In the processes of industrial defects detections, deep neural networks have received much favor for its high efficiency and low labor cost. As is known, a big amount of dataset is the precondition to train any network. However, the datasets of industrial defects tended to be small and hard to obtain. To solve the problem above, we raise a thought of simulation based on MCMC aiming to sample from the posterior distribution of the defect’s images, which is viewed as the limit distribution of certain Markov Chain. Once we capture the posterior distribution, the law of the defects is revealed. 1Therefore, generating pseudo samples by the law is quite reasonable. It has been proved that the algorithm is practicable by advanced devices and economical in the long term. The significance of this work is to raise a practicable thought towards the problem of mini-batch industrial datasets. Code is available at https://github.com/MrSmallWang/solutions-tosmall- datasets.
{"title":"Solutions to small datasets in defects detection based on Markov chain Monte Carlo simulations","authors":"Xin Wang, Hua Fan","doi":"10.1117/12.2679161","DOIUrl":"https://doi.org/10.1117/12.2679161","url":null,"abstract":"In the processes of industrial defects detections, deep neural networks have received much favor for its high efficiency and low labor cost. As is known, a big amount of dataset is the precondition to train any network. However, the datasets of industrial defects tended to be small and hard to obtain. To solve the problem above, we raise a thought of simulation based on MCMC aiming to sample from the posterior distribution of the defect’s images, which is viewed as the limit distribution of certain Markov Chain. Once we capture the posterior distribution, the law of the defects is revealed. 1Therefore, generating pseudo samples by the law is quite reasonable. It has been proved that the algorithm is practicable by advanced devices and economical in the long term. The significance of this work is to raise a practicable thought towards the problem of mini-batch industrial datasets. Code is available at https://github.com/MrSmallWang/solutions-tosmall- datasets.","PeriodicalId":301595,"journal":{"name":"Conference on Pure, Applied, and Computational Mathematics","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123710065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the article, at the first, the new notion of LP well-posedness has been generalized in the paper. the LP well-posedness is related to a approximate function ℎ1(𝜀, 𝑢) and ℎ2(𝜀, 𝑢) rather than simple parameter 𝜀. And so as to to discuss the LP well-posedness, then some different metric characterizations of LP well-posedness was established and approximating solution set was constructed. In the end some equivalence results of strong LP well-posedness (resp., in the generalized sense) is proved.
{"title":"Levitin-Polyak well-posedness for systems of time-dependent variational-hemivariational inequalities","authors":"Huamin Luo, Chang-jie Fang","doi":"10.1117/12.2679215","DOIUrl":"https://doi.org/10.1117/12.2679215","url":null,"abstract":"In the article, at the first, the new notion of LP well-posedness has been generalized in the paper. the LP well-posedness is related to a approximate function ℎ1(𝜀, 𝑢) and ℎ2(𝜀, 𝑢) rather than simple parameter 𝜀. And so as to to discuss the LP well-posedness, then some different metric characterizations of LP well-posedness was established and approximating solution set was constructed. In the end some equivalence results of strong LP well-posedness (resp., in the generalized sense) is proved.","PeriodicalId":301595,"journal":{"name":"Conference on Pure, Applied, and Computational Mathematics","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128905367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Liaoning Province, as a national traditional heavy industry area, contains 30 cities facing varying degrees of urban contraction. We classify these 30 cities by K-means clustering analysis. Then, the grey correlation model is established. By solving the grey correlation coefficient between the economic and social indicators and the total population of shrinking cities, the factors affecting the shrinking urban population are obtained. Finally, we establish a comprehensive evaluation system of shrinking cities with population, indicators and GDP as evaluation indicators. The entropy weight method model is established to determine the weight of each evaluation index in order to obtain the contraction comprehensive index of each city. The change rate of the comprehensive index of each city is calculated respectively, and then the development and evolution trend of each shrinking city is analyzed.
{"title":"Analysis of urban contraction based on grey correlation and entropy weight models","authors":"T. Yan, Long Ma","doi":"10.1117/12.2678959","DOIUrl":"https://doi.org/10.1117/12.2678959","url":null,"abstract":"Liaoning Province, as a national traditional heavy industry area, contains 30 cities facing varying degrees of urban contraction. We classify these 30 cities by K-means clustering analysis. Then, the grey correlation model is established. By solving the grey correlation coefficient between the economic and social indicators and the total population of shrinking cities, the factors affecting the shrinking urban population are obtained. Finally, we establish a comprehensive evaluation system of shrinking cities with population, indicators and GDP as evaluation indicators. The entropy weight method model is established to determine the weight of each evaluation index in order to obtain the contraction comprehensive index of each city. The change rate of the comprehensive index of each city is calculated respectively, and then the development and evolution trend of each shrinking city is analyzed.","PeriodicalId":301595,"journal":{"name":"Conference on Pure, Applied, and Computational Mathematics","volume":"178 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126763625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study a predator-prey model with Beddington-DeAngelis functional response and two delays. In this model, selective harvesting of predator species is discussed and two delays describe the time that juveniles take to mature. We have analyzed the effects of delay and harvesting on the model dynamics. First, the existence, uniqueness of positive equilibrium are discussed. Then, by analyzing the associated characteristic equation, stability of positive equilibrium and some sufficient conditions for the existence of Hopf bifurcation are given. Finally, the theoretical prediction is proved by matlab numerical simulation results.
{"title":"Hopf bifurcation of a prey-predator system with two delays and selective harvesting","authors":"Feng-mei Zhang, Wencheng Chen, Peng Liu","doi":"10.1117/12.2679278","DOIUrl":"https://doi.org/10.1117/12.2679278","url":null,"abstract":"In this paper, we study a predator-prey model with Beddington-DeAngelis functional response and two delays. In this model, selective harvesting of predator species is discussed and two delays describe the time that juveniles take to mature. We have analyzed the effects of delay and harvesting on the model dynamics. First, the existence, uniqueness of positive equilibrium are discussed. Then, by analyzing the associated characteristic equation, stability of positive equilibrium and some sufficient conditions for the existence of Hopf bifurcation are given. Finally, the theoretical prediction is proved by matlab numerical simulation results.","PeriodicalId":301595,"journal":{"name":"Conference on Pure, Applied, and Computational Mathematics","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127102249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wasserstein distances in optimal transport provides a mathematical tool to measure distances between functions or more general objects. By Wasserstein distances, we define a distance on the moduli space of a class of statistical manifolds. We construct a Riemannian metric of this space and verify that the defined distance can be regarded as the induced distance of the metric.
{"title":"A metric structure of statistical manifolds based on optimal transportation theory","authors":"Chunyan Zhao, Yujie Huang, Qin Zhong, Mei Zhang","doi":"10.1117/12.2679132","DOIUrl":"https://doi.org/10.1117/12.2679132","url":null,"abstract":"Wasserstein distances in optimal transport provides a mathematical tool to measure distances between functions or more general objects. By Wasserstein distances, we define a distance on the moduli space of a class of statistical manifolds. We construct a Riemannian metric of this space and verify that the defined distance can be regarded as the induced distance of the metric.","PeriodicalId":301595,"journal":{"name":"Conference on Pure, Applied, and Computational Mathematics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128525440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we focus on the Cauchy problem for the modified Camassa-Holm-Novikov equation with an additional weakly dissipative term. We will investigate 3 aspects. First, we present some key facts about local well-posedness and blow-up criteria. Second, the wave-breaking phenomenon will be ensured by displaying some conditions related to the initial data. Then we present some results about the wave breaking criteria. We finally explore the global existence problem.
