Mathematics

33 pages, 5698 KiB

Open AccessArticle

DiFastBit: Transaction Differentiation Scheme to Avoid Double-Spending for Fast Bitcoin Payments

by David Melo, Saúl Eduardo Pomares-Hernández, Lil María Rodríguez-Henríquez and Julio César Pérez-Sansalvador

Mathematics 2024, 12(16), 2484; https://doi.org/10.3390/math12162484 (registering DOI) - 11 Aug 2024

Abstract

Bitcoin is a payment system that generates a decentralized digital currency without ensuring temporal constraints in its transactions; therefore, it is vulnerable to double-spending attacks. Karame has proposed a formalization for a successful double-spending attack based on meeting three requirements. This focuses on [...] Read more.

Bitcoin is a payment system that generates a decentralized digital currency without ensuring temporal constraints in its transactions; therefore, it is vulnerable to double-spending attacks. Karame has proposed a formalization for a successful double-spending attack based on meeting three requirements. This focuses on fast payment scenarios where the product is delivered immediately after the payment is announced in the mempool, without waiting for transaction confirmation. This scenario is key in Bitcoin to increase the probability of a successful double-spending attack. Different approaches have been proposed to mitigate these attacks by addressing one or more of Karame’s three requirements. These include the following: flooding every transaction without restrictions, introducing listeners/observers, avoiding isolation by blocking incoming connections, penalizing malicious users by revealing their identity, and using machine learning and bio-inspired techniques. However, to our knowledge, no proposal deterministically avoids double-spending attacks in fast payment scenarios. In this paper, we introduce DiFastBit: a distributed transaction differentiation scheme that shields Bitcoin from double-spending attacks in fast payment scenarios. To achieve this, we modeled Bitcoin from a distributed perspective of events and processes, reformulated Karame’s requirements based on Lamport’s happened-before relation (HBR), and introduced a new theorem that consolidates the reformulated requirements and establishes the necessary conditions for a successful attack on fast Bitcoin payments. Finally, we introduce the specifications for DiFastBit, formally prove its correctness, and analyze DiFastBit’s confirmation time. Full article

(This article belongs to the Special Issue Modeling and Simulation Analysis of Blockchain System)

14 pages, 266 KiB

Open AccessArticle

On the Stability of the Linear Complexity of Some Generalized Cyclotomic Sequences of Order Two

by Chi Yan and Chengliang Tian

Mathematics 2024, 12(16), 2483; https://doi.org/10.3390/math12162483 (registering DOI) - 11 Aug 2024

Abstract

Linear complexity is an important pseudo-random measure of the key stream sequence in a stream cipher system. The 1-error linear complexity is used to measure the stability of the linear complexity, which means the minimal linear complexity of the new sequence by changing [...] Read more.

Linear complexity is an important pseudo-random measure of the key stream sequence in a stream cipher system. The 1-error linear complexity is used to measure the stability of the linear complexity, which means the minimal linear complexity of the new sequence by changing one bit of the original key stream sequence. This paper contributes to calculating the exact values of the linear complexity and 1-error linear complexity of the binary key stream sequence with two prime periods defined by Ding–Helleseth generalized cyclotomy. We provide a novel method to solve such problems by employing the discrete Fourier transform and the M–S polynomial of the sequence. Our results show that, by choosing appropriate parameters p and q, the linear complexity and 1-error linear complexity can be no less than half period, which shows that the linear complexity of this sequence not only meets the requirements of cryptography but also has good stability. Full article

(This article belongs to the Special Issue Coding Theory and the Impact of AI)

22 pages, 5949 KiB

Open AccessArticle

Deduplication-Aware Healthcare Data Distribution in IoMT

by Saleh M. Altowaijri

Mathematics 2024, 12(16), 2482; https://doi.org/10.3390/math12162482 (registering DOI) - 11 Aug 2024

Abstract

As medical sensors undergo expeditious advancements, there is rising interest in the realm of healthcare applications within the Internet of Medical Things (IoMT) because of its broad applicability in monitoring the health of patients. IoMT proves beneficial in monitoring, disease diagnosis, and better [...] Read more.

As medical sensors undergo expeditious advancements, there is rising interest in the realm of healthcare applications within the Internet of Medical Things (IoMT) because of its broad applicability in monitoring the health of patients. IoMT proves beneficial in monitoring, disease diagnosis, and better treatment recommendations. This emerging technology aggregates real-time patient health data from sensors deployed on their bodies. This data collection mechanism consumes excessive power due to the transmission of data of similar types. It necessitates a deduplication mechanism, but this is complicated by the variable sizes of the data chunks, which may be either very small or larger in size. This reduces the likelihood of efficient chunking and, hence, deduplication. In this study, a deduplication-based data aggregation scheme was presented. It includes a Delimiter-Based Incremental Chunking Algorithm (DICA), which recognizes the breakpoint among two frames. The scheme includes static as well as variable-length windows. The proposed algorithm identifies a variable-length chunk using a terminator that optimizes the windows that are variable in size, with a threshold limit for the window size. To validate the scheme, a simulation was performed by utilizing NS-2.35 with the C language in the Ubuntu operating system. The TCL language was employed to set up networks, as well as for messaging purposes. The results demonstrate that the rise in the number of windows of variable size amounts to 62%, 66.7%, 68%, and 72.1% for DSW, RAM, CWCA, and DICA, respectively. The proposed scheme exhibits superior performance in terms of the probability of the false recognition of breakpoints, the static and dynamic sizes of chunks, the average sizes of chunks, the total attained chunks, and energy utilization. Full article

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

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15 pages, 5469 KiB

Open AccessArticle

Aerodynamic Analysis of Rigid Wing Sail Based on CFD Simulation for the Design of High-Performance Unmanned Sailboats

by Shipeng Fang, Cunwei Tian, Yuqi Zhang, Changbin Xu, Tianci Ding, Huimin Wang and Tao Xia

Mathematics 2024, 12(16), 2481; https://doi.org/10.3390/math12162481 (registering DOI) - 11 Aug 2024

Viewed by 118

Abstract

The utilization of unmanned sailboats as a burgeoning instrument for ocean exploration and monitoring is steadily rising. In this study, a dual sail configuration is put forth to augment the sailboats’ proficiency in its wind-catching ability and adapt to the harsh environment of [...] Read more.

