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arXiv 2023年

作者： Zhang, Duo Liu, Xinzijian Zhang, Xiangyu Zhang, Chengqian Cai, Chun Bi, Hangrui Du, Yiming Qin, Xuejian Peng, Anyang Huang, Jiameng Li, Bowen Shan, Yifan Zeng, Jinzhe Zhang, Yuzhi Liu, Siyuan Li, Yifan Chang, Junhan Wang, Xinyan Zhou, Shuo Liu, Jianchuan Luo, Xiaoshan Wang, Zhenyu Jiang, Wanrun Wu, Jing Yang, Yudi Yang, Jiyuan Yang, Manyi Gong, Fu-Qiang Zhang, Linshuang Shi, Mengchao Dai, Fu-Zhi York, Darrin M. Liu, Shi Zhu, Tong Zhong, Zhicheng Lv, Jian Cheng, Jun Jia, Weile Chen, Mohan Ke, Guolin Weinan, E. Zhang, Linfeng Wang, Han AI for Science Institute Beijing100080 China DP Technology Beijing100080 China Academy for Advanced Interdisciplinary Studies Peking University Beijing100871 China State Key Lab of Processors Institute of Computing Technology Chinese Academy of Sciences Beijing100871 China University of Chinese Academy of Sciences Beijing100871 China HEDPS CAPT College of Engineering Peking University Beijing100871 China Ningbo Institute of Materials Technology and Engineering Chinese Academy of Sciences Ningbo315201 China CAS Key Laboratory of Magnetic Materials and Devices Zhejiang Province Key Laboratory of Magnetic Materials and Application Technology Chinese Academy of Sciences Ningbo315201 China School of Electronics Engineering and Computer Science Peking University Beijing100871 China Shanghai Engineering Research Center of Molecular Therapeutics & New Drug Development School of Chemistry and Molecular Engineering East China Normal University Shanghai200062 China Laboratory for Biomolecular Simulation Research Institute for Quantitative Biomedicine Department of Chemistry and Chemical Biology Rutgers University PiscatawayNJ08854 United States Department of Chemistry Princeton University PrincetonNJ08540 United States College of Chemistry and Molecular Engineering Peking University Beijing100871 China Yuanpei College Peking University Beijing100871 China School of Electrical Engineering and Electronic Information Xihua University Chengdu610039 China State Key Laboratory of Superhard Materials College of Physics Jilin University Changchun130012 China Key Laboratory of Material Simulation Methods & Software of Ministry of Education College of Physics Jilin University Changchun130012 China International Center of Future Science Jilin University Changchun130012 China Key Laboratory for Quantum Materials of Zhejiang Province Department of Physics School of Science Westlake University Zhejiang Hangzhou310030 China Atomistic Simulations Italia

The rapid advancements in artificial intelligence (AI) are catalyzing transformative changes in atomic modeling, simulation, and design. AI-driven potential energy models have demonstrated the capability to conduct large-scale, long-duration simulations with the accuracy of ab initio electronic structure methods. However, the model generation process remains a bottleneck for large-scale applications. We propose a shift towards a model-centric ecosystem, wherein a large atomic model (LAM), pre-trained across multiple disciplines, can be efficiently fine-tuned and distilled for various downstream tasks, thereby establishing a new framework for molecular modeling. In this study, we introduce the DPA-2 architecture as a prototype for LAMs. Pre-trained on a diverse array of chemical and materials systems using a multi-task approach, DPA-2 demonstrates superior generalization capabilities across multiple downstream tasks compared to the traditional single-task pre-training and fine-tuning methodologies. Our approach sets the stage for the development and broad application of LAMs in molecular and materials simulation research. Copyright © 2023, The Authors. All rights reserved.

关键词： Multi-task learning

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Historical tree phenology data reveal the seasonal rhythms of the Congo Basin rainforest

