Mathematics

31 pages, 7137 KiB

Open AccessArticle

Distributed Batch Learning of Growing Neural Gas for Quick and Efficient Clustering

by Chyan Zheng Siow, Azhar Aulia Saputra, Takenori Obo and Naoyuki Kubota

Mathematics 2024, 12(12), 1909; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121909 (registering DOI) - 20 Jun 2024

Abstract

Growing neural gas (GNG) has been widely used in topological mapping, clustering and unsupervised tasks. It starts from two random nodes and grows until it forms a topological network covering all data. The time required for growth depends on the total amount of [...] Read more.

Growing neural gas (GNG) has been widely used in topological mapping, clustering and unsupervised tasks. It starts from two random nodes and grows until it forms a topological network covering all data. The time required for growth depends on the total amount of data and the current network nodes. To accelerate growth, we introduce a novel distributed batch processing method to extract the rough distribution called Distributed Batch Learning Growing Neural Gas (DBL-GNG). First, instead of using a for loop in standard GNG, we adopt a batch learning approach to accelerate learning. To do this, we replace most of the standard equations with matrix calculations. Next, instead of starting with two random nodes, we start with multiple nodes in different distribution areas. Furthermore, we also propose to add multiple nodes to the network instead of adding them one by one. Finally, we introduce an edge cutting method to reduce unimportant links between nodes to obtain a better cluster network. We demonstrate DBL-GNG on multiple benchmark datasets. From the results, DBL-GNG performs faster than other GNG methods by at least 10 times. We also demonstrate the scalability of DBL-GNG by implementing a multi-scale batch learning process in it, named MS-DBL-GNG, which successfully obtains fast convergence results. In addition, we also demonstrate the dynamic data adaptation of DBL-GNG to 3D point cloud data. It is capable of processing and mapping topological nodes on point cloud objects in real time. Full article

(This article belongs to the Special Issue Advanced Machine Vision with Mathematics)

► Show Figures

Figure 1

15 pages, 267 KiB

Open AccessArticle

New Upper Bounds for Covering Arrays of Order Seven

by Jose Torres-Jimenez and Idelfonso Izquierdo-Marquez

Mathematics 2024, 12(12), 1908; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121908 (registering DOI) - 20 Jun 2024

Abstract

A covering array is a combinatorial object that is used to test hardware and software components. The covering array number is the minimum number of rows needed to construct a specific covering array. The search for better upper bounds for covering array numbers [...] Read more.

A covering array is a combinatorial object that is used to test hardware and software components. The covering array number is the minimum number of rows needed to construct a specific covering array. The search for better upper bounds for covering array numbers is a very active area of research. Although there are many methods for defining new upper bounds for covering array numbers, recently the use of covering perfect hash families has significantly improved a large number of covering array numbers for alphabets that are prime powers. Currently, excellent upper bounds have been reported for alphabets 2, 3, 4, and 5; therefore, the focus of this article is on defining new upper bounds on the size of covering arrays for the alphabet seven using perfect hash families. For this purpose, a greedy column extension algorithm was constructed to increase the number of columns in a covering perfect hash family while keeping the number of rows constant. Our greedy algorithm begins with a random covering perfect hash family containing only eight columns and alternates between adding and removing columns. Adding columns increases the size of the covering perfect hash family while removing columns reduces the number of missing combinations in covering perfect hash families with different column counts. The construction process continues with the covering perfect hash family with the smallest number of columns being refined (i.e., missing combinations reduced). Thus, columns are dynamically added and removed to refine the covering perfect hash families being built. To illustrate the advantages of our greedy approach, 152 new covering perfect hash families of order seven with strengths 3, 4, 5, and 6 were constructed, enabling us to improve 12,556 upper bounds of covering array numbers; 903 of these improvements are for strength three, 8910 for strength four, 1957 for strength five, and 786 for strength six. Full article

(This article belongs to the Special Issue Combinatorial Optimization for Constructing Covering Arrays and Sequence Covering Arrays)

1 pages, 119 KiB

Open AccessCorrection

Correction: Li et al. Attitude Control of UAVs with Search Optimization and Disturbance Rejection Strategies. Mathematics 2023, 11, 3794

by Wensheng Li, Fanke Yang, Liqiang Zhong, Hao Wu, Xiangyuan Jiang and Andrei V. Chukalin

Mathematics 2024, 12(12), 1907; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121907 (registering DOI) - 20 Jun 2024

Abstract

In the original publication [...] Full article

25 pages, 3335 KiB

Open AccessArticle

A Rumor Propagation Model Considering Media Effect and Suspicion Mechanism under Public Emergencies

by Shan Yang, Shihan Liu, Kaijun Su and Jianhong Chen

Mathematics 2024, 12(12), 1906; https://doi.org/10.3390/math12121906 - 19 Jun 2024

Abstract

In this paper, we collect the basic information data of online rumors and highly topical public opinions. In the research of the propagation model of online public opinion rumors, we use the improved SCIR model to analyze the characteristics of online rumor propagation [...] Read more.

In this paper, we collect the basic information data of online rumors and highly topical public opinions. In the research of the propagation model of online public opinion rumors, we use the improved SCIR model to analyze the characteristics of online rumor propagation under the suspicion mechanism at different propagation stages, based on considering the flow of rumor propagation. We analyze the stability of the evolution of rumor propagation by using the time-delay differential equation under the punishment mechanism. In this paper, the evolution of heterogeneous views with different acceptance and exchange thresholds is studied, using the standard Deffuant model and the improved model under the influence of the media, to analyze the evolution process and characteristics of rumor opinions. Based on the above results, it is found that improving the recovery rate is better than reducing the deception rate, and increasing the eviction rate is better than improving the detection rate. When the time lag τ < 110, it indicates that the spread of rumors tends to be asymptotic and stable, and the punishment mechanism can reduce the propagation time and the maximum proportion of deceived people. The proportion of deceived people increases with the decrease in the exchange threshold, and the range of opinion clusters increases with the decline in acceptance. Full article

18 pages, 1120 KiB

Open AccessFeature PaperArticle

Research on Vehicle AEB Control Strategy Based on Safety Time–Safety Distance Fusion Algorithm

by Xiang Fu, Jiaqi Wan, Daibing Wu, Wei Jiang, Wang Ma and Tianqi Yang

Mathematics 2024, 12(12), 1905; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121905 - 19 Jun 2024

Abstract

With the increasing consumer focus on automotive safety, Autonomous Emergency Braking (AEB) systems, recognized as effective active safety technologies for collision avoidance and the mitigation of collision-related injuries, are gaining wider application in the automotive industry. To address the issues of the insufficient [...] Read more.

