where $ B_1 $ is the unit ball in $ mathbb{R}^N(Ngeq 3) $, $ q(x) = q(|x|) $ is a continuous radial function satifying $ 2leq q(x) < 2^* = frac{2N}{N-2} $ and $ q(0) > 2 $. Using variational methods and a priori estimate, the existence of a positive radial solution for (0.1) is obtained.
This paper consider that the following semilinear elliptic equation 0.1 begin{document}$ begin{equation} left{ begin{array}{ll} -Delta u = u^{q(x)-1}, & {mbox{in}} B_1, u>0, & {mbox{in}} B_1, u = 0, & {mbox{in}} partial B_1, end{array} right. end{equation} $end{document} where $ B_1 $ is the unit ball in $ mathbb{R}^N(Ngeq 3) $, $ q(x) = q(|x|) $ is a continuous radial function satifying $ 2leq q(x) < 2^* = frac{2N}{N-2} $ and $ q(0) > 2 $. Using variational methods and a priori estimate, the existence of a positive radial solution for (0.1) is obtained.
{"title":"Existence of a positive radial solution for semilinear elliptic problem involving variable exponent","authors":"Changmu Chu, Shan Li, H. Suo","doi":"10.3934/era.2023125","DOIUrl":"https://doi.org/10.3934/era.2023125","url":null,"abstract":"<abstract><p>This paper consider that the following semilinear elliptic equation</p> <p><disp-formula> <label>0.1</label> <tex-math id=\"E0.1\"> begin{document}$ begin{equation} left{ begin{array}{ll} -Delta u = u^{q(x)-1}, & {mbox{in}} B_1, u>0, & {mbox{in}} B_1, u = 0, & {mbox{in}} partial B_1, end{array} right. end{equation} $end{document} </tex-math></disp-formula></p> <p>where $ B_1 $ is the unit ball in $ mathbb{R}^N(Ngeq 3) $, $ q(x) = q(|x|) $ is a continuous radial function satifying $ 2leq q(x) < 2^* = frac{2N}{N-2} $ and $ q(0) > 2 $. Using variational methods and a priori estimate, the existence of a positive radial solution for (0.1) is obtained.</p></abstract>","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70244680","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}
This paper considers blow-up and global existence for a semilinear space-time fractional pseudo-parabolic equation with nonlinear memory in a bounded domain. We determine the critical exponents of the Cauchy problem when $ alpha < gamma $ and $ alphage gamma, $ respectively. The results obtained in this study are noteworthy extension to the results of time-fractional differential equation. The critical exponent is consistent with the corresponding Cauchy problem for the time-fractional differential equation with nonlinear memory, which illustrates that the diffusion effect of the third order term is not strong enough to change the critical exponents.
{"title":"The critical exponents for a semilinear fractional pseudo-parabolic equation with nonlinear memory in a bounded domain","authors":"Yaning Li, Yuting Yang","doi":"10.3934/era.2023129","DOIUrl":"https://doi.org/10.3934/era.2023129","url":null,"abstract":"This paper considers blow-up and global existence for a semilinear space-time fractional pseudo-parabolic equation with nonlinear memory in a bounded domain. We determine the critical exponents of the Cauchy problem when $ alpha < gamma $ and $ alphage gamma, $ respectively. The results obtained in this study are noteworthy extension to the results of time-fractional differential equation. The critical exponent is consistent with the corresponding Cauchy problem for the time-fractional differential equation with nonlinear memory, which illustrates that the diffusion effect of the third order term is not strong enough to change the critical exponents.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70244749","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}
In this paper, for given mass $ m > 0 $, we focus on the existence and nonexistence of constrained minimizers of the energy functional begin{document}$ begin{equation*} I(u): = frac{a}{2}int_{mathbb{R}^3}left|nabla uright|^2dx+frac{b}{4}left(int_{mathbb{R}^3}left|nabla uright|^2dxright)^2-int_{mathbb{R}^3}F(u)dx end{equation*} $end{document} on $ S_m: = left{uin H^1(mathbb{R}^3):, |u|^2_2 = mright}, $where $ a, b > 0 $ and $ F $ satisfies the almost optimal mass subcritical growth assumptions. We also establish the relationship between the normalized ground state solutions and the ground state to the action functional $ I(u)-frac{lambda}{2}|u|_2^2 $. Our results extend, nontrivially, the ones in Shibata (Manuscripta Math. 143 (2014) 221–237) and Jeanjean and Lu (Calc. Var. 61 (2022) 214) to the Kirchhoff type equations, and generalize and sharply improve the ones in Ye (Math. Methods. Appl. Sci. 38 (2015) 2603–2679) and Chen et al. (Appl. Math. Optim. 84 (2021) 773–806).
