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Superconvergence for General Convex Optimal Control Problems Governed by Semilinear Parabolic Equations

International Scholarly Research Notices 2014年第1期2014卷

作者： Yongquan Dai Yanping Chen Hunan Key Laboratory for Computation and Simulation in Science and Engineering Department of Mathematics Xiangtan University Xiangtan Hunan 411105 *** School of Mathematical Sciences South China Normal University Guangzhou Guangdong 510631 ***

We will investigate the superconvergence for the semidiscrete finite element approximation of distributed convex optimal control problems governed by semilinear parabolic equations. The state and costate are approximated by the piecewise linear functions and the control is approximated by piecewise constant functions. We present the superconvergence analysis for both the control variable and the state variables.

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Naive gabor networks for hyperspectral image classification

arXiv

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arXiv 2019年

作者： Liu, Chenying Li, Jun He, Lin Plaza, Antonio Li, Shutao Li, Bo Guangdong Provincial Key Laboratory of Urbanization and Geo-simulation School of Geography and Planning Sun Yat-sen University Guangzhou510275 China School of Automation Science and Engineering South China University of Technology Guangzhou510640 China College of Electrical and Information Engineering Hunan University Changsha410082 China Hyperspectral Computing Laboratory Department of Technology of Computers and Communications Escuela Politécnica University of Extremadura CáceresE-10071 Spain Beijing Key Laboratory of Digital Media School of Computer Science and Engineering State Key Laboratory of Virtual Reality Technology and Systems Beihang University Beijing100191 China

Recently, many convolutional neural network (CNN) methods have been designed for hyperspectral image (HSI) classification since CNNs are able to produce good representations of data, which greatly benefits from a huge number of parameters. However, solving such a high-dimensional optimization problem often requires a large amount of training samples in order to avoid overfitting. Additionally, it is a typical non-convex problem affected by many local minima and flat regions. To address these problems, in this paper, we introduce naive Gabor Networks or Gabor-Nets which, for the first time in the literature, design and learn CNN kernels strictly in the form of Gabor filters, aiming to reduce the number of involved parameters and constrain the solution space, and hence improve the performances of CNNs. Specifically, we develop an innovative phase-induced Gabor kernel, which is trickily designed to perform the Gabor feature learning via a linear combination of local low-frequency and high-frequency components of data controlled by the kernel phase. With the phase-induced Gabor kernel, the proposed Gabor-Nets gains the ability to automatically adapt to the local harmonic characteristics of the HSI data and thus yields more representative harmonic features. Also, this kernel can fulfill the traditional complex-valued Gabor filtering in a real-valued manner, hence making Gabor-Nets easily perform in a usual CNN thread. We evaluated our newly developed Gabor-Nets on three well-known HSIs, suggesting that our proposed Gabor-Nets can significantly improve the performance of CNNs, particularly with a small training set. Copyright © 2019, The Authors. All rights reserved.

关键词： Spectroscopy

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Reference Vector Adaptation and Mating Selection Strategy via Adaptive Resonance Theory-based Clustering for Many-objective Optimization

arXiv

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arXiv 2022年

作者： Kinoshita, Takato Masuyama, Naoki Liu, Yiping Nojima, Yusuke Ishibuchi, Hisao Graduate School of Engineering Osaka Prefecture University 1-1 Gakuen-cho Naka-ku Sakai-Shi Osaka599-8531 Japan Graduate School of Informatics Osaka Metropolitan University 1-1 Gakuen-cho Naka-ku Sakai-Shi Osaka599-8531 Japan College of Computer Science and Electronic Engineering Hunan University Hunan 410082 China Guangdong Provincial Key Laboratory of Brain-Inspired Intelligent Computation Department of Computer Science and Engineering Southern University of Science and Technology Shenzhen518055 China

