; https://doi.org/10.3390/math11184017 - 21 Sep 2023

Viewed by 1587

Abstract

Mathematical models are becoming indispensable tools to explore the complexities of biological systems at cellular levels. We present a model to explore the baseline immune cell interactions for in vitro polyclonal antibody synthesis via B-cells regulated by helper and regulatory T-cells. The model [...] Read more.

Mathematical models are becoming indispensable tools to explore the complexities of biological systems at cellular levels. We present a model to explore the baseline immune cell interactions for in vitro polyclonal antibody synthesis via B-cells regulated by helper and regulatory T-cells. The model incorporates interactions of antigen-presenting cells, T-cells, regulatory T-cells, and B-cells with each other and predicts time-dependent trajectories of these cells and antibody synthesis stimulated by pokeweed mitogen. We used an ordinary differential equation-based approach to simulate the dynamic changes in the cells and cytokines numbers due to the cellular and humoral response to pokeweed mitogen stimulation. The parameters of the ordinary differential equations model are determined to yield a normal immune response as observed in the pokeweed mitogen-stimulated in vitro antibody synthesis via normal T, B, and antigen-presenting cells. The dose effects of antigen load and basal values of regulatory T-cells on the profiles of various immune response variables are also evaluated. Full article

(This article belongs to the Special Issue Mathematical Modeling in Cell Biology and Its Applications)

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19 pages, 5517 KiB

Open AccessArticle

The Impact of Investments in Physical Capital, Labor, and Knowledge Capital on Enterprise Market Value: Estimation and Optimization

by Yuanbo Qiao, Xiaoyan Shao, Zhuolin Han and Hao Duan

Mathematics 2023, 11(18), 4016; https://doi.org/10.3390/math11184016 - 21 Sep 2023

Viewed by 1948

Abstract

This study analyzes the market value of listed companies in Mainland China across different industries, including capital-intensive, labor-intensive, technology-intensive, and other industries. A generalized neoclassical investment model that considers physical capital, labor, and knowledge capital as input variables is built to theoretically decompose [...] Read more.

This study analyzes the market value of listed companies in Mainland China across different industries, including capital-intensive, labor-intensive, technology-intensive, and other industries. A generalized neoclassical investment model that considers physical capital, labor, and knowledge capital as input variables is built to theoretically decompose firm value. The empirical results indicate that knowledge capital accounts for an increasing proportion of the market value of companies, rising sharply from 21.5% in 2009 to 37.9% in 2018. In contrast, the share of labor in enterprise market value has been decreasing year by year, dropping from 56.5% in 2009 to 36.4% in 2018. The share of physical capital in enterprise market value remains relatively stable. Based on these findings, the study simulates the optimal investment behaviors and their influence on the firm value of various types of enterprises, providing valuable insights for investment decision-making for managers in different industries. Full article

(This article belongs to the Special Issue Economic Model Analysis and Application)

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16 pages, 2525 KiB

Open AccessArticle

Predator–Prey Model Considering Implicit Marine Reserved Area and Linear Function of Critical Biomass Level

by Arjun Hasibuan, Asep Kuswandi Supriatna, Endang Rusyaman and Md. Haider Ali Biswas

Mathematics 2023, 11(18), 4015; https://doi.org/10.3390/math11184015 - 21 Sep 2023

Cited by 2 | Viewed by 1762

Abstract

In this work, we examine a predator–prey model that considers the implicit marine reserve in prey species and a linear function of critical biomass level. The model’s basic properties (existence, uniqueness, positivity, boundedness, and permanence) and equilibrium points are determined. We obtain three [...] Read more.

In this work, we examine a predator–prey model that considers the implicit marine reserve in prey species and a linear function of critical biomass level. The model’s basic properties (existence, uniqueness, positivity, boundedness, and permanence) and equilibrium points are determined. We obtain three equilibrium points: the trivial equilibrium point, the equilibrium point where there is no harvest, and the co-existing equilibrium point. The local and global stability of each equilibrium point of the model is explored. Moreover, the interior equilibrium point is always globally asymptotically stable, and the system experiences no limit cycles around the interior equilibrium point. Numerical simulations are conducted to illustrate the theoretical results obtained. Finally, we find overlapping conditions regarding the dynamics between the model we developed and a model that considers a constant critical biomass level for certain parameters. Full article

(This article belongs to the Special Issue Mathematical Modeling, Numerical Analysis and Scientific Computing, with Their Applications)

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19 pages, 764 KiB

Open AccessArticle

UDCO-SAGiMEC: Joint UAV Deployment and Computation Offloading for Space–Air–Ground Integrated Mobile Edge Computing

by Yinghao Xu, Fukang Deng and Jianshan Zhang

Mathematics 2023, 11(18), 4014; https://doi.org/10.3390/math11184014 - 21 Sep 2023

Cited by 4 | Viewed by 1338

Abstract

Computation-intensive applications offloading is challenging, especially in the designated regions where communication infrastructure is absent or compromised. In this paper, we present a Space–Air–Ground integrated Mobile Edge Computing (SAGiMEC) system for these regions to provide quality computational services, where the unmanned aerial vehicles [...] Read more.