In this paper, for given mass $ m > 0 $, we focus on the existence and nonexistence of constrained minimizers of the energy functional begin{document}$ begin{equation*} I(u): = frac{a}{2}int_{mathbb{R}^3}left|nabla uright|^2dx+frac{b}{4}left(int_{mathbb{R}^3}left|nabla uright|^2dxright)^2-int_{mathbb{R}^3}F(u)dx end{equation*} $end{document} on $ S_m: = left{uin H^1(mathbb{R}^3):, |u|^2_2 = mright}, $where $ a, b > 0 $ and $ F $ satisfies the almost optimal mass subcritical growth assumptions. We also establish the relationship between the normalized ground state solutions and the ground state to the action functional $ I(u)-frac{lambda}{2}|u|_2^2 $. Our results extend, nontrivially, the ones in Shibata (Manuscripta Math. 143 (2014) 221–237) and Jeanjean and Lu (Calc. Var. 61 (2022) 214) to the Kirchhoff type equations, and generalize and sharply improve the ones in Ye (Math. Methods. Appl. Sci. 38 (2015) 2603–2679) and Chen et al. (Appl. Math. Optim. 84 (2021) 773–806).
{"title":"On constrained minimizers for Kirchhoff type equations with Berestycki-Lions type mass subcritical conditions","authors":"Jing Hu, Jijiang Sun$ ^{} $","doi":"10.3934/era.2023131","DOIUrl":"https://doi.org/10.3934/era.2023131","url":null,"abstract":"In this paper, for given mass $ m > 0 $, we focus on the existence and nonexistence of constrained minimizers of the energy functional begin{document}$ begin{equation*} I(u): = frac{a}{2}int_{mathbb{R}^3}left|nabla uright|^2dx+frac{b}{4}left(int_{mathbb{R}^3}left|nabla uright|^2dxright)^2-int_{mathbb{R}^3}F(u)dx end{equation*} $end{document} on $ S_m: = left{uin H^1(mathbb{R}^3):, |u|^2_2 = mright}, $where $ a, b > 0 $ and $ F $ satisfies the almost optimal mass subcritical growth assumptions. We also establish the relationship between the normalized ground state solutions and the ground state to the action functional $ I(u)-frac{lambda}{2}|u|_2^2 $. Our results extend, nontrivially, the ones in Shibata (Manuscripta Math. 143 (2014) 221–237) and Jeanjean and Lu (Calc. Var. 61 (2022) 214) to the Kirchhoff type equations, and generalize and sharply improve the ones in Ye (Math. Methods. Appl. Sci. 38 (2015) 2603–2679) and Chen et al. (Appl. Math. Optim. 84 (2021) 773–806).","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70244821","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}
Xuecheng Tian, Ran Yan, Shuaian Wang, Yannick Liu, Lu Zhen
The development of the Internet of things (IoT) and online platforms enables companies and governments to collect data from a much broader spatial and temporal area in the logistics industry. The huge amount of data provides new opportunities to handle uncertainty in optimization problems within the logistics system. Accordingly, various prescriptive analytics frameworks have been developed to predict different parts of uncertain optimization problems, including the uncertain parameter, the combined coefficient consisting of the uncertain parameter, the objective function, and the optimal solution. This tutorial serves as the pioneer to introduce existing literature on state-of-the-art prescriptive analytics methods, such as the predict-then-optimize framework, the smart predict-then-optimize framework, the weighted sample average approximation framework, the empirical risk minimization framework, and the kernel optimization framework. Based on these frameworks, this tutorial further proposes possible improvements and practical tips to be considered when we use these methods. We hope that this tutorial will serve as a reference for future prescriptive analytics research on the logistics system in the era of big data.