The utilization of unmanned sailboats as a burgeoning instrument for ocean exploration and monitoring is steadily rising. In this study, a dual sail configuration is put forth to augment the sailboats’ proficiency in its wind-catching ability and adapt to the harsh environment of the sea. This proposition is based on a thorough investigation of sail aerodynamics. The symmetric rigid wing sails NACA 0020 and NACA 0016 are selected for use as the mainsail and trailing wing sail, respectively, after considering the operational environment of unmanned sailboats. The wing sail structure is modeled using SolidWorks, and computational fluid dynamics (CFD) simulations are conducted using ANSYS Fluent 2022R1 software to evaluate the aerodynamic performance of the sails. Key aerodynamic parameters, including lift, drag, lift coefficient, drag coefficient, and thrust coefficient, are obtained under different angles of attack. Furthermore, the effects of mainsail aspect ratios, mainsail taper ratios, and the positional relationship between the mainsail and trailing sail on performance are analyzed to determine the optimal structure. The thrust provided by the sail to the boat is mainly generated by the decomposition of lift, and the lift coefficient is used to measure the efficiency of an object in generating lift in the air. The proposed sail structure demonstrates a 37.1% improvement in the peak lift coefficient compared to traditional flexible sails and exhibits strong propulsion capability, indicating its potential for widespread application in the marine field. Full article

(This article belongs to the Special Issue Computational Fluid Dynamics: Modeling and Industrial Applications)

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13 pages, 833 KiB

Open AccessArticle

Multi-Layer Feature Restoration and Projection Model for Unsupervised Anomaly Detection

by Fuzhen Cai and Siyu Xia

Mathematics 2024, 12(16), 2480; https://doi.org/10.3390/math12162480 (registering DOI) - 11 Aug 2024

Viewed by 107

Abstract

The anomaly detection of products is a classical problem in the field of computer vision. Image reconstruction-based methods have shown promising results in the field of abnormality detection. Most of the existing methods use convolutional neural networks to build encoding–decoding structures to do [...] Read more.

The anomaly detection of products is a classical problem in the field of computer vision. Image reconstruction-based methods have shown promising results in the field of abnormality detection. Most of the existing methods use convolutional neural networks to build encoding–decoding structures to do image restoration. However, the limited receptive field of convolutional neural networks makes the information considered in the image restoration process limited, and the downsampling in the encoder causes information loss, which is not conducive to performing fine-grained restoration of images. To solve this problem, we propose a multi-layer feature restoration and projection model (MLFRP), which enables the restoration process to be carried out on multi-scale feature maps through a block-level feature restoration module that fully considers the detail information and semantic information required for the restoration process. We conducted in-depth experiments on the MvtecAD anomaly detection benchmark dataset, which showed that our model outperforms current state-of-the-art anomaly detection methods. Full article

(This article belongs to the Special Issue Object Detection: Algorithms, Computations and Practices)

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21 pages, 1315 KiB

Open AccessArticle

EVFL: Towards Efficient Verifiable Federated Learning via Parameter Reuse and Adaptive Sparsification

by Jianping Wu , Chunming Wu , Chaochao Chen , Jiahe Jin and Chuan Zhou

Mathematics 2024, 12(16), 2479; https://doi.org/10.3390/math12162479 (registering DOI) - 10 Aug 2024

Viewed by 205

Abstract

Federated learning (FL) demonstrates significant potential in Industrial Internet of Things (IIoT) settings, as it allows multiple institutions to jointly construct a shared learning model by exchanging model parameters or gradient updates without the need to transmit raw data. However, FL faces risks [...] Read more.

Federated learning (FL) demonstrates significant potential in Industrial Internet of Things (IIoT) settings, as it allows multiple institutions to jointly construct a shared learning model by exchanging model parameters or gradient updates without the need to transmit raw data. However, FL faces risks related to data poisoning and model poisoning. To address these issues, we propose an efficient verifiable federated learning (EVFL) method, which integrates adaptive gradient sparsification (AdaGS), Boneh–Lynn–Shacham (BLS) signatures, and fully homomorphic encryption (FHE). The combination of BLS signatures and the AdaGS algorithm is used to build a secure aggregation protocol. These protocols verify the integrity of parameters uploaded by industrial agents and the consistency of the server’s aggregation results. Simulation experiments demonstrate that the AdaGS algorithm significantly reduces verification overhead through parameter sparsification and reuse. Our proposed algorithm achieves better verification efficiency compared to existing solutions. Full article

(This article belongs to the Special Issue Privacy-Preserving Techniques in AI, Blockchain and Cloud Systems with Formal Mathematical Analysis)

27 pages, 800 KiB

Open AccessArticle

Maximizing Computation Rate for Sustainable Wireless-Powered MEC Network: An Efficient Dynamic Task Offloading Algorithm with User Assistance

by Huaiwen He, Feng Huang, Chenghao Zhou, Hong Shen and Yihong Yang

Mathematics 2024, 12(16), 2478; https://doi.org/10.3390/math12162478 (registering DOI) - 10 Aug 2024

Viewed by 184

Abstract

In the Internet of Things (IoT) era, Mobile Edge Computing (MEC) significantly enhances the efficiency of smart devices but is limited by battery life issues. Wireless Power Transfer (WPT) addresses this issue by providing a stable energy supply. However, effectively managing overall energy [...] Read more.

In the Internet of Things (IoT) era, Mobile Edge Computing (MEC) significantly enhances the efficiency of smart devices but is limited by battery life issues. Wireless Power Transfer (WPT) addresses this issue by providing a stable energy supply. However, effectively managing overall energy consumption remains a critical and under-addressed aspect for ensuring the network’s sustainable operation and growth. In this paper, we consider a WPT-MEC network with user cooperation to migrate the double near–far effect for the mobile node (MD) far from the base station. We formulate the problem of maximizing long-term computation rates under a power consumption constraint as a multi-stage stochastic optimization (MSSO) problem. This approach is tailored for a sustainable WPT-MEC network, considering the dynamic and varying MEC network environment, including randomness in task arrivals and fluctuating channels. We introduce a virtual queue to transform the time-average energy constraint into a queue stability problem. Using the Lyapunov optimization technique, we decouple the stochastic optimization problem into a deterministic problem for each time slot, which can be further transformed into a convex problem and solved efficiently. Our proposed algorithm works efficiently online without requiring further system information. Extensive simulation results demonstrate that our proposed algorithm outperforms baseline schemes, achieving approximately 4% enhancement while maintain the queues stability. Rigorous mathematical analysis and experimental results show that our algorithm achieves

[O (1 / V), O (V)]

trade-off between computation rate and queue stability. Full article

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

23 pages, 3359 KiB

Open AccessArticle

Evaluating Taiwan’s Geothermal Sites: A Bounded Rationality Data Envelopment Analysis Approach

by Chia-Nan Wang and Tien-Lin Chao

Mathematics 2024, 12(16), 2477; https://doi.org/10.3390/math12162477 (registering DOI) - 10 Aug 2024

Viewed by 175

Abstract

Amid rising global demand for renewable energy, geothermal power emerges as a vital, low-carbon solution to enhance energy security and sustainability. Taiwan, strategically located on the seismically active Pacific Ring of Fire, possesses an untapped geothermal potential that is underutilized due to complex [...] Read more.

