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NUMERICAL METHODS AND ANALYSIS OF computing QUASIPERIODIC SYSTEMS

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arXiv 2022年

作者： Jiang, Kai Li, Shifeng Zhang, Pingwen 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 Mathematics and Statistics Wuhan University Wuhan430072 China School of Mathematical Sciences Peking University Beijing100871 China

Quasiperiodic systems are important space-filling ordered structures, without decay and translational invariance. How to solve quasiperiodic systems accurately and efficiently is of great challenge. A useful approach, the projection method (PM) [J. Comput. Phys., 256: 428, 2014], has been proposed to compute quasiperiodic systems. Various studies have demonstrated that the PM is an accurate and efficient method to solve quasiperiodic systems. However, there is a lack of theoretical analysis of PM. In this paper, we present a rigorous convergence analysis of the PM by establishing a mathematical framework of quasiperiodic functions and their high-dimensional periodic functions. We also give a theoretical analysis of quasiperiodic spectral method (QSM) based on this framework. Results demonstrate that PM and QSM both have exponential decay, and the QSM (PM) is a generalization of the periodic Fourier spectral (pseudo-spectral) method. Then we analyze the computational complexity of PM and QSM in calculating quasiperiodic systems. The PM can use fast Fourier transform, while the QSM cannot. Moreover, we investigate the accuracy and efficiency of PM, QSM and periodic approximation method in solving the linear time-dependent quasiperiodic Schrödinger equation. Copyright © 2022, The Authors. All rights reserved.

关键词： Fast Fourier transforms

Sequential Manipulation Against Rank Aggregation: Theory and Algorithm

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arXiv 2024年

作者： Ma, Ke Xu, Qianqian Zeng, Jinshan Liu, Wei Cao, Xiaochun Sun, Yingfei Huang, Qingming The School of Electronic Electrical and Communication Engineering University of Chinese Academy of Sciences Beijing100049 China The Key Laboratory of Intelligent Information Processing Institute of Computing Technology Chinese Academy of Sciences Beijing100190 China The School of Computer and Information Engineering Jiangxi Normal University Jiangxi Nanchang330022 China The Tencent Data Platform Shenzhen518054 China The School of Cyber Science and Technology Shenzhen Campus of Sun Yat-Sen University Shenzhen518107 China The School of Computer Science and Technology University of Chinese Academy of Sciences Beijing100049 China University of Chinese Academy of Sciences Beijing100049 China

Rank aggregation with pairwise comparisons is widely encountered in sociology, politics, economics, psychology, sports, etc. Given the enormous social impact and the consequent incentives, the potential adversary has a strong motivation to manipulate the ranking list. However, the ideal attack opportunity and the excessive adversarial capability cause the existing methods to be impractical. To fully explore the potential risks, we leverage an online attack on the vulnerable data collection process. Since it is independent of rank aggregation and lacks effective protection mechanisms, we disrupt the data collection process by fabricating pairwise comparisons without knowledge of the future data or the true distribution. From the game-theoretic perspective, the confrontation scenario between the online manipulator and the ranker who takes control of the original data source is formulated as a distributionally robust game that deals with the uncertainty of knowledge. Then we demonstrate that the equilibrium in the above game is potentially favorable to the adversary by analyzing the vulnerability of the sampling algorithms such as Bernoulli and reservoir methods. According to the above theoretical analysis, different sequential manipulation policies are proposed under a Bayesian decision framework and a large class of parametric pairwise comparison models. For attackers with complete knowledge, we establish the asymptotic optimality of the proposed policies. To increase the success rate of the sequential manipulation with incomplete knowledge, a distributionally robust estimator, which replaces the maximum likelihood estimation in a saddle point problem, provides a conservative data generation solution. Finally, the corroborating empirical evidence shows that the proposed method manipulates the results of rank aggregation methods in a sequential manner. © 2024, CC BY.