Plant-Environment Interactions

引用

Plant-Environment Interactions 2024年第2期5卷 e10136页

作者： Kearsley, Elizabeth Verbeeck, Hans Stoffelen, Piet Janssens, Steven B. Yakusu, Emmanuel Kasongo Kosmala, Margaret De Mil, Tom Bauters, Marijn Kitima, Elasi Ramanzani Ndiapo, José Mbifo Chuda, Adelard Lonema Richardson, Andrew D. Wingate, Lisa Ilondea, Bhély Angoboy Beeckman, Hans van den Bulcke, Jan Boeckx, Pascal Hufkens, Koen Computational and Applied Vegetation Ecology Lab Department of Environment Faculty of Bioscience Engineering Ghent University Gent Belgium BlueGreen Labs Melsele Belgium Meise Botanic Garden Meise Belgium Department of Biology Leuven Plant Institute KULeuven Leuven Belgium UGent-Woodlab (Laboratory of Wood Technology) Department of Environment Faculty of Bioscience Engineering Ghent University Gent Belgium Service of Wood Biology Royal Museum for Central Africa Tervuren Belgium Faculté de gestion des ressources naturelles renouvelables Université de Kisangani Kisangani Democratic Republic Congo Department of Organismic and Evolutionary Biology Harvard University Cambridge MA United States CIBO Technologies Cambridge MA United States Forest is Life TERRA Teaching and Research Centre Gembloux Agro Bio-Tech University of Liège Gembloux Belgium Isotope Bioscience Laboratory - ISOFYS Department of Green Chemistry and Technology Ghent University Gent Belgium Research Group of Plants and Ecosystems (PLECO) Department of Biology University of Antwerp Wilrijk Belgium Institut National pour l'Etude et la Recherche Agronomiques-INERA Yangambi Democratic Republic Congo Center for Ecosystem Science and Society Northern Arizona University Flagstaff AZ United States School of Informatics Computing and Cyber Systems Northern Arizona University Flagstaff AZ United States INRAE UMR ISPA Villenave d'Ornon France Institut National pour l'Étude et la Recherche Agronomiques Kinshasa Democratic Republic Congo

Tropical forest phenology directly affects regional carbon cycles, but the relation between species-specific and whole-canopy phenology remains largely uncharacterized. We present a unique analysis of historical tropical tree phenology collected in the central Congo Basin, before large-scale impacts of human-induced climate change. Ground-based long-term (1937–1956) phenological observations of 140 tropical tree species are recovered, species-specific phenological patterns analyzed and related to historical meteorological records, and scaled to characterize stand-level canopy dynamics. High phenological variability within and across species and in climate–phenology relationships is observed. The onset of leaf phenophases in deciduous species was triggered by drought and light availability for a subset of species and showed a species-specific decoupling in time along a bi-modal seasonality. The majority of the species remain evergreen, although central African forests experience relatively low rainfall. Annually a maximum of 1.5% of the canopy is in leaf senescence or leaf turnover, with overall phenological variability dominated by a few deciduous species, while substantial variability is attributed to asynchronous events of large and/or abundant trees. Our results underscore the importance of accounting for constituent signals in canopy-wide scaling and the interpretation of remotely sensed phenology signals. © 2024 The Authors. Plant-Environment Interactions published by New Phytologist Foundation and John Wiley & Sons Ltd.

关键词： leaf senescence leaf turnover phenology scaling tropical forest

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JARVIS-Leaderboard: A Large Scale Benchmark of Materials Design Methods

arXiv

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arXiv 2023年

作者： Choudhary, Kamal Wines, Daniel Garrity, Kevin F. Williams, Maureen Tavazza, Francesca Li, Kangming Hattrick-Simpers, Jason Gupta, Vishu Romero, Aldo H. Krogel, Jaron T. Saritas, Kayahan Fuhr, Addis Ganesh, Panchapakesan Kent, Paul R.C. Yan, Keqiang Lin, Yuchao Ji, Shuiwang Blaiszik, Ben Reiser, Patrick Friederich, Pascal Agrawal, Ankit Tiwary, Pratyush Beyerle, Eric Minch, Peter Rhone, Trevor David Takeuchi, Ichiro Wexler, Robert B. Mannodi-Kanakkithodi, Arun Ertekin, Elif Mishra, Avanish Mathew, Nithin Wood, Mitchell Rohskopf, Andrew Dale Wang, Shih-Han Achenie, Luke E.K. Xin, Hongliang Biacchi, Adam J. Material Measurement Laboratory National Institute of Standards and Technology MD20899 United States Department of Materials Science and Engineering University of Toronto 27 King’s College Cir TorontoON Canada Department of Electrical and Computer Engineering Northwestern University EvanstonIL60208 United States Lewis-Sigler Institute for Integrative Genomics Princeton University PrincetonNJ08544 United States Ludwig Institute for Cancer Research Princeton University PrincetonNJ08544 United States Department of Physics and Astronomy West Virginia University MorgantownWV26506 United States Materials Science and Technology Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Center for Nanophase Materials Science Oak Ridge National Laboratory Oak RidgeTN37831 United States Computational Sciences and Engineering Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Department of Computer Science and Engineering Texas A&M University College StationTX77843 United States Globus University of Chicago IL60637 United States Data Science Learning Division National Lab ArgonneIL60439 United States Institute of Nanotechnology Karlsruhe Institute of Technology Kaiserstraße 12 Karlsruhe76131 Germany Institute of Theoretical Informatics Karlsruhe Institute of Technology Kaiserstraße 12 Karlsruhe76131 Germany Department of Chemistry and Biochemistry Institute for Physical Science and Technology University of Maryland College ParkMD20742 United States Department of Physics Applied Physics and Astronomy Rensselaer Polytechnic Institute TroyNY12180 United States Department of Materials Science and Engineering University of Maryland College ParkMD20742 United States Department of Chemistry Institute of Materials Science and Engineering Washington University in St. Louis St. LouisMO63130 United States School of Materials Engineering Purdue University West LafayetteIN47907 United States Department of Mechan