With the increasing consumer focus on automotive safety, Autonomous Emergency Braking (AEB) systems, recognized as effective active safety technologies for collision avoidance and the mitigation of collision-related injuries, are gaining wider application in the automotive industry. To address the issues of the insufficient working reliability of AEB systems and their unsatisfactory level of accordance with the psychological expectations of drivers, this study proposes an optimized second-order Time to Collision (TTC) safety time algorithm based on the motion state of the preceding vehicle. Additionally, the study introduces a safety distance algorithm derived from an analysis of the braking process of the main vehicle. The safety time algorithm focusing on comfort and the safety distance algorithm focusing on safety are effectively integrated in the time domain and the space domain to obtain the safety time–safety distance fusion algorithm. A MATLAB/Simulink–Carsim joint simulation platform has been established to validate the AEB control strategy in terms of safety, comfort, and system responsiveness. The simulation results show that the proposed safety time–safety distance fusion algorithm consistently achieves complete collision avoidance, indicating a higher safety level for the AEB system. Furthermore, the application of active hierarchical braking minimizes the distance error, at under 0.37 m, which meets psychological expectations of drivers and improves the comfort of the AEB system. Full article

(This article belongs to the Special Issue Modeling, Optimization and Control of Industrial Processes)

28 pages, 4562 KiB

Open AccessArticle

Exploring the Therapeutic Potential of Defective Interfering Particles in Reducing the Replication of SARS-CoV-2

by Macauley Locke, Dmitry Grebennikov, Igor Sazonov, Martín López-García, Marina Loguinova, Andreas Meyerhans, Gennady Bocharov and Carmen Molina-París

Mathematics 2024, 12(12), 1904; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121904 - 19 Jun 2024

Viewed by 41

Abstract

SARS-CoV-2 still presents a global threat to human health due to the continued emergence of new strains and waning immunity among vaccinated populations. Therefore, it is still relevant to investigate potential therapeutics, such as therapeutic interfering particles (TIPs). Mathematical and computational modeling are [...] Read more.

SARS-CoV-2 still presents a global threat to human health due to the continued emergence of new strains and waning immunity among vaccinated populations. Therefore, it is still relevant to investigate potential therapeutics, such as therapeutic interfering particles (TIPs). Mathematical and computational modeling are valuable tools to study viral infection dynamics for predictive analysis. Here, we expand on the previous work on SARS-CoV-2 intra-cellular replication dynamics to include defective interfering particles (DIPs) as potential therapeutic agents. We formulate a deterministic model that describes the replication of wild-type (WT) SARS-CoV-2 virus in the presence of DIPs. Sensitivity analysis of parameters to several model outputs is employed to inform us on those parameters to be carefully calibrated from experimental data. We then study the effects of co-infection on WT replication and how DIP dose perturbs the release of WT viral particles. Furthermore, we provide a stochastic formulation of the model that is compared to the deterministic one. These models could be further developed into population-level models or used to guide the development and dose of TIPs. Full article

(This article belongs to the Special Issue Nonlinear Dynamics Research in Biomedicine)

► Show Figures

Figure 1

10 pages, 227 KiB

Open AccessArticle

Bayesian Control Chart for Number of Defects in Production Quality Control

by Yadpirun Supharakonsakun

Mathematics 2024, 12(12), 1903; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121903 - 19 Jun 2024

Viewed by 64

Abstract

This study investigates the extension of the c-chart control chart to Bayesian methodology, utilizing the gamma distribution to establish control limits. By comparing the performance of the Bayesian approach with that of two existing methods (the traditional frequentist method and the Bayesian with [...] Read more.

This study investigates the extension of the c-chart control chart to Bayesian methodology, utilizing the gamma distribution to establish control limits. By comparing the performance of the Bayesian approach with that of two existing methods (the traditional frequentist method and the Bayesian with Jeffreys method), we assess its effectiveness in terms of the average run lengths (ARLs) and false alarm rates (FARs). Simulation results indicate that the proposed Bayesian method consistently outperforms the existing techniques, offering larger ARLs and smaller FARs that closely approximate the expected nominal values. While the Bayesian approach excels in most scenarios, challenges may arise with large values of the λ parameter, necessitating adjustments to the hyperparameters of the gamma prior. Specifically, smaller values of the rate parameter are recommended for optimal performance. Overall, our findings suggest that the Bayesian extension of the c-chart provides a promising alternative for enhanced process monitoring and control. Full article

19 pages, 1456 KiB

Open AccessArticle

A Method for Evaluating the Data Integrity of Microseismic Monitoring Systems in Mines Based on a Gradient Boosting Algorithm

by Cong Wang, Kai Zhan, Xigui Zheng, Cancan Liu and Chao Kong

Mathematics 2024, 12(12), 1902; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121902 - 19 Jun 2024

Viewed by 55

Abstract

Microseismic data are widely employed for assessing rockburst risks; however, significant disparities exist in the monitoring capabilities of seismic networks across different mines, and none can capture a complete dataset of microseismic events. Such differences introduce unfairness when applying the same methodologies to [...] Read more.