Amid rising global demand for renewable energy, geothermal power emerges as a vital, low-carbon solution to enhance energy security and sustainability. Taiwan, strategically located on the seismically active Pacific Ring of Fire, possesses an untapped geothermal potential that is underutilized due to complex site selection challenges. This study specifically addresses the need for a more precise and psychologically attuned site selection process, aiming to optimize the development of geothermal resources in regions with complex geological settings. Utilizing the Modified Bounded Rationality Data Envelopment Analysis (MB-DEA) model, this research integrates traditional DEA with bounded rationality to factor in the risk preferences of decision-makers, offering a novel approach that enhances accuracy in evaluating geothermal sites. This study addresses the critical challenge of accurately selecting geothermal energy sites in geologically complex regions like Taiwan, where traditional methods fall short, aiming to significantly boost the efficiency and effectiveness of geothermal energy exploitation as part of Taiwan’s transition to renewable energy sources. Applied to 30 potential sites across Taiwan, our model provides a detailed assessment based on technical, economic, and psychological criteria, revealing variations in site suitability influenced by stakeholder risk attitudes. Key locations such as Datun Mountain, Maoxing, and Taolin consistently rank highly, confirming their robust potential irrespective of risk preferences. At the same time, other sites show marked sensitivity to shifts in decision-making attitudes. This work significantly advances the methodology of renewable energy site selection by demonstrating the utility of incorporating psychological factors into analytical models, which not only refines decision-making processes but also aligns with Taiwan’s strategic energy planning goals. This study also underscores the importance of accurate geographical data in complex terrains, suggesting further refinement and dynamic integration of bounded rationality for future research. Full article

(This article belongs to the Special Issue Application of Mathematical Methods to Economics, Management, Finance and Social Problems II)

26 pages, 1012 KiB

Open AccessArticle

On the Optimization of Kubernetes toward the Enhancement of Cloud Computing

by Subrota Kumar Mondal, Zhen Zheng and Yuning Cheng

Mathematics 2024, 12(16), 2476; https://doi.org/10.3390/math12162476 (registering DOI) - 10 Aug 2024

Viewed by 186

Abstract

With the vigorous development of big data and cloud computing, containers are becoming the main platform for running applications due to their flexible and lightweight features. Using a container cluster management system can more effectively manage multiocean containers on multiple machine nodes, and [...] Read more.

With the vigorous development of big data and cloud computing, containers are becoming the main platform for running applications due to their flexible and lightweight features. Using a container cluster management system can more effectively manage multiocean containers on multiple machine nodes, and Kubernetes has become a leader in container cluster management systems, with its powerful container orchestration capabilities. However, the current default Kubernetes components and settings have appeared to have a performance bottleneck and are not adaptable to complex usage environments. In particular, the issues are data distribution latency, inefficient cluster backup and restore leading to poor disaster recovery, poor rolling update leading to downtime, inefficiency in load balancing and handling requests, poor autoscaling and scheduling strategy leading to quality of service (QoS) violations and insufficient resource usage, and many others. Aiming at the insufficient performance of the default Kubernetes platform, this paper focuses on reducing the data distribution latency, improving the cluster backup and restore strategies toward better disaster recovery, optimizing zero-downtime rolling updates, incorporating better strategies for load balancing and handling requests, optimizing autoscaling, introducing better scheduling strategy, and so on. At the same time, the relevant experimental analysis is carried out. The experiment results show that compared with the default settings, the optimized Kubernetes platform can handle more than 2000 concurrent requests, reduce the CPU overhead by more than 1.5%, reduce the memory by more than 0.6%, reduce the average request time by an average of 7.6%, and reduce the number of request failures by at least 32.4%, achieving the expected effect. Full article

(This article belongs to the Special Issue Advanced Computational Intelligence in Cloud/Edge Computing)

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14 pages, 284 KiB

Open AccessArticle

A Minimax-Program-Based Approach for Robust Fractional Multi-Objective Optimization

by Henan Li, Zhe Hong and Do Sang Kim

Mathematics 2024, 12(16), 2475; https://doi.org/10.3390/math12162475 (registering DOI) - 10 Aug 2024

Viewed by 183

Abstract

In this paper, by making use of some advanced tools from variational analysis and generalized differentiation, we establish necessary optimality conditions for a class of robust fractional minimax programming problems. Sufficient optimality conditions for the considered problem are also obtained by means of [...] Read more.

In this paper, by making use of some advanced tools from variational analysis and generalized differentiation, we establish necessary optimality conditions for a class of robust fractional minimax programming problems. Sufficient optimality conditions for the considered problem are also obtained by means of generalized convex functions. Additionally, we formulate a dual problem to the primal one and examine duality relations between them. In our results, by using the obtained results, we obtain necessary and sufficient optimality conditions for a class of robust fractional multi-objective optimization problems. Full article

(This article belongs to the Special Issue Applied Functional Analysis and Applications: 2nd Edition)

20 pages, 728 KiB

Open AccessArticle

The Period Function of the Generalized Sine-Gordon Equation and the Sinh-Poisson Equation

by Lin Lu, Xiaokai He and Xing Zhou

Mathematics 2024, 12(16), 2474; https://doi.org/10.3390/math12162474 (registering DOI) - 10 Aug 2024

Viewed by 177

Abstract

In this paper, we consider the generalized sine-Gordon equation

ψ_{t x} = (1 + a \partial_{x}^{2}) \sin ψ

and the sinh-Poisson equation

u_{x x} + u_{y y} + σ \sinh u = 0

, where a [...] Read more.

In this paper, we consider the generalized sine-Gordon equation

ψ_{t x} = (1 + a \partial_{x}^{2}) \sin ψ

and the sinh-Poisson equation

u_{x x} + u_{y y} + σ \sinh u = 0

, where a is a real parameter, and

σ

is a positive parameter. Under different conditions, e.g.,

a = 0

,

a \neq 0

, and

σ > 0

, the periods of the periodic wave solutions for the above two equations are discussed. By the transformation of variables, the generalized sine-Gordon equation and sinh-Poisson equations are reduced to planar dynamical systems whose first integral includes trigonometric terms and exponential terms, respectively. We successfully handle the trigonometric terms and exponential terms in the study of the monotonicity of the period function of periodic solutions. Full article

(This article belongs to the Section Dynamical Systems)

22 pages, 2822 KiB

Open AccessArticle

Automatic Foreign Matter Segmentation System for Superabsorbent Polymer Powder: Application of Diffusion Adversarial Representation Learning

by Ssu-Han Chen, Meng-Jey Youh, Yan-Ru Chen, Jer-Huan Jang, Hung-Yi Chen, Hoang-Giang Cao, Yang-Shen Hsueh, Chuan-Fu Liu and Kevin Fong-Rey Liu

Mathematics 2024, 12(16), 2473; https://doi.org/10.3390/math12162473 (registering DOI) - 10 Aug 2024

Viewed by 177

Abstract

In current industries, sampling inspections of the quality of powders, such as superabsorbent polymers (SAPs) still are conducted via visual inspection. The size of samples and foreign matter are around 500 μm, making them difficult for humans to identify. An automatic foreign matter [...] Read more.