Decomposition-based multiobjective evolutionary algorithms (MOEAs) with clustering-based reference vector adaptation show good optimization performance for many-objective optimization problems (MaOPs). Especially, algorithms that employ a clustering algorithm with a topological structure (i.e., a network composed of nodes and edges) show superior optimization performance to other MOEAs for MaOPs with irregular Pareto optimal fronts (PFs). These algorithms, however, do not effectively utilize information of the topological structure in the search process. Moreover, the clustering algorithms typically used in conventional studies have limited clustering performance, inhibiting the ability to extract useful information for the search process. This paper proposes an adaptive reference vector-guided evolutionary algorithm using an adaptive resonance theory-based clustering with a topological structure. The proposed algorithm utilizes the information of the topological structure not only for reference vector adaptation but also for mating selection. The proposed algorithm is compared with 8 state-of-the-art MOEAs on 78 test problems. Experimental results reveal the outstanding optimization performance of the proposed algorithm over the others on MaOPs with various properties. © 2022, CC BY-NC-ND.

关键词： Clustering algorithms

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Heterogeneous Graph Reinforcement Learning for Dependency-aware Multi-task Allocation in Spatial Crowdsourcing

arXiv

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arXiv 2024年

作者： Zhao, Yong Zhu, Zhengqiu Gao, Chen Wang, En Huang, Jincai Wang, Fei-Yue College of Systems Engineering National University of Defense Technology Hunan Province Changsha410073 China BNRist Tsinghua University Beijing100084 China College of Computer Science and Technology Jilin University Changchun130012 China Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education Jilin University Changchun130012 China State Key Laboratory for Management and Control of Complex Systems Institute of Automation Chinese Academy of Sciences Beijing100190 China

Spatial Crowdsourcing (SC) is gaining traction in both academia and industry, with tasks on SC platforms becoming increasingly complex and requiring collaboration among workers with diverse skills. Recent research works address complex tasks by dividing them into subtasks with dependencies and assigning them to suitable workers. However, the dependencies among subtasks and their heterogeneous skill requirements, as well as the need for efficient utilization of workers’ limited work time in the multi-task allocation mode, pose challenges in achieving an optimal task allocation scheme. Therefore, this paper formally investigates the problem of Dependency-aware Multi-task Allocation (DMA) and presents a well-designed framework to solve it, known as Heterogeneous Graph Reinforcement Learning-based Task Allocation (HGRL-TA). To address the challenges associated with representing and embedding diverse problem instances to ensure robust generalization, we propose a multi-relation graph model and a Compound-path-based Heterogeneous Graph Attention Network (CHANet) for effectively representing and capturing intricate relations among tasks and workers, as well as providing embedding of problem state. The task allocation decision is determined sequentially by a policy network, which undergoes simultaneous training with CHANet using the proximal policy optimization algorithm. Extensive experiment results demonstrate the effectiveness and generality of the proposed HGRL-TA in solving the DMA problem, leading to average profits that is 21.78% higher than those achieved using the metaheuristic methods. © 2024, CC BY-NC-ND.

关键词： Reinforcement learning

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Causes and Trends of Hydrological Processes in Areas with Intensive Human Activity: A Case Study in Daqing River Basin

SSRN

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SSRN 2024年

作者： Song, Xinyi Xu, Qiwen Liu, Hai Shen, Yalan Lu, Fan School of Hydraulic and Environmental Engineering Changsha University of Science & Technology Changsha410114 China Hydrology and Water Resources Survey Center of Hunan Province Yueyang410201 China State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin China Institute of Water Resources and Hydropower Research Beijing100038 China

