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Mathematics
Volume 11
Issue 21
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Mathematics, Volume 11, Issue 21 (November-1 2023) – 159 articles

Cover Story (view full-size image): We consider the evolution of a finite population constituted by susceptible and infectious individuals and compare several time-inhomogeneous deterministic models with their stochastic counterpart based on finite birth processes. For these processes, we determine the explicit expressions of the transition probabilities and of the first-passage time densities. For time-homogeneous finite birth processes, the behavior of the mean and the variance of the first-passage time density is also analyzed. Moreover, the approximate duration until the entire population is infected is obtained for a large population size. View this paper
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33 pages, 6066 KiB  
Article
A Novel Two-Stage, Dual-Layer Distributed Optimization Operational Approach for Microgrids with Electric Vehicles
by Bowen Zhou, Zhibo Zhang, Chao Xi and Boyu Liu
Mathematics 2023, 11(21), 4563; https://doi.org/10.3390/math11214563 - 06 Nov 2023
Viewed by 1071
Abstract
As the ownership of electric vehicles (EVs) continues to rise, EVs are becoming an integral part of urban microgrids. Incorporating the charging and discharging processes of EVs into the microgrid’s optimization scheduling process can serve to load leveling, reducing the reliance of the [...] Read more.
As the ownership of electric vehicles (EVs) continues to rise, EVs are becoming an integral part of urban microgrids. Incorporating the charging and discharging processes of EVs into the microgrid’s optimization scheduling process can serve to load leveling, reducing the reliance of the microgrid on external power networks. This paper proposes a novel two-stage, dual-layer distributed optimization operational approach for microgrids with EVs. The lower layer is a distributed control layer, which ensures, through consensus control methods, that every EV maintains a consistent charging/discharging and state of charge (SOC). The upper layer is the optimization scheduling layer, determining the optimal operational strategy of the microgrid using the multiagent reinforcement learning method and providing control reference signals for the lower layer. Additionally, this paper categorizes the charging process of EVs into two stages based on their SOC: the constrained scheduling stage and the free scheduling stage. By employing distinct control methods during these two stages, we ensure that EVs can participate in the microgrid scheduling while fully respecting the charging interests of the EV owners. Full article
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17 pages, 1391 KiB  
Article
The Field Technician Scheduling Problem with Experience-Dependent Service Times
by Vincent F. Yu, Yueh-Sheng Lin, Panca Jodiawan, Shih-Wei Lin and Yu-Chi Lai
Mathematics 2023, 11(21), 4562; https://doi.org/10.3390/math11214562 - 06 Nov 2023
Viewed by 686
Abstract
This research studies the Field Technician Scheduling Problem with Experience-Dependent Service Times (FTSP–EDST), involving three main features: matching maintenance tasks with available technicians, sequencing the tasks, and considering the experience-dependent service times. Given a limited number of technicians, the objective is to maximize [...] Read more.
This research studies the Field Technician Scheduling Problem with Experience-Dependent Service Times (FTSP–EDST), involving three main features: matching maintenance tasks with available technicians, sequencing the tasks, and considering the experience-dependent service times. Given a limited number of technicians, the objective is to maximize the collected profit for servicing tasks. This study formulates the problem as a mixed-integer linear programming model and proposes a Modified Iterated Local Search (MILS) to solve the benchmark problem instances of various sizes. A set of FTSP–EDST instances is generated based on existing publicly accessible data, and MILS is utilized to solve these newly generated instances. Computational results confirm the effectiveness of MILS in solving FTSP–EDST. Full article
(This article belongs to the Section Engineering Mathematics)
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22 pages, 848 KiB  
Article
An Integrated Model of Deep Learning and Heuristic Algorithm for Load Forecasting in Smart Grid
by Hisham Alghamdi, Ghulam Hafeez, Sajjad Ali, Safeer Ullah, Muhammad Iftikhar Khan, Sadia Murawwat and Lyu-Guang Hua
Mathematics 2023, 11(21), 4561; https://doi.org/10.3390/math11214561 - 06 Nov 2023
Cited by 2 | Viewed by 1052
Abstract
Accurate load forecasting plays a crucial role in the effective energy management of smart cities. However, the smart cities’ residents’ load profile is nonlinear, having high volatility, uncertainty, and randomness. Forecasting such nonlinear profiles requires accurate and stable prediction models. On this note, [...] Read more.
Accurate load forecasting plays a crucial role in the effective energy management of smart cities. However, the smart cities’ residents’ load profile is nonlinear, having high volatility, uncertainty, and randomness. Forecasting such nonlinear profiles requires accurate and stable prediction models. On this note, a prediction model has been developed by combining feature preprocessing, a multilayer perceptron, and a genetic wind-driven optimization algorithm, namely FPP-MLP-GWDO. The developed hybrid model has three parts: (i) feature preprocessing (FPP), (ii) a multilayer perceptron (MLP), and (iii) a genetic wind-driven optimization (GWDO) algorithm. The MLP is the key part of the developed model, which uses a multivariate autoregressive algorithm and rectified linear unit (ReLU) for network training. The developed hybrid model known as FPP-MLP-GWDO is evaluated using Dayton Ohio grid load data regarding aspects of accuracy (the mean absolute percentage error (MAPE), Theil’s inequality coefficient (TIC), and the correlation coefficient (CC)) and convergence speed (computational time (CT) and convergence rate (CR)). The findings endorsed the validity and applicability of the developed model compared to other literature models such as the feature selection–support vector machine–modified enhanced differential evolution (FS-SVM-mEDE) model, the feature selection–artificial neural network (FS-ANN) model, the support vector machine–differential evolution algorithm (SVM-DEA) model, and the autoregressive (AR) model regarding aspects of accuracy and convergence speed. The findings confirm that the developed FPP-MLP-GWDO model achieved an accuracy of 98.9%, thus surpassing benchmark models such as the FS-ANN (96.5%), FS-SVM-mEDE (97.9%), SVM-DEA (97.5%), and AR (95.7%). Furthermore, the FPP-MLP-GWDO significantly reduced the CT (299s) compared to the FS-SVM-mEDE (350s), SVM-DEA (240s), FS-ANN (159s), and AR (132s) models. Full article
(This article belongs to the Special Issue Heuristic Optimization and Machine Learning)
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19 pages, 493 KiB  
Article
Reliability Analysis and Optimal Replacement Policy for Systems with Generalized Pólya Censored δ Shock Model
by Lina Bian, Bo Peng and Yong Ye
Mathematics 2023, 11(21), 4560; https://doi.org/10.3390/math11214560 - 06 Nov 2023
Viewed by 772
Abstract
A fresh censored δ shock model is investigated. The arrival of random shocks follows a generalized Pólya process, and the failure mechanism of the system occurs based on the censored δ shock model. The generalized Pólya process is used for modeling because the [...] Read more.
