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Editor’s Choice Articles

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to readers, or important in the respective research area. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.

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16 pages, 763 KiB  
Article
Digital Triplet: A Sequential Methodology for Digital Twin Learning
by Xueru Zhang, Dennis K. J. Lin and Lin Wang
Mathematics 2023, 11(12), 2661; https://doi.org/10.3390/math11122661 - 11 Jun 2023
Cited by 6 | Viewed by 2540
Abstract
A digital twin is a simulator of a physical system, which is built upon a series of models and computer programs with real-time data (from sensors or devices). Digital twins are used in various industries, such as manufacturing, healthcare, and transportation, to understand [...] Read more.
A digital twin is a simulator of a physical system, which is built upon a series of models and computer programs with real-time data (from sensors or devices). Digital twins are used in various industries, such as manufacturing, healthcare, and transportation, to understand complex physical systems and make informed decisions. However, predictions and optimizations with digital twins can be time-consuming due to the high computational requirements and complexity of the underlying computer programs. This poses significant challenges in making well-informed and timely decisions using digital twins. This paper proposes a novel methodology, called the “digital triplet”, to facilitate real-time prediction and decision-making. A digital triplet is an efficient representation of a digital twin, constructed using statistical models and effective experimental designs. It offers two noteworthy advantages. Firstly, by leveraging modern statistical models, a digital triplet can effectively capture and represent the complexities of a digital twin, resulting in accurate predictions and reliable decision-making. Secondly, a digital triplet adopts a sequential design and modeling approach, allowing real-time updates in conjunction with its corresponding digital twin. We conduct comprehensive simulation studies to explore the application of various statistical models and designs in constructing a digital triplet. It is shown that Gaussian process regression coupled with sequential MaxPro designs exhibits superior performance compared to other modeling and design techniques in accurately constructing the digital triplet. Full article
(This article belongs to the Special Issue Advances in Multivariate Statistics and Related Topics for the Fourth Industrial Revolution)
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14 pages, 417 KiB  
Article
Exponential Stability of a Class of Neutral Inertial Neural Networks with Multi-Proportional Delays and Leakage Delays
by Chao Wang, Yinfang Song, Fengjiao Zhang and Yuxiao Zhao
Mathematics 2023, 11(12), 2596; https://doi.org/10.3390/math11122596 - 6 Jun 2023
Cited by 10 | Viewed by 1252
Abstract
This paper investigates the exponential stability of a class of neutral inertial neural networks with multi-proportional delays and leakage delays. By utilizing the Lyapunov stability theory, the approach of parametric variation, and the differential inequality technique, some criteria are acquired that can guarantee [...] Read more.
This paper investigates the exponential stability of a class of neutral inertial neural networks with multi-proportional delays and leakage delays. By utilizing the Lyapunov stability theory, the approach of parametric variation, and the differential inequality technique, some criteria are acquired that can guarantee that all solutions of the addressed system converge exponentially to the equilibrium point. In particular, the neutral term, multi-proportional delays, and leakage delays are incorporated simultaneously, resulting in a more general model, and the findings are novel and refine the previous works. Finally, one example is provided to indicate that the dynamic behavior is consistent with the theoretical analysis. Full article
(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering, 2nd Edition)
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15 pages, 312 KiB  
Article
On the Rate of Convergence of Greedy Algorithms
by Vladimir Temlyakov
Mathematics 2023, 11(11), 2559; https://doi.org/10.3390/math11112559 - 2 Jun 2023
Cited by 3 | Viewed by 2090
Abstract
In this paper, a new criterion for the evaluation of the theoretical efficiency of a greedy algorithm is suggested. Using this criterion, we prove some results on the rate of convergence of greedy algorithms, which provide expansions. We consider both the case of [...] Read more.
In this paper, a new criterion for the evaluation of the theoretical efficiency of a greedy algorithm is suggested. Using this criterion, we prove some results on the rate of convergence of greedy algorithms, which provide expansions. We consider both the case of Hilbert spaces and the more general case of Banach spaces. The new component of this paper is that we bound the error of approximation by the product of two norms—the norm of f and the A1-norm of f. Typically, only the A1-norm of f is used. In particular, we establish that some greedy algorithms (Pure Greedy Algorithm (PGA) and its modifications) are as good as the Orthogonal Greedy Algorithm (OGA) in this new sense of the rate of convergence, while it is known that the PGA is much worse than the OGA in the standard sense. Our new results provide better bounds for the accuracy than known results in the case of small ∥f∥. Full article
(This article belongs to the Special Issue Fourier Analysis, Approximation Theory and Applications)
19 pages, 484 KiB  
Article
Graphical Local Genetic Algorithm for High-Dimensional Log-Linear Models
by Lyndsay Roach and Xin Gao
Mathematics 2023, 11(11), 2514; https://doi.org/10.3390/math11112514 - 30 May 2023
Cited by 2 | Viewed by 2633
Abstract
Graphical log-linear models are effective for representing complex structures that emerge from high-dimensional data. It is challenging to fit an appropriate model in the high-dimensional setting and many existing methods rely on a convenient class of models, called decomposable models, which lend well [...] Read more.
Graphical log-linear models are effective for representing complex structures that emerge from high-dimensional data. It is challenging to fit an appropriate model in the high-dimensional setting and many existing methods rely on a convenient class of models, called decomposable models, which lend well to a stepwise approach. However, these methods restrict the pool of candidate models from which they can search, and these methods are difficult to scale. It can be shown that a non-decomposable model can be approximated by the decomposable model which is its minimal triangulation, thus extending the convenient computational properties of decomposable models to any model. In this paper, we propose a local genetic algorithm with a crossover-hill-climbing operator, adapted for log-linear graphical models. We show that the graphical local genetic algorithm can be used successfully to fit non-decomposable models for both a low number of variables and a high number of variables. We use the posterior probability as a measure of fitness and parallel computing to decrease the computation time. Full article
(This article belongs to the Special Issue Machine Learning and Statistical Methods to Prediction and Optimal Decision-Making)
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28 pages, 7316 KiB  
Article
Supply Chain Demand Forecasting and Price Optimisation Models with Substitution Effect
by Keun Hee Lee, Mali Abdollahian, Sergei Schreider and Sona Taheri
Mathematics 2023, 11(11), 2502; https://doi.org/10.3390/math11112502 - 29 May 2023
Cited by 6 | Viewed by 10632
Abstract
Determining the optimal price of products is essential, as it plays a critical role in improving a company’s profitability and market competitiveness. This requires the ability to calculate customers’ demand in the Fast Moving Consumer Goods (FMCG) industry as various effects exist between [...] Read more.
Determining the optimal price of products is essential, as it plays a critical role in improving a company’s profitability and market competitiveness. This requires the ability to calculate customers’ demand in the Fast Moving Consumer Goods (FMCG) industry as various effects exist between multiple products within a product category. The substitution effect is one of the challenging effects at retail stores, as it requires investigating an exponential number of combinations of price changes and the availability of other products. This paper suggests a systematic price decision support tool for demand prediction and price optimise in online and stationary retailers considering the substitution effect. Two procedures reflecting the product price changes and the demand correlation structure are introduced for demand prediction and price optimisation models. First, the developed demand prediction procedure is carried out considering the combination of price changes of all products reflecting the effect of substitution. Time series and different well-known machine learning approaches with hyperparameter tuning and rolling forecasting methods are utilised to select each product’s best demand forecast. Demand forecast results are used as input in the price optimisation model. Second, the developed price optimisation procedure is a constraint programming problem based on a week time frame and a product category level aggregation and is capable of maximising profit out of the many price combinations. The results using real-world transaction data with 12 products and 4 discount rates demonstrate that including some business rules as constraints in the proposed price optimisation model reduces the number of price combinations from 11,274,924 to 19,440 and execution time from 129.59 to 25.831 min. The utilisation of the presented price optimisation support tool enables the supply chain managers to identify the optimal discount rate for individual products in a timely manner, resulting in a net profit increase. Full article
(This article belongs to the Special Issue Advances of Machine Learning and Data Mining Using Mathematical Optimization in Honor of the 65th Birthday of Prof. Adil M. Bagirov)
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10 pages, 267 KiB  
Article
On Ulam Stability of a Partial Differential Operator in Banach Spaces
by Adela Novac, Diana Otrocol and Dorian Popa
Mathematics 2023, 11(11), 2488; https://doi.org/10.3390/math11112488 - 28 May 2023
Cited by 1 | Viewed by 1309
Abstract
In this paper, we prove that, if infx∈A|f(x)|=m>0, then the partial differential operator D defined by [...] Read more.
In this paper, we prove that, if infx∈A|f(x)|=m>0, then the partial differential operator D defined by D(u)=∑k=1nfk∂u∂xk−fu, where f,fi∈C(A,R),u∈C1(A,X),i=1,…,n,I⊂R is an interval, A=I×Rn−1 and X is a Banach space, is Ulam stable with the Ulam constant K=1m. Moreover, if infx∈A|f(x)|=0, we prove that D is not generally Ulam stable. Full article
(This article belongs to the Section C1: Difference and Differential Equations)
20 pages, 2248 KiB  
Review
A Review of High-Performance Computing Methods for Power Flow Analysis
by Shadi G. Alawneh, Lei Zeng and Seyed Ali Arefifar
Mathematics 2023, 11(11), 2461; https://doi.org/10.3390/math11112461 - 26 May 2023
Cited by 6 | Viewed by 3710
Abstract
Power flow analysis is critical for power systems due to the development of multiple energy supplies. For safety, stability, and real-time response in grid operation, grid planning, and analysis of power systems, it requires designing high-performance computing methods, accelerating power flow calculation, obtaining [...] Read more.
Power flow analysis is critical for power systems due to the development of multiple energy supplies. For safety, stability, and real-time response in grid operation, grid planning, and analysis of power systems, it requires designing high-performance computing methods, accelerating power flow calculation, obtaining the voltage magnitude and phase angle of buses inside the power system, and coping with the increasingly complex large-scale power system. This paper provides an overview of the available parallel methods to fix the issues. Specifically, these methods can be classified into three categories from a hardware perspective: multi-cores, hybrid CPU-GPU architecture, and FPGA. In addition, from the perspective of numerical computation, the power flow algorithm is generally classified into iterative and direct methods. This review paper introduces models of power flow and hardware computing architectures and then compares their performance in parallel power flow calculations depending on parallel numerical methods on different computing platforms. Furthermore, this paper analyzes the challenges and pros and cons of these methods and provides guidance on how to exploit the parallelism of future power flow applications. Full article
(This article belongs to the Section E: Applied Mathematics)
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19 pages, 386 KiB  
Article
A Mathematical Interpretation of Autoregressive Generative Pre-Trained Transformer and Self-Supervised Learning
by Minhyeok Lee
Mathematics 2023, 11(11), 2451; https://doi.org/10.3390/math11112451 - 25 May 2023
Cited by 17 | Viewed by 9147
Abstract
In this paper, we present a rigorous mathematical examination of generative pre-trained transformer (GPT) models and their autoregressive self-supervised learning mechanisms. We begin by defining natural language space and knowledge space, which are two key concepts for understanding the dimensionality reduction process in [...] Read more.
In this paper, we present a rigorous mathematical examination of generative pre-trained transformer (GPT) models and their autoregressive self-supervised learning mechanisms. We begin by defining natural language space and knowledge space, which are two key concepts for understanding the dimensionality reduction process in GPT-based large language models (LLMs). By exploring projection functions and their inverses, we establish a framework for analyzing the language generation capabilities of these models. We then investigate the GPT representation space, examining its implications for the models’ approximation properties. Finally, we discuss the limitations and challenges of GPT models and their learning mechanisms, considering trade-offs between complexity and generalization, as well as the implications of incomplete inverse projection functions. Our findings demonstrate that GPT models possess the capability to encode knowledge into low-dimensional vectors through their autoregressive self-supervised learning mechanism. This comprehensive analysis provides a solid mathematical foundation for future advancements in GPT-based LLMs, promising advancements in natural language processing tasks such as language translation, text summarization, and question answering due to improved understanding and optimization of model training and performance. Full article
(This article belongs to the Special Issue Current Trends in Natural Language Processing (NLP) and Human Language Technology (HLT))
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23 pages, 797 KiB  
Article
HAP-Assisted RSMA-Enabled Vehicular Edge Computing: A DRL-Based Optimization Framework
by Tri-Hai Nguyen and Laihyuk Park
Mathematics 2023, 11(10), 2376; https://doi.org/10.3390/math11102376 - 19 May 2023
Cited by 14 | Viewed by 2061
Abstract
In recent years, the demand for vehicular edge computing (VEC) has grown rapidly due to the increasing need for low-latency and high-throughput applications such as autonomous driving and smart transportation systems. Nevertheless, offering VEC services in rural locations remains a difficulty owing to [...] Read more.
In recent years, the demand for vehicular edge computing (VEC) has grown rapidly due to the increasing need for low-latency and high-throughput applications such as autonomous driving and smart transportation systems. Nevertheless, offering VEC services in rural locations remains a difficulty owing to a lack of network facilities. We tackle this issue by taking advantage of high-altitude platforms (HAPs) and rate-splitting multiple access (RSMA) techniques to propose an HAP-assisted RSMA-enabled VEC system, which can enhance connectivity and provide computational capacity in rural locations. We also introduce a deep deterministic policy gradient (DDPG)-based framework that optimizes the allocation of resources and task offloading by jointly considering the offloading rate, splitting rate, transmission power, and decoding order parameters. Via results from extensive simulations, the proposed framework shows superior performance in comparison with conventional schemes regarding task success rate and energy consumption. Full article
(This article belongs to the Section E: Applied Mathematics)
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13 pages, 289 KiB  
Article
Some Conformal Transformations on Finsler Warped Product Manifolds
by Yuze Ren, Xiaoling Zhang and Lili Zhao
Mathematics 2023, 11(10), 2361; https://doi.org/10.3390/math11102361 - 18 May 2023
Viewed by 1446
Abstract
The conformal transformation, which preserves Einstein metrics on Finsler warped product manifolds, is studied in this paper. We obtain sufficient and necessary conditions of a conformal transformation preserving Einstein metrics. In addition, we provide nontrivial examples of conformal transformations. Furthermore, we completely classify [...] Read more.
The conformal transformation, which preserves Einstein metrics on Finsler warped product manifolds, is studied in this paper. We obtain sufficient and necessary conditions of a conformal transformation preserving Einstein metrics. In addition, we provide nontrivial examples of conformal transformations. Furthermore, we completely classify Einstein Riemannian warped product metrics and obtain the existence of a nontrivial conformal transformation that preserves Einstein metrics. Full article
(This article belongs to the Section B: Geometry and Topology)
17 pages, 436 KiB  
Article
A Mathematical Investigation of Hallucination and Creativity in GPT Models
by Minhyeok Lee
Mathematics 2023, 11(10), 2320; https://doi.org/10.3390/math11102320 - 16 May 2023
Cited by 56 | Viewed by 12385
Abstract
In this paper, we present a comprehensive mathematical analysis of the hallucination phenomenon in generative pretrained transformer (GPT) models. We rigorously define and measure hallucination and creativity using concepts from probability theory and information theory. By introducing a parametric family of GPT models, [...] Read more.
In this paper, we present a comprehensive mathematical analysis of the hallucination phenomenon in generative pretrained transformer (GPT) models. We rigorously define and measure hallucination and creativity using concepts from probability theory and information theory. By introducing a parametric family of GPT models, we characterize the trade-off between hallucination and creativity and identify an optimal balance that maximizes model performance across various tasks. Our work offers a novel mathematical framework for understanding the origins and implications of hallucination in GPT models and paves the way for future research and development in the field of large language models (LLMs). Full article
(This article belongs to the Special Issue Deep Learning for Natural Language Processing: Advances and Challenges)
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15 pages, 316 KiB  
Article
Formulation of Impulsive Ecological Systems Using the Conformable Calculus Approach: Qualitative Analysis
by Anatoliy Martynyuk, Gani Stamov, Ivanka Stamova and Ekaterina Gospodinova
Mathematics 2023, 11(10), 2221; https://doi.org/10.3390/math11102221 - 9 May 2023
Cited by 4 | Viewed by 1608
Abstract
In this paper, an impulsive conformable fractional Lotka–Volterra model with dispersion is introduced. Since the concept of conformable derivatives avoids some limitations of the classical fractional-order derivatives, it is more suitable for applied problems. The impulsive control approach which is common for population [...] Read more.
In this paper, an impulsive conformable fractional Lotka–Volterra model with dispersion is introduced. Since the concept of conformable derivatives avoids some limitations of the classical fractional-order derivatives, it is more suitable for applied problems. The impulsive control approach which is common for population dynamics’ models is applied and fixed moments impulsive perturbations are considered. The combined concept of practical stability with respect to manifolds is adapted to the introduced model. Sufficient conditions for boundedness and generalized practical stability of the solutions are obtained by using an analogue of the Lyapunov function method. The uncertain case is also studied. Examples are given to demonstrate the effectiveness of the established results. Full article
(This article belongs to the Special Issue Stability Analysis of Fractional Systems-II)
25 pages, 954 KiB  
Article
From Cell–Cell Interaction to Stochastic and Deterministic Descriptions of a Cancer–Immune System Competition Model
by Gabriel Morgado, Annie Lemarchand and Carlo Bianca
Mathematics 2023, 11(9), 2188; https://doi.org/10.3390/math11092188 - 6 May 2023
Cited by 2 | Viewed by 1885
Abstract
We consider a cell–cell interaction model of competition between cancer cells and immune system cells, first introduced in the framework of the thermostatted kinetic theory, and derive a master equation for the probability of the number of cancer cells and immune system cells [...] Read more.
We consider a cell–cell interaction model of competition between cancer cells and immune system cells, first introduced in the framework of the thermostatted kinetic theory, and derive a master equation for the probability of the number of cancer cells and immune system cells for a given activity. Macroscopic deterministic equations for the concentrations and mean activities of cancer cells and immune system cells are deduced from the kinetic equations. The conditions for which the 3Es of immunotherapy (elimination, equilibrium, and escape) are reproduced are discussed. Apparent elimination of cancer followed by a long pseudo-equilibrium phase and the eventual escape of cancer from the control of the immune system are observed in the three descriptions. The macroscopic equations provide an analytical approach to the transition observed in the simulations of both the kinetic equations and the master equation. For efficient control of activity fluctuations, the steady states associated with the elimination of either cancer or immune system disappear and are replaced by a steady state in which cancer is controlled by the immune system. Full article
(This article belongs to the Section E3: Mathematical Biology)
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14 pages, 739 KiB  
Article
A Depth-Progressive Initialization Strategy for Quantum Approximate Optimization Algorithm
by Xinwei Lee, Ningyi Xie, Dongsheng Cai, Yoshiyuki Saito and Nobuyoshi Asai
Mathematics 2023, 11(9), 2176; https://doi.org/10.3390/math11092176 - 5 May 2023
Cited by 10 | Viewed by 2331
Abstract
The quantum approximate optimization algorithm (QAOA) is known for its capability and universality in solving combinatorial optimization problems on near-term quantum devices. The results yielded by QAOA depend strongly on its initial variational parameters. Hence, parameter selection for QAOA becomes an active area [...] Read more.
The quantum approximate optimization algorithm (QAOA) is known for its capability and universality in solving combinatorial optimization problems on near-term quantum devices. The results yielded by QAOA depend strongly on its initial variational parameters. Hence, parameter selection for QAOA becomes an active area of research, as bad initialization might deteriorate the quality of the results, especially at great circuit depths. We first discuss the patterns of optimal parameters in QAOA in two directions: the angle index and the circuit depth. Then, we discuss the symmetries and periodicity of the expectation that is used to determine the bounds of the search space. Based on the patterns in optimal parameters and the bounds restriction, we propose a strategy that predicts the new initial parameters by taking the difference between the previous optimal parameters. Unlike most other strategies, the strategy we propose does not require multiple trials to ensure success. It only requires one prediction when progressing to the next depth. We compare this strategy with our previously proposed strategy and the layerwise strategy for solving the Max-cut problem in terms of the approximation ratio and the optimization cost. We also address the non-optimality in previous parameters, which is seldom discussed in other works despite its importance in explaining the behavior of variational quantum algorithms. Full article
(This article belongs to the Special Issue Advances in Quantum Computing and Applications)
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12 pages, 2790 KiB  
Article
Antithetic Power Transformation in Monte Carlo Simulation: Correcting Hidden Errors in the Response Variable
by Dennis Ridley and Pierre Ngnepieba
Mathematics 2023, 11(9), 2097; https://doi.org/10.3390/math11092097 - 28 Apr 2023
Cited by 2 | Viewed by 1570
Abstract
Monte Carlo simulation is performed with uniformly distributed U(0,1) pseudo-random numbers. Because the numbers are generated from a mathematical formula, they will contain some serial correlation, even if very small. This serial correlation becomes embedded in the correlation structure of the response variable. [...] Read more.
Monte Carlo simulation is performed with uniformly distributed U(0,1) pseudo-random numbers. Because the numbers are generated from a mathematical formula, they will contain some serial correlation, even if very small. This serial correlation becomes embedded in the correlation structure of the response variable. The response variable becomes an asynchronous time series. This leads to hidden errors in the response variable. The purpose of this paper is to illustrate how this happens and how it can be corrected. The method is demonstrated for the case of a simple queue for which the time in the system is known exactly from theory. The paper derives the correlation between an exponential random variable and its antithetic counterpart obtained by power transform with an infinitesimal negative exponent. Full article
(This article belongs to the Special Issue Modelling and Analysis in Time Series and Econometrics)
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18 pages, 10054 KiB  
Article
Stock Price Prediction Using CNN-BiLSTM-Attention Model
by Jilin Zhang, Lishi Ye and Yongzeng Lai
Mathematics 2023, 11(9), 1985; https://doi.org/10.3390/math11091985 - 23 Apr 2023
Cited by 56 | Viewed by 16480
Abstract
Accurate stock price prediction has an important role in stock investment. Because stock price data are characterized by high frequency, nonlinearity, and long memory, predicting stock prices precisely is challenging. Various forecasting methods have been proposed, from classical time series methods to machine-learning-based [...] Read more.
Accurate stock price prediction has an important role in stock investment. Because stock price data are characterized by high frequency, nonlinearity, and long memory, predicting stock prices precisely is challenging. Various forecasting methods have been proposed, from classical time series methods to machine-learning-based methods, such as random forest (RF), recurrent neural network (RNN), convolutional neural network (CNN), Long Short-Term Memory (LSTM) neural networks and their variants, etc. Each method can reach a certain level of accuracy but also has its limitations. In this paper, a CNN-BiLSTM-Attention-based model is proposed to boost the accuracy of predicting stock prices and indices. First, the temporal features of sequence data are extracted using a convolutional neural network (CNN) and bi-directional long and short-term memory (BiLSTM) network. Then, an attention mechanism is introduced to fit weight assignments to the information features automatically; and finally, the final prediction results are output through the dense layer. The proposed method was first used to predict the price of the Chinese stock index—the CSI300 index and was found to be more accurate than any of the other three methods—LSTM, CNN-LSTM, CNN-LSTM-Attention. In order to investigate whether the proposed model is robustly effective in predicting stock indices, three other stock indices in China and eight international stock indices were selected to test, and the robust effectiveness of the CNN-BiLSTM-Attention model in predicting stock prices was confirmed. Comparing this method with the LSTM, CNN-LSTM, and CNN-LSTM-Attention models, it is found that the accuracy of stock price prediction is highest using the CNN-BiLSTM-Attention model in almost all cases. Full article
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10 pages, 1766 KiB  
Article
Phi, Fei, Fo, Fum: Effect Sizes for Categorical Data That Use the Chi-Squared Statistic
by Mattan S. Ben-Shachar, Indrajeet Patil, Rémi Thériault, Brenton M. Wiernik and Daniel Lüdecke
Mathematics 2023, 11(9), 1982; https://doi.org/10.3390/math11091982 - 22 Apr 2023
Cited by 16 | Viewed by 7859
Abstract
In both theoretical and applied research, it is often of interest to assess the strength of an observed association. Existing guidelines also frequently recommend going beyond null-hypothesis significance testing and reporting effect sizes and their confidence intervals. As such, measures of effect sizes [...] Read more.
In both theoretical and applied research, it is often of interest to assess the strength of an observed association. Existing guidelines also frequently recommend going beyond null-hypothesis significance testing and reporting effect sizes and their confidence intervals. As such, measures of effect sizes are increasingly reported, valued, and understood. Beyond their value in shaping the interpretation of the results from a given study, reporting effect sizes is critical for meta-analyses, which rely on their aggregation. We review the most common effect sizes for analyses of categorical variables that use the χ2 (chi-square) statistic and introduce a new effect size—פ (Fei, pronounced “fay”). We demonstrate the implementation of these measures and their confidence intervals via the effectsize package in the R programming language. Full article
(This article belongs to the Special Issue Advances in Statistical Computing)
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18 pages, 3920 KiB  
Article
Multi-Scale Annulus Clustering for Multi-Label Classification
by Yan Liu, Changshun Liu, Jingjing Song, Xibei Yang, Taihua Xu and Pingxin Wang
Mathematics 2023, 11(8), 1969; https://doi.org/10.3390/math11081969 - 21 Apr 2023
Cited by 3 | Viewed by 1650
Abstract
Label-specific feature learning has become a hot topic as it induces classification models by accounting for the underlying features of each label. Compared with single-label annotations, multi-label annotations can describe samples from more comprehensive perspectives. It is generally believed that the compelling classification [...] Read more.
Label-specific feature learning has become a hot topic as it induces classification models by accounting for the underlying features of each label. Compared with single-label annotations, multi-label annotations can describe samples from more comprehensive perspectives. It is generally believed that the compelling classification features of a data set often exist in the aggregation of label distribution. In this in-depth study of a multi-label data set, we find that the distance between all samples and the sample center is a Gaussian distribution, which means that the label distribution has the tendency to cluster from the center and spread to the surroundings. Accordingly, the double annulus field based on this distribution trend, named DEPT for double annulusfield and label-specific features for multi-label classification, is proposed in this paper. The double annulus field emphasizes that samples of a specific size can reflect some unique features of the data set. Through intra-annulus clustering for each layer of annuluses, the distinctive feature space of these labels is captured and formed. Then, the final classification model is obtained by training the feature space. Contrastive experiments on 10 benchmark multi-label data sets verify the effectiveness of the proposed algorithm. Full article
(This article belongs to the Section D2: Operations Research and Fuzzy Decision Making)
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11 pages, 303 KiB  
Article
Generalized Halanay Inequalities and Relative Application to Time-Delay Dynamical Systems
by Chunsheng Wang, Xiangdong Liu, Feng Jiao, Hong Mai, Han Chen and Runpeng Lin
Mathematics 2023, 11(8), 1940; https://doi.org/10.3390/math11081940 - 20 Apr 2023
Cited by 11 | Viewed by 1489
Abstract
A class of generalized Halanay inequalities is studied via the Banach fixed point method and comparison principle. The conditions to ensure the boundedness and stability of the zero solution are obtained in this study. This research provides a new approach to the study [...] Read more.
A class of generalized Halanay inequalities is studied via the Banach fixed point method and comparison principle. The conditions to ensure the boundedness and stability of the zero solution are obtained in this study. This research provides a new approach to the study of the boundedness and stability of Halanay inequality. Numerical examples and simulation results verify the validity and superiority of the conclusions obtained in this study. Full article
(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering, 2nd Edition)
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24 pages, 4680 KiB  
Article
AdaBoost Algorithm Could Lead to Weak Results for Data with Certain Characteristics
by Olivér Hornyák and László Barna Iantovics
Mathematics 2023, 11(8), 1801; https://doi.org/10.3390/math11081801 - 10 Apr 2023
Cited by 22 | Viewed by 3229
Abstract
There are many state-of-the-art algorithms presented in the literature that perform very well on some evaluation data but are not studied with the data properties on which they are applied; therefore, they could have low performance on data with other characteristics. In this [...] Read more.
There are many state-of-the-art algorithms presented in the literature that perform very well on some evaluation data but are not studied with the data properties on which they are applied; therefore, they could have low performance on data with other characteristics. In this paper, the results of comprehensive research regarding the prediction with the frequently applied AdaBoost algorithm on real-world sensor data are presented. The chosen dataset has some specific characteristics, and it contains error and failure data of several machines and their components. The research aims to investigate whether the AdaBoost algorithm has the capability of predicting failures, thus providing the necessary information for monitoring and condition-based maintenance (CBM). The dataset is analyzed, and the principal characteristics are presented. Performance evaluations of the AdaBoost algorithm that we present show a prediction capability below expectations for this algorithm. The specificity of this study is that it indicates the limitation of the AdaBoost algorithm, which could perform very well on some data, but not so well on others. Based on this research and some others that we performed, and actual research from worldwide studies, we must outline that the mathematical analysis of the data is especially important to develop or adapt algorithms to be very efficient. Full article
(This article belongs to the Special Issue Industrial Big Data and Process Modelling for Smart Manufacturing)
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12 pages, 611 KiB  
Article
Non-Associative Structures and Their Applications in Differential Equations
by Yakov Krasnov
Mathematics 2023, 11(8), 1790; https://doi.org/10.3390/math11081790 - 9 Apr 2023
Cited by 3 | Viewed by 2317
Abstract
This article establishes a connection between nonlinear DEs and linear PDEs on the one hand, and non-associative algebra structures on the other. Such a connection simplifies the formulation of many results of DEs and the methods of their solution. The main link between [...] Read more.
This article establishes a connection between nonlinear DEs and linear PDEs on the one hand, and non-associative algebra structures on the other. Such a connection simplifies the formulation of many results of DEs and the methods of their solution. The main link between these theories is the nonlinear spectral theory developed for algebra and homogeneous differential equations. A nonlinear spectral method is used to prove the existence of an algebraic first integral, interpretations of various phase zones, and the separatrices construction for ODEs. In algebra, the same methods exploit subalgebra construction and explain fusion rules. In conclusion, perturbation methods may also be interpreted for near-Jordan algebra construction. Full article
(This article belongs to the Special Issue Non-associative Structures and Their Applications in Physics and Geometry)
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20 pages, 1646 KiB  
Article
Output Feedback Robust Tracking Control for a Variable-Speed Pump-Controlled Hydraulic System Subject to Mismatched Uncertainties
by Manh Hung Nguyen and Kyoung Kwan Ahn
Mathematics 2023, 11(8), 1783; https://doi.org/10.3390/math11081783 - 8 Apr 2023
Cited by 11 | Viewed by 2179
Abstract
In this paper, a novel simple, but effective output feedback robust control (OFRC) for achieving a highly accurate position tracking of a pump-controlled electro-hydraulic system is presented. To cope with the unavailability of all system state information, an extended state observer (ESO) was [...] Read more.
In this paper, a novel simple, but effective output feedback robust control (OFRC) for achieving a highly accurate position tracking of a pump-controlled electro-hydraulic system is presented. To cope with the unavailability of all system state information, an extended state observer (ESO) was adopted to estimate the angular velocity and load-pressure-related state variable of the actuator and total matched disturbance, which enters the system through the same channel as the control input in the system dynamics. In addition, for the first time, another ESO acting as a disturbance observer (DOB) was skillfully integrated to effectively compensate for the adverse effects of the lumped mismatched uncertainty caused by parameter perturbation and external loads in the velocity dynamics. Then, a dynamic surface-control-based backstepping controller (DSC-BC) based on the constructed ESOs for the tracking control of the studied electro-hydraulic system was synthesized to guarantee that the system output closely tracks the desired trajectory and avoid the inherent computational burden of the conventional backstepping method because of repetitive analytical derivative calculation at each backstepping iteration. Furthermore, the stability of the two observes and overall closed-loop system was verified by using the Lyapunov theory. Finally, several extensive comparative experiments were carried out to demonstrate the advantage of the recommended control approach in comparison with some reference control methods. Full article
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12 pages, 402 KiB  
Article
On Optimal Embeddings in 3-Ary n-Cubes
by S. Rajeshwari and M. Rajesh
Mathematics 2023, 11(7), 1711; https://doi.org/10.3390/math11071711 - 3 Apr 2023
Cited by 4 | Viewed by 1639
Abstract
The efficiency of a graph embedding problem when simulating one interconnection network in another interconnection network is characterized by the influential parameter of wirelength. Obtaining the minimum wirelength in an embedding problem determines the quality of that embedding. In this paper, we obtained [...] Read more.
The efficiency of a graph embedding problem when simulating one interconnection network in another interconnection network is characterized by the influential parameter of wirelength. Obtaining the minimum wirelength in an embedding problem determines the quality of that embedding. In this paper, we obtained the convex edge partition of 3-Ary n-Cubes and the minimized wirelength of the embeddings of both 3-Ary n-Cubes and circulant networks. Full article
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18 pages, 446 KiB  
Article
Hybrid Impulsive Pinning Control for Mean Square Synchronization of Uncertain Multi-Link Complex Networks with Stochastic Characteristics and Hybrid Delays
by Yong Tang, Lang Zhou, Jiahui Tang, Yue Rao, Hongguang Fan and Jihong Zhu
Mathematics 2023, 11(7), 1697; https://doi.org/10.3390/math11071697 - 2 Apr 2023
Cited by 29 | Viewed by 2176
Abstract
This study explores the synchronization issue for uncertain multi-link complex networks incorporating stochastic characteristics and hybrid delays. Unlike previous works, internal delays, coupling delays, and stochastic delays considered in our model change over time; meanwhile, the impulse strength and position change with time [...] Read more.
This study explores the synchronization issue for uncertain multi-link complex networks incorporating stochastic characteristics and hybrid delays. Unlike previous works, internal delays, coupling delays, and stochastic delays considered in our model change over time; meanwhile, the impulse strength and position change with time evolution. To actualize network synchronization, a strategy called hybrid impulsive pinning control is applied, which combines the virtue of impulsive control and pinning control as well as two categories of impulses (i.e., synchronization and desynchronization). By decomposing the complicated topological structures into diagonal items and off-diagonal items, multiple nonlinear coupling terms are linearly decomposed in the process of theoretical analysis. Combining inequality technology and matrix decomposition theory, several novel synchronization criteria have been gained to ensure synchronization for the concerning multi-link model. The criteria get in touch with the uncertain strengths, coupling strengths, hybrid impulse strengths, delay sizes, impulsive intervals, and network topologies. Full article
(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering, 2nd Edition)
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16 pages, 1170 KiB  
Article
A Novel Fractional-Order RothC Model
by Vsevolod Bohaienko, Fasma Diele, Carmela Marangi, Cristiano Tamborrino, Sebastian Aleksandrowicz and Edyta Woźniak
Mathematics 2023, 11(7), 1677; https://doi.org/10.3390/math11071677 - 31 Mar 2023
Cited by 1 | Viewed by 2578
Abstract
A new fractional q-order variation of the RothC model for the dynamics of soil organic carbon is introduced. A computational method based on the discretization of the analytic solution along with the finite-difference technique are suggested and the stability results for the [...] Read more.
A new fractional q-order variation of the RothC model for the dynamics of soil organic carbon is introduced. A computational method based on the discretization of the analytic solution along with the finite-difference technique are suggested and the stability results for the latter are given. The accuracy of the scheme, in terms of the temporal step size h, is confirmed through numerical testing of a constructed analytic solution. The effectiveness of the proposed discrete method is compared with that of the classical discrete RothC model. Results from real-world experiments show that, by adjusting the fractional order q and the multiplier term ζ(t,q), a better match between simulated and actual data can be achieved compared to the traditional integer-order model. Full article
(This article belongs to the Special Issue Differential Equation Models in Applied Mathematics: Theoretical and Numerical Challenges-II)
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22 pages, 1007 KiB  
Article
Heat and Mass Transfer Analysis for the Viscous Fluid Flow: Dual Approximate Solutions
by Remus-Daniel Ene, Nicolina Pop and Rodica Badarau
Mathematics 2023, 11(7), 1648; https://doi.org/10.3390/math11071648 - 29 Mar 2023
Cited by 4 | Viewed by 2242
Abstract
The aim of this paper is to investigate effective and accurate dual analytic approximate solutions, while taking into account thermal effects. The heat and mass transfer problem in a viscous fluid flow are analytically explored by using the modified Optimal Homotopy Asymptotic Method [...] Read more.
The aim of this paper is to investigate effective and accurate dual analytic approximate solutions, while taking into account thermal effects. The heat and mass transfer problem in a viscous fluid flow are analytically explored by using the modified Optimal Homotopy Asymptotic Method (OHAM). By using similarity transformations, the motion equations are reduced to a set of nonlinear ordinary differential equations. Based on the numerical results, it was revealed that there are dual analytic approximate solutions within the mass transfer problem. The variation of the physical parameters (the Prandtl number and the temperature distribution parameter) over the temperature profile is analytically explored and graphically depicted for the first approximate and the corresponding dual solution, respectively. The advantage of the proposed method arises from using only one iteration for obtaining the dual analytical solutions. The presented results are effective, accurate and in good agreement with the corresponding numerical results with relevance for further engineering applications of heat and mass transfer problems. Full article
(This article belongs to the Special Issue Analysis and Applications of Mathematical Fluid Dynamics)
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15 pages, 1201 KiB  
Article
Fixed-Time Synchronization of Reaction-Diffusion Fuzzy Neural Networks with Stochastic Perturbations
by Hayrengul Sadik, Abdujelil Abdurahman and Rukeya Tohti
Mathematics 2023, 11(6), 1493; https://doi.org/10.3390/math11061493 - 18 Mar 2023
Cited by 6 | Viewed by 1529
Abstract
In this paper, we investigated the fixed-time synchronization problem of a type of reaction-diffusion fuzzy neural networks with stochastic perturbations by developing simple control schemes. First, some generalized fixed-time stability results are introduced for stochastic nonlinear systems. Based on these results, some generic [...] Read more.
In this paper, we investigated the fixed-time synchronization problem of a type of reaction-diffusion fuzzy neural networks with stochastic perturbations by developing simple control schemes. First, some generalized fixed-time stability results are introduced for stochastic nonlinear systems. Based on these results, some generic fixed-time stability criteria are established and upper bounds of settling time are directly calculated by using several special functions. Then, the fixed-time synchronization of a type of reaction-diffusion fuzzy neural networks with stochastic perturbations is analysed by designing a type of controller which is more simple and thus have a better applicability. Finally, one numerical example with its Matlab simulations is provided to show the feasibility of developed theoretical results. Full article
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13 pages, 317 KiB  
Article
The Global Property of Generic Conformally Flat Hypersurfaces in R4
by Yayun Chen and Tongzhu Li
Mathematics 2023, 11(6), 1435; https://doi.org/10.3390/math11061435 - 16 Mar 2023
Viewed by 1253
Abstract
A conformally flat hypersurface f:M3→R4 in the four-dimensional Euclidean space R4 is said to be generic if the hypersurface has three distinct principal curvatures everywhere. In this paper, we study the generic conformally flat hypersurfaces in [...] Read more.
A conformally flat hypersurface f:M3→R4 in the four-dimensional Euclidean space R4 is said to be generic if the hypersurface has three distinct principal curvatures everywhere. In this paper, we study the generic conformally flat hypersurfaces in R4 using the framework of Möbius geometry. First, we classify locally the generic conformally flat hypersurfaces with a vanishing Möbius form under the Möbius transformation group of R4. Second, we investigate the global behavior of the compact generic conformally flat hypersurfaces and give some integral formulas about the Möbius invariant of these hypersurfaces. Full article
(This article belongs to the Section B: Geometry and Topology)
21 pages, 690 KiB  
Article
New Results on Finite-Time Synchronization of Complex-Valued BAM Neural Networks with Time Delays by the Quadratic Analysis Approach
by Zhen Yang and Zhengqiu Zhang
Mathematics 2023, 11(6), 1378; https://doi.org/10.3390/math11061378 - 12 Mar 2023
Cited by 3 | Viewed by 1597
Abstract
In this paper, we are interested in the finite-time synchronization of complex-valued BAM neural networks with time delays. Without applying Lyapunov–Krasovskii functional theory, finite-time convergence theorem, graph-theoretic method, the theory of complex functions or the integral inequality method, by using the quadratic analysis [...] Read more.
In this paper, we are interested in the finite-time synchronization of complex-valued BAM neural networks with time delays. Without applying Lyapunov–Krasovskii functional theory, finite-time convergence theorem, graph-theoretic method, the theory of complex functions or the integral inequality method, by using the quadratic analysis approach, inequality techniques and designing two classes of novel controllers, two novel sufficient conditions are achieved to guarantee finite-time synchronization between the master system and the slave system. The quadratic analysis method used in our paper is a different study approach of finite-time synchronization from those in existing papers. Therefore the controllers designed in our paper are fully novel. Full article
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20 pages, 5607 KiB  
Article
Machine Learning Techniques Applied to the Harmonic Analysis of Railway Power Supply
by Manuela Panoiu, Caius Panoiu, Sergiu Mezinescu, Gabriel Militaru and Ioan Baciu
Mathematics 2023, 11(6), 1381; https://doi.org/10.3390/math11061381 - 12 Mar 2023
Cited by 10 | Viewed by 4671
Abstract
Harmonic generation in power system networks presents significant issues that arise in power utilities. This paper describes a machine learning technique that was used to conduct a research study on the harmonic analysis of railway power stations. The research was an investigation of [...] Read more.
Harmonic generation in power system networks presents significant issues that arise in power utilities. This paper describes a machine learning technique that was used to conduct a research study on the harmonic analysis of railway power stations. The research was an investigation of a time series whose values represented the total harmonic distortion (THD) for the electric current. This study was based on information collected at a railway power station. In an electrified substation, measurements of currents and voltages were made during a certain interval of time. From electric current values, the THD was calculated using a fast Fourier transform analysis (FFT) and the results were used to train an adaptive ANN—GMDH (artificial neural network–group method of data handling) algorithm. Following the training, a prediction model was created, the performance of which was investigated in this study. The model was based on the ANN—GMDH method and was developed for the prediction of the THD. The performance of this model was studied based on its parameters. The model’s performance was evaluated using the regression coefficient (R), root-mean-square error (RMSE), and mean absolute error (MAE). The model’s performance was very good, with an RMSE (root-mean-square error) value of less than 0.01 and a regression coefficient value higher than 0.99. Another conclusion from our research was that the model also performed very well in terms of the training time (calculation speed). Full article
(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems)
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16 pages, 789 KiB  
Article
A Full-Body Relative Orbital Motion of Spacecraft Using Dual Tensor Algebra and Dual Quaternions
by Daniel Condurache
Mathematics 2023, 11(6), 1366; https://doi.org/10.3390/math11061366 - 11 Mar 2023
Cited by 1 | Viewed by 1740
Abstract
This paper proposes a new non-linear differential equation for the six degrees of freedom (6-DOF) relative rigid bodies motion. A representation theorem is provided for the 6-DOF differential equation of motion in the arbitrary non-inertial reference frame. The problem of the 6-DOF relative [...] Read more.
This paper proposes a new non-linear differential equation for the six degrees of freedom (6-DOF) relative rigid bodies motion. A representation theorem is provided for the 6-DOF differential equation of motion in the arbitrary non-inertial reference frame. The problem of the 6-DOF relative motion of two spacecraft in the specific case of Keplerian confocal orbits is proposed. The result is an analytical method without secular terms and singularities. Tensors dual algebra and dual quaternions play a fundamental role, with the solution representation being the relative problem. Furthermore, the representation theorems for the rotation and translation parts of the 6-DOF relative orbital motion problems are obtained. Full article
(This article belongs to the Special Issue Analytical Approaches to Nonlinear Dynamical Systems and Applications II)
14 pages, 582 KiB  
Article
Optimal Homotopy Asymptotic Method for an Anharmonic Oscillator: Application to the Chen System
by Remus-Daniel Ene and Nicolina Pop
Mathematics 2023, 11(5), 1124; https://doi.org/10.3390/math11051124 - 23 Feb 2023
Cited by 1 | Viewed by 1835
Abstract
The aim of our work is to obtain the analytic solutions for a new nonlinear anharmonic oscillator by means of the Optimal Homotopy Asymptotic Method (OHAM), using only one iteration. The accuracy of the obtained results comes from the comparison with the corresponding [...] Read more.
The aim of our work is to obtain the analytic solutions for a new nonlinear anharmonic oscillator by means of the Optimal Homotopy Asymptotic Method (OHAM), using only one iteration. The accuracy of the obtained results comes from the comparison with the corresponding numerical ones for specified physical parameters. Moreover, the OHAM method has a greater degree of flexibility than an iterative method as is presented in this paper. Based on these results, the analytically solutions of the Chen system were obtained for a special case (just one analytic first integral). The chaotic behaviors were excluded here. The provided solutions are usefully for many engineering applications. Full article
(This article belongs to the Special Issue Analytical Approaches to Nonlinear Dynamical Systems and Applications II)
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13 pages, 1124 KiB  
Article
Facing a Risk: To Insure or Not to Insure—An Analysis with the Constant Relative Risk Aversion Utility Function
by M. Mercè Claramunt, Maite Mármol and Xavier Varea
Mathematics 2023, 11(5), 1070; https://doi.org/10.3390/math11051070 - 21 Feb 2023
Cited by 1 | Viewed by 2400
Abstract
The decision to transfer or share an insurable risk is critical for the decision maker’s economy. This paper deals with this decision, starting with the definition of a function that represents the difference between the expected utility of insuring, with or without deductibles, [...] Read more.
The decision to transfer or share an insurable risk is critical for the decision maker’s economy. This paper deals with this decision, starting with the definition of a function that represents the difference between the expected utility of insuring, with or without deductibles, and the expected utility of not insuring. Considering a constant relative risk aversion (CRRA) utility function, we provide a decision pattern for the potential policyholders as a function of their wealth level. The obtained rule applies to any premium principle, any per-claim deductible and any risk distribution. Furthermore, numerical results are presented based on the mean principle, a per-claim absolute deductible and a Poisson-exponential model, and a sensitivity analysis regarding the deductible parameter and the insurer security loading was performed. One of the main conclusions of the paper is that the initial level of wealth is the main variable that determines the decision to insure or not to insure; thus, for high levels of wealth, the decision is always not to insure regardless of the risk aversion of the decision maker. Moreover, the parameters defining the deductible and the premium only have an influence at low levels of wealth. Full article
(This article belongs to the Special Issue Mathematical Economics and Insurance)
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12 pages, 2888 KiB  
Article
Multimodal Movie Recommendation System Using Deep Learning
by Yongheng Mu and Yun Wu
Mathematics 2023, 11(4), 895; https://doi.org/10.3390/math11040895 - 10 Feb 2023
Cited by 55 | Viewed by 14152
Abstract
Recommendation systems, the best way to deal with information overload, are widely utilized to provide users with personalized content and services with high efficiency. Many recommendation algorithms have been researched and deployed extensively in various e-commerce applications, including the movie streaming services over [...] Read more.
Recommendation systems, the best way to deal with information overload, are widely utilized to provide users with personalized content and services with high efficiency. Many recommendation algorithms have been researched and deployed extensively in various e-commerce applications, including the movie streaming services over the last decade. However, sparse data cold-start problems are often encountered in many movie recommendation systems. In this paper, we reported a personalized multimodal movie recommendation system based on multimodal data analysis and deep learning. The real-world MovieLens datasets were selected to test the effectiveness of our new recommendation algorithm. With the input information, the hidden features of the movies and the users were mined using deep learning to build a deep-learning network algorithm model for training to further predict movie scores. With a learning rate of 0.001, the root mean squared error (RMSE) scores achieved 0.9908 and 0.9096 for test sets of MovieLens 100 K and 1 M datasets, respectively. The scoring prediction results show improved accuracy after incorporating the potential features and connections in multimodal data with deep-learning technology. Compared with the traditional collaborative filtering algorithms, such as user-based collaborative filtering (User-CF), item-based content-based filtering (Item-CF), and singular-value decomposition (SVD) approaches, the multimodal movie recommendation system using deep learning could provide better personalized recommendation results. Meanwhile, the sparse data problem was alleviated to a certain degree. We suggest that the recommendation system can be improved through the combination of the deep-learning technology and the multimodal data analysis. Full article
(This article belongs to the Special Issue Nature Inspired Computing and Optimisation)
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9 pages, 3640 KiB  
Article
Identifying Combination of Dark–Bright Binary–Soliton and Binary–Periodic Waves for a New Two-Mode Model Derived from the (2 + 1)-Dimensional Nizhnik–Novikov–Veselov Equation
by Marwan Alquran and Imad Jaradat
Mathematics 2023, 11(4), 861; https://doi.org/10.3390/math11040861 - 8 Feb 2023
Cited by 33 | Viewed by 1943
Abstract
In this paper, we construct a new two-mode model derived from the (2+1)-dimensional Nizhnik–Novikov–Veselov (TMNNV) equation. We generalize the concept of Korsunsky to accommodate the derivation of higher-dimensional two-mode equations. Since the TMNNV is presented here, for the [...] Read more.
In this paper, we construct a new two-mode model derived from the (2+1)-dimensional Nizhnik–Novikov–Veselov (TMNNV) equation. We generalize the concept of Korsunsky to accommodate the derivation of higher-dimensional two-mode equations. Since the TMNNV is presented here, for the first time, we identify some of its solutions by means of two recent and effective schemes. As a result, the Kudryashov-expansion method exports a combination of bright–dark binary solitons, which simulate many applications in optics, photons, and plasma. The modified rational sine and cosine functions export binary–periodic waves that arise in the field of surface water waves. Moreover, by using 2D and 3D graphs, some physical properties of the TMNNV were investigated by means of studying the effect of the following parameters of the model: nonlinearity, dispersion, and phase–velocity. Finally, we checked the validity of the obtained solutions by verifying the correctness of the original governing model. Full article
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23 pages, 1258 KiB  
Article
Train Delay Predictions Using Markov Chains Based on Process Time Deviations and Elastic State Boundaries
by Thomas Spanninger, Beda Büchel and Francesco Corman
Mathematics 2023, 11(4), 839; https://doi.org/10.3390/math11040839 - 7 Feb 2023
Cited by 5 | Viewed by 3590
Abstract
Train delays are inconvenient for passengers and major problems in railway operations. When delays occur, it is vital to provide timely information to passengers regarding delays at their departing, interchanging, and final stations. Furthermore, real-time traffic control requires information on how delays propagate [...] Read more.
Train delays are inconvenient for passengers and major problems in railway operations. When delays occur, it is vital to provide timely information to passengers regarding delays at their departing, interchanging, and final stations. Furthermore, real-time traffic control requires information on how delays propagate throughout the network. Among a multitude of applied models to predict train delays, Markov chains have proven to be stochastic benchmark approaches due to their simplicity, interpretability, and solid performances. In this study, we introduce an advanced Markov chain setting to predict train delays using historical train operation data. Therefore, we applied Markov chains based on process time deviations instead of absolute delays and we relaxed commonly used stationarity assumptions for transition probabilities in terms of direction, train line, and location. Additionally, we defined the state space elastically and analyzed the benefit of an increasing state space dimension. We show (via a test case in the Swiss railway network) that our proposed advanced Markov chain model achieves a prediction accuracy gain of 56% in terms of mean absolute error (MAE) compared to state-of-the-art Markov chain models based on absolute delays. We also illustrate the prediction performance advantages of our proposed model in the case of training data sparsity. Full article
(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems)
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20 pages, 4679 KiB  
Article
Application of Solar Activity Time Series in Machine Learning Predictive Modeling of Precipitation-Induced Floods
by Slavica Malinović-Milićević, Milan M. Radovanović, Sonja D. Radenković, Yaroslav Vyklyuk, Boško Milovanović, Ana Milanović Pešić, Milan Milenković, Vladimir Popović, Marko Petrović, Petro Sydor and Mirjana Gajić
Mathematics 2023, 11(4), 795; https://doi.org/10.3390/math11040795 - 4 Feb 2023
Cited by 5 | Viewed by 3732
Abstract
This research is devoted to the determination of hidden dependencies between the flow of particles that come from the Sun and precipitation-induced floods in the United Kingdom (UK). The analysis covers 20 flood events during the period from October 2001 to December 2019. [...] Read more.
This research is devoted to the determination of hidden dependencies between the flow of particles that come from the Sun and precipitation-induced floods in the United Kingdom (UK). The analysis covers 20 flood events during the period from October 2001 to December 2019. The parameters of solar activity were used as model input data, while precipitations data in the period 10 days before and during each flood event were used as model output. The time lag of 0–9 days was taken into account in the research. Correlation analysis was conducted to determine the degree of randomness for the time series of input and output parameters. For establishing a potential causative link, machine learning classification predictive modeling was applied. Two approaches, the decision tree, and the random forest were used. We analyzed the accuracy of classification models forecast from 0 to 9 days in advance. It was found that the most important factors for flood forecasting are proton density with a time lag of 9, differential proton flux in the range of 310–580 keV, and ion temperature. Research in this paper has shown that the decision tree model is more accurate and adequate in predicting the appearance of precipitation-induced floods up to 9 days ahead with an accuracy of 91%. The results of this study confirmed that by increasing technical capabilities, using improved machine learning techniques and large data sets, it is possible to improve the understanding of the physical link between the solar wind and tropospheric weather and help improve severe weather forecasting. Full article
(This article belongs to the Special Issue Complex Network Analysis of Nonlinear Time Series)
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36 pages, 558 KiB  
Article
Fuzzy Property Grammars for Gradience in Natural Language
by Adrià Torrens-Urrutia, Vilém Novák and María Dolores Jiménez-López
Mathematics 2023, 11(3), 735; https://doi.org/10.3390/math11030735 - 1 Feb 2023
Cited by 3 | Viewed by 2265
Abstract
This paper introduces a new grammatical framework, Fuzzy Property Grammars (FPGr). This is a model based on Property Grammars and Fuzzy Natural Logic. Such grammatical framework is constraint-based and provides a new way to formally characterize gradience by representing grammaticality degrees regarding linguistic [...] Read more.
