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Mathematics
Volume 11
Issue 23
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Mathematics, Volume 11, Issue 23 (December-1 2023) – 160 articles

Cover Story (view full-size image): The two-dimensional strip-packing problem (2D-SPP) aims to optimize the arrangement of small rectangular items within unique strips with a fixed width and infinite height to minimize the usage of height. Despite extensive academic exploration, applying 2D-SPP solutions in industrial settings remains challenging. Our paper addresses this academia–industry gap by proposing a robust optimization model for an uncertain 2D-SPP with variable-sized bins, ensuring resilience to fluctuating demands. We employ the contiguous one-dimensional relaxation technique in conjunction with column generation to minimize the lower bound of the problem, augmenting the solution accuracy. We leverage the Karush–Kuhn–Tucker condition to transform the model into a more tractable form, leading to an exact solution. View this paper
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26 pages, 5895 KiB  
Article
Modeling the Solution of the Pursuit–Evasion Problem Based on the Intelligent–Geometric Control Theory
by Mikhail Khachumov and Vyacheslav Khachumov
Mathematics 2023, 11(23), 4869; https://doi.org/10.3390/math11234869 - 04 Dec 2023
Viewed by 1003
Abstract
An important action-planning problem is considered for participants of the pursuit–evasion game with multiple pursuers and a high-speed evader. The objects of study are mobile robotic systems and specifically small unmanned aerial vehicles (UAVs). The problem is complicated by the presence of significant [...] Read more.
An important action-planning problem is considered for participants of the pursuit–evasion game with multiple pursuers and a high-speed evader. The objects of study are mobile robotic systems and specifically small unmanned aerial vehicles (UAVs). The problem is complicated by the presence of significant wind loads that affect the trajectory and motion strategies of the players. It is assumed that UAVs have limited computing resources, which involves the use of computationally fast and real-time heuristic approaches. A novel and rapidly developing intelligent–geometric theory is applied to address the discussed problem. To accurately calculate the points of the participant’s rapprochement, we use a geometric approach based on the construction of circles or spheres of Apollonius. Intelligent control methods are applied to synthesize complex motion strategies of participants. A method for quickly predicting the evader’s trajectory is proposed based on a two-layer neural network containing a new activation function of the “s-parabola” type. We consider a special backpropagation training scheme for the model under study. A simulation scheme has been developed and tested, which includes mathematical models of dynamic objects and wind loads. The conducted simulations on pursuit–evasion games in close to real conditions showed the prospects and expediency of the presented approach. Full article
(This article belongs to the Special Issue Mathematical Modeling, Optimization and Machine Learning, 2nd Edition)
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13 pages, 1085 KiB  
Article
3D Multi-Organ and Tumor Segmentation Based on Re-Parameterize Diverse Experts
by Ping Liu, Chunbin Gu, Bian Wu, Xiangyun Liao, Yinling Qian and Guangyong Chen
Mathematics 2023, 11(23), 4868; https://doi.org/10.3390/math11234868 - 04 Dec 2023
Viewed by 916
Abstract
Automated segmentation of abdominal organs and tumors in medical images is a challenging yet essential task in medical image analysis. Deep learning has shown excellent performance in many medical image segmentation tasks, but most prior efforts were fragmented, addressing individual organ and tumor [...] Read more.
Automated segmentation of abdominal organs and tumors in medical images is a challenging yet essential task in medical image analysis. Deep learning has shown excellent performance in many medical image segmentation tasks, but most prior efforts were fragmented, addressing individual organ and tumor segmentation tasks with specialized networks. To tackle the challenges of abdominal organ and tumor segmentation using partially labeled datasets, we introduce Re-parameterizing Mixture-of-Diverse-Experts (RepMode) to abdominal organ and tumor segmentation. Within the RepMode framework, the Mixture-of-Diverse-Experts (MoDE) block forms the foundation, learning generalized parameters applicable across all tasks. We seamlessly integrate the MoDE block into a U-shaped network with dynamic heads, addressing multi-scale challenges by dynamically combining experts with varying receptive fields for each organ and tumor. Our framework incorporates task encoding in both the encoder–decoder section and the segmentation head, enabling the network to adapt throughout the entire system based on task-related information. We evaluate our approach on the multi-organ and tumor segmentation (MOTS) dataset. Experiments show that DoDRepNet outperforms previous methods, including multi-head networks and single-network approaches, giving a highly competitive performance compared with the original single network with dynamic heads. DoDRepNet offers a promising approach to address the complexities of abdominal organ and tumor segmentation using partially labeled datasets, enhancing segmentation accuracy and robustness. Full article
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21 pages, 5232 KiB  
Article
An Enhanced Hybrid-Level Interface-Reduction Method Combined with an Interface Discrimination Algorithm
by Seunghee Cheon and Jaehun Lee
Mathematics 2023, 11(23), 4867; https://doi.org/10.3390/math11234867 - 04 Dec 2023
Viewed by 677
Abstract
This study proposes an interface localizing scheme to enhance the performance of the previous hybrid-level interface-reduction method. The conventional component mode synthesis (CMS) only focuses on interior reduction, while the interface is fully retained for convenient synthesis. Thus, various interface-reduction methods have been [...] Read more.
This study proposes an interface localizing scheme to enhance the performance of the previous hybrid-level interface-reduction method. The conventional component mode synthesis (CMS) only focuses on interior reduction, while the interface is fully retained for convenient synthesis. Thus, various interface-reduction methods have been suggested to obtain a satisfactory size for the reduced systems. Although previous hybrid-level interface-reduction approaches have addressed major issues associated with conventional interface-reduction methods—in terms of accuracy and efficiency through considering partial substructure synthesis—this method can be applied to limited modeling conditions where interfaces and substructures are independently defined. To overcome this limitation, an interface localizing algorithm is developed to ensure an enhanced performance in the conventional hybrid-level interface-reduction method. The interfaces are discriminated through considering the Boolean operation of substructures, and the interface reduction basis is computed at the localized interface level, which is constructed by a partially coupled system. As a result, a large amount of computational resources are saved, achieving the possibility of efficient design modifications at the semi-substructural level. Full article
(This article belongs to the Special Issue Computational Mechanics and Applied Mathematics)
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16 pages, 415 KiB  
Article
Laguerre–Freud Equations for the Gauss Hypergeometric Discrete Orthogonal Polynomials
by Itsaso Fernández-Irisarri and Manuel Mañas
Mathematics 2023, 11(23), 4866; https://doi.org/10.3390/math11234866 - 04 Dec 2023
Cited by 1 | Viewed by 585
Abstract
The Cholesky factorization of the moment matrix is considered for the Gauss hypergeometric discrete orthogonal polynomials. This family of discrete orthogonal polynomials has a weight with first moment given by [...] Read more.