Study region: The Daqing River Basin (DRB), North *** focus: Human activities have indirectly or directly altered the natural hydrological processes by changing the land surface and water withdrawal. Understanding the impact of various human actions on the hydrological cycle, combined with potential climate change, is essential to ensure reasonable regional water resource planning. This study uses a physically based hydrological model (DHSVM) to quantify the causes of runoff evolution from multiple dimensions (climate change, human water consumption, land cover changes, and other engineering measures). Using downscaled CMIP6 scenario data, the future trends of hydrological processes are *** hydrological insights for the regions: Surface runoff in the basin decreased by approximately 70% during the historical period, with two significant change points detected. The contribution of human activities to runoff reduction far exceeds that of climate change, with engineering measures accounting for the majority of the decrease (around 50%). Precipitation and temperature in the basin are projected to increase under different emission scenarios, with the increase intensifying along with rising emission concentrations. The accelerated frequency of land-atmosphere water-heat exchanges is beneficial for the recovery of surface runoff but also leads to more uneven intra-annual runoff distribution. This study provides valuable insights for developing water resource management strategies and watershed governance policies for similar basins under the context of climate change. © 2024, The Authors. All rights reserved.

关键词： Rivers

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Multifractal temporally weighted detrended partial cross-correlation analysis of two non-stationary time series affected by common external factors

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Physica A: Statistical Mechanics and its Applications 2021年 573卷

作者： Bao-Gen Li Dian-Yi Ling Zu-Guo Yu Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China School of Electrical Engineering and Computer Science Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia

When common factors strongly influence two cross-correlated time series recorded in complex natural and social systems, the results will be biased if we use multifractal detrended cross-correlation analysis (MF-DXA) without considering these common factors. In order to better study the time series of such cases, we extend the multifractal temporally weighted detrended cross-correlation analysis (MF-TWXDFA) proposed by our group (Wei et al., 2017) and propose multifractal temporally weighted detrended partial cross-correlation analysis (MF-TWDPCCA) to quantify intrinsic power-law cross-correlation of two non-stationary time series affected by common external factors in this paper. To test the performance of MF-TWDPCCA, we apply it and multifractal partial cross-correlation analysis (MF-DPXA) proposed by Qian et al. (2015) on simulated series. Numerical tests on artificially simulated series demonstrate that MF-TWDPCCA can more accurately detect the intrinsic cross-correlations for two simultaneously recorded series than MF-DPXA and MF-TWXDFA. To further show the utility of MF-TWDPCCA, we apply it on time series from stock markets and find that there exists significantly multifractal power-law cross-correlation between stock returns. In addition, a new partial cross-correlation coefficient is defined to quantify the level of intrinsic cross-correlation between two time series.

关键词： Partial cross-correlation Multifractal temporally weighted detrended partial cross-correlation analysis Partial cross-correlation coefficient

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Weak localization and crossover from Lifshitz transition in two dimensions

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Physical Review B 2021年第15期104卷 155135-155135页

作者： Kai-He Ding Zhen-Gang Zhu Yong-Le Hu Gang Su Department of Physics and Electronic Science Changsha University of Science and Technology Changsha 410076 China Hunan Provincial Key Laboratory of Flexible Electronic Materials Genome Engineering Changsha University of Science and Technology Changsha 410076 China School of Electronic Electrical and Communication Engineering University of Chinese Academy of Sciences Beijing 100049 China Theoretical Condensed Matter Physics and Computational Materials Physics Laboratory College of Physical Sciences University of Chinese Academy of Sciences Beijing 100049 China CAS Center for Excellence in Topological Quantum Computation University of Chinese Academy of Sciences Beijing 100190 China College of Automobile and Mechanical Engineering Changsha University of Science and Technology Changsha 410076 China Kavli Institute of Theoretical Sciences University of Chinese Academy of Sciences Beijing 100049 China

Dirac point plays a crucial role in regulating electronic properties of topological semimetals. In two dimensions, the manipulation of Dirac points can spur a transition from Dirac semimetal through semi-Dirac phase to a gapped phase. Across such a so-called Lifshitz transition, we find that the quantum interference corrections to the conductivity δσxx and δσyy are always negative, giving rise to a weak localization behavior. The ratio δσxx/δσyy undergoes a transition from linear to parabolic dependence on the merging parameter across the Lifshitz transition, which leads to a crossover of the temperature dependence of the inverse inelastic scattering time 1/τɛ from ∼T to ∼Tln(T0/T). This fingerprint behavior can be readily tested experimentally through merging Dirac points in two-dimensional lattices. This work presents an alternative perspective to understand weak localization through Lifshitz transition.