关键词： Maximum likelihood estimation

A Jacobi Collocation Method for the Fractional Ginzburg-Landau Differential Equation

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Advances in Applied Mathematics and Mechanics 2020年第1期12卷 57-86页

作者： Yin Yang Jianyong Tao Shangyou Zhang Petr V.Sivtsev 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 UniversityXiangtanHunan 411105China Department of Mathematical Sciences University of DelawareNewarkDE 19716USA International Scientific and Research Laboratory of Multiscale Model Reduction and High Performance Computing Ammosov North Eastern UniversityKulakovskogo677013YakutskRussia

In this paper,we design a collocation method to solve the fractional Ginzburg-Landau equation.A Jacobi collocation method is developed and implemented in two ***,we space-discretize the equation by the Jacobi-Gauss-Lobatto collocation(JGLC)method in one-and two-dimensional *** equation is then converted to a system of ordinary differential equations(ODEs)with the time variable based on *** second step applies the Jacobi-Gauss-Radau collocation(JGRC)method for the time ***,we give a theoretical proof of convergence of this Jacobi collocation method and some numerical results showing the proposed scheme is an effective and high-precision algorithm.

关键词： The fractional Ginzburg-Landau equation Jacobi collocation method convergence

Study of Resistive Properties and Neural Response of Zro2/Tio2 Heterojunction Nanowire Array (Nwa) Rram

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SSRN

SSRN 2024年

作者： Sun, Tangyou Qin, Zubin Yu, Fantao Gao, Shuai Wangyang, Peihua Tang, Xiaosheng Li, Haiou Zhang, Fabi Xu, Zhimou Cai, Ping Jiang, Chunsheng Xue, Xiaogang Guangxi Key Laboratory of Precision Navigation Technology and Application Guilin University of Electronic Technology Guilin541004 China College of Optoelectronic Engineering Chongqing University Chongqing400044 China School of Optical and Electronic Information Huazhong University of Science and Technology Wuhan430074 China Guangxi Key Laboratory of Information Materials Guilin University of Electronic Technology Guilin541004 China Guangxi Key Laboratory of Brain-inspired Computing and Intelligent Chips Guangxi Normal University Guilin541004 China School of Optoelectronic Engineering Guangxi Key Laboratory of Optoelectronic Information Processing Guilin University of Electronic Technology Guilin541004 China

Nowadays, researcher has an eye on enhancing the performance of resistive random-access memory (RRAM) and exploring new demands and applications, particularly in the field of artificial intelligence and neural computing. It is crucially important for accurately replicating the observed plasticity within synapses to achieve superior RRAM performance in low-dimensional nanomaterials. In this work, we focus on addressing certainly unsatisfactory electrical property of titanium oxide nanowire array (NWA)-based RRAM, for example short retention time (~ 103 s). Theoretically and experimentally, a novel and solution-based RRAM structure, namely ZrO2/TiO2(NWA), has been conducted. With the help of ZrO2 insertion layer, the RRAM devices shows impressive resistive switching characteristics, including endurance cycling (> 105 cycles), and a long retention time (~ 9×104 s). These findings hold significant implications for digital computing systems. Moreover, successful implementation of the proposed device enables the emulation of fundamental synaptic biological features such as long-term potentiation (LTP), long-term depression (LTD), non-linear transmission properties, and learning experiences. This research provides evidence of the immense potential of the ZrO2/TiO2(NWA) RRAM device in non-volatile memory (NVM) and biomimetic neuromorphic systems. © 2024, The Authors. All rights reserved.

关键词： Heterojunctions

Cross-domain Contrastive Learning for Unsupervised Domain Adaptation

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arXiv 2021年

作者： Wang, Rui Wu, Zuxuan Weng, Zejia Chen, Jingjing Qi, Guo-Jun Jiang, Yu-Gang Shanghai Key Lab of Intelligent Information Processing School of Computer Science Fudan University Shanghai Collaborative Innovation Center on Intelligent Visual Computing China Seattle Cloud Lab Futurewei Technologies BellevueWA98004 United States