Computation-intensive applications offloading is challenging, especially in the designated regions where communication infrastructure is absent or compromised. In this paper, we present a Space–Air–Ground integrated Mobile Edge Computing (SAGiMEC) system for these regions to provide quality computational services, where the unmanned aerial vehicles (UAVs) act as in-fight edge servers to provide low-latency edge computing and the satellite provides resident cloud computing. A joint optimization problem is formulated considering UAV deployment, ground device (GD) access, and computation offloading to minimize the system average response latency. To cope with the problem’s complexity, we propose a Particle Swarm Optimization (PSO) and Greedy Strategy (GS)-based algorithm (PSO&GS) to obtain an approximate optimal solution. Extensive simulations validate the convergence of the proposed algorithm. Numerical results show that the proposed approach has excellent convergence, and the system average response latency is about 0.65x–0.85x that of the benchmark algorithm. Full article

(This article belongs to the Special Issue Advanced Algorithms in Wireless Communication and Internet of Things (IoT))

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24 pages, 25404 KiB

Open AccessArticle

Residual Strength Modeling and Reliability Analysis of Wind Turbine Gear under Different Random Loadings

by Jianxiong Gao, Yuanyuan Liu, Yiping Yuan and Fei Heng

Mathematics 2023, 11(18), 4013; https://doi.org/10.3390/math11184013 - 21 Sep 2023

Cited by 2 | Viewed by 1451

Abstract

A novel method is proposed to investigate the pattern of variation in the residual strength and reliability of wind turbine gear. First, the interaction between loads and the effect of the loading sequence is considered based on the fatigue damage accumulation theory, and [...] Read more.

A novel method is proposed to investigate the pattern of variation in the residual strength and reliability of wind turbine gear. First, the interaction between loads and the effect of the loading sequence is considered based on the fatigue damage accumulation theory, and a residual strength degradation model with few parameters is established. Experimental data from two materials are used to verify the predictive performance of the proposed model. Secondly, the modeling and simulation of the wind turbine gear is conducted to analyze the types of fatigue failures and obtain their fatigue life curves. Due to the randomness of the load on the gear, the rain flow counting method and the Goodman method are employed. Thirdly, considering the seasonal variation of load, the decreasing trend of gear fatigue strength under multistage random load is calculated. Finally, the dynamic failure rate and reliability of gear fatigue failure under multistage random loads are analyzed. The results demonstrate that the randomness of residual strength increases with increasing service time. The seasonality of load causes fluctuations in the reliability of gear, providing a new idea for evaluating the reliability of the wind turbine gear. Full article

(This article belongs to the Special Issue Modeling and Optimization of Complex Engineering Systems under Uncertainties)

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20 pages, 5818 KiB

Open AccessFeature PaperArticle

Adaptively Learned Modeling for a Digital Twin of Hydropower Turbines with Application to a Pilot Testing System

by Hong Wang, Shiqi (Shawn) Ou, Ole Gunnar Dahlhaug, Pål-Tore Storli, Hans Ivar Skjelbred and Ingrid Vilberg

Mathematics 2023, 11(18), 4012; https://doi.org/10.3390/math11184012 - 21 Sep 2023

Cited by 7 | Viewed by 1530

Abstract

In the development of a digital twin (DT) for hydropower turbines, dynamic modeling of the system (e.g., penstock, turbine, speed control) is crucial, along with all the necessary data interface, virtualization, and dashboard designs. Since the DT must mimic the actual dynamics of [...] Read more.

In the development of a digital twin (DT) for hydropower turbines, dynamic modeling of the system (e.g., penstock, turbine, speed control) is crucial, along with all the necessary data interface, virtualization, and dashboard designs. Since the DT must mimic the actual dynamics of the hydropower turbine accurately, adaptive learning is required to train these dynamic models online so that the models in the DT can effectively follow the representation of the actual hydropower turbine dynamics accurately and reliably. This study presents an adaptive learning method for obtaining the hydropower turbine models for DT development of hydropower systems using the recursive least squares algorithm. To simplify the formulation, the hydropower turbine under consideration was assumed to operate near a fixed operating point, where the system dynamics can be well represented by a set of linear differential equations with constant parameters. In this context, the well-known six-coefficient model for the Francis turbine was formulated as the starting point to obtain input and output models for the turbine. Then, an adaptive learning mechanism was developed to learn model parameters using real-time data from a hydropower turbine testing system. This led to semi-physical modeling, in which first principles and data-driven modeling are integrated to produce dynamic models for DT development. Applications to a pilot system at the Norwegian University of Science and Technology (NTNU) were made, and the models learned adaptively using the data collected from the university’s pilot system. Desired modeling and validation results were obtained. Full article

(This article belongs to the Special Issue Advances in Control Systems and Automatic Control)

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22 pages, 63373 KiB

Open AccessArticle

Plant Image Classification with Nonlinear Motion Deblurring Based on Deep Learning

by Ganbayar Batchuluun, Jin Seong Hong, Abdul Wahid and Kang Ryoung Park

Mathematics 2023, 11(18), 4011; https://doi.org/10.3390/math11184011 - 21 Sep 2023

Cited by 2 | Viewed by 1239

Abstract

Despite the significant number of classification studies conducted using plant images, studies on nonlinear motion blur are limited. In general, motion blur results from movements of the hands of a person holding a camera for capturing plant images, or when the plant moves [...] Read more.