Lack of rigorous reproducibility and validation are significant hurdles for scientific development across many fields. Materials science, in particular, encompasses a variety of experimental and theoretical approaches that require careful benchmarking. Leaderboard efforts have been developed previously to mitigate these issues. However, a comprehensive comparison and benchmarking on an integrated platform with multiple data modalities with perfect and defect materials data is still lacking. This work introduces JARVIS-Leaderboard, an open-source and community-driven platform that facilitates benchmarking and enhances reproducibility. The platform allows users to set up benchmarks with custom tasks and enables contributions in the form of dataset, code, and meta-data submissions. We cover the following materials design categories: Artificial Intelligence (AI), Electronic Structure (ES), Force-fields (FF), Quantum Computation (QC) and Experiments (EXP). For AI, we cover several types of input data, including atomic structures, atomistic images, spectra, and text. For ES, we consider multiple ES approaches, software packages, pseudopotentials, materials, and properties, comparing results to experiment. For FF, we compare multiple approaches for material property predictions. For QC, we benchmark Hamiltonian simulations using various quantum algorithms and circuits. Finally, for experiments, we use the inter-laboratory approach to establish benchmarks. There are 1281 contributions to 274 benchmarks using 152 methods with more than 8 million data-points, and the leaderboard is continuously expanding. The JARVIS-Leaderboard is available at the website: https://***/jarvis_leaderboard/ © 2023, CC BY.

关键词： Electronic structure

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A causal lens for peeking into black box predictive models: Predictive model interpretation via causal attribution

arXiv

引用

arXiv 2020年

作者： Khademi, Aria Honavar, Vasant Artificial Intelligence Research Laboratory College of Information Sciences and Technology United States Department of Computer Science and Engineering Institute of Computational and Data Sciences Pennsylvania State University United States

With the increasing adoption of predictive models trained using machine learning across a wide range of high-stakes applications, e.g., health care, security, criminal justice, finance, and education, there is a growing need for effective techniques for explaining such models and their predictions. We aim to address this problem in settings where the predictive model is a black box;That is, we can only observe the response of the model to various inputs, but have no knowledge about the internal structure of the predictive model, its parameters, the objective function, and the algorithm used to optimize the model. We reduce the problem of interpreting a black box predictive model to that of estimating the causal effects of each of the model inputs on the model output, from observations of the model inputs and the corresponding outputs. We estimate the causal effects of model inputs on model output using variants of the Rubin Neyman potential outcomes framework for estimating causal effects from observational data. We show how the resulting causal attribution of responsibility for model output to the different model inputs can be used to interpret the predictive model and to explain its predictions. We present results of experiments that demonstrate the effectiveness of our approach to the interpretation of black box predictive models via causal attribution in the case of deep neural network models trained on one synthetic data set (where the input variables that impact the output variable are known by design) and two real-world data sets: Handwritten digit classification, and Parkinson’s disease severity prediction. Because our approach does not require knowledge about the predictive model algorithm and is free of assumptions regarding the black box predictive model except that its input-output responses be observable, it can be applied, in principle, to any black box predictive model. Copyright © 2020, The Authors. All rights reserved.