Microseismic data are widely employed for assessing rockburst risks; however, significant disparities exist in the monitoring capabilities of seismic networks across different mines, and none can capture a complete dataset of microseismic events. Such differences introduce unfairness when applying the same methodologies to evaluate rockburst risks in various mines. This paper proposes a method for assessing the monitoring capability of seismic networks applicable to heterogeneous media in mines. It achieves this by integrating three gradient boosting algorithms: Extreme Gradient Boosting (XGBoost), Light Gradient Boosting Machine (LightGBM), and Categorical Boosting (CatBoost). Initially, the isolation forest algorithm is utilized for preliminary data cleansing, and feature engineering is constructed based on the relative locations of event occurrences to monitoring stations and the working face. Subsequently, the optimal hyperparameters for three models are searched for using 8508 microseismic events from the a Coal Mine in eastern China as samples, and 18 sub-models are trained. Model weights are then determined based on the performance metrics of different algorithms, and an ensemble model is created to predict the monitoring capability of the network. The model demonstrated excellent performance on the training and test sets, achieving log loss, accuracy, and recall scores of 7.13, 0.81, and 0.76 and 6.99, 0.80, and 0.77, respectively. Finally, the method proposed in this study was compared with traditional approaches. The results indicated that, under the same conditions, the proposed method calculated the monitoring capability of the key areas to be 11% lower than that of the traditional methods. The reasons for the differences between these methods were identified and partially explained. Full article

(This article belongs to the Special Issue Advanced Analyses and Algorithms for Trustworthy AI Systems and Applications)

16 pages, 15928 KiB

Open AccessArticle

An Optimal ADMM for Unilateral Obstacle Problems

by Shougui Zhang, Xiyong Cui, Guihua Xiong and Ruisheng Ran

Mathematics 2024, 12(12), 1901; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121901 - 19 Jun 2024

Viewed by 85

Abstract

We propose a new alternating direction method of multipliers (ADMM) with an optimal parameter for the unilateral obstacle problem. We first use the five-point difference scheme to discretize the problem. Then, we present an augmented Lagrangian by introducing an auxiliary unknown, and an [...] Read more.

We propose a new alternating direction method of multipliers (ADMM) with an optimal parameter for the unilateral obstacle problem. We first use the five-point difference scheme to discretize the problem. Then, we present an augmented Lagrangian by introducing an auxiliary unknown, and an ADMM is applied to the corresponding saddle-point problem. Through eliminating the primal and auxiliary unknowns, a pure dual algorithm is then used. The convergence of the proposed method is analyzed, and a simple strategy is presented for selecting the optimal parameter, with the largest and smallest eigenvalues of the iterative matrix. Several numerical experiments confirm the theoretical findings of this study. Full article

(This article belongs to the Special Issue Variational Inequality and Mathematical Analysis)

► Show Figures

Figure 1

24 pages, 647 KiB

Open AccessArticle

A Hybrid Reproducing Kernel Particle Method for Three-Dimensional Helmholtz Equation

by Piaopiao Peng, Ning Wang and Yumin Cheng

Mathematics 2024, 12(12), 1900; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121900 - 19 Jun 2024

Viewed by 62

Abstract

The reproducing kernel particle method (RKPM) is one of the most universal meshless methods. However, when solving three-dimensional (3D) problems, the computational efficiency is relatively low because of the complexity of the shape function. To overcome this disadvantage, in this study, we introduced [...] Read more.

The reproducing kernel particle method (RKPM) is one of the most universal meshless methods. However, when solving three-dimensional (3D) problems, the computational efficiency is relatively low because of the complexity of the shape function. To overcome this disadvantage, in this study, we introduced the dimension splitting method into the RKPM to present a hybrid reproducing kernel particle method (HRKPM), and the 3D Helmholtz equation is solved. The 3D Helmholtz equation is transformed into a series of related two-dimensional (2D) ones, in which the 2D RKPM shape function is used, and the Galerkin weak form of these 2D problems is applied to obtain the discretized equations. In the dimension-splitting direction, the difference method is used to combine the discretized equations in all 2D domains. Three example problems are given to illustrate the performance of the HRKPM. Moreover, the numerical results show that the HRKPM can improve the computational efficiency of the RKPM significantly. Full article

(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 2nd Edition)

21 pages, 990 KiB

Open AccessArticle

A Complex-Valued Stationary Kalman Filter for Positive and Negative Sequence Estimation in DER Systems

by Ricardo Pérez-Ibacache, Rodrigo Carvajal, Ramón Herrera-Hernández, Juan C. Agüero and César A. Silva

Mathematics 2024, 12(12), 1899; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121899 - 19 Jun 2024

Viewed by 94

Abstract

In medium- and low-voltage three-phase distribution networks, the load imbalance among the phases may compromise the network voltage symmetry. Inverter-interfaced distributed energy resources (DERs) can contribute to compensating for such imbalances by sharing the required negative sequence current while providing active power synchronized [...] Read more.

In medium- and low-voltage three-phase distribution networks, the load imbalance among the phases may compromise the network voltage symmetry. Inverter-interfaced distributed energy resources (DERs) can contribute to compensating for such imbalances by sharing the required negative sequence current while providing active power synchronized with the positive sequence voltage. However, positive and negative sequences are conventionally defined in a steady state and are not directly observed from the instantaneous voltage and current measurements at the DER unit’s point of connection. In this article, an estimation algorithm for sequence separation based on the Kalman filter is proposed. Furthermore, the proposed filter uses a complex vector representation of the asymmetric three-phase signals in synchronous coordinates to allow for the implementation of the Kalman filter in its stationary form, resulting in a simple dynamic filter able to estimate positive and negative sequences even during transient operation. The proposed stationary complex Kalman filter performs better than state-of-the-art techniques like DSOGI and very similarly to other Kalman filter implementations found in the literature but at a fraction of its computational cost (23.5%). Full article

(This article belongs to the Section Engineering Mathematics)

39 pages, 12684 KiB

Open AccessArticle

Exploring Data Augmentation and Active Learning Benefits in Imbalanced Datasets

by Luis Moles, Alain Andres, Goretti Echegaray and Fernando Boto

Mathematics 2024, 12(12), 1898; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121898 - 19 Jun 2024

Viewed by 132

Abstract

Despite the increasing availability of vast amounts of data, the challenge of acquiring labeled data persists. This issue is particularly serious in supervised learning scenarios, where labeled data are essential for model training. In addition, the rapid growth in data required by cutting-edge [...] Read more.