{"title":"Global existence and wave breaking for the modified Camassa-Holm-Novikov equation with an additional weakly dissipative term","authors":"Jiaxing Li","doi":"10.1117/12.2679043","DOIUrl":"https://doi.org/10.1117/12.2679043","url":null,"abstract":"In this paper, we focus on the Cauchy problem for the modified Camassa-Holm-Novikov equation with an additional weakly dissipative term. We will investigate 3 aspects. First, we present some key facts about local well-posedness and blow-up criteria. Second, the wave-breaking phenomenon will be ensured by displaying some conditions related to the initial data. Then we present some results about the wave breaking criteria. We finally explore the global existence problem.","PeriodicalId":301595,"journal":{"name":"Conference on Pure, Applied, and Computational Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115343981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In Game Theory, the computation and counting of equilibrium and the structural features of equilibrium are major research topics. The existence of equilibrium naturally forms a decision problem. The Nash equilibrium composed of mixed strategies always exists in the matrix and double matrix games. Therefore, calculating Nash equilibrium is the main task in the matrix and double matrix games. For the double matrix game, the measure of its Nash equilibrium can be based on the stability implied in the Nash equilibrium definition. Besides, a propositional formula can construct a two-player game given as a bi-matrix by specifying a proper finite set of strategies and adding a transformation. In this study, we investigate the development of Nash equilibriums by analyzing the structure-property of bi-matrix. We examine the characterization of Nash equilibrium creation and the relationship between satisfiable assignments of formula and Nash equilibriums of generated Game based on the characterization of bi-matrix formation and the stability principle of Nash equilibriums. The method from analysis and logic helps examine some relationships between combination optimization issues in graph theory and game systems by examining the structure of bi-matrix and combining the stability principle of Nash equilibriums to research the characterization of Nash equilibriums.
{"title":"The formation analysis of Nash equilibriums in bi-matrix game generated by propositional formulas","authors":"Jiaozhen Zhao, Tsing Lee, Chun Li, Changyi Lu","doi":"10.1117/12.2679098","DOIUrl":"https://doi.org/10.1117/12.2679098","url":null,"abstract":"In Game Theory, the computation and counting of equilibrium and the structural features of equilibrium are major research topics. The existence of equilibrium naturally forms a decision problem. The Nash equilibrium composed of mixed strategies always exists in the matrix and double matrix games. Therefore, calculating Nash equilibrium is the main task in the matrix and double matrix games. For the double matrix game, the measure of its Nash equilibrium can be based on the stability implied in the Nash equilibrium definition. Besides, a propositional formula can construct a two-player game given as a bi-matrix by specifying a proper finite set of strategies and adding a transformation. In this study, we investigate the development of Nash equilibriums by analyzing the structure-property of bi-matrix. We examine the characterization of Nash equilibrium creation and the relationship between satisfiable assignments of formula and Nash equilibriums of generated Game based on the characterization of bi-matrix formation and the stability principle of Nash equilibriums. The method from analysis and logic helps examine some relationships between combination optimization issues in graph theory and game systems by examining the structure of bi-matrix and combining the stability principle of Nash equilibriums to research the characterization of Nash equilibriums.","PeriodicalId":301595,"journal":{"name":"Conference on Pure, Applied, and Computational Mathematics","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123433789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper mainly introduces several kinds of global conformal parameterization theories and algorithms, which can deal with complex surfaces under different genus. Pure first-order differential algorithm and pure second-order differential algorithm are based on the contents of global differential geometry, whose core ideas come from Riemann’s single-valued theorem and Teichmuller theory. Ricci flow algorithm and quasi-conformal mapping algorithm are based on the contents of the field of geometric partial differential equations, which can be optimized by minimizing energy to get results. The optimal transport algorithm is based on convex differential geometry and geometric variational principle, which can be transformed into computational geometry algorithm to find the solution.
