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A posteriori error estimation for an interior penalty virtual element method of Kirchhoff plates

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arXiv 2024年

作者： Feng, Fang Hu, Yuming Yu, Yue Zhao, Jikun School of Mathematics and Statistics Nanjing University of Science and Technology Nanjing China 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 School of Mathematics and Statistics Zhengzhou University Zhengzhou450001 China

In this paper, we develop a residual-type a posteriori error estimation for an interior penalty virtual element method (IPVEM) for the Kirchhoff plate bending problem. Building on the work in [18], we adopt a modified discrete variational formulation that incorporates the H1-elliptic projector in the jump and average terms. This allows us to simplify the numerical implementation by including the H1-elliptic projector in the computable error estimators. We derive the reliability and efficiency of the a posteriori error bound by constructing an enriching operator and establishing some related error estimates that align with C0-continuous interior penalty finite element methods. As observed in the a priori analysis, the interior penalty virtual elements exhibit similar behaviors to C0continuous elements despite its discontinuity. This observation extends to the a posteriori estimate since we do not need to account for the jumps of the function itself in the discrete scheme and the error estimators. As an outcome of the error estimator, an adaptive VEM is introduced by means of the mesh refinement strategy with the one-hanging-node rule. Numerical results from several benchmark tests confirm the robustness of the proposed error estimators and show the efficiency of the resulting adaptive VEM. Copyright © 2024, The Authors. All rights reserved.

关键词： Discrete element methods

Stability of diverse dodecagonal quasicrystals in T-shaped liquid crystalline molecules

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arXiv 2024年

作者： Wang, Xin Shi, An-Chang Zhang, Pingwen Jiang, Kai Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China Department of Physics and Astronomy McMaster University HamiltonONL8S4M1 Canada School of Mathematics and Statistics Wuhan University Wuhan430072 China

Quasicrystals are intriguing ordered structures characterized by the lack of translational symmetry and the existence of rotational symmetry. The tiling of different geometric units such as triangles and squares in two-dimensional space can result in a great variety of quasicrystals that could be realized by the self-assembly of liquid crystalline molecules. In this study, we introduce three self-similar dodecagonal tilings, including a novel Diamond-Square-Triangle pattern, composed of triangular and quadrangular tiles and examine their thermodynamic stability by using the self-consistent field theory applied to T-shaped liquid crystalline molecules. Specifically, we detail the inflation rules for the construction of these dodecagonal tilings and analyze their self-similarity, and show that these tilings can be viewed as projections of higher-dimensional periodic lattice points with projection windows. Using these dodecagonal tilings as initial configurations of the SCFT results in solutions corresponding to quasicrystals that could form from the T-shaped liquid crystalline molecules. The relative stability of these aperiodic phases is analyzed to obtain design rules that could stabilize quasicrystals. Meanwhile, we provide two criteria for distinguishing three dodecagonal quasicrystals and their approximants by analyzing their diffraction peaks. These findings shed new lighten on the discovery of new quasicrystals in soft materials. Copyright © 2024, The Authors. All rights reserved.

关键词： Quasicrystals

SCESP: An Edge Server Placement Method Based on Spectral Clustering in Mobile Edge computing 8th

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SCESP: An Edge Server Placement Method Based on Spectral Cl...

8th International Conference on Artificial Intelligence and Security , ICAIS 2022

作者： Wang, Lijuan Guo, Yingya Yao, Jiangyuan Zhou, Siyu College of Computer and Data Science Fuzhou University Fuzhou350000 China Fujian Key Laboratory of Network Computing and Intelligent Information Processing Fuzhou University Fuzhou350000 China Key Laboratory of Spatial Data Mining and Information Sharing Ministry of Education Fuzhou350003 China School of Computer Science and Cyberspace Security Hainan University Haikou570228 China Tandon School of Engineering New York University New York10012 United States

ISBN: (纸本)9783031067600

With the rapid development of Internet of Things (IoT) and 5G, mobile edge computing is gaining popularity for its low computation latency, bandwidth costs and energy consumption. In mobile edge computing, the placement of edge servers is one of the most significant problems and attracts worldwide attention. However, two major problems of edge server placement: high access delay and unbalanced workload of edge servers, have not been completely solved yet. To better solve these two problems, this paper proposes a new Spectral-Clustering-based Edge Server Placement (SCESP) algorithm, which can effectively reduce the access delay and make the workload of each edge server more balanced. In the evaluation, we use the Shanghai Telecom’s base station dataset to test the performance of SCESP and extensive experiments demonstrate the superior performance of SCESP in reducing the access delay and balancing the edge server workload. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Mobile edge computing

