Mathematics

17 pages, 359 KiB

Open AccessArticle

Functional Ergodic Time Series Analysis Using Expectile Regression

by Fatimah Alshahrani, Ibrahim M. Almanjahie, Zouaoui Chikr Elmezouar, Zoulikha Kaid, Ali Laksaci and Mustapha Rachdi

Mathematics 2022, 10(20), 3919; https://doi.org/10.3390/math10203919 - 21 Oct 2022

Cited by 4 | Viewed by 1236

Abstract

In this article, we study the problem of the recursive estimator of the expectile regression of a scalar variable Y given a random variable X that belongs in functional space. We construct a new estimator and study the asymptotic properties over a general [...] Read more.

In this article, we study the problem of the recursive estimator of the expectile regression of a scalar variable Y given a random variable X that belongs in functional space. We construct a new estimator and study the asymptotic properties over a general functional time structure. Precisely, the strong consistency of this estimator is established, considering that the sampled observations are taken from an ergodic functional process. Next, a simulation experiment is conducted to highlight the great impact of the constructed estimator as well as the ergodic functional time series data. Finally, a real data analysis is used to demonstrate the superiority of the constructed estimator. Full article

(This article belongs to the Special Issue Functional Data Analysis: Theory and Applications to Different Scenarios)

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17 pages, 5485 KiB

Open AccessArticle

Analysis of Mixed Convection on Two-Phase Nanofluid Flow Past a Vertical Plate in Brinkman-Extended Darcy Porous Medium with Nield Conditions

by Hatem Gasmi, Umair Khan, Aurang Zaib, Anuar Ishak, Sayed M. Eldin and Zehba Raizah

Mathematics 2022, 10(20), 3918; https://doi.org/10.3390/math10203918 - 21 Oct 2022

Cited by 5 | Viewed by 1404

Abstract

The rapid advancement in technology in recent years has shown that nanofluids are very vital to further development in science and technology. Moreover, many industrial specifications cannot be met by allowing natural convection only, hence the need to incorporate forced convection and natural [...] Read more.

The rapid advancement in technology in recent years has shown that nanofluids are very vital to further development in science and technology. Moreover, many industrial specifications cannot be met by allowing natural convection only, hence the need to incorporate forced convection and natural convection into a single flow regime. The research aims to quantify the mixed convective two-phase flow past a vertical permeable surface in a Brinkman-Extended Darcy porous medium (BEDPM) induced by nanofluid, with heat and mass transfer. In addition, the Nield condition is also incorporated. The model of the problem was initially constructed in the vital form of leading governing equations (LGEs). These LGEs are specifically called partial differential equations (PDEs) (because of two or more independent variables) which were later converted into a set of the single independent variable of ordinary differential equations (ODEs) by implementing the similarity transformations. The set of single independent ODEs was numerically solved via the boundary value problem of fourth-order (bvp4c) technique. The bvp4c is one of the most frequently recommended built-in MATLAB subroutines based on the three-stage Labatto formula. The impact of several physically embedded influential parameters on the fluid flow, along with mass and thermal properties of the nanofluid in a Brinkman-Extended Darcy porous medium for the cases of buoyancy assisting flow (BAF) and buoyancy opposing flow (BOF), were investigated and argued. The numerical outcomes clarify that the porosity parameter reduces the velocity, whereas the concentration and the temperature enhance in the case of the buoyancy assisting and buoyancy opposing flows. In addition, the wall drag force elevates for the larger value of the dimensionless permeability parameter

K_{1}

and the buoyancy ratio parameter

N

, while it declines for the modified porosity parameter

ε_{1}

. Full article

(This article belongs to the Special Issue Computational Fluid Dynamics II)

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13 pages, 6421 KiB

Open AccessArticle

Modeling the Interplay between HDV and HBV in Chronic HDV/HBV Patients

by Adequate Mhlanga, Rami Zakh, Alexander Churkin, Vladimir Reinharz, Jeffrey S. Glenn, Ohad Etzion, Scott J. Cotler, Cihan Yurdaydin, Danny Barash and Harel Dahari

Mathematics 2022, 10(20), 3917; https://doi.org/10.3390/math10203917 - 21 Oct 2022

Cited by 3 | Viewed by 1502

Abstract

Hepatitis D virus is an infectious subviral agent that can only propagate in people infected with hepatitis B virus. In this study, we modified and further developed a recent model for early hepatitis D virus and hepatitis B virus kinetics to better reproduce [...] Read more.

Hepatitis D virus is an infectious subviral agent that can only propagate in people infected with hepatitis B virus. In this study, we modified and further developed a recent model for early hepatitis D virus and hepatitis B virus kinetics to better reproduce hepatitis D virus and hepatitis B virus kinetics measured in infected patients during anti-hepatitis D virus treatment. The analytical solutions were provided to highlight the new features of the modified model. The improved model offered significantly better prospects for modeling hepatitis D virus and hepatitis B virus interactions. Full article

(This article belongs to the Special Issue Mathematical and Computational Biology of Viruses at the Molecular or Cellular Levels)

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18 pages, 805 KiB

Open AccessArticle

Synchronization of Fractional-Order Neural Networks with Time Delays and Reaction-Diffusion Terms via Pinning Control

by M. Hymavathi, Tarek F. Ibrahim, M. Syed Ali, Gani Stamov, Ivanka Stamova, B. A. Younis and Khalid I. Osman

Mathematics 2022, 10(20), 3916; https://doi.org/10.3390/math10203916 - 21 Oct 2022

Cited by 5 | Viewed by 1324

Abstract

This paper introduces a novel synchronization scheme for fractional-order neural networks with time delays and reaction-diffusion terms via pinning control. We consider Caputo fractional derivatives, constant delays and distributed delays in our model. Based on the stability behavior, fractional inequalities and Lyapunov-type functions, [...] Read more.