{"title":"Tutorial on prescriptive analytics for logistics: What to predict and how to predict","authors":"Xuecheng Tian, Ran Yan, Shuaian Wang, Yannick Liu, Lu Zhen","doi":"10.3934/era.2023116","DOIUrl":"https://doi.org/10.3934/era.2023116","url":null,"abstract":"The development of the Internet of things (IoT) and online platforms enables companies and governments to collect data from a much broader spatial and temporal area in the logistics industry. The huge amount of data provides new opportunities to handle uncertainty in optimization problems within the logistics system. Accordingly, various prescriptive analytics frameworks have been developed to predict different parts of uncertain optimization problems, including the uncertain parameter, the combined coefficient consisting of the uncertain parameter, the objective function, and the optimal solution. This tutorial serves as the pioneer to introduce existing literature on state-of-the-art prescriptive analytics methods, such as the predict-then-optimize framework, the smart predict-then-optimize framework, the weighted sample average approximation framework, the empirical risk minimization framework, and the kernel optimization framework. Based on these frameworks, this tutorial further proposes possible improvements and practical tips to be considered when we use these methods. We hope that this tutorial will serve as a reference for future prescriptive analytics research on the logistics system in the era of big data.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70244932","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}
In this paper, fast numerical methods for solving the real quasi-symmetric Toeplitz linear system are studied in two stages. First, based on an order-reduction algorithm and the factorization of Toeplitz matrix inversion, a sequence of linear systems with a constant symmetric Toeplitz matrix are solved. Second, two new fast algorithms are employed to solve the real quasi-symmetric Toeplitz linear system. Furthermore, we show a fast algorithm for quasi-symmetric Toeplitz matrix-vector multiplication. In addition, the stability analysis of the splitting symmetric Toeplitz inversion is discussed. In mathematical or engineering problems, the proposed algorithms are extraordinarily effective for solving a sequence of linear systems with a constant symmetric Toeplitz matrix. Fast matrix-vector multiplication and a quasi-symmetric Toeplitz linear solver are proven to be suitable for image encryption and decryption.
{"title":"Algorithms for solving a class of real quasi-symmetric Toeplitz linear systems and its applications","authors":"Xinglong Zhang, Xiaoyu Jiang, Zhaolin Jiang, Hee-Young Byun","doi":"10.3934/era.2023101","DOIUrl":"https://doi.org/10.3934/era.2023101","url":null,"abstract":"In this paper, fast numerical methods for solving the real quasi-symmetric Toeplitz linear system are studied in two stages. First, based on an order-reduction algorithm and the factorization of Toeplitz matrix inversion, a sequence of linear systems with a constant symmetric Toeplitz matrix are solved. Second, two new fast algorithms are employed to solve the real quasi-symmetric Toeplitz linear system. Furthermore, we show a fast algorithm for quasi-symmetric Toeplitz matrix-vector multiplication. In addition, the stability analysis of the splitting symmetric Toeplitz inversion is discussed. In mathematical or engineering problems, the proposed algorithms are extraordinarily effective for solving a sequence of linear systems with a constant symmetric Toeplitz matrix. Fast matrix-vector multiplication and a quasi-symmetric Toeplitz linear solver are proven to be suitable for image encryption and decryption.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70244968","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}
Wuhua Jiang, Yuexin Zhang, Jie Liu, Daisheng Zhang, Y. Yan, Chuanzheng Song
In order to solve the problem of insufficient range caused by the excessive weight of the pure electric bus, a multi-objective genetic algorithm (GA) and radial basis function (RBF) model are combined in this paper to realize the lightweighting of steel and aluminum hybrid body of the pure electric bus. First, the upper and lower frames of the pure electric bus body are initially designed with aluminum alloy and steel materials respectively to meet the lightweight requirements. Second, a finite element (FE) model of the bus body is established, and the validity of the model is validated through physical tests. Then, the sensitivity analysis is performed to identify the relative importance of individual design parameters over the entire domain. The Hamosilei sampling method is selected for the design of the experiment (DOE) because users can specify the number of experiments and ensure that the set of random numbers is a good representative of real variability, and the RBF model is adopted to approximate the responses of objectives and constraints. Finally, the multi-objective optimization (MOO) method based on GA with RBF model is used to solve the optimization problem of the lightweight steel-aluminum hybrid bus body. The results show that compared with the traditional fully steel body, the use of the aluminum alloy lower-frame structure can reduce body mass by 38.4%, and the proposed optimization method can further reduce the mass of the steel-aluminum body to 4.28% without affecting the structural stiffness and strength performance of the body.
