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Finite-/fixed-time synchronization of leakage and discrete delayed Hopfield neural networks with diffusion effects 具有扩散效应的泄漏和离散延迟Hopfield神经网络的有限/固定时间同步

IF 0.8 4区数学 Q1 MATHEMATICS

Electronic Research Archive

Pub Date : 2023-01-01 DOI: 10.3934/era.2023208

Minglei Fang, Jin-zhi Liu, Wei Wang

In this paper, the problem on finite-/fixed-time synchronization (FFTS) is investigated for a class of diffusive Hopfield neural networks with leakage and discrete delays. Some new and useful criteria independent on time delays but dependent on the diffusion coefficients are established to guarantee the FFTS for the addressed network model under a unified framework. In sharp contrast to the existed results which can only finite-timely or fixed-timely synchronize the systems with both diffusion effects and leakage delays, the theoretical results of this paper are more general and practical. Finally, a numerical example is presented to show the effectiveness of the proposed control methods.

研究了一类具有泄漏和离散延迟的扩散Hopfield神经网络的有限/固定时间同步问题。为了保证寻址网络模型在统一框架下的FFTS性能，建立了一些新的、有用的、不依赖于时滞而依赖于扩散系数的准则。与既有扩散效应又有泄漏延迟的系统只能有限及时或固定及时同步的结果形成鲜明对比，本文的理论结果更具通用性和实用性。最后，通过数值算例验证了所提控制方法的有效性。

引用次数: 1

A simple and efficient numerical method for the Allen–Cahn equation on effective symmetric triangular meshes 有效对称三角形网格上Allen-Cahn方程的一种简单有效的数值求解方法

IF 0.8 4区数学 Q1 MATHEMATICS

Electronic Research Archive

Pub Date : 2023-01-01 DOI: 10.3934/era.2023233

Youngjin Hwang, Seokju Ham, Chaeyoung Lee, Gyeonggyu Lee, S. Kang, Junseok Kim

In this paper, we propose a novel, simple, efficient, and explicit numerical method for the Allen–Cahn (AC) equation on effective symmetric triangular meshes. First, we compute the net vector of all vectors starting from each node point to its one-ring neighbor vertices and virtually adjust the neighbor vertices so that the net vector is zero. Then, we define the values at the virtually adjusted nodes using linear and quadratic interpolations. Finally, we define a discrete Laplace operator on triangular meshes. We perform several computational experiments to demonstrate the performance of the proposed numerical method for the Laplace operator, the diffusion equation, and the AC equation on triangular meshes.

本文提出了一种新颖、简单、高效、显式的有效对称三角网格上Allen-Cahn (AC)方程的数值求解方法。首先，我们计算从每个节点点到其单环相邻顶点的所有向量的净向量，并虚拟地调整相邻顶点，使净向量为零。然后，我们使用线性插值和二次插值来定义虚拟调整节点的值。最后，我们在三角网格上定义了一个离散拉普拉斯算子。我们进行了几个计算实验来证明所提出的拉普拉斯算子、扩散方程和三角形网格上的AC方程的数值方法的性能。

引用次数: 0

Induced 3-Hom-Lie superalgebras 诱导3- homlie超代数

IF 0.8 4区数学 Q1 MATHEMATICS

Electronic Research Archive

Pub Date : 2023-01-01 DOI: 10.3934/era.2023237

Baoling Guan, Xinxin Tian, Lijun Tian

We construct 3-Hom-Lie superalgebras on a commutative Hom-superalgebra by means of involution and even degree derivation. We construct a representation of induced 3-Hom-Lie superalgebras by means of supertrace.