{"title":"A survey of global conformal parameterization","authors":"Yanjun Shen","doi":"10.1117/12.2679279","DOIUrl":"https://doi.org/10.1117/12.2679279","url":null,"abstract":"This paper mainly introduces several kinds of global conformal parameterization theories and algorithms, which can deal with complex surfaces under different genus. Pure first-order differential algorithm and pure second-order differential algorithm are based on the contents of global differential geometry, whose core ideas come from Riemann’s single-valued theorem and Teichmuller theory. Ricci flow algorithm and quasi-conformal mapping algorithm are based on the contents of the field of geometric partial differential equations, which can be optimized by minimizing energy to get results. The optimal transport algorithm is based on convex differential geometry and geometric variational principle, which can be transformed into computational geometry algorithm to find the solution.","PeriodicalId":301595,"journal":{"name":"Conference on Pure, Applied, and Computational Mathematics","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128359101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Stability of non-autonomous system is in general difficult to analyze and the frozen in time assumption is known to break down in high dimensional system. This work proposes another criterion to analyze the stability of non-autonomous system by obtaining its upper bound on the energy growth. The computation of upper bound is then formulated as a convex optimization problem based on linear matrix inequality. We also perform pendulum experiments with a linear varying or oscillating length to analyze its stability. The experimental results demonstrate that the time-varying length of pendulum will lead to a growing oscillation amplitude of pendulum and the associated growth rate also agree well with the upper bound prediction based on the linear matrix inequality. This work provides a new analysis framework to analyze stability of non-autonomous system.
{"title":"Growth rate of a pendulum with a time-varying length","authors":"Zhifei Zhang","doi":"10.1117/12.2679216","DOIUrl":"https://doi.org/10.1117/12.2679216","url":null,"abstract":"Stability of non-autonomous system is in general difficult to analyze and the frozen in time assumption is known to break down in high dimensional system. This work proposes another criterion to analyze the stability of non-autonomous system by obtaining its upper bound on the energy growth. The computation of upper bound is then formulated as a convex optimization problem based on linear matrix inequality. We also perform pendulum experiments with a linear varying or oscillating length to analyze its stability. The experimental results demonstrate that the time-varying length of pendulum will lead to a growing oscillation amplitude of pendulum and the associated growth rate also agree well with the upper bound prediction based on the linear matrix inequality. This work provides a new analysis framework to analyze stability of non-autonomous system.","PeriodicalId":301595,"journal":{"name":"Conference on Pure, Applied, and Computational Mathematics","volume":"12725 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130063791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nowadays, the data generated by expressway operation is large in scale and various in types. When analyzing expressway safety risk, the traditional methods are easily subject to the subjective limitations of analysts, as well as the limitations of experience or knowledge, making it impossible to accurately predict traffic risk, and the traditional attribution theory model cannot simultaneously process and analyze multiple heterogeneous data. The data warehouse and data mining technology based on big data drive can analyze the operation data of different ranges and regions in a unified way, mine the spatio-temporal distribution characteristics, improve the scientific utilization efficiency of traffic data resources, and improve the information service level for traffic safety and early warning. This paper starts with the characteristics of road traffic accident information collection data and the key problems of data analysis and application in China point, reduce the occurrence of road traffic accidents through multi angle and all-round grey clustering evaluation method analysis.
{"title":"Research on intelligent traffic risk assessment method based on grey clustering","authors":"Shaoxin Pu","doi":"10.1117/12.2678975","DOIUrl":"https://doi.org/10.1117/12.2678975","url":null,"abstract":"Nowadays, the data generated by expressway operation is large in scale and various in types. When analyzing expressway safety risk, the traditional methods are easily subject to the subjective limitations of analysts, as well as the limitations of experience or knowledge, making it impossible to accurately predict traffic risk, and the traditional attribution theory model cannot simultaneously process and analyze multiple heterogeneous data. The data warehouse and data mining technology based on big data drive can analyze the operation data of different ranges and regions in a unified way, mine the spatio-temporal distribution characteristics, improve the scientific utilization efficiency of traffic data resources, and improve the information service level for traffic safety and early warning. This paper starts with the characteristics of road traffic accident information collection data and the key problems of data analysis and application in China point, reduce the occurrence of road traffic accidents through multi angle and all-round grey clustering evaluation method analysis.","PeriodicalId":301595,"journal":{"name":"Conference on Pure, Applied, and Computational Mathematics","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127503219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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