{"title":"Multi-objective optimization design for steel-aluminum lightweight body of pure electric bus based on RBF model and genetic algorithm","authors":"Wuhua Jiang, Yuexin Zhang, Jie Liu, Daisheng Zhang, Y. Yan, Chuanzheng Song","doi":"10.3934/era.2023102","DOIUrl":"https://doi.org/10.3934/era.2023102","url":null,"abstract":"In order to solve the problem of insufficient range caused by the excessive weight of the pure electric bus, a multi-objective genetic algorithm (GA) and radial basis function (RBF) model are combined in this paper to realize the lightweighting of steel and aluminum hybrid body of the pure electric bus. First, the upper and lower frames of the pure electric bus body are initially designed with aluminum alloy and steel materials respectively to meet the lightweight requirements. Second, a finite element (FE) model of the bus body is established, and the validity of the model is validated through physical tests. Then, the sensitivity analysis is performed to identify the relative importance of individual design parameters over the entire domain. The Hamosilei sampling method is selected for the design of the experiment (DOE) because users can specify the number of experiments and ensure that the set of random numbers is a good representative of real variability, and the RBF model is adopted to approximate the responses of objectives and constraints. Finally, the multi-objective optimization (MOO) method based on GA with RBF model is used to solve the optimization problem of the lightweight steel-aluminum hybrid bus body. The results show that compared with the traditional fully steel body, the use of the aluminum alloy lower-frame structure can reduce body mass by 38.4%, and the proposed optimization method can further reduce the mass of the steel-aluminum body to 4.28% without affecting the structural stiffness and strength performance of the body.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70245009","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}
Breast cancer is the cancer with the highest incidence in women worldwide, and seriously threatens the lives and health of women. Mammography, which is commonly used for screening, is considered to be the most effective means of diagnosing breast cancer. Currently, computer-assisted breast mass systems based on mammography can help doctors improve film reading efficiency, but improving the accuracy of assisted diagnostic systems and reducing the false positive rate are still challenging tasks. In the image classification field, convolutional neural networks have obvious advantages over other classification algorithms. Aiming at the very small percentage of breast lesion area in breast X-ray images, in this paper, the classical VGG16 network model is improved by simplifying the network structure, optimizing the convolution form and introducing an attention mechanism. The improved model achieves 99.8 and 98.05% accuracy on the Mammographic Image Analysis Society (MIAS) and The Digital Database for Screening Mammography (DDSM), respectively, which is obviously superior to some methods of recent studies.
{"title":"A classification method for breast images based on an improved VGG16 network model","authors":"Yi Dong, Jinjiang Liu, Yihua Lan","doi":"10.3934/era.2023120","DOIUrl":"https://doi.org/10.3934/era.2023120","url":null,"abstract":"Breast cancer is the cancer with the highest incidence in women worldwide, and seriously threatens the lives and health of women. Mammography, which is commonly used for screening, is considered to be the most effective means of diagnosing breast cancer. Currently, computer-assisted breast mass systems based on mammography can help doctors improve film reading efficiency, but improving the accuracy of assisted diagnostic systems and reducing the false positive rate are still challenging tasks. In the image classification field, convolutional neural networks have obvious advantages over other classification algorithms. Aiming at the very small percentage of breast lesion area in breast X-ray images, in this paper, the classical VGG16 network model is improved by simplifying the network structure, optimizing the convolution form and introducing an attention mechanism. The improved model achieves 99.8 and 98.05% accuracy on the Mammographic Image Analysis Society (MIAS) and The Digital Database for Screening Mammography (DDSM), respectively, which is obviously superior to some methods of recent studies.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70245051","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}
Virtual reality (VR) technology has been increasingly employed in human-robot interaction (HRI) research to enhance the immersion and realism of the interaction. However, the integration of VR into HRI also introduces new challenges, such as latency, mismatch between virtual and real environments and potential adverse effects on human users. Despite these challenges, the use of VR in HRI has the potential to provide numerous benefits, including improved communication, increased safety and enhanced training and education. Yet, little research has been done by scholars to review the state of the art of VR applications in human-robot interaction. To bridge the gap, this paper provides an overview of the challenges and benefits of using VR in HRI, as well as current research in the field and future directions for development. It has been found that robots are getting more personalized, interactive and engaging than ever; and with the popularization of virtual reality innovations, we might be able to foresee the wide adoption of VR in controlling robots to fulfill various tasks of hospitals, schools and factories. Still, there are several challenges, such as the need for more advanced VR technologies to provide more realistic and immersive experiences, the development of more human-like robot models to improve social interactions and the need for better methods of evaluating the effectiveness of VR in human-robot interaction.
{"title":"Virtual reality in human-robot interaction: Challenges and benefits","authors":"Yuanzhong Lei, Zhi Su, Chao Cheng","doi":"10.3934/era.2023121","DOIUrl":"https://doi.org/10.3934/era.2023121","url":null,"abstract":"Virtual reality (VR) technology has been increasingly employed in human-robot interaction (HRI) research to enhance the immersion and realism of the interaction. However, the integration of VR into HRI also introduces new challenges, such as latency, mismatch between virtual and real environments and potential adverse effects on human users. Despite these challenges, the use of VR in HRI has the potential to provide numerous benefits, including improved communication, increased safety and enhanced training and education. Yet, little research has been done by scholars to review the state of the art of VR applications in human-robot interaction. To bridge the gap, this paper provides an overview of the challenges and benefits of using VR in HRI, as well as current research in the field and future directions for development. It has been found that robots are getting more personalized, interactive and engaging than ever; and with the popularization of virtual reality innovations, we might be able to foresee the wide adoption of VR in controlling robots to fulfill various tasks of hospitals, schools and factories. Still, there are several challenges, such as the need for more advanced VR technologies to provide more realistic and immersive experiences, the development of more human-like robot models to improve social interactions and the need for better methods of evaluating the effectiveness of VR in human-robot interaction.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70245058","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}
Learning from imbalanced data is a challenging task, as with this type of data, most conventional supervised learning algorithms tend to favor the majority class, which has significantly more instances than the other classes. Ensemble learning is a robust solution for addressing the imbalanced classification problem. To construct a successful ensemble classifier, the diversity of base classifiers should receive specific attention. In this paper, we present a novel ensemble learning algorithm called Selective Evolutionary Heterogeneous Ensemble (SEHE), which produces diversity by two ways, as follows: 1) adopting multiple different sampling strategies to generate diverse training subsets and 2) training multiple heterogeneous base classifiers to construct an ensemble. In addition, considering that some low-quality base classifiers may pull down the performance of an ensemble and that it is difficult to estimate the potential of each base classifier directly, we profit from the idea of a selective ensemble to adaptively select base classifiers for constructing an ensemble. In particular, an evolutionary algorithm is adopted to conduct the procedure of adaptive selection in SEHE. The experimental results on 42 imbalanced data sets show that the SEHE is significantly superior to some state-of-the-art ensemble learning algorithms which are specifically designed for addressing the class imbalance problem, indicating its effectiveness and superiority.
{"title":"A selective evolutionary heterogeneous ensemble algorithm for classifying imbalanced data","authors":"Xiaomeng An, Sen Xu","doi":"10.3934/era.2023138","DOIUrl":"https://doi.org/10.3934/era.2023138","url":null,"abstract":"Learning from imbalanced data is a challenging task, as with this type of data, most conventional supervised learning algorithms tend to favor the majority class, which has significantly more instances than the other classes. Ensemble learning is a robust solution for addressing the imbalanced classification problem. To construct a successful ensemble classifier, the diversity of base classifiers should receive specific attention. In this paper, we present a novel ensemble learning algorithm called Selective Evolutionary Heterogeneous Ensemble (SEHE), which produces diversity by two ways, as follows: 1) adopting multiple different sampling strategies to generate diverse training subsets and 2) training multiple heterogeneous base classifiers to construct an ensemble. In addition, considering that some low-quality base classifiers may pull down the performance of an ensemble and that it is difficult to estimate the potential of each base classifier directly, we profit from the idea of a selective ensemble to adaptively select base classifiers for constructing an ensemble. In particular, an evolutionary algorithm is adopted to conduct the procedure of adaptive selection in SEHE. The experimental results on 42 imbalanced data sets show that the SEHE is significantly superior to some state-of-the-art ensemble learning algorithms which are specifically designed for addressing the class imbalance problem, indicating its effectiveness and superiority.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70245123","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}
We study the following quasilinear pursuit-evasion model: begin{document}$ begin{equation*} left{ begin{array}{ll} u_{t} = Delta u-chinabla cdot (u(u+1)^{alpha}nabla w)+u(lambda_{1}-mu_{1}u^{r_{1}-1}+ av), & xin Omega, t>0,[2.5mm] v_{t} = Delta v+xinabla cdot(v(v+1)^{beta}nabla z)+v(lambda_{2}-mu_{2}v^{r_{2}-1}-bu), & xin Omega, t>0,[2.5mm] 0 = Delta w-w+v, & xin Omega, t>0 ,[2.5mm] 0 = Delta z-z+u, & xin Omega, t>0 , end{array} right. end{equation*} $end{document} in a smooth and bounded domain $ Omegasubsetmathbb{R}^{n}(ngeq 1), $ where $ a, b, chi, xi, lambda_{1}, lambda_{2}, mu_{1}, mu_{2} > 0, $ $ alpha, beta inmathbb{R}, $ and $ r_{1}, r_{2} > 1. $ When $ r_{1} > max{1, 1+alpha}, r_{2} > max{1, 1+beta}, $ it has been proved that if $ min{(r_{1}-1)(r_{2}-beta-1), (r_{1}-alpha-1)(r_{2}-beta-1)} > frac{(n-2)_{+}}{n}, $ then for some suitable nonnegative initial data $ u_{0} $ and $ v_{0}, $ the system admits a unique globally classical solution which is bounded in $ Omegatimes(0, infty) $.