利用对合和偶次求导的方法，在可交换的homlie超代数上构造了3- homlie超代数。利用超迹构造了诱导3- homlie超代数的表示。

引用次数: 0

A fair evaluation of the potential of machine learning in maritime transportation 对机器学习在海上运输中的潜力进行公平评估

IF 0.8 4区数学 Q1 MATHEMATICS

Electronic Research Archive

Pub Date : 2023-01-01 DOI: 10.3934/era.2023243

Xi Luo, Ran Yan, Shuaian Wang, Lu Zhen

Machine learning (ML) techniques are extensively applied to practical maritime transportation issues. Due to the difficulty and high cost of collecting large volumes of data in the maritime industry, in many maritime studies, ML models are trained with small training datasets. The relative predictive performances of these trained ML models are then compared with each other and with the conventional model using the same test set. The ML model that performs the best out of the ML models and better than the conventional model on the test set is regarded as the most effective in terms of this prediction task. However, in scenarios with small datasets, this common process may lead to an unfair comparison between the ML and the conventional model. Therefore, we propose a novel process to fairly compare multiple ML models and the conventional model. We first select the best ML model in terms of predictive performance for the validation set. Then, we combine the training and the validation sets to retrain the best ML model and compare it with the conventional model on the same test set. Based on historical port state control (PSC) inspection data, we examine both the common process and the novel process in terms of their ability to fairly compare ML models and the conventional model. The results show that the novel process is more effective at fairly comparing the ML models with the conventional model on different test sets. Therefore, the novel process enables a fair assessment of ML models' ability to predict key performance indicators in the context of limited data availability in the maritime industry, such as predicting the ship fuel consumption and port traffic volume, thereby enhancing their reliability for real-world applications.

机器学习(ML)技术广泛应用于实际的海上运输问题。由于在航运业中收集大量数据的难度和高成本，在许多海事研究中，ML模型使用小型训练数据集进行训练。然后使用相同的测试集相互比较这些训练好的ML模型的相对预测性能，并与传统模型进行比较。在ML模型中表现最好且在测试集上优于传统模型的ML模型被认为是在该预测任务中最有效的。然而，在小数据集的场景中，这种常见的过程可能会导致机器学习和传统模型之间的不公平比较。因此，我们提出了一种新的过程来公平地比较多个ML模型和传统模型。我们首先根据验证集的预测性能选择最佳ML模型。然后，我们结合训练集和验证集对最佳ML模型进行重新训练，并在同一测试集上将其与常规模型进行比较。基于历史港口国控制(PSC)检查数据，我们从公平比较ML模型和传统模型的能力方面检查了通用过程和新过程。结果表明，在不同的测试集上，该方法可以更有效地比较机器学习模型和传统模型。因此，新过程可以公平评估ML模型在航运业有限数据可用性背景下预测关键性能指标的能力，例如预测船舶燃料消耗和港口交通量，从而提高其在实际应用中的可靠性。

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引用次数: 0

Liner alliance shipping network design model with shippers' choice inertia and empty container relocation 考虑托运人选择惯性和空箱搬迁的班轮联盟运输网络设计模型

IF 0.8 4区数学 Q1 MATHEMATICS

Electronic Research Archive

Pub Date : 2023-01-01 DOI: 10.3934/era.2023280

Xu Xin, Xiaoli Wang, Zhang Tao, Haichao Chen, Qian Guo, Shaorui Zhou

Liner companies have responded to escalating trade conflicts and the impact of the COVID-19 pandemic by forming alliances and implementing streamlined approaches to manage empty containers, which has strengthened the resilience of their supply chains. Meanwhile, shippers have grown more sensitive during these turbulent times. Motivated by the market situation, we investigate a liner alliance shipping network design problem considering the choice inertia of shippers and empty container relocation. To address this problem, we propose a bilevel programming model. The upper model aims to maximize the alliance's profit by optimizing the alliance's shipping network and fleet design scheme. The lower model focuses on optimizing the slot allocation scheme and the empty container relocation scheme. To ensure the sustainable operation of the alliance, we develop an inverse optimization model to allocate profits among alliance members. Furthermore, we design a differential evolution metaheuristic algorithm to solve the model. To validate the effectiveness of the proposed model and algorithm, numerical experiments are conducted using actual shipping data from the Asia-Western Europe shipping route. The results confirm the validity of the proposed model and algorithm, which can serve as a crucial decision-making reference for the daily operations of a liner shipping alliance.