This paper introduces a novel synchronization scheme for fractional-order neural networks with time delays and reaction-diffusion terms via pinning control. We consider Caputo fractional derivatives, constant delays and distributed delays in our model. Based on the stability behavior, fractional inequalities and Lyapunov-type functions, several criteria are derived, which ensure the achievement of a synchronization for the drive-response systems. The obtained criteria are easy to test and are in the format of inequalities between the system parameters. Finally, numerical examples are presented to illustrate the results. The obtained criteria in this paper consider the effect of time delays as well as the reaction-diffusion terms, which generalize and improve some existing results. Full article

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25 pages, 360 KiB

Open AccessReview

A Review of Methods, and Analytical and Experimental Studies on the Use of Coal–Water Suspensions

by Konstantin Osintsev, Sergei Aliukov and Anatoliy Alabugin

Mathematics 2022, 10(20), 3915; https://doi.org/10.3390/math10203915 - 21 Oct 2022

Cited by 2 | Viewed by 1247

Abstract

Research in the field of building mathematical models for combustion processes has been ongoing ever since the chemical reactions of combustion were first discovered. The authors of this review have systematized mathematical models of coal–water suspension (CWS) combustion processes, the sequence of analytical [...] Read more.

Research in the field of building mathematical models for combustion processes has been ongoing ever since the chemical reactions of combustion were first discovered. The authors of this review have systematized mathematical models of coal–water suspension (CWS) combustion processes, the sequence of analytical and experimental studies, and have also shown the global genesis of the CWS use. In addition, this review touches upon a topic that is inextricably linked with the combustion of CWS, namely their transportation from the place of coal mining to their place of thermal utilization. For developing countries, their own energy independence is in the foreground, as it is the basis for their economic independence and also a means for other sectors of their economy to be protected from the impact of market changes in fuel prices in the future spot world market. The authors of this review explored the possibility of using Kyrgyz brown coal and transporting it through a coal pipeline from a mountainous area to an industrial site for thermal utilization in specialized steam boiler units. As the economic analysis showed, for the conditions of the Republic of Kyrgyzstan, the use of CWS and coal pipelines with rising prices for natural gas is economically justified. The recommendations of the authors are used in scientific reports and methodological recommendations for the energy and mining sectors of the Republic of Kyrgyzstan, how the recommendations can also be applied to similar conditions in the highlands of Russia, China, and India. Full article

(This article belongs to the Special Issue Mathematical Modeling of Engineering and Socio-Economic Processes and Systems)

22 pages, 6138 KiB

Open AccessArticle

Deep-Learning-Based Complex Scene Text Detection Algorithm for Architectural Images

by Weiwei Sun, Huiqian Wang, Yi Lu, Jiasai Luo, Ting Liu, Jinzhao Lin, Yu Pang and Guo Zhang

Mathematics 2022, 10(20), 3914; https://doi.org/10.3390/math10203914 - 21 Oct 2022

Cited by 3 | Viewed by 1987

Abstract

With the advent of smart cities, the text information in an image can be accurately located and recognized, and then applied to the fields of instant translation, image retrieval, card surface information recognition, and license plate recognition. Thus, people’s lives and work will [...] Read more.

With the advent of smart cities, the text information in an image can be accurately located and recognized, and then applied to the fields of instant translation, image retrieval, card surface information recognition, and license plate recognition. Thus, people’s lives and work will become more convenient and comfortable. Owing to the varied orientations, angles, and shapes of text, identifying textual features from images is challenging. Therefore, we propose an improved EAST detector algorithm for detecting and recognizing slanted text in images. The proposed algorithm uses reinforcement learning to train a recurrent neural network controller. The optimal fully convolutional neural network structure is selected, and multi-scale features of text are extracted. After importing this information into the output module, the Generalized Intersection over Union algorithm is used to enhance the regression effect of the text bounding box. Next, the loss function is adjusted to ensure a balance between positive and negative sample classes before outputting the improved text detection results. Experimental results indicate that the proposed algorithm can address the problem of category homogenization and improve the low recall rate in target detection. When compared with other image detection algorithms, the proposed algorithm can better identify slanted text in natural scene images. Finally, its ability to recognize text in complex environments is also excellent. Full article

(This article belongs to the Special Issue Computer Vision and Pattern Recognition with Applications)

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17 pages, 16578 KiB

Open AccessArticle

OCPHN: Outfit Compatibility Prediction with Hypergraph Networks

by Zhuo Li, Jian Li, Tongtong Wang, Xiaolin Gong, Yinwei Wei and Peng Luo

Mathematics 2022, 10(20), 3913; https://doi.org/10.3390/math10203913 - 21 Oct 2022

Cited by 1 | Viewed by 1327

Abstract

With the rapid development of the online shopping, the pursuit of outfit compatibility has become a basic requirement for an increasing number of customers. The existing work on outfit compatibility prediction largely focuses on modeling pairwise item compatibility without considering modeling the whole [...] Read more.

With the rapid development of the online shopping, the pursuit of outfit compatibility has become a basic requirement for an increasing number of customers. The existing work on outfit compatibility prediction largely focuses on modeling pairwise item compatibility without considering modeling the whole outfit directly. To address the problem, in this paper, we propose a novel hypergraph-based compatibility modeling scheme named OCPHN, which is able to better model complex relationships among outfits. In OCPHN, we represent the outfit as a hypergraph, where each hypernode represents a category and each hyperedge represents the interactions between multiple categories (i.e., they appear in the same outfit). To better predict outfit compatibility, the hypergraph is transformed into a simple graph, and the message propagation mechanism in the graph convolution network is used to aggregate the neighbours’ information on the node and update the node representations. Furthermore, with learned node representations, an attention mechanism is introduced to compute the outfit compatibility score. Using a benchmark dataset, the experimental results show that the proposed method is an improvement over the strangest baselines in terms of accuracy by about 3% and 1% in the fill-in-the-blank and compatibility prediction tasks, respectively. Full article

(This article belongs to the Special Issue Artificial Intelligence and Internet of Things for Intelligent Systems)

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18 pages, 1640 KiB

Open AccessFeature PaperArticle

Open-Source Computational Photonics with Auto Differentiable Topology Optimization

by Benjamin Vial and Yang Hao

Mathematics 2022, 10(20), 3912; https://doi.org/10.3390/math10203912 - 21 Oct 2022

Cited by 3 | Viewed by 1949

Abstract

In recent years, technological advances in nanofabrication have opened up new applications in the field of nanophotonics. To engineer and develop novel functionalities, rigorous and efficient numerical methods are required. In parallel, tremendous advances in algorithmic differentiation, in part pushed by the intensive [...] Read more.

