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Mathematics
Volume 11
Issue 20
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Mathematics, Volume 11, Issue 20 (October-2 2023) – 181 articles

Cover Story (view full-size image): The article is a natural continuation of the systematic research of the properties of the generalized concept of differentiability for functions with a domain \({X \subset \mathbb{R}^{n}}\) that is not necessarily open, at points that allow a neighbourhood ray in the domain. In the new context, the well-known Lagrange’s mean value theorem for scalar functions is stated and proved, even for the case when the differential is not unique at all points of the observed segment in the domain. Likewise, it has been proven that its variant is valid for vector functions as well. Additionally, the paper provides a proof of the generalization of the mean value theorem for continuous scalar functions continuously differentiable in the interior of a compact domain. View this paper
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30 pages, 382 KiB  
Article
A Hybrid Method for All Types of Solutions of the System of Cauchy-Type Singular Integral Equations of the First Kind
by H. X. Mamatova, Z. K. Eshkuvatov and Sh. Ismail
Mathematics 2023, 11(20), 4404; https://doi.org/10.3390/math11204404 - 23 Oct 2023
Viewed by 1082
Abstract
In this note, the hybrid method (combination of the homotopy perturbation method (HPM) and the Gauss elimination method (GEM)) is developed as a semi-analytical solution for the first kind system of Cauchy-type singular integral equations (CSIEs) with constant coefficients. Before applying the HPM, [...] Read more.
In this note, the hybrid method (combination of the homotopy perturbation method (HPM) and the Gauss elimination method (GEM)) is developed as a semi-analytical solution for the first kind system of Cauchy-type singular integral equations (CSIEs) with constant coefficients. Before applying the HPM, we have to first reduce the system of CSIEs into a triangle system of algebraic equations using GEM, which is then carried out using the HPM. Using the theory of the bounded, unbounded and semi-bounded solutions of CSIEs, we are able to find inverse operators for the system of CSIEs of the first kind. A stability analysis and convergent of the proposed method has been conducted in the weighted Lp space. Moreover, the proposed method is proven to be exact in the Holder class of functions for the system of characteristic SIEs for any type of initial guess. For each of the four cases, several examples are provided and examined to demonstrate the proposed method’s validity and accuracy. Obtained results are compared with the Chebyshev collocation method and modified HPM (MHPM). Example 3 reveals that the error term of the MHPM is slightly superior to that of the HPM. One of the features of the proposed method is that it can be solved as a complex-valued system of CSIEs. Numerical results revealed that the hybrid method dominates others. Full article
(This article belongs to the Special Issue Convolution Equations: Theory, Numerical Methods and Applications)
27 pages, 361 KiB  
Article
Boundedness and Compactness of Weighted Composition Operators from α-Bloch Spaces to Bers-Type Spaces on Generalized Hua Domains of the First Kind
by Jiaqi Wang and Jianbing Su
Mathematics 2023, 11(20), 4403; https://doi.org/10.3390/math11204403 - 23 Oct 2023
Cited by 1 | Viewed by 850
Abstract
We address weighted composition operators ψCϕ from α-Bloch spaces to Bers-type spaces of bounded holomorphic functions on Y, where Y is a generalized Hua domain of the first kind, and obtain some necessary and sufficient conditions for the boundedness and [...] Read more.
We address weighted composition operators ψCϕ from α-Bloch spaces to Bers-type spaces of bounded holomorphic functions on Y, where Y is a generalized Hua domain of the first kind, and obtain some necessary and sufficient conditions for the boundedness and compactness of those operators. Full article
(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory, 2nd Edition)
22 pages, 342 KiB  
Article
On the Concept of Equilibrium in Sanctions and Countersanctions in a Differential Game
by Vladislav I. Zhukovskiy and Lidiya V. Zhukovskaya
Mathematics 2023, 11(20), 4402; https://doi.org/10.3390/math11204402 - 23 Oct 2023
Viewed by 1524
Abstract
This paper develops the methodology for modeling decision processes in complex controlled dynamic systems. The idea of balancing such systems (driving them to equilibrium) is implemented, and a new mechanism for the equilibria’s stability is proposed. Such an approach involves economic–mathematical modeling jointly [...] Read more.
This paper develops the methodology for modeling decision processes in complex controlled dynamic systems. The idea of balancing such systems (driving them to equilibrium) is implemented, and a new mechanism for the equilibria’s stability is proposed. Such an approach involves economic–mathematical modeling jointly with systems analysis methods, economics, law, sociology, game theory, management, and performance measurement. A linear-quadratic positional differential game of several players is considered. Coefficient criteria under which the game has an equilibrium in sanctions and countersanctions and, simultaneously, no Nash equilibrium are derived. The economic and legal model of active equilibrium is studied through the legal concept of sanctions, which enlarges the practical application of this class of problems. Full article
(This article belongs to the Special Issue Modeling and Simulation of Social-Behavioral Phenomena)
13 pages, 3083 KiB  
Article
BaMSGAN: Self-Attention Generative Adversarial Network with Blur and Memory for Anime Face Generation
by Xu Li, Bowei Li, Minghao Fang, Rui Huang and Xiaoran Huang
Mathematics 2023, 11(20), 4401; https://doi.org/10.3390/math11204401 - 23 Oct 2023
Viewed by 1601
Abstract
In this paper, we propose a novel network, self-attention generative adversarial network with blur and memory (BaMSGAN), for generating anime faces with improved clarity and faster convergence while retaining the capacity for continuous learning. Traditional self-attention generative adversarial networks (SAGANs) produce anime faces [...] Read more.