Existence of Solutions for the Continuous Algebraic Riccati Equation via Polynomial Optimization

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arXiv 2024年

作者： Zhang, Juan Zhao, Wenjie Key Laboratory of Intelligent Computing and Information Processing Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China School of Mathematics and Statistics Hunan First Normal University Hunan Changsha410205 China School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

This paper studies the solution existence of the continuous-time algebraic Riccati equation (CARE). We formulate the CARE as two constrained polynomial optimization problems, and then use Lasserre's hierarchy of semi-definite relaxations to solve them. Compared to the existing work, our approaches can obtain the exact positive semi-definite solution of the CARE when the coefficient matrices are symmetric. Moreover, our methods can detect the nonexistence of the positive semi-definite solution for the CARE. Numerical examples show that our approaches are effective compared to the existing methods. Copyright © 2024, The Authors. All rights reserved.

关键词： Riccati equations

Direct Contrastive Learning for Incomplete Multi-view Clustering

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Direct Contrastive Learning for Incomplete Multi-view Cluste...

Chinese Control and Decision Conference, CCDC

作者： Kaiwu Zhang Yaoying Wang Shengxia Gao Shiqiang Du Xiangzhen He Key Laboratory of Linguistic and Cultural Computing of Ministry of Education Northwest Minzu University Lanzhou China Chinese National Information Technology Research Institute Northwest Minzu University Lanzhou China College of Mathematics and Computer Science Northwest Minzu University Lanzhou China Key Laboratory of Minzu Languages and Cultures Intelligent Information Processing Gansu Province Northwest Minzu University Lanzhou China

ISBN: (数字)9798350387780

ISBN: (纸本)9798350387797

Incomplete multi-view clustering (IMVC) is a emerging research topic. Although several attempts to solve IMVC have been proposed, they suffered from the following problems: (1) Most existing methods usually solve the dimensional collapse problem by adding additional projection heads, whereby the latent features are only effective in low-dimensional subspaces. However this approach will increase the complexity of the model. (2) Most existing methods typically use consistent learning and reconstruction learning on the same feature, which can result in irrelevant private information affecting the learning of the common representation. In this paper, a novel incomplete multi-view clustering framework based on direct contrastive learning is proposed to solve the above problems. Specifically, our method prevents dimensionality collapse without adding additional projection heads by utilizing sub-vectors of learned feature vectors for consistency learning. Furthermore, this framework reduces the adverse effects of inconsistent and useless private information by performing reconstruction loss and contrastive loss on the feature vector and its sub-vectors respectively. To handle incomplete data, a cross-view prediction mechanism is adopted to recover missing information. Extensive experimental results show the effectiveness of the proposed method and obtain significant performance improvements on public datasets.

关键词： Contrastive learning Vectors Complexity theory

Design of reconfigurable monopole antenna with switchable dual band-notches for UWB applications

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Progress In Electromagnetics Research C 2019年 96卷 97-107页

作者： Li, Ji Sun, Yufa Key Lab of Intelligent Computing and Signal Processing Ministry of Education Anhui University Hefei230601 China

A reconfigurable antenna with on-demand single-band or dual-band rejection capability for ultra-wideband (UWB) applications is presented. A modified monopole structure is integrated with a U-shaped slot and an open-ended slot to realize band-rejection. The antenna operates in four modes: A full UWB (3.1–10.6 GHz) coverage antenna, a UWB antenna with a single-band WiMax or wide local area network (WLAN) rejection, and a UWB antenna with dual-band WiMax/WLAN rejection. On-demand single and dual-band rejections are implemented by controlling two slots using two PIN diodes. Thus, the adopted control technique is quite easy and requires low operating power. Details of the design process and reconfiguration mechanism are presented. The band-rejection performance is explained by return loss and surface current distribution at single-band mode. A prototype is built on a Rogers substrate and tested to validate the performances. The antenna exhibits stable radiation characteristics and almost flat gain responses across the whole band, while significantly gain reduction is achieved at the rejected bands. Therefore, this antenna is suitable for high-performance UWB systems in WiMax/WLAN dense environments with the aim to improve signal quality, system capacity, and communication efficiency. © 2019, Electromagnetics Academy. All rights reserved.

