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TWO-GRID ALGORITHM OF H^(1)-GALERKIN MIXED FINITE ELEMENT METHODS FOR SEMILINEAR PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS

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Journal of Computational mathematics 2022年第5期40卷 667-685页

作者： Tianliang Hou Chunmei Liu Chunlei Dai Luoping Chen Yin Yang School of Mathematics and Statistics Beihua UniversityJilin 132013China College of Science Hunan University of Science and EngineeringYongzhou 425199China School of Mathematics Southwest Jiaotong UniversityChengdu 611756China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationSchool of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China

In this paper,we present a two-grid discretization scheme for semilinear parabolic integro-differential equations by H1-Galerkin mixed finite element *** use the lowest order Raviart-Thomas mixed finite elements and continuous linear finite element for spatial discretization,and backward Euler scheme for temporal ***,a priori error estimates and some superclose properties are ***,a two-grid scheme is presented and its convergence is *** the proposed two-grid scheme,the solution of the nonlinear system on a fine grid is reduced to the solution of the nonlinear system on a much coarser grid and the solution of two symmetric and positive definite linear algebraic equations on the fine grid and the resulting solution still maintains optimal ***,a numerical experiment is implemented to verify theoretical results of the proposed *** theoretical and numerical results show that the two-grid method achieves the same convergence property as the one-grid method with the choice h=H^(2).

关键词： Semilinear parabolic integro-differential equations H^(1)-Galerkin mixed finite element method A priori error estimates Two-grid Superclose.

Positive-Guided Knowledge Distillation for Document-Level Relation Extraction with Noisy Labeled Data 12th

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Positive-Guided Knowledge Distillation for Document-Level R...

12th National CCF Conference on Natural Language processing and Chinese Computing, NLPCC 2023

作者： Zeng, Daojian Zhu, Jianling Jiang, Lincheng Dai, Jianhua Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing Hunan Normal University Changsha China Institute of AI and Targeted International Communication Hunan Normal University Changsha China College of Advanced Interdisciplinary Studies National University of Defense Technology Changsha China

ISBN: (纸本)9783031446924

Since one entity may have multiple mentions and relations between entities may stretch across multiple sentences in a document, the annotation of document-level relation extraction datasets becomes a challenging task. Many studies have identified that these datasets contain a large number of noisy labels, hindering performance improvement for the document-level relation extraction task. The previous and most straightforward method is denoising noisy labeled data from a data annotation perspective. However, this time-consuming approach is not suitable for large-scale datasets. In this paper, we propose a novel Positive-Guided Knowledge Distillation (PGKD) model to address the noisy labeled data problem for document-level relation extraction. We design a new teacher-student architecture. The teacher model trained with only positive samples can partially supervise the student model. The positive-guided knowledge distillation algorithm transfers the clean positive-class patterns from the teacher model to the student model. In this way, the student model trained with all samples can efficiently prevent the interference of false negative samples. Extensive experiments on Mix-DocRED demonstrate that PGKD achieves state-of-the-art effectiveness for document-level relation extraction with noisy labeled data. Moreover, PGKD also surpasses other baselines even on the well-annotated Re-DocRED. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Distillation

INTEGER TILE AND SPECTRALITY OF CANTOR-MORAN MEASURES WITH EQUIDIFFERENT DIGIT SETS

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arXiv 2024年

作者： Wu, Sha Xiao, Yingqing School of Mathematics Hunan University Hunan Changsha410082 China School of Mathematics Hunan Province Key Lab of Intelligent Information Processing and Applied Mathematics Hunan University Changsha410082 China