We study the following quasilinear pursuit-evasion model: begin{document}$ begin{equation*} left{ begin{array}{ll} u_{t} = Delta u-chinabla cdot (u(u+1)^{alpha}nabla w)+u(lambda_{1}-mu_{1}u^{r_{1}-1}+ av), & xin Omega, t>0,[2.5mm] v_{t} = Delta v+xinabla cdot(v(v+1)^{beta}nabla z)+v(lambda_{2}-mu_{2}v^{r_{2}-1}-bu), & xin Omega, t>0,[2.5mm] 0 = Delta w-w+v, & xin Omega, t>0 ,[2.5mm] 0 = Delta z-z+u, & xin Omega, t>0 , end{array} right. end{equation*} $end{document} in a smooth and bounded domain $ Omegasubsetmathbb{R}^{n}(ngeq 1), $ where $ a, b, chi, xi, lambda_{1}, lambda_{2}, mu_{1}, mu_{2} > 0, $ $ alpha, beta inmathbb{R}, $ and $ r_{1}, r_{2} > 1. $ When $ r_{1} > max{1, 1+alpha}, r_{2} > max{1, 1+beta}, $ it has been proved that if $ min{(r_{1}-1)(r_{2}-beta-1), (r_{1}-alpha-1)(r_{2}-beta-1)} > frac{(n-2)_{+}}{n}, $ then for some suitable nonnegative initial data $ u_{0} $ and $ v_{0}, $ the system admits a unique globally classical solution which is bounded in $ Omegatimes(0, infty) $.
{"title":"The effects of cross-diffusion and logistic source on the boundedness of solutions to a pursuit-evasion model","authors":"Chang-Jian Wang, Zi-Han Zheng","doi":"10.3934/era.2023170","DOIUrl":"https://doi.org/10.3934/era.2023170","url":null,"abstract":"We study the following quasilinear pursuit-evasion model: begin{document}$ begin{equation*} left{ begin{array}{ll} u_{t} = Delta u-chinabla cdot (u(u+1)^{alpha}nabla w)+u(lambda_{1}-mu_{1}u^{r_{1}-1}+ av), & xin Omega, t>0,[2.5mm] v_{t} = Delta v+xinabla cdot(v(v+1)^{beta}nabla z)+v(lambda_{2}-mu_{2}v^{r_{2}-1}-bu), & xin Omega, t>0,[2.5mm] 0 = Delta w-w+v, & xin Omega, t>0 ,[2.5mm] 0 = Delta z-z+u, & xin Omega, t>0 , end{array} right. end{equation*} $end{document} in a smooth and bounded domain $ Omegasubsetmathbb{R}^{n}(ngeq 1), $ where $ a, b, chi, xi, lambda_{1}, lambda_{2}, mu_{1}, mu_{2} > 0, $ $ alpha, beta inmathbb{R}, $ and $ r_{1}, r_{2} > 1. $ When $ r_{1} > max{1, 1+alpha}, r_{2} > max{1, 1+beta}, $ it has been proved that if $ min{(r_{1}-1)(r_{2}-beta-1), (r_{1}-alpha-1)(r_{2}-beta-1)} > frac{(n-2)_{+}}{n}, $ then for some suitable nonnegative initial data $ u_{0} $ and $ v_{0}, $ the system admits a unique globally classical solution which is bounded in $ Omegatimes(0, infty) $.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70245622","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}
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