Despite the significant number of classification studies conducted using plant images, studies on nonlinear motion blur are limited. In general, motion blur results from movements of the hands of a person holding a camera for capturing plant images, or when the plant moves owing to wind while the camera is stationary. When these two cases occur simultaneously, nonlinear motion blur is highly probable. Therefore, a novel deep learning-based classification method applied on plant images with various nonlinear motion blurs is proposed. In addition, this study proposes a generative adversarial network-based method to reduce nonlinear motion blur; accordingly, the method is explored for improving classification performance. Herein, experiments are conducted using a self-collected visible light images dataset. Evidently, nonlinear motion deblurring results in a structural similarity index measure (SSIM) of 73.1 and a peak signal-to-noise ratio (PSNR) of 21.55, whereas plant classification results in a top-1 accuracy of 90.09% and F1-score of 84.84%. In addition, the experiment conducted using two types of open datasets resulted in PSNRs of 20.84 and 21.02 and SSIMs of 72.96 and 72.86, respectively. The proposed method of plant classification results in top-1 accuracies of 89.79% and 82.21% and F1-scores of 84% and 76.52%, respectively. Thus, the proposed network produces higher accuracies than the existing state-of-the-art methods. Full article

(This article belongs to the Special Issue Computer Vision, Image Processing Technologies and Artificial Intelligence)

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25 pages, 941 KiB

Open AccessArticle

Project Group Program Generation and Decision Making Method Integrating Coupling Network and Hesitant Fuzzy

by Liwei Qian, Yajie Dou, Chang Gong, Xiangqian Xu and Yuejin Tan

Mathematics 2023, 11(18), 4010; https://doi.org/10.3390/math11184010 - 21 Sep 2023

Viewed by 980

Abstract

Modern urban construction relies on a large number of projects. Project groups are an effective way to manage a large number of projects. In view of the current lack of scientific methods for constructing and evaluating project group programs, which are mainly based [...] Read more.

Modern urban construction relies on a large number of projects. Project groups are an effective way to manage a large number of projects. In view of the current lack of scientific methods for constructing and evaluating project group programs, which are mainly based on subjective experience, this article proposes a scientific method for project group program generation and decision-making. The method proposed in this article applies a multi-layer coupling network to the modeling of project groups and divides projects into planning projects and execution projects to form a heterogeneous coupling network. Then, starting from the principle of project information dissemination, the evaluation indicators of the project group program were defined, and finally, the hesitant fuzzy decision-making method was used to assist in decision making. This article can provide a new method for project group construction and management, and provide strong support for the construction of smart cities and digital governments. Full article

(This article belongs to the Special Issue Multi-attribute Decision Making and Intelligent Computing in Smart Governance)

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19 pages, 3549 KiB

Open AccessArticle

Fully Electromagnetic Code KARAT Applied to the Problem of Aneutronic Proton–Boron Fusion

by Stepan N. Andreev, Yuri K. Kurilenkov and Alexander V. Oginov

Mathematics 2023, 11(18), 4009; https://doi.org/10.3390/math11184009 - 21 Sep 2023

Viewed by 1204

Abstract

In this paper, the full electromagnetic code KARAT is presented in detail, the scope of which is a computational experiment in applied problems of engineering electrodynamics. The basis of the physical model used is Maxwell’s equations together with boundary conditions for fields, as [...] Read more.

In this paper, the full electromagnetic code KARAT is presented in detail, the scope of which is a computational experiment in applied problems of engineering electrodynamics. The basis of the physical model used is Maxwell’s equations together with boundary conditions for fields, as well as material equations linking currents with field strengths. The Particle in Cell (PiC) method for the kinetic description of plasma is implemented in the code. A unique feature of the code KARAT is the possibility of the self-consistent modeling of inelastic processes, in particular, nuclear reactions, at each time step in the process of electrodynamic calculation. The aneutronic proton–boron nuclear reaction, accompanied by the release of almost only α-particles, is extremely in demand in medicine and, perhaps, in the future, will form the basis for obtaining “clean” nuclear energy. The results of a numerical simulation within the framework of the code KARAT of the key physical processes leading to the proton–boron fusion are presented and discussed both for laser-driven plasma and for a plasma oscillatory confinement scheme. Full article

(This article belongs to the Special Issue Numerical Simulations and Mathematical Modelling in Engineering Physics)

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15 pages, 385 KiB

Open AccessArticle

Density-Based Clustering to Deal with Highly Imbalanced Data in Multi-Class Problems

by Julio Cesar Munguía Mondragón, Eréndira Rendón Lara, Roberto Alejo Eleuterio, Everardo Efrén Granda Gutirrez and Federico Del Razo López

Mathematics 2023, 11(18), 4008; https://doi.org/10.3390/math11184008 - 21 Sep 2023

Cited by 2 | Viewed by 2156

Abstract

In machine learning and data mining applications, an imbalanced distribution of classes in the training dataset can drastically affect the performance of learning models. The class imbalance problem is frequently observed during classification tasks in real-world scenarios when the available instances of one [...] Read more.