The Cholesky factorization of the moment matrix is considered for the Gauss hypergeometric discrete orthogonal polynomials. This family of discrete orthogonal polynomials has a weight with first moment given by ρ0=2F1a,bc+1;η. For the Gauss hypergeometric discrete orthogonal polynomials, also known as generalized Hahn of type I, Laguerre–Freud equations are found, and the differences with the equations found by Dominici and by Filipuk and Van Assche are provided. Full article
37 pages, 2323 KiB  
Article
Smart Lithium-Ion Battery Monitoring in Electric Vehicles: An AI-Empowered Digital Twin Approach
by Mitra Pooyandeh and Insoo Sohn
Mathematics 2023, 11(23), 4865; https://doi.org/10.3390/math11234865 - 04 Dec 2023
Cited by 2 | Viewed by 1381
Abstract
This paper presents a transformative methodology that harnesses the power of digital twin (DT) technology for the advanced condition monitoring of lithium-ion batteries (LIBs) in electric vehicles (EVs). In contrast to conventional solutions, our approach eliminates the need to calibrate sensors or add [...] Read more.
This paper presents a transformative methodology that harnesses the power of digital twin (DT) technology for the advanced condition monitoring of lithium-ion batteries (LIBs) in electric vehicles (EVs). In contrast to conventional solutions, our approach eliminates the need to calibrate sensors or add additional hardware circuits. The digital replica works seamlessly alongside the embedded battery management system (BMS) in an EV, delivering real-time signals for monitoring. Our system is a significant step forward in ensuring the efficiency and sustainability of EVs, which play an essential role in reducing carbon emissions. A core innovation lies in the integration of the digital twin into the battery monitoring process, reshaping the landscape of energy storage and alternative power sources such as lithium-ion batteries. Our comprehensive system leverages a cloud-based IoT network and combines both physical and digital components to provide a holistic solution. The physical side encompasses offline modeling, where a long short-term memory (LSTM) algorithm trained with various learning rates (LRs) and optimized by three types of optimizers ensures precise state-of-charge (SOC) predictions. On the digital side, the digital twin takes center stage, enabling the real-time monitoring and prediction of battery activity. A particularly innovative aspect of our approach is the utilization of a time-series generative adversarial network (TS-GAN) to generate synthetic data that seamlessly complement the monitoring process. This pioneering use of a TS-GAN offers an effective solution to the challenge of limited real-time data availability, thus enhancing the system’s predictive capabilities. By seamlessly integrating these physical and digital elements, our system enables the precise analysis and prediction of battery behavior. This innovation—particularly the application of a TS-GAN for data generation—significantly contributes to optimizing battery performance, enhancing safety, and extending the longevity of lithium-ion batteries in EVs. Furthermore, the model developed in this research serves as a benchmark for future digital energy storage in lithium-ion batteries and comprehensive energy utilization. According to statistical tests, the model has a high level of precision. Its exceptional safety performance and reduced energy consumption offer promising prospects for sustainable and efficient energy solutions. This paper signifies a pivotal step towards realizing a cleaner and more sustainable future through advanced EV battery management. Full article
(This article belongs to the Special Issue Artificial Intelligence and Algorithms in Intelligent Systems for Augmented Human)
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15 pages, 532 KiB  
Article
Empiric Solutions to Full Fuzzy Linear Programming Problems Using the Generalized “min” Operator
by Bogdana Stanojević and Sorin Nǎdǎban
Mathematics 2023, 11(23), 4864; https://doi.org/10.3390/math11234864 - 04 Dec 2023
Viewed by 761
Abstract
Solving optimization problems in a fuzzy environment is an area widely addressed in the recent literature. De-fuzzification of data, construction of crisp more or less equivalent problems, unification of multiple objectives, and solving a single crisp optimization problem are the general descriptions of [...] Read more.
Solving optimization problems in a fuzzy environment is an area widely addressed in the recent literature. De-fuzzification of data, construction of crisp more or less equivalent problems, unification of multiple objectives, and solving a single crisp optimization problem are the general descriptions of many procedures that approach fuzzy optimization problems. Such procedures are misleading (since relevant information is lost through de-fuzzyfication and aggregation of more objectives into a single one), but they are still dominant in the literature due to their simplicity. In this paper, we address the full fuzzy linear programming problem, and provide solutions in full accordance with the extension principle. The main contribution of this paper is in modeling the conjunction of the fuzzy sets using the “product” operator instead of “min” within the definition of the solution concept. Our theoretical findings show that using a generalized “min” operator within the extension principle assures thinner shapes to the derived fuzzy solutions compared to those available in the literature. Thinner shapes are always desirable, since such solutions provide the decision maker with more significant information. Full article
(This article belongs to the Special Issue Fuzzy Logic and Soft Computing—In Memory of Lotfi A. Zadeh)
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26 pages, 2290 KiB  
Article
Modelling Predator–Prey Interactions: A Trade-Off between Seasonality and Wind Speed
by Dipesh Barman and Ranjit Kumar Upadhyay
Mathematics 2023, 11(23), 4863; https://doi.org/10.3390/math11234863 - 04 Dec 2023
Cited by 1 | Viewed by 714
Abstract
Predator–prey interactions do not solely depend on biotic factors: rather, they depend on many other abiotic factors also. One such abiotic factor is wind speed, which can crucially change the predation efficiency of the predator population. In this article, the impact of wind [...] Read more.