In recent years, technological advances in nanofabrication have opened up new applications in the field of nanophotonics. To engineer and develop novel functionalities, rigorous and efficient numerical methods are required. In parallel, tremendous advances in algorithmic differentiation, in part pushed by the intensive development of machine learning and artificial intelligence, has made possible large-scale optimization of devices with a few extra modifications of the underlying code. We present here our development of three different software libraries for solving Maxwell’s equations in various contexts: a finite element code with a high-level interface for problems commonly encountered in photonics, an implementation of the Fourier modal method for multilayered bi-periodic metasurfaces and a plane wave expansion method for the calculation of band diagrams in two-dimensional photonic crystals. All of them are endowed with automatic differentiation capabilities and we present typical inverse design examples. Full article

(This article belongs to the Special Issue Advanced Mathematical and Numerical Modeling in Electrodynamics and Photonics)

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21 pages, 2087 KiB

Open AccessArticle

Numerical Investigation into the Effects of a Viscous Fluid Seabed on Wave Scattering with a Fixed Rectangular Obstacle

by Kuan-Yu Zheng, Chen-Wei Chang and I-Chi Chan

Mathematics 2022, 10(20), 3911; https://doi.org/10.3390/math10203911 - 21 Oct 2022

Viewed by 1188

Abstract

We study numerically the effects of a viscous fluid seabed on wave scattering with a solid obstacle of rectangular shape fixed at the free surface, on the seafloor, or internally within the water layer. The computational model is based on OpenFOAM and it [...] Read more.

We study numerically the effects of a viscous fluid seabed on wave scattering with a solid obstacle of rectangular shape fixed at the free surface, on the seafloor, or internally within the water layer. The computational model is based on OpenFOAM and it is validated using existing analytical solutions for waves encountering an obstacle on a solid bed and available experimental data for waves propagating over a muddy seabed with no obstacles. With the consideration of a solid obstacle on a viscous fluid bottom, we examine the corresponding transformations of incident, reflected, and transmitted wave components. The velocity field near the obstacle and the wave forces exerted on the obstacle are also analyzed. Our simulations show that all wave components experience significant amplitude attenuation caused by the viscous fluid bed. For both surface and bottom obstacles, the presence of an obstacle enhances the damping of reflected waves. When an internally submerged obstacle is considered, transmitted waves are the most affected due to a prominent vortex generated in the lee of the obstacle. Patterns of the velocity field in the vicinity of the obstacle are shown to be controlled mainly by the obstacle with some modulations in magnitude and wavelength contributed by the viscous fluid bed. In view of the vertical wave force on the obstacle surface, both a phase shift and decrease in magnitude are observed. These findings enhance our understanding of the underlying physical processes in the wave–obstacle–mud problems. More studies are still needed in order to provide the necessary technical tools for the engineering design of coastal structures in muddy marine environments. Full article

(This article belongs to the Section Engineering Mathematics)

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15 pages, 3686 KiB

Open AccessArticle

Multifractal Characteristics on Temporal Maximum of Air Pollution Series

by Nurulkamal Masseran

Mathematics 2022, 10(20), 3910; https://doi.org/10.3390/math10203910 - 21 Oct 2022

Cited by 3 | Viewed by 1057

Abstract

Presenting and describing a temporal series of air pollution data with longer time lengths provides more concise information and is, in fact, one of the simplest techniques of data reduction in a time series. However, this process can result in the loss of [...] Read more.

Presenting and describing a temporal series of air pollution data with longer time lengths provides more concise information and is, in fact, one of the simplest techniques of data reduction in a time series. However, this process can result in the loss of important information related to data features. Thus, the purpose of this study is to determine the type of data characteristics that might be lost when describing data with different time lengths corresponding to a process of data reduction. In parallel, this study proposes the application of a multifractal technique to investigate the properties on an air pollution series with different time lengths. A case study has been carried out using an air pollution index data in Klang, Malaysia. Results show that hourly air pollution series contain the most informative knowledge regarding the behaviors and characteristics of air pollution, particularly in terms of the strength of multifractality, long-term persistent correlations, and heterogeneity of variations. On the other hand, the statistical findings found that data reduction corresponding to a longer time length will change the multifractal properties of the original data. Full article

(This article belongs to the Special Issue Data Analysis and Domain Knowledge)

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15 pages, 683 KiB

Open AccessReview

Fuzziness, Indeterminacy and Soft Sets: Frontiers and Perspectives

by Michael Gr. Voskoglou

Mathematics 2022, 10(20), 3909; https://doi.org/10.3390/math10203909 - 21 Oct 2022

Cited by 6 | Viewed by 1245

Abstract

The present paper comes across the main steps that were laid from Zadeh’s fuzziness and Atanassov’s intuitionistic fuzzy sets to Smarandache’s indeterminacy and to Molodstov’s soft sets. Two hybrid methods for assessment and decision making, respectively, under fuzzy conditions are also presented using [...] Read more.