In machine learning and data mining applications, an imbalanced distribution of classes in the training dataset can drastically affect the performance of learning models. The class imbalance problem is frequently observed during classification tasks in real-world scenarios when the available instances of one class are much fewer than the amount of data available in other classes. Machine learning algorithms that do not consider the class imbalance could introduce a strong bias towards the majority class, while the minority class is usually despised. Thus, sampling techniques have been extensively used in various studies to overcome class imbalances, mainly based on random undersampling and oversampling methods. However, there is still no final solution, especially in the domain of multi-class problems. A strategy that combines density-based clustering algorithms with random undersampling and oversampling techniques is studied in this work. To analyze the performance of the studied method, an experimental validation was achieved on a collection of hyperspectral remote sensing images, and a deep learning neural network was utilized as the classifier. This data bank contains six datasets with different imbalance ratios, from slight to severe. The experimental results outperform the classification measured by the geometric mean of the precision compared with other state-of-the-art methods, mainly for highly imbalanced datasets. Full article

(This article belongs to the Special Issue Class-Imbalance and Cost-Sensitive Learning)

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15 pages, 462 KiB

Open AccessArticle

Identifying Bias in Social and Health Research: Measurement Invariance and Latent Mean Differences Using the Alignment Approach

by Ioannis Tsaousis and Fathima M. Jaffari

Mathematics 2023, 11(18), 4007; https://doi.org/10.3390/math11184007 - 21 Sep 2023

Cited by 1 | Viewed by 1439

Abstract

When comparison among groups is of major importance, it is necessary to ensure that the measuring tool exhibits measurement invariance. This means that it measures the same construct in the same way for all groups. In the opposite case, the test results in [...] Read more.

When comparison among groups is of major importance, it is necessary to ensure that the measuring tool exhibits measurement invariance. This means that it measures the same construct in the same way for all groups. In the opposite case, the test results in measurement error and bias toward a particular group of respondents. In this study, a new approach to examine measurement invariance was applied, which was appropriately designed when a large number of group comparisons are involved: the alignment approach. We used this approach to examine whether the factor structure of a cognitive ability test exhibited measurement invariance across the 26 universities of the Kingdom of Saudi Arabia. The results indicated that the P-GAT subscales were invariant across the 26 universities. Moreover, the aligned factor mean values were estimated, and factor mean comparisons of every group’s mean with all the other group means were conducted. The findings from this study showed that the alignment procedure is a valuable method to assess measurement invariance and latent mean differences when a large number of groups are involved. This technique provides an unbiased statistical estimation of group means, with significance tests between group pairs that adjust for sampling errors and missing data. Full article

(This article belongs to the Special Issue Methods and Applications of Statistics in the Social and Health Sciences, 2nd Edition)

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7 pages, 273 KiB

Open AccessArticle

Gilbreath Equation, Gilbreath Polynomials, and Upper and Lower Bounds for Gilbreath Conjecture

by Riccardo Gatti

Mathematics 2023, 11(18), 4006; https://doi.org/10.3390/math11184006 - 21 Sep 2023

Viewed by 891

Abstract

Let

S = (s_{1}, \dots, s_{n})

be a finite sequence of integers. Then, S is a Gilbreath sequence of length n,

S \in G_{n}

, iff

s_{1}

is even or odd and [...] Read more.

Let

S = (s_{1}, \dots, s_{n})

be a finite sequence of integers. Then, S is a Gilbreath sequence of length n,

S \in G_{n}

, iff

s_{1}

is even or odd and

s_{2}, \dots, s_{n}

are, respectively, odd or even and

\min K_{(s_{1}, \dots, s_{m})} \leq s_{m + 1} \leq \max K_{(s_{1}, \dots, s_{m})}, \forall m \in [1, n)

. This, applied to the order sequence of prime number P, defines Gilbreath polynomials and two integer sequences, A347924 and A347925, which are used to prove that Gilbreath conjecture

G C

is implied by

p_{n} - 2^{n - 1} ⩽ P_{n - 1} (1)

, where

P_{n - 1} (1)

is the

n - 1

-th Gilbreath polynomial at 1. Full article

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

23 pages, 2074 KiB

Open AccessArticle

Spillovers across the Asian OPEC+ Financial Market

by Darko B. Vuković, Senanu Dekpo-Adza, Vladislav Khmelnitskiy and Mustafa Özer

Mathematics 2023, 11(18), 4005; https://doi.org/10.3390/math11184005 - 21 Sep 2023

Cited by 2 | Viewed by 1727

Abstract

This research utilizes the Diebold and Yilmaz spillover model to examine the correlation between geopolitical events, natural disasters, and oil stock returns in Asian OPEC+ member countries. The study extends prior research by investigating the dynamics of the Asian OPEC+ oil market in [...] Read more.