A fresh censored δ shock model is investigated. The arrival of random shocks follows a generalized Pólya process, and the failure mechanism of the system occurs based on the censored δ shock model. The generalized Pólya process is used for modeling because the generalized Pólya process has excellent properties, including the homogeneous Poisson process, the non-homogeneous Poisson process, and the Pólya process. Thus far, the lifetime properties of the censored δ shock model under the generalized Pólya process have not been studied. Therefore, for the established generalized Pólya censored δ shock model, the corresponding reliability function, the upper bound of the reliability function, the mean lifetime, the failure rate, and the class of life distribution are obtained. In addition, a replacement strategy N, based on the number of failures of the system, is considered using a geometric process. We determined the optimal replacement policy N* by objective function minimization. Finally, a numerical example is presented to verify the rationality of the model. Full article
(This article belongs to the Special Issue Applied Probability and Statistical Inference in Reliability Engineering)
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14 pages, 927 KiB  
Article
A Multi-Objective Optimization-Algorithm-Based ANFIS Approach for Modeling Dynamic Customer Preferences with Explicit Nonlinearity
by Huimin Jiang and Farzad Sabetzadeh
Mathematics 2023, 11(21), 4559; https://doi.org/10.3390/math11214559 - 06 Nov 2023
Viewed by 700
Abstract
In previous studies, customer preferences were assumed to be static when modeling their preferences based on online reviews. However, in fact, customer preferences for products are dynamic and changing over time. Few research has been conducted to model dynamic customer preferences as the [...] Read more.
In previous studies, customer preferences were assumed to be static when modeling their preferences based on online reviews. However, in fact, customer preferences for products are dynamic and changing over time. Few research has been conducted to model dynamic customer preferences as the time series data of customer preference are difficult to be obtained. Based on online reviews, an adaptive neuro fuzzy inference system (ANFIS) was introduced to model customer preferences, which can take into account the fuzzy nature of customers’ emotions and the nonlinearity of the model. However, ANFIS is plagued with black box problems, and the nonlinearity of the model cannot be directly demonstrated. To address the above research issues, a multi-objective chaos optimization algorithm (MOCOA)-based ANFIS approach is proposed to generate customer preferences models by using online reviews, which has explicit nonlinear inputs. Firstly, a sentiment analysis approach is used to derive information from online reviews by periods, which is used as the time series data sets of the proposed model. A MOCOA is combined into ANFIS to identify the nonlinear inputs, which include single items, interactive items, and terms of second order and/or higher-order terms. Consequently, the fuzzy rules in ANFIS are expressed in polynomial form, which allows for the explicit representation of the nonlinearity between customer preferences and product attributes. A case study of sweeping robots is used to compare the validation results of the proposed approach with those of ANFIS, subtractive cluster-based ANFIS, fuzzy c-means-based ANFIS, and K-means-based ANFIS. Moreover, the proposed approach provides better performance than the other four approaches in terms of mean relative error and variance of error. Full article
(This article belongs to the Special Issue Advanced Research in Fuzzy Systems and Artificial Intelligence)
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16 pages, 2485 KiB  
Article
Higher Order Sliding Mode Control of MIMO Induction Motors: A New Adaptive Approach
by Ali Karami-Mollaee and Oscar Barambones
Mathematics 2023, 11(21), 4558; https://doi.org/10.3390/math11214558 - 06 Nov 2023
Viewed by 777
Abstract
In this paper the objective is to force the outputs of nonlinear nonaffine multi-input multi-output (MIMO) systems to track those of a linear system with the desired properties. The approach is based on designing higher order sliding mode controller (HOSMC) with the definition [...] Read more.
In this paper the objective is to force the outputs of nonlinear nonaffine multi-input multi-output (MIMO) systems to track those of a linear system with the desired properties. The approach is based on designing higher order sliding mode controller (HOSMC) with the definition of a new proportional-integral (PI) sliding surface. To this end, a linear state feedback with an adaptive switching gain (ASG) is applied to the nonlinear MIMO systems. Therefore, the switching gain can increase or decrease based on the system conditions. Then, the chattering is completely removed using a combination of HOSMC and ASG. Moreover, the proposed procedure is independent from the upper bound of the matched uncertainty, which is in the direction of system inputs. The finite time convergence to the sliding surface is also proved, which provides an invariance property in finite time. Note that invariance is the most important property of SMC. Finally, the general model of MIMO induction motors (IM) is used to address and to verify the proposed controller. Full article
(This article belongs to the Special Issue Control Theory and Applications)
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28 pages, 2949 KiB  
Article
Study on Economic Data Forecasting Based on Hybrid Intelligent Model of Artificial Neural Network Optimized by Harris Hawks Optimization
by Renbo Liu, Yuhui Ge and Peng Zuo
Mathematics 2023, 11(21), 4557; https://doi.org/10.3390/math11214557 - 06 Nov 2023
Viewed by 886
Abstract
To use different models for forecasting economic data suitably, three main basic models (the grey system model, time series analysis model, and artificial neural network (ANN) model) are analyzed and compared comprehensively. Based on the analysis results of forecasting models, one new hybrid [...] Read more.