In current industries, sampling inspections of the quality of powders, such as superabsorbent polymers (SAPs) still are conducted via visual inspection. The size of samples and foreign matter are around 500 μm, making them difficult for humans to identify. An automatic foreign matter detection system for powder has been developed in the present study. The powder samples can be automatically delivered, distributed, and recycled, and images of them are captured through the hardware of the system, while the identification software of this system was developed based on diffusion adversarial representation learning (DARL). The background image is a foreign-matter-free powder image with an input image size of 1024 × 1024 × 3. Since DARL includes adversarial segmentation, a diffusion process, and synthetic image generation, the DARL model was trained using a diffusion block with the employment of a U-Net attention mechanism and a spatial-adaptation de-normalization (SPADE) layer through the adoption of a loss function from a vanilla generative adversarial network (GAN). This model was then compared with supervised models such as a fully convolutional network (FCN), U-Net, and DeepLABV3+, as well as with an unsupervised Otsu threshold segmentation. It should be noted that only 10% of the training samples were utilized for the DARL to learn and the intersection over union (IoU) of the DARL can reach up to 80.15%, which is much higher than the 59.00%, 53.47%, 49.39%, and 30.08% for the Otsu threshold segmentation, FCN, U-Net, and DeepLABV3+ models. Therefore, the performance of the model developed in the present study would not be degraded due to an insufficient number of samples containing foreign matter. In practical applications, there is no need to collect, label, and design features for a large number of foreign matter samples before using the developed system. Full article

(This article belongs to the Section Engineering Mathematics)

29 pages, 1647 KiB

Open AccessArticle

Battery Mode Selection and Carbon Emission Decisions of Competitive Electric Vehicle Manufacturers

by Zhihua Han, Yinyuan Si, Xingye Wang and Shuai Yang

Mathematics 2024, 12(16), 2472; https://doi.org/10.3390/math12162472 (registering DOI) - 10 Aug 2024

Viewed by 186

Abstract

Competition in China’s electric vehicle industry has intensified significantly in recent years. The production mode of power batteries, serving as the pivotal component in these vehicles, has emerged as a critical challenge for electric vehicle manufacturers. We considered a system comprising an electric [...] Read more.

Competition in China’s electric vehicle industry has intensified significantly in recent years. The production mode of power batteries, serving as the pivotal component in these vehicles, has emerged as a critical challenge for electric vehicle manufacturers. We considered a system comprising an electric vehicle (EV) manufacturer with power battery production technology and another EV manufacturer lacking power battery production technology. In the context of carbon trading policy, we constructed and solved Cournot competitive game models and asymmetric Nash negotiation game models in the CC, PC, and WC modes. We examined the decision-making process of electric vehicle manufacturers regarding power battery production modes and carbon emission reduction strategies. Our research indicates the following: (1) The reasonable patent fee for power batteries and the wholesale price of power batteries can not only compensate power battery production technology manufacturers for the losses caused by market competition but can also strengthen the cooperative relationship between manufacturers. (2) EV manufacturers equipped with power battery production technology exhibit higher profitability within the framework of a perfectly competitive power battery production mode. Conversely, manufacturers lacking power cell production technology demonstrate greater profitability when operating under a more collaborative power cell production mode. (3) Refraining from blindly persisting with and advocating for carbon emission reduction measures is advisable for manufacturers amidst rising carbon trading prices. Full article

25 pages, 4785 KiB

Open AccessArticle

Task-Importance-Oriented Task Selection and Allocation Scheme for Mobile Crowdsensing

by Sha Chang, Yahui Wu, Su Deng, Wubin Ma and Haohao Zhou

Mathematics 2024, 12(16), 2471; https://doi.org/10.3390/math12162471 (registering DOI) - 10 Aug 2024

Viewed by 170

Abstract

In Mobile Crowdsensing (MCS), sensing tasks have different impacts and contributions to the whole system or specific targets, so the importance of the tasks is different. Since resources for performing tasks are usually limited, prioritizing the allocation of resources to more important tasks [...] Read more.

In Mobile Crowdsensing (MCS), sensing tasks have different impacts and contributions to the whole system or specific targets, so the importance of the tasks is different. Since resources for performing tasks are usually limited, prioritizing the allocation of resources to more important tasks can ensure that key data or information can be collected promptly and accurately, thus improving overall efficiency and performance. Therefore, it is very important to consider the importance of tasks in the task selection and allocation of MCS. In this paper, a task queue is established, the importance of tasks, the ability of participants to perform tasks, and the stability of the task queue are considered, and a novel task selection and allocation scheme (TSAS) in the MCS system is designed. This scheme introduces the Lyapunov optimization method, which can be used to dynamically keep the task queue stable, balance the execution ability of participants and the system load, and perform more important tasks in different system states, even when the participants are limited. In addition, the Double Deep Q-Network (DDQN) method is introduced to improve on the traditional solution of the Lyapunov optimization problem, so this scheme has a certain predictive ability and foresight on the impact of future system states. This paper also proposes action-masking and iterative training methods for the MCS system, which can accelerate the training process of the neural network in the DDQN and improve the training effect. Experiments show that the TSAS based on the Lyapunov optimization method and DDQN performs better than other algorithms, considering the long-term stability of the queue, the number and importance of tasks to be executed, and the congestion degree of tasks. Full article

(This article belongs to the Topic AI and Data-Driven Advancements in Industry 4.0)

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17 pages, 3915 KiB

Open AccessArticle

The Potential Changes and Stereocilia Movements during the Cochlear Sound Perception Process

by Bin Liu, Junyi Liang, Wenjuan Yao and Chun Xu

Mathematics 2024, 12(16), 2470; https://doi.org/10.3390/math12162470 (registering DOI) - 10 Aug 2024

Viewed by 182

Abstract

Sound vibrations generate electrical signals called cochlear potentials, which can reflect cochlear stereocilia movement and outer hair cells (OHC) mechanical activity. However, because the cochlear structure is delicate and complex, it is difficult for existing measurement techniques to pinpoint the origin of potentials. [...] Read more.