This research utilizes the Diebold and Yilmaz spillover model to examine the correlation between geopolitical events, natural disasters, and oil stock returns in Asian OPEC+ member countries. The study extends prior research by investigating the dynamics of the Asian OPEC+ oil market in light of recent exogenous events. The analysis commences by creating a self-generated Asian OPEC+ index, which demonstrates significant volatility, as indicated by GARCH (1, 1) model estimation. The results obtained from the Diebold and Yilmaz spillover test indicate that, on average, there is a moderate degree of connectedness among the variables. However, in the event of global-level shocks or shocks specifically affecting Asian OPEC+ countries, a heightened level of connectedness is found. Prominent instances of spillover events observed in the volatility analysis conducted during the previous decade include the COVID-19 pandemic, the conflict between Russia and Ukraine, and the Turkey earthquake of 2023. Based on the facts, it is recommended that investors take into account the potential risks linked to regions that are susceptible to natural calamities and geopolitical occurrences while devising their portfolios for oil stocks. The results further highlight the significance of integrating these aspects into investors’ decision-making procedures and stress the need for risk management tactics that consider geopolitical risks and natural disasters in the oil equity market. Full article

(This article belongs to the Special Issue The Econometric Analysis of Financial Markets)

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21 pages, 6308 KiB

Open AccessArticle

An Ensemble of Long Short-Term Memory Networks with an Attention Mechanism for Upper Limb Electromyography Signal Classification

by Naif D. Alotaibi, Hadi Jahanshahi, Qijia Yao, Jun Mou and Stelios Bekiros

Mathematics 2023, 11(18), 4004; https://doi.org/10.3390/math11184004 - 21 Sep 2023

Cited by 3 | Viewed by 1411

Abstract

Advancing cutting-edge techniques to accurately classify electromyography (EMG) signals are of paramount importance given their extensive implications and uses. While recent studies in the literature present promising findings, a significant potential still exists for substantial enhancement. Motivated by this need, our current paper [...] Read more.

Advancing cutting-edge techniques to accurately classify electromyography (EMG) signals are of paramount importance given their extensive implications and uses. While recent studies in the literature present promising findings, a significant potential still exists for substantial enhancement. Motivated by this need, our current paper introduces a novel ensemble neural network approach for time series classification, specifically focusing on the classification of upper limb EMG signals. Our proposed technique integrates long short-term memory networks (LSTM) and attention mechanisms, leveraging their capabilities to achieve accurate classification. We provide a thorough explanation of the architecture and methodology, considering the unique characteristics and challenges posed by EMG signals. Furthermore, we outline the preprocessing steps employed to transform raw EMG signals into a suitable format for classification. To evaluate the effectiveness of our proposed technique, we compare its performance with a baseline LSTM classifier. The obtained numerical results demonstrate the superiority of our method. Remarkably, the method we propose attains an average accuracy of 91.5%, with all motion classifications surpassing the 90% threshold. Full article

(This article belongs to the Special Issue Analysis and Mathematical Modeling of Control Engineering and Path Planning)

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15 pages, 576 KiB

Open AccessFeature PaperArticle

Complexity-Efficient Sidelink Synchronization Signal Detection Scheme for Cellular Vehicle-to-Everything Communication Systems

by Young-Hwan You and Yong-An Jung

Mathematics 2023, 11(18), 4003; https://doi.org/10.3390/math11184003 - 20 Sep 2023

Viewed by 1363

Abstract

Synchronization is a challenging issue in vehicle-to-everything (V2X) cellular communication, especially when V2X devices need to directly communicate with each other outside the network coverage area. By adopting the maximum likelihood principle, we propose joint detection of the sidelink secondary synchronization signal (SL-SSS) [...] Read more.

Synchronization is a challenging issue in vehicle-to-everything (V2X) cellular communication, especially when V2X devices need to directly communicate with each other outside the network coverage area. By adopting the maximum likelihood principle, we propose joint detection of the sidelink secondary synchronization signal (SL-SSS) and carrier frequency offset (CFO) in a V2X system using 5G new radio sidelink. We formulate an effective joint coherent synchronization scheme for cellular V2X applications by decoupling the estimation of the sidelink identity and CFO, which requires a priori knowledge of channel state information. To verify the feasibility of the proposed detection scheme, we derive a simplified implementation of the proposed SL-SSS detector and a closed-form expression for the detection probability. Simulation results demonstrate that the proposed SL-SSS detector exhibits either comparable performance in terms of detection probability or reduced complexity when compared with conventional SL-SSS detectors. Using the proposed method in the cellular V2X system enables V2X devices to achieve robust synchronization with reduced power consumption during the initial synchronization procedure, while also offering valuable insights for designing a simple, efficient sidelink synchronization receiver. Full article

(This article belongs to the Section Network Science)

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14 pages, 440 KiB

Open AccessArticle

Robustness of the cμ-Rule for an Unreliable Single-Server Two-Class Queueing System with Constant Retrial Rates

by Dmitry Efrosinin, Natalia Stepanova and Janos Sztrik

Mathematics 2023, 11(18), 4002; https://doi.org/10.3390/math11184002 - 20 Sep 2023

Viewed by 994

Abstract

We study the robustness of the

c μ

-rule for the optimal allocation of a resource consisting of one unreliable server to parallel queues with two different classes of customers. The customers in queues can be served with respect to a FIFO retrial [...] Read more.