班轮公司为应对不断升级的贸易冲突和2019冠状病毒病大流行的影响，结成了联盟，并采用了简化的方法来管理空集装箱，从而增强了其供应链的抵御能力。与此同时，托运人在动荡时期变得更加敏感。在市场形势的激励下，研究了考虑托运人选择惯性和空箱搬迁的班轮联盟运输网络设计问题。为了解决这个问题，我们提出了一个双层规划模型。上层模型旨在通过优化联盟的航运网络和船队设计方案，使联盟的利润最大化。下一模型着重于优化槽位分配方案和空箱搬迁方案。为了保证联盟的可持续运行，我们建立了一个逆向优化模型来分配联盟成员之间的利润。此外，我们设计了一个差分进化元启发式算法来求解该模型。为了验证所提模型和算法的有效性，利用亚洲-西欧航线的实际航运数据进行了数值实验。研究结果验证了模型和算法的有效性，为班轮运输联盟的日常运营提供了重要的决策参考。

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引用次数: 3

Age estimation algorithm based on deep learning and its application in fall detection 基于深度学习的年龄估计算法及其在跌倒检测中的应用

IF 0.8 4区数学 Q1 MATHEMATICS

Electronic Research Archive

Pub Date : 2023-01-01 DOI: 10.3934/era.2023251

Jiayi Yu, Ye Tao, Huang Zhang, Zhibiao Wang, Wenhua Cui, Tianwei Shi

With the continuous development and progress of society, age estimation based on deep learning has gradually become a key link in human-computer interaction. Widely combined with other fields of application, this paper performs a gradient division of human fall behavior according to the age estimation of the human body, a complete priority detection of the key population, and a phased single aggregation backbone network VoVNetv4 was proposed for feature extraction. At the same time, the regional single aggregation module ROSA module was constructed to encapsulate the feature module regionally. The adaptive stage module was used for feature smoothing. Consistent predictions for each task were made using the CORAL framework as a classifier and tasks were divided in binary. At the same time, a gradient two-node fall detection framework combined with age estimation was designed. The detection was divided into a primary node and a secondary node. In the first-level node, the age estimation algorithm based on VoVNetv4 was used to classify the population of different age groups. A face tracking algorithm was constructed by combining the key point matrices of humans, and the body processed by OpenPose with the central coordinates of the human face. In the secondary node, human age gradient information was used to detect human falls based on the AT-MLP model. The experimental results show that compared with Resnet-34, the MAE value of the proposed method decreased by 0.41. Compared with curriculum learning and the CORAL-CNN method, MAE value decreased by 0.17 relative to the RMSE value. Compared with other methods, the method in this paper was significantly lower, with a biggest drop of 0.51.

随着社会的不断发展和进步，基于深度学习的年龄估计逐渐成为人机交互的关键环节。本文广泛结合其他应用领域，根据人体年龄估计对人体跌倒行为进行梯度划分，对关键人群进行完整的优先级检测，提出了分阶段的单聚合骨干网VoVNetv4进行特征提取。同时，构建区域单聚合模块ROSA模块，对特征模块进行区域封装。采用自适应阶段模块进行特征平滑。使用CORAL框架作为分类器对每个任务进行一致的预测，并将任务分为二值。同时，设计了一种结合年龄估计的梯度双节点跌倒检测框架。检测分为主节点和次节点。在第一级节点，使用基于VoVNetv4的年龄估计算法对不同年龄组的人群进行分类。将人体关键点矩阵与OpenPose处理的人体与人脸中心坐标相结合，构建人脸跟踪算法。在次要节点，基于AT-MLP模型，利用人类年龄梯度信息检测人类跌倒。实验结果表明，与Resnet-34相比，该方法的MAE值降低了0.41。与课程学习和CORAL-CNN方法相比，MAE值相对RMSE值降低了0.17。与其他方法相比，本文方法显著降低，最大降幅为0.51。

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引用次数: 0

The exact solutions of the fractional-stochastic Fokas-Lenells equation in optical fiber communication 光纤通信中分数-随机Fokas-Lenells方程的精确解

IF 0.8 4区数学 Q1 MATHEMATICS

Electronic Research Archive

Pub Date : 2023-01-01 DOI: 10.3934/era.2023180

S. Albosaily, W. Mohammed, M. El-Morshedy

The fractional-stochastic Fokas-Lenells equation (FSFLE) in the Stratonovich sense is taken into account here. The modified mapping method is used to generate new trigonometric, hyperbolic, elliptic and rational stochastic fractional solutions. Because the Fokas-Lenells equation has many implementations in telecommunication modes, complex system theory, quantum field theory, and quantum mechanics, the obtained solutions can be employed to describe a wide range of exciting physical phenomena. We plot several 2D and 3D diagrams to demonstrate how multiplicative noise and fractional derivatives affect the analytical solutions of the FSFLE. Also, we show how multiplicative noise at zero stabilizes FSFLE solutions.

这里考虑了Stratonovich意义上的分数随机Fokas-Lenells方程(fsle)。利用改进的映射方法生成新的三角解、双曲解、椭圆解和有理随机分式解。由于Fokas-Lenells方程在通信模式、复杂系统理论、量子场论和量子力学中有许多实现，所得到的解可以用来描述广泛的令人兴奋的物理现象。我们绘制了几个2D和3D图表来演示乘法噪声和分数阶导数如何影响fsle的解析解。此外，我们还展示了零处的乘法噪声如何稳定fsle解。

引用次数: 0

On the regularization and matrix Lyapunov functions for fuzzy differential systems with uncertain parameters 参数不确定模糊微分系统的正则化与矩阵Lyapunov函数

4区数学 Q1 MATHEMATICS

Electronic Research Archive

Pub Date : 2023-01-01 DOI: 10.3934/era.2023310

Anatoliy Martynyuk, Gani Stamov, Ivanka Stamova, Yulya Martynyuk–Chernienko

In this paper, for a regularized fuzzy system, a generalization of the direct Lyapunov method is adapted on the base of matrix-valued Lyapunov-like functions. First, the new concept of a regularization scheme for fuzzy systems is discussed and the matrix-valued Lyapunov function technique is introduced. Then, sufficient conditions are established for the boundedness and stability of the equilibrium set of solutions of the regularized fuzzy system of differential equations. Scalar and vector Lyapunov-type functions are used based on an auxiliary matrix-valued function. Finally, a discussion is offered for the future directions of the proposed approach. Since the strategies for the analysis of the stability of fuzzy models are very important in numerous aspects, we expect that our results will inspire researchers to develop the introduced concept.

本文在矩阵值类李雅普诺夫函数的基础上，对正则化模糊系统进行了直接李雅普诺夫方法的推广。首先，讨论了模糊系统正则化方案的新概念，并引入了矩阵值李雅普诺夫函数技术。然后，建立了正则化模糊微分方程组平衡解集的有界性和稳定性的充分条件。标量和矢量李雅普诺夫型函数是基于辅助矩阵值函数使用的。最后，对该方法的未来发展方向进行了讨论。由于模糊模型稳定性分析的策略在许多方面都非常重要，我们期望我们的结果将激励研究人员发展所引入的概念。</ </abstract>

引用次数: 0

Microscopic mechanism of subgrade vibration compaction based on discrete element method 基于离散元法的路基振动压实细观机理

4区数学 Q1 MATHEMATICS

Electronic Research Archive

Pub Date : 2023-01-01 DOI: 10.3934/era.2023358

Xin Gao, Hao Liu, Zhou Fang, Yang Zhang

The discrete element is an important tool for vibration compaction simulation from the microscopic viewpoint. The irregular particle model was established by the disc filling method, and the linear contact model with anti-rolling was selected to reflect the contact characteristics between the particles, so as to establish the simulation model of subgrade vibratory compaction. Based on this model, the stress characteristics of the area below the center of the vibrating wheel and the surface area of the soil were studied, and the principle of vibratory compaction was discussed. The results show that the distribution of vertical stresses below the center of drum basically presents a decreasing trend in the depth range during vibration, with the stress amplitude of the lower structure increasing and the stress magnitude of the upper structure decreasing. The distribution of horizontal stresses in the area below the center of the vibrating wheel is similar to the stress distribution in the splitting test. The soil at the surface has an obvious pushing and squeezing effect, and the transmission distance of horizontal stresses is larger than that of vertical stresses. The soil at the surface is pushed and the horizontal stresses are transmitted at a greater distance than the vertical stresses, which, together with a certain degree of shear effect, causes a certain uplift deformation of the soil around the vibrating wheel. In general, the vibration compaction process is relatively consistent with the theory of repeated loading and the theory of alternating shear strain.

& lt; abstract>从微观角度看，离散元是振动压实模拟的重要工具。采用圆盘填充法建立不规则颗粒模型，选择具有抗滚动的线性接触模型来反映颗粒之间的接触特性，从而建立路基振动压实仿真模型。在此基础上，研究了振动轮中心以下区域和土体表面积的应力特性，并对振动压实原理进行了探讨。结果表明:在振动深度范围内，鼓心以下垂直应力分布基本呈减小趋势，下部结构应力幅值增大，上部结构应力幅值减小;振动轮中心以下区域的水平应力分布与劈裂试验时的应力分布相似。地表土体具有明显的推挤作用，且水平应力的传递距离大于垂直应力的传递距离。表面土体受到推力作用，水平应力传递距离大于垂直应力，加之一定程度的剪切效应，使振动轮周围土体产生一定的上扬变形。总体而言，振动压实过程相对符合重复加载理论和交变剪切应变理论。& lt; / abstract>

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引用次数: 0

Dynamic analysis of a stochastic epidemic model incorporating the double epidemic hypothesis and Crowley-Martin incidence term 结合双重流行病假设和Crowley-Martin发生率项的随机流行病模型的动态分析

4区数学 Q1 MATHEMATICS

Electronic Research Archive

Pub Date : 2023-01-01 DOI: 10.3934/era.2023312

Wenxuan Li, Suli Liu

The host population in epidemiology may actually be at risk of more than two infectious diseases with stochastic complicated interaction, e.g., HIV and HBV. In this paper, we propose a class of stochastic epidemic model that applies the double epidemic hypothesis and Crowley-Martin incidence rate in order to explore how stochastic disturbances affect the spread of diseases. While disregarding stochastic disturbances, we examine the dynamic features of the system in which the local stability of equilibria are totally determined by the basic reproduction numbers. We focus particularly on the threshold dynamics of the corresponding stochastic system, and we obtain the extinction and permanency conditions for a pair of infectious diseases. We find that the threshold dynamics of the deterministic and stochastic systems vary significantly: (ⅰ) disease outbreaks can be controlled by appropriate stochastic disturbances; (ⅱ) diseases die out when the intensity of environmental perturbations is higher. The effects of certain important parameters on deterministic and stochastic disease transmission were obtained through numerical simulations. Our observations indicate that controlling epidemics should improve the effectiveness of prevention measures for susceptible individuals while improving the effectiveness of treatment for infected individuals.

<abstract>< >流行病学中的宿主人群实际上可能存在两种以上随机复杂相互作用的传染病风险，如HIV和HBV。本文提出了一类应用双重流行假设和Crowley-Martin发病率的随机流行病模型，以探讨随机干扰对疾病传播的影响。在不考虑随机干扰的情况下，我们研究了平衡态的局部稳定性完全由基本再生数决定的系统的动态特征。重点研究了相应随机系统的阈值动力学，得到了一对传染病的灭绝和永久条件。我们发现，确定性系统和随机系统的阈值动力学差异显著:(1)疾病暴发可以通过适当的随机干扰来控制;(ⅱ)环境扰动强度越大，疾病就会死亡。通过数值模拟得到了某些重要参数对确定性和随机疾病传播的影响。我们的观察结果表明，控制流行病应提高易感个体预防措施的有效性，同时提高对感染个体的治疗有效性。</ </abstract>

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