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Probability of disease extinction and outbreak in a stochastic tuberculosis model with fast-slow progression and relapse 快速-缓慢进展和复发的随机结核模型中疾病消失和爆发的概率
4区 数学
Electronic Research Archive Pub Date : 2023-01-01 DOI: 10.3934/era.2023360
Tao Zhang, Mengjuan Wu, Chunjie Gao, Yingdan Wang, Lei Wang
{"title":"Probability of disease extinction and outbreak in a stochastic tuberculosis model with fast-slow progression and relapse","authors":"Tao Zhang, Mengjuan Wu, Chunjie Gao, Yingdan Wang, Lei Wang","doi":"10.3934/era.2023360","DOIUrl":"https://doi.org/10.3934/era.2023360","url":null,"abstract":"A stochastic continuous-time Markov chain tuberculosis model with fast-slow progression and relapse is established to explore the impact of the demographic variation on TB transmission. At first, the extinction threshold and probability of the disease extinction and outbreak are obtained by applying the multitype Galton-Waston branching process for the stochastic model. In numerical simulations, the probability of the disease extinction and outbreak and expected epidemic duration of the disease are estimated. To see how demographic stochasticity affects TB dynamics, we compare dynamical behaviors of both stochastic and deterministic models, and these results show that the disease extinction in stochastic model would occur while the disease is persistent for the deterministic model. Our results suggest that minimizing the contact between the infectious and the susceptible, and detecting the latently infected as early as possible, etc., could effectively prevent the spread of tuberculosis.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"22 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":"135506301","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}
引用次数: 0
A multi-objective optimization model for green demand responsive airport shuttle scheduling with a stop location problem 考虑停站位置问题的绿色需求响应机场班车调度多目标优化模型
4区 数学
Electronic Research Archive Pub Date : 2023-01-01 DOI: 10.3934/era.2023322
Ming Wei, Congxin Yang, Bo Sun, Binbin Jing
{"title":"A multi-objective optimization model for green demand responsive airport shuttle scheduling with a stop location problem","authors":"Ming Wei, Congxin Yang, Bo Sun, Binbin Jing","doi":"10.3934/era.2023322","DOIUrl":"https://doi.org/10.3934/era.2023322","url":null,"abstract":"<abstract> <p>We proposed a multi-objective optimization framework for green demand responsive airport shuttle scheduling, which simultaneously aims at assigning demand points to selected stops and routing airport shuttles to visit these stops in their overlapping time windows to transport all passengers from their homes or workplaces to the airport. Our objectives were to minimize total travel time for passengers, the punishment expense of violating the time-window as well as carbon emissions for all shuttles. Since such issues belongs to the NP-problem, a two-stage Multi-objective ant lion optimizer (MOALO)-based algorithm incorporating dynamic programming search method was developed to acquire the optimal scheduling schemes. Finally, a case study of airport shuttle service in Tianjin Airport, China, was used to demonstrate the validity of the model and algorithm.</p> </abstract>","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"89 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":"135755092","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}
引用次数: 0
Second-order time integrators with the Fourier spectral method in application to multidimensional space-fractional FitzHugh-Nagumo model 二阶时间积分法在多维空间分数型FitzHugh-Nagumo模型中的应用
4区 数学
Electronic Research Archive Pub Date : 2023-01-01 DOI: 10.3934/era.2023369
Harish Bhatt
{"title":"Second-order time integrators with the Fourier spectral method in application to multidimensional space-fractional FitzHugh-Nagumo model","authors":"Harish Bhatt","doi":"10.3934/era.2023369","DOIUrl":"https://doi.org/10.3934/era.2023369","url":null,"abstract":"<abstract><p>This paper investigated the propagation and interaction behavior of the fractional-in-space multidimensional FitzHugh-Nagumo model using second-order time integrators in combination with the Fourier spectral method. The study focused on analyzing the accuracy, efficiency and stability of these time integrators by comparing numerical results. The experimental findings highlight the ease of implementation and suitability of the methods for long-time simulations. Furthermore, the method's capability to capture the influence of the fractional operator on the equation's dynamics was examined.</p></abstract>","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"40 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":"135759419","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}
引用次数: 0
Fourth power mean values of one kind special Kloosterman's sum 一类特殊的Kloosterman和的四次方均值
4区 数学
Electronic Research Archive Pub Date : 2023-01-01 DOI: 10.3934/era.2023326
Li Rui, Nilanjan Bag
{"title":"Fourth power mean values of one kind special Kloosterman's sum","authors":"Li Rui, Nilanjan Bag","doi":"10.3934/era.2023326","DOIUrl":"https://doi.org/10.3934/era.2023326","url":null,"abstract":"<abstract><p>The main purpose of this article is using the analytic methods and properties of classical Gauss sums to study the calculating problem of fourth power mean values of one kind special Kloosterman's sum, and give a sharp asymptotic formula for it. At the same time, the paper also provides a new and effective method for the study of related power mean value problems.</p></abstract>","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"38 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":"135799714","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}
