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Mathematics, Volume 12, Issue 7 (April-1 2024) – 193 articles

Cover Story (view full-size image): In this paper, we consider the strong convergence of Lp-norms (p ≥ 1) of a kernel estimator of a cumulative distribution function (CDF). Under some mild conditions, the law of the iterated logarithm (LIL) for the Lp-norms of empirical processes is extended to the kernel estimator of the CDF. View this paper
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15 pages, 299 KiB  
Article
A collection of seminorms linking the A-numerical radius and the operator A-seminorm
by Salma Aljawi, Kais Feki and Zakaria Taki
Mathematics 2024, 12(7), 1122; https://doi.org/10.3390/math12071122 - 8 Apr 2024
Viewed by 486
Abstract
We investigate a novel operator seminorm, QA,mλ,f, for an A-bounded operator Q, where A is a positive operator on a complex Hilbert space (K,·,·). This [...] Read more.
We investigate a novel operator seminorm, QA,mλ,f, for an A-bounded operator Q, where A is a positive operator on a complex Hilbert space (K,·,·). This seminorm is defined using a continuous increasing and bijective function f:R+R+ and an interpolational path mλ of the symmetric mean m. Specifically, QA,mλ,f=supf1fQy,yAmλfQyA:yK,yA=1, where f1 represents the reciprocal function of f, and ·,·A and ·A denote the semi-inner product and seminorm, respectively, induced by A on K. We explore various bounds and relationships associated with this new concept, establishing connections with existing literature. Full article
13 pages, 1882 KiB  
Article
Efficient Fourth-Order Weights in Kernel-Type Methods without Increasing the Stencil Size with an Application in a Time-Dependent Fractional PDE Problem
by Tao Liu and Stanford Shateyi
Mathematics 2024, 12(7), 1121; https://doi.org/10.3390/math12071121 - 8 Apr 2024
Viewed by 539
Abstract
An effective strategy to enhance the convergence order of nodal approximations in interpolation or PDE problems is to increase the size of the stencil, albeit at the cost of increased computational burden. In this study, our goal is to improve the convergence orders [...] Read more.
An effective strategy to enhance the convergence order of nodal approximations in interpolation or PDE problems is to increase the size of the stencil, albeit at the cost of increased computational burden. In this study, our goal is to improve the convergence orders for approximating the first and second derivatives of sufficiently differentiable functions using the radial basis function-generated Hermite finite-difference (RBF-HFD) scheme. By utilizing only three equally spaced points in 1D, we are able to boost the convergence rate to four. Extensive tests have been conducted to demonstrate the effectiveness of the proposed theoretical weighting coefficients in solving interpolation and PDE problems. Full article
(This article belongs to the Special Issue Computational Mathematics and Numerical Analysis)
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19 pages, 1394 KiB  
Article
A Blockchain-Based Secure Sharing Scheme for Electrical Impedance Tomography Data
by Ruwen Zhao, Chuanpei Xu, Zhibin Zhu and Wei Mo
Mathematics 2024, 12(7), 1120; https://doi.org/10.3390/math12071120 - 8 Apr 2024
Viewed by 567
Abstract
Real-time electrical impedance tomography (EIT) data sharing is becoming increasingly necessary, due to the extensive use of EIT technology in various sectors, including material analysis, biomedicine, and industrial process monitoring. The prevalence of portable EIT equipment and remote imaging technology has led to [...] Read more.
Real-time electrical impedance tomography (EIT) data sharing is becoming increasingly necessary, due to the extensive use of EIT technology in various sectors, including material analysis, biomedicine, and industrial process monitoring. The prevalence of portable EIT equipment and remote imaging technology has led to a predominance of centralized storage, Internet protocol transmission, and certificates from certificate authorities (CA) in telemedicine data. This has resulted in compromised data security, network communication delays, high CA maintenance costs, increased risks of medical data privacy breaches, and low security. Therefore, this paper offers a consortia blockchain-based method for exchanging EIT data that addresses security and integrity concerns during data storage and exchange, while maintaining transparency and traceability. Proprietary re-encryption techniques are employed to guarantee traceability when exchanging anonymous data, enabling precise control over data access. This scheme serves to protect both data and identity privacy, as well as to trace the actual identity of potential malicious users, while also thwarting any coordinated efforts between partially trusted parties and data requesters seeking unauthorized access to confidential information. Additionally, a combination of blockchain and InterPlanetary File System (IPFS) distributed storage technology is utilized to ease the burden of EIT data storage. The feasibility and effectiveness of the proposed solution were validated through a series of experiments, demonstrating its ability to effectively prevent data tampering and misuse, reduce data management costs, and enhance the efficiency and quality of data sharing. Full article
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18 pages, 846 KiB  
Article
Distantly Supervised Explainable Stance Detection via Chain-of-Thought Supervision
by Daijun Ding, Genan Dai, Cheng Peng, Xiaojiang Peng, Bowen Zhang and Hu Huang
Mathematics 2024, 12(7), 1119; https://doi.org/10.3390/math12071119 - 8 Apr 2024
Viewed by 524
Abstract
Investigating public attitudes on social media is crucial for opinion mining systems. Stance detection aims to predict the attitude towards a specific target expressed in a text. However, effective neural stance detectors require substantial training data, which are challenging to curate due to [...] Read more.