关键词： Deep neural networks

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Tensor Decomposition Based Relaxed Linear Regression for Hyperspectral Image Classification

引用

IEEE Transactions on Geoscience and Remote Sensing 2025年 63卷

作者： Deng, Yang-Jun Zhang, Lv-Wei Ren, Longfei Zhu, Xinghui Li, Heng-Chao Du, Qian Hunan Agricultural University College of Information and Intelligence Changsha410128 China Chinese Academy of Sciences Key Laboratory of Computational Optical Imaging Technology Aerospace Information Research Institute Beijing100094 China Southwest Jiaotong University School of Information Science and Technology Chengdu611756 China Mississippi State University Department of Electrical and Computer Engineering StarkvilleMS39762 United States

Linear regression and its variants have achieved considerable success in image classification. However, those methods still encounter two challenges when dealing with hyperspectral image (HSI) classification. On the one hand, the existing ones focus on mining the relationship between the label space and original data space during the classifier training, which is generally sensitive to noise corruptions. On the other hand, transforming the training samples into a strict binary label matrix makes the generalization ability of the classifier limited. To address these challenges, this paper constructs a novel integrative model called tensor decomposition-based relaxed linear regression (TDRLR) for HSI classification. Firstly, the model adopts tensor canonical polyadic (CP) decomposition to learn two dictionaries from spatial and spectral directions respectively, which can help to generate a double dictionary representation for HSI data. Then, the linear regression classifier is integrated to learn a transformation that reveals the mapping relation between the double dictionary representation and label space rather than the original data for enhancing robustness. Meanwhile, a more flexible way, label relaxation, is employed to enlarge the margins between different classes. More importantly, the learned double dictionary representation and classifier can be fine-tuned in tandem to enhance performance through the designed alternate iterative jointly learning algorithm. Experiments conducted on four real-world HSI datasets demonstrate that the proposed method achieves significant improvements in classification performance with a small size training set, when compared with state-of-the-art HSI classification methods. © 1980-2012 IEEE.

关键词： Linear transformations

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Data-driven surrogate modeling of seismic uplift capacity for strip anchors in frictional–cohesive soils with surcharge using isogeometric analysis

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Ocean engineering 2025年 336卷

作者： Toan Nguyen-Minh Tram Bui-Ngoc Jim Shiau Tan Nguyen Trung Nguyen-Thoi Faculty of Civil Engineering Ton Duc Thang University Ho Chi Minh City Vietnam Laboratory for Computational Mechanics Institute for Computational Science and Artificial Intelligence Van Lang University Ho Chi Minh City Viet Nam Faculty of Mechanical - Electrical and Computer Engineering School of Technology Van Lang University Ho Chi Minh City Viet Nam School of Engineering University of Southern Queensland Toowoomba 4350 QLD Australia Smart Computing in Civil Engineering Research Group Faculty of Civil Engineering Ton Duc Thang University Ho Chi Minh City Vietnam Laboratory for Applied and Industrial Mathematics Institute for Computational Science and Artificial Intelligence Van Lang University Ho Chi Minh City Viet Nam

The behavior of strip anchors under uplift loads in complex conditions, such as frictional–cohesive soils with surcharge and seismic loading, poses significant engineering challenges. This study presents a data-driven surrogate modeling framework to predict seismic uplift capacity, combining high-fidelity simulations with machine learning. A large dataset is generated using Upper Bound Limit Analysis (UBLA) implemented via Isogeometric Analysis (IGA) and Second-Order Cone Programming (SOCP). Key input variables i.e., cohesion factor ( c '/ γB ), internal friction angle ( φ ′), embedment ratio ( H / B ), seismic coefficients ( K h , K v ), and surcharge factor ( q / γB ), are evaluated to explore their impact on uplift capacity ( P u / γB ). Sensitivity analysis highlights embedment ratio and internal friction angle as major factors enhancing uplift, while seismic coefficients reduce it, especially in low-cohesion soils. The Levenberg-Marquardt Neural Network (LMNN) outperforms other machine learning models, achieving a mean squared error (MSE) of 0.006 ± 0.000 on training and 0.005 ± 0.001 on testing data, with an R 2 of 1.000. This integration of IGA-UB with LMNN provides reliable upper-bound estimates for uplift capacity, particularly in high-cohesion soils. The development of a closed-form solution ensures practical relevance, making this hybrid approach a powerful tool for engineering design under varied loading scenarios.

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Quantum Metamaterial for Broadband Detection of Single Microwave Photons

引用

Physical Review Applied 2021年第3期15卷 034074-034074页

作者： Arne L. Grimsmo Baptiste Royer John Mark Kreikebaum Yufeng Ye Kevin O’Brien Irfan Siddiqi Alexandre Blais Institut quantique and Départment de Physique Université de Sherbrooke Sherbrooke Québec J1K 2R1 Canada Centre for Engineered Quantum Systems School of Physics The University of Sydney Sydney Australia Department of Physics Yale University New Haven Connecticut 06520 USA Materials Science Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA Quantