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Nonseparating Independent Sets and Maximum Genus of Graphs

Acta Mathematicae Applicatae Sinica 2022年第3期38卷 719-728页

作者： Chao YANG Han REN Er-ling WEI Center of Intelligent Computing and Applied Statistics School of MathematicsPhysics and StatisticsShanghai University of Engineering ScienceShanghai 201620China School of Mathematical Sciences East China Normal UniversityShanghai 200241China Shanghai Key Laboratory of PMMP Shanghai 200241China School of Mathematics Renmin University of ChinaBeijing 100872China

A subset I of vertices of an undirected connected graph G is a nonseparating independent set(NSIS)if no two vertices of I are adjacent and G􀀀I is *** Z(G)denote the cardinality of a maximum NSIS of G.A nonseparating independent set containing Z(G)vertices is called the maximum nonseparating independent *** this paper,we firstly give an upper bound for Z(G)of regular graphs and determine Z(G)for some types of circular ***,we show a relationship between Z(G)and the maximum genus M(G)of a general ***,an important formula is provided to compute Z(G),i.e.,Z(G)=Σx∈I dI(x)+2(M(G-I)-γM(G))+(ξ(G-I)-ξ(G));where I is the maximum nonseparating independent set and ξ(G)is the Betti deficiency(Xuong,1979)of G.

关键词： nonseparating independent sets maximum genus graph embedding decycling set

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Dynamic properties and chaotic behaviors of pure-cubic complex Ginzburg–Landau equation with different nonlinearities

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Results in Physics 2024年 64卷

作者： Wang, Yining Yin, Zhixiang Lu, Lin Kai, Yue School of Mathematics Physics and Statistics Center of Intelligent Computing and Applied Statistics Shanghai University of Engineering Science Shanghai Xinhao Information Technology Co. Ltd.

This paper investigates the pure-cubic complex Ginzburg–Landau equation (PC-CGLE) with different nonlinearities such as Kerr law, power law and so on. We get the dynamic systems and show that solitons and periodic solutions exist through the complete discrimination system for the polynomial method (CDSPM). To verify these conclusions, we construct the traveling wave solution via the CDSPM, and some new solutions are also built. The soliton stability and modulation instability with two types of nonlinearities are discussed. Finally, by adding perturbed terms to the dynamic system, we obtain the largest Lyapunov exponents and the phase diagrams of the equation, which proves there are chaotic behaviors in PC-CGLE. The results such as Gaussian soliton solutions and chaotic behavior for PC-CGLE are initially discovered in the present paper. © 2024 The Authors

关键词： Chaotic behavior Complete discrimination system for polynomial method Qualitative analysis Traveling wave solution

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A Spectral Bipartite Analogue of the Erdős-Sós Conjecture

SSRN

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SSRN 2024年

作者： Geng, Xianya Wei, Wei Feng, Zhiming Center of Intelligent Computing and Applied Statistics School of Mathematics Physics and Statistics Shanghai University of Engineering Science Shanghai China School of Mathematics and Big Data Anhui University of Science & Technology Huainan China School of Mathematics and Statistics Xinyang Normal University Xinyang China

A well-known conjecture of Erdős and Sós states that each graph on ν vertices with size more than ν(t2−1) contains every tree with order t + 1 as a subgraph. In 2010, Nikiforov presented the spectral Erdős-Sós conjecture: Let G be a graph with sufficiently large order ν and spectral radius λ(G), and let t ≥ 2 be an integer, (i) if λ(G) ≥ λ(Kt ∨ Kν−t), then G contains all trees of order 2t + 2 unless G ∼= Kt ∨ Kν−t;(ii) if λ(G) ≥ λ(Kt ∨ (Kν−t−2 ∪ K2)), then G contains all trees of order 2t + 3 unless G ∼= Kt ∨ (Kν−t−2 ∪ K2). Recently, this conjecture was confirmed by Cioabă, Desai and Tait (2022). In this contribution, we resolve the spectral bipartite analogue of the Erdős-Sós conjecture. For sufficiently large ν and positive integer t ≥ 2, we show that the complete bipartite graph Kt,ν−t uniquely maximizes the spectral radius over the set of ν-vertex bipartite graphs each of which does not contain some trees with order 2t + 2 (resp. 2t + 3) as subgraphs. Our proof technique is mainly based on the Zarankiewicz number of a tree, and with the aid of the eigenvector method from Cioabă, Desai and Tait (2022). Some problems are proposed in the end for future research. © 2024, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

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Spectral Extrema of Bipartite Graphs: Forbidden an Even Cycle of Specified Length

SSRN

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SSRN 2024年

作者： Feng, Zhimin Luo, Xiaobing Wei, Wei School of Mathematics and Statistics Xinyang Normal University Xinyang China School of Computer Technology and Software Engineering Wuhan Polytechnic Wuhan China Center of Intelligent Computing and Applied Statistics School of Mathematics Physics and Statistics Shanghai University of Engineering Science Shanghai201620 China