Despite the increasing availability of vast amounts of data, the challenge of acquiring labeled data persists. This issue is particularly serious in supervised learning scenarios, where labeled data are essential for model training. In addition, the rapid growth in data required by cutting-edge technologies such as deep learning makes the task of labeling large datasets impractical. Active learning methods offer a powerful solution by iteratively selecting the most informative unlabeled instances, thereby reducing the amount of labeled data required. However, active learning faces some limitations with imbalanced datasets, where majority class over-representation can bias sample selection. To address this, combining active learning with data augmentation techniques emerges as a promising strategy. Nonetheless, the best way to combine these techniques is not yet clear. Our research addresses this question by analyzing the effectiveness of combining both active learning and data augmentation techniques under different scenarios. Moreover, we focus on improving the generalization capabilities for minority classes, which tend to be overshadowed by the improvement seen in majority classes. For this purpose, we generate synthetic data using multiple data augmentation methods and evaluate the results considering two active learning strategies across three imbalanced datasets. Our study shows that data augmentation enhances prediction accuracy for minority classes, with approaches based on CTGANs obtaining improvements of nearly 50% in some cases. Moreover, we show that combining data augmentation techniques with active learning can reduce the amount of real data required. Full article

(This article belongs to the Special Issue Signal Processing, Machine Learning, and Scientific Computing: Algorithms and Applications)

► Show Figures

Figure 1

18 pages, 318 KiB

Open AccessArticle

Dynamics for a Ratio-Dependent Prey–Predator Model with Different Free Boundaries

by Lingyu Liu, Xiaobo Li and Pengcheng Li

Mathematics 2024, 12(12), 1897; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121897 - 19 Jun 2024

Viewed by 113

Abstract

In this paper, we study the dynamics of the ratio-dependent type prey–predator model with different free boundaries. The two free boundaries, determined by prey and predator, respectively, implying that they may intersect with each other as time evolves, are used to describe the [...] Read more.

In this paper, we study the dynamics of the ratio-dependent type prey–predator model with different free boundaries. The two free boundaries, determined by prey and predator, respectively, implying that they may intersect with each other as time evolves, are used to describe the spreading of prey and predator. Our primary focus lies in analyzing the long-term behaviors of both predator and prey. We establish sufficient conditions for the spreading and vanishing of prey and predator. Furthermore, in cases where spread occurs, we offer estimates for the asymptotic spreading speeds of prey and predator, denoted as u and v, respectively, as well as the asymptotic speeds of the free boundaries, denoted by h and g. Our findings reveal that when the predator’s speed is lower than that of the prey, it leads to a reduction in the prey’s asymptotic speed. Full article

(This article belongs to the Special Issue Nonlinear Analysis and Application)

8 pages, 219 KiB

Open AccessArticle

On Hyperbolic Equations with a Translation Operator in Lowest Derivatives

by Vladimir Vasilyev and Natalya Zaitseva

Mathematics 2024, 12(12), 1896; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121896 - 19 Jun 2024

Viewed by 100

Abstract

In the half-plane, a solution to a two-dimensional hyperbolic equation with a translation operator in the lowest derivative with respect to a spatial variable varying along the entire real axis is constructed in an explicit form. It is proven that the solutions obtained [...] Read more.

In the half-plane, a solution to a two-dimensional hyperbolic equation with a translation operator in the lowest derivative with respect to a spatial variable varying along the entire real axis is constructed in an explicit form. It is proven that the solutions obtained are classical if the real part of the symbol of a differential-difference operator in the equation is positive. Full article

(This article belongs to the Special Issue Analytical and Computational Methods in Differential Equations, Special Functions, Transmutations and Integral Transforms, 2nd Edition)

17 pages, 885 KiB

Open AccessArticle

SSA-ELM: A Hybrid Learning Model for Short-Term Traffic Flow Forecasting

by Fei Wang, Yinxi Liang, Zhizhe Lin, Jinglin Zhou and Teng Zhou

Mathematics 2024, 12(12), 1895; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121895 - 19 Jun 2024

Viewed by 194

Abstract

Nowadays, accurate and efficient short-term traffic flow forecasting plays a critical role in intelligent transportation systems (ITS). However, due to the fact that traffic flow is susceptible to factors such as weather and road conditions, traffic flow data tend to exhibit dynamic uncertainty [...] Read more.

Nowadays, accurate and efficient short-term traffic flow forecasting plays a critical role in intelligent transportation systems (ITS). However, due to the fact that traffic flow is susceptible to factors such as weather and road conditions, traffic flow data tend to exhibit dynamic uncertainty and nonlinearity, making the construction of a robust and reliable forecasting model still a challenging task. Aiming at this nonlinear and complex traffic flow forecasting problem, this paper constructs a short-term traffic flow forecasting hybrid optimization model, SSA-ELM, based on extreme learning machine by embedding the sparrow search algorithm in order to solve the above problem. Extreme learning machine has been widely used in short-term traffic flow forecasting due to its characteristics such as low computational complexity and fast learning speed. By using the sparrow search algorithm to optimize the input weight values and hidden layer deviations in the extreme learning machine, the sparrow search algorithm is utilized to search for the global optimal solution while taking into account the original characteristics of the extreme learning machine, so that the model improves stability while increasing prediction accuracy. Experimental results on the Amsterdam A10 road traffic flow dataset show that the traffic flow forecasting model proposed in this paper has higher forecasting accuracy and stability, revealing the potential of hybrid optimization models in the field of short-term traffic flow forecasting. Full article

► Show Figures

Figure 1

32 pages, 734 KiB

Open AccessArticle

A Multi-Criteria Assessment Model for Cooperative Technology Transfer Projects from Universities to Industries

by Rui Xiong, Hongyi Sun, Shufen Zheng and Sichu Liu

Mathematics 2024, 12(12), 1894; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121894 - 18 Jun 2024

Viewed by 303

Abstract

Cooperative Technology Transfer (CTT) is a technology transfer model where universities and enterprises jointly participate throughout the entire process of technology transfer activities. Most discussions focus on its mechanisms and influencing factors, yet a framework to guide CTT projects in practice is still [...] Read more.