In this paper, we propose a novel network, self-attention generative adversarial network with blur and memory (BaMSGAN), for generating anime faces with improved clarity and faster convergence while retaining the capacity for continuous learning. Traditional self-attention generative adversarial networks (SAGANs) produce anime faces of higher quality compared to deep convolutional generative adversarial networks (DCGANs); however, some edges remain blurry and distorted, and the generation speed is sluggish. Additionally, common issues hinder the model’s ability to learn continuously. To address these challenges, we introduce a blurring preprocessing step on a portion of the training dataset, which is then fed to the discriminator as fake data to encourage the model to avoid blurry edges. Furthermore, we incorporate regulation into the optimizer to mitigate mode collapse. Additionally, memory data stored in the memory repository is presented to the model every epoch to alleviate catastrophic forgetting, thereby enhancing performance throughout the training process. Experimental results demonstrate that BaMSGAN outperforms prior work in anime face generation, significantly reducing distortion rates and accelerating shape convergence. Full article
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35 pages, 482 KiB  
Article
General Fractional Noether Theorem and Non-Holonomic Action Principle
by Vasily E. Tarasov
Mathematics 2023, 11(20), 4400; https://doi.org/10.3390/math11204400 - 23 Oct 2023
Cited by 4 | Viewed by 1306
Abstract
Using general fractional calculus (GFC) of the Luchko form and non-holonomic variational equations of Sedov type, generalizations of the standard action principle and first Noether theorem are proposed and proved for non-local (general fractional) non-Lagrangian field theory. The use of the GFC allows [...] Read more.
Using general fractional calculus (GFC) of the Luchko form and non-holonomic variational equations of Sedov type, generalizations of the standard action principle and first Noether theorem are proposed and proved for non-local (general fractional) non-Lagrangian field theory. The use of the GFC allows us to take into account a wide class of nonlocalities in space and time compared to the usual fractional calculus. The use of non-holonomic variation equations allows us to consider field equations and equations of motion for a wide class of irreversible processes, dissipative and open systems, non-Lagrangian and non-Hamiltonian field theories and systems. In addition, the proposed GF action principle and the GF Noether theorem are generalized to equations containing general fractional integrals (GFI) in addition to general fractional derivatives (GFD). Examples of field equations with GFDs and GFIs are suggested. The energy–momentum tensor, orbital angular-momentum tensor and spin angular-momentum tensor are given for general fractional non-Lagrangian field theories. Examples of application of generalized first Noether’s theorem are suggested for scalar end vector fields of non-Lagrangian field theory. Full article
(This article belongs to the Section Mathematical Physics)
19 pages, 6023 KiB  
Article
Efficient Trajectory Planning for Optimizing Energy Consumption and Completion Time in UAV-Assisted IoT Networks
by Mengtang Li, Guoku Jia, Xun Li and Hao Qiu
Mathematics 2023, 11(20), 4399; https://doi.org/10.3390/math11204399 - 23 Oct 2023
Cited by 3 | Viewed by 1671
Abstract
Quadrotor unmanned aerial vehicles (UAVs) have emerged as ubiquitous and agile robots and data carriers within the framework of the future Internet of Things (IoT) and mobile wireless networks. Yet, the insufficient onboard battery necessitates the optimization of energy consumption for both the [...] Read more.
Quadrotor unmanned aerial vehicles (UAVs) have emerged as ubiquitous and agile robots and data carriers within the framework of the future Internet of Things (IoT) and mobile wireless networks. Yet, the insufficient onboard battery necessitates the optimization of energy consumption for both the UAV and IoT devices while ensuring that communication requirements are met. This paper therefore proposes a more accurate and mathematically tractable model for characterizing a UAV’s energy consumption concerning desired trajectories. This nonlinear model takes into account the UAV’s dynamics, brushless direct current (BLDC) motor dynamics, and aerodynamics. To optimize the communication time between IoT devices and the UAV, IoT devices are clustered using a modified GAK-means algorithm, with dynamically optimized communication coverage radii. Subsequently, a fly–circle–communicate (FCC) trajectory design algorithm is introduced and derived to conserve energy and save mission time. Under the FCC approach, the UAV sequentially visits the cluster centers and performs circular flight and communication. Transitions between cluster centers are smoothed via 3D Dubins curves, which provide physically achievable trajectories. Comprehensive numerical studies indicate that the proposed trajectory planning method reduces overall communication time and preserves UAV battery energy compared to other benchmark schemes. Full article
(This article belongs to the Special Issue Mathematical Modeling in Nonlinear Control and Robotics)
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12 pages, 3942 KiB  
Article
Music through Curve Insights
by Shai Gul
Mathematics 2023, 11(20), 4398; https://doi.org/10.3390/math11204398 - 23 Oct 2023
Viewed by 1218
Abstract
This manuscript endeavors to establish a framework for the mapping of music onto a three-dimensional structure. Our objective is to transform the guitar choruses of Beatles songs into curves, with each chorus corresponding to its respective curve. We aim to investigate and characterize [...] Read more.
This manuscript endeavors to establish a framework for the mapping of music onto a three-dimensional structure. Our objective is to transform the guitar choruses of Beatles songs into curves, with each chorus corresponding to its respective curve. We aim to investigate and characterize the intricacy of each song by employing mathematical techniques derived from differential geometry, specifically focusing on the total curvature of the chorus curve. Given that a single song may possess varying chord progressions in different verses, the performer can determine the geometric representation they aim to convey through the number of loops and the direction of the curve. The overarching objective of our study is to enable viewers to identify specific songs or motives by visually examining an object and exploring its geometric properties. Furthermore, we posit that these ideas can provide composers with a fresh perspective on their own musical compositions while also granting non-professional audiences a glimpse into the intricacies involved in the process of composing. Full article
(This article belongs to the Special Issue Mathematics and Computation in Music)
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30 pages, 1379 KiB  
Article
Default Probabilities and the Credit Spread of Mexican Companies: The Modified Merton Model
by Paula Morales-Bañuelos and Guillermo Fernández-Anaya
Mathematics 2023, 11(20), 4397; https://doi.org/10.3390/math11204397 - 23 Oct 2023
Viewed by 1536
Abstract
This study aims to identify the model that best approximates the credit spread that should be fixed on debt instruments issued by both companies listed on the Mexican Stock Market, considering the particularities of the Mexican market. Five models were analyzed: Merton’s model, [...] Read more.