Predator–prey interactions do not solely depend on biotic factors: rather, they depend on many other abiotic factors also. One such abiotic factor is wind speed, which can crucially change the predation efficiency of the predator population. In this article, the impact of wind speed along with seasonality on various parameters has been investigated. Here, we present two continuous-time models with specialist and generalist type predators incorporating the effect of wind and the seasonality on the model parameters. It has been observed that wind speed plays a significant role in controlling the system dynamics for both systems. It makes the systems stable for both of the seasonally unperturbed systems. However, it controls the chaotic dynamics that occur in case of no wind for the seasonally perturbed system with the predator as a specialist. On the other hand, for the seasonally perturbed system with a generalist predator, it controls period-four oscillations (which occur considering no wind speed) to simple limit-cycle oscillations. Furthermore, the wind parameter has a huge impact on the survival of predator species. The survival of predator species may be achieved by ensuring a suitable range of wind speeds in the ecosystem. Therefore, we observe that seasonality introduces chaos, but wind reduces it. These results may be very useful for adopting necessary management for the conservation of endangered species that are massively affected by wind speed in an ecosystem. Full article
(This article belongs to the Special Issue Advances in Bio-Dynamics and Applications)
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21 pages, 15644 KiB  
Article
Driver Distraction Detection Based on Cloud Computing Architecture and Lightweight Neural Network
by Xueda Huang, Shaowen Wang, Guanqiu Qi, Zhiqin Zhu, Yuanyuan Li, Linhong Shuai, Bin Wen, Shiyao Chen and Xin Huang
Mathematics 2023, 11(23), 4862; https://doi.org/10.3390/math11234862 - 04 Dec 2023
Viewed by 717
Abstract
Distracted behavior detection is an important task in computer-assisted driving. Although deep learning has made significant progress in this area, it is still difficult to meet the requirements of the real-time analysis and processing of massive data by relying solely on local computing [...] Read more.
Distracted behavior detection is an important task in computer-assisted driving. Although deep learning has made significant progress in this area, it is still difficult to meet the requirements of the real-time analysis and processing of massive data by relying solely on local computing power. To overcome these problems, this paper proposes a driving distraction detection method based on cloud–fog computing architecture, which introduces scalable modules and a model-driven optimization based on greedy pruning. Specifically, the proposed method makes full use of cloud–fog computing to process complex driving scene data, solves the problem of local computing resource limitations, and achieves the goal of detecting distracted driving behavior in real time. In terms of feature extraction, scalable modules are used to adapt to different levels of feature extraction to effectively capture the diversity of driving behaviors. Additionally, in order to improve the performance of the model, a model-driven optimization method based on greedy pruning is introduced to optimize the model structure to obtain a lighter and more efficient model. Through verification experiments on multiple driving scene datasets such as LDDB and Statefarm, the effectiveness of the proposed driving distraction detection method is proved. Full article
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19 pages, 329 KiB  
Article
An Improved Inverse DEA for Assessing Economic Growth and Environmental Sustainability in OPEC Member Nations
by Kelvin K. Orisaremi, Felix T. S. Chan and Xiaowen Fu
Mathematics 2023, 11(23), 4861; https://doi.org/10.3390/math11234861 - 04 Dec 2023
Cited by 1 | Viewed by 803
Abstract
Economic growth is essential for nations endowed with natural resources as it reflects how well those resources are utilized in an efficient and sustainable way. For instance, OPEC member nations, which hold a large proportion of the world’s oil and gas reserves, may [...] Read more.
Economic growth is essential for nations endowed with natural resources as it reflects how well those resources are utilized in an efficient and sustainable way. For instance, OPEC member nations, which hold a large proportion of the world’s oil and gas reserves, may require a frequent evaluation of economic growth patterns to ensure that the natural resources are best used. For this purpose, this study proposes an inverse data envelopment analysis model for assessing the optimal increase in input resources required for economic growth among OPEC member nations. In this context, economic growth is reflected in the GDP per capita, taking into account possible environmental degradation. Such a model is applied to the selected OPEC member nations, which suggests that in terms of increasing the GDP per capita, only one member was able to achieve the best efficiency (i.e., reaching the efficiency frontier), resulting in a hierarchy or dominance within the sample countries. The analysis results further identify the economic growth potential for each member country. For the case of Indonesia, the analysis suggests that further economic growth may be achieved for Indonesia without additional input resources. This calls for diversification of the nation’s economy or investment in other input resources. In addition, the overall results indicated that each member nation could increase its GDP per capita while experiencing minimal environmental degradation. Our analysis not only benchmarks the growth efficiency of countries, but also identifies opportunities for more efficient and sustainable growth. Full article
(This article belongs to the Special Issue Data Envelopment Analysis for Decision Making)
15 pages, 490 KiB  
Article
Properties and Estimations of a Multivariate Folded Normal Distribution
by Xi Liu, Yiqiao Jin, Yifan Yang and Xiaoqing Pan
Mathematics 2023, 11(23), 4860; https://doi.org/10.3390/math11234860 - 04 Dec 2023
Viewed by 851
Abstract
A multivariate folded normal distribution is a distribution of the absolute value of a Gaussian random vector. In this paper, we provide the marginal and conditional distributions of the multivariate folded normal distribution, and also prove that independence and non-correlation are equivalent for [...] Read more.
A multivariate folded normal distribution is a distribution of the absolute value of a Gaussian random vector. In this paper, we provide the marginal and conditional distributions of the multivariate folded normal distribution, and also prove that independence and non-correlation are equivalent for it. In addition, we provide a numerical approach using the R language to fit a multivariate folded normal distribution. The accuracy of the estimated mean and variance parameters is then examined. Finally, a real data application to body mass index data are presented. Full article
(This article belongs to the Section Probability and Statistics)
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17 pages, 932 KiB  
Article
A Nyström Method for 2D Linear Fredholm Integral Equations on Curvilinear Domains
by Anna Lucia Laguardia and Maria Grazia Russo
Mathematics 2023, 11(23), 4859; https://doi.org/10.3390/math11234859 - 03 Dec 2023
Viewed by 921
Abstract
This paper is devoted to the numerical treatment of two-dimensional Fredholm integral equations, defined on general curvilinear domains of the plane. A Nyström method, based on a suitable Gauss-like cubature formula, recently proposed in the literature is proposed. The convergence, stability and good [...] Read more.
This paper is devoted to the numerical treatment of two-dimensional Fredholm integral equations, defined on general curvilinear domains of the plane. A Nyström method, based on a suitable Gauss-like cubature formula, recently proposed in the literature is proposed. The convergence, stability and good conditioning of the method are proved in suitable subspaces of continuous functions of Sobolev type. The cubature formula, on which the Nyström method is constructed, has an error that behaves like the best polynomial approximation of the integrand function. Consequently, it is also shown how the Nyström method inherits this property and, hence, the proposed numerical strategy is fast when the involved known functions are smooth. Some numerical examples illustrate the efficiency of the method, also in comparison with other methods known in the literature. Full article
(This article belongs to the Special Issue Approximation Theory and Applications)
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18 pages, 427 KiB  
Article
Efficient Automatic Subdifferentiation for Programs with Linear Branches
by Sejun Park
Mathematics 2023, 11(23), 4858; https://doi.org/10.3390/math11234858 - 03 Dec 2023
Viewed by 639
Abstract
Computing an element of the Clarke subdifferential of a function represented by a program is an important problem in modern non-smooth optimization. Existing algorithms either are computationally inefficient in the sense that the computational cost depends on the input dimension or can only [...] Read more.
Computing an element of the Clarke subdifferential of a function represented by a program is an important problem in modern non-smooth optimization. Existing algorithms either are computationally inefficient in the sense that the computational cost depends on the input dimension or can only cover simple programs such as polynomial functions with branches. In this work, we show that a generalization of the latter algorithm can efficiently compute an element of the Clarke subdifferential for programs consisting of analytic functions and linear branches, which can represent various non-smooth functions such as max, absolute values, and piecewise analytic functions with linear boundaries, as well as any program consisting of these functions such as neural networks with non-smooth activation functions. Our algorithm first finds a sequence of branches used for computing the function value at a random perturbation of the input; then, it returns an element of the Clarke subdifferential by running the backward pass of the reverse-mode automatic differentiation following those branches. The computational cost of our algorithm is at most that of the function evaluation multiplied by some constant independent of the input dimension n, if a program consists of piecewise analytic functions defined by linear branches, whose arities and maximum depths of branches are independent of n. Full article
(This article belongs to the Special Issue High-Speed Computing and Parallel Algorithms)
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14 pages, 339 KiB  
Article
A Conjugate Gradient Method: Quantum Spectral Polak–Ribiére–Polyak Approach for Unconstrained Optimization Problems
by Kin Keung Lai, Shashi Kant Mishra, Bhagwat Ram and Ravina Sharma
Mathematics 2023, 11(23), 4857; https://doi.org/10.3390/math11234857 - 03 Dec 2023
Viewed by 774
Abstract
Quantum computing is an emerging field that has had a significant impact on optimization. Among the diverse quantum algorithms, quantum gradient descent has become a prominent technique for solving unconstrained optimization (UO) problems. In this paper, we propose a quantum spectral Polak–Ribiére–Polyak (PRP) [...] Read more.
Quantum computing is an emerging field that has had a significant impact on optimization. Among the diverse quantum algorithms, quantum gradient descent has become a prominent technique for solving unconstrained optimization (UO) problems. In this paper, we propose a quantum spectral Polak–Ribiére–Polyak (PRP) conjugate gradient (CG) approach. The technique is considered as a generalization of the spectral PRP method which employs a q-gradient that approximates the classical gradient with quadratically better dependence on the quantum variable q. Additionally, the proposed method reduces to the classical variant as the quantum variable q approaches closer to 1. The quantum search direction always satisfies the sufficient descent condition and does not depend on any line search (LS). This approach is globally convergent with the standard Wolfe conditions without any convexity assumption. Numerical experiments are conducted and compared with the existing approach to demonstrate the improvement of the proposed strategy. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications, 2nd Edition)
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26 pages, 1500 KiB  
Article
Construction of Software Supply Chain Threat Portrait Based on Chain Perspective
by Maoyang Wang, Peng Wu and Qin Luo
Mathematics 2023, 11(23), 4856; https://doi.org/10.3390/math11234856 - 02 Dec 2023
Viewed by 1106
Abstract
With the rapid growth of the software industry, the software supply chain (SSC) has become the most intricate system in the complete software life cycle, and the security threat situation is becoming increasingly severe. For the description of the SSC, the relevant research [...] Read more.
With the rapid growth of the software industry, the software supply chain (SSC) has become the most intricate system in the complete software life cycle, and the security threat situation is becoming increasingly severe. For the description of the SSC, the relevant research mainly focuses on the perspective of developers, lacking a comprehensive understanding of the SSC. This paper proposes a chain portrait framework of the SSC based on a resource perspective, which comprehensively depicts the threat model and threat surface indicator system of the SSC. The portrait model includes an SSC threat model and an SSC threat indicator matrix. The threat model has 3 levels and 32 dimensions and is based on a generative artificial intelligence model. The threat indicator matrix is constructed using the Attack Net model comprising 14-dimensional attack strategies and 113-dimensional attack techniques. The proposed portrait model’s effectiveness is verified through existing SSC security events, domain experts, and event visualization based on security analysis models. Full article
(This article belongs to the Special Issue Numerical Simulation and Analysis in Applied Mechanics and Engineering)
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28 pages, 1220 KiB  
Article
Handling Non-Linearities in Modelling the Optimal Design and Operation of a Multi-Energy System
by Antoine Mallégol, Arwa Khannoussi, Mehrdad Mohammadi, Bruno Lacarrière and Patrick Meyer
Mathematics 2023, 11(23), 4855; https://doi.org/10.3390/math11234855 - 02 Dec 2023
Viewed by 747
Abstract
Multi-energy systems (MESs) combining different energy carriers like electricity and heat allow for more efficient and sustainable energy solutions. However, optimizing the design and operation of MESs is challenging due to non-linearities in the mathematical models used, especially the performance curves of technologies [...] Read more.