The present paper comes across the main steps that were laid from Zadeh’s fuzziness and Atanassov’s intuitionistic fuzzy sets to Smarandache’s indeterminacy and to Molodstov’s soft sets. Two hybrid methods for assessment and decision making, respectively, under fuzzy conditions are also presented using suitable examples that use soft sets and real intervals as tools. The decision making method improves on an earlier method of Maji et al. Further, it is described how the concept of topological space, the most general category of mathematical spaces, can be extended to fuzzy structures and how to generalize the fundamental mathematical concepts of limit, continuity compactness and Hausdorff space within such kinds of structures. In particular, fuzzy and soft topological spaces are defined and examples are given to illustrate these generalizations. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications 2021)

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12 pages, 1421 KiB

Open AccessArticle

A KGE Based Knowledge Enhancing Method for Aspect-Level Sentiment Classification

by Haibo Yu, Guojun Lu, Qianhua Cai and Yun Xue

Mathematics 2022, 10(20), 3908; https://doi.org/10.3390/math10203908 - 21 Oct 2022

Cited by 7 | Viewed by 1474

Abstract

ALSC (Aspect-level Sentiment Classification) is a fine-grained task in the field of NLP (Natural Language Processing) which aims to identify the sentiment toward a given aspect. In addition to exploiting the sentence semantics and syntax, current ALSC methods focus on introducing external knowledge [...] Read more.

ALSC (Aspect-level Sentiment Classification) is a fine-grained task in the field of NLP (Natural Language Processing) which aims to identify the sentiment toward a given aspect. In addition to exploiting the sentence semantics and syntax, current ALSC methods focus on introducing external knowledge as a supplementary to the sentence information. However, the integration of the three categories of information is still challenging. In this paper, a novel method is devised to effectively combine sufficient semantic and syntactic information as well as use of external knowledge. The proposed model contains a sentence encoder, a semantic learning module, a syntax learning module, a knowledge enhancement module, an information fusion module and a sentiment classifier. The semantic information and syntactic information are respectively extracted via a self-attention network and a graphical convolutional network. Specifically, the KGE (Knowledge Graph Embedding) is employed to enhance the feature representation of the aspect. Then, the attention-based gate mechanism is taken to fuse three types of information. We evaluated the proposed model on three benchmark datasets and the experimental results establish strong evidence of high accuracy. Full article

(This article belongs to the Special Issue Advancement of Mathematical Methods in Feature Representation Learning for Artificial Intelligence, Data Mining and Robotics)

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23 pages, 1996 KiB

Open AccessReview

Parametric Distributions for Survival and Reliability Analyses, a Review and Historical Sketch

by Nanami Taketomi, Kazuki Yamamoto, Christophe Chesneau and Takeshi Emura

Mathematics 2022, 10(20), 3907; https://doi.org/10.3390/math10203907 - 21 Oct 2022

Cited by 17 | Viewed by 3693

Abstract

During its 330 years of history, parametric distributions have been useful for survival and reliability analyses. In this paper, we comprehensively review the historical backgrounds and statistical properties of a number of parametric distributions used in survival and reliability analyses. We provide encyclopedic [...] Read more.

During its 330 years of history, parametric distributions have been useful for survival and reliability analyses. In this paper, we comprehensively review the historical backgrounds and statistical properties of a number of parametric distributions used in survival and reliability analyses. We provide encyclopedic coverage of the important parametric distributions, which is more extensive than the existing textbooks on survival and reliability analyses. We also explain how these distributions have been adopted in survival and reliability analyses with original and state-of-the-art references. We cover the exponential, Weibull, Rayleigh, lognormal, log-logistic, gamma, generalized gamma, Pareto (types I, II, and IV), Hjorth, Burr (types III and XII), Dagum, exponential power, Gompertz, Birnbaum-Saunders, exponential-logarithmic, piecewise exponential, generalized exponential, exponentiated Weibull, generalized modified Weibull, and spline distributions. We analyze a real dataset for illustration. Full article

(This article belongs to the Special Issue Current Developments in Theoretical and Applied Statistics)

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15 pages, 4044 KiB

Open AccessArticle

State Prediction Method for A-Class Insulation Board Production Line Based on Transfer Learning

by Yong Wang, Hui Wang, Xiaoqiang Guo, Xinhua Liu and Xiaowen Liu

Mathematics 2022, 10(20), 3906; https://doi.org/10.3390/math10203906 - 21 Oct 2022

Viewed by 1080

Abstract

It is essential to determine the running state of a production line to monitor the production status and make maintenance plans. In order to monitor the real-time running state of an A-class insulation board production line conveniently and accurately, a novel state prediction [...] Read more.

It is essential to determine the running state of a production line to monitor the production status and make maintenance plans. In order to monitor the real-time running state of an A-class insulation board production line conveniently and accurately, a novel state prediction method based on deep learning and long short-term memory (LSTM) network is proposed. The multiple layers of the Res-block are introduced to fuse local features and improve hidden feature extraction. The transfer learning strategy is studied and the improved loss function is proposed, which makes the model training process fast and stable. The experimental results show that the proposed Res-LSTM model reached 98.9% prediction accuracy, and the average R²-score of the industrial experiments can reach 0.93. Compared with other mainstream algorithms, the proposed Res-LSTM model obtained excellent performance in prediction speed and accuracy, which meets the needs of industrial production. Full article

(This article belongs to the Special Issue Recent Advances in Artificial Intelligence and Machine Learning)

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16 pages, 2460 KiB

Open AccessArticle

Hyperbolic Directed Hypergraph-Based Reasoning for Multi-Hop KBQA

by Guanchen Xiao, Jinzhi Liao, Zhen Tan, Yiqi Yu and Bin Ge

Mathematics 2022, 10(20), 3905; https://doi.org/10.3390/math10203905 - 21 Oct 2022

Cited by 1 | Viewed by 1415

Abstract

The target of the multi-hop knowledge base question-answering task is to find answers of some factoid questions by reasoning across multiple knowledge triples in the knowledge base. Most of the existing methods for multi-hop knowledge base question answering based on a general knowledge [...] Read more.