This study aims to identify the model that best approximates the credit spread that should be fixed on debt instruments issued by both companies listed on the Mexican Stock Market, considering the particularities of the Mexican market. Five models were analyzed: Merton’s model, Brownian Motion Model, Power Law Brownian Motion Model, Bloomberg’s model, and the model presented in this paper, which includes the conformable derivatives, taking as a reference the change in the variable as other authors have done, and the Bloomberg corporate default risk model (DRSK) for publics firms. We concluded that the modified Merton model approximates, to a greater extent, the credit spreads that fix on a prime rate on the loans granted to Mexican non-financial companies. Full article
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12 pages, 269 KiB  
Article
Hidden Markov Model Based on Logistic Regression
by Byeongheon Lee, Joowon Park and Yongku Kim
Mathematics 2023, 11(20), 4396; https://doi.org/10.3390/math11204396 - 23 Oct 2023
Cited by 1 | Viewed by 1892
Abstract
A hidden Markov model (HMM) is a useful tool for modeling dependent heterogeneous phenomena. It can be used to find factors that affect real-world events, even when those factors cannot be directly observed. HMMs differ from traditional methods by using state variables and [...] Read more.
A hidden Markov model (HMM) is a useful tool for modeling dependent heterogeneous phenomena. It can be used to find factors that affect real-world events, even when those factors cannot be directly observed. HMMs differ from traditional methods by using state variables and mixture distributions to model the hidden states. This allows HMMs to find relationships between variables even when the variables cannot be directly observed. HMM can be extended, allowing the transition probabilities to depend on covariates. This makes HMMs more flexible and powerful, as they can be used to model a wider range of sequential data. Modeling covariates in a hidden Markov model is particularly difficult when the dimension of the state variable is large. To avoid these difficulties, Markovian properties are achieved by implanting the previous state variables to the logistic regression model. We apply the proposed method to find the factors that affect the hidden state of matsutake mushroom growth, in which it is hard to find covariates that directly affect matsutake mushroom growth in Korea. We believe that this method can be used to identify factors that are difficult to find using traditional methods. Full article
(This article belongs to the Section Probability and Statistics)
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20 pages, 10168 KiB  
Article
Risk Premium of Bitcoin and Ethereum during the COVID-19 and Non-COVID-19 Periods: A High-Frequency Approach
by José Antonio Núñez-Mora, Mario Iván Contreras-Valdez and Roberto Joaquín Santillán-Salgado
Mathematics 2023, 11(20), 4395; https://doi.org/10.3390/math11204395 - 23 Oct 2023
Viewed by 1448
Abstract
This paper reports our findings on the return dynamics of Bitcoin and Ethereum using high-frequency data (minute-by-minute observations) from 2015 to 2022 for Bitcoin and from 2016 to 2022 for Ethereum. The main objective of modeling these two series was to obtain a [...] Read more.
This paper reports our findings on the return dynamics of Bitcoin and Ethereum using high-frequency data (minute-by-minute observations) from 2015 to 2022 for Bitcoin and from 2016 to 2022 for Ethereum. The main objective of modeling these two series was to obtain a dynamic estimation of risk premium with the intention of characterizing its behavior. To this end, we estimated the Generalized Autoregressive Conditional Heteroskedasticity in Mean with Normal-Inverse Gaussian distribution (GARCH-M-NIG) model for the residuals. We also estimated the other parameters of the model and discussed their evolution over time, including the skewness and kurtosis of the Normal-Inverse Gaussian distribution. Similarly, we determined the parameters that define the evolution of the estimated variance, i.e., the parameters related to the fitted past variance, square error and long-term average value. We found that, despite the market uncertainty during the COVID-19 emergency period (2020 and 2021), the selected cryptocurrencies’ return volatility and kurtosis were even greater for several other subperiods within our sample’s time frame. Our model represents an analytical tool that estimates the risk premium that should be delivered by Bitcoin and Ethereum and is therefore of interest to risk managers, traders and investors. Full article
(This article belongs to the Special Issue Mathematical, Statistical, and Soft Computing Methods for Uncertainty Management)
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28 pages, 686 KiB  
Article
Age of Information Cost Minimization with No Buffers, Random Arrivals and Unreliable Channels: A PCL-Indexability Analysis
by José Niño-Mora
Mathematics 2023, 11(20), 4394; https://doi.org/10.3390/math11204394 - 23 Oct 2023
Cited by 1 | Viewed by 1069
Abstract
Over the last decade, the Age of Information has emerged as a key concept and metric for applications where the freshness of sensor-provided data is critical. Limited transmission capacity has motivated research on the design of tractable policies for scheduling information updates to [...] Read more.
Over the last decade, the Age of Information has emerged as a key concept and metric for applications where the freshness of sensor-provided data is critical. Limited transmission capacity has motivated research on the design of tractable policies for scheduling information updates to minimize Age of Information cost based on Markov decision models, in particular on the restless multi-armed bandit problem (RMABP). This allows the use of Whittle’s popular index policy, which is often nearly optimal, provided indexability (index existence) is proven, which has been recently accomplished in some models. We aim to extend the application scope of Whittle’s index policy in a broader AoI scheduling model. We address a model with no buffers incorporating random packet arrivals, unreliable channels, and nondecreasing AoI costs. We use sufficient indexability conditions based on partial conservation laws previously introduced by the author to establish the model’s indexability and evaluate its Whittle index in closed form under discounted and average cost criteria. We further use the index formulae to draw insights on how scheduling priority depends on model parameters. Full article
(This article belongs to the Section Probability and Statistics)
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17 pages, 4607 KiB  
Article
Enhancing Autonomous Guided Vehicles with Red-Black TOR Iterative Method
by A’Qilah Ahmad Dahalan, Azali Saudi and Jumat Sulaiman
Mathematics 2023, 11(20), 4393; https://doi.org/10.3390/math11204393 - 23 Oct 2023
Cited by 1 | Viewed by 1075
Abstract
To address an autonomous guided vehicle problem, this article presents extended variants of the established block over-relaxation method known as the Block Modified Two-Parameter Over-relaxation (B-MTOR) method. The main challenge in handling autonomous-driven vehicles is to offer an efficient and reliable path-planning algorithm [...] Read more.
To address an autonomous guided vehicle problem, this article presents extended variants of the established block over-relaxation method known as the Block Modified Two-Parameter Over-relaxation (B-MTOR) method. The main challenge in handling autonomous-driven vehicles is to offer an efficient and reliable path-planning algorithm equipped with collision-free feature. This work intends to solve the path navigation with obstacle avoidance problem explicitly by using a numerical approach, where the mobile robot must project a route to outperform the efficiency of its travel from any initial position to the target location in the designated area. The solution builds on the potential field technique that uses Laplace’s equation to restrict the formation of potential functions across operating mobile robot regions. The existing block over-relaxation method and its variants evaluate the computation by obtaining four Laplacian potentials per computation in groups. These groups can also be viewed as groups of two points and single points if they’re close to the boundary. The proposed B-MTOR technique employs red-black ordering with four different weighted parameters. By carefully choosing the optimal parameter values, the suggested B-MTOR improved the computational execution of the algorithm. In red-black ordering, the computational molecules of red and black nodes are symmetrical. When the computation of red nodes is performed, the updated values of their four neighbouring black nodes are applied, and conversely. The performance of the newly proposed B-MTOR method is compared against the existing methods in terms of computational complexity and execution time. The simulation findings reveal that the red-black variants are superior to their corresponding regular variants, with the B-MTOR approach giving the best performance. The experiment also shows that, by applying a finite difference method, the mobile robot is capable of producing a collision-free path from any start to a given target point. In addition, the findings also verified that numerical techniques could provide an accelerated solution and have generated a smoother path than earlier work on the same issue. Full article
(This article belongs to the Special Issue Analysis and Mathematical Modeling of Control Engineering and Path Planning)
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19 pages, 3746 KiB  
Article
Path Planning Algorithm for Dual-Arm Robot Based on Depth Deterministic Gradient Strategy Algorithm
by Xiaomei Zhang, Fan Yang, Qiwen Jin, Ping Lou and Jiwei Hu
Mathematics 2023, 11(20), 4392; https://doi.org/10.3390/math11204392 - 23 Oct 2023
Cited by 4 | Viewed by 1866
Abstract
In recent years, the utilization of dual-arm robots has gained substantial prominence across various industries owing to their collaborative operational capabilities. In order to achieve collision avoidance and facilitate cooperative task completion, efficient path planning plays a pivotal role. The high dimensionality associated [...] Read more.
In recent years, the utilization of dual-arm robots has gained substantial prominence across various industries owing to their collaborative operational capabilities. In order to achieve collision avoidance and facilitate cooperative task completion, efficient path planning plays a pivotal role. The high dimensionality associated with collaborative task execution in dual-arm robots renders existing path planning methods ineffective for conducting efficient exploration. This paper introduces a multi-agent path planning reinforcement learning algorithm that integrates an experience replay strategy, a shortest-path constraint, and the policy gradient method. To foster collaboration and avoid competition between the robot arms, the proposed approach incorporates a mechanism known as “reward cooperation, punishment competition” during the training process. Our algorithm demonstrates strong performance in the control of dual-arm robots and exhibits the potential to mitigate the challenge of reward sparsity encountered during the training process. The effectiveness of the proposed algorithm is validated through simulations and experiments, comparing the results with existing methods and showcasing its superiority in dual-arm robot path planning. Full article
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17 pages, 389 KiB  
Article
On Consistency of the Nearest Neighbor Estimator of the Density Function for m-AANA Samples
by Xin Liu, Yi Wu, Wei Wang and Yong Zhu
Mathematics 2023, 11(20), 4391; https://doi.org/10.3390/math11204391 - 23 Oct 2023
Viewed by 856
Abstract
In this paper, by establishing a Bernstein inequality for m-asymptotically almost negatively associated random variables, some results on consistency for the nearest neighbor estimator of the density function are further established. The results generalize some existing ones in the literature. Some numerical [...] Read more.
In this paper, by establishing a Bernstein inequality for m-asymptotically almost negatively associated random variables, some results on consistency for the nearest neighbor estimator of the density function are further established. The results generalize some existing ones in the literature. Some numerical simulations are also provided to support the results. Full article
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11 pages, 5525 KiB  
Article
Decomposition Is All You Need: Single-Objective to Multi-Objective Optimization towards Artificial General Intelligence
by Wendi Xu, Xianpeng Wang, Qingxin Guo, Xiangman Song, Ren Zhao, Guodong Zhao, Dakuo He, Te Xu, Ming Zhang and Yang Yang
Mathematics 2023, 11(20), 4390; https://doi.org/10.3390/math11204390 - 23 Oct 2023
Cited by 1 | Viewed by 1915
Abstract
As a new abstract computational model in evolutionary transfer optimization (ETO), single-objective to multi-objective optimization (SMO) is conducted at the macroscopic level rather than the intermediate level for specific algorithms or the microscopic level for specific operators; this method aims to develop systems [...] Read more.
As a new abstract computational model in evolutionary transfer optimization (ETO), single-objective to multi-objective optimization (SMO) is conducted at the macroscopic level rather than the intermediate level for specific algorithms or the microscopic level for specific operators; this method aims to develop systems with a profound grasp of evolutionary dynamic and learning mechanism similar to human intelligence via a “decomposition” style (in the abstract of the well-known “Transformer” article “Attention is All You Need”, they use “attention” instead). To the best of our knowledge, it is the first work of SMO for discrete cases because we extend our conference paper and inherit its originality status. In this paper, by implementing the abstract SMO in specialized memetic algorithms, key knowledge from single-objective problems/tasks to the multi-objective core problem/task can be transferred or “gathered” for permutation flow shop scheduling problems, which will reduce the notorious complexity in combinatorial spaces for multi-objective settings in a straight method; this is because single-objective tasks are easier to complete than their multi-objective versions. Extensive experimental studies and theoretical results on benchmarks (1) emphasize our decomposition root in mathematical programming, such as Lagrangian relaxation and column generation; (2) provide two “where to go” strategies for both SMO and ETO; and (3) contribute to the mission of building safe and beneficial artificial general intelligence for manufacturing via evolutionary computation. Full article
(This article belongs to the Special Issue Operations and Supply Chain Management with the Application of Mathematical Models)
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20 pages, 7069 KiB  
Article
An Improved Multi-Objective Particle Swarm Optimization-Based Hybrid Intelligent Algorithm for Index Screening of Underwater Manned/Unmanned Cooperative System of Systems Architecture Evaluation
by Hao Zhou, Yunsheng Mao and Xuan Guo
Mathematics 2023, 11(20), 4389; https://doi.org/10.3390/math11204389 - 23 Oct 2023
Cited by 2 | Viewed by 1202
Abstract
An improved multi-objective particle swarm optimization algorithm is combined with a machine learning classifier to meet the needs of underwater manned/unmanned cooperative warfare architecture evaluation. Firstly, based on the traditional Cauchy variation method, the particles in the population are disturbed in a dynamic [...] Read more.
An improved multi-objective particle swarm optimization algorithm is combined with a machine learning classifier to meet the needs of underwater manned/unmanned cooperative warfare architecture evaluation. Firstly, based on the traditional Cauchy variation method, the particles in the population are disturbed in a dynamic way so that the particles trapped in the local optimal can jump out of the local optimal, and the convergence performance of the particle swarm optimization is improved. Secondly, the accuracy of the index set is analyzed based on the CART decision tree algorithm and the IWRF algorithm. A screening method of key indexes with fewer evaluation indexes and high evaluation accuracy is developed to solve the problem of a large number of evaluation indexes and unclear correlation of the underwater combat system. Through simulation, the extraction results of key indicators were verified, and the reliability coefficient of the final simulation experiment was 0.93, which can be considered as high reliability and effectiveness of the key indicators extracted in this study. By combining multi-objective optimization with machine learning and weighing evaluation efficiency and accuracy, a high-precision and rapid evaluation of a few indicators is achieved, which provides support for establishing an evaluation model of SoS architecture for underwater manned/unmanned cooperative operations. This research result can provide inspiration for the evaluation and evaluation of the system in order to analyze the accuracy of indicators and the evaluation effect and carry out research by simulating the actual system with tools with a high simulation degree. Full article
(This article belongs to the Section Mathematics and Computer Science)
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28 pages, 2135 KiB  
Article
Predicting Glycemic Control in a Small Cohort of Children with Type 1 Diabetes Using Machine Learning Algorithms
by Bogdan Neamtu, Mihai Octavian Negrea and Iuliana Neagu
Mathematics 2023, 11(20), 4388; https://doi.org/10.3390/math11204388 - 22 Oct 2023
Cited by 1 | Viewed by 1524
Abstract
Type 1 diabetes, a chronic condition characterized by insulin deficiency, is associated with various complications and reduced life expectancy and is increasing in global prevalence. Maintaining glycaemic control in children with type 1 diabetes, as reflected by glycated hemoglobin levels (A1C), is a [...] Read more.
Type 1 diabetes, a chronic condition characterized by insulin deficiency, is associated with various complications and reduced life expectancy and is increasing in global prevalence. Maintaining glycaemic control in children with type 1 diabetes, as reflected by glycated hemoglobin levels (A1C), is a challenging task. The American Association of Diabetes (ADA), the Pediatric Endocrine Society, and the International Diabetes Federation (ISPAD) recommend the adoption of a harmonized A1C of <7.5% across all pediatric groups. Our retrospective study included 79 children with type 1 diabetes and aimed to identify determinants pivotal to forecasting glycemic control, focusing on a single A1C cut-off value and exploring how machine learning algorithms can enhance clinical understanding, particularly with smaller sample sizes. Bivariate analysis identified correlations between glycemic control and disease duration, body mass index (BMI) Z-score at onset, A1C at onset above 7.5 g/dL, family income, living environment, maternal education level, episodes of ketoacidosis, and elevated cholesterol or triglyceride. Binary logistic regression stressed the association of ketoacidosis episodes (β = 21.1, p < 0.01) and elevated A1C levels at onset (β = 3.12, p < 0.01) and yielded an area under the receiver operating characteristic curve (AUROC) of 0.916. Two-step clustering emphasized socioeconomic factors, as well as disease complications and comorbidities, and delineated clusters based on these traits. The classification and regression tree (CART) yielded an AUROC of 0.954, slightly outperforming binary regression, providing a comprehensive view of interactions between disease characteristics, comorbidities, and socioeconomic status. Common to all methods were predictors regarding ketoacidosis episodes, the onset of A1C levels, and family income, signifying their overarching importance in glycaemic control. While logistic regression quantified risk, CART visually elucidated complex interactions and two-step clustering exposed patient subgroups that might require different intervention strategies, highlighting how the complementary nature of these analytical methods can enrich clinical interpretation. Full article
(This article belongs to the Special Issue Statistics and Probabilities and Their Role within Health Sciences)
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22 pages, 7149 KiB  
Article
Digital Authentication System in Avatar Using DID and SBT
by Geunyoung Kim and Jaecheol Ryou
Mathematics 2023, 11(20), 4387; https://doi.org/10.3390/math11204387 - 22 Oct 2023
Cited by 8 | Viewed by 2766
Abstract
Anonymity forms the basis of decentralized ecosystems, leading to an increase in criminal activities such as money laundering and illegal currency trading. Especially in blockchain-based metaverse services, activities such as preventing sexual crimes and verifying the identity of adults are becoming essential. Therefore, [...] Read more.
Anonymity forms the basis of decentralized ecosystems, leading to an increase in criminal activities such as money laundering and illegal currency trading. Especially in blockchain-based metaverse services, activities such as preventing sexual crimes and verifying the identity of adults are becoming essential. Therefore, avatar authentication and the KYC (Know Your Customer) process have become crucial elements. This paper proposes a mechanism to achieve the KYC process by verifying user identity using smart contracts. Users obtain an SBT (Soul Bound Token) from the metaverse service provider through the DID (Decentralized Identity) credential issued during the KYC process. The identity verification of avatars occurs within smart contracts, ensuring user privacy and protection through ZKP (Zero Knowledge Proof). Tools for generating ZKP are also provided, enabling users, even those who are unfamiliar with ZKP, to use them conveniently. Additionally, an integrated wallet is offered to seamlessly manage DID credentials and SBTs. Furthermore, in case of avatar identity issues, users can request an audit by the issuer through the associated DID tokens. Full article
(This article belongs to the Special Issue Advances in Blockchain Technology)
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27 pages, 4774 KiB  
Article
A Functional Data Approach for Continuous-Time Analysis Subject to Modeling Discrepancy under Infill Asymptotics
by Tao Chen, Yixuan Li and Renfang Tian
Mathematics 2023, 11(20), 4386; https://doi.org/10.3390/math11204386 - 22 Oct 2023
Viewed by 1405
Abstract
Parametric continuous-time analysis often entails derivations of continuous-time models from predefined discrete formulations. However, undetermined convergence rates of frequency-dependent parameters can result in ill-defined continuous-time limits, leading to modeling discrepancy, which impairs the reliability of fitting and forecasting. To circumvent this issue, we [...] Read more.
Parametric continuous-time analysis often entails derivations of continuous-time models from predefined discrete formulations. However, undetermined convergence rates of frequency-dependent parameters can result in ill-defined continuous-time limits, leading to modeling discrepancy, which impairs the reliability of fitting and forecasting. To circumvent this issue, we propose a simple solution based on functional data analysis (FDA) and truncated Taylor series expansions. It is demonstrated through a simulation study that our proposed method is superior—compared with misspecified parametric methods—in fitting and forecasting continuous-time stochastic processes, while the parametric method slightly dominates under correct specification, with comparable forecast errors to the FDA-based method. Due to its generally consistent and more robust performance against possible misspecification, the proposed FDA-based method is recommended in the presence of modeling discrepancy. Further, we apply the proposed method to predict the future return of the S&P 500, utilizing observations extracted from a latent continuous-time process, and show the practical efficacy of our approach in accurately discerning the underlying dynamics. Full article
(This article belongs to the Special Issue Financial Econometrics and Machine Learning)
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39 pages, 1840 KiB  
Article
Effect of Impaired B-Cell and CTL Functions on HIV-1 Dynamics
by Noura H. AlShamrani, Reham H. Halawani and Ahmed M. Elaiw
Mathematics 2023, 11(20), 4385; https://doi.org/10.3390/math11204385 - 22 Oct 2023
Cited by 2 | Viewed by 945
Abstract
This paper formulates and analyzes two mathematical models that describe the within-host dynamics of human immunodeficiency virus type 1 (HIV-1) with impairment of both cytotoxic T lymphocytes (CTLs) and B cells. Both viral transmission (VT) and cellular infection (CT) mechanisms are considered. The [...] Read more.
This paper formulates and analyzes two mathematical models that describe the within-host dynamics of human immunodeficiency virus type 1 (HIV-1) with impairment of both cytotoxic T lymphocytes (CTLs) and B cells. Both viral transmission (VT) and cellular infection (CT) mechanisms are considered. The second model is a generalization of the first model that includes distributed time delays. For the two models, we establish the non-negativity and boundedness of the solutions, find the basic reproductive numbers, determine all possible steady states and establish the global asymptotic stability properties of all steady states by means of the Lyapunov method. We confirm the theoretical results by conducting numerical simulations. We conduct a sensitivity analysis to show the effect of the values of the parameters on the basic reproductive number. We discuss the results, showing that impaired B cells and CTLs, time delay and latent CT have significant effects on the HIV-1 dynamics. Full article
(This article belongs to the Special Issue Mathematical Modeling and Analysis in Biology and Medicine, 2nd Edition)
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19 pages, 583 KiB  
Article
An Improved Mayfly Optimization Algorithm for Type-2 Multi-Objective Integrated Process Planning and Scheduling
by Ke Yang and Dazhi Pan
Mathematics 2023, 11(20), 4384; https://doi.org/10.3390/math11204384 - 21 Oct 2023
Viewed by 1586
Abstract
The type-2 multi-objective integrated process planning and scheduling problem, as an NP-hard problem, is required to deal with both process planning and job shop scheduling, and to generate optimal schedules while planning optimal machining paths for the workpieces. For the type-2 multi-objective integrated [...] Read more.
The type-2 multi-objective integrated process planning and scheduling problem, as an NP-hard problem, is required to deal with both process planning and job shop scheduling, and to generate optimal schedules while planning optimal machining paths for the workpieces. For the type-2 multi-objective integrated process planning and scheduling problem, a mathematical model with the minimization objectives of makespan, total machine load, and critical machine load is developed. A multi-objective mayfly optimization algorithm with decomposition and adaptive neighborhood search is designed to solve this problem. The algorithm uses two forms of encoding, a transformation scheme designed to allow the two codes to switch between each other during evolution, and a hybrid population initialization strategy designed to improve the quality of the initial solution while taking into account diversity. In addition, an adaptive neighborhood search cycle based on the average distance of the Pareto optimal set to the ideal point is designed to improve the algorithm’s merit-seeking ability while maintaining the diversity of the population. The proposed encoding and decoding scheme can better transform the continuous optimization algorithm to apply to the combinatorial optimization problem. Finally, it is experimentally verified that the proposed algorithm achieves better experimental results and can effectively deal with type-2 MOIPPS. Full article
(This article belongs to the Special Issue Data-Driven Algorithms for Optimal Decision Making in Logistics and Supply Chain Management)
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22 pages, 696 KiB  
Article
Nonparametric Estimation of Multivariate Copula Using Empirical Bayes Methods
by Lu Lu and Sujit Ghosh
Mathematics 2023, 11(20), 4383; https://doi.org/10.3390/math11204383 - 21 Oct 2023
Cited by 3 | Viewed by 1780
Abstract
In the fields of finance, insurance, system reliability, etc., it is often of interest to measure the dependence among variables by modeling a multivariate distribution using a copula. The copula models with parametric assumptions are easy to estimate but can be highly biased [...] Read more.