To use different models for forecasting economic data suitably, three main basic models (the grey system model, time series analysis model, and artificial neural network (ANN) model) are analyzed and compared comprehensively. Based on the analysis results of forecasting models, one new hybrid intelligent model based on the ANN model and Harris hawks optimization (HHO) has been proposed. In this hybrid model, HHO is used to select the hyperparameters of the ANN and also to optimize the linking weights and thresholds of the ANN. At last, by using four economic data cases including two simple data sets and two complex ones, the analysis of the basic models and the proposed hybrid model have been verified comprehensively. The results show that the grey system model can suitably analyze exponential data sequences, the time series analysis model can analyze random sequences, and the ANN model can be applied to any kind of data sequence. Moreover, when compared with the basic models, the new hybrid model can be suitably applied for both simple data sets and complex ones, and its forecasting performance is always very suitable. In comparison with other hybrid models, not only for computing accuracy but also for computing efficiency, the performance of the new hybrid model is the best. For the least initial parameters used in the new hybrid model, which can be determined easily and simply, the application of the new hybrid model is the most convenient too. Full article
(This article belongs to the Special Issue Research and Application of Data Optimization Model in Finance)
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17 pages, 7251 KiB  
Article
Depth Map Super-Resolution Based on Semi-Couple Deformable Convolution Networks
by Botao Liu, Kai Chen, Sheng-Lung Peng and Ming Zhao
Mathematics 2023, 11(21), 4556; https://doi.org/10.3390/math11214556 - 05 Nov 2023
Cited by 1 | Viewed by 980
Abstract
Depth images obtained from lightweight, real-time depth estimation models and consumer-oriented sensors typically have low-resolution issues. Traditional interpolation methods for depth image up-sampling result in a significant information loss, especially in edges with discontinuous depth variations (depth discontinuities). To address this issue, this [...] Read more.
Depth images obtained from lightweight, real-time depth estimation models and consumer-oriented sensors typically have low-resolution issues. Traditional interpolation methods for depth image up-sampling result in a significant information loss, especially in edges with discontinuous depth variations (depth discontinuities). To address this issue, this paper proposes a semi-coupled deformable convolution network (SCD-Net) based on the idea of guided depth map super-resolution (GDSR). The method employs a semi-coupled feature extraction scheme to learn unique and similar features between RGB images and depth images. We utilize a Coordinate Attention (CA) to suppress redundant information in RGB features. Finally, a deformable convolutional module is employed to restore the original resolution of the depth image. The model is tested on NYUv2, Middlebury, Lu, and a Real-Sense real-world dataset created using an Intel Real-sense D455 structured-light camera. The super-resolution accuracy of SCD-Net at multiple scales is much higher than that of traditional methods and superior to recent state-of-the-art (SOTA) models, which demonstrates the effectiveness and flexibility of our model on GDSR tasks. In particular, our method further solves the problem of an RGB texture being over-transferred in GDSR tasks. Full article
(This article belongs to the Special Issue Advances in Data Mining, Machine Learning and Causal Inference and Their Applications)
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14 pages, 350 KiB  
Article
Bifurcating Limit Cycles with a Perturbation of Systems Composed of Piecewise Smooth Differential Equations Consisting of Four Regions
by Erli Zhang, Jihua Yang and Stanford Shateyi
Mathematics 2023, 11(21), 4555; https://doi.org/10.3390/math11214555 - 05 Nov 2023
Viewed by 747
Abstract
Systems composed of piecewise smooth differential (PSD) mappings have quantitatively been searched for answers to a substantial issue of limit cycle (LC) bifurcations. In this paper, LC numbers (LCNs) of a PSD system (PSDS) consisting of four regions are dealt with. A Melnikov [...] Read more.
Systems composed of piecewise smooth differential (PSD) mappings have quantitatively been searched for answers to a substantial issue of limit cycle (LC) bifurcations. In this paper, LC numbers (LCNs) of a PSD system (PSDS) consisting of four regions are dealt with. A Melnikov mapping whose order is one is implicitly obtained by finding its originators when the system is perturbed under any nth degree of real polynomials. Then, the approach employing the Picard–Fuchs mapping is utilized to attain a higher boundary of bifurcation LCNs of systems composed of PSD functions with a global center. The method we used could be implemented to examine the problems related to the LC of other PSDS. Full article
(This article belongs to the Topic Fractal and Design of Multipoint Iterative Methods for Nonlinear Problems)
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15 pages, 321 KiB  
Article
On the Convergence of the Randomized Block Kaczmarz Algorithm for Solving a Matrix Equation
by Lili Xing, Wendi Bao and Weiguo Li
Mathematics 2023, 11(21), 4554; https://doi.org/10.3390/math11214554 - 05 Nov 2023
Viewed by 791
Abstract
A randomized block Kaczmarz method and a randomized extended block Kaczmarz method are proposed for solving the matrix equation AXB=C, where the matrices A and B may be full-rank or rank-deficient. These methods are iterative methods without matrix [...] Read more.
A randomized block Kaczmarz method and a randomized extended block Kaczmarz method are proposed for solving the matrix equation AXB=C, where the matrices A and B may be full-rank or rank-deficient. These methods are iterative methods without matrix multiplication, and are especially suitable for solving large-scale matrix equations. It is theoretically proved that these methods converge to the solution or least-square solution of the matrix equation. The numerical results show that these methods are more efficient than the existing algorithms for high-dimensional matrix equations. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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24 pages, 15757 KiB  
Article
Finite Control Set Model Predictive Control (FCS-MPC) for Enhancing the Performance of a Single-Phase Inverter in a Renewable Energy System (RES)
by Chang-Hua Lin, Shoeb Azam Farooqui, Hwa-Dong Liu, Jian-Jang Huang and Mohd Fahad
Mathematics 2023, 11(21), 4553; https://doi.org/10.3390/math11214553 - 05 Nov 2023
Cited by 1 | Viewed by 1209
Abstract
A single-phase five-level T-type topology has been investigated in this article. This topology has emerged as a viable option for renewable energy systems (RES) due to its inherent benefits. The finite control set model predictive control (FCS-MPC) strategy has been implemented to this [...] Read more.
A single-phase five-level T-type topology has been investigated in this article. This topology has emerged as a viable option for renewable energy systems (RES) due to its inherent benefits. The finite control set model predictive control (FCS-MPC) strategy has been implemented to this topology in order to improve the performance and overall reliability of the system. This control strategy empowers the inverter to predict future behavior based on a discrete set of control signals, enabling precise modulation and high-speed response to system dynamics. In the realm of RES, integration of FCS-MPC with multilevel inverters (MLIs) holds great potential to enhance energy conversion efficiency, grid integration, and overall system reliability. The article is structured to present an overview of the evolving landscape of power electronic systems, and the advantages of FCS-MPC. This paper provides a comprehensive analysis of the FCS-MPC control strategy applied to the single-phase five-level T-type topology. The study covers various aspects including the theoretical framework, hardware development, and experimental evaluation. It is obvious from the analysis that this inverter topology is reliable. Several redundant states make it fault-tolerant which helps in maintaining the output voltage at the same level even in the fault conditions. Additionally, the results show that the output load voltage is maintained at the same level irrespective of load change. Also, output load voltage has maintained the high-quality sinusoidal characteristics as the total harmonic distortion (THD) is very low. With all these features, this system is suitable within the framework of RES. Full article
(This article belongs to the Special Issue Modeling and Simulation for the Electrical Power System)
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20 pages, 8244 KiB  
Article
Mobile Robot Path Planning Based on Kinematically Constrained A-Star Algorithm and DWA Fusion Algorithm
by Yanjie Liu, Chao Wang, Heng Wu and Yanlong Wei
Mathematics 2023, 11(21), 4552; https://doi.org/10.3390/math11214552 - 05 Nov 2023
Viewed by 1489
Abstract
Path-planning research has been the key to mobile-robot-navigation technology. However, traditional path-planning algorithms have some shortcomings. To solve these problems, this paper proposes a fusion algorithm that combines the kinematical constrained A* algorithm with the Dynamic Window Approach (DWA) algorithm. The kinematical constrained [...] Read more.
Path-planning research has been the key to mobile-robot-navigation technology. However, traditional path-planning algorithms have some shortcomings. To solve these problems, this paper proposes a fusion algorithm that combines the kinematical constrained A* algorithm with the Dynamic Window Approach (DWA) algorithm. The kinematical constrained A* algorithm can plan the global path, and then the DWA algorithm can plan the local path under the global path’s guidance. Firstly, combined with robot kinematics, we improve the node-expansion method and heuristic-function model of the A* algorithm, which improves the search efficiency, reduces the number of path bends and lowers the computational cost so that the path generated by the A* algorithm better meets the needs of robot motion. Secondly, we optimize the trajectory-evaluation function of the DWA algorithm so that the local paths planned by the DWA algorithm are smoother and more coherent, which is easier for robot-motion execution. Finally, we extract the key nodes from the global path planned by the A* algorithm to guide the DWA algorithm for local path planning and dynamic-obstacle avoidance and to make the local path closer to the global path. Through simulation and practical experiments, the effectiveness of the fusion algorithm proposed in this paper is verified. Full article
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19 pages, 349 KiB  
Article
Enhancing Equation Solving: Extending the Applicability of Steffensen-Type Methods
by Ramandeep Behl, Ioannis K. Argyros and Monairah Alansari
Mathematics 2023, 11(21), 4551; https://doi.org/10.3390/math11214551 - 05 Nov 2023
Viewed by 717
Abstract
Local convergence analysis is mostly carried out using the Taylor series expansion approach, which requires the utilization of high-order derivatives, not iterative methods. There are other limitations to this approach, such as the following: the analysis is limited to finite-dimensional Euclidean spaces; no [...] Read more.
Local convergence analysis is mostly carried out using the Taylor series expansion approach, which requires the utilization of high-order derivatives, not iterative methods. There are other limitations to this approach, such as the following: the analysis is limited to finite-dimensional Euclidean spaces; no a priori computable error bounds on the distance or uniqueness of the solution results are provided. The local convergence analysis in this paper positively addresses these concerns in the more general setting of a Banach space. The convergence conditions involve only the operators in the methods. The more important semi-local convergence analysis not studied before is developed by using majorizing sequences. Both types of convergence analyses are based on the concept of generalized continuity. Although we study a certain class of methods, the same approach applies to extend the applicability of other schemes along the same lines. Full article
16 pages, 398 KiB  
Article
Exploring Spatial-Based Position Encoding for Image Captioning
by Xiaobao Yang, Shuai He, Junsheng Wu, Yang Yang, Zhiqiang Hou and Sugang Ma
Mathematics 2023, 11(21), 4550; https://doi.org/10.3390/math11214550 - 04 Nov 2023
Cited by 1 | Viewed by 929
Abstract
Image captioning has become a hot topic in artificial intelligence research and sits at the intersection of computer vision and natural language processing. Most recent imaging captioning models have adopted an “encoder + decoder” architecture, in which the encoder is employed generally to [...] Read more.
