{"title":"Finite-/fixed-time synchronization of leakage and discrete delayed Hopfield neural networks with diffusion effects","authors":"Minglei Fang, Jin-zhi Liu, Wei Wang","doi":"10.3934/era.2023208","DOIUrl":"https://doi.org/10.3934/era.2023208","url":null,"abstract":"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.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70246553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Youngjin Hwang, Seokju Ham, Chaeyoung Lee, Gyeonggyu Lee, S. Kang, Junseok Kim
{"title":"A simple and efficient numerical method for the Allen–Cahn equation on effective symmetric triangular meshes","authors":"Youngjin Hwang, Seokju Ham, Chaeyoung Lee, Gyeonggyu Lee, S. Kang, Junseok Kim","doi":"10.3934/era.2023233","DOIUrl":"https://doi.org/10.3934/era.2023233","url":null,"abstract":"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.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70246882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Induced 3-Hom-Lie superalgebras","authors":"Baoling Guan, Xinxin Tian, Lijun Tian","doi":"10.3934/era.2023237","DOIUrl":"https://doi.org/10.3934/era.2023237","url":null,"abstract":"<abstract><p>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.</p></abstract>","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70246949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A fair evaluation of the potential of machine learning in maritime transportation","authors":"Xi Luo, Ran Yan, Shuaian Wang, Lu Zhen","doi":"10.3934/era.2023243","DOIUrl":"https://doi.org/10.3934/era.2023243","url":null,"abstract":"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.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70247104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Liner alliance shipping network design model with shippers' choice inertia and empty container relocation","authors":"Xu Xin, Xiaoli Wang, Zhang Tao, Haichao Chen, Qian Guo, Shaorui Zhou","doi":"10.3934/era.2023280","DOIUrl":"https://doi.org/10.3934/era.2023280","url":null,"abstract":"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.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70247216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jiayi Yu, Ye Tao, Huang Zhang, Zhibiao Wang, Wenhua Cui, Tianwei Shi
{"title":"Age estimation algorithm based on deep learning and its application in fall detection","authors":"Jiayi Yu, Ye Tao, Huang Zhang, Zhibiao Wang, Wenhua Cui, Tianwei Shi","doi":"10.3934/era.2023251","DOIUrl":"https://doi.org/10.3934/era.2023251","url":null,"abstract":"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.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70247555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The exact solutions of the fractional-stochastic Fokas-Lenells equation in optical fiber communication","authors":"S. Albosaily, W. Mohammed, M. El-Morshedy","doi":"10.3934/era.2023180","DOIUrl":"https://doi.org/10.3934/era.2023180","url":null,"abstract":"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.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70246015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the regularization and matrix Lyapunov functions for fuzzy differential systems with uncertain parameters","authors":"Anatoliy Martynyuk, Gani Stamov, Ivanka Stamova, Yulya Martynyuk–Chernienko","doi":"10.3934/era.2023310","DOIUrl":"https://doi.org/10.3934/era.2023310","url":null,"abstract":"<abstract><p>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.</p></abstract>","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"220 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135400796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Microscopic mechanism of subgrade vibration compaction based on discrete element method","authors":"Xin Gao, Hao Liu, Zhou Fang, Yang Zhang","doi":"10.3934/era.2023358","DOIUrl":"https://doi.org/10.3934/era.2023358","url":null,"abstract":"<abstract> <p>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.</p> </abstract>","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135445276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dynamic analysis of a stochastic epidemic model incorporating the double epidemic hypothesis and Crowley-Martin incidence term","authors":"Wenxuan Li, Suli Liu","doi":"10.3934/era.2023312","DOIUrl":"https://doi.org/10.3934/era.2023312","url":null,"abstract":"<abstract><p>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.</p></abstract>","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135494641","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}