Unsupervised domain adaptation (UDA) aims to transfer knowledge learned from a fully-labeled source domain to a different unlabeled target domain. Most existing UDA methods learn domain-invariant feature representations by minimizing feature distances across domains. In this work, we build upon contrastive self-supervised learning to align features so as to reduce the domain discrepancy between training and testing sets. Exploring the same set of categories shared by both domains, we introduce a simple yet effective framework CDCL, for domain alignment. In particular, given an anchor image from one domain, we minimize its distances to cross-domain samples from the same class relative to those from different categories. Since target labels are unavailable, we use a clustering-based approach with carefully initialized centers to produce pseudo labels. In addition, we demonstrate that CDCL is a general framework and can be adapted to the data-free setting, where the source data are unavailable during training, with minimal modification. We conduct experiments on two widely used domain adaptation benchmarks, i.e., Office-31 and VisDA-2017, for image classification tasks, and demonstrate that CDCL achieves state-of-the-art performance on both datasets. Copyright © 2021, The Authors. All rights reserved.

关键词： Benchmarking

Diagnosis of Alzheimer's disease based on logistic regression algorithm

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Diagnosis of Alzheimer's disease based on logistic regressio...

computing, Robotics and System sciences (ICRSS), International Conference on

作者： YuSi Chen Ning Liu PeiKun Chen School of Mathematics and Computer Science Quanzhou Normal University Fujian Provincial Key Laboratory of Data-Intensive Computing Key Laboratory of Intelligent Computing and Information Processing Quanzhou China School of Public Health Hangzhou Normal University Hangzhou China Department of mathematics and computer science Quanzhou Normal University Fujian Provincial Key Laboratory of Data-Intensive Computing Quanzhou China Xiamen Silicon Field System Engineering Co. Ltd. Xiamen China

Language impairment may be an important early manifestation of dementia. In this study, we propose a multi-feature fusion to distinguish MCI and AD patients. In this paper, a set of acoustic, demographic and linguistic features were selected, and after data processing, logistic regression algorithm was used to diagnose MCI and AD patients. In order to get better results, comparative experiments are also effectively conducted, including different combination methods and different group distinctions with the three most popular algorithms. Studies have shown that this method is more advantageous and the classification results are more accurate.

关键词： Fuses Linguistics Feature extraction Data processing Acoustics Classification algorithms Data mining

Sequential Recommendation via Cross-Domain Novelty Seeking Trait Mining

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Journal of Computer science & Technology 2020年第2期35卷 305-319页

作者： Fu-Zhen Zhuang Ying-Min Zhou Hao-Chao Ying Fu-Zheng Zhang Xiang Ao Xing Xie Qing He Hui Xiong Key Laboratory of Intelligent Information Processing of Chinese Academy of Sciences Institute of Computing Technology Chinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100049China School of Public Health Zhejiang University School of MedicineHangzhou 310027China Meituan-Dianping Group Beijing 100102China Microsoft Research Asia Beijing 100080China Department of Management Science and Information Systems Rutgers UniversityNew Jersey 07102U.S.A.

Transfer learning has attracted a large amount of interest and research in last decades, and some effort has been made to build more precise recommendation systems. Most previous transfer recommendation systems assume that the target domain shares the same/similar rating patterns with the auxiliary source domain, which is used to improve the recommendation performance. However, almost all existing transfer learning work does not consider the characteristics of sequential data. In this paper, we study the new cross-domain recommendation scenario by mining novelty-seeking trait. Recent studies in psychology suggest that novelty-seeking trait is highly related to consumer behavior, which has a profound business impact on online recommendation. Previous work performed on only one single target domain may not fully characterize users' novelty-seeking trait well due to the data scarcity and sparsity, leading to the poor recommendation performance. Along this line, we propose a new cross-domain novelty-seeking trait mining model (CDNST for short) to improve the sequential recommendation performance by transferring the knowledge from auxiliary source domain. We conduct systematic experiments on three domain datasets crawled from Douban to demonstrate the effectiveness of our proposed model. Moreover, we analyze the directed influence of the temporal property at the source and target domains in detail.

关键词： sequential recommendation novelty-seeking trait transfer learning

A many-objective evolutionary algorithm based on rotation and decomposition

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Swarm and Evolutionary Computation 2021年 60卷

作者： Zou, Juan Liu, Jing Yang, Shengxiang Zheng, Jinhua Key Laboratory of Hunan Province for Internet of Things and Information Security Xiangtan University XiangtanHunan411105 China Key Laboratory of Intelligent Computing and Information Processing Ministry of Education Information Engineering College of Xiangtan University XiangtanHunan411105 China Hunan Provincial Key Laboratory of Intelligent Information Processing and Application Hengyang421002 China School of Computer Science and Informatics De Montfort University LeicesterLE1 9BH United Kingdom

Evolutionary algorithms have shown their promise in addressing multiobjective problems (MOPs). However, the Pareto dominance used in multiobjective optimization loses its effectiveness when addressing many-objective problems (MaOPs), which are defined as having more than three objectives. This is because the Pareto dominance loses its ability to distinguish between individuals. In this paper, a many-objective evolutionary algorithm based on rotation and decomposition is proposed (MaOEA-RD) to overcome the shortcoming of insufficient selection pressure caused by the Pareto dominance. First, the coordinates system is rotated and a hyperplane is established to distinguish between the nondominated individuals. Then, a novel individual selection mechanism incorporating decomposition is adopted to maintain the diversity of the population. In order to compensate for the deficiency of the predefined reference vectors, a reference vector adjustment mechanism is proposed. Experimental studies on several well-known benchmark problems show that the proposed algorithm is competitive compared with nine state-of-the-art many-objective algorithms. © 2020 Elsevier B.V.

关键词： Evolutionary algorithms

Generalized Face Forgery Detection via Adaptive Learning for Pre-trained Vision Transformer

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arXiv 2023年

作者： Luo, Anwei Cai, Rizhao Kong, Chenqi Ju, Yakun Kang, Xiangui Huang, Jiwu Kot, Alex C. The School of Information Technology Jiangxi University of Finance and Economics Nanchang330013 China The School of Computer Science and Engineering Sun Yat-Sen University Guangzhou510006 China Lab. School of Electrical and Electronic Engineering Nanyang Technology University Singapore The Guangdong Key Laboratory of Intelligent Information Processing National Engineering Laboratory for Big Data System Computing Technology Shenzhen University Shenzhen518060 China The China-Singapore International Joint Research Institute Singapore

With the rapid progress of generative models, the current challenge in face forgery detection is how to effectively detect realistic manipulated faces from different unseen domains. Though previous studies show that pre-trained Vision Transformer (ViT) based models can achieve some promising results after fully fine-tuning on the Deepfake dataset, their generalization performances are still unsatisfactory. One possible reason is that fully fine-tuned ViT-based models may disrupt the pre-trained features [1], [2] and overfit to some data-specific patterns [3]. To alleviate this issue, we present a Forgery-aware Adaptive Vision Transformer (FA-ViT) under the adaptive learning paradigm, where the parameters in the pre-trained ViT are kept fixed while the designed adaptive modules are optimized to capture forgery features. Specifically, a global adaptive module is designed to model long-range interactions among input tokens, which takes advantage of self-attention mechanism to mine global forgery clues. To further explore essential local forgery clues, a local adaptive module is proposed to expose local inconsistencies by enhancing the local contextual association. In addition, we introduce a fine-grained adaptive learning module that emphasizes the common compact representation of genuine faces through relationship learning in fine-grained pairs, driving these proposed adaptive modules to be aware of fine-grained forgery-aware information. Extensive experiments demonstrate that our FA-ViT achieves state-of-the-arts results in the cross-dataset evaluation, and enhances the robustness against unseen perturbations. Particularly, FA-ViT achieves 93.83% and 78.32% AUC scores on Celeb-DF and DFDC datasets in the cross-dataset evaluation. The code and trained model have been released at: https://***/LoveSiameseCat/FAViT. Copyright © 2023, The Authors. All rights reserved.

关键词： Contrastive Learning