Sound vibrations generate electrical signals called cochlear potentials, which can reflect cochlear stereocilia movement and outer hair cells (OHC) mechanical activity. However, because the cochlear structure is delicate and complex, it is difficult for existing measurement techniques to pinpoint the origin of potentials. This limitation in measurement capability makes it difficult to fully understand the contribution of stereocilia and transduction channels to cochlear potentials. In view of this, firstly, this article obtains the stereocilia movement generated by basilar membrane (BM) vibration based on the positional relationship between the various structures of the organ Corti. Secondly, Kirchhoff’s law is used to establish an electric field model of the cochlear cavity, and the stereocilia movement is embedded in the electric field by combining the gated spring model. Finally, a force-electric coupling mathematical model of the cochlea is established. The results indicated that the resistance variation between different cavities in the cochlea leads to a sharp tuning curve. As the displacement of the BM increased, the longitudinal potential along the cochlea continued to move toward the base. The decrease in stereocilia stiffness reduced the deflection angle, thereby reducing the transduction current and lymphatic potential. Full article

(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 3rd Edition)

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25 pages, 3921 KiB

Open AccessArticle

Graph Neural Network Based Asynchronous Federated Learning for Digital Twin-Driven Distributed Multi-Agent Dynamical Systems

by Xuanzhu Sheng, Yang Zhou and Xiaolong Cui

Mathematics 2024, 12(16), 2469; https://doi.org/10.3390/math12162469 (registering DOI) - 9 Aug 2024

Viewed by 256

Abstract

The rapid development of artificial intelligence (AI) and 5G paradigm brings infinite possibilities for data annotation for new applications in the industrial Internet of Things (IIoT). However, the problem of data annotation consistency under distributed architectures and growing concerns about issues such as [...] Read more.

The rapid development of artificial intelligence (AI) and 5G paradigm brings infinite possibilities for data annotation for new applications in the industrial Internet of Things (IIoT). However, the problem of data annotation consistency under distributed architectures and growing concerns about issues such as data privacy and cybersecurity are major obstacles to improving the quality of distributed data annotation. In this paper, we propose a reputation-based asynchronous federated learning approach for digital twins. First, this paper integrates digital twins into an asynchronous federated learning framework, and utilizes a smart contract-based reputation mechanism to enhance the interconnection and internal interaction of asynchronous mobile terminals. In addition, in order to enhance security and privacy protection in the distributed smart annotation system, this paper introduces blockchain technology to optimize the data exchange, storage, and sharing process to improve system security and reliability. The data results show that the consistency of our proposed FedDTrep distributed intelligent labeling system reaches 99%. Full article

(This article belongs to the Special Issue Advanced Control of Complex Dynamical Systems with Applications)

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Block diagram of a distributed intelligent marking system based on digital twins. Full article ">Figure 2
Digital twin modeling framework of GCN intelligent annotation. Full article ">Figure 3
A diagram of the proposed method. Full article ">Figure 4
The left-hand and right-hand side show a comparison of the accuracy of the four algorithms of the model for the synchronous and asynchronous cases. Full article ">Figure 5
The left and right sides show the accuracy comparison of the four algorithms of the global smart marking model for the synchronous and asynchronous cases, respectively, with the number of local models being 10. Full article ">Figure 6
Comparison of the accuracy of the four algorithms of the global intelligent marking model for the synchronous and asynchronous cases with 15 local models on the left and right sides. Full article ">Figure 7
The precision curves when the number of individuals participating in the training of the local model is 20 and the degree of heterogeneity varies. Full article ">Figure 8
This figure compares the model accuracy curves for centralized training with those of the FedDTrep method proposed in this paper for different numbers of malicious nodes. Full article ">

19 pages, 941 KiB

Open AccessArticle

Pricing Decisions in Dual-Channel Supply Chains Considering the Offline Channel Preference and Service Level

by Yanting Chen and Mengling Wu

Mathematics 2024, 12(16), 2468; https://doi.org/10.3390/math12162468 (registering DOI) - 9 Aug 2024

Viewed by 226

Abstract

With the rapid development of e-commerce, the online channels encroaching on the offline sales market are becoming more serious, which will definitely harm the offline market. Moreover, there exists a certain percentage of consumers (mostly elderly people) who are not able to purchase [...] Read more.

With the rapid development of e-commerce, the online channels encroaching on the offline sales market are becoming more serious, which will definitely harm the offline market. Moreover, there exists a certain percentage of consumers (mostly elderly people) who are not able to purchase online because they lack digital skills. Therefore, understanding the impact of the purchase channel preference and service level on pricing decisions is vital for the dual-channel supply chain management. Focusing on the channel preference and service level, we first develop an optimal pricing model containing centralized and decentralized decision-making for an online and offline retailer by deploying the Stackelberg game. We first develop a Stackleberg game to capture such a dual-channel supply chain with the offline channel preference and service level. Secondly, under centralized decision-making, we derive the optimal retail prices and obtain the optimal total profit. Thirdly, under decentralized decision-making, we obtain the optimal retail prices and optimal total profit as well. Moreover, extensive monotonicity properties when system parameters change are obtained. Relying on the theoretical results, firstly, we show that the improvement of the offline service level would lead to higher pricing of the commodities for both online and offline channels. From our numerical results, when the service level is improved, the offline and online optimal pricing increases by 47.5% and 31.1%, respectively, which may contradict the conventional belief that the improvement of one channel would harm another one. Secondly, we demonstrate that the benefit of improving the offline service level has a diminishing marginal effect. The numerical results show that when the current service level is low, the effectives of improving the service level is roughly five times that when the service level is high. This indicates that the investment in improving the offline service level should not be unlimited. Thirdly, we show that the pricing decision under centralized decision-making should be adopted with the existence of both the offline channel preference and offline service. Full article

27 pages, 666 KiB

Open AccessFeature PaperArticle

Ownership of Cash Value Life Insurance among Rural Households: Utilization of Machine Learning Algorithms to Find Predictors

by Wookjae Heo, Eun Jin Kwak, John Grable and Hye Jun Park

Mathematics 2024, 12(16), 2467; https://doi.org/10.3390/math12162467 (registering DOI) - 9 Aug 2024

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Abstract

This study examines the determinants of life insurance ownership with a focus on rural areas and farming households in the United States. Utilizing data from online surveys conducted in 2019 and 2021, this paper explores how psychological factors, financial knowledge, and household characteristics [...] Read more.

This study examines the determinants of life insurance ownership with a focus on rural areas and farming households in the United States. Utilizing data from online surveys conducted in 2019 and 2021, this paper explores how psychological factors, financial knowledge, and household characteristics influence life insurance ownership. Traditional indicators like wealth, income, and age were evaluated alongside less frequently discussed variables such as farm loans and rural residency. Machine learning techniques, including neural networks, Support Vector Machine modeling, Gradient Boosting, and logistic regression, were employed to identify the most robust predictors of life insurance demand. The findings reveal that farming-associated factors, particularly holding a farm loan and living in a farming household, significantly predict life insurance ownership. The study also highlights the complexity of life insurance demand, showing that financial education and management practices are critical determinants. This research underscores the need for tailored financial risk management strategies for rural and farming households and contributes to a nuanced understanding of life insurance demand in varying contexts. Full article

(This article belongs to the Special Issue Machine Learning and Finance)

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29 pages, 10214 KiB

Open AccessArticle

Revisiting the Use of the Gumbel Distribution: A Comprehensive Statistical Analysis Regarding Modeling Extremes and Rare Events

by Cristian Gabriel Anghel

Mathematics 2024, 12(16), 2466; https://doi.org/10.3390/math12162466 (registering DOI) - 9 Aug 2024

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Abstract

The manuscript presents the applicability of the Gumbel distribution in the frequency analysis of extreme events in hydrology. The advantages and disadvantages of using the distribution are highlighted, as well as recommendations regarding its proper use. A literature review was also carried out [...] Read more.