In the fields of finance, insurance, system reliability, etc., it is often of interest to measure the dependence among variables by modeling a multivariate distribution using a copula. The copula models with parametric assumptions are easy to estimate but can be highly biased when such assumptions are false, while the empirical copulas are nonsmooth and often not genuine copulas, making the inference about dependence challenging in practice. As a compromise, the empirical Bernstein copula provides a smooth estimator, but the estimation of tuning parameters remains elusive. The proposed empirical checkerboard copula within a hierarchical empirical Bayes model alleviates the aforementioned issues and provides a smooth estimator based on multivariate Bernstein polynomials that itself is shown to be a genuine copula. Additionally, the proposed copula estimator is shown to provide a more accurate estimate of several multivariate dependence measures. Both theoretical asymptotic properties and finite-sample performances of the proposed estimator based on simulated data are presented and compared with some nonparametric estimators. An application to portfolio risk management is included based on stock prices data. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
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23 pages, 397 KiB  
Review
Stability of Differential Systems with Impulsive Effects
by Chunxiang Li, Fangshu Hui and Fangfei Li
Mathematics 2023, 11(20), 4382; https://doi.org/10.3390/math11204382 - 21 Oct 2023
Cited by 1 | Viewed by 1281
Abstract
In this paper, a brief survey on the stability of differential systems with impulsive effects is provided. A large number of research results on the stability of differential systems with impulsive effects are considered. These systems include impulsive differential systems, stochastic impulsive differential [...] Read more.
In this paper, a brief survey on the stability of differential systems with impulsive effects is provided. A large number of research results on the stability of differential systems with impulsive effects are considered. These systems include impulsive differential systems, stochastic impulsive differential systems and differential systems with several specific impulses (non-instantaneous impulses, delayed impulses, impulses suffered by logic choice and impulse time windows). The stability issues as well as the applications in neural networks are discussed in detail. Full article
(This article belongs to the Special Issue Advances of Intelligent Systems)
22 pages, 789 KiB  
Article
Fuzzy Assessment of Management Consulting Projects: Model Validation and Case Studies
by Hongyi Sun, Wenbin Ni and Lanxuan Huang
Mathematics 2023, 11(20), 4381; https://doi.org/10.3390/math11204381 - 21 Oct 2023
Cited by 2 | Viewed by 1364
Abstract
Management consulting (MC) has been heavily involved in emerging business opportunities in mainland China. However, there are no well-known local MC project management models to help evaluate whether an MC project can be successful or not. This paper reports a model for the [...] Read more.
Management consulting (MC) has been heavily involved in emerging business opportunities in mainland China. However, there are no well-known local MC project management models to help evaluate whether an MC project can be successful or not. This paper reports a model for the self-assessment of management consulting projects, which has been validated by 15 experts and 13 cases. The new model, with seven factors that are critical to the success of MC projects, was developed from a literature review. The model was then verified by developing a questionnaire that was sent to 15 experts and using Dempster–Shafer theory to obtain the weight of each part of the model. The model was applied to 13 real cases to verify its effectiveness in evaluating an MC project. This new MC model can help consulting teams to conduct assessments in the early and middle stages, and evaluate in the late stage, of consulting projects, and also can help teams improve the probability of project success and client satisfaction. It can be used by consultants, client companies, or both. Full article
(This article belongs to the Special Issue Fuzzy Sets in Business Management, Finance, and Economics, 2nd Edition)
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15 pages, 303 KiB  
Article
Fourth-Order Neutral Differential Equation: A Modified Approach to Optimizing Monotonic Properties
by Amany Nabih, Osama Moaaz, Sameh S. Askar, Ahmad M. Alshamrani and Elmetwally M. Elabbasy
Mathematics 2023, 11(20), 4380; https://doi.org/10.3390/math11204380 - 21 Oct 2023
Cited by 1 | Viewed by 983
Abstract
In this article, we investigate some qualitative properties of solutions to a class of functional differential equations with multi-delay. Using a modified approach, we first derive a number of optimized relations and inequalities that relate the solution xs to its corresponding function [...] Read more.
In this article, we investigate some qualitative properties of solutions to a class of functional differential equations with multi-delay. Using a modified approach, we first derive a number of optimized relations and inequalities that relate the solution xs to its corresponding function zs and its derivatives. After classifying the positive solutions, we follow the Riccati approach and principle of comparison, where fourth-order differential equations are compared with first-order differential equations to obtain conditions that exclude the positive solutions. Then, we introduce new oscillation conditions. With regard to previous relevant results, our results are an extension and complement to them. This work has theoretical significance in that it uncovers some new relationships that aid in developing the oscillation theory of higher-order equations in addition to the applied relevance of neutral differential equations. Full article
(This article belongs to the Section Difference and Differential Equations)
26 pages, 3879 KiB  
Article
Stochastic Time Complexity Surfaces of Computing Node
by Andrey Borisov and Alexey Ivanov
Mathematics 2023, 11(20), 4379; https://doi.org/10.3390/math11204379 - 21 Oct 2023
Cited by 1 | Viewed by 1165
Abstract
The paper is devoted to the formal description of the running time of the user task on some virtual nodes in the computing network. Based on the probability theory framework, this time represents a random value with a finite mean and variance. For [...] Read more.
