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Convergence analysis of PM-BDF2 method for quasiperiodic parabolic equations

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arXiv 2024年

作者： Jiang, Kai Li, Meng Zhang, Juan Zhang, Lei Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing Ministry of Education Department of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China School of Mathematical Sciences Institute of Natural Sciences MOE-LSC Shanghai Jiao Tong University Shanghai200240 China

Numerically solving parabolic equations with quasiperiodic coefficients is a significant challenge due to the potential formation of space-filling quasiperiodic structures that lack translational symmetry or decay. In this paper, we introduce a highly accurate numerical method for solving time-dependent quasiperiodic parabolic equations. We discretize the spatial variables using the projection method (PM) and the time variable with the second-order backward differentiation formula (BDF2). We provide a complexity analysis for the resulting PM-BDF2 method. Furthermore, we conduct a detailed convergence analysis, demonstrating that the proposed method exhibits spectral accuracy in space and second-order accuracy in time. Numerical results in both one and two dimensions validate these convergence results, highlighting the PMBDF2 method as a highly efficient algorithm for addressing quasiperiodic parabolic equations. Copyright © 2024, The Authors. All rights reserved.

关键词： Convergence of numerical methods

Meta-causal Learning for Single Domain Generalization

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arXiv 2023年

作者： Chen, Jin Gao, Zhi Wu, Xinxiao Luo, Jiebo Beijing Key Laboratory of Intelligent Information Technology School of Computer Science & Technology Beijing Institute of Technology China Guangdong Laboratory of Machine Perception and Intelligent Computing Shenzhen MSU-BIT University China Department of Computer Science University of Rochester RochesterNY14627 United States

Single domain generalization aims to learn a model from a single training domain (source domain) and apply it to multiple unseen test domains (target domains). Existing methods focus on expanding the distribution of the training domain to cover the target domains, but without estimating the domain shift between the source and target domains. In this paper, we propose a new learning paradigm, namely simulate-analyze-reduce, which first simulates the domain shift by building an auxiliary domain as the target domain, then learns to analyze the causes of domain shift, and finally learns to reduce the domain shift for model adaptation. Under this paradigm, we propose a meta-causal learning method to learn meta-knowledge, that is, how to infer the causes of domain shift between the auxiliary and source domains during training. We use the meta-knowledge to analyze the shift between the target and source domains during testing. Specifically, we perform multiple transformations on source data to generate the auxiliary domain, perform counterfactual inference to learn to discover the causal factors of the shift between the auxiliary and source domains, and incorporate the inferred causality into factor-aware domain alignments. Extensive experiments on several benchmarks of image classification show the effectiveness of our method. Copyright © 2023, The Authors. All rights reserved.

关键词： Machine learning

The interior penalty virtual element method for fourth-order singular perturbation problems

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arXiv 2023年

作者： Feng, Fang Yu, Yue School of Mathematics and Statistics Nanjing University of Science and Technology Nanjing China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing Ministry of Education Xiangtan University Hunan Xiangtan411105 China

This paper is dedicated to the numerical solution of a fourth-order singular perturbation problem using the interior penalty virtual element method (IPVEM) proposed in [42]. The study introduces modifications to the jumps and averages in the penalty term, as well as presents an automated mesh-dependent selection of the penalty parameter. Drawing inspiration from the modified Morley finite element methods, we leverage the conforming interpolation technique to handle the lower part of the bilinear form. Through our analysis, we establish optimal convergence in the energy norm and provide a rigorous proof of uniform convergence concerning the perturbation parameter in the lowest-order case. © 2023, CC BY-NC-ND.

关键词： Numerical methods

PROJECTION METHOD FOR QUASIPERIODIC ELLIPTIC EQUATIONS AND APPLICATION TO QUASIPERIODIC HOMOGENIZATION

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arXiv 2024年

作者： Jiang, Kai Li, Meng Zhang, Juan Zhang, Lei Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China School of Mathematical Sciences Institute of Natural Sciences MOE-LSC Shanghai Jiao Tong University Shanghai200240 China

In this study, we address the challenge of solving elliptic equations with quasiperiodic coefficients. To achieve accurate and efficient computation, we introduce the projection method, which enables the embedding of quasiperiodic systems into higher-dimensional periodic systems. To enhance the computational efficiency, we propose a compressed storage strategy for the stiffness matrix by its multi-level block circulant structure, significantly reducing memory requirements. Furthermore, we design a diagonal preconditioner to efficiently solve the resulting high-dimensional linear system by reducing the condition number of the stiffness matrix. These techniques collectively contribute to the computational effectiveness of our proposed approach. Convergence analysis shows the spectral accuracy of the proposed method. We demonstrate the effectiveness and accuracy of our approach through a series of numerical examples. Moreover, we apply our method to achieve a highly accurate computation of the homogenized coefficients for a quasiperiodic multiscale elliptic *** Codes 65D05, 65D15, 65F08, 35B15, 35B27 Copyright © 2024, The Authors. All rights reserved.

关键词： Stiffness matrix

Autoregressive Queries for Adaptive Tracking with Spatio-Temporal Transformers

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Autoregressive Queries for Adaptive Tracking with Spatio-Tem...

Conference on Computer Vision and Pattern Recognition (CVPR)

作者： Jinxia Xie Bineng Zhong Zhiyi Mo Shengping Zhang Liangtao Shi Shuxiang Song Rongrong Ji Key Laboratory of Education Blockchain and Intelligent Technology Ministry of Education Guangxi Normal University Guilin China Guangxi Key Lab of Multi-Source Information Mining & Security Guangxi Normal University Guilin China Guangxi Key Laboratory of Machine Vision and Intelligent Control Wuzhou University School of Computer Science and Technology Harbin Institute of Technology Media Analytics and Computing Lab School of Informatics Xiamen University

ISBN: (数字)9798350353006

ISBN: (纸本)9798350353013

The rich spatio-temporal information is crucial to capture the complicated target appearance variations in visual tracking. However, most top-performing tracking algorithms rely on many hand-crafted components for spatio-temporal information aggregation. Consequently, the spatio-temporal information is far away from being fully explored. To alleviate this issue, we propose an adaptive tracker with spatio-temporal transformers (named AQA-Track), which adopts simple autoregressive queries to effectively learn spatio-temporal information without many hand-designed components. Firstly, we introduce a set of learnable and autoregressive queries to capture the instantaneous target appearance changes in a sliding window fashion. Then, we design a novel attention mechanism for the interaction of existing queries to generate a new query in current frame. Finally, based on the initial target template and learnt autoregressive queries, a spatio-temporal information fusion module (STM) is designed for spatiotemporal formation aggregation to locate a target object. Benefiting from the STM, we can effectively combine the static appearance and instantaneous changes to guide robust tracking. Extensive experiments show that our method significantly improves the tracker's performance on six popular tracking benchmarks: LaSOT, LaSOT ext , TrackingNet, GOT-10k, TNL2K, and UAV123. Code and models will be https://***/orgs/GXNU-ZhongLab.

关键词： Adaptation models Visualization Computer vision Target tracking Computational modeling Transformers Market research

Autoregressive Queries for Adaptive Tracking with Spatio-Temporal Transformers

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arXiv 2024年

作者： Xie, Jinxia Zhong, Bineng Mo, Zhiyi Zhang, Shengping Shi, Liangtao Song, Shuxiang Ji, Rongrong Key Laboratory of Education Blockchain and Intelligent Technology Ministry of Education China Guangxi Key Lab of Multi-Source Information Mining & Security China Guangxi Normal University Guilin541004 China Guangxi Key Laboratory of Machine Vision and Intelligent Control Wuzhou University China School of Computer Science and Technology Harbin Institute of Technology China Media Analytics and Computing Lab School of Informatics Xiamen University China

The rich spatio-temporal information is crucial to capture the complicated target appearance variations in visual tracking. However, most top-performing tracking algorithms rely on many hand-crafted components for spatio-temporal information aggregation. Consequently, the spatio-temporal information is far away from being fully explored. To alleviate this issue, we propose an adaptive tracker with spatio-temporal transformers (named AQATrack), which adopts simple autoregressive queries to effectively learn spatio-temporal information without many hand-designed components. Firstly, we introduce a set of learnable and autoregressive queries to capture the instantaneous target appearance changes in a sliding window fashion. Then, we design a novel attention mechanism for the interaction of existing queries to generate a new query in current frame. Finally, based on the initial target template and learnt autoregressive queries, a spatio-temporal information fusion module (STM) is designed for spatio-temporal formation aggregation to locate a target object. Benefiting from the STM, we can effectively combine the static appearance and instantaneous changes to guide robust tracking. Extensive experiments show that our method significantly improves the tracker’s performance on six popular tracking benchmarks: LaSOT, LaSOText, TrackingNet, GOT-10k, TNL2K, and *** and models will be here. Copyright © 2024, The Authors. All rights reserved.

关键词： Benchmarking

2023 7th International Conference on Communication and information Systems An Improved IOTA Protocol Based on Optimal Midway Walk

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2023 7th International Conference on Communication and Infor...