A graph is called $H$-free if the graph has no subgraph being isomorphic to $H$. The classical Tur\'an problem aims to determine the maximum size of an $H$-free graph with given order. In 2010, Nikiforov introduced the spectral Tur\'an-type problem: Determine the maximum spectral radius of an $H$-free graph with given order. He also presented the following conjecture: For sufficiently large $\nu$ and for $k\geq 2$, the graph $K_k\vee (\overline{K_{\nu-k-2}}\cup K_2)$ is the unique $\nu$-vertex $\{C_{2k+1}, C_{2k+2}\}$-free graph having the largest spectral radius and $K_k\vee \overline{K_{\nu-k}}$ is the unique $\nu$-vertex $C_{2k+2}$-free graph having the largest spectral radius. Recently, this conjecture was confirmed by Cioab\u{a}, Desai and Tait. In this contribution, we resolve the Nikiforov's even cycle conjecture for bipartite graphs. Let $\nu$ and $k$ be two integers satisfying $\nu\geq 1$ if $k=1,$ and $\nu \geq \left(\frac{7^22^{24}k\left(2k-1\right)^2(k+1)^{20}} {(2k-3)^2}\right)^{\frac{k+1}{k-1}}$ if $k\geq 2$. Then we show that the complete bipartite graph $K_{k,\nu-k}$ uniquely maximizes the spectral radius over the set of $C_{2k+2}$-free bipartite graphs of order $\nu$. © 2024, The Authors. All rights reserved.

关键词： Graph theory

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Interval quantile correlations with applications to testing high-dimensional quantile effects

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Journal of Econometrics 2025年 249卷

作者： Zhang, Yaowu Zhou, Yeqing Zhu, Liping Research Institute for Interdisciplinary Sciences School of Information Management and Engineering Shanghai University of Finance and Economics China School of Mathematical Sciences School of Economics and Management and Key Laboratory of Intelligent Computing and Applications Tongji University China Center for Applied Statistics and Institute of Statistics and Big Data Renmin University of China China

In this article, we propose interval quantile correlation and interval quantile partial correlation to measure the association between two random variables over an interval of quantile levels. We construct efficient estimators for the proposed correlations, and establish their asymptotic properties under the null and alternative hypotheses. We further use the interval quantile partial correlation to test for the significance of covariate effects in high-dimensional quantile regression when a subset of covariates are controlled. We calculate marginal interval quantile partial correlations for each covariate, then aggregate them to construct a sum-type test statistic. The null distribution of our proposed test statistic is asymptotically standard normal. We use extensive simulations and an application to illustrate that our proposed test, which pools information across an interval of quantile levels to enhance power performances, is very effective in detecting quantile effects. © 2024 Elsevier B.V.

关键词： Interval quantile Partial correlation Quantile regression

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Matching extension and matching exclusion via the size or the spectral radius of graphs

arXiv

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arXiv 2023年

作者： Miao, Shujing Li, Shuchao Wei, Wei Hubei Key Laboratory of Mathematical Science Faculty of Mathematics and Statistics Central China Normal University Wuhan430079 China Center of Intelligent Computing and Applied Statistics School of Mathematics Physics and Statistics Shanghai University of Engineering Science Shanghai201620 China

A graph G is said to be k-extendable if every matching of size k in G can be extended to a perfect matching of G, where k is a positive integer. We say G is 1-excludable if for every edge e of G, there exists a perfect matching excluding e. In this paper, we first establish a lower bound on the size (resp. the spectral radius) of G to guarantee that G is k-extendable. Then we determine a lower bound on the size (resp. the spectral radius) of G to guarantee that G is 1-excludable. All the corresponding extremal graphs are characterized. Copyright © 2023, The Authors. All rights reserved.

关键词： Matrix algebra

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Spectral Galerkin Approximation of Fractional Optimal Control Problems with Fractional Laplacian

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Advances in applied Mathematics and Mechanics 2023年第6期15卷 1631-1654页

作者： Jiaqi Zhang Yin Yang Zhaojie Zhou School of Mathematics and Computational Science Xiangtan UniversityHunan Key Laboratory for Computation and Simulation in Science and EngineeringKey Laboratory of Intelligent Computing and Information Processing of Ministry of EducationXiangtan 411105HunanChina School of Mathematics and Computational Science Xiangtan UniversityNational Center for Applied Mathematics in HunanHunan International Scientific and Technological Innovation Cooperation Base of Computational ScienceXiangtan 411105HunanChina School of Mathematics and Statistics Shandong Normal UniversityJinan 250014ShandongChina

In this paper spectral Galerkin approximation of optimal control problem governed by fractional elliptic equation is *** deal with the nonlocality of fractional Laplacian operator the Caffarelli-Silvestre extension is *** first order optimality condition of the extended optimal control problem is derived.A spectral Galerkin discrete scheme for the extended problem based on weighted Laguerre polynomials is developed.A priori error estimates for the spectral Galerkin discrete scheme is *** experiments are presented to show the effectiveness of our methods and to verify the theoretical findings.