The paper is devoted to the formal description of the running time of the user task on some virtual nodes in the computing network. Based on the probability theory framework, this time represents a random value with a finite mean and variance. For any class of user task, these moments are the functions of the node resources, task numerical characteristics, and the parameters of the current node state. These functions of the vector arguments can be treated as some surfaces in the multidimensional Euclidean spaces, so the proposed models are called the stochastic time complexity surfaces. The paper also presents a class of functions suitable for the description of both the mean and variance. They contain unknown parameters which should be estimated. The article includes the statement of the parameter identification problem given the statistical results of the node stress testing, recommendations concerning the test planning, and preprocessing of the raw experiment data. To illustrate the performance of the proposed model, the authors design it for an actual database application—the prototype of the passengers’ personal data anonymization system. Its application functions are classified into two user task classes: the data anonymization procedures and fulfillment of the statistical queries. The authors identify the stochastic time complexity surfaces for both task types. The additional testing experiments confirm the high performance of the suggested model and its applicability to the solution of the practical providers’ problems. Full article
(This article belongs to the Special Issue Mathematical Modeling, Optimization and Machine Learning, 2nd Edition)
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38 pages, 547 KiB  
Article
Malliavin Calculus and Its Application to Robust Optimal Investment for an Insider
by Chao Yu and Yuhan Cheng
Mathematics 2023, 11(20), 4378; https://doi.org/10.3390/math11204378 - 21 Oct 2023
Viewed by 1492
Abstract
In the theory of portfolio selection, there are few methods that effectively address the combined challenge of insider information and model uncertainty, despite numerous methods proposed for each individually. This paper studies the problem of the robust optimal investment for an insider under [...] Read more.
In the theory of portfolio selection, there are few methods that effectively address the combined challenge of insider information and model uncertainty, despite numerous methods proposed for each individually. This paper studies the problem of the robust optimal investment for an insider under model uncertainty. To address this, we extend the Itô formula for forward integrals by Malliavin calculus, and use it to establish an implicit anticipating stochastic differential game model for the robust optimal investment. Since traditional stochastic control theory proves inadequate for solving anticipating control problems, we introduce a new approach. First, we employ the variational method to convert the original problem into a nonanticipative stochastic differential game problem. Then we use the stochastic maximum principle to derive the Hamiltonian system governing the robust optimal investment. In cases where the insider information filtration is of the initial enlargement type, we derive the closed-form expression for the investment by using the white noise theory when the insider is ’small’. When the insider is ’large’, we articulate a quadratic backward stochastic differential equation characterization of the investment. We present the numerical result and conduct an economic analysis of the optimal strategy across various scenarios. Full article
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10 pages, 282 KiB  
Article
Weak Nearly Sasakian and Weak Nearly Cosymplectic Manifolds
by Vladimir Rovenski
Mathematics 2023, 11(20), 4377; https://doi.org/10.3390/math11204377 - 21 Oct 2023
Cited by 4 | Viewed by 1166
Abstract
Weak contact metric structures on a smooth manifold, introduced by V. Rovenski and R. Wolak in 2022, have provided new insight into the theory of classical structures. In this paper, we define new structures of this kind (called weak nearly Sasakian and weak [...] Read more.
Weak contact metric structures on a smooth manifold, introduced by V. Rovenski and R. Wolak in 2022, have provided new insight into the theory of classical structures. In this paper, we define new structures of this kind (called weak nearly Sasakian and weak nearly cosymplectic and nearly Kähler structures), study their geometry and give applications to Killing vector fields. We introduce weak nearly Kähler manifolds (generalizing nearly Kähler manifolds), characterize weak nearly Sasakian and weak nearly cosymplectic hypersurfaces in such Riemannian manifolds and prove that a weak nearly cosymplectic manifold with parallel Reeb vector field is locally the Riemannian product of a real line and a weak nearly Kähler manifold. Full article
(This article belongs to the Special Issue Differentiable Manifolds and Geometric Structures)
16 pages, 340 KiB  
Article
On a New Class of Bi-Close-to-Convex Functions with Bounded Boundary Rotation
by Daniel Breaz, Prathviraj Sharma, Srikandan Sivasubramanian and Sheza M. El-Deeb
Mathematics 2023, 11(20), 4376; https://doi.org/10.3390/math11204376 - 21 Oct 2023
Cited by 3 | Viewed by 1222
Abstract
In the current article, we introduce a new class of bi-close-to-convex functions with bounded boundary rotation. For this new class, the authors obtain the first three initial coefficient bounds of the newly defined bi-close-to-convex functions with bounded boundary rotation. By choosing special bi-convex [...] Read more.
In the current article, we introduce a new class of bi-close-to-convex functions with bounded boundary rotation. For this new class, the authors obtain the first three initial coefficient bounds of the newly defined bi-close-to-convex functions with bounded boundary rotation. By choosing special bi-convex functions, the authors obtain the first three initial coefficient bounds in the last section. The authors also verify the special cases where the familiar Brannan and Clunie’s conjecture is satisfied. Furthermore, the famous Fekete–Szegö inequality is also obtained for this new class of functions. Apart from the new interesting results, some of the results presented here improves the earlier results existing in the literature. Full article
(This article belongs to the Special Issue Current Topics in Geometric Function Theory)
27 pages, 700 KiB  
Article
A Unified Formal Framework for Factorial and Probabilistic Topic Modelling
by Karina Gibert and Yaroslav Hernandez-Potiomkin
Mathematics 2023, 11(20), 4375; https://doi.org/10.3390/math11204375 - 21 Oct 2023
Viewed by 1032
Abstract
Topic modelling has become a highly popular technique for extracting knowledge from texts. It encompasses various method families, including Factorial methods, Probabilistic methods, and Natural Language Processing methods. This paper introduces a unified conceptual framework for Factorial and Probabilistic methods by identifying shared [...] Read more.
Topic modelling has become a highly popular technique for extracting knowledge from texts. It encompasses various method families, including Factorial methods, Probabilistic methods, and Natural Language Processing methods. This paper introduces a unified conceptual framework for Factorial and Probabilistic methods by identifying shared elements and representing them using a homogeneous notation. The paper presents 12 different methods within this framework, enabling easy comparative analysis to assess the flexibility and how realistic the assumptions of each approach are. This establishes the initial stage of a broader analysis aimed at relating all method families to this common framework, comprehensively understanding their strengths and weaknesses, and establishing general application guidelines. Also, an experimental setup reinforces the convenience of having harmonized notational schema. The paper concludes with a discussion on the presented methods and outlines future research directions. Full article
(This article belongs to the Special Issue Advances of Applied Probability and Statistics)
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