The manuscript presents the applicability of the Gumbel distribution in the frequency analysis of extreme events in hydrology. The advantages and disadvantages of using the distribution are highlighted, as well as recommendations regarding its proper use. A literature review was also carried out regarding the methods for estimating the parameters of the Gumbel distribution in hydrology. Thus, for the verification of the methods, case studies are presented regarding the determination of the maximum annual flows and precipitations using nine methods for estimating the distribution parameters. The influence of the variability of the observed data lengths on the estimation of the statistical indicators, the estimation of the parameters, and the quantiles corresponding to the field of small exceedance probabilities (p < 1%) is also highlighted. In each case, the results are analyzed compared to those obtained with the Generalized Extreme Value distribution, the four-parameter Burr distribution, and the five-parameter Wakeby distribution estimated using the L-moments method. The results of the case studies highlight and reaffirm the statistical, mathematical, and hydrological recommendations regarding the avoidance of applying the Gumbel distribution in flood frequency analysis and its use with reservations in the case of maximum precipitation analysis, especially when the statistical indicators of the analyzed data are not close to the characteristic ones and unique to the distribution. Full article

(This article belongs to the Special Issue Mathematical and Statistical Methods in Detecting and Modeling Abnormalities, Extremes, and Rare Events)

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23 pages, 1378 KiB

Open AccessArticle

Strong Stability Preserving Two-Derivative Two-Step Runge-Kutta Methods

by Xueyu Qin, Zhenhua Jiang and Chao Yan

Mathematics 2024, 12(16), 2465; https://doi.org/10.3390/math12162465 (registering DOI) - 9 Aug 2024

Viewed by 220

Abstract

In this study, we introduce the explicit strong stability preserving (SSP) two-derivative two-step Runge-Kutta (TDTSRK) methods. We propose the order conditions using Albrecht’s approach, comparing to the order conditions expressed in terms of rooted trees, these conditions present a more straightforward form with [...] Read more.

In this study, we introduce the explicit strong stability preserving (SSP) two-derivative two-step Runge-Kutta (TDTSRK) methods. We propose the order conditions using Albrecht’s approach, comparing to the order conditions expressed in terms of rooted trees, these conditions present a more straightforward form with fewer equations. Furthermore, we develop the SSP theory for the TDTSRK methods under certain assumptions and identify its optimal parameters. We also conduct a comparative analysis of the SSP coefficient among TDTSRK methods, two-derivative Runge-Kutta (TDRK) methods, and Runge-Kutta (RK) methods, both theoretically and numerically. The comparison reveals that the TDTSRK methods in the same order of accuracy have the most effective SSP coefficient. Numerical results demonstrate that the TDTSRK methods are highly efficient in solving the partial differential equation, and the TDTSRK methods can achieve the expected order of accuracy. Full article

(This article belongs to the Special Issue Numerical Methods for Differential Equations and Applications)

33 pages, 436 KiB

Open AccessArticle

Bounds of Different Integral Operators in Tensorial Hilbert and Variable Exponent Function Spaces

by Waqar Afzal, Mujahid Abbas and Omar Mutab Alsalami

Mathematics 2024, 12(16), 2464; https://doi.org/10.3390/math12162464 (registering DOI) - 9 Aug 2024

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Abstract

In dynamical systems, Hilbert spaces provide a useful framework for analyzing and solving problems because they are able to handle infinitely dimensional spaces. Many dynamical systems are described by linear operators acting on a Hilbert space. Understanding the spectrum, eigenvalues, and eigenvectors of [...] Read more.

In dynamical systems, Hilbert spaces provide a useful framework for analyzing and solving problems because they are able to handle infinitely dimensional spaces. Many dynamical systems are described by linear operators acting on a Hilbert space. Understanding the spectrum, eigenvalues, and eigenvectors of these operators is crucial. Functional analysis typically involves the use of tensors to represent multilinear mappings between Hilbert spaces, which can result in inequality in tensor Hilbert spaces. In this paper, we study two types of function spaces and use convex and harmonic convex mappings to establish various operator inequalities and their bounds. In the first part of the article, we develop the operator Hermite–Hadamard and upper and lower bounds for weighted discrete Jensen-type inequalities in Hilbert spaces using some relational properties and arithmetic operations from the tensor analysis. Furthermore, we use the Riemann–Liouville fractional integral and develop several new identities which are used in operator Milne-type inequalities to develop several new bounds using different types of generalized mappings, including differentiable, quasi-convex, and convex mappings. Furthermore, some examples and consequences for logarithm and exponential functions are also provided. Furthermore, we provide an interesting example of a physics dynamical model for harmonic mean. Lastly, we develop Hermite–Hadamard inequality in variable exponent function spaces, specifically in mixed norm function space (

ℓ^{q (\cdot)} (L^{p (\cdot)})

). Moreover, it was developed using classical Lebesgue space (

L_{p}

) space, in which the exponent is constant. This inequality not only refines Jensen and triangular inequality in the norm sense, but we also impose specific conditions on exponent functions to show whether this inequality holds true or not. Full article

(This article belongs to the Special Issue Variational Problems and Applications, 2nd Edition)

7 pages, 317 KiB

Open AccessArticle

Self-Intersections of Cubic Bézier Curves Revisited

by Javier Sánchez-Reyes

Mathematics 2024, 12(16), 2463; https://doi.org/10.3390/math12162463 - 9 Aug 2024

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Abstract

Recently, Yu et al. derived a factorization procedure for detecting and computing the potential self-intersection of 3D integral Bézier cubics, claiming that their proposal distinctly outperforms existing methodologies. First, we recall that in the 2D case, explicit formulas already exist for the parameter [...] Read more.

Recently, Yu et al. derived a factorization procedure for detecting and computing the potential self-intersection of 3D integral Bézier cubics, claiming that their proposal distinctly outperforms existing methodologies. First, we recall that in the 2D case, explicit formulas already exist for the parameter values at the self-intersection (the singularity called crunode in algebraic geometry). Such values are the solutions of a quadratic equation, and affine invariants depend only on the curve hodograph. Also, the factorization procedure for cubics is well known. Second, we note that only planar Bézier cubics can display a self-intersection, so there is no need to address the problem in the more involved 3D setting. Finally, we elucidate the connections with the previous literature and provide a geometric interpretation, in terms of the affine classification of cubics, of the algebraic conditions necessary for the existence of a self-intersection. Cubics with a self-intersection are affine versions of the celebrated Tschirnhausen cubic. Full article

(This article belongs to the Section Algebra, Geometry and Topology)

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16 pages, 1852 KiB

Open AccessArticle

Universal Network for Image Registration and Generation Using Denoising Diffusion Probability Model

by Huizhong Ji, Peng Xue and Enqing Dong

Mathematics 2024, 12(16), 2462; https://doi.org/10.3390/math12162462 - 9 Aug 2024

Viewed by 271

Abstract

Classical diffusion model-based image registration approaches require separate diffusion and deformation networks to learn the reverse Gaussian transitions and predict deformations between paired images, respectively. However, such cascaded architectures introduce noisy inputs in the registration, leading to excessive computational complexity and issues with [...] Read more.