Investigating public attitudes on social media is crucial for opinion mining systems. Stance detection aims to predict the attitude towards a specific target expressed in a text. However, effective neural stance detectors require substantial training data, which are challenging to curate due to the dynamic nature of social media. Moreover, deep neural networks (DNNs) lack explainability, rendering them unsuitable for scenarios requiring explanations. We propose a distantly supervised explainable stance detection framework (DS-ESD), comprising an instruction-based chain-of-thought (CoT) method, a generative network, and a transformer-based stance predictor. The CoT method employs prompt templates to extract stance detection explanations from a very large language model (VLLM). The generative network learns the input-explanation mapping, and a transformer-based stance classifier is trained with VLLM-annotated stance labels, implementing distant supervision. We propose a label rectification strategy to mitigate the impact of erroneous labels. Experiments on three benchmark datasets showed that our model outperformed the compared methods, validating its efficacy in stance detection tasks. This research contributes to the advancement of explainable stance detection frameworks, leveraging distant supervision and label rectification strategies to enhance performance and interpretability. Full article
(This article belongs to the Section Mathematics and Computer Science)
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12 pages, 9015 KiB  
Article
Robust Control for Underactuated Fixed-Wing Unmanned Aerial Vehicles
by Tianyi Wang, Luxin Zhang and Zhihua Chen
Mathematics 2024, 12(7), 1118; https://doi.org/10.3390/math12071118 - 8 Apr 2024
Viewed by 501
Abstract
Dynamic surface control (DSC) is a recognized nonlinear control approach for high-order systems. However, as the complexity of the system increases and the first-order filter (FOF) is introduced, there exists a singularity problem, i.e., the control input will reach infinity. This limits the [...] Read more.
Dynamic surface control (DSC) is a recognized nonlinear control approach for high-order systems. However, as the complexity of the system increases and the first-order filter (FOF) is introduced, there exists a singularity problem, i.e., the control input will reach infinity. This limits the application of the DSC algorithm to a class of real-world systems with complex dynamics. To address the problem of singularity, we present a novel DSC approach called nonsingular dynamic surface control (NDSC), which completely avoids the singularity problem and significantly improves the overall control performance. NDSC includes a nonsingular hypersurface, which is constructed by the error between system states and virtual control inputs. Then the nonsingular hypersurface will be applied to derive the corresponding control law with the aid of the DSC approach to ensure the output of the system can track arbitrary desired trajectories. NDSC has the following novel features: (1) finite time asymptotic stabilization can be guaranteed; (2) the performance of NDSC is insensitive to the FOF’s parameter variation once the maximum tracking error of FOF is bounded, which significantly reduces reliance on the control sampling frequency. We thoroughly evaluate the proposed NDSC algorithm in an unmanned aerial vehicle (UAV) system with an underactuated nature. Finally, the simulation results illustrate and highlight the effectiveness and superiority of the proposed control algorithm. Full article
(This article belongs to the Special Issue Dynamics and Control of Complex Systems and Robots)
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17 pages, 4171 KiB  
Article
Trends and Paradoxes of Competitive Evolution in the Predation Mechanism
by Evariste Sanchez-Palencia and M. A. Aziz-Alaoui
Mathematics 2024, 12(7), 1117; https://doi.org/10.3390/math12071117 - 8 Apr 2024
Viewed by 464
Abstract
We give a series of numerical examples of competitive evolution in the predation system, showing in some cases how the choice is made to increase the efficiency of the predation mechanism (or other significant parameters) to the detriment of populations (both of prey [...] Read more.
We give a series of numerical examples of competitive evolution in the predation system, showing in some cases how the choice is made to increase the efficiency of the predation mechanism (or other significant parameters) to the detriment of populations (both of prey and predators). We then develop the mathematical theory that enables us to understand the causality involved, and we identify a trend towards the emergence of the functional predation mechanism as such (and not of populations of the species involved). The realization of this trend only takes place when the conditions for it are offered by the hazards proposed to successive competitive choices. The logical structure of this trend is similar to that of the “tendency of rate of profit to fall” in certain economic models. Full article
(This article belongs to the Special Issue Advances in Bio-Dynamics and Applications)
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21 pages, 352 KiB  
Article
Global Solution and Stability of a Haptotaxis Mathematical Model for Complex MAP
by Hongbing Chen and Fengling Jia
Mathematics 2024, 12(7), 1116; https://doi.org/10.3390/math12071116 - 8 Apr 2024
Viewed by 430
Abstract
A critical function of polymeric matrices in biological systems is to exert selective control over the transport of thousands of nanoparticulate species. Utilizing “third-party” molecular anchors to crosslink nanoparticulates to the matrix is an effective strategy, and a trapped nanoparticulate formed a desired [...] Read more.
A critical function of polymeric matrices in biological systems is to exert selective control over the transport of thousands of nanoparticulate species. Utilizing “third-party” molecular anchors to crosslink nanoparticulates to the matrix is an effective strategy, and a trapped nanoparticulate formed a desired complex MAP that is necessary to keep the nanoparticulate immobilized at any given time. In this paper, the global solution and stability of a parabolic–ordinary-parabolic haptotaxis system to complex MAP are studied. First, the existence of a local classical solution to system (4) has been observed using fixed point argument and parabolic Schauder estimates. Furthermore, some a priori estimates that can raise the regularity estimate of the solution for the relatively complicated first equation of system (3) from Lρ to L2ρ (ρ1) are given; then, the local classic solution can thus extend to the global classic solution when the space dimension N3. Lastly, by using various analytical methods, a threshold value ξ00(ξ00<0) is found, such that positive constant steady state (u,v,w) becomes unstable when ξ<ξ00. Our results show that the haptotaxis plays a crucial role in determining the stability to the model (3), that is, it can have a destabilizing effect. Full article
(This article belongs to the Special Issue Partial Differential Equation Theory and Its Applications)
21 pages, 491 KiB  
Article
A Novel Gaussian Process Surrogate Model with Expected Prediction Error for Optimization under Constraints
by Hongri Cong, Bo Wang and Zhe Wang
Mathematics 2024, 12(7), 1115; https://doi.org/10.3390/math12071115 - 8 Apr 2024
Viewed by 512
Abstract
Optimization, particularly constrained optimization problems (COPs), is fundamental in engineering, influencing various sectors with its critical role in enhancing design efficiency, reducing experimental costs, and shortening testing cycles. This study explores the challenges inherent in COPs, with a focus on developing efficient solution [...] Read more.
Optimization, particularly constrained optimization problems (COPs), is fundamental in engineering, influencing various sectors with its critical role in enhancing design efficiency, reducing experimental costs, and shortening testing cycles. This study explores the challenges inherent in COPs, with a focus on developing efficient solution methodologies under stringent constraints. Surrogate models, especially Gaussian Process Regression (GPR), are pivotal in our approach, enabling the approximation of complex systems with reduced computational demand. We evaluate the efficacy of the Efficient Global Optimization (EGO) algorithm, which synergizes GPR with the Expected Improvement (EI) function, and further extend this framework to Constrained Expected Improvement (CEI) and our novel methodology Constrained Expected Prediction Error (CEPE). We demonstrate the effectiveness of these methodologies by numerical benchmark simulations and the real-world application of optimizing a Three-Bar Truss Design. In essence, the innovative CEPE approach promises a potent balance between solution accuracy and computational prowess, offering significant potential in the broader engineering field. Full article
(This article belongs to the Special Issue AI for Brain Science and Brain-Inspired Computing)
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11 pages, 272 KiB  
Article
Tolerance Interval for the Mixture Normal Distribution Based on Generalized Extreme Value Theory
by Junjun Jiao and Ruijie Guan
Mathematics 2024, 12(7), 1114; https://doi.org/10.3390/math12071114 - 8 Apr 2024
Viewed by 432
Abstract
For a common type of mixture distribution, namely the mixture normal distribution, existing methods for constructing its tolerance interval are unsatisfactory for cases of small sample size and large content. In this study, we propose a method to construct a tolerance interval for [...] Read more.
For a common type of mixture distribution, namely the mixture normal distribution, existing methods for constructing its tolerance interval are unsatisfactory for cases of small sample size and large content. In this study, we propose a method to construct a tolerance interval for the mixture normal distribution based on the generalized extreme value theory. The proposed method is implemented on simulated as well as real-life datasets and its performance is compared with the existing methods. Full article
(This article belongs to the Section Probability and Statistics)
10 pages, 311 KiB  
Article
Hadamard Product of Monomial Ideals and the Hadamard Package
by Iman Bahmani Jafarloo, Cristiano Bocci and Elena Guardo
Mathematics 2024, 12(7), 1113; https://doi.org/10.3390/math12071113 - 8 Apr 2024
Viewed by 1001
Abstract
In this paper, we generalize and study the concept of Hadamard product of ideals of projective varieties to the case of monomial ideals. We have a research direction similar to the one of the join of monomial ideals contained in a paper of [...] Read more.
In this paper, we generalize and study the concept of Hadamard product of ideals of projective varieties to the case of monomial ideals. We have a research direction similar to the one of the join of monomial ideals contained in a paper of Sturmfels and Sullivant. In the second part of the paper, we give a brief tutorial on the Hadamard.m2 package of Macaulay2. Full article
(This article belongs to the Special Issue Advanced Algebraic Geometry and Applications)
2 pages, 432 KiB  
Correction
Correction: Jasim et al. Optimized Sizing of Energy Management System for Off-Grid Hybrid Solar/Wind/Battery/Biogasifier/Diesel Microgrid System. Mathematics 2023, 11, 1248
by Ali M. Jasim, Basil H. Jasim, Florin-Constantin Baiceanu and Bogdan-Constantin Neagu
Mathematics 2024, 12(7), 1112; https://doi.org/10.3390/math12071112 - 8 Apr 2024
Viewed by 313
Abstract
In the original publication [...] Full article
(This article belongs to the Special Issue Artificial Intelligence Techniques Applications on Power Systems)
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24 pages, 6320 KiB  
Article
Application of Dandelion Optimization Algorithm in Pattern Synthesis of Linear Antenna Arrays
by Jianhui Li, Yan Liu, Wanru Zhao and Tianning Zhu
Mathematics 2024, 12(7), 1111; https://doi.org/10.3390/math12071111 - 7 Apr 2024
Viewed by 667
Abstract
This paper introduces an application of the dandelion optimization (DO) algorithm in antenna arrays. This is the first time that the DO algorithm has been used for optimizing antenna arrays. For antenna array optimization, sidelobe level (SLL) and deep nulls are key technical [...] Read more.
