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RECONSTRUCTION-BASED A POSTERIORI ERROR ESTIMATES FOR THE L1 METHOD FOR TIME FRACTIONAL PARABOLIC PROBLEMS

Journal of Computational Mathematics 2025年第2期43卷 345-368页

作者： Jiliang Cao Aiguo Xiao Wansheng Wang Department of Mathematics Shanghai Normal UniversityShanghai 200234China Hunan Key Laboratory for Computation and Simulation in Science and Engineering&Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan UniversityXiangtan 411105China

In this paper,we study a posteriori error estimates of the L1 scheme for time discretizations of time fractional parabolic differential equations,whose solutions have generally the initial *** derive optimal order a posteriori error estimates,the quadratic reconstruction for the L1 method and the necessary fractional integral reconstruction for the first-step integration are *** using these continuous,piecewise time reconstructions,the upper and lower error bounds depending only on the discretization parameters and the data of the problems are *** numerical experiments for the one-dimensional linear fractional parabolic equations with smooth or nonsmooth exact solution are used to verify and complement our theoretical results,with the convergence ofαorder for the nonsmooth case on a uniform *** recover the optimal convergence order 2-αon a nonuniform mesh,we further develop a time adaptive algorithm by means of barrier function recently *** numerical implementations are performed on nonsmooth case again and verify that the true error and a posteriori error can achieve the optimal convergence order in adaptive mesh.

关键词： Time fractional parabolic differential equations A posteriori error estimates Ll method Fractional integral reconstruction Quadratic reconstruction

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Online Streaming Feature Selection Using Bidirectional Complementarity Based on Fuzzy Gini Entropy

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IEEE Transactions on Fuzzy Systems 2025年第5期33卷 1592-1604页

作者： Zhang, Chucai Lu, Zhengxiang Zhang, Yongkang Dai, Jianhua Hunan Normal University Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing College of Information Science and Engineering Changsha410081 China School of Mathematics and Statistics Changsha410081 China

Online streaming feature selection has garnered widespread attention due to its efficiency and adaptability in dynamic data environments. However, existing methods primarily focus on the correlation and redundancy among features, often overlooking the complementarity between candidate and selected features. In this article, we address this gap by introducing three key innovations. First, we construct a novel metric, fuzzy Gini entropy (FGE), to measure feature uncertainty within datasets. Unlike traditional information entropy, fuzzy Gini entropy inherits the advantages of the Gini index, effectively measuring the impurity of datasets, while also being capable of handling common fuzzy environments. Accordingly, related metrics such as fuzzy joint Gini entropy, fuzzy conditional Gini entropy, and fuzzy mutual Gini information are developed. Second, we innovatively propose the concept of the bidirectional complementarity ratio, which captures the relationship between candidate features and previously selected features in online streaming feature selection. This mitigates the unfairness associated with the late arrival of features, ensuring that candidate features with a bidirectional complementary effect that outweighs their redundancy effect with the selected features are chosen. Third, we design an online streaming feature selection method named FGE-OSFS. The method evaluates streaming features through three steps: Online relevance analysis, online bidirectional complementarity analysis, and online redundancy analysis. Finally, we compare the proposed method with five state-of-the-art online streaming feature selection methods, demonstrating the effectiveness of our new approach. © 1993-2012 IEEE.

关键词： Redundancy

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JDC-GCN: joint diversity and consistency graph convolutional network

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Neural computing and Applications 2025年 1-17页

作者： Lin, Renjie Yao, Jie Wang, Shiping Guo, Wenzhong College of Computer and Data Science Fuzhou University Fuzhou350116 China Fujian Provincial Key Laboratory of Network Computing and Intelligent Information Processing Fuzhou University Fuzhou350116 China

In real-world scenarios, multi-view data comprises heterogeneous features, with each feature corresponding to a specific view. The objective of multi-view semi-supervised classification is to enhance classification performance by leveraging the inherent complementary and consistent information present within diverse views. Nevertheless, many existing frameworks primarily focus on assigning suitable weights to different views while neglecting the importance of consistent information. In this paper, a multi-view semi-supervised classification framework called joint diversity and consistency graph convolutional network (JDC-GCN) is proposed. Firstly, the structure of graph convolutional network is introduced to the multi-view semi-supervised classification, capable of propagating the label information over the topological structure of multi-view data. Secondly, the proposed JDC-GCN captures the complementary and consistent information from multiple views through two indispensable sub-modules, Diversity-GCN and Consistency-GCN, respectively. Finally, the attention mechanism is leveraged to dynamically adjust the weights of various views, allowing us to measure the significance of heterogeneous features and the consistent graph without introducing additional parameters. Comprehensive experiments on eight multi-view datasets are conducted to validate the effectiveness of the JDC-GCN algorithm. The results show that the proposed method exhibits superior classification performance compared to other state-of-the-art methods. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2025.

关键词： Self-supervised learning

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PRPFD: Polynomial Resampling Particle Filter Based Deconvolution Approach for Resting-State BOLD-fMRI Data Analysis 24

PRPFD: Polynomial Resampling Particle Filter Based Deconvolu...

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5th International Symposium on Artificial Intelligence for Medicine Science, ISAIMS 2024

作者： Luo, Yunying Zeng, Weiming Key Laboratory for Digital Imaging Processing and Intelligent Computing School of Information Engineering Shanghai Maritime University Shanghai China

ISBN: (纸本)9798400717826

Functional Magnetic Resonance Imaging (fMRI) stands out in brain science research due to its non-invasive, non-intrusive, radiation-free, high spatial resolution, and precise localization advantages. However, the BOLD-fMRI signals it generates exhibit a several-second delay compared to neural activity, making it unable to reflect brain neural activity directly. This discrepancy may lead to differences from the actual situation. Therefore, this study aims to enhance the deconvolution of fMRI by refining existing methods to reconstruct the brain’s neural signals more faithfully. Building upon the foundation of particle filtering deconvolution, this paper introduced a novel approach to deconvolving resting-state fMRI data: the polynomial resampling particle filtering deconvolution (PRPFD). They adapted the particle distribution better to match the actual state through weight computation and resampling. We performed a simulation-based experiment to validate the feasibility of our approach. Besides, we validated the performance of our method using group data, focusing on both effective connectivity and functional connectivity, providing strong evidence for the usability and stability of our approach, and compared our method with other deconvolution techniques, demonstrating improvements in accuracy and computational efficiency. © 2024 Copyright held by the owner/author(s).

关键词： Polynomials

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An Improved Compressive Sensing-Based Model for Efficient Analysis of Monostatic Electromagnetic Scattering Problems

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IEEE Microwave and Wireless Technology Letters 2025年第4期35卷 388-391页

作者： Qi, Qi Fan, Yunuo Cao, Xinyuan Liu, Yi Kong, Meng Huang, Zhixiang Wu, Xianliang Hefei Normal University Anhui Province Key Laboratory of Simulation Calculation and Design for Electronic Information System Hefei230601 China Anhui University Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education Hefei230601 China

To further accelerate the analysis of monostatic electromagnetic (EM) scattering problems of objects, an improved compressive sensing (CS)-based model is proposed. First, an orthogonal subspace spanned by the wide-angle induced currents is identified by means of the wide-angle incident sources. Then, the sparse transform of the induced currents is replaced by the subspace projection. In addition, an optimal number of measurements is determined, only slightly larger than the dimension of the subspace. Finally, the recovery algorithm is simplified to the least-squares method to solve the resulting overdetermined system. Compared with the traditional CS-based model, the proposed model significantly improves the efficiency of the recovery step and optimizes both the requirement for and the way of determining the number of measurements. © 2023 IEEE.

关键词： Least squares approximations

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Efficient Algorithms for Minimizing the Kirchhoff Index via Adding Edges

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IEEE Transactions on Knowledge and Data Engineering 2025年第6期37卷 3342-3355页

作者： Zhou, Xiaotian Zehmakan, Ahad N. Zhang, Zhongzhi Shanghai Key Laboratory of Intelligent Information Processing School of Computer Science Fudan University Shanghai200433 China School of Computing Australian National University CanberraACT2601 Australia Research Institute of Intelligent Complex Systems Fudan University Shanghai200433 China

The Kirchhoff index, which is the sum of the resistance distance between every pair of nodes in a network, is a key metric for gauging network performance, where lower values signify enhanced performance. In this paper, we study the problem of minimizing the Kirchhoff index by adding edges. We first provide a greedy algorithm for solving this problem and give an analysis of its quality based on the bounds of the submodularity ratio and the curvature. Then, we introduce a gradient-based greedy algorithm as a new paradigm to solve this problem. To accelerate the computation cost, we leverage geometric properties, convex hull approximation, and approximation of the projected coordinate of each point. To further improve this algorithm, we use pre-pruning and fast update techniques, making it particularly suitable for large networks. Our proposed algorithms have nearly-linear time complexity. We provide extensive experiments on ten real networks to evaluate the quality of our algorithms. The results demonstrate that our proposed algorithms outperform the state-of-the-art methods in terms of efficiency and effectiveness. Moreover, our algorithms are scalable to large graphs with over 5 million nodes and 12 million edges. © 2025 IEEE.

关键词： Graph algorithms

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Multi-objective Balanced Task Offloading in Vehicular Networks Based on Edge computing 27th

Multi-objective Balanced Task Offloading in Vehicular Networ...