关键词： Monopole antennas

ESO-Based Control for 2-D Networked Control Systems With Markov-Type DoS Attacks

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IEEE Transactions on Network Science and Engineering 2025年

作者： Cheng, Peng He, Shuping Xiao, Gaoxi Zhang, Weidong Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education School of Electrical Engineering and Automation Anhui University 230601 China Anhui University National Key Laboratory of Opto-Electronic Information Acquisition and Protection Technology School of Electrical Engineering and Automation Hefei230601 China Nanyang Technological University School of Electrical and Electronic Engineering 639798 Singapore Shanghai Jiao Tong University Department of Automation Shanghai200240 China

This article aims to investigate the issue of the extended state observer (ESO)-based controller design for a two-dimensional (2-D) networked control system (NCS), where the communication channel suffers from Markov-type denial-of-service (DoS) attacks. The concerned system is developed by the Fornasini-Marchesini second (FMII) model. Firstly, the evolution of the DoS attacks is characterized with the help of a Markov jump process with two modes, which can eliminate the need for an explicit energy description. Moreover, a 2-D information compensation mechanism is devised, which utilizes the most recently received bidirectional signals unaffected by DoS attacks to ensure continuous input to the ESO, thereby mitigating the impact of communication interruptions. With the aid of the ESO, the developed control scheme ensures system stabilization and guarantees ultimate uniform boundedness under DoS attacks. Finally, a simulation example is conducted to validate the soundness and effectiveness of the presented control strategy, and the analysis of the Markov-type DoS attack intensity on system stability is presented as well. © 2013 IEEE.

关键词： Networked control systems

Emotion Recognition of Virtual Reality Scenes Under Olfactory Stimulation: An ECG Study

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SSRN

SSRN 2023年

作者： Liu, Wanqing Zhong, Xinyue Feng, Weibin Xie, Jialan Luo, Yutong Guangyuan, Liu College of Electronic and Information Engineering Southwest University Chongqing400715 China Institute of Affective Computing and Intelligent Information Processing Southwest University Chongqing400715 China Key Laboratory of Cognition and Personality Ministry of Education Faculty of Psychology Southwest University Chongqing400715 China

Virtual Reality (VR) technology enhanced by olfactory stimulation has introduced novel dimensions to human-computer interaction (HCI). While there have been studies utilizing electrocardiogram (ECG) signals to explore the impact of olfaction on the emotional experiences of traditional multimedia users, little research has delved into the influence of heightened olfactory stimulation on emotion recognition within virtual reality scenarios. To explore this issue in depth, we first initiated an olfactory stimulation experiment within a VR environment, collecting ECG data from 65 participants as they interacted with VR scenes and olfactory-enhanced virtual reality (OVR) scenes, each characterized by varying emotional valence and levels of emotional arousal. Subsequently, we extracted time-domain, frequency-domain, and nonlinear features from the ECG data. Finally, we employed three widely used machine learning classification models, namely, light gradient boosting machine, SVM, and adaptive enhancement algorithm, to discern the emotional valence and arousal levels in OVR and VR states, respectively. The results indicate that the classification recognition rates of all three classifiers are significantly higher (> 4%) within the OVR environment than in the VR context, both in terms of valence and arousal dimensions. The results are consistent with the analysis and comparison of behavioral data. This finding underscores the capacity of ECG data to effectively capture distinctions in emotional responses between OVR and VR experiences and highlights the contributory role of olfactory enhancement in VR-based emotion recognition. Our discoveries will contribute to the advancement of OVR emotion recognition research and offer fresh insights for enhancing the overall HCI emotional experience. © 2023, The Authors. All rights reserved.

关键词： Electrocardiograms

Periodicity Analysis of the Logistic Map over Ring Z3n

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arXiv 2023年

作者： Lu, Xiaoxiong Xie, Eric Yong Li, Chengqing School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China School of Computer Science Xiangtan University Hunan Xiangtan411105 China Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education Xiangtan University Hunan Xiangtan411105 China

Periodicity analysis of sequences generated by a deterministic system is a long-standing challenge in both theoretical research and engineering applications. To overcome the inevitable degradation of the Logistic map on a finite-precision circuit, its numerical domain is commonly converted from a real number field to a ring or a finite field. This paper studies the period of sequences generated by iterating the Logistic map over ring Z3n from the perspective of its associate functional network, where every number in the ring is considered as a node, and the existing mapping relation between any two nodes is regarded as a directed edge. The complete explicit form of the period of the sequences starting from any initial value is given theoretically and verified experimentally. Moreover, conditions on the control parameter and initial value are derived, ensuring the corresponding sequences to achieve the maximum period over the ring. The results can be used as ground truth for dynamical analysis and cryptographical applications of the Logistic map over various *** Codes 65P20 Copyright © 2023, The Authors. All rights reserved.

关键词： Mapping