IEEE International Conference on Communication and information Systems (ICCIS)

作者： Hongcheng Wu Hui Zhi Yangyang Liu Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education Anhui University School of Electronic and Information Engineering Anhui University Hefei China Hefei Zhilian Technology Industry Investment Co. Ltd Hefei China

IOTA (Internet of Things Applications) protocol aims to provide a secure and trustworthy protocol for realizing data-value interactions between IoT devices, and it has become the next possible direction for the development of Blockchain applications. IOTA protocol has the problem that the time-consuming cumulative weight update grows too fast with the increase of the number of transactions, this paper proposed an improved IOTA protocol based on optimal midway walk, the improved protocol uses cutting-edge transaction selection algorithm of weighted Monte Carlo Markov random walk to reduce cumulative weight update delay. Firstly, this improved IOTA protocol mainly ensures the efficiency of transaction confirmation without losing the security of consensus by introducing the optimal midway walk method, i.e., the starting point of each walk is chosen to depart at an optimal location. Secondly, this paper designs the indirect verification identity record algorithm and the layer degree of confirmation principle are designed to realize the improved IOTA protocol's resilience and resistance to Parasite chain attack. The experimental results show that the improved IOTA using random function to select the midway walk starting point from i-50λ, to i-75λsubstantially solves the system computational burden problem and greatly reduces the cumulative weight update delay.

关键词：

Distilled Transformers with Locally Enhanced Global Representations for Face Forgery Detection

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arXiv 2024年

作者： Zhang, Yaning Li, Qiufu Yu, Zitong Shen, Linlin Computer Vision Institute College of Computer Science and Software Engineering Shenzhen University Guangdong Shenzhen518060 China National Engineering Laboratory for Big Data System Computing Technology Shenzhen University Guangdong Shenzhen518060 China Shenzhen Institute of Artificial Intelligence and Robotics for Society Guangdong Shenzhen518129 China Guangdong Key Laboratory of Intelligent Information Processing Shenzhen University Guangdong Shenzhen518060 China School of Computing and Information Technology Great Bay University Guangdong Dongguan523000 China

Face forgery detection (FFD) is devoted to detecting the authenticity of face images. Although current CNN-based works achieve outstanding performance in FFD, they are susceptible to capturing local forgery patterns generated by various manipulation methods. Though transformer-based detectors exhibit improvements in modeling global dependencies, they are not good at exploring local forgery artifacts. Hybrid transformer-based networks are designed to capture local and global manipulated traces, but they tend to suffer from the attention collapse issue as the transformer block goes deeper. Besides, soft labels are rarely available. In this paper, we propose a distilled transformer network (DTN) to capture both rich local and global forgery traces and learn general and common representations for different forgery faces. Specifically, we design a mixture of expert (MoE) module to mine various robust forgery embeddings. Moreover, a locally-enhanced vision transformer (LEVT) module is proposed to learn locally-enhanced global representations. We design a lightweight multi-attention scaling (MAS) module to avoid attention collapse, which can be plugged and played in any transformer-based models with only a slight increase in computational costs. In addition, we propose a deepfake self-distillation (DSD) scheme to provide the model with abundant soft label information. Extensive experiments show that the proposed method surpasses the state of the arts on five deepfake datasets. Copyright © 2024, The Authors. All rights reserved.

关键词： Face recognition

Dynamic Prefix-Tuning for Generative Template-based Event Extraction

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arXiv 2022年

作者： Liu, Xiao Huang, Heyan Shi, Ge Wang, Bo School of Computer Science and Technology Beijing Institute of Technology China Beijing Engineering Research Center of High Volume Language Information Processing and Cloud Computing Applications China Key Laboratory of Intelligent Information Processing and Information Security Ministry of Industry and Information Technology China Southeast Academy of Information Technology Beijing Institute of Technology China Faculty of Information Technology Beijing University of Technology China

We consider event extraction in a generative manner with template-based conditional generation. Although there is a rising trend of casting the task of event extraction as a sequence generation problem with prompts, these generation-based methods have two significant challenges, including using suboptimal prompts and static event type information. In this paper, we propose a generative template-based event extraction method with dynamic prefix (GTEE-DYNPREF) by integrating context information with type-specific prefixes to learn a context-specific prefix for each context. Experimental results show that our model achieves competitive results with the state-of-the-art classification-based model ONEIE on ACE 2005 and achieves the best performances on ERE. Additionally, our model is proven to be portable to new types of events effectively. Copyright © 2022, The Authors. All rights reserved.

关键词： Extraction