The target of the multi-hop knowledge base question-answering task is to find answers of some factoid questions by reasoning across multiple knowledge triples in the knowledge base. Most of the existing methods for multi-hop knowledge base question answering based on a general knowledge graph ignore the semantic relationship between each hop. However, modeling the knowledge base as a directed hypergraph has the problems of sparse incidence matrices and asymmetric Laplacian matrices. To make up for the deficiency, we propose a directed hypergraph convolutional network modeled on hyperbolic space, which can better deal with the sparse structure, and effectively adapt to the problem of an asymmetric incidence matrix of directed hypergraphs modeled on a knowledge base. We propose an interpretable KBQA model based on the hyperbolic directed hypergraph convolutional neural network named HDH-GCN which can update relation semantic information hop-by-hop and pays attention to different relations at different hops. The model can improve the accuracy of the multi-hop knowledge base question-answering task, and has application value in text question answering, human–computer interactions and other fields. Extensive experiments on benchmarks—PQL, MetaQA—demonstrate the effectiveness and universality of our HDH-GCN model, leading to state-of-the-art performance. Full article

(This article belongs to the Special Issue Mathematics-Based Methods in Graph Machine Learning)

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18 pages, 481 KiB

Open AccessArticle

On Convergence of Support Operator Method Schemes for Differential Rotational Operations on Tetrahedral Meshes Applied to Magnetohydrodynamic Problems

by Yury Poveshchenko, Viktoriia Podryga and Parvin Rahimly

Mathematics 2022, 10(20), 3904; https://doi.org/10.3390/math10203904 - 20 Oct 2022

Viewed by 843

Abstract

The problem of constructing and justifying the discrete algorithms of the support operator method for numerical modeling of differential repeated rotational operations of vector analysis (

c u r l c u r l

) in application to problems of magnetohydrodynamics is considered. [...] Read more.

The problem of constructing and justifying the discrete algorithms of the support operator method for numerical modeling of differential repeated rotational operations of vector analysis (

c u r l c u r l

) in application to problems of magnetohydrodynamics is considered. Difference schemes of the support operator method on the unstructured meshes do not approximate equations in the local sense. Therefore, it is necessary to prove the convergence of these schemes to the exact solution, which is possible after analyzing the error structure of their approximation. For this analysis, a decomposition of the space of mesh vector functions into an orthogonal direct sum of subspaces of potential and vortex fields is introduced. Generalized centroid-tensor metric representations of repeated operations of tensor analysis (

d i v

,

g r a d

, and

c u r l

) are constructed. Representations have flux-circulation properties that are integrally consistent on spatial meshes of irregular structure. On smooth solutions of the model magnetostatic problem on a tetrahedral mesh with the first order of accuracy in the rms sense, the convergence of the constructed difference schemes is proved. The algorithms constructed in this work can be used to solve physical problems with discontinuous magnetic viscosity, dielectric permittivity, or thermal resistance of the medium. Full article

(This article belongs to the Special Issue Nonlinear Partial Differential Equations: Exact Solutions, Symmetries, Methods, and Applications)

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26 pages, 438 KiB

Open AccessFeature PaperArticle

Integral Representations of Ratios of the Gauss Hypergeometric Functions with Parameters Shifted by Integers

by Alexander Dyachenko and Dmitrii Karp

Mathematics 2022, 10(20), 3903; https://doi.org/10.3390/math10203903 - 20 Oct 2022

Cited by 1 | Viewed by 982

Abstract

Given real parameters

a, b, c

and integer shifts

n_{1}, n_{2}, m

, we consider the ratio [...] Read more.

Given real parameters

a, b, c

and integer shifts

n_{1}, n_{2}, m

, we consider the ratio

R (z) =_{2} F_{1} (a + n_{1}, b + n_{2}; c + m; z) /_{2} F_{1} (a, b; c; z)

of the Gauss hypergeometric functions. We find a formula for

Im R (x \pm i 0)

with

x > 1

in terms of real hypergeometric polynomial P, beta density and the absolute value of the Gauss hypergeometric function. This allows us to construct explicit integral representations for R when the asymptotic behaviour at unity is mild and the denominator does not vanish. The results are illustrated with a large number of examples. Full article

(This article belongs to the Special Issue Analytical and Computational Methods in Differential Equations, Special Functions, Transmutations and Integral Transforms)

23 pages, 2104 KiB

Open AccessFeature PaperArticle

Deep Reinforcement Learning for Crowdshipping Last-Mile Delivery with Endogenous Uncertainty

by Marco Silva and João Pedro Pedroso

Mathematics 2022, 10(20), 3902; https://doi.org/10.3390/math10203902 - 20 Oct 2022

Cited by 3 | Viewed by 2183

Abstract

In this work, we study a flexible compensation scheme for last-mile delivery where a company outsources part of the activity of delivering products to its customers to occasional drivers (ODs), under a scheme named crowdshipping. All deliveries are completed at the minimum total [...] Read more.

In this work, we study a flexible compensation scheme for last-mile delivery where a company outsources part of the activity of delivering products to its customers to occasional drivers (ODs), under a scheme named crowdshipping. All deliveries are completed at the minimum total cost incurred with their vehicles and drivers plus the compensation paid to the ODs. The company decides on the best compensation scheme to offer to the ODs at the planning stage. We model our problem based on a stochastic and dynamic environment where delivery orders and ODs volunteering to make deliveries present themselves randomly within fixed time windows. The uncertainty is endogenous in the sense that the compensation paid to ODs influences their availability. We develop a deep reinforcement learning (DRL) algorithm that can deal with large instances while focusing on the quality of the solution: we combine the combinatorial structure of the action space with the neural network of the approximated value function, involving techniques from machine learning and integer optimization. The results show the effectiveness of the DRL approach by examining out-of-sample performance and that it is suitable to process large samples of uncertain data, which induces better solutions. Full article

(This article belongs to the Special Issue New Insights in Machine Learning and Deep Neural Networks)

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21 pages, 6554 KiB

Open AccessArticle

Trajectory Tracking Design for a Swarm of Autonomous Mobile Robots: A Nonlinear Adaptive Optimal Approach

by Yung-Hsiang Chen and Yung-Yue Chen

Mathematics 2022, 10(20), 3901; https://doi.org/10.3390/math10203901 - 20 Oct 2022

Cited by 5 | Viewed by 1473

Abstract

This research presents a nonlinear adaptive optimal control approach to the trajectory tracking problem of a swarm of autonomous mobile robots. Mathematically, finding an analytical adaptive control solution that meets the H₂ performance index for the trajectory tracking problem when controlling a [...] Read more.