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27th International Conference on Pattern Recognition, ICPR 2024

作者： Wang, Lingjiao Meng, Lingwei Guo, Hua Xiangtan University Hunan Xiangtan411105 China Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Hunan Xiangtan411105 China

ISBN: (纸本)9783031783821

The increasing number of vehicular networking devices and application demands has made the limited computing and communication resources a significant challenge. The heuristic task offloading strategy mechanism was proposed to improve the efficiency of task offloading in vehicular networks. This strategy mechanism utilized the Nondominated Sorting Genetic Fireworks Algorithm (NSGFA) based on the characteristics of the problem, integrated consideration of the multi-target balance between system offloading costs and load balancing. Experimental data results demonstrate that this method performs well in reducing latency, energy consumption, and load balancing, effectively enhancing the quality of service for vehicular network users. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Computation offloading

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An Evolutionary Multitasking Algorithm for Efficient Multiobjective Recommendations

IEEE Transactions on Artificial Intelligence

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IEEE Transactions on Artificial Intelligence 2025年第3期6卷 518-532页

作者： Tian, Ye Ji, Luke Hu, Yiwei Ma, Haiping Wu, Le Zhang, Xingyi Anhui University Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education School of Computer Science and Technology Hefei230601 China Anhui University Institutes of Physical Science and Information Technology Hefei230601 China Hefei University of Technology Key Laboratory of Knowledge Engineering with Big Data Hefei230029 China

Represented by evolutionary algorithms and swarm intelligence algorithms, nature-inspired metaheuristics have been successfully applied to recommender systems and amply demonstrated effectiveness, in particular, for multiobjective recommendation. Owing to the population-based search paradigm, these algorithms can produce a number of recommendation lists, making diverse tradeoffs between multiple metrics and meeting the requirements of accuracy, novelty, diversity, and other user preferences. However, these algorithms are criticized for the low efficiency of the optimization process, especially when the number of users is large. To address this issue, this article proposes an evolutionary multitasking-based recommendation method, where each task corresponds to a user and all the tasks are optimized simultaneously, thus highly improving the efficiency of recommendation. To enhance the convergence speed, all the users are divided into multiple populations according to the similarity between their preferences, where each population evolves with internal knowledge transfer between users, and all the populations evolve with external knowledge transfer between populations. Experimental results on various datasets verify that the proposed method can better balance between multiple metrics than classical and deep neural network-based recommendation methods and exhibits significantly higher efficiency than evolutionary multiobjective optimization-based recommendation methods. © 2024 IEEE. All rights reserved.

关键词： Multiobjective optimization

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Unsupervised Domain Transfer for Object Classification in 3D Point Clouds via Hierarchical Prompt Learning

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IEEE Signal processing Letters 2025年 32卷 1750-1754页

作者： Luo, Huan Fu, Kaiwei Fang, Lina Fuzhou University College of Computer and Data Science China Fuzhou University Fujian Provincial Key Laboratory of Network Computing and Intelligent Information Processing China Ministry of Education Key Laboratory of Spatial Data Mining & Information Sharing Fuzhou350003 China Chinese Academy of Sciences Quanzhou Institute of Equipment Manufacturing Haixi Institute Fujian Quanzhou362216 China

Traditional object classification in 3D point cloud scenes relies heavily on large-scale labeled training data, which is both time-consuming and labor-intensive to obtain. Unsupervised Domain Transfer (UDT) mitigates this challenge by transferring knowledge from a labeled source domain to an unlabeled target domain. However, existing UDT-based methods often require complex neural architectures and substantial computational resources. This letter proposes a novel UDT framework that integrates hierarchical prompt learning with a 3D foundational model. The proposed method consists of a modality alignment stage and an unsupervised transfer stage. In the modality alignment stage, cross-modal hierarchical prompts are employed to align the Visual-Language (V-L) modality in the 3D foundational model through a V-L coupling module. In the unsupervised transfer stage, cross-domain hierarchical prompts and a Target-Source (T-S) coupling module facilitate the alignment of multi-scale contextual information across domains, ensuring efficient and accurate knowledge transfer. Extensive experiments conducted on multiple datasets collected from various laser scanners demonstrate the effectiveness of our proposed approach. © 1994-2012 IEEE.

关键词： Visual languages

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Relaxing Distillation Constraints for Improved New Class Learning in Continual Semantic Segmentation

Relaxing Distillation Constraints for Improved New Class Lea...

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2025 IEEE International Conference on Acoustics, Speech, and Signal processing, ICASSP 2025

作者： Ti, Zheng Hao, Xuze Chen, Renhai College of Intelligence and Computing Tianjin University Tianjin China School of Computer Science Shanghai Key Laboratory of Intelligent Information Processing Fudan University Shanghai China

ISBN: (纸本)9798350368741

Continual Semantic Segmentation (CSS) aims to continuously learn new classes while mitigating catastrophic forgetting. Existing CSS methods primarily address this challenge through knowledge distillation. While they focus on maintaining stability for old classes, this emphasis often restricts plasticity in learning new ones. In this work, we propose two plug-and-play methods to better balance stability and plasticity. First, for feature map distillation, we replace pixel-level constraints with statistical information extraction within a window, improving the learning of new classes while preserving structural integrity to overcome forgetting. Second, we use relative ranks of predictions to replace exact probabilistic values to loosen the constraints in the logit distribution of old classes. Extensive experiments demonstrate that our methods outperform state-of-the-art methods when integrating into several baselines across various CSS scenarios. © 2025 IEEE.

关键词： Continual Learning Knowledge Distillation Semantic Segmentation

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