Let {bk}∞k=1 be a sequence of integers with |bk| ≥ 2 and {Dk}∞k=1 be a sequence of equidifferent digit sets with Dk = {0, 1, · · ·, N − 1} tk, where N ≥ 2 is a prime number and {tk}∞k=1 is bounded. In this paper, we study the existence of the Cantor-Moran measure µ{bk},{Dk} and show that Dk := DkbkDk−1 bkbk−1Dk−2 · · bkbk−1 · · · b2D1 is an integer tile for all k ∈ N+ if and only if si , sj for all i , j ∈ N+, where si is defined as the numbers of factor N in b1bNt2···ibi . Moreover, we prove that Dk being an integer tile for all k ∈ N+ is a necessary condition for the Cantor-Moran measure to be a spectral measure, and we provide an example to demonstrate that it cannot become a sufficient condition. Furthermore, under some additional assumptions, we establish that the Cantor-Moran measure to be a spectral measure is equivalent to Dk being an integer tile for all k ∈ N+MSC Codes Primary 28A25, 28A80, Secondary 42C05, 46C05 © 2024, CC BY.

关键词： Integer linear programming

On the spectrality of a class of Moran measures

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arXiv 2024年

作者： Zheng, Yali Xiao, Yingqing School of Mathematics Hunan University Changsha410082 China School of Mathematics Hunan Province Key Lab of Intelligent Information Processing and Applied Mathematics Hunan University Changsha410082 China

In this paper, we study the spectrality of a class of Moran measures µP,D on R generated by {(pn, Dn)}∞n=1, where P = {pn}∞n=1 is a sequence of positive integers with pn > 1 and D = {Dn}∞n=1 is a sequence of digit sets of N with the cardinality #Dn ∈ {2, 3, Nn}. We find a countable set Λ ⊂ R such that the set {e−2πiλx|λ ∈ Λ} is a orthonormal basis of L2(µP,D) under some conditions. As an application, we show that when µP,D is absolutely continuous, µP,D not only is a spectral measure, but also its support set tiles R with *** Codes 28A80, 28A25, 42C05, 46C05 © 2024, CC BY.

关键词：

NEHARI MANIFOLD OPTIMIZATION AND ITS APPLICATION FOR FINDING UNSTABLE SOLUTIONS OF SEMILINEAR ELLIPTIC PDES∗

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arXiv 2024年

作者： Chen, Zhaoxing Liu, Wei Xie, Ziqing Yi, Wenfan MOE-LCSM School of Mathematics and Statistics Hunan Normal University Changsha410081 China Department of Mathematics National University of Defense Technology Changsha410073 China Hunan Provincial Key Laboratory of Intelligent Information Processing and Applied Mathematics School of Mathematics Hunan University Changsha410082 China

A Nehari manifold optimization method (NMOM) is introduced for finding 1-saddles, i.e., saddle points with the Morse index equal to one, of a generic nonlinear functional in Hilbert spaces. Actually, it is based on the variational characterization that 1-saddles of this functional are local minimizers of the same functional restricted on the associated Nehari manifold. The framework contains two important ingredients: one is the retraction mapping to make the iterative points always lie on the Nehari manifold;the other is the tangential search direction to decrease the functional with suitable step-size search rules. Particularly, the global convergence is rigorously established by virtue of some crucial analysis techniques (including a weak convergence method) that overcome difficulties in the infinite-dimensional setting. In practice, combining with an easy-to-implement Nehari retraction and the negative Riemannian gradient direction, the NMOM is successfully applied to compute the unstable ground-state solutions of a class of typical semilinear elliptic PDEs, such as the Hénon equation and the stationary nonlinear Schrödinger equation. In particular, the symmetry-breaking phenomenon of the ground states of the Hénon equation is explored numerically in 1D and 2D with interesting numerical findings on the critical value of the symmetry-breaking *** Codes 35B38, 58E30, 65K10, 65N12 Copyright © 2024, The Authors. All rights reserved.

关键词： Schrodinger equation

Investigation on a quantum algorithm for linear differential equations

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arXiv 2024年

作者： Dong, Xiaojing Peng, Yizhe Tang, Qili Yang, Yin Yu, Yue Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education National Center for Applied Mathematics in Hunan School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

Ref. [BCOW17] introduced a pioneering quantum approach (coined BCOW algorithm) for solving linear differential equations with optimal error tolerance. Originally designed for a specific class of diagonalizable linear differential equations, the algorithm was extended by Krovi in [Kro23] to encompass broader classes, including non-diagonalizable and even singular matrices. Despite the common misconception, the original algorithm is indeed applicable to non-diagonalizable matrices, with diagonalisation primarily serving for theoretical analyses to establish bounds on condition number and solution error. By leveraging basic estimates from [Kro23], we derive bounds comparable to those outlined in the Krovi algorithm, thereby reinstating the advantages of the BCOW approach. Furthermore, we extend the BCOW algorithm to address time-dependent linear differential equations by transforming non-autonomous systems into higher-dimensional autonomous ones, a technique also applicable for the Krovi algorithm. © 2024, CC BY-NC-ND.

关键词： Consensus algorithm

On book thickness parameterized by the vertex cover number

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Science China(information Sciences) 2022年第4期65卷 112-113页

作者： Yunlong LIU Jie CHEN Jingui HUANG School of Information Science and Engineering Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing Hunan Normal University

Dear editor,Book thickness for graphs forms a major theme in graph theory and has a broad application in the fields of sorting permutations, fault tolerant VLSI design, parallel computing, and others. The book Thickness problem, even if the vertex order is taken as part of the input, was shown to be NP-complete in general [1, 2]. Just because of this, parameterized algorithms have been proposed to deal with it [3].

关键词： Book Thickness Vertex Cover Number Linear Order 1-page embedding graph kernel

Research on Security Trust Model of P2P Network Based on Improved Search Algorithm 11th

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Research on Security Trust Model of P2P Network Based on Imp...

11th International Conference on Computer Engineering and Networks, CENet2021

作者： Zheng, Guangyong Xu, Yuming Hengyang Normal University HengyangHunan421002 China Hunan Provincial Key Laboratory of Intelligent Information Processing and Application Hengyang421002 China Changsha Normal University ChangshaHunan410199 China

ISBN: (纸本)9789811665530

With the rapid development and popularization of the Internet, Peer-to-Peer (P2P) network technology has been developing rapidly, and the security trust mechanism of P2P network has become a prominent problem. This paper presents an improved node resource search algorithm. The algorithm improves the reliability of the system and the success rate of the search by setting the parameter value whether the node is trusted or not and the maximum value of the valid reply message received by the node. At the same time, in view of the shortcomings of the existing credibility calculation methods, an improved credibility update calculation method is proposed. This method can effectively prevent malicious nodes from attacking the trusted nodes and normal nodes and also prevent malicious nodes from improving the credibility of each node by means of small group cooperation. © 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

关键词： Network security

FGCM: Modality-behavior Fusion Model Integrated with Graph Contrastive Learning for Multimodal Recommendation

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IEEE Multimedia 2025年

作者： Mo, Feng Xiao, Lin Song, Qiya Gao, Xieping Song, Wenzhuo Wang, Shoujin Hunan Normal University Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing Changsha410081 China Northeast Normal University Changchun China University of Technology Sydney Sydney Australia

Multimodal recommender systems (MRSs) aim to integrate information from multiple modalities, for better capturing users' preferences. However, existing MRSs usually face the challenge of data sparsity, especially for the limited user-item interactions. It is not uncommon that a user interacts with only a few items out of millions. More importantly, the interaction information is easy to be overwhelmed, leading to poor recommendation performance. To tackle these significant gaps for further improving the performance of MRSs, we propose a Modality-behavior Fusion Model Integrated with Graph Contrastive Learning for Multimodal Recommendation (FGCM). First, through the introduction of random noise into graph contrastive learning, FGCM adeptly mitigates data sparsity. Then, a modality-behavior fuser is proposed to effectively fuse interaction data and multimodal side information data by taking cooperative signals and multimodal signals as the guidance. Extensive experiments on three datasets demonstrate that our proposed approach outperforms several state-of-the-art methods. © 2025 IEEE.

关键词： Contrastive Learning