Cooperative Technology Transfer (CTT) is a technology transfer model where universities and enterprises jointly participate throughout the entire process of technology transfer activities. Most discussions focus on its mechanisms and influencing factors, yet a framework to guide CTT projects in practice is still lacking. This study proposes an assessment model based on the life-cycle of CTT projects, covering the initial cooperation relationship, project management during the mid-term, and technological achievements at the end. The model was evaluated by 14 experts first and then validated through two CTT projects in China. Gray Relation Analysis was employed to calculate the weights of different factors based on their relative importance, while the Dempster–Shafer theory was utilized to combine evidence from various sources and address the uncertainty in the assessment. The results of the case analysis indicate that the attitudes of universities and enterprises are considered critical in influencing the success of CTT projects, while management issues that arise during the projects can pose potential risks. This research serves as an applied exploration and has three functions. Firstly, the model can be used as a feasibility study before the project commences. Secondly, it can be utilized to analyze and improve potential issues during the project. Finally, it can be used for a post-project experience summary. Full article

(This article belongs to the Special Issue Multi-criteria Decision Making and Data Mining, 2nd Edition)

25 pages, 2266 KiB

Open AccessArticle

Fuzzy-Augmented Model Reference Adaptive PID Control Law Design for Robust Voltage Regulation in DC–DC Buck Converters

by Omer Saleem, Khalid Rasheed Ahmad and Jamshed Iqbal

Mathematics 2024, 12(12), 1893; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121893 - 18 Jun 2024

Viewed by 224

Abstract

This paper presents a novel fuzzy-augmented model reference adaptive voltage regulation strategy for the DC–DC buck converters to enhance their resilience against random input variations and load-step transients. The ubiquitous proportional-integral-derivative (PID) controller is employed as the baseline scheme, whose gains are tuned [...] Read more.

This paper presents a novel fuzzy-augmented model reference adaptive voltage regulation strategy for the DC–DC buck converters to enhance their resilience against random input variations and load-step transients. The ubiquitous proportional-integral-derivative (PID) controller is employed as the baseline scheme, whose gains are tuned offline via a pre-calibrated linear-quadratic optimization scheme. However, owing to the inefficacy of the fixed-gain PID controller against parametric disturbances, it is retrofitted with a model reference adaptive controller that uses Lyapunov gain adaptation law for the online modification of PID gains. The adaptive controller is also augmented with an auxiliary fuzzy self-regulation system that acts as a superior regulator to dynamically update the adaptation rates of the Lyapunov gain adaptation law as a nonlinear function of the system’s classical error and its normalized acceleration. The proposed fuzzy system utilizes the knowledge of the system’s relative rate to execute better self-regulation of the adaptation rates, which in turn, flexibly steers the adaptability and response speed of the controller as the error conditions change. The propositions above are validated by performing tailored hardware experiments on a low-power DC–DC buck converter prototype. The experimental results validate the improved reference tracking and disturbance rejection ability of the proposed control law compared to the fixed PID controller. Full article

(This article belongs to the Special Issue Control, Optimization and Intelligent Computing in Energy)

11 pages, 3909 KiB

Open AccessArticle

Solution of the Elliptic Interface Problem by a Hybrid Mixed Finite Element Method

by Yuhan Wang, Peiyao Wang, Rongpei Zhang and Jia Liu

Mathematics 2024, 12(12), 1892; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121892 - 18 Jun 2024

Viewed by 112

Abstract

This paper addresses the elliptic interface problem involving jump conditions across the interface. We propose a hybrid mixed finite element method on the triangulation where the interfaces are aligned with the mesh. The second-order elliptic equation is initially decomposed into two equations by [...] Read more.

This paper addresses the elliptic interface problem involving jump conditions across the interface. We propose a hybrid mixed finite element method on the triangulation where the interfaces are aligned with the mesh. The second-order elliptic equation is initially decomposed into two equations by introducing a gradient term. Subsequently, weak formulations are applied to these equations. Scheme continuity is enforced using the Lagrange multiplier technique. Finally, we derive an explicit formula for the entries of the matrix equation representing Lagrange multiplier unknowns resulting from hybridization. The method yields approximations of all variables, including the solution and gradient, with optimal order. Furthermore, the matrix representing the final linear algebra systems is not only symmetric but also positive definite. Numerical examples convincingly demonstrate the effectiveness of the hybrid mixed finite element method in addressing elliptic interface problems. Full article

(This article belongs to the Section Mathematics and Computer Science)

17 pages, 4881 KiB

Open AccessArticle

Dynamic Analysis and FPGA Implementation of a New Linear Memristor-Based Hyperchaotic System with Strong Complexity

by Lijuan Chen, Mingchu Yu, Jinnan Luo, Jinpeng Mi, Kaibo Shi and Song Tang

Mathematics 2024, 12(12), 1891; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121891 - 18 Jun 2024

Viewed by 109

Abstract

Chaotic or hyperchaotic systems have a significant role in engineering applications such as cryptography and secure communication, serving as primary signal generators. To ensure stronger complexity, memristors with sufficient nonlinearity are commonly incorporated into the system, suffering a limitation on the physical implementation. [...] Read more.

Chaotic or hyperchaotic systems have a significant role in engineering applications such as cryptography and secure communication, serving as primary signal generators. To ensure stronger complexity, memristors with sufficient nonlinearity are commonly incorporated into the system, suffering a limitation on the physical implementation. In this paper, we propose a new four-dimensional (4D) hyperchaotic system based on the linear memristor which is the most straightforward to implement physically. Through numerical studies, we initially demonstrate that the proposed system exhibits robust hyperchaotic behaviors under typical parameter conditions. Subsequently, we theoretically prove the existence of solid hyperchaos by combining the topological horseshoe theory with computer-assisted research. Finally, we present the realization of the proposed hyperchaotic system using an FPGA platform. This proposed system possesses two key properties. Firstly, this work suggests that the simplest memristor can also induce strong nonlinear behaviors, offering a new perspective for constructing memristive systems. Secondly, compared to existing systems, our system not only has the largest Kaplan-Yorke dimension, but also has clear advantages in areas related to engineering applications, such as the parameter range and signal bandwidth, indicating promising potential in engineering applications. Full article

(This article belongs to the Special Issue Advance in Control Theory and Optimization)

► Show Figures

Figure 1

23 pages, 417 KiB

Open AccessArticle

Multivariate Universal Local Linear Kernel Estimators in Nonparametric Regression: Uniform Consistency

by Yuliana Linke, Igor Borisov, Pavel Ruzankin, Vladimir Kutsenko, Elena Yarovaya and Svetlana Shalnova

Mathematics 2024, 12(12), 1890; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121890 - 18 Jun 2024

Viewed by 120

Abstract

In this paper, for a wide class of nonparametric regression models, new local linear kernel estimators are proposed that are uniformly consistent under close-to-minimal and visual conditions on design points. These estimators are universal in the sense that their designs can be either [...] Read more.

In this paper, for a wide class of nonparametric regression models, new local linear kernel estimators are proposed that are uniformly consistent under close-to-minimal and visual conditions on design points. These estimators are universal in the sense that their designs can be either fixed and not necessarily satisfying the traditional regularity conditions, or random, while not necessarily consisting of independent or weakly dependent random variables. With regard to the design elements, only dense filling of the regression function domain with the design points without any specification of their correlation is assumed. This study extends the dense data methodology and main results of the authors’ previous work for the case of regression functions of several variables. Full article

(This article belongs to the Section Probability and Statistics)

25 pages, 21068 KiB

Open AccessFeature PaperArticle

Change-Point Detection in Functional First-Order Auto-Regressive Models

by Algimantas Birbilas and Alfredas Račkauskas

Mathematics 2024, 12(12), 1889; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121889 (registering DOI) - 18 Jun 2024

Viewed by 242

Abstract

A sample of continuous random functions with auto-regressive structures and possible change-point of the means are considered. We present test statistics for the change-point based on a functional of partial sums. To study their asymptotic behavior, we prove functional limit theorems for polygonal [...] Read more.

A sample of continuous random functions with auto-regressive structures and possible change-point of the means are considered. We present test statistics for the change-point based on a functional of partial sums. To study their asymptotic behavior, we prove functional limit theorems for polygonal line processes in the space of continuous functions. For some situations, we use a block bootstrap procedure to construct the critical region and provide applications. We also study the finite sample behavior via simulations. Eventually, we apply the statistics to a telecommunications data sample. Full article

► Show Figures

Figure 1

22 pages, 400 KiB

Open AccessArticle

Two Block Splitting Iteration Methods for Solving Complex Symmetric Linear Systems from Complex Helmholtz Equation

by Yanan Zhu, Naimin Zhang and Zhen Chao

Mathematics 2024, 12(12), 1888; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121888 (registering DOI) - 18 Jun 2024

Viewed by 134

Abstract

In this paper, we study the improved block splitting (IBS) iteration method and its accelerated variant, the accelerated improved block splitting (AIBS) iteration method, for solving linear systems of equations stemming from the discretization of the complex Helmholtz equation. We conduct a comprehensive [...] Read more.

In this paper, we study the improved block splitting (IBS) iteration method and its accelerated variant, the accelerated improved block splitting (AIBS) iteration method, for solving linear systems of equations stemming from the discretization of the complex Helmholtz equation. We conduct a comprehensive convergence analysis and derive optimal iteration parameters aimed at minimizing the spectral radius of the iteration matrix. Through numerical experiments, we validate the efficiency of both iteration methods. Full article

(This article belongs to the Special Issue Advanced Research in Numerical Analysis of Partial Differential Equations)

► Show Figures

Figure 1

21 pages, 314 KiB

Open AccessArticle

Analyzing Interval-Censored Recurrence Event Data with Adjusting Informative Observation Times by Propensity Scores

by Ni Li, Meiting Lin and Yakun Shang

Mathematics 2024, 12(12), 1887; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121887 (registering DOI) - 18 Jun 2024

Viewed by 178

Abstract

In this paper, we discuss the statistical inference of interval-censored recurrence event data under an informative observation process. We establish an additive semiparametric mean model for the recurrence event process. Since the observation process may contain relevant information about potential underlying recurrence event [...] Read more.

In this paper, we discuss the statistical inference of interval-censored recurrence event data under an informative observation process. We establish an additive semiparametric mean model for the recurrence event process. Since the observation process may contain relevant information about potential underlying recurrence event processes, which leads to confounding bias, therefore, we introduced a propensity score into the additive semiparametric mean model to adjust for confounding bias, which possibly exists. Furthermore, the estimation equations were used to estimate the parameters of the covariate effects, and the asymptotic normality of the estimator under large samples is proven. Through simulation studies, we illustrated that the proposed method works well, and it was applied to the analysis of bladder cancer data. Full article

(This article belongs to the Special Issue Advances in Statistical Methods with Applications)

23 pages, 1911 KiB

Open AccessArticle

DFNet: Decoupled Fusion Network for Dialectal Speech Recognition

by Qianqiao Zhu, Lu Gao and Ling Qin

Mathematics 2024, 12(12), 1886; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121886 - 17 Jun 2024

Viewed by 244

Abstract

Deep learning is often inadequate for achieving effective dialect recognition in situations where data are limited and model training is complex. Differences between Mandarin and dialects, such as the varied pronunciation variants and distinct linguistic features of dialects, often result in a significant [...] Read more.

Deep learning is often inadequate for achieving effective dialect recognition in situations where data are limited and model training is complex. Differences between Mandarin and dialects, such as the varied pronunciation variants and distinct linguistic features of dialects, often result in a significant decline in recognition performance. In addition, existing work often overlooks the similarities between Mandarin and its dialects and fails to leverage these connections to enhance recognition accuracy. To address these challenges, we propose the Decoupled Fusion Network (DFNet). This network extracts acoustic private and shared features of different languages through feature decoupling, which enhances adaptation to the uniqueness and similarity of these two speech patterns. In addition, we designed a heterogeneous information-weighted fusion module to effectively combine the decoupled Mandarin and dialect features. This strategy leverages the similarity between Mandarin and its dialects, enabling the sharing of multilingual information, and notably enhance the model’s recognition capabilities on low-resource dialect data. An evaluation of our method on the Henan and Guangdong datasets shows that the DFNet performance has improved by 2.64% and 2.68%, respectively. Additionally, a significant number of ablation comparison experiments demonstrate the effectiveness of the method. Full article

(This article belongs to the Special Issue Complex Network Modeling in Artificial Intelligence Applications)

► Show Figures

Figure 1

19 pages, 22639 KiB

Open AccessArticle

Fast Semi-Supervised t-SNE for Transfer Function Enhancement in Direct Volume Rendering-Based Medical Image Visualization

by Walter Serna-Serna, Andrés Marino Álvarez-Meza and Álvaro Orozco-Gutiérrez

Mathematics 2024, 12(12), 1885; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121885 - 17 Jun 2024

Viewed by 242

Abstract

Magnetic resonance imaging and computed tomography produce three-dimensional volumetric medical images. While a scalar value represents each individual volume element, or voxel, volumetric data are characterized by features derived from groups of neighboring voxels and their inherent relationships, which may vary depending on [...] Read more.

Magnetic resonance imaging and computed tomography produce three-dimensional volumetric medical images. While a scalar value represents each individual volume element, or voxel, volumetric data are characterized by features derived from groups of neighboring voxels and their inherent relationships, which may vary depending on the specific clinical application. Labeled samples are also required in most applications, which can be problematic for large datasets such as medical images. We propose a direct volume rendering (DVR) framework based on multi-scale dimensionality reduction neighbor embedding that generates two-dimensional transfer function (TF) domains. In this way, we present FSS.t-SNE, a fast semi-supervised version of the t-distributed stochastic neighbor embedding (t-SNE) method that works over hundreds of thousands of voxels without the problem of crowding and with better separation in a 2D histogram compared to traditional TF domains. Our FSS.t-SNE scatters voxels of the same sub-volume in a wider region through multi-scale neighbor embedding, better preserving both local and global data structures and allowing for its internal exploration based on the original features of the multi-dimensional space, taking advantage of the partially provided labels. Furthermore, FSS.t-SNE untangles sample paths among sub-volumes, allowing us to explore edges and transitions. In addition, our approach employs a Barnes–Hut approximation to reduce computational complexity from

O (N^{2})

(t-SNE) to

O (N l o g N)

. Although we require the additional step of generating the 2D TF domain from multiple features, our experiments show promising performance in volume segmentation and visual inspection. Full article

(This article belongs to the Special Issue Deep Learning Methods for Biomedical and Medical Images)

► Show Figures

Figure 1

19 pages, 613 KiB

Open AccessArticle

A Parallel Optimization Method for Robustness Verification of Deep Neural Networks

by Renhao Lin, Qinglei Zhou, Xiaofei Nan and Tianqing Hu

Mathematics 2024, 12(12), 1884; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121884 - 17 Jun 2024

Viewed by 190

Abstract

Deep neural networks (DNNs) have gained considerable attention for their expressive capabilities, but unfortunately they have serious robustness risks. Formal verification is an important technique to ensure network reliability. However, current verification techniques are unsatisfactory in time performance, which hinders the practical applications. [...] Read more.

Deep neural networks (DNNs) have gained considerable attention for their expressive capabilities, but unfortunately they have serious robustness risks. Formal verification is an important technique to ensure network reliability. However, current verification techniques are unsatisfactory in time performance, which hinders the practical applications. To address this issue, we propose an efficient optimization method based on parallel acceleration with more computing resources. The method involves the speedup configuration of a partition-based verification aligned with the structures and robustness formal specifications of DNNs. A parallel verification framework is designed specifically for neural network verification systems, which integrates various auxiliary modules and accommodates diverse verification modes. The efficient parallel scheduling of verification queries within the framework enhances resource utilization and enables the system to process a substantial volume of verification tasks. We conduct extensive experiments on multiple commonly used verification benchmarks to demonstrate the rationality and effectiveness of the proposed method. The results show that higher efficiency is achieved after parallel optimization integration. Full article

(This article belongs to the Topic Adversarial Machine Learning: Theories and Applications)

20 pages, 902 KiB

Open AccessArticle

A Consensus-Based 360 Degree Feedback Evaluation Method with Linguistic Distribution Assessments

by Chuanhao Fan, Jiaxin Wang, Yan Zhu and Hengjie Zhang

Mathematics 2024, 12(12), 1883; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121883 - 17 Jun 2024

Viewed by 184

Abstract

The 360 degree feedback evaluation method is a multidimensional, comprehensive assessment method. Evaluators may hesitate among multiple evaluation values and be simultaneously constrained by the biases and cognitive errors of the evaluators, evaluation results are prone to unfairness and conflicts. To overcome these [...] Read more.