引用次数: 0
Dynamic analysis of a delayed differential equation for <i>Tropidothorax elegans</i> pests &lt;i&gt;长三角胸&lt;/i&gt;害虫
4区 数学
Electronic Research Archive Pub Date : 2023-01-01 DOI: 10.3934/era.2023352
Tingru Yang, Yuting Ding
{"title":"Dynamic analysis of a delayed differential equation for &lt;i&gt;Tropidothorax elegans&lt;/i&gt; pests","authors":"Tingru Yang, Yuting Ding","doi":"10.3934/era.2023352","DOIUrl":"https://doi.org/10.3934/era.2023352","url":null,"abstract":"<abstract><p>In this paper, we establish an infectious disease model of <italic>Tropidothorax elegans</italic> to study the impact of them on plants. Our model involves the time delay for <italic>Tropidothorax elegans</italic> to hatch eggs, which is influenced by temperature. Second, we theoretically analyze the existence and the stability of the equilibrium and the normal form near the Hopf bifurcating critical point. Next, we choose three groups of parameters for numerical simulations to verify theoretical analysis of our model. Then, based on numerical simulations, we give bioanalysis which are consistent with the patterns of <italic>Tropidothorax elegans</italic> pests, such as dying off in large numbers of adults during the winter and one or two generations a year.</p></abstract>","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"28 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":"135261005","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}
引用次数: 0
A survey of generative adversarial networks and their application in text-to-image synthesis 生成对抗网络及其在文本到图像合成中的应用综述
4区 数学
Electronic Research Archive Pub Date : 2023-01-01 DOI: 10.3934/era.2023362
Wu Zeng, Heng-liang Zhu, Chuan Lin, Zheng-ying Xiao
{"title":"A survey of generative adversarial networks and their application in text-to-image synthesis","authors":"Wu Zeng, Heng-liang Zhu, Chuan Lin, Zheng-ying Xiao","doi":"10.3934/era.2023362","DOIUrl":"https://doi.org/10.3934/era.2023362","url":null,"abstract":"<abstract><p>With the continuous development of science and technology (especially computational devices with powerful computing capabilities), the image generation technology based on deep learning has also made significant achievements. Most cross-modal technologies based on deep learning can generate information from text into images, which has become a hot topic of current research. Text-to-image (T2I) synthesis technology has applications in multiple fields of computer vision, such as image enhancement, artificial intelligence painting, games and virtual reality. The T2I generation technology using generative adversarial networks can generate more realistic and diverse images, but there are also some shortcomings and challenges, such as difficulty in generating complex backgrounds. This review will be introduced in the following order. First, we introduce the basic principles and architecture of basic and classic generative adversarial networks (GANs). Second, this review categorizes T2I synthesis methods into four main categories. There are methods based on semantic enhancement, methods based on progressive structure, methods based on attention and methods based on introducing additional signals. We have chosen some of the classic and latest T2I methods for introduction and explain their main advantages and shortcomings. Third, we explain the basic dataset and evaluation indicators in the T2I field. Finally, prospects for future research directions are discussed. This review provides a systematic introduction to the basic GAN method and the T2I method based on it, which can serve as a reference for researchers.</p></abstract>","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"12 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":"135609329","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}
引用次数: 0
Changes in public travel willingness in the post-COVID-19 era: Evidence from social network data 后新冠肺炎时代公众出行意愿的变化:来自社交网络数据的证据
IF 0.8 4区 数学
Electronic Research Archive Pub Date : 2023-01-01 DOI: 10.3934/era.2023187
Yazao Yang, Haodong Tang, Tangzheng Weng
{"title":"Changes in public travel willingness in the post-COVID-19 era: Evidence from social network data","authors":"Yazao Yang, Haodong Tang, Tangzheng Weng","doi":"10.3934/era.2023187","DOIUrl":"https://doi.org/10.3934/era.2023187","url":null,"abstract":"Amid the impact of COVID-19, the public's willingness to travel has changed, which has had a fundamental impact on the ridership of urban public transport. Usually, travel willingness is mainly analyzed by questionnaire survey, but it needs to reflect the accurate psychological perception of the public entirely. Based on Weibo text data, this paper used natural language processing technology to quantify the public's willingness to travel in the post-COVID-19 era. First, web crawler technology was used to collect microblog text data, which will discuss COVID-19 and travel at the same time. Then, based on the Naive Bayes classification algorithm, travel sentiment analysis was carried out on the data, and the relationship between public travel willingness and urban public transport ridership was analyzed by Spearman correlation analysis. Finally, the LDA topic model was used to conduct content topic research on microblog text data during and after COVID-19. The results showed that the mean values of compelling travel emotion were -0.8197 and -0.0640 during and after COVID-19, respectively. The willingness of the public to travel directly affects the ridership of urban public transport. Compared with the COVID-19 period, the public's fear of travel infection in the post-COVID-19 era has significantly improved, but it still exists. The public pays more attention to the level of COVID-19 prevention and control and the length of travel time on public transport.","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":"70245735","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}
引用次数: 0
Positive solutions for fractional iterative functional differential equation with a convection term 带对流项的分数阶迭代泛函微分方程的正解
IF 0.8 4区 数学
Electronic Research Archive Pub Date : 2023-01-01 DOI: 10.3934/era.2023096
Qingcong Song, Xinan Hao
{"title":"Positive solutions for fractional iterative functional differential equation with a convection term","authors":"Qingcong Song, Xinan Hao","doi":"10.3934/era.2023096","DOIUrl":"https://doi.org/10.3934/era.2023096","url":null,"abstract":"In this paper, we deal with the fractional iterative functional differential equation nonlocal boundary value problem with a convection term. By using the fixed point theorems, some results about existence, uniqueness, continuous dependence and multiplicity of positive solutions are derived.","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":"70244393","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}
引用次数: 1
Spatiotemporal patterns and multiple bifurcations of a reaction- diffusion model for hair follicle spacing 毛囊间距反应扩散模型的时空模式和多重分岔
IF 0.8 4区 数学
Electronic Research Archive Pub Date : 2023-01-01 DOI: 10.3934/era.2023099
Zhili Zhang, A. Wan, Hongyan Lin
{"title":"Spatiotemporal patterns and multiple bifurcations of a reaction- diffusion model for hair follicle spacing","authors":"Zhili Zhang, A. Wan, Hongyan Lin","doi":"10.3934/era.2023099","DOIUrl":"https://doi.org/10.3934/era.2023099","url":null,"abstract":"In this paper, the dynamical behaviors of a 2-component coupled diffusive system modeling hair follicle spacing is considered. For the corresponding ODEs, we not only consider the stability and instability of the unique positive equilibrium solutions, but also show the existence of unstable Hopf bifurcating periodic solutions. For the reaction-diffusion equations, we are mainly interested in the Turing instability of the positive equilibrium solution, as well as Hopf bifurcations and steady-state bifurcations. Our results showed that, under certain conditions, the reaction-diffusion system not only has Hopf bifurcating periodic solutions (both spatially homogeneous and non-homogeneous, all unstable), but it also has non-constant positive bifurcating equilibrium solutions. This allows for a clearer understanding of the mechanism for the spatiotemporal patterns of this particular system.","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":"70244835","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}
引用次数: 0
Investigation on dynamic response and compaction degree characterization of multi-layer asphalt pavement under vibration rolling 振动碾压下多层沥青路面动力响应及压实度特性研究
IF 0.8 4区 数学
Electronic Research Archive Pub Date : 2023-01-01 DOI: 10.3934/era.2023114
Hongyu Shan, H. Dan, Shiping Wang, Zhi Zhang, Renkun Zhang
{"title":"Investigation on dynamic response and compaction degree characterization of multi-layer asphalt pavement under vibration rolling","authors":"Hongyu Shan, H. Dan, Shiping Wang, Zhi Zhang, Renkun Zhang","doi":"10.3934/era.2023114","DOIUrl":"https://doi.org/10.3934/era.2023114","url":null,"abstract":"Asphalt mixture is composed of asphalt binder with aggregates of different sizes and compacted under static or dynamic forces. In practical engineering, compaction is a critical step in asphalt pavement construction to determine the quality and service life of pavement. Since the dynamic response characteristics of asphalt pavement can reflect the compaction state of asphalt mixture in the process of compaction, the establishment of the relationship between dynamic response characteristics and compaction degree is definitely significant. In this paper, a series of vibration sensors were adopted to capture the dynamic response signal of the vibration drum and asphalt mixture in the process of vibrating compaction for different surface courses of pavement. Then, the change regulations of vibration acceleration of vibrating drum and asphalt mixture were analyzed, and the quantitative linear relationship was established between accelerations of vibrating drum and asphalt pavement compactness. Further, the concept of evaluation unit (i.e., within 2 meters along the driving direction of the roller) and prediction method of compaction degree were proposed as well. The results showed that under the same vibration compaction condition, the compaction degree values of the top, middle and bottom layers have obvious differences, which should be taken seriously into consideration in the compaction process. Meanwhile, there is little difference which respectively are 2.8, 1.3 and 0.82% for the top, middle and bottom layers between the compaction degrees obtained by the proposed method and measured test. Therefore, the average value of the acceleration peak value of vibration drum within the evaluation unit can be adopted as the characterization index of the compaction degree of asphalt pavement. The investigation of this study can provide the technical reference for compaction control of asphalt pavement to a large extent.","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":"70244854","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}
引用次数: 1
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