Multi-energy systems (MESs) combining different energy carriers like electricity and heat allow for more efficient and sustainable energy solutions. However, optimizing the design and operation of MESs is challenging due to non-linearities in the mathematical models used, especially the performance curves of technologies like combined heat and power units. Unlike similar work from the literature, this paper proposes an improved piecewise linearization method to efficiently handle the non-linearities, models an MES as a multi-objective mixed-integer linear program (MILP), and solves the optimization problem over a year with hourly resolution to enable detailed operation and faithful system design. The method uses fewer linear pieces to approximate non-linear functions compared to a standard technique, resulting in lower complexity while preserving accuracy. The MES design and operation problem maximizes cost reduction and the rate of renewable energy sources. A case study on an MES with electricity and heat over one year with hourly resolution demonstrates the effectiveness of the new method. It allows for solving a long-term MES optimization problem in reasonable computation times. Full article
(This article belongs to the Special Issue Operations Research and Its Applications)
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24 pages, 510 KiB  
Article
Queueing-Inventory Systems with Catastrophes under Various Replenishment Policies
by Serife Ozkar, Agassi Melikov and Janos Sztrik
Mathematics 2023, 11(23), 4854; https://doi.org/10.3390/math11234854 - 02 Dec 2023
Cited by 1 | Viewed by 907
Abstract
We discuss two queueing-inventory systems with catastrophes in the warehouse. Catastrophes occur according to the Poisson process and instantly destroy all items in the inventory. The arrivals of the consumer customers follow a Markovian arrival process and they can be queued in an [...] Read more.
We discuss two queueing-inventory systems with catastrophes in the warehouse. Catastrophes occur according to the Poisson process and instantly destroy all items in the inventory. The arrivals of the consumer customers follow a Markovian arrival process and they can be queued in an infinite buffer. The service time of a consumer customer follows a phase-type distribution. The system receives negative customers which have Poisson flows and as soon as a negative customer comes into the system, he causes a consumer customer to leave the system, if any. One of two inventory policies is used in the systems: either (s,S) or (s,Q). If the inventory level is zero when a consumer customer arrives, then this customer is either lost (lost sale) or joins the queue (backorder sale). The system is formulated by a four-dimensional continuous-time Markov chain. Ergodicity condition for both systems is established and steady-state distribution is obtained using the matrix-geometric method. By numerical studies, the influence of the distributions of the arrival process and the service time and the system parameters on performance measures are deeply analyzed. Finally, an optimization study is presented in which the criterion is the minimization of expected total costs and the controlled parameter is warehouse capacity. Full article
(This article belongs to the Special Issue Mathematical Modelling for Solving Engineering Problems)
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20 pages, 549 KiB  
Article
Estimation in Semi-Varying Coefficient Heteroscedastic Instrumental Variable Models with Missing Responses
by Weiwei Zhang, Jingxuan Luo and Shengyun Ma
Mathematics 2023, 11(23), 4853; https://doi.org/10.3390/math11234853 - 02 Dec 2023
Viewed by 755
Abstract
This paper studies the estimation problem for semi-varying coefficient heteroscedastic instrumental variable models with missing responses. First, we propose the adjusted estimators for unknown parameters and smooth functional coefficients utilizing the ordinary profile least square method and instrumental variable adjustment technique with complete [...] Read more.
This paper studies the estimation problem for semi-varying coefficient heteroscedastic instrumental variable models with missing responses. First, we propose the adjusted estimators for unknown parameters and smooth functional coefficients utilizing the ordinary profile least square method and instrumental variable adjustment technique with complete data. Second, we present an adjusted estimator of the stochastic error variance by employing the Nadaraya–Watson kernel estimation technique. Third, we apply the inverse probability-weighted method and instrumental variable adjustment technique to construct the adaptive-weighted adjusted estimators for unknown parameters and smooth functional coefficients. The asymptotic properties of our proposed estimators are established under some regularity conditions. Finally, numerous simulation studies and a real data analysis are conducted to examine the finite sample performance of the proposed estimators. Full article
(This article belongs to the Special Issue Computational Statistics and Data Analysis, 2nd Edition)
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32 pages, 730 KiB  
Review
Event-Centric Temporal Knowledge Graph Construction: A Survey
by Timotej Knez and Slavko Žitnik
Mathematics 2023, 11(23), 4852; https://doi.org/10.3390/math11234852 - 02 Dec 2023
Viewed by 2149
Abstract
Textual documents serve as representations of discussions on a variety of subjects. These discussions can vary in length and may encompass a range of events or factual information. Present trends in constructing knowledge bases primarily emphasize fact-based common sense reasoning, often overlooking the [...] Read more.
Textual documents serve as representations of discussions on a variety of subjects. These discussions can vary in length and may encompass a range of events or factual information. Present trends in constructing knowledge bases primarily emphasize fact-based common sense reasoning, often overlooking the temporal dimension of events. Given the widespread presence of time-related information, addressing this temporal aspect could potentially enhance the quality of common-sense reasoning within existing knowledge graphs. In this comprehensive survey, we aim to identify and evaluate the key tasks involved in constructing temporal knowledge graphs centered around events. These tasks can be categorized into three main components: (a) event extraction, (b) the extraction of temporal relationships and attributes, and (c) the creation of event-based knowledge graphs and timelines. Our systematic review focuses on the examination of available datasets and language technologies for addressing these tasks. An in-depth comparison of various approaches reveals that the most promising results are achieved by employing state-of-the-art models leveraging large pre-trained language models. Despite the existence of multiple datasets, a noticeable gap exists in the availability of annotated data that could facilitate the development of comprehensive end-to-end models. Drawing insights from our findings, we engage in a discussion and propose four future directions for research in this domain. These directions encompass (a) the integration of pre-existing knowledge, (b) the development of end-to-end systems for constructing event-centric knowledge graphs, (c) the enhancement of knowledge graphs with event-centric information, and (d) the prediction of absolute temporal attributes. Full article
(This article belongs to the Special Issue Recent Trends and Advances in the Natural Language Processing)
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12 pages, 901 KiB  
Article
On the Dynamics of the Complex Hirota-Dynamical Model
by Arzu Akbulut, Melike Kaplan, Rubayyi T. Alqahtani and W. Eltayeb Ahmed
Mathematics 2023, 11(23), 4851; https://doi.org/10.3390/math11234851 - 02 Dec 2023
Viewed by 683
Abstract
The complex Hirota-dynamical Model (HDM) finds multifarious applications in fields such as plasma physics, fusion energy exploration, astrophysical investigations, and space studies. This study utilizes several soliton-type solutions to HDM via the modified simple equation and generalized and modified Kudryashov approaches. Modulation instability [...] Read more.