Image captioning has become a hot topic in artificial intelligence research and sits at the intersection of computer vision and natural language processing. Most recent imaging captioning models have adopted an “encoder + decoder” architecture, in which the encoder is employed generally to extract the visual feature, while the decoder generates the descriptive sentence word by word. However, the visual features need to be flattened into sequence form before being forwarded to the decoder, and this results in the loss of the 2D spatial position information of the image. This limitation is particularly pronounced in the Transformer architecture since it is inherently not position-aware. Therefore, in this paper, we propose a simple coordinate-based spatial position encoding method (CSPE) to remedy this deficiency. CSPE firstly creates the 2D position coordinates for each feature pixel, and then encodes them by row and by column separately via trainable or hard encoding, effectively strengthening the position representation of visual features and enriching the generated description sentences. In addition, in order to reduce the time cost, we also explore a diagonal-based spatial position encoding (DSPE) approach. Compared with CSPE, DSPE is slightly inferior in performance but has a faster calculation speed. Extensive experiments on the MS COCO 2014 dataset demonstrate that CSPE and DSPE can significantly enhance the spatial position representation of visual features. CSPE, in particular, demonstrates BLEU-4 and CIDEr metrics improved by 1.6% and 5.7%, respectively, compared with a baseline model without sequence-based position encoding, and also outperforms current sequence-based position encoding approaches by a significant margin. In addition, the robustness and plug-and-play ability of the proposed method are validated based on a medical captioning generation model. Full article
(This article belongs to the Special Issue Mathematical Methods in Image Processing and Computer Vision)
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13 pages, 328 KiB  
Article
Variable-Order Fractional Scale Calculus
by Duarte Valério and Manuel D. Ortigueira
Mathematics 2023, 11(21), 4549; https://doi.org/10.3390/math11214549 - 04 Nov 2023
Cited by 1 | Viewed by 687
Abstract
General variable-order fractional scale derivatives are introduced and studied. Both the stretching and the shrinking cases are considered for definitions of the derivatives of the GL type and of the Hadamard type. Their properties are deduced and discussed. Fractional variable-order systems of autoregressive–moving-average [...] Read more.
General variable-order fractional scale derivatives are introduced and studied. Both the stretching and the shrinking cases are considered for definitions of the derivatives of the GL type and of the Hadamard type. Their properties are deduced and discussed. Fractional variable-order systems of autoregressive–moving-average type are introduced and exemplified. The corresponding transfer functions are obtained and used to find the corresponding impulse responses. Full article
(This article belongs to the Special Issue Fractional Calculus and Mathematical Applications, 2nd Edition)
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24 pages, 6407 KiB  
Article
Self-Tuning Controller Using Shifting Method
by Milan Hofreiter, Michal Moučka and Pavel Trnka
Mathematics 2023, 11(21), 4548; https://doi.org/10.3390/math11214548 - 04 Nov 2023
Viewed by 790
Abstract
This paper presents a newly implemented self-tuning PID controller that uses a relay feedback identification using a recently designed relay shifting method to determine the mathematical model of the process and subsequently adjust the controller parameters. The controller is applicable to proportional and [...] Read more.
This paper presents a newly implemented self-tuning PID controller that uses a relay feedback identification using a recently designed relay shifting method to determine the mathematical model of the process and subsequently adjust the controller parameters. The controller is applicable to proportional and integrating systems and is even applicable to systems with transport delays if steady-state oscillation can be achieved in the relay control of the system. After briefly introducing the relay shifting method, the current paper describes the hardware (HW) and software (SW) of the proposed controller in detail. The relay feedback identification and control of a laboratory setup by an automatically tuned controller is demonstrated on a real laboratory device called “Hot air tunnel”. The evaluation of the experiment and the characteristics of the controller are presented at the end of the paper. The advantage of the relay method is that it is not as computationally intensive as other identification methods. It can thus be implemented on more energy-efficient microcontrollers, which is very important nowadays. Full article
(This article belongs to the Special Issue Identification, Knowledge Engineering and Digital Modeling for Adaptive and Intelligent Control, 2nd Edition)
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20 pages, 2375 KiB  
Article
CVFL: A Chain-like and Verifiable Federated Learning Scheme with Computational Efficiency Based on Lagrange Interpolation Functions
by Mengnan Wang, Chunjie Cao, Xiangyu Wang, Qi Zhang, Zhaoxing Jing, Haochen Li and Jingzhang Sun
Mathematics 2023, 11(21), 4547; https://doi.org/10.3390/math11214547 - 04 Nov 2023
Viewed by 904
Abstract
Data privacy and security concerns have attracted significant attention, leading to the frequent occurrence of data silos in deep learning. To address this issue, federated learning (FL) has emerged. However, simple federated learning frameworks still face two security risks during the training process. [...] Read more.
Data privacy and security concerns have attracted significant attention, leading to the frequent occurrence of data silos in deep learning. To address this issue, federated learning (FL) has emerged. However, simple federated learning frameworks still face two security risks during the training process. Firstly, sharing local gradients instead of private datasets among users does not completely eliminate the possibility of data leakage. Secondly, malicious servers could obtain inaccurate aggregation parameters by forging or simplifying the aggregation process, ultimately leading to model training failures. To address these issues and achieve high-performance training models, we have designed a verifiable federated learning scheme called CVFL, where users exist in a serial manner to resist inference attacks and further protect the privacy of user dataset information through serial encryption. We ensure the secure aggregation of models through a verification protocol based on Lagrange interpolation functions. The serial transmission of local gradients effectively reduces the communication burden on cloud servers, and our verification protocol avoids the computational overhead caused by a large number of encryption and decryption operations without sacrificing model accuracy. Experimental results on the MNIST dataset demonstrate that, after 10 epochs of training with 100 users, our solution achieves a model accuracy of 90.63% for MLP architecture under IID data distribution and 87.47% under non-IID data distribution. For CNN architecture, our solution achieves a model accuracy of 96.72% under IID data distribution and 93.53% under non-IID data distribution. Experimental evaluations corroborate the practical performance of the presented scheme with high accuracy and efficiency. Full article
(This article belongs to the Special Issue Parallel and Distributed Computing: Theory and Applications)
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15 pages, 449 KiB  
Article
An Automatic Train Operation Based Real-Time Rescheduling Model for High-Speed Railway
by Fan Liu and Jing Xun
Mathematics 2023, 11(21), 4546; https://doi.org/10.3390/math11214546 - 04 Nov 2023
Viewed by 807
Abstract
With the continuous development of the Automatic Train Operation (ATO) system in high-speed railways, automatic driving is progressively supplanting manual operations, ushering in a new era of predictability and reliability for high-speed railway transport. Concurrently, the advent of the ATO system provides a [...] Read more.