This paper introduces an application of the dandelion optimization (DO) algorithm in antenna arrays. This is the first time that the DO algorithm has been used for optimizing antenna arrays. For antenna array optimization, sidelobe level (SLL) and deep nulls are key technical indicators. A lower SLL can improve the signal-to-noise ratio and reduce the impact of clutter signals outside the main beam. Deep nulls need to be aligned with the direction of interference to eliminate the influence of interference sources. The combination of the two can effectively improve the anti-interference ability of the entire system. Therefore, antenna arrays with ultra-low sidelobes and ultra-deep nulls are currently hot in the field of antenna array design and are also some of the key technologies needed to achieve modern high-performance radar systems. As a new type of evolutionary algorithm inspired by nature, the DO algorithm is inspired by the wind propagation behavior of dandelions in nature. This algorithm iteratively updates the population from three stages of ascent, descent, and landing, ultimately finding the optimal position. It has good optimization ability in solving complex problems such as those involving nonlinearity, discreteness, and non-convexity, and the antenna array pattern synthesis optimization problem belongs to multivariate nonlinear problems. Therefore, the DO algorithm can be effectively applied in the field of antenna array optimization. In this work, we use the following method to obtain an optimized pattern of a linear array with the lowest sidelobe level (SLL), null placement in particular directions, and a lower notch in particular directions: by controlling the antenna array’s element spacing and leaving the phase unchanged to optimize the current amplitudes and by controlling the excitation current and phase fixation of the antenna array and changing the element spacing. In the first and second examples, different algorithms are used to reduce the SLL of the antenna. In the first example, the DO algorithm reduces the SLL to −33.37 dB, which is 2.67 dB, 2.67 dB, 3.77 dB, 2.74 dB, and 2.52 dB lower than five other algorithms. In the second example, the SLL optimized by the DO algorithm is −42.56 dB, which is 5.04 dB and 1.48 dB lower than two other algorithms. In both examples, the DO algorithm reduces the SLL lower than other algorithms when the main lobe of the antenna is not significantly widened. Examples 3, 4, and 5 use the DO algorithm to optimize the amplitude of the current, generating deep nulls and deep notches in specific directions. In Example 3, the DO algorithm obtains a depth of nulls equal to −187.6 dB, which is 66.7 dB and 44.3 dB lower than that of the flower pollination algorithm (FPA) and the chaotic colony predation algorithm (CCPA), respectively. In Example 4, the deep null obtained by the DO algorithm is as low as −98.69 dB, which is 6.67 dB lower than the deep null obtained by the grey wolf optimization (GWO) algorithm. In Example 5, the deep notch obtained by the DO algorithm is as low as −63.1 dB, which is 6.4 dB and 1.9 dB lower than the spider monkey optimization (SMO) algorithm and the grasshopper optimization algorithm (GOA), respectively. The data prove that the DO algorithm produces deeper nulls and notches than other algorithms. The last two examples involve reducing sidelobe levels and generating deep nulls by optimizing the spacing between elements. In Example 5, the SLL obtained using the DO algorithm is −22.8766 dB, which is 0.1998 dB lower than the lowest SLL of −22.6768 dB among other algorithms. In Example 6, the SLL obtained using the DO algorithm is −20.1012 dB, and the null depth is −125.1 dB, which is 1.592 dB lower than the SLL obtained by the cat swarm optimization (CSO) algorithm and 19.1 dB lower than the deep null obtained by the GWO algorithm, respectively. In summary, the results of six simulation experiments indicate that the DO algorithm has better optimization ability in linear array optimization than other evolutionary algorithms. Full article
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14 pages, 891 KiB  
Article
The Conservative and Efficient Numerical Method of 2-D and 3-D Fractional Nonlinear Schrödinger Equation Using Fast Cosine Transform
by Peiyao Wang, Shangwen Peng, Yihao Cao and Rongpei Zhang
Mathematics 2024, 12(7), 1110; https://doi.org/10.3390/math12071110 - 7 Apr 2024
Viewed by 594
Abstract
This paper introduces a novel approach employing the fast cosine transform to tackle the 2-D and 3-D fractional nonlinear Schrödinger equation (fNLSE). The fractional Laplace operator under homogeneous Neumann boundary conditions is first defined through spectral decomposition. The difference matrix Laplace operator is [...] Read more.
This paper introduces a novel approach employing the fast cosine transform to tackle the 2-D and 3-D fractional nonlinear Schrödinger equation (fNLSE). The fractional Laplace operator under homogeneous Neumann boundary conditions is first defined through spectral decomposition. The difference matrix Laplace operator is developed by the second-order central finite difference method. Then, we diagonalize the difference matrix based on the properties of Kronecker products. The time discretization employs the Crank–Nicolson method. The conservation of mass and energy is proved for the fully discrete scheme. The advantage of this method is the implementation of the Fast Discrete Cosine Transform (FDCT), which significantly improves computational efficiency. Finally, the accuracy and effectiveness of the method are verified through two-dimensional and three-dimensional numerical experiments, solitons in different dimensions are simulated, and the influence of fractional order on soliton evolution is obtained; that is, the smaller the alpha, the lower the soliton evolution. Full article
(This article belongs to the Section Mathematical Physics)
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31 pages, 6086 KiB  
Article
A Case Study of Accident Analysis and Prevention for Coal Mining Transportation System Based on FTA-BN-PHA in the Context of Smart Mining Process
by Longlong He, Ruiyu Pan, Yafei Wang, Jiani Gao, Tianze Xu, Naqi Zhang, Yue Wu and Xuhui Zhang
Mathematics 2024, 12(7), 1109; https://doi.org/10.3390/math12071109 - 7 Apr 2024
Viewed by 550
Abstract
In the face of the increasing complexity of risk factors in the coal mining transportation system (CMTS) during the process of intelligent transformation, this study proposes a method for analyzing accidents in CMTS based on fault tree analysis (FTA) combined with Bayesian networks [...] Read more.
In the face of the increasing complexity of risk factors in the coal mining transportation system (CMTS) during the process of intelligent transformation, this study proposes a method for analyzing accidents in CMTS based on fault tree analysis (FTA) combined with Bayesian networks (BN) and preliminary hazard analysis (PHA). Firstly, the fault tree model of CMTS was transformed into a risk Bayesian network, and the inference results of the fault tree and Bayesian network were integrated to identify the key risk factors in the transportation system. Subsequently, based on the preliminary hazard analysis of these key risk factors, corresponding rectification measures and a risk control system construction plan are proposed. Finally, a case study was carried out on the X coal mine as a pilot mine to verify the feasibility of the method. The application of this method effectively identifies and evaluates potential risk factors in CMTS, providing a scientific basis for accident prevention. This research holds significant importance for the safety management and decision making of coal mine enterprises during the process of intelligent transformation and is expected to provide strong support for enhancing the safety and reliability of CMTS. Full article
(This article belongs to the Special Issue Mathematical Techniques and New ITs for Smart Manufacturing Systems)
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22 pages, 1528 KiB  
Article
Finite-Time Adaptive Synchronization and Fixed-Time Synchronization of Fractional-Order Memristive Cellular Neural Networks with Time-Varying Delays
by Yihong Liu and Yeguo Sun
Mathematics 2024, 12(7), 1108; https://doi.org/10.3390/math12071108 - 7 Apr 2024
Viewed by 409
Abstract
Asymptotic synchronization requires continuous external control of the system, which is unrealistic considering the cost of control. Adaptive control methods have strong robustness to uncertainties such as disturbances and unknowns. On the other hand, for finite-time synchronization, if the initial value of the [...] Read more.
Asymptotic synchronization requires continuous external control of the system, which is unrealistic considering the cost of control. Adaptive control methods have strong robustness to uncertainties such as disturbances and unknowns. On the other hand, for finite-time synchronization, if the initial value of the system is unknown, the synchronization time of the finite-time synchronization cannot be estimated. This paper explores the finite-time adaptive synchronization (FTAS) and fixed-time synchronization (FDTS) of fractional-order memristive cellular neural networks (FMCNNs) with time-varying delays (TVD). Utilizing the properties and principles of fractional order, we introduce a novel lemma. Based on this lemma and various analysis techniques, we establish new criteria to guarantee FTAS and FDTS of FMCNNs with TVD through the implementation of a delay-dependent feedback controller and fractional-order adaptive controller. Additionally, we estimate the upper bound of the synchronization setting time. Finally, numerical simulations are conducted to confirm the validity of the finite-time and fixed-time stability theorems. Full article
(This article belongs to the Special Issue Theory, Modeling and Applications of Fractional-Order Systems)
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20 pages, 4716 KiB  
Article
SSGCL: Simple Social Recommendation with Graph Contrastive Learning
by Zhihua Duan, Chun Wang and Wending Zhong
Mathematics 2024, 12(7), 1107; https://doi.org/10.3390/math12071107 - 7 Apr 2024
Viewed by 508
Abstract
As user–item interaction information is typically limited, collaborative filtering (CF)-based recommender systems often suffer from the data sparsity issue. To address this issue, recent recommender systems have turned to graph neural networks (GNNs) due to their superior performance in capturing high-order relationships. Furthermore, [...] Read more.
As user–item interaction information is typically limited, collaborative filtering (CF)-based recommender systems often suffer from the data sparsity issue. To address this issue, recent recommender systems have turned to graph neural networks (GNNs) due to their superior performance in capturing high-order relationships. Furthermore, some of these GNN-based recommendation models also attempt to incorporate other information. They either extract self-supervised signals to mitigate the data sparsity problem or employ social information to assist with learning better representations under a social recommendation setting. However, only a few methods can take full advantage of these different aspects of information. Based on some testing, we believe most of these methods are complex and redundantly designed, which may lead to sub-optimal results. In this paper, we propose SSGCL, which is a recommendation system model that utilizes both social information and self-supervised information. We design a GNN-based propagation strategy that integrates social information with interest information in a simple yet effective way to learn user–item representations for recommendations. In addition, a specially designed contrastive learning module is employed to take advantage of the self-supervised signals for a better user–item representation distribution. The contrastive learning module is jointly optimized with the recommendation module to benefit the final recommendation result. Experiments on several benchmark data sets demonstrate the significant improvement in performance achieved by our model when compared with baseline models. Full article
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16 pages, 8070 KiB  
Article
Ultrasound Computed Tomography Reflection Imaging with Coherence-Factor Beamforming for Breast Tumor Early Detection
by Zuoxun Hou, Ruichen Yuan, Zihao Wang, Xiaorui Wei, Chujian Ren, Jiale Zhou and Xiaolei Qu
Mathematics 2024, 12(7), 1106; https://doi.org/10.3390/math12071106 - 7 Apr 2024
Viewed by 535
Abstract
Breast cancer is a global health concern, emphasizing the need for early detection. However, current mammography struggles to effectively image dense breasts. Breast ultrasound can be an adjunctive method, but it is highly dependent on operator skill. Ultrasound computed tomography (USCT) reflection imaging [...] Read more.
Breast cancer is a global health concern, emphasizing the need for early detection. However, current mammography struggles to effectively image dense breasts. Breast ultrasound can be an adjunctive method, but it is highly dependent on operator skill. Ultrasound computed tomography (USCT) reflection imaging provides high-quality 3D images, but often uses delay-and-sum (DAS) beamforming, which limits its image quality. This article proposes the integration of coherence-factor (CF) beamforming into ultrasound computed tomography (USCT) reflection imaging to enhance image quality. CF assesses the focus quality of beamforming by analyzing the signal coherence across different channels, assigning higher weights to high-quality focus points and thereby improving overall image quality. Numerical simulations and phantom experiments using our built USCT prototype were conducted to optimize the imaging parameters and assess and compare the image quality of CF and DAS beamforming. Numerical simulations demonstrated that CF beamforming can significantly enhance image quality. Phantom experiments with our prototype revealed that CF beamforming significantly improves image resolution (from 0.35 mm to 0.14 mm) and increases contrast ratio (from 24.54 dB to 63.28 dB). The integration of CF beamforming into USCT reflection imaging represents a substantial improvement in image quality, offering promise for enhanced breast cancer detection and imaging capabilities. Full article
(This article belongs to the Special Issue Advanced Methods and Applications in Medical Informatics)
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7 pages, 231 KiB  
Article
On Fall-Colorable Graphs
by Shaojun Wang, Fei Wen, Guoxing Wang and Zepeng Li
Mathematics 2024, 12(7), 1105; https://doi.org/10.3390/math12071105 - 7 Apr 2024
Viewed by 376
Abstract
A fall k-coloring of a graph G is a proper k-coloring of G such that each vertex has at least one neighbor in each of the other color classes. A graph G which has a fall k-coloring is equivalent to [...] Read more.
A fall k-coloring of a graph G is a proper k-coloring of G such that each vertex has at least one neighbor in each of the other color classes. A graph G which has a fall k-coloring is equivalent to having a partition of the vertex set V(G) in k independent dominating sets. In this paper, we first prove that for any fall k-colorable graph G with order n, the number of edges of G is at least (n(k1)+r(kr))/2, where rn(modk) and 0rk1, and the bound is tight. Then, we obtain that if G is k-colorable (k2) and the minimum degree of G is at least k2k1n, then G is fall k-colorable and this condition of minimum degree is the best possible. Moreover, we give a simple proof for an NP-hard result of determining whether a graph is fall k-colorable, where k3. Finally, we show that there exist an infinite family of fall k-colorable planar graphs for k{5,6}. Full article
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11 pages, 255 KiB  
Article
A Full-Newton Step Interior-Point Method for Weighted Quadratic Programming Based on the Algebraic Equivalent Transformation
by Yongsheng Rao, Jianwei Su and Behrouz Kheirfam
Mathematics 2024, 12(7), 1104; https://doi.org/10.3390/math12071104 - 7 Apr 2024
Viewed by 490
Abstract
In this paper, a new full-Newton step feasible interior-point method for convex quadratic programming is presented and analyzed. The idea behind this method is to replace the complementarity condition with a non-negative weight vector and use the algebraic equivalent transformation for the obtained [...] Read more.
In this paper, a new full-Newton step feasible interior-point method for convex quadratic programming is presented and analyzed. The idea behind this method is to replace the complementarity condition with a non-negative weight vector and use the algebraic equivalent transformation for the obtained equation. Under the selection of appropriate parameters, the quadratic rate of convergence of the new algorithm is established. In addition, the iteration complexity of the algorithm is obtained. Finally, some numerical results are presented to demonstrate the practical performance of the proposed algorithm. Full article
(This article belongs to the Section Computational and Applied Mathematics)
17 pages, 6257 KiB  
Article
Real-Time Motorbike Detection: AI on the Edge Perspective
by Awais Akhtar, Rehan Ahmed, Muhammad Haroon Yousaf and Sergio A. Velastin
Mathematics 2024, 12(7), 1103; https://doi.org/10.3390/math12071103 - 7 Apr 2024
Viewed by 618
Abstract
Motorbikes are an integral part of transportation in emerging countries, but unfortunately, motorbike users are also one the most vulnerable road users (VRUs) and are engaged in a large number of yearly accidents. So, motorbike detection is very important for proper traffic surveillance, [...] Read more.
Motorbikes are an integral part of transportation in emerging countries, but unfortunately, motorbike users are also one the most vulnerable road users (VRUs) and are engaged in a large number of yearly accidents. So, motorbike detection is very important for proper traffic surveillance, road safety, and security. Most of the work related to bike detection has been carried out to improve accuracy. If this task is not performed in real-time then it loses practical significance, but little to none has been reported for its real-time implementation. In this work, we have looked at multiple real-time deployable cost-efficient solutions for motorbike detection using various state-of-the-art embedded edge devices. This paper discusses an investigation of a proposed methodology on five different embedded devices that include Jetson Nano, Jetson TX2, Jetson Xavier, Intel Compute Stick, and Coral Dev Board. Running the highly compute-intensive object detection model on edge devices (in real-time) is made possible by optimization. As a result, we have achieved inference rates on different devices that are twice as high as GPUs, with only a marginal drop in accuracy. Secondly, the baseline accuracy of motorbike detection has been improved by developing a custom network based on YoloV5 by introducing sparsity and depth reduction. Dataset augmentation has been applied at both image and object levels to enhance robustness of detection. We have achieved 99% accuracy as compared to the previously reported 97% accuracy, with better FPS. Additionally, we have provided a performance comparison of motorbike detection on the different embedded edge devices, for practical implementation. Full article
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3 pages, 150 KiB  
Editorial
Preface to: Submanifolds in Metric Manifolds
by Cristina E. Hretcanu
Mathematics 2024, 12(7), 1102; https://doi.org/10.3390/math12071102 - 7 Apr 2024
Viewed by 443
Abstract
The present editorial contains 11 research articles, published in the Special Issue entitled “Submanifolds in metric manifolds” of the MDPI mathematics journal, which cover a wide range of topics from differential geometry in relation to the theory and applications of the structure induced [...] Read more.
The present editorial contains 11 research articles, published in the Special Issue entitled “Submanifolds in metric manifolds” of the MDPI mathematics journal, which cover a wide range of topics from differential geometry in relation to the theory and applications of the structure induced on submanifolds by the structure defined on various ambient manifolds [...] Full article
(This article belongs to the Special Issue Submanifolds in Metric Manifolds)
20 pages, 592 KiB  
Article
Analysis of Queueing System with Dynamic Rating-Dependent Arrival Process and Price of Service
by C. D’Apice, A. N. Dudin, O. S. Dudina and R. Manzo
Mathematics 2024, 12(7), 1101; https://doi.org/10.3390/math12071101 - 6 Apr 2024
Viewed by 429
Abstract
We consider a multi-server queueing system with a visible queue and an arrival flow that is dynamically dependent on the system’s rating. This rating reflects the level of customer satisfaction with the quality and price of the provided service. A higher rating implies [...] Read more.
We consider a multi-server queueing system with a visible queue and an arrival flow that is dynamically dependent on the system’s rating. This rating reflects the level of customer satisfaction with the quality and price of the provided service. A higher rating implies a higher arrival rate, which motivates the service provider to increase the price of the service. A steady-state analysis of this system using the proposed mechanism for changing the rating and a threshold strategy for changing the price is performed. This is carried out via the consideration of a suitably constructed multidimensional Markov chain. The impact of the variation in the threshold defining the strategy for changing the price on the key performance indicators is numerically illustrated. The results can be used to make managerial decisions, leading to an increase in the effectiveness of system operations. Full article
(This article belongs to the Special Issue Advances in Queueing Theory, 2nd Edition)
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30 pages, 4023 KiB  
Article
Modeling Implied Volatility Surface Using B-Splines with Time-Dependent Coefficients Predicted by Tree-Based Machine Learning Methods
by Zihao Chen, Yuyang Li and Cindy Long Yu
Mathematics 2024, 12(7), 1100; https://doi.org/10.3390/math12071100 - 6 Apr 2024
Viewed by 471
Abstract
Implied volatility is known to have a string structure (smile curve) for a given time to maturity and can be captured by the B-spline. The parameters characterizing the curves can change over time, which complicates the modeling of the implied volatility surface. Although [...] Read more.
Implied volatility is known to have a string structure (smile curve) for a given time to maturity and can be captured by the B-spline. The parameters characterizing the curves can change over time, which complicates the modeling of the implied volatility surface. Although machine learning models could improve the in-sample fitting, they ignore the structure in common over time and might have poor prediction power. In response to these challenges, we propose a two-step procedure to model the dynamic implied volatility surface (IVS). In the first step, we construct the bivariate tensor-product B-spline (BTPB) basis to approximate cross-sectional structures, under which the surface can be represented by a vector of coefficients. In the second step, we allow for the time-dependent coefficients and model the dynamic coefficients with the tree-based method to provide more flexibility. We show that our approach has better performance than the traditional linear models (parametric models) and the tree-based machine learning methods (nonparametric models). The simulation study confirms that the tensor-product B-spline is able to capture the classical parametric model for IVS given different sample sizes and signal-to-noise ratios. The empirical study shows that our two-step approach outperforms the traditional parametric benchmark, nonparametric benchmark, and parametric benchmark with time-varying coefficients in predicting IVS for the S&P 500 index options in the US market. Full article
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13 pages, 313 KiB  
Article
On Linear Codes over Finite Singleton Local Rings
by Sami Alabiad, Alhanouf Ali Alhomaidhi and Nawal A. Alsarori
Mathematics 2024, 12(7), 1099; https://doi.org/10.3390/math12071099 - 6 Apr 2024
Cited by 1 | Viewed by 483
Abstract
The study of linear codes over local rings, particularly non-chain rings, imposes difficulties that differ from those encountered in codes over chain rings, and this stems from the fact that local non-chain rings are not principal ideal rings. In this paper, we present [...] Read more.
The study of linear codes over local rings, particularly non-chain rings, imposes difficulties that differ from those encountered in codes over chain rings, and this stems from the fact that local non-chain rings are not principal ideal rings. In this paper, we present and successfully establish a new approach for linear codes of any finite length over local rings that are not necessarily chains. The main focus of this study is to produce generating characters, MacWilliams identities and generator matrices for codes over singleton local Frobenius rings of order 32. To do so, we first start by characterizing all singleton local rings of order 32 up to isomorphism. These rings happen to have strong connections to linear binary codes and Z4 codes, which play a significant role in coding theory. Full article
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14 pages, 290 KiB  
Article
A New Class of Bayes Minimax Estimators of the Mean Matrix of a Matrix Variate Normal Distribution
by Shokofeh Zinodiny and Saralees Nadarajah
Mathematics 2024, 12(7), 1098; https://doi.org/10.3390/math12071098 - 5 Apr 2024
Viewed by 536
Abstract
Bayes minimax estimation is important because it provides a robust approach to statistical estimation that considers the worst-case scenario while incorporating prior knowledge. In this paper, Bayes minimax estimation of the mean matrix of a matrix variate normal distribution is considered under the [...] Read more.
Bayes minimax estimation is important because it provides a robust approach to statistical estimation that considers the worst-case scenario while incorporating prior knowledge. In this paper, Bayes minimax estimation of the mean matrix of a matrix variate normal distribution is considered under the quadratic loss function. A large class of (proper and generalized) Bayes minimax estimators of the mean matrix is presented. Two examples are given to illustrate the class of estimators, showing, among other things, that the class includes classes of estimators presented by Tsukuma. Full article
15 pages, 1254 KiB  
Article
Turing Instability and Spatial Pattern Formation in a Model of Urban Crime
by Isabella Torcicollo and Maria Vitiello
Mathematics 2024, 12(7), 1097; https://doi.org/10.3390/math12071097 - 5 Apr 2024
Viewed by 519
Abstract
A nonlinear crime model is generalized by introducing self- and cross-diffusion terms. The effect of diffusion on the stability of non-negative constant steady states is applied. In particular, the cross-diffusion-driven instability, called Turing instability, is analyzed by linear stability analysis, and several Turing [...] Read more.
A nonlinear crime model is generalized by introducing self- and cross-diffusion terms. The effect of diffusion on the stability of non-negative constant steady states is applied. In particular, the cross-diffusion-driven instability, called Turing instability, is analyzed by linear stability analysis, and several Turing patterns driven by the cross-diffusion are studied through numerical investigations. When the Turing–Hopf conditions are satisfied, the type of instability highlighted in the ODE model persists in the PDE system, still showing an oscillatory behavior. Full article
(This article belongs to the Special Issue Transport Phenomena Equations: Modelling and Applications)
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13 pages, 259 KiB  
Article
On the Oscillatory Behavior of Solutions of Second-Order Non-Linear Differential Equations with Damping Term
by Mohamed Mazen, Mohamed M. A. El-Sheikh, Samah Euat Tallah and Gamal A. F. Ismail
Mathematics 2024, 12(7), 1096; https://doi.org/10.3390/math12071096 - 5 Apr 2024
Viewed by 517
Abstract
In this paper, we discuss the oscillatory behavior of solutions of two general classes of nonlinear second-order differential equations. New criteria are obtained using Riccati transformations and the integral averaging techniques. The obtained results improve and generalize some recent criteria in the literature. [...] Read more.
In this paper, we discuss the oscillatory behavior of solutions of two general classes of nonlinear second-order differential equations. New criteria are obtained using Riccati transformations and the integral averaging techniques. The obtained results improve and generalize some recent criteria in the literature. Moreover, a traditional condition is relaxed. Three examples are given to justify the results. Full article
18 pages, 397 KiB  
Article
Shrinkage Testimator for the Common Mean of Several Univariate Normal Populations
by Peter M. Mphekgwana, Yehenew G. Kifle and Chioneso S. Marange
Mathematics 2024, 12(7), 1095; https://doi.org/10.3390/math12071095 - 5 Apr 2024
Viewed by 511
Abstract
The challenge of combining two unbiased estimators is a common occurrence in applied statistics, with significant implications across diverse fields such as manufacturing quality control, medical research, and the social sciences. Despite the widespread relevance of estimating the common population mean μ, [...] Read more.
The challenge of combining two unbiased estimators is a common occurrence in applied statistics, with significant implications across diverse fields such as manufacturing quality control, medical research, and the social sciences. Despite the widespread relevance of estimating the common population mean μ, this task is not without its challenges. A particularly intricate issue arises when the variations within populations are unknown or possibly unequal. Conventional approaches, like the two-sample t-test, fall short in addressing this problem as they assume equal variances among the two populations. When there exists prior information regarding population variances (σi2,i=1,2), with the consideration that σ12 and σ22 might be equal, a hypothesis test can be conducted: H0:σ12=σ22 versus H1:σ12σ22. The initial sample is utilized to test H0, and if we fail to reject H0, we gain confidence in incorporating our prior knowledge (after testing) to estimate the common mean μ. However, if H0 is rejected, indicating unequal population variances, the prior knowledge is discarded. In such cases, a second sample is obtained to compensate for the loss of prior knowledge. The estimation of the common mean μ is then carried out using either the Graybill–Deal estimator (GDE) or the maximum likelihood estimator (MLE). A noteworthy discovery is that the proposed preliminary testimators, denoted as μ^PT1 and μ^PT2, exhibit superior performance compared to the widely used unbiased estimators (GDE and MLE). Full article
(This article belongs to the Special Issue Clustered Data Modeling and Statistical Meta-Analysis)
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16 pages, 1714 KiB  
Article
An Agile Super-Resolution Network via Intelligent Path Selection
by Longfei Jia, Yuguo Hu, Xianlong Tian, Wenwei Luo and Yanning Ye
Mathematics 2024, 12(7), 1094; https://doi.org/10.3390/math12071094 - 5 Apr 2024
Viewed by 458
Abstract
In edge computing environments, limited storage and computational resources pose significant challenges to complex super-resolution network models. To address these challenges, we propose an agile super-resolution network via intelligent path selection (ASRN) that utilizes a policy network for dynamic path selection, thereby optimizing [...] Read more.
In edge computing environments, limited storage and computational resources pose significant challenges to complex super-resolution network models. To address these challenges, we propose an agile super-resolution network via intelligent path selection (ASRN) that utilizes a policy network for dynamic path selection, thereby optimizing the inference process of super-resolution network models. Its primary objective is to substantially reduce the computational burden while maximally maintaining the super-resolution quality. To achieve this goal, a unique reward function is proposed to guide the policy network towards identifying optimal policies. The proposed ASRN not only streamlines the inference process but also significantly boosts inference speed on edge devices without compromising the quality of super-resolution images. Extensive experiments across multiple datasets confirm ASRN’s remarkable ability to accelerate inference speeds while maintaining minimal performance degradation. Additionally, we explore the broad applicability and practical value of ASRN in various edge computing scenarios, indicating its widespread potential in this rapidly evolving domain. Full article
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15 pages, 1019 KiB  
Article
Randomized Nonuniform Sampling for Random Signals Bandlimited in the Special Affine Fourier Transform Domain
by Yingchun Jiang, Ni Gao and Haizhen Li
Mathematics 2024, 12(7), 1092; https://doi.org/10.3390/math12071092 - 5 Apr 2024
Viewed by 464
Abstract
The nonuniform sampling and reconstruction of bandlimited random signals in the SAFT domain is discussed in the paper, where the nonuniform samples are obtained by randomly disturbing the uniform sampling. First, we prove that the concerned nonuniform problem is equivalent to the process [...] Read more.
The nonuniform sampling and reconstruction of bandlimited random signals in the SAFT domain is discussed in the paper, where the nonuniform samples are obtained by randomly disturbing the uniform sampling. First, we prove that the concerned nonuniform problem is equivalent to the process of uniform sampling after a prefilter in the statistic sense. Then, an approximate reconstruction method based on sinc interpolation is proposed for the randomized nonuniform sampling of SAFT-bandlimited random signals. Finally, we offer the mean square error estimate for the corresponding approximate recovery approach. The results generalize the conclusions of nonuniform sampling of bandlimited random signals in the FrFT and LCT domains to the SAFT domain. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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