This research presents a nonlinear adaptive optimal control approach to the trajectory tracking problem of a swarm of autonomous mobile robots. Mathematically, finding an analytical adaptive control solution that meets the H₂ performance index for the trajectory tracking problem when controlling a swarm of autonomous mobile robots is an almost impossible task, due to the great complexity and high dimensions of the dynamics. For deriving an analytical adaptive control law for this tracking problem, a particular formulation for the trajectory tracking error dynamics between a swarm of autonomous mobile robots and the desired trajectory is made via a filter link. Based on this prior analysis of the trajectory tracking error dynamics, a closed-form adaptive control law is analytically derived from a high-dimensional nonlinear partial differential equation, which is equivalent to solving the trajectory tracking problem of a swarm of autonomous mobile robots with respect to an H₂ performance index. This delivered adaptive nonlinear control solution offers the advantages of a simple control structure and good energy-saving performance. From the trajectory tracking verification, this proposed control approach possesses satisfactory trajectory tracking performance for a swarm of autonomous mobile robots, even under the effects of huge modeling uncertainties. Full article

(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications)

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20 pages, 2474 KiB

Open AccessArticle

Analysis of the Stability and Optimal Control Strategy for an ISCR Rumor Propagation Model with Saturated Incidence and Time Delay on a Scale-Free Network

by Xuefeng Yue and Liangan Huo

Mathematics 2022, 10(20), 3900; https://doi.org/10.3390/math10203900 - 20 Oct 2022

Cited by 2 | Viewed by 1079

Abstract

The spread of rumors in the era of new media poses a serious challenge to sustaining social order. Models regarding rumor propagation should be proposed in order to prevent them. Taking the cooling-off period into account in this paper, a modified ISCR model [...] Read more.

The spread of rumors in the era of new media poses a serious challenge to sustaining social order. Models regarding rumor propagation should be proposed in order to prevent them. Taking the cooling-off period into account in this paper, a modified ISCR model with saturated incidence and time delay on a scale-free network is introduced. The basic reproduction number

R_{0}

, which does not depend on time delay

τ

, is given by simple calculation. The stability of the rumor-free and rumor-endemic equilibrium points is proved by constructing proper Lyapunov functions. The study of the ISCR rumor-spreading process acquires an understanding of the impact of many factors on the prevalence of rumors. Then, the optimal control strategy for restraining rumors is studied. Numerous sensitivity studies and numerical simulations are carried out. Based on the saturated incidence and time delay, results indicate that the effect of time delay plays a significant part in rumor propagation on a scale-free network. Full article

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29 pages, 8562 KiB

Open AccessArticle

Vaccination’s Role in Combating the Omicron Variant Outbreak in Thailand: An Optimal Control Approach

by Jiraporn Lamwong, Puntani Pongsumpun, I-Ming Tang and Napasool Wongvanich

Mathematics 2022, 10(20), 3899; https://doi.org/10.3390/math10203899 - 20 Oct 2022

Cited by 2 | Viewed by 1198

Abstract

COVID-19 is the name of the new infectious disease which has reached the pandemic stage and is named after the coronavirus (COVs) which causes it. COV is a single-stranded RNA virus which in humans leads to respiratory tract symptoms which can lead to [...] Read more.

COVID-19 is the name of the new infectious disease which has reached the pandemic stage and is named after the coronavirus (COVs) which causes it. COV is a single-stranded RNA virus which in humans leads to respiratory tract symptoms which can lead to death in those with low immunities, particularly older people. In this study, a standard dynamic model for COVID-19 was proposed by comparing a simple model and the optimal control model to reduce the number of infected people and become a guideline to control the outbreak. Control strategies are the vaccination rate and vaccine-induced immunity. An analysis was performed to find an equilibrium point, the basic reproduction number

(R_{0})

, and conditions that generate stability by using Lyapunov functions to prove the stability of the solution at the equilibrium point. Pontryagin’s maximum principle was used to find the optimal control condition. Moreover, sensitivity analysis of the parameters was performed to learn about the parameters that might affect the outbreak in order to be able to control the outbreak. According to the analysis, it is seen that the efficacy of vaccines

(b)

and the infection rate

(β_{a n}, β_{s n}, β_{a v}, β_{s v})

will affect the increased (decreased) incidence of the outbreak. Numerical analyses were performed on the Omicron variant outbreak data collected from the Thailand Ministry of Health, whose analyses then indicated that the optimal control strategy could lead to planning management and policy setting to control the COVID-19 outbreak. Full article

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21 pages, 369 KiB

Open AccessArticle

The Imprecision Issues of Four Powers and Eight Predictive Powers with Historical and Interim Data

by Ying-Ying Zhang and Qian Ran

Mathematics 2022, 10(20), 3898; https://doi.org/10.3390/math10203898 - 20 Oct 2022

Viewed by 853

Abstract

Imprecision is commonly encountered with respect to powers and predictive powers in clinical trials. In this article, we investigate the imprecision issues of four powers (Classical Power, Classical Conditional Power, Bayesian Power, and Bayesian Conditional Power) and eight predictive powers. To begin with, [...] Read more.