This paper introduces a new grammatical framework, Fuzzy Property Grammars (FPGr). This is a model based on Property Grammars and Fuzzy Natural Logic. Such grammatical framework is constraint-based and provides a new way to formally characterize gradience by representing grammaticality degrees regarding linguistic competence (without involving speakers judgments). The paper provides a formal-logical characterization of FPGr. A test of the framework is presented by implementing an FPGr for Spanish. FPGr is a formal theory that may serve linguists, computing scientists, and mathematicians since it can capture infinite grammatical structures within the variability of a language. Full article
(This article belongs to the Special Issue FSTA: Fuzzy Set Theory and Applications)
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15 pages, 307 KiB  
Article
Reduced Clustering Method Based on the Inversion Formula Density Estimation
by Mantas Lukauskas and Tomas Ruzgas
Mathematics 2023, 11(3), 661; https://doi.org/10.3390/math11030661 - 28 Jan 2023
Cited by 5 | Viewed by 2270
Abstract
Unsupervised learning is one type of machine learning with an exceptionally high number of applications in various fields. The most popular and best-known group of unsupervised machine learning methods is clustering methods. The main goal of clustering is to find hidden relationships between [...] Read more.
Unsupervised learning is one type of machine learning with an exceptionally high number of applications in various fields. The most popular and best-known group of unsupervised machine learning methods is clustering methods. The main goal of clustering is to find hidden relationships between individual observations. There is great interest in different density estimation methods, especially when there are outliers in the data. Density estimation also can be applied to data clustering methods. This paper presents the extension to the clustering method based on the modified inversion formula density estimation to solve previous method limitations. This new method’s extension works within higher dimensions (d > 15) cases, which was the limitation of the previous method. More than 20 data sets are used in comparative data analysis to prove the effectiveness of the developed method improvement. The results showed that the new method extension positively affects the data clustering results. The new reduced clustering method, based on the modified inversion formula density estimation, outperforms popular data clustering methods on test data sets. In cases when the accuracy is not the best, the data clustering accuracy is close to the best models’ obtained accuracies. Lower dimensionality data were used to compare the standard clustering based on the inversion formula density estimation method with the extended method. The new modification method has better results than the standard method in all cases, which confirmed the hypothesis about the new method’s positive impact on clustering results. Full article
(This article belongs to the Special Issue Advances in Computational Statistics and Applications)
16 pages, 727 KiB  
Article
Stochastic Configuration Based Fuzzy Inference System with Interpretable Fuzzy Rules and Intelligence Search Process
by Wei Zhou, Hongxing Li and Menghong Bao
Mathematics 2023, 11(3), 614; https://doi.org/10.3390/math11030614 - 26 Jan 2023
Cited by 4 | Viewed by 1940
Abstract
In this paper, a stochastic configuration based fuzzy inference system with interpretable fuzzy rules (SCFS-IFRs) is proposed to improve the interpretability and performance of the fuzzy inference system and determine autonomously an appropriate model structure. The proposed SCFS-IFR first accomplishes a fuzzy system [...] Read more.
In this paper, a stochastic configuration based fuzzy inference system with interpretable fuzzy rules (SCFS-IFRs) is proposed to improve the interpretability and performance of the fuzzy inference system and determine autonomously an appropriate model structure. The proposed SCFS-IFR first accomplishes a fuzzy system through interpretable linguistic fuzzy rules (ILFRs), which endows the system with clear semantic interpretability. Meanwhile, using an incremental learning method based on stochastic configuration, the appropriate architecture of the system is determined by incremental generation of ILFRs under a supervision mechanism. In addition, the particle swarm optimization (PSO) algorithm, an intelligence search technique, is used in the incremental learning process of ILFRs to obtain better random parameters and improve approximation accuracy. The performance of SCFS-IFRs is verified by regression and classification benchmark datasets. Regression experiments show that the proposed SCFS-IFRs perform best on 10 of the 20 data sets, statistically significantly outperforming the other eight state-of-the-art algorithms. Classification experiments show that, compared with the other six fuzzy classifiers, SCFS-IFRs achieve higher classification accuracy and better interpretation with fewer rules. Full article
(This article belongs to the Special Issue Intelligent and Fuzzy Systems in Engineering and Technology)
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12 pages, 432 KiB  
Article
Adaptive Nonparametric Density Estimation with B-Spline Bases
by Yanchun Zhao, Mengzhu Zhang, Qian Ni and Xuhui Wang
Mathematics 2023, 11(2), 291; https://doi.org/10.3390/math11020291 - 5 Jan 2023
Cited by 10 | Viewed by 3049
Abstract
Learning density estimation is important in probabilistic modeling and reasoning with uncertainty. Since B-spline basis functions are piecewise polynomials with local support, density estimation with B-splines shows its advantages when intensive numerical computations are involved in the subsequent applications. To obtain an optimal [...] Read more.
Learning density estimation is important in probabilistic modeling and reasoning with uncertainty. Since B-spline basis functions are piecewise polynomials with local support, density estimation with B-splines shows its advantages when intensive numerical computations are involved in the subsequent applications. To obtain an optimal local density estimation with B-splines, we need to select the bandwidth (i.e., the distance of two adjacent knots) for uniform B-splines. However, the selection of bandwidth is challenging, and the computation is costly. On the other hand, nonuniform B-splines can improve on the approximation capability of uniform B-splines. Based on this observation, we perform density estimation with nonuniform B-splines. By introducing the error indicator attached to each interval, we propose an adaptive strategy to generate the nonuniform knot vector. The error indicator is an approximation of the information entropy locally, which is closely related to the number of kernels when we construct the nonuniform estimator. The numerical experiments show that, compared with the uniform B-spline, the local density estimation with nonuniform B-splines not only achieves better estimation results but also effectively alleviates the overfitting phenomenon caused by the uniform B-splines. The comparison with the existing estimation procedures, including the state-of-the-art kernel estimators, demonstrates the accuracy of our new method. Full article
(This article belongs to the Section D1: Probability and Statistics)
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17 pages, 888 KiB  
Article
Delayed Impulsive Control for μ-Synchronization of Nonlinear Multi-Weighted Complex Networks with Uncertain Parameter Perturbation and Unbounded Delays
by Hongguang Fan, Jiahui Tang, Kaibo Shi, Yi Zhao and Hui Wen
Mathematics 2023, 11(1), 250; https://doi.org/10.3390/math11010250 - 3 Jan 2023
Cited by 7 | Viewed by 2133
Abstract
The global μ-synchronization problem for nonlinear multi-weighted complex dynamical networks with uncertain parameter perturbation and mixed time-varying delays is investigated in this paper. Unlike other existing works, all delays, including sampling and internal and coupling delays, are assumed to be unbounded, making [...] Read more.
The global μ-synchronization problem for nonlinear multi-weighted complex dynamical networks with uncertain parameter perturbation and mixed time-varying delays is investigated in this paper. Unlike other existing works, all delays, including sampling and internal and coupling delays, are assumed to be unbounded, making the considered model more general and practical. Based on the generalized impulsive comparison principles, a time-varying impulsive controller with sampling delays is designed, and some new sufficient conditions are obtained to make drive–response multi-weighted networks reach μ-synchronization. In addition, the external coupling matrices do not need to meet the requirement of zero-row sum, and the limitation of time delay on pulse interval is weakened. The results obtained in this article can be seen as extensions of previous related research. Full article
(This article belongs to the Topic Engineering Mathematics)
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21 pages, 4493 KiB  
Article
A Combined Model Based on Recurrent Neural Networks and Graph Convolutional Networks for Financial Time Series Forecasting
by Ana Lazcano, Pedro Javier Herrera and Manuel Monge
Mathematics 2023, 11(1), 224; https://doi.org/10.3390/math11010224 - 2 Jan 2023
Cited by 69 | Viewed by 8164
Abstract
Accurate and real-time forecasting of the price of oil plays an important role in the world economy. Research interest in forecasting this type of time series has increased considerably in recent decades, since, due to the characteristics of the time series, it was [...] Read more.
Accurate and real-time forecasting of the price of oil plays an important role in the world economy. Research interest in forecasting this type of time series has increased considerably in recent decades, since, due to the characteristics of the time series, it was a complicated task with inaccurate results. Concretely, deep learning models such as Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) have appeared in this field with promising results compared to traditional approaches. To improve the performance of existing networks in time series forecasting, in this work two types of neural networks are brought together, combining the characteristics of a Graph Convolutional Network (GCN) and a Bidirectional Long Short-Term Memory (BiLSTM) network. This is a novel evolution that improves existing results in the literature and provides new possibilities in the analysis of time series. The results confirm a better performance of the combined BiLSTM-GCN approach compared to the BiLSTM and GCN models separately, as well as to the traditional models, with a lower error in all the error metrics used: the Root Mean Squared Error (RMSE), the Mean Squared Error (MSE), the Mean Absolute Percentage Error (MAPE) and the R-squared (R2). These results represent a smaller difference between the result returned by the model and the real value and, therefore, a greater precision in the predictions of this model. Full article
(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Economics, Econometrics, and Financial Management)
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12 pages, 316 KiB  
Article
Practical Exponential Stability of Impulsive Stochastic Food Chain System with Time-Varying Delays
by Yuxiao Zhao and Linshan Wang
Mathematics 2023, 11(1), 147; https://doi.org/10.3390/math11010147 - 28 Dec 2022
Cited by 49 | Viewed by 2699
Abstract
This paper studies the practical exponential stability of an impulsive stochastic food chain system with time-varying delays (ISOFCSs). By constructing an auxiliary system equivalent to the original system and comparison theorem, the existence of global positive solutions to the suggested system is discussed. [...] Read more.
This paper studies the practical exponential stability of an impulsive stochastic food chain system with time-varying delays (ISOFCSs). By constructing an auxiliary system equivalent to the original system and comparison theorem, the existence of global positive solutions to the suggested system is discussed. Moreover, we investigate the sufficient conditions for the exponential stability and practical exponential stability of the system, which is given by Razumikhin technique and the Lyapunov method. In addition, when Razumikhin’s condition holds, the exponential stability and practical exponential stability of species are independent of time delay. Finally, numerical simulation finds the validity of the method. Full article
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19 pages, 2470 KiB  
Article
Quasar Identification Using Multivariate Probability Density Estimated from Nonparametric Conditional Probabilities
by Jenny Farmer, Eve Allen and Donald J. Jacobs
Mathematics 2023, 11(1), 155; https://doi.org/10.3390/math11010155 - 28 Dec 2022
Cited by 2 | Viewed by 2177
Abstract
Nonparametric estimation for a probability density function that describes multivariate data has typically been addressed by kernel density estimation (KDE). A novel density estimator recently developed by Farmer and Jacobs offers an alternative high-throughput automated approach to univariate nonparametric density estimation based on [...] Read more.
Nonparametric estimation for a probability density function that describes multivariate data has typically been addressed by kernel density estimation (KDE). A novel density estimator recently developed by Farmer and Jacobs offers an alternative high-throughput automated approach to univariate nonparametric density estimation based on maximum entropy and order statistics, improving accuracy over univariate KDE. This article presents an extension of the single variable case to multiple variables. The univariate estimator is used to recursively calculate a product array of one-dimensional conditional probabilities. In combination with interpolation methods, a complete joint probability density estimate is generated for multiple variables. Good accuracy and speed performance in synthetic data are demonstrated by a numerical study using known distributions over a range of sample sizes from 100 to 106 for two to six variables. Performance in terms of speed and accuracy is compared to KDE. The multivariate density estimate developed here tends to perform better as the number of samples and/or variables increases. As an example application, measurements are analyzed over five filters of photometric data from the Sloan Digital Sky Survey Data Release 17. The multivariate estimation is used to form the basis for a binary classifier that distinguishes quasars from galaxies and stars with up to 94% accuracy. Full article
(This article belongs to the Special Issue Probability Distributions and Their Applications)
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11 pages, 290 KiB  
Article
Symmetries and Solutions for a Class of Advective Reaction-Diffusion Systems with a Special Reaction Term
by Mariano Torrisi and Rita Tracinà
Mathematics 2023, 11(1), 160; https://doi.org/10.3390/math11010160 - 28 Dec 2022
Cited by 2 | Viewed by 1743
Abstract
This paper is devoted to apply the Lie methods to a class of reaction diffusion advection systems of two interacting species u and v with two arbitrary constitutive functions f and g. The reaction term appearing in the equation for the species [...] Read more.
This paper is devoted to apply the Lie methods to a class of reaction diffusion advection systems of two interacting species u and v with two arbitrary constitutive functions f and g. The reaction term appearing in the equation for the species v is a logistic function of Lotka-Volterra type. Once obtained the Lie algebra for any form of f and g a Lie classification is carried out. Interesting reduced systems are derived admitting wide classes of exact solutions. Full article
(This article belongs to the Special Issue Applications of Partial Differential Equations in Engineering, 2nd Edition)
9 pages, 261 KiB  
Article
Hopf Differential Graded Galois Extensions
by Bo-Ye Zhang
Mathematics 2023, 11(1), 128; https://doi.org/10.3390/math11010128 - 27 Dec 2022
Cited by 1 | Viewed by 1551
Abstract
We introduce the concept of Hopf dg Galois extensions. For a finite dimensional semisimple Hopf algebra H and an H-module dg algebra R, we show that D(R#H)≅D(RH) is equivalent to [...] Read more.
We introduce the concept of Hopf dg Galois extensions. For a finite dimensional semisimple Hopf algebra H and an H-module dg algebra R, we show that D(R#H)≅D(RH) is equivalent to that R/RH is a Hopf differential graded Galois extension. We present a weaker version of Hopf differential graded Galois extensions and show the relationships between Hopf differential graded Galois extensions and Hopf Galois extensions. Full article
(This article belongs to the Special Issue Algebraic Structures and Graph Theory)
17 pages, 384 KiB  
Article
On the Regularity of Weak Solutions to Time-Periodic Navier–Stokes Equations in Exterior Domains
by Thomas Eiter
Mathematics 2023, 11(1), 141; https://doi.org/10.3390/math11010141 - 27 Dec 2022
Cited by 1 | Viewed by 1752
Abstract
Consider the time-periodic viscous incompressible fluid flow past a body with non-zero velocity at infinity. This article gives sufficient conditions such that weak solutions to this problem are smooth. Since time-periodic solutions do not have finite kinetic energy in general, the well-known regularity [...] Read more.
Consider the time-periodic viscous incompressible fluid flow past a body with non-zero velocity at infinity. This article gives sufficient conditions such that weak solutions to this problem are smooth. Since time-periodic solutions do not have finite kinetic energy in general, the well-known regularity results for weak solutions to the corresponding initial-value problem cannot be transferred directly. The established regularity criterion demands a certain integrability of the purely periodic part of the velocity field or its gradient, but it does not concern the time mean of these quantities. Full article
(This article belongs to the Special Issue Maximal Regularity, Stability Estimates and Mathematical Fluid Dynamics II)
14 pages, 7952 KiB  
Article
Heterogeneous Feature Fusion Module Based on CNN and Transformer for Multiview Stereo Reconstruction
by Rui Gao, Jiajia Xu, Yipeng Chen and Kyungeun Cho
Mathematics 2023, 11(1), 112; https://doi.org/10.3390/math11010112 - 26 Dec 2022
Cited by 5 | Viewed by 3380
Abstract
For decades, a vital area of computer vision research has been multiview stereo (MVS), which creates 3D models of a scene using photographs. This study presents an effective MVS network for 3D reconstruction utilizing multiview pictures. Alternative learning-based reconstruction techniques work well, because [...] Read more.
For decades, a vital area of computer vision research has been multiview stereo (MVS), which creates 3D models of a scene using photographs. This study presents an effective MVS network for 3D reconstruction utilizing multiview pictures. Alternative learning-based reconstruction techniques work well, because CNNs (convolutional neural network) can extract only the image’s local features; however, they contain many artifacts. Herein, a transformer and CNN are used to extract the global and local features of the image, respectively. Additionally, hierarchical aggregation and heterogeneous interaction modules were used to improve these features. They are based on the transformer and can extract dense features with 3D consistency and global context that are necessary to provide accurate matching for MVS. Full article
(This article belongs to the Special Issue Advances of Mathematical Image Processing)
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18 pages, 1450 KiB  
Article
Explicit Gaussian Variational Approximation for the Poisson Lognormal Mixed Model
by Xiaoping Shi, Xiang-Sheng Wang and Augustine Wong
Mathematics 2022, 10(23), 4542; https://doi.org/10.3390/math10234542 - 1 Dec 2022
Viewed by 1609
Abstract
In recent years, the Poisson lognormal mixed model has been frequently used in modeling count data because it can accommodate both the over-dispersion of the data and the existence of within-subject correlation. Since the likelihood function of this model is expressed in terms [...] Read more.
In recent years, the Poisson lognormal mixed model has been frequently used in modeling count data because it can accommodate both the over-dispersion of the data and the existence of within-subject correlation. Since the likelihood function of this model is expressed in terms of an intractable integral, estimating the parameters and obtaining inference for the parameters are challenging problems. Some approximation procedures have been proposed in the literature; however, they are computationally intensive. Moreover, the existing studies of approximate parameter inference using the Gaussian variational approximation method are usually restricted to models with only one predictor. In this paper, we consider the Poisson lognormal mixed model with more than one predictor. By extending the Gaussian variational approximation method, we derive explicit forms for the estimators of the parameters and examine their properties, including the asymptotic distributions of the estimators of the parameters. Accurate inference for the parameters is also obtained. A real-life example demonstrates the applicability of the proposed method, and simulation studies illustrate the accuracy of the proposed method. Full article
(This article belongs to the Special Issue Machine Learning and Statistical Methods to Prediction and Optimal Decision-Making)
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