关键词： Topological phases of matter Weak localization Dirac semimetal Disordered systems Two-dimensional electron system

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Numerical homogenization of elastoplastic deformations of composite material with small proportion of inclusions

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Journal of Physics: Conference Series 2019年第1期1392卷

作者： Petr V. Sivtsev Aleksandr E. Kolesov Petr E. Zakharov Ying Yang Research Laboratory 'Multiscale Matheatical Modeling and Computing' Ammosov North-Eastern Federal University 58 Belinskogo 677000 Yakutsk Russia Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan 411105 Hunan China

Numerical simulation of the stress-strain state of a composite material may be difficult due to large computational complexity associated with a grid resolution of a large number of inclusions. To overcome the problem one may use the homogenization method. But for material with plastic properties, proper modeling of yield stress and hardening may be overcomplicated. In this work we use some simplification associated with a small proportion of inclusions and restriction of stress values by matrix material strength. As model problem, we use deformation of concrete deep beam reinforced with steel or basalt fiber inclusions. For the numerical solution, the finite element method was applied using the FEniCS computing platform.

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computational design of GeSe/graphene heterojunction based on density functional theory

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Materials Research Express 2018年第3期6卷

作者： Congsheng Xu Jianmei Yuan Dandan Wang Yuliang Mao Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan 411105 People's Republic of China Hunan Key Laboratory for Micro–Nano Energy Materials and Devices School of Physics and Optoelectronic Xiangtan University Hunan 411105 People's Republic of China Authors to whom any correspondence should be addressed.

Based on density functional theory, we computational designed the hetero junction composed by GeSe monolayer and graphene. The effects of interlayer coupling, strains and electric fields on the electronic structures of the designed GeSe/graphene (G/g) hetero structure are explored. We demonstrated that both the intrinsic electric properties of the GeSe monolayer and graphene are well preserved in G/g hetero structure. It is found that an energy gap of 0.17 eV in graphene is opened by decreasing the interlayer distance in G/g hetero structure. The height of Schottky barrier can be effectively tuned by the interlayer distance between GeSe monolayer and graphene. Moreover, we found that applying in-plane strains and the electric fields perpendicular to the G/g hetero structure can control the Schottky barriers at the G/g interface. Our results predict that the ultra-thin G/g hetero structure can be used as two-dimensional semiconductor-based optoelectronic devices.

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Multifractal analysis of weighted networks by a modified sandbox algorithm

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Scientific reports 2015年第1期5卷 17628页

作者： Yu-Qin Song Jin-Long Liu Zu-Guo Yu Bao-Gen Li Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China. College of Science Hunan University of technology Zhuzhou Hunan 412007 China. School of Mathematical Sciences Queensland University of Technology Brisbane Q4001 Australia.

Complex networks have attracted growing attention in many fields. As a generalization of fractal analysis, multifractal analysis (MFA) is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. Some algorithms for MFA of unweighted complex networks have been proposed in the past a few years, including the sandbox (SB) algorithm recently employed by our group. In this paper, a modified SB algorithm (we call it SBw algorithm) is proposed for MFA of weighted networks. First, we use the SBw algorithm to study the multifractal property of two families of weighted fractal networks (WFNs): "Sierpinski" WFNs and "Cantor dust" WFNs. We also discuss how the fractal dimension and generalized fractal dimensions change with the edge-weights of the WFN. From the comparison between the theoretical and numerical fractal dimensions of these networks, we can find that the proposed SBw algorithm is efficient and feasible for MFA of weighted networks. Then, we apply the SBw algorithm to study multifractal properties of some real weighted networks - collaboration networks. It is found that the multifractality exists in these weighted networks, and is affected by their edge-weights.

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