We study the robustness of the

c μ

-rule for the optimal allocation of a resource consisting of one unreliable server to parallel queues with two different classes of customers. The customers in queues can be served with respect to a FIFO retrial discipline, when the customers at the heads of queues repeatedly try to occupy the server at a random time. It is proved that for scheduling problems in the system without arrivals, the

c μ

-rule minimizes the total average cost. For the system with arrivals, it is difficult directly to prove the optimality of the same policy with explicit relations. We derived for an infinite-buffer model a static control policy that also prescribes the service for certain values of system parameters exclusively for the class-i customers if both of the queues are not empty, with the aim to minimize the average cost per unit of time. It is also shown that in a finite buffer case, the

c μ

-rule fails. Full article

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24 pages, 2387 KiB

Open AccessArticle

Ranking of Service Quality Index and Solutions for Online English Teaching in the Post-COVID-19 Crisis

by Yu-Yu Ma, Chia-Liang Lin and Hung-Lung Lin

Mathematics 2023, 11(18), 4001; https://doi.org/10.3390/math11184001 - 20 Sep 2023

Cited by 3 | Viewed by 1335

Abstract

Online English teaching remains prevalent post-pandemic, yet there is a significant research gap in assessing service quality during this period. Thus, this study employs a hybrid FANP and GRA method to evaluate critical factors sustaining high service quality in online English teaching in [...] Read more.

Online English teaching remains prevalent post-pandemic, yet there is a significant research gap in assessing service quality during this period. Thus, this study employs a hybrid FANP and GRA method to evaluate critical factors sustaining high service quality in online English teaching in the post-coronavirus era. The FANP model highlights key contributors like professional employees, trustworthy staff, flexible transaction times, and a secure transaction environment. In contrast, GRA identifies personnel quality, responsiveness to customer needs, and a secure transaction mechanism as top factors. Individual customer needs and service facilities are of less importance in both models. This study’s primary contribution is proposing an integrated FANP and GRA approach to rank potential solutions for online English teaching service quality in the post-COVID-19 fuzzy context. The findings guide the online English teaching industry in maintaining service quality in future similar scenarios. Full article

(This article belongs to the Special Issue Practice and Application of Emergency Management in Social Systems: Mathematical Modeling and the Use of Information Technology)

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15 pages, 482 KiB

Open AccessArticle

Accelerated Maximum Entropy Method for Time Series Models Estimation

by Yuri A. Dubnov and Alexandr V. Boulytchev

Mathematics 2023, 11(18), 4000; https://doi.org/10.3390/math11184000 - 20 Sep 2023

Viewed by 1089

Abstract

The work is devoted to the development of a maximum entropy estimation method with soft randomization for restoring the parameters of probabilistic mathematical models from the available observations. Soft randomization refers to the technique of adding regularization to the functional of information entropy [...] Read more.

The work is devoted to the development of a maximum entropy estimation method with soft randomization for restoring the parameters of probabilistic mathematical models from the available observations. Soft randomization refers to the technique of adding regularization to the functional of information entropy in order to simplify the optimization problem and speed up the learning process compared to the classical maximum entropy method. Entropic estimation makes it possible to restore probability distribution functions for model parameters without introducing additional assumptions about the likelihood function; thus, this estimation method can be used in problems with an unspecified type of measurement noise, such as analysis and forecasting of time series. Full article

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

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16 pages, 320 KiB

Open AccessArticle

Application of Wavelet Transform to Urysohn-Type Equations

by V. Lukianenko, M. Kozlova and V. Belozub

Mathematics 2023, 11(18), 3999; https://doi.org/10.3390/math11183999 - 20 Sep 2023

Viewed by 884

Abstract

This paper deals with convolution-type Urysohn equations of the first kind. Finding a solution for such equations is an ill-posed problem. For it to be solved, regularization algorithms and the continuous wavelet transform are used. Similar to the Fourier transform, the continuous wavelet [...] Read more.

This paper deals with convolution-type Urysohn equations of the first kind. Finding a solution for such equations is an ill-posed problem. For it to be solved, regularization algorithms and the continuous wavelet transform are used. Similar to the Fourier transform, the continuous wavelet transform is applied to convolution-type equations (based on the Fourier and wavelet transforms) and to Urysohn equations with unknown shift. The wavelet transform is preferable for the cases with approximated right-hand sides and for type 1 equations. We demonstrated that the application of the wavelet transform to Urysohn-type equations with unknown shift translates into a solution of a nonlinear equation with an oscillating kernel. Depending on the availability of a priori information, a combination of regularization and iterative algorithms with the use of close equations are effective for solving convolution-type equations based on the continuous wavelet transform and Urysohn equation. Full article

(This article belongs to the Special Issue Convolution Equations: Theory, Numerical Methods and Applications)

12 pages, 552 KiB

Open AccessArticle

Polynomial-Time Verification of Decentralized Fault Pattern Diagnosability for Discrete-Event Systems

by Ye Liang, Gaiyun Liu and Ahmed M. El-Sherbeeny

Mathematics 2023, 11(18), 3998; https://doi.org/10.3390/math11183998 - 20 Sep 2023

Viewed by 1115

Abstract

This paper considers the verification of decentralized fault pattern diagnosability for discrete event systems, where the pattern is modeled as a finite automaton whose accepted language is the objective to be diagnosed. We introduce a notion of codiagnosability to formalize the decentralized fault [...] Read more.

This paper considers the verification of decentralized fault pattern diagnosability for discrete event systems, where the pattern is modeled as a finite automaton whose accepted language is the objective to be diagnosed. We introduce a notion of codiagnosability to formalize the decentralized fault pattern diagnosability, which requires the pattern to be detected by one of the external local observers within a bounded delay. To this end, a structure, namely a verifier, is proposed to verify the codiagnosability of the system and the fault pattern. By studying an indeterminate cycle of the verifier, sufficient and necessary conditions are provided to test the codiagnosability. It is shown that the proposed method requires polynomial time at most. In addition, we present an approach to extend the proposed verifier structure so that it can be applied to centralized cases. Full article

(This article belongs to the Special Issue Systems Engineering, Control, and Automation, 2nd Edition)

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24 pages, 838 KiB

Open AccessArticle

Regularized Normalization Methods for Solving Linear and Nonlinear Eigenvalue Problems

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

Mathematics 2023, 11(18), 3997; https://doi.org/10.3390/math11183997 - 20 Sep 2023

Viewed by 1189

Abstract

To solve linear and nonlinear eigenvalue problems, we develop a simple method by directly solving a nonhomogeneous system obtained by supplementing a normalization condition on the eigen-equation for the uniqueness of the eigenvector. The novelty of the present paper is that we transform [...] Read more.

To solve linear and nonlinear eigenvalue problems, we develop a simple method by directly solving a nonhomogeneous system obtained by supplementing a normalization condition on the eigen-equation for the uniqueness of the eigenvector. The novelty of the present paper is that we transform the original homogeneous eigen-equation to a nonhomogeneous eigen-equation by a normalization technique and the introduction of a simple merit function, the minimum of which leads to a precise eigenvalue. For complex eigenvalue problems, two normalization equations are derived utilizing two different normalization conditions. The golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues, and simultaneously, we can obtain precise eigenvectors to satisfy the eigen-equation. Two regularized normalization methods can accelerate the convergence speed for two extensions of the simple method, and a derivative-free fixed-point Newton iterative scheme is developed to compute real eigenvalues, the convergence speed of which is ten times faster than the golden section search algorithm. Newton methods are developed for solving two systems of nonlinear regularized equations, and the efficiency and accuracy are significantly improved. Over ten examples demonstrate the high performance of the proposed methods. Among them, the two regularization methods are better than the simple method. Full article

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7 pages, 252 KiB

Open AccessArticle

Trace Formulae for Second-Order Differential Pencils with a Frozen Argument

by Yi-Teng Hu and Murat Şat

Mathematics 2023, 11(18), 3996; https://doi.org/10.3390/math11183996 - 20 Sep 2023

Cited by 2 | Viewed by 881

Abstract

This paper deals with second-order differential pencils with a fixed frozen argument on a finite interval. We obtain the trace formulae under four boundary conditions: Dirichlet–Dirichlet, Neumann–Neumann, Dirichlet–Neumann, Neumann–Dirichlet. Although the boundary conditions and the corresponding asymptotic behaviour of the eigenvalues are different, [...] Read more.

This paper deals with second-order differential pencils with a fixed frozen argument on a finite interval. We obtain the trace formulae under four boundary conditions: Dirichlet–Dirichlet, Neumann–Neumann, Dirichlet–Neumann, Neumann–Dirichlet. Although the boundary conditions and the corresponding asymptotic behaviour of the eigenvalues are different, the trace formulae have the same form which reveals the impact of the frozen argument. Full article

(This article belongs to the Special Issue Direct and Inverse Spectral Problems for Ordinary Differential and Functional-Differential Operators)

23 pages, 2611 KiB

Open AccessArticle

Fuzzy CNN Autoencoder for Unsupervised Anomaly Detection in Log Data

by Oleg Gorokhov, Mikhail Petrovskiy, Igor Mashechkin and Maria Kazachuk

Mathematics 2023, 11(18), 3995; https://doi.org/10.3390/math11183995 - 20 Sep 2023

Cited by 1 | Viewed by 1595

Abstract

Currently, the task of maintaining cybersecurity and reliability in various computer systems is relevant. This problem can be solved by detecting anomalies in the log data, which are represented as a stream of textual descriptions of events taking place. For these purposes, reduction [...] Read more.

Currently, the task of maintaining cybersecurity and reliability in various computer systems is relevant. This problem can be solved by detecting anomalies in the log data, which are represented as a stream of textual descriptions of events taking place. For these purposes, reduction to a One-class classification problem is used. Standard One-class classification methods do not achieve good results. Deep learning approaches are more effective. However, they are not robust to outliers and require a lot of computational effort. In this paper, we propose a new robust approach based on a convolutional autoencoder using fuzzy clustering. The proposed approach uses a parallel convolution operation to feature extraction, which makes it more efficient than the currently popular Transformer architecture. In the course of the experiments, the proposed approach showed the best results for both the cybersecurity and the reliability problems compared to existing approaches. It was also shown that the proposed approach is robust to outliers in the training set. Full article

(This article belongs to the Special Issue Mathematical Modeling, Optimization and Machine Learning, 2nd Edition)

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30 pages, 1750 KiB

Open AccessArticle

An Analytic Network Process to Support Financial Decision-Making in the Context of Behavioural Finance

by Roberta Martino and Viviana Ventre

Mathematics 2023, 11(18), 3994; https://doi.org/10.3390/math11183994 - 20 Sep 2023

Cited by 3 | Viewed by 1299

Abstract

Following the financial crisis of the last decade and the increasing complexity of financial products, the European Union has introduced investor protection tools that require professionals to carry out a client profiling process. The aim is to offer products that are in line [...] Read more.

Following the financial crisis of the last decade and the increasing complexity of financial products, the European Union has introduced investor protection tools that require professionals to carry out a client profiling process. The aim is to offer products that are in line with the characteristics of the individual. The classes of variables for comprehensive profiling are obtained by matching the elements proposed by the Markets in Financial Instruments Directive and studies of classical finance. However, behavioural finance studies, which emphasise the importance of behavioural attitudes, are not clearly considered in this structured profiling. The present paper discusses the implementation of an analytic network process to support financial decision-making in a behavioural context, combining regulatory guidance and qualitative and quantitative evidence from the literature. The Kersey Temperament Model is used as the behavioural model to construct the network cluster that incorporates personality into the valuation. Uncertainty management is incorporated through recent studies in the context of intertemporal choice theory. The functionality of the network is verified through a case study, where two alternatives with different characteristics are considered to meet the same investment objective. The present approach proves how the generated structure can provide strong support for financial decision-making. Full article

(This article belongs to the Special Issue Computational Intelligence in Management Science and Finance)

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16 pages, 1634 KiB

Open AccessArticle

DINA Model with Entropy Penalization

by Juntao Wang and Yuan Li

Mathematics 2023, 11(18), 3993; https://doi.org/10.3390/math11183993 - 20 Sep 2023

Viewed by 964

Abstract

The cognitive diagnosis model (CDM) is an effective statistical tool for extracting the discrete attributes of individuals based on their responses to diagnostic tests. When dealing with cases that involve small sample sizes or highly correlated attributes, not all attribute profiles may be [...] Read more.

The cognitive diagnosis model (CDM) is an effective statistical tool for extracting the discrete attributes of individuals based on their responses to diagnostic tests. When dealing with cases that involve small sample sizes or highly correlated attributes, not all attribute profiles may be present. The standard method, which accounts for all attribute profiles, not only increases the complexity of the model but also complicates the calculation. Thus, it is important to identify the empty attribute profiles. This paper proposes an entropy-penalized likelihood method to eliminate the empty attribute profiles. In addition, the relation between attribute profiles and the parameter space of item parameters is discussed, and two modified expectation–maximization (EM) algorithms are designed to estimate the model parameters. Simulations are conducted to demonstrate the performance of the proposed method, and a real data application based on the fraction–subtraction data is presented to showcase the practical implications of the proposed method. Full article

(This article belongs to the Special Issue Statistical Methods in Data Science and Applications)

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17 pages, 1131 KiB

Open AccessArticle

Using Noisy Evaluation to Accelerate Parameter Optimization of Medical Image Segmentation Ensembles

by János Tóth, Henrietta Tomán, Gabriella Hajdu and András Hajdu

Mathematics 2023, 11(18), 3992; https://doi.org/10.3390/math11183992 - 20 Sep 2023

Viewed by 949

Abstract

An important concern with regard to the ensembles of algorithms is that using the individually optimal parameter settings of the members does not necessarily maximize the performance of the ensemble itself. In this paper, we propose a novel evaluation method for simulated annealing [...] Read more.

An important concern with regard to the ensembles of algorithms is that using the individually optimal parameter settings of the members does not necessarily maximize the performance of the ensemble itself. In this paper, we propose a novel evaluation method for simulated annealing that combines dataset sampling and image downscaling to accelerate the parameter optimization of medical image segmentation ensembles. The scaling levels and sample sizes required to maintain the convergence of the search are theoretically determined by adapting previous results for simulated annealing with imprecise energy measurements. To demonstrate the efficiency of the proposed method, we optimize the parameters of an ensemble for lung segmentation in CT scans. Our experimental results show that the proposed method can maintain the solution quality of the base method with significantly lower runtime. In our problem, optimization with simulated annealing yielded an

F_{1}

score of 0.9397 and an associated

M C C

of 0.7757. Our proposed method maintained the solution quality with an

F_{1}

score of 0.9395 and

M C C

of 0.7755 while exhibiting a 42.01% reduction in runtime. It was also shown that the proposed method is more efficient than simulated annealing with only sampling-based evaluation when the dataset size is below a problem-specific threshold. Full article

(This article belongs to the Special Issue Data Mining, Machine Learning and Network Analysis in Biomedical Informatics)

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Mathematics, Volume 11, Issue 18 (September-2 2023) – 220 articles

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