Imprecision is commonly encountered with respect to powers and predictive powers in clinical trials. In this article, we investigate the imprecision issues of four powers (Classical Power, Classical Conditional Power, Bayesian Power, and Bayesian Conditional Power) and eight predictive powers. To begin with, we derive the probabilities of Control Superior (CS), Treatment Superior (TS), and Equivocal (E) of the four powers and the eight predictive powers, and evaluate the limits of the probabilities at point 0. Moreover, we conduct extensive numerical experiments to exemplify the imprecision issues of the four powers and the eight predictive powers. In the numerical experiments, first, we compute the probabilities of CS, TS, and E for the four powers as functions of the sample size of the future data when the true treatment effect favors control, treatment, and equivocal, respectively. Second, we compute the probabilities of CS, TS, and E for the eight predictive powers as functions of the sample size of the future data under the sceptical prior and the optimistic prior, respectively. Finally, we carry out a real data example to show the prominence of the methods. Full article

(This article belongs to the Section Probability and Statistics)

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10 pages, 259 KiB

Open AccessArticle

On Balanced Host Games: A Sufficient Condition for Non-Emptiness of the Core

by Yan-An Hwang, Yu-Hsien Liao and Bo-Yao Wang

Mathematics 2022, 10(20), 3897; https://doi.org/10.3390/math10203897 - 20 Oct 2022

Viewed by 787

Abstract

Non-transferable utility (NTU) games arise from many economic situations. A classic example is the exchange economy. By pooling and redistributing their initial endowments, coalitions can achieve certain distributions of gains (utilities) that make up the coalition’s feasible set. This paper studies a new [...] Read more.

Non-transferable utility (NTU) games arise from many economic situations. A classic example is the exchange economy. By pooling and redistributing their initial endowments, coalitions can achieve certain distributions of gains (utilities) that make up the coalition’s feasible set. This paper studies a new class of NTU games called host games. A host game is an agent-parametrized family of NTU games, and an NTU game is associated with any agent (called the host in that case). We provide an adequate presumption for the existence of an allocation that is part of the host game’s core. Full article

(This article belongs to the Special Issue A Themed Issue Dedicated to Professor Lloyd S. Shapley on the Occasion of His 100th Birthday Anniversary)

29 pages, 8936 KiB

Open AccessArticle

XAI for Churn Prediction in B2B Models: A Use Case in an Enterprise Software Company

by Gabriel Marín Díaz, José Javier Galán and Ramón Alberto Carrasco

Mathematics 2022, 10(20), 3896; https://doi.org/10.3390/math10203896 - 20 Oct 2022

Cited by 9 | Viewed by 3005

Abstract

The literature related to Artificial Intelligence (AI) models and customer churn prediction is extensive and rich in Business to Customer (B2C) environments; however, research in Business to Business (B2B) environments is not sufficiently addressed. Customer churn in the business environment and more so [...] Read more.

The literature related to Artificial Intelligence (AI) models and customer churn prediction is extensive and rich in Business to Customer (B2C) environments; however, research in Business to Business (B2B) environments is not sufficiently addressed. Customer churn in the business environment and more so in a B2B context is critical, as the impact on turnover is generally greater than in B2C environments. On the other hand, the data used in the context of this paper point to the importance of the relationship between customer and brand through the Contact Center. Therefore, the recency, frequency, importance and duration (RFID) model used to obtain the customer’s assessment from the point of view of their interactions with the Contact Center is a novelty and an additional source of information to traditional models based on purchase transactions, recency, frequency, and monetary (RFM). The objective of this work consists of the design of a methodological process that contributes to analyzing the explainability of AI algorithm predictions, Explainable Artificial Intelligence (XAI), for which we analyze the binary target variable abandonment in a B2B environment, considering the relationships that the partner (customer) has with the Contact Center, and focusing on a business software distribution company. The model can be generalized to any environment in which classification or regression algorithms are required. Full article

(This article belongs to the Special Issue Advances in Machine Learning and Applications)

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23 pages, 1544 KiB

Open AccessArticle

Improved Recurrent Neural Network Schema for Validating Digital Signatures in VANET

by Arpit Jain, Jaspreet Singh, Sandeep Kumar, Țurcanu Florin-Emilian, Mihaltan Traian Candin and Premkumar Chithaluru

Mathematics 2022, 10(20), 3895; https://doi.org/10.3390/math10203895 - 20 Oct 2022

Cited by 17 | Viewed by 1507

Abstract

Vehicular ad hoc networks (VANETs) allow communication between stationary or moving vehicles with the assistance of wireless technology. Among various existing issues in smart VANETs, secure communication is the key challenge in VANETs with a 5G network. Smart vehicles must communicate with a [...] Read more.

Vehicular ad hoc networks (VANETs) allow communication between stationary or moving vehicles with the assistance of wireless technology. Among various existing issues in smart VANETs, secure communication is the key challenge in VANETs with a 5G network. Smart vehicles must communicate with a broad range of advanced road systems including traffic control and smart payment systems. Many security mechanisms are used in VANETs to ensure safe transmission; one such mechanism is cryptographic digital signatures based on public key infrastructure (PKI). In this mechanism, secret private keys are used for digital signatures to validate the identity of the message along with the sender. However, the validation of the digital signatures in fast-moving vehicles is extremely difficult. Based on an improved perceptron model of an artificial neural network (ANN), this paper proposes an efficient technique for digital signature verification. Still, manual signatures are extensively used for authentication across the world. However, manual signatures are still not employed for security in automotive and mobile networks. The process of converting manual signatures to pseudo-digital-signatures was simulated using the improved Elman backpropagation (I-EBP) model. A digital signature was employed during network connection to authenticate the legitimacy of the sender’s communications. Because it contained information about the vehicle on the road, there was scope for improvement in protecting the data from attackers. Compared to existing schemes, the proposed technique achieved significant gains in computational overhead, aggregate verification delay, and aggregate signature size. Full article

(This article belongs to the Special Issue Advancements in Machine Learning and Statistical Modeling, and Real-World Applications)

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18 pages, 328 KiB

Open AccessArticle

The Intrinsic Structure of High-Dimensional Data According to the Uniqueness of Constant Mean Curvature Hypersurfaces

by Junhong Dong, Qiong Li and Ximin Liu

Mathematics 2022, 10(20), 3894; https://doi.org/10.3390/math10203894 - 20 Oct 2022

Viewed by 959

Abstract

In this paper, we study the intrinsic structures of high-dimensional data sets for analyzing their geometrical properties, where the core message of the high-dimensional data is hiding on some nonlinear manifolds. Using the manifold learning technique with a particular focus on the mean [...] Read more.