The 360 degree feedback evaluation method is a multidimensional, comprehensive assessment method. Evaluators may hesitate among multiple evaluation values and be simultaneously constrained by the biases and cognitive errors of the evaluators, evaluation results are prone to unfairness and conflicts. To overcome these issues, this paper proposes a consensus-based 360 degree feedback evaluation method with linguistic distribution assessments. Firstly, evaluators provide evaluation information in the form of linguistic distribution. Secondly, utilizing an enhanced ordered weighted averaging (OWA) operator, the model aggregates multi-source evaluation information to handle biased evaluation information effectively. Subsequently, a consensus-reaching process is established to coordinate conflicting viewpoints among the evaluators, and a feedback adjustment mechanism is designed to guide evaluators in refining their evaluation information, facilitating the attainment of a unanimous evaluation outcome. Finally, the improved 360 degree feedback evaluation method was applied to the performance evaluation of the project leaders in company J, thereby validating the effectiveness and rationality of the method. Full article

(This article belongs to the Special Issue Advances in Fuzzy Decision Theory and Applications, 2nd Edition)

16 pages, 4304 KiB

Open AccessArticle

PDE-Constrained Scale Optimization Selection for Feature Detection in Remote Sensing Image Matching

by Yunchao Peng, Bin Zhou and Feng Qi

Mathematics 2024, 12(12), 1882; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121882 - 17 Jun 2024

Viewed by 211

Abstract

Feature detection and matching is the key technique for remote sensing image processing and related applications. In this paper, a PDE-constrained optimization model is proposed to determine the scale levels advantageous for feature detection. A variance estimation technique is introduced to treat the [...] Read more.

Feature detection and matching is the key technique for remote sensing image processing and related applications. In this paper, a PDE-constrained optimization model is proposed to determine the scale levels advantageous for feature detection. A variance estimation technique is introduced to treat the observation optical images polluted by additive zero-mean Gaussian noise and determine the parameter of a nonlinear scale space governed by the partial differential equation. Additive Operator Splitting is applied to efficiently solve the PDE constraint, and an iterative algorithm is proposed to approximate the optimal subset of the original scale level set. The selected levels are distributed more uniformly in the total variation sense and helpful for generating more accurate and robust feature points. The experimental results show that the proposed method can achieve about a 30% improvement in the number of correct matches with only a small increase in time cost. Full article

(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering, 3rd Edition)

► Show Figures

Figure 1

26 pages, 2715 KiB

Open AccessArticle

Hybrid Genetic Algorithm and Tabu Search for Solving Preventive Maintenance Scheduling Problem for Cogeneration Plants

by Khaled Alhamad and Yousuf Alkhezi

Mathematics 2024, 12(12), 1881; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121881 - 17 Jun 2024

Viewed by 209

Abstract

Preventive Maintenance (PM) is a periodic maintenance strategy that has great results for devices in extending their lives, increasing productivity, and, most importantly, helping to avoid unexpected breakdowns and their costly consequences. Preventive maintenance scheduling (PMS) is determining the time for carrying out [...] Read more.

Preventive Maintenance (PM) is a periodic maintenance strategy that has great results for devices in extending their lives, increasing productivity, and, most importantly, helping to avoid unexpected breakdowns and their costly consequences. Preventive maintenance scheduling (PMS) is determining the time for carrying out PM, and it represents a sensitive issue in terms of impact on production if the time for the PM process is not optimally distributed. This study employs hybrid heuristic methods, integrating Genetic Algorithm (GA) and Tabu Search (TS), to address the PMS problem. Notably, the search for an optimal solution remained elusive with GA alone until the inclusion of TS. The resultant optimal solution is achieved swiftly, surpassing the time benchmarks set by conventional methods like integer programming and nonlinear integer programming. A comparison with a published article that used metaheuristics was also applied in order to evaluate the effectiveness of the proposed hybrid approach in terms of solution quality and convergence speed. Moreover, sensitivity analysis underscores the robustness and efficacy of the hybrid approach, consistently yielding optimal solutions across diverse scenarios. The schedule created exceeds standards set by waterworks experts, yielding significant water and electricity surpluses—16.6% and 12.1%, respectively—while simultaneously matching or surpassing total production levels. This method can be used for power plants in private or public sectors to generate an optimal PMS, save money, and avoid water or electricity cuts. In summary, this hybrid approach offers an efficient and effective solution for optimizing PMS, presenting opportunities for enhancement across various industries. Full article

► Show Figures

Figure 1

15 pages, 1538 KiB

Open AccessArticle

Adaptive Neural Network Prescribed Time Control for Constrained Multi-Robotics Systems with Parametric Uncertainties

by Ruizhi Tang, Hai Lin, Zheng Liu, Xiaoyang Zhou and Yixiang Gu

Mathematics 2024, 12(12), 1880; https://0-doi-org.brum.beds.ac.uk/10.3390/math12121880 - 17 Jun 2024

Viewed by 210

Abstract

This study designed an adaptive neural network (NN) control method for a category of multi-robotic systems with parametric uncertainties. In practical engineering applications, systems commonly face design challenges due to uncertainties in their parameters. Especially when a system’s parameters are completely unknown, the [...] Read more.

This study designed an adaptive neural network (NN) control method for a category of multi-robotic systems with parametric uncertainties. In practical engineering applications, systems commonly face design challenges due to uncertainties in their parameters. Especially when a system’s parameters are completely unknown, the unpredictability caused by parametric uncertainties may increase control complexity, and even cause system instability. To address these problems, an adaptive NN compensation mechanism is proposed. Moreover, using backstepping and barrier Lyapunov functions (BLFs), guarantee that state constraints can be ensured. With the aid of the transform function, systems’ convergence speeds were greatly improved. Under the implemented control strategy, the prescribed time control of multi-robotic systems with parametric uncertainties under the prescribed performance was achieved. Finally, the efficacy of the proposed control strategy was verified through the application of several cases. Full article

(This article belongs to the Topic Distributed Optimization for Control)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Mathematics, Volume 12, Issue 12 (June-2 2024) – 136 articles

Further Information

Guidelines

MDPI Initiatives

Follow MDPI