The complex Hirota-dynamical Model (HDM) finds multifarious applications in fields such as plasma physics, fusion energy exploration, astrophysical investigations, and space studies. This study utilizes several soliton-type solutions to HDM via the modified simple equation and generalized and modified Kudryashov approaches. Modulation instability (MI) analysis is investigated. We also offer visual representations for the HDM. Full article
(This article belongs to the Special Issue Exact Solutions and Numerical Solutions of Differential Equations)
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9 pages, 263 KiB  
Article
New Criteria of Oscillation for Linear Sturm–Liouville Delay Noncanonical Dynamic Equations
by Taher S. Hassan, Martin Bohner, Iambor Loredana Florentina, Amir Abdel Menaem and Mouataz Billah Mesmouli
Mathematics 2023, 11(23), 4850; https://doi.org/10.3390/math11234850 - 01 Dec 2023
Cited by 2 | Viewed by 696
Abstract
In this work, we deduce a new criterion that guarantees the oscillation of solutions to linear Sturm–Liouville delay noncanonical dynamic equations; these results emulate the criteria of the Hille and Ohriska types for canonical dynamic equations, and these results also solve an open [...] Read more.
In this work, we deduce a new criterion that guarantees the oscillation of solutions to linear Sturm–Liouville delay noncanonical dynamic equations; these results emulate the criteria of the Hille and Ohriska types for canonical dynamic equations, and these results also solve an open problem in many works in the literature. Several examples are offered, demonstrating that the findings achieved are precise, practical, and adaptable. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena)
19 pages, 618 KiB  
Article
Rewarded Meta-Pruning: Meta Learning with Rewards for Channel Pruning
by Athul Shibu, Abhishek Kumar, Heechul Jung and Dong-Gyu Lee
Mathematics 2023, 11(23), 4849; https://doi.org/10.3390/math11234849 - 01 Dec 2023
Viewed by 659
Abstract
Convolutional neural networks (CNNs) have gained recognition for their remarkable performance across various tasks. However, the sheer number of parameters and the computational demands pose challenges, particularly on edge devices with limited processing power. In response to these challenges, this paper presents a [...] Read more.
Convolutional neural networks (CNNs) have gained recognition for their remarkable performance across various tasks. However, the sheer number of parameters and the computational demands pose challenges, particularly on edge devices with limited processing power. In response to these challenges, this paper presents a novel approach aimed at enhancing the efficiency of deep learning models. Our method introduces the concept of accuracy and efficiency coefficients, offering a fine-grained control mechanism to balance the trade-off between network accuracy and computational efficiency. At our core is the Rewarded Meta-Pruning algorithm, guiding neural network training to generate pruned model weight configurations. The selection of this pruned model is based on approximations of the final model’s parameters, and it is precisely controlled through a reward function. This reward function empowers us to tailor the optimization process, leading to more effective fine-tuning and improved model performance. Extensive experiments and evaluations underscore the superiority of our proposed method when compared to state-of-the-art techniques. We conducted rigorous pruning experiments on well-established architectures such as ResNet-50, MobileNetV1, and MobileNetV2. The results not only validate the efficacy of our approach but also highlight its potential to significantly advance the field of model compression and deployment on resource-constrained edge devices. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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22 pages, 345 KiB  
Article
On the Study of Starlike Functions Associated with the Generalized Sine Hyperbolic Function
by Baseer Gul, Muhammad Arif, Reem K. Alhefthi, Daniel Breaz, Luminiţa-Ioana Cotîrlă and Eleonora Rapeanu
Mathematics 2023, 11(23), 4848; https://doi.org/10.3390/math11234848 - 01 Dec 2023
Viewed by 720
Abstract
Geometric function theory, a subfield of complex analysis that examines the geometrical characteristics of analytic functions, has seen a sharp increase in research in recent years. In particular, by employing subordination notions, the contributions of different subclasses of analytic functions associated with innovative [...] Read more.
Geometric function theory, a subfield of complex analysis that examines the geometrical characteristics of analytic functions, has seen a sharp increase in research in recent years. In particular, by employing subordination notions, the contributions of different subclasses of analytic functions associated with innovative image domains are of significant interest and are extensively investigated. Since ℜ(1+sinh(z))≯0, it implies that the class Ssinh* introduced in reference third by Kumar et al. is not a subclass of starlike functions. Now, we have introduced a parameter λ with the restriction 0≤λ≤ln(1+2), and by doing that, ℜ(1+sinh(λz))>0. The present research intends to provide a novel subclass of starlike functions in the open unit disk U, denoted as Ssinhλ*, and investigate its geometric nature. For this newly defined subclass, we obtain sharp upper bounds of the coefficients an for n=2,3,4,5. Then, we prove a lemma, in which the largest disk contained in the image domain of q0(z)=1+sinh(λz) and the smallest disk containing q0(U) are investigated. This lemma has a central role in proving our radius problems. We discuss radius problems of various known classes, including S*(β) and K(β) of starlike functions of order β and convex functions of order β. Investigating Ssinhλ* radii for several geometrically known classes and some classes of functions defined as ratios of functions are also part of the present research. The methodology used for finding Ssinhλ* radii of different subclasses is the calculation of that value of the radius r<1 for which the image domain of any function belonging to a specified class is contained in the largest disk of this lemma. A new representation of functions in this class, but for a more restricted range of λ, is also obtained. Full article
(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory, 2nd Edition)
17 pages, 3642 KiB  
Article
A Secure Multi-Party Computation Protocol for Graph Editing Distance against Malicious Attacks
by Xin Liu, Jianwei Kong, Lu Peng, Dan Luo, Gang Xu, Xiubo Chen and Xiaomeng Liu
Mathematics 2023, 11(23), 4847; https://doi.org/10.3390/math11234847 - 01 Dec 2023
Viewed by 777
Abstract
The secure computation of the graph structure is an important element in the field of secure calculation of graphs, which is important in querying data in graphs, since there are no algorithms for the graph edit distance problem that can resist attacks by [...] Read more.
The secure computation of the graph structure is an important element in the field of secure calculation of graphs, which is important in querying data in graphs, since there are no algorithms for the graph edit distance problem that can resist attacks by malicious adversaries. In this paper, for the problem of secure computation of similarity edit distance of graphs, firstly, the encoding method applicable to the Paillier encryption algorithm is proposed, and the XOR operation scheme is proposed according to the Paillier homomorphic encryption algorithm. Then, the security algorithm under the semi-honest model is designed, which adopts the new encoding method and the XOR operation scheme. Finally, for the malicious behaviors that may be implemented by malicious participants in the semi-honest algorithm, using the hash function, a algorithm for secure computation of graph editing distance under the malicious model is designed, and the security of the algorithm is proved, and the computational complexity and the communication complexity of the algorithm are analyzed, which is more efficient compared with the existing schemes, and has practical value. The algorithm designed in this paper fills the research gap in the existing literature on the problem of graph edit distance and contributes to solving the problem. Full article
(This article belongs to the Special Issue Advanced Analyses and Algorithms for Trustworthy AI Systems and Applications)
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23 pages, 1560 KiB  
Article
Vehicle Routing Problem with Time Windows to Minimize Total Completion Time in Home Healthcare Systems
by Payakorn Saksuriya and Chulin Likasiri
Mathematics 2023, 11(23), 4846; https://doi.org/10.3390/math11234846 - 01 Dec 2023
Cited by 1 | Viewed by 1086
Abstract
We propose a vehicle routing problem with time windows (VRPTW) with compatibility-matching constraints and total completion time as the objective function, with applications in home healthcare routing and scheduling. Mixed integer linear programming is provided with total completion time minimization as the objective [...] Read more.
We propose a vehicle routing problem with time windows (VRPTW) with compatibility-matching constraints and total completion time as the objective function, with applications in home healthcare routing and scheduling. Mixed integer linear programming is provided with total completion time minimization as the objective function. The solution approach has two objectives, total completion time (primary objective) and total distance (secondary objective). A heuristic is proposed comprising three phases: initializing to find an initial feasible routing (inserting the procedure with a modified K-means algorithm), swapping and moving the procedure to find a local optimal routing, and shooting the procedure to move away from the local optimum. Proof of feasibility for the inserting procedure is provided to prevent unnecessary insertions. Phases 2 and 3 will be repeated as needed to ensure solution quality. Solving our model with the proposed heuristic algorithm increases the total distance by 90.00% but reduces the total completion time by 25.86%. To test our model and heuristic, we examined a system with 400 home-healthcare cases in Chiang Mai. The heuristic quickly solved the problem. When total completion time is minimized, some caretakers serve up to twice as many patients as their coworkers; when total distance is minimized, workload discrepancies can increase up to seven-fold. Full article
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13 pages, 296 KiB  
Article
Anticipated BSDEs Driven by Fractional Brownian Motion with a Time-Delayed Generator
by Pei Zhang, Adriana Irawati Nur Ibrahim and Nur Anisah Mohamed
Mathematics 2023, 11(23), 4845; https://doi.org/10.3390/math11234845 - 01 Dec 2023
Viewed by 611
Abstract
This article describes a new form of an anticipated backward stochastic differential equation (BSDE) with a time-delayed generator driven by fractional Brownian motion, further known as fractional BSDE, with a Hurst parameter H∈(1/2,1). This [...] Read more.
This article describes a new form of an anticipated backward stochastic differential equation (BSDE) with a time-delayed generator driven by fractional Brownian motion, further known as fractional BSDE, with a Hurst parameter H∈(1/2,1). This study expands upon the findings of the anticipated BSDE by considering the scenario when the driver is fractional Brownian motion rather instead of standard Brownian motion. Additionally, the generator incorporates not only the present and future but also the past. We will demonstrate the existence and uniqueness of the solutions to these equations by employing the fixed point theorem. Furthermore, an equivalent comparison theorem is derived. Full article
(This article belongs to the Special Issue Differential Equations and Stochastic Processes: Trends and Challenges)
16 pages, 1935 KiB  
Article
An Optimized and Scalable Blockchain-Based Distributed Learning Platform for Consumer IoT
by Zhaocheng Wang, Xueying Liu, Xinming Shao, Abdullah Alghamdi, Mesfer Alrizq, Md. Shirajum Munir and Sujit Biswas
Mathematics 2023, 11(23), 4844; https://doi.org/10.3390/math11234844 - 01 Dec 2023
Cited by 1 | Viewed by 870
Abstract
Consumer Internet of Things (CIoT) manufacturers seek customer feedback to enhance their products and services, creating a smart ecosystem, like a smart home. Due to security and privacy concerns, blockchain-based federated learning (BCFL) ecosystems can let CIoT manufacturers update their machine learning (ML) [...] Read more.
Consumer Internet of Things (CIoT) manufacturers seek customer feedback to enhance their products and services, creating a smart ecosystem, like a smart home. Due to security and privacy concerns, blockchain-based federated learning (BCFL) ecosystems can let CIoT manufacturers update their machine learning (ML) models using end-user data. Federated learning (FL) uses privacy-preserving ML techniques to forecast customers’ needs and consumption habits, and blockchain replaces the centralized aggregator to safeguard the ecosystem. However, blockchain technology (BCT) struggles with scalability and quick ledger expansion. In BCFL, local model generation and secure aggregation are other issues. This research introduces a novel architecture, emphasizing gateway peer (GWP) in the blockchain network to address scalability, ledger optimization, and secure model transmission issues. In the architecture, we replace the centralized aggregator with the blockchain network, while GWP limits the number of local transactions to execute in BCN. Considering the security and privacy of FL processes, we incorporated differential privacy and advanced normalization techniques into ML processes. These approaches enhance the cybersecurity of end-users and promote the adoption of technological innovation standards by service providers. The proposed approach has undergone extensive testing using the well-respected Stanford (CARS) dataset. We experimentally demonstrate that the proposed architecture enhances network scalability and significantly optimizes the ledger. In addition, the normalization technique outperforms batch normalization when features are under DP protection. Full article
(This article belongs to the Special Issue Advances in Communication Systems, IoT and Blockchain)
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18 pages, 4992 KiB  
Article
Detecting Structural Changes in Time Series by Using the BDS Test Recursively: An Application to COVID-19 Effects on International Stock Markets
by Lorenzo Escot, Julio E. Sandubete and Łukasz Pietrych
Mathematics 2023, 11(23), 4843; https://doi.org/10.3390/math11234843 - 01 Dec 2023
Viewed by 1727
Abstract
Structural change tests aim to identify evidence of a structural break or change in the underlying generating process of a time series. The BDS test has its origins in chaos theory and seeks to test, using the correlation integral, the hypothesis that a [...] Read more.
Structural change tests aim to identify evidence of a structural break or change in the underlying generating process of a time series. The BDS test has its origins in chaos theory and seeks to test, using the correlation integral, the hypothesis that a time series is generated by an identically and independently distributed (IID) stochastic process over time. The BDS test is already widely used as a powerful tool for testing the hypothesis of white noise in the residuals of time series models. In this paper, we illustrate how the BDS test can be implemented also in a recursive manner to evaluate the hypothesis of structural change in a time series, taking advantage of its ability to test the IID hypothesis. We apply the BDS test repeatedly, starting with a sub-sample of the original time series and incrementally increasing the number of observations until it is applied to the full sample time series. A structural change in the unknown underlying generator model is detected when a change in the trend shown by this recursively computed BDS statistic is detected. The strength of this recursive BDS test lies in the fact that it does not require making any assumptions about the underlying time series generator model. We ilustrate the power and potential of this recursive BDS test through an application to real economic data. In this sense, we apply the test to assess the structural changes caused by the COVID-19 pandemic in international financial markets. Using daily data from the world’s top stock indices, we have detected strong and statistically significant evidence of two major structural changes during the period from June 2018 to June 2022. The first occurred in March 2020, coinciding with the onset of economic restrictions in the main Western countries as a result of the pandemic. The second occurred towards the end of August 2020, with the end of the main economic restrictions and the beginning of a new post-pandemic economic scenario. This methodology to test for structural changes in a time series is easy to implement and can detect changes in any system or process behind the time series even when this generating system is not known, and without the need to specify or estimate any a priori generating model. In this sense, the recursive BDS test could be incorporated as an initial preliminary step to any exercise of time series modeling. If a structural change is detected in a time series, rather than estimating a single predictive model for the full-sample time series, efforts should be made to estimate different predictive models, one for the time before and one for the time after the detected structural change. Full article
(This article belongs to the Special Issue Chaos Theory and Its Applications to Economic Dynamics)
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21 pages, 4191 KiB  
Article
New Third-Order Finite Volume Unequal-Sized WENO Lagrangian Schemes for Solving Euler Equations
by Yan Tan, Hui Lv and Jun Zhu
Mathematics 2023, 11(23), 4842; https://doi.org/10.3390/math11234842 - 01 Dec 2023
Viewed by 640
Abstract
In this paper, new third-order finite volume unequal-sized weighted essentially non-oscillatory (US-WENO) Lagrangian schemes are designed to solve Euler equations in two and three dimensions. The spatial reconstruction procedures are implemented by using a convex combination of a quadratic polynomial with several linear [...] Read more.
In this paper, new third-order finite volume unequal-sized weighted essentially non-oscillatory (US-WENO) Lagrangian schemes are designed to solve Euler equations in two and three dimensions. The spatial reconstruction procedures are implemented by using a convex combination of a quadratic polynomial with several linear polynomials specified on unequal-sized stencils, so the new US-WENO Lagrangian schemes can achieve the designed third-order accuracy and maintain an essentially non-oscillatory property near strong discontinuities in multi-dimensions. Unlike the traditional WENO reconstruction procedures specified on unstructured meshes, the linear weights of these new two-dimensional and three-dimensional US-WENO spatial reconstructions can be selected as any positive numbers as long as their summation equals one and they are not related to the local mesh topology or the location of quadrature points. Moreover, the linear weights do not have to be recalculated even if the grid moves with the fluid, avoiding the appearance of negative linear weights, thus improving computation efficiency and robustness in multi-dimensional Lagrangian numerical simulations. Finally, extensive benchmark numerical cases are employed to display the excellent capability of the presented US-WENO Lagrangian schemes. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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15 pages, 1153 KiB  
Article
Adaptive Event-Triggered Neural Network Fast Finite-Time Control for Uncertain Robotic Systems
by Jianhui Wang, Yongping Du, Yuanqing Zhang, Yixiang Gu and Kairui Chen
Mathematics 2023, 11(23), 4841; https://doi.org/10.3390/math11234841 - 01 Dec 2023
Viewed by 643
Abstract
A fast convergence adaptive neural network event-triggered control strategy is proposed for the trajectory tracking issue of uncertain robotic systems with output constraints. To cope with the constraints on the system output in the actual industrial field while reducing the burden on communication [...] Read more.
A fast convergence adaptive neural network event-triggered control strategy is proposed for the trajectory tracking issue of uncertain robotic systems with output constraints. To cope with the constraints on the system output in the actual industrial field while reducing the burden on communication resources, an adaptive event-triggered mechanism is designed by using logarithm-type barrier Lyapunov functions and an event-triggered mechanism. Meanwhile, the combination of neural networks and fast finite-time stability theory can not only approximate the unknown nonlinear function of the system, but also construct the control law and adaptive law with a fractional exponential power to accelerate the system’s convergence speed. Furthermore, the tracking errors converge quickly to a bounded and adjustable compact set in finite time. Finally, the effectiveness of the strategy is verified by simulation examples. Full article
(This article belongs to the Section Dynamical Systems)
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14 pages, 646 KiB  
Article
Unitary Diagonalization of the Generalized Complementary Covariance Quaternion Matrices with Application in Signal Processing
by Zhuo-Heng He, Xiao-Na Zhang and Xiaojing Chen
Mathematics 2023, 11(23), 4840; https://doi.org/10.3390/math11234840 - 01 Dec 2023
Viewed by 634
Abstract
Let H denote the quaternion algebra. This paper investigates the generalized complementary covariance, which is the ϕ-Hermitian quaternion matrix. We give the properties of the generalized complementary covariance matrices. In addition, we explore the unitary diagonalization of the covariance and generalized complementary [...] Read more.
Let H denote the quaternion algebra. This paper investigates the generalized complementary covariance, which is the ϕ-Hermitian quaternion matrix. We give the properties of the generalized complementary covariance matrices. In addition, we explore the unitary diagonalization of the covariance and generalized complementary covariance. Moreover, we give the generalized quaternion unitary transform algorithm and test the performance by numerical simulation. Full article
(This article belongs to the Special Issue Infinite Matrices and Their Applications)
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