In this paper, we study the intrinsic structures of high-dimensional data sets for analyzing their geometrical properties, where the core message of the high-dimensional data is hiding on some nonlinear manifolds. Using the manifold learning technique with a particular focus on the mean curvature, we develop new methods to investigate the uniqueness of constant mean curvature spacelike hypersurfaces in the Lorentzian warped product manifolds. Furthermore, we extend the uniqueness of stochastically complete hypersurfaces using the weak maximum principle. For the more general cases, we propose some non-existence results and a priori estimates for the constant higher-order mean curvature spacelike hypersurface. Full article

(This article belongs to the Special Issue Machine Learning and Statistical Methods to Prediction and Optimal Decision-Making)

26 pages, 456 KiB

Open AccessFeature PaperArticle

Some Technical Remarks on Negations of Discrete Probability Distributions and Their Information Loss

by Ingo Klein

Mathematics 2022, 10(20), 3893; https://doi.org/10.3390/math10203893 - 20 Oct 2022

Cited by 1 | Viewed by 1301

Abstract

Negation of a discrete probability distribution was introduced by Yager. To date, several papers have been published discussing generalizations, properties, and applications of negation. The recent work by Wu et al. gives an excellent overview of the literature and the motivation to deal [...] Read more.

Negation of a discrete probability distribution was introduced by Yager. To date, several papers have been published discussing generalizations, properties, and applications of negation. The recent work by Wu et al. gives an excellent overview of the literature and the motivation to deal with negation. Our paper focuses on some technical aspects of negation transformations. First, we prove that independent negations must be affine-linear. This fact was established by Batyrshin et al. as an open problem. Secondly, we show that repeated application of independent negations leads to a progressive loss of information (called monotonicity). In contrast to the literature, we try to obtain results not only for special but also for the general class of

ϕ

-entropies. In this general framework, we can show that results need to be proven only for Yager negation and can be transferred to the entire class of independent (=affine-linear) negations. For general

ϕ

-entropies with strictly concave generator function

ϕ

, we can show that the information loss increases separately for sequences of odd and even numbers of repetitions. By using a Lagrangian approach, this result can be extended, in the neighbourhood of the uniform distribution, to all numbers of repetition. For Gini, Shannon, Havrda–Charvát (Tsallis), Rényi and Sharma–Mittal entropy, we prove that the information loss has a global minimum of 0. For dependent negations, it is not easy to obtain analytical results. Therefore, we simulate the entropy distribution and show how different repeated negations affect Gini and Shannon entropy. The simulation approach has the advantage that the entire simplex of discrete probability vectors can be considered at once, rather than just arbitrarily selected probability vectors. Full article

(This article belongs to the Section Probability and Statistics)

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2 pages, 187 KiB

Open AccessEditorial

Mathematical Biology: Modeling, Analysis, and Simulations

by Ricardo López-Ruiz

Mathematics 2022, 10(20), 3892; https://doi.org/10.3390/math10203892 - 20 Oct 2022

Viewed by 1833

Abstract

Mathematical biology has been an area of wide interest during the recent decades, as the modeling of complicated biological processes has enabled the creation of analytical and computational approaches to many different bio-inspired problems originating from different branches such as population dynamics, molecular [...] Read more.

Mathematical biology has been an area of wide interest during the recent decades, as the modeling of complicated biological processes has enabled the creation of analytical and computational approaches to many different bio-inspired problems originating from different branches such as population dynamics, molecular dynamics in cells, neuronal and heart diseases, the cardiovascular system, genetics, etc [...] Full article

(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations)

13 pages, 3181 KiB

Open AccessArticle

Iterative Dual CNNs for Image Deblurring

by Jinbin Wang, Ziqi Wang and Aiping Yang

Mathematics 2022, 10(20), 3891; https://doi.org/10.3390/math10203891 - 20 Oct 2022

Cited by 2 | Viewed by 1829

Abstract

Image deblurring attracts research attention in the field of image processing and computer vision. Traditional deblurring methods based on statistical prior largely depend on the selected prior type, which limits their restoring ability. Moreover, the constructed deblurring model is difficult to solve, and [...] Read more.

Image deblurring attracts research attention in the field of image processing and computer vision. Traditional deblurring methods based on statistical prior largely depend on the selected prior type, which limits their restoring ability. Moreover, the constructed deblurring model is difficult to solve, and the operation is comparatively complicated. Meanwhile, deep learning has become a hotspot in various fields in recent years. End-to-end convolutional neural networks (CNNs) can learn the pixel mapping relationships between degraded images and clear images. In addition, they can also obtain the result of effectively eliminating spatial variable blurring. However, conventional CNNs have some disadvantages in generalization ability and details of the restored image. Therefore, this paper presents an iterative dual CNN called IDC for image deblurring, where the task of image deblurring is divided into two sub-networks: deblurring and detail restoration. The deblurring sub-network adopts a U-Net structure to learn the semantical and structural features of the image, and the detail restoration sub-network utilizes a shallow and wide structure without downsampling, where only the image texture features are extracted. Finally, to obtain the deblurred image, this paper presents a multiscale iterative strategy that effectively improves the robustness and precision of the model. The experimental results showed that the proposed method has an excellent effect of deblurring on a real blurred image dataset and is suitable for various real application scenes. Full article

(This article belongs to the Special Issue Advances in Computer Vision and Machine Learning)

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3 pages, 176 KiB

Open AccessEditorial

Business and Economics Mathematics

by Octavian Dospinescu

Mathematics 2022, 10(20), 3890; https://doi.org/10.3390/math10203890 - 20 Oct 2022

Viewed by 970

Abstract

Nowadays, the field of economics is a versatile one and of extraordinary importance for both practitioners and theorists [...] Full article

(This article belongs to the Special Issue Business and Economics Mathematics)

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Mathematics, Volume 10, Issue 20 (October-2 2022) – 201 articles

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