关键词： Fractional Laplacian optimal control problem Caffarelli-Silvestre extension weighted Laguerre polynomials

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An Extension on Neighbor Sum Distinguishing Total Coloring of Graphs

arXiv

引用

arXiv 2022年

作者： Chang, Jing-Zhi Yang, Chao Yin, Zhi-Xiang Yao, Bing School of Mathematics Physics and Statistics Center of Intelligent Computing and Applied Statistics Shanghai University of Engineering Science Shanghai 201620 China College of Mathematics and Statistics Northwest Normal University Lanzhou730070 China

Let f: V (G) ∪ E(G) → {1, 2,..., k} be a non-proper total k-coloring of G. Define a weight function on total coloring as (Equation presented) where (Equation presented) for any edge xy ∈ E(G), then f is called a neighbor full sum distinguishing total k-coloring of G. The smallest value k for which G has such a coloring is called the neighbor full sum distinguishing total chromatic number of G and denoted by fgndi∑(G). The coloring is an extension of neighbor sum distinguishing non-proper total coloring. In this paper we conjecture that fgndi∑(G) ≤ 3 for any connected graph G of order at least three. We prove that the conjecture is true for (i) paths and cycles;(ii) 3-regular graphs and (iii) stars, complete graphs, trees, hypercubes, bipartite graphs and complete r-partite graphs. In particular, complete graphs can achieve the upper bound for the above *** Codes 05C15 Copyright © 2022, The Authors. All rights reserved.

关键词： Graphic methods

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An Artificial Intelligence Approach for Solving Stochastic Transportation Problems

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Computers, Materials & Continua 2022年第1期70卷 817-829页

作者： Prachi Agrawal Khalid Alnowibet Talari Ganesh Adel F.Alrasheedi Hijaz Ahmad Ali Wagdy Mohamed Department of Mathematics and Scientific Computing National Institute of Technology HamirpurHimachal Pradesh177005India Statistics and Operations Research Department College of ScienceKing Saud UniversityRiyadh11451Kingdom of Saudi Arabia Section of Mathematics International Telematic University UninettunoRoma00186Italy Operations Research Department Faculty of Graduate Studies for Statistical ResearchCairo UniversityGiza12613Egypt Wireless Intelligent Networks Center(WINC) School of Engineering and Applied SciencesNile UniversityGizaEgypt

Recent years witness a great deal of interest in artificial intelligence(AI)tools in the area of *** has developed a large number of tools to solve themost difficult search-and-optimization problems in computer science and operations ***,metaheuristic-based algorithms are a sub-field of *** study presents the use of themetaheuristic algorithm,that is,water cycle algorithm(WCA),in the transportation problem.A stochastic transportation problem is considered in which the parameters supply and demand are considered as random variables that follow the Weibull *** the parameters are stochastic,the corresponding constraints are *** are converted into deterministic constraints using the stochastic programming *** this study,we propose evolutionary algorithms to handle the difficulties of the complex high-dimensional optimization *** is influenced by the water cycle process of how streams and rivers flow toward the sea(optimal solution).WCA is applied to the stochastic transportation problem,and obtained results are compared with that of the new metaheuristic optimization algorithm,namely the neural network algorithm which is inspired by the biological nervous *** is concluded that WCA presents better results when compared with the neural network algorithm.

关键词： Artificial intelligence metaheuristic algorithm stochastic programming transportation problem water cycle algorithm weibull distribution

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Fast θ -Maruyama scheme for stochastic Volterra integral equations of convolution type: mean-square stability and strong convergence analysis

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Computational and applied Mathematics 2023年第3期42卷

作者： Wang, Mengjie Dai, Xinjie Yu, Yanyan Xiao, Aiguo Hunan Key Laboratory for Computation and Simulation in Science and Engineering National Center for Applied Mathematics in Hunan Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Hunan Xiangtan411105 China School of Mathematics and Statistics Yunnan University Yunnan Kunming650504 China

In this paper, a fast θ-Maruyama method is proposed for solving stochastic Volterra integral equations of convolution type with singular and Hölder continuous kernels based on the sum-of-exponentials approximation. Furthermore, the average storage O(N) and the calculation cost O(N2) of θ-Maruyama scheme are reduced to O(log N) and O(Nlog N) for T 1 or O(log 2N) and O(Nlog 2N) for T≈ 1 , respectively, which implies that the fast θ-Maruyama scheme is confirmed to improve the computational efficiency of the θ-Maruyama method. Under the local Lipschitz and linear growth conditions, strong convergence of the given numerical scheme are obtained. Then, for the linear test equation, we show the asymptotic behavior of solutions in mean square sense. Further, we obtain the explicit structure of the stability matrices and some numerical results of the mean-square stability for the fast θ-Maruyama method applied to the linear test equation. Finally, some numerical experiments are also given to illustrate the effectiveness of the method. © 2023, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.

关键词： Computational efficiency

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