With the continuous development of the Automatic Train Operation (ATO) system in high-speed railways, automatic driving is progressively supplanting manual operations, ushering in a new era of predictability and reliability for high-speed railway transport. Concurrently, the advent of the ATO system provides a notable impact on real-time rescheduling during disruptions, as it equips dispatchers with precise insights into train operation statuses. This paper is dedicated to a thorough analysis of how the transition to automatic driving in train operations influences the real-time rescheduling model. Based on the distinctive impact of the ATO system on real-time rescheduling, we have proposed a mixed-integer linear programming model that combines train re-timing, reordering, and the minimization of passenger delays. To validate the effectiveness of our model, we present several experiments conducted using data from the Beijing–Shanghai high-speed railway line. The results unequivocally demonstrate that our ATO-based model significantly mitigates train delay time, demonstrating its practical value in optimizing high-speed railway operations. Full article
(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems)
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13 pages, 1222 KiB  
Article
Integrability Properties of the Slepyan–Palmov Model Arising in the Slepyan–Palmov Medium
by Muhammad Usman, Akhtar Hussain, F. D. Zaman, Asier Ibeas and Yahya Almalki
Mathematics 2023, 11(21), 4545; https://doi.org/10.3390/math11214545 - 03 Nov 2023
Cited by 6 | Viewed by 508
Abstract
This study investigates the Slepyan–Palmov (SP) model, which describes plane longitudinal waves propagating within a medium comprising a carrier medium and nonlinear oscillators. The primary objective is to analyze the integrability properties of this model. The research entails two key aspects. Firstly, the [...] Read more.
This study investigates the Slepyan–Palmov (SP) model, which describes plane longitudinal waves propagating within a medium comprising a carrier medium and nonlinear oscillators. The primary objective is to analyze the integrability properties of this model. The research entails two key aspects. Firstly, the study explores the group invariant solution by utilizing reductions in symmetry subalgebras based on the optimal system. Secondly, the conservation laws are studied using the homotopy operator, which offers advantages over the conventional multiplier approach, especially when arbitrary functions are absent from both the equation and characteristics. This method proves advantageous in handling complex multipliers and yields significant outcomes. Full article
(This article belongs to the Section Engineering Mathematics)
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14 pages, 2556 KiB  
Article
Mathematical Models for Forecasting Unstable Economic Processes in the Eurozone
by Askar Akaev, Alexander Zvyagintsev, Tessaleno Devezas, Askar Sarygulov and Andrea Tick
Mathematics 2023, 11(21), 4544; https://doi.org/10.3390/math11214544 - 03 Nov 2023
Viewed by 817
Abstract
In an unstable economic climate, all market participants want to know is when is the timing to overcome a recession, and what measures and means to use for economic recovery. In this regard, the process through which the Eurozone economy has gained momentum [...] Read more.
In an unstable economic climate, all market participants want to know is when is the timing to overcome a recession, and what measures and means to use for economic recovery. In this regard, the process through which the Eurozone economy has gained momentum since the summer of 2022 has been a volatile one. This was reflected in a sharp rise in the price level, followed by a sharp rise in the ECB interest rates. The purpose of this paper is to provide short-term forecasts of the main parameters of monetary and fiscal policy by the euro area monetary authorities, based on a model developed by the authors. The distinctive feature of the presented and proposed model lies in the particularly careful selection of the parameter values based on actual statistical data. The statistics used for the proposed model cover the period from 2015 to December 2022. The simulation results show that the European Central Bank (ECB) needs to maintain a policy of high interest rates for a period of 12 to 14 months, which will help to bring inflation down to 2–3 percent in the future and move to a stage and phase of sustainable economic growth. Full article
(This article belongs to the Special Issue Quantitative Methods for Economic Policy and Public Economics)
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18 pages, 1039 KiB  
Article
A Client-Cloud-Chain Data Annotation System of Internet of Things for Semi-Supervised Missing Data
by Chao Yu, Yang Zhou and Xiaolong Cui
Mathematics 2023, 11(21), 4543; https://doi.org/10.3390/math11214543 - 03 Nov 2023
Viewed by 609
Abstract
With continuous progress in science and technology, a large amount of data are produced in all fields of the world at anytime and anywhere. These data are unmarked and lack marking information, while manual marking is time-consuming and laborious. Herein, this paper introduces [...] Read more.
With continuous progress in science and technology, a large amount of data are produced in all fields of the world at anytime and anywhere. These data are unmarked and lack marking information, while manual marking is time-consuming and laborious. Herein, this paper introduces a distributed semi-supervised labeling framework. This framework addresses the issue of missing data by proposing an attribute-filling method based on subspace learning. Furthermore, this paper presents a distributed semi-supervised learning strategy that trains sub-models (private models) within each sub-system. Finally, this paper develops a distributed graph convolutional neural network fusion technique with enhanced interpretability grounded on the attention mechanism. This paper assigns weights of importance to the edges of each layer in the graph neural network based on sub-models and public data, thereby enabling distributed and interpretable graph convolutional attention. Extensive experimentation using public datasets demonstrates the superiority of the proposed scheme over other state-of-the-art baselines, achieving a reduction in loss of 50% compared to the original approach. Full article
(This article belongs to the Special Issue Advances of Intelligent Systems)
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26 pages, 870 KiB  
Article
Decentralized News-Retrieval Architecture Using Blockchain Technology
by Adrian Alexandrescu and Cristian Nicolae Butincu
Mathematics 2023, 11(21), 4542; https://doi.org/10.3390/math11214542 - 03 Nov 2023
Cited by 1 | Viewed by 744
Abstract
Trust is a critical element when it comes to news articles, and an important problem is how to ensure trust in the published information on news websites. First, this paper describes the inner workings of a proposed news-retrieval and aggregation architecture employed by [...] Read more.
Trust is a critical element when it comes to news articles, and an important problem is how to ensure trust in the published information on news websites. First, this paper describes the inner workings of a proposed news-retrieval and aggregation architecture employed by a blockchain-based solution for fighting disinformation; this includes a comparison between existing information retrieval solutions. The decentralized nature of the solution is achieved by separating the crawling (i.e., extracting the web page links) from the scraping (i.e., extracting the article information) and having third-party actors extract the data. A majority-rule mechanism is used to determine the correctness of the information, and the blockchain network is used for traceability. Second, the steps needed to deploy the distributed components in a cloud environment seamlessly are discussed in detail, with a special focus on the open-source OpenStack cloud solution. Lastly, novel methods for achieving a truly decentralized architecture based on community input and blockchain technology are presented, thus ensuring maximum trust and transparency in the system. The results obtained by testing the proposed news-retrieval system are presented, and the optimizations that can be made are discussed based on the crawling and scraping test results. Full article
(This article belongs to the Special Issue Application of Cloud Computing and Distributed Systems)
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16 pages, 491 KiB  
Article
A Mechanistic Model for Long COVID Dynamics
by Jacob Derrick, Ben Patterson, Jie Bai and Jin Wang
Mathematics 2023, 11(21), 4541; https://doi.org/10.3390/math11214541 - 03 Nov 2023
Viewed by 660
Abstract
Long COVID, a long-lasting disorder following an acute infection of COVID-19, represents a significant public health burden at present. In this paper, we propose a new mechanistic model based on differential equations to investigate the population dynamics of long COVID. By connecting long [...] Read more.
Long COVID, a long-lasting disorder following an acute infection of COVID-19, represents a significant public health burden at present. In this paper, we propose a new mechanistic model based on differential equations to investigate the population dynamics of long COVID. By connecting long COVID with acute infection at the population level, our modeling framework emphasizes the interplay between COVID-19 transmission, vaccination, and long COVID dynamics. We conducted a detailed mathematical analysis of the model. We also validated the model using numerical simulation with real data from the US state of Tennessee and the UK. Full article
(This article belongs to the Special Issue Complex Biological Systems and Mathematical Biology)
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36 pages, 458 KiB  
Article
Rolling Stiefel Manifolds Equipped with α-Metrics
by Markus Schlarb, Knut Hüper, Irina Markina and Fátima Silva Leite
Mathematics 2023, 11(21), 4540; https://doi.org/10.3390/math11214540 - 03 Nov 2023
Viewed by 510
Abstract
We discuss the rolling, without slipping and without twisting, of Stiefel manifolds equipped with α-metrics, from an intrinsic and an extrinsic point of view. We, however, start with a more general perspective, namely, by investigating the intrinsic rolling of normal naturally reductive [...] Read more.
We discuss the rolling, without slipping and without twisting, of Stiefel manifolds equipped with α-metrics, from an intrinsic and an extrinsic point of view. We, however, start with a more general perspective, namely, by investigating the intrinsic rolling of normal naturally reductive homogeneous spaces. This gives evidence as to why a seemingly straightforward generalization of the intrinsic rolling of symmetric spaces to normal naturally reductive homogeneous spaces is not possible, in general. For a given control curve, we derive a system of explicit time-variant ODEs whose solutions describe the desired rolling. These findings are applied to obtain the intrinsic rolling of Stiefel manifolds, which is then extended to an extrinsic one. Moreover, explicit solutions of the kinematic equations are obtained, provided that the development curve is the projection of a not necessarily horizontal one-parameter subgroup. In addition, our results are put into perspective with examples of the rolling Stiefel manifolds known from the literature. Full article
10 pages, 253 KiB  
Article
A Finite-Dimensional Integrable System Related to the Kadometsev–Petviashvili Equation
by Wei Liu, Yafeng Liu, Junxuan Wei and Shujuan Yuan
Mathematics 2023, 11(21), 4539; https://doi.org/10.3390/math11214539 - 03 Nov 2023
Viewed by 399
Abstract
In this paper, the Kadometsev–Petviashvili equation and the Bargmann system are obtained from a second-order operator spectral problem Lφ=(∂2−v∂−λu)φ=λφx. By means of the Euler–Lagrange equations, [...] Read more.
In this paper, the Kadometsev–Petviashvili equation and the Bargmann system are obtained from a second-order operator spectral problem Lφ=(∂2−v∂−λu)φ=λφx. By means of the Euler–Lagrange equations, a suitable Jacobi–Ostrogradsky coordinate system is established. Using Cao’s method and the associated Bargmann constraint, the Lax pairs of the differential equations are nonlinearized. Then, a new kind of finite-dimensional Hamilton system is generated. Moreover, involutive representations of the solutions of the Kadometsev–Petviashvili equation are derived. Full article
(This article belongs to the Section Mathematical Physics)
18 pages, 423 KiB  
Article
A Resource Allocation Scheme for Packet Delay Minimization in Multi-Tier Cellular-Based IoT Networks
by Jin Li, Wenyang Guan and Zuoyin Tang
Mathematics 2023, 11(21), 4538; https://doi.org/10.3390/math11214538 - 03 Nov 2023
Cited by 1 | Viewed by 605
Abstract
With advances in Internet of Things (IoT) technologies, billions of devices are becoming connected, which can result in the unprecedented sensing and control of the physical environments. IoT devices have diverse quality of service (QoS) requirements, including data rate, latency, reliability, and energy [...] Read more.
With advances in Internet of Things (IoT) technologies, billions of devices are becoming connected, which can result in the unprecedented sensing and control of the physical environments. IoT devices have diverse quality of service (QoS) requirements, including data rate, latency, reliability, and energy consumption. Meeting the diverse QoS requirements presents great challenges to existing fifth-generation (5G) cellular networks, especially in unprecedented scenarios in 5G networks, such as connected vehicle networks, where strict data packet latency may be required. The IoT devices with these scenarios have higher requirements on the packet latency in networking, which is essential to the utilization of 5G networks. In this paper, we propose a multi-tier cellular-based IoT network to address this challenge, with a particular focus on meeting application latency requirements. In the multi-tier network, access points (APs) can relay and forward packets from IoT devices or other APs, which can support higher data rates with multi-hops between IoT devices and cellular base stations. However, as multiple-hop relaying may cause additional delay, which is crucial to delay-sensitive applications, we develop new schemes to mitigate the adverse impact. Firstly, we design a traffic-prioritization scheduling scheme to classify packets with different priorities in each AP based on the age of information (AoI). Then, we design different channel-access protocols for the transmission of packets according to their priorities to ensure the QoS in networking and the effective utilization of the limited network resources. A queuing-theory-based theoretical model is proposed to analyze the packet delay for each type of packet at each tier of the multi-tier IoT networks. An optimal algorithm for the distribution of spectrum and power resources is developed to reduce the overall packet delay in a multi-tier way. The numerical results achieved in a two-tier cellular-based IoT network show that the target packet delay for delay-sensitive applications can be achieved without a large cost in terms of traffic fairness. Full article
(This article belongs to the Special Issue Advances in Mobile Network and Intelligent Communication)
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22 pages, 4089 KiB  
Article
General Image Manipulation Detection Using Feature Engineering and a Deep Feed-Forward Neural Network
by Sajjad Ahmed, Byungun Yoon, Sparsh Sharma, Saurabh Singh and Saiful Islam
Mathematics 2023, 11(21), 4537; https://doi.org/10.3390/math11214537 - 03 Nov 2023
Viewed by 748
Abstract
Within digital forensics, a notable emphasis is placed on the detection of the application of fundamental image-editing operators, including but not limited to median filters, average filters, contrast enhancement, resampling, and various other operations closely associated with these techniques. When conducting a historical [...] Read more.
Within digital forensics, a notable emphasis is placed on the detection of the application of fundamental image-editing operators, including but not limited to median filters, average filters, contrast enhancement, resampling, and various other operations closely associated with these techniques. When conducting a historical analysis of an image that has potentially undergone various modifications in the past, it is a logical initial approach to search for alterations made by fundamental operators. This paper presents the development of a deep-learning-based system designed for the purpose of detecting fundamental manipulation operations. The research involved training a multilayer perceptron using a feature set of 36 dimensions derived from the gray-level co-occurrence matrix, gray-level run-length matrix, and normalized streak area. The system detected median filtering, mean filtering, the introduction of additive white Gaussian noise, and the application of JPEG compression in digital Images. Our system, which utilizes a multilayer perceptron trained with a 36-feature set, achieved an accuracy of 99.46% and outperformed state-of-the-art deep-learning-based solutions, which achieved an accuracy of 97.89%. Full article
(This article belongs to the Special Issue Computer Vision, Image Processing Technologies and Artificial Intelligence)
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12 pages, 236 KiB  
Article
Superiorization with a Projected Subgradient Algorithm on the Solution Sets of Common Fixed Point Problems
by Alexander J. Zaslavski
Mathematics 2023, 11(21), 4536; https://doi.org/10.3390/math11214536 - 03 Nov 2023
Viewed by 596
Abstract
In this work, we investigate a minimization problem with a convex objective function on a domain, which is the solution set of a common fixed point problem with a finite family of nonexpansive mappings. Our algorithm is a combination of a projected subgradient [...] Read more.
In this work, we investigate a minimization problem with a convex objective function on a domain, which is the solution set of a common fixed point problem with a finite family of nonexpansive mappings. Our algorithm is a combination of a projected subgradient algorithm and string-averaging projection method with variable strings and variable weights. This algorithm generates a sequence of iterates which are approximate solutions of the corresponding fixed point problem. Additionally, either this sequence also has a minimizing subsequence for our optimization problem or the sequence is strictly Fejer monotone regarding the approximate solution set of the common fixed point problem. Full article
(This article belongs to the Special Issue Variational Problems and Applications, 2nd Edition)
17 pages, 4078 KiB  
Article
A Novel Real-Time Robust Controller of a Four-Wheel Independent Steering System for EV Using Neural Networks and Fuzzy Logic
by Alexis Kosmidis, Georgios Ioannidis, Georgios Vokas and Stavros Kaminaris
Mathematics 2023, 11(21), 4535; https://doi.org/10.3390/math11214535 - 03 Nov 2023
Viewed by 659
Abstract
In this study a four-wheel independent steering (4WIS) system for an electric vehicle (EV) steered by stepper motors is presented as a revolutionary real-time control technique employing neural networks in combination with fuzzy logic, where the use of the neural network greatly simplifies [...] Read more.
In this study a four-wheel independent steering (4WIS) system for an electric vehicle (EV) steered by stepper motors is presented as a revolutionary real-time control technique employing neural networks in combination with fuzzy logic, where the use of the neural network greatly simplifies the computational process of fuzzy logic. The control of the four wheels is based on a variation of a Hopfield Neural Network (VHNN) method, in which the input is the error of each steering motor and the output is processed by a hyperbolic tangent function (HTF) feeding the fuzzy logic controller (FLC), which ultimately drives the stepper motor. The whole system consists of the four aforementioned blocks which work in sync and are inseparable from each other with the common goal of driving all the steering stepper motors at the same time. The novelty of this system is that each wheel monitors the condition of the others, so even in the case of the failure of one wheel, the vehicle does not veer off course. The results of the simulation show that the suggested control system is very resilient and workable at all angles and speeds. Full article
(This article belongs to the Special Issue Control, Optimization and Intelligent Computing in Energy)
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9 pages, 666 KiB  
Article
Stretch-Energy-Minimizing B-Spline Interpolation Curves and Their Applications
by Qian Ni and Chen Xie
Mathematics 2023, 11(21), 4534; https://doi.org/10.3390/math11214534 - 03 Nov 2023
Viewed by 1015
Abstract
In this paper, we propose a new method to construct energy-minimizing cubic B-spline interpolation curves by minimizing the approximated stretch energy. The construction of a B-spline interpolation curve with a minimal approximated stretch energy can be addressed by solving a sparse linear system. [...] Read more.
In this paper, we propose a new method to construct energy-minimizing cubic B-spline interpolation curves by minimizing the approximated stretch energy. The construction of a B-spline interpolation curve with a minimal approximated stretch energy can be addressed by solving a sparse linear system. The proof of both the existence and uniqueness of the solution for the linear system is provided. In addition, we analyze the computational cost of cubic B-spline curves with an approximated stretch energy, which is close to that of the ordinary interpolation method with cubic B-splines without the requirement of stretch energy. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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