Classical diffusion model-based image registration approaches require separate diffusion and deformation networks to learn the reverse Gaussian transitions and predict deformations between paired images, respectively. However, such cascaded architectures introduce noisy inputs in the registration, leading to excessive computational complexity and issues with low registration accuracy. To overcome these limitations, a diffusion model-based universal network for image registration and generation (UNIRG) is proposed. Specifically, the training process of the diffusion model is generalized as a process of matching the posterior mean of the forward process to the modified mean. Subsequently, the equivalence between the training process for image generation and that for image registration is verified by incorporating the deformation information of the paired images to obtain the modified mean. In this manner, UNIRG integrates image registration and generation within a unified network, achieving shared training parameters. Experimental results on 2D facial and 3D cardiac medical images demonstrate that the proposed approach integrates the capabilities of image registration and guided image generation. Meanwhile, UNIRG achieves registration performance with NMSE of 0.0049, SSIM of 0.859, and PSNR of 27.28 on the 2D facial dataset, along with Dice of 0.795 and PSNR of 12.05 on the 3D cardiac dataset. Full article

(This article belongs to the Special Issue Mathematical Methods for Image Processing and Computer Vision)

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19 pages, 3214 KiB

Open AccessArticle

Adaptive Mission Abort Planning Integrating Bayesian Parameter Learning

by Yuhan Ma, Fanping Wei, Xiaobing Ma, Qingan Qiu and Li Yang

Mathematics 2024, 12(16), 2461; https://doi.org/10.3390/math12162461 - 8 Aug 2024

Viewed by 333

Abstract

Failure of a safety-critical system during mission execution can result in significant financial losses. Implementing mission abort policies is an effective strategy to mitigate the system failure risk. This research delves into systems that are subject to cumulative shock degradation, considering uncertainties in [...] Read more.

Failure of a safety-critical system during mission execution can result in significant financial losses. Implementing mission abort policies is an effective strategy to mitigate the system failure risk. This research delves into systems that are subject to cumulative shock degradation, considering uncertainties in shock damage. To account for the varied degradation parameters, we employ a dynamic Bayesian learning method using real-time sensor data for accurate degradation estimation. Our primary focus is on modeling the mission abort policy with an integrated parameter learning approach within the framework of a finite-horizon Markov decision process. The key objective is to minimize the expected costs related to routine inspections, system failures, and mission disruptions. Through an examination of the structural aspects of the value function, we establish the presence and monotonicity of optimal mission abort thresholds, thereby shaping the optimal policy into a controlled limit strategy. Additionally, we delve into the relationship between optimal thresholds and cost parameters to discern their behavior patterns. Through a series of numerical experiments, we showcase the superior performance of the optimal policy in mitigating losses compared with traditional heuristic methods. Full article

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15 pages, 479 KiB

Open AccessArticle

A Class of Distributed Online Aggregative Optimization in Unknown Dynamic Environment

by Chengqian Yang, Shuang Wang, Shuang Zhang, Shiwei Lin and Bomin Huang

Mathematics 2024, 12(16), 2460; https://doi.org/10.3390/math12162460 - 8 Aug 2024

Viewed by 261

Abstract

This paper considers a class of distributed online aggregative optimization problems over an undirected and connected network. It takes into account an unknown dynamic environment and some aggregation functions, which is different from the problem formulation of the existing approach, making the aggregative [...] Read more.

This paper considers a class of distributed online aggregative optimization problems over an undirected and connected network. It takes into account an unknown dynamic environment and some aggregation functions, which is different from the problem formulation of the existing approach, making the aggregative optimization problem more challenging. A distributed online optimization algorithm is designed for the considered problem via the mirror descent algorithm and the distributed average tracking method. In particular, the dynamic environment and the gradient are estimated by the averaged tracking methods, and then an online optimization algorithm is designed via a dynamic mirror descent method. It is shown that the dynamic regret is bounded in the order of

O (\sqrt{T})

. Finally, the effectiveness of the designed algorithm is verified by some simulations of cooperative control of a multi-robot system. Full article

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

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14 pages, 905 KiB

Open AccessArticle

Several Characterizations of the Generalized 1-Parameter 3-Variable Hermite Polynomials

by Shahid Ahmad Wani, Khalil Hadi Hakami and Hamad Zogan

Mathematics 2024, 12(16), 2459; https://doi.org/10.3390/math12162459 - 8 Aug 2024

Viewed by 244

Abstract

This paper presents a novel framework for introducing generalized 1-parameter 3-variable Hermite polynomials. These polynomials are characterized through generating functions and series definitions, elucidating their fundamental properties. Moreover, utilising a factorisation method, this study establishes recurrence relations, shift operators, and various differential equations, [...] Read more.

This paper presents a novel framework for introducing generalized 1-parameter 3-variable Hermite polynomials. These polynomials are characterized through generating functions and series definitions, elucidating their fundamental properties. Moreover, utilising a factorisation method, this study establishes recurrence relations, shift operators, and various differential equations, including differential, integro-differential, and partial differential equations. Full article

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

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23 pages, 1980 KiB

Open AccessArticle

GaitSTAR: Spatial–Temporal Attention-Based Feature-Reweighting Architecture for Human Gait Recognition

by Muhammad Bilal, He Jianbiao, Husnain Mushtaq, Muhammad Asim, Gauhar Ali and Mohammed ElAffendi

Mathematics 2024, 12(16), 2458; https://doi.org/10.3390/math12162458 - 8 Aug 2024

Viewed by 228

Abstract

Human gait recognition (HGR) leverages unique gait patterns to identify individuals, but the effectiveness of this technique can be hindered due to various factors such as carrying conditions, foot shadows, clothing variations, and changes in viewing angles. Traditional silhouette-based systems often neglect the [...] Read more.

Human gait recognition (HGR) leverages unique gait patterns to identify individuals, but the effectiveness of this technique can be hindered due to various factors such as carrying conditions, foot shadows, clothing variations, and changes in viewing angles. Traditional silhouette-based systems often neglect the critical role of instantaneous gait motion, which is essential for distinguishing individuals with similar features. We introduce the ”Enhanced Gait Feature Extraction Framework (GaitSTAR)”, a novel method that incorporates dynamic feature weighting through the discriminant analysis of temporal and spatial features within a channel-wise architecture. Key innovations in GaitSTAR include dynamic stride flow representation (DSFR) to address silhouette distortion, a transformer-based feature set transformation (FST) for integrating image-level features into set-level features, and dynamic feature reweighting (DFR) for capturing long-range interactions. DFR enhances contextual understanding and improves detection accuracy by computing attention distributions across channel dimensions. Empirical evaluations show that GaitSTAR achieves impressive accuracies of 98.5%, 98.0%, and 92.7% under NM, BG, and CL conditions, respectively, with the CASIA-B dataset; 67.3% with the CASIA-C dataset; and 54.21% with the Gait3D dataset. Despite its complexity, GaitSTAR demonstrates a favorable balance between accuracy and computational efficiency, making it a powerful tool for biometric identification based on gait patterns. Full article

(This article belongs to the Special Issue Computer Vision, Image Processing Technologies and Artificial Intelligence, 2nd Edition)

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Figure 1
The pyramid framework of GaitSTAR integrates silhouette edge information and optical flow to capture shape and motion. It uses the Lucas–Kanade algorithm to handle the full dynamic range of pixel values. The framework extracts discriminative features through a scatter matrix and a temporal-attention mechanism, computing a decoding weight vector that enhances the focus on relevant temporal and spatial features. This process generates per-channel decoding weight vectors, leading to a linear projection of reweighted features into a unified channel-wise decoding vector. Full article ">Figure 2
This figure illustrates feature selection from instances of the CASIA-B. (a) denotes the mask of the targeted area, and the (b) images depict the maximum possible feature area using a discriminative analysis approach. Full article ">Figure 3
Illustration of feature set transformation capturing contextual linkages and dependencies. These are processed through a multi-head self-attention mechanism [<a href="#B41-mathematics-12-02458" class="html-bibr">41</a>] and integrated into an FFN architecture with residual connections for refined feature transformations. Full article ">Figure 4
The figure depicts the data flow through a multi-head attention mechanism in transformer models. It details the steps involved in dynamic feature weighting, which expands the feature decoding space and computes attention distributions across key embeddings for each channel. This process improves query–key interactions, and it enhances expressiveness in both temporal and spatial contexts. Full article ">Figure 5
This figure illustrates appearance-feature selection from instances of CASIA-B with different angles of a person carrying a bag. Full article ">Figure 6
This figure illustrates the Gait Energy Images (GEIs), presented in sequence from left to right. Full article ">Figure 7
This figure illustrates instances from the CASIA-B (a) and CASIA-C (b) datasets. In panel (a), the images depict the BG, NM, and CL conditions, arranged from left to right across different perspectives. Panel (b) showcases images depicting the FW, SW, and BW conditions, presented in sequence from left to right. Full article ">Figure 8
ROC curves for two models. The black dashed line represents the baseline performance of a random classifier. The blue curve represents the ROC curve for Model 1 (GaitSTAR), and the red curve represents the ROC curve for Model 2 (MSGG). Full article ">

21 pages, 535 KiB

Open AccessArticle

A Mathematical Optimization Model Designed to Determine the Optimal Timing of Online Rumor Intervention Based on Uncertainty Theory

by Meiling Jin, Fengming Liu, Yufu Ning, Yichang Gao and Dongmei Li

Mathematics 2024, 12(16), 2457; https://doi.org/10.3390/math12162457 - 8 Aug 2024

Viewed by 258

Abstract

The multifaceted nature of online rumors poses challenges to their identification and control. Current approaches to online rumor governance are evolving from fragmented management to collaborative efforts, emphasizing the proactive management of rumor propagation processes. This transformation considers diverse rumor types, the response [...] Read more.

The multifaceted nature of online rumors poses challenges to their identification and control. Current approaches to online rumor governance are evolving from fragmented management to collaborative efforts, emphasizing the proactive management of rumor propagation processes. This transformation considers diverse rumor types, the response behaviors of self-media and netizens, and the capabilities of regulatory bodies. This study proposes a multi-agent intervention model rooted in uncertainty theory to mitigate online rumor dissemination. Its empirical validation includes comparing three rumor categories and testing it against a single-agent model, highlighting the efficacy of collaborative governance. Quantitative assessments underscore the model’s utility in providing regulatory authorities with a robust theoretical framework for adaptive decision-making and strategy adjustments based on real-world conditions. Full article

(This article belongs to the Special Issue Mathematical Optimization and Decision Making Analysis)

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12 pages, 248 KiB

Open AccessArticle

Existence and Nonexistence Results for a Fourth-Order Boundary Value Problem with Sign-Changing Green’s Function

by Nikolay D. Dimitrov and Jagan Mohan Jonnalagadda

Mathematics 2024, 12(16), 2456; https://doi.org/10.3390/math12162456 - 8 Aug 2024

Viewed by 264

Abstract

In this paper, we consider a fourth-order three-point boundary value problem. Despite the fact that the corresponding Green’s function changes its sign on the square of its definition, we obtain the existence of at least one positive and decreasing solution under some suitable [...] Read more.

In this paper, we consider a fourth-order three-point boundary value problem. Despite the fact that the corresponding Green’s function changes its sign on the square of its definition, we obtain the existence of at least one positive and decreasing solution under some suitable conditions. The results are based on the classical Krasosel’skii’s fixed point theorem in cones. Then, we impose some sufficient conditions that allow us to deduce nonexistence results. In the end, some examples are given in order to illustrate our main results. Full article

21 pages, 392 KiB

Open AccessArticle

Testing Coefficient Randomness in Multivariate Random Coefficient Autoregressive Models Based on Locally Most Powerful Test

by Li Bi, Deqi Wang, Libo Cheng and Dequan Qi

Mathematics 2024, 12(16), 2455; https://doi.org/10.3390/math12162455 - 7 Aug 2024

Viewed by 320

Abstract

The multivariate random coefficient autoregression (RCAR) process is widely used in time series modeling applications. Random autoregressive coefficients are usually assumed to be independent and identically distributed sequences of random variables. This paper investigates the issue of coefficient constancy testing in a class [...] Read more.

The multivariate random coefficient autoregression (RCAR) process is widely used in time series modeling applications. Random autoregressive coefficients are usually assumed to be independent and identically distributed sequences of random variables. This paper investigates the issue of coefficient constancy testing in a class of static multivariate first-order random coefficient autoregressive models. We construct a new test statistic based on the locally most powerful-type test and derive its limiting distribution under the null hypothesis. The simulation compares the empirical sizes and powers of the LMP test and the empirical likelihood test, demonstrating that the LMP test outperforms the EL test in accuracy by 10.2%, 10.1%, and 30.9% under conditions of normal, Beta-distributed, and contaminated errors, respectively. We provide two sets of real data to illustrate the practical effectiveness of the LMP test. Full article

(This article belongs to the Section Probability and Statistics)

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Mathematics, Volume 12, Issue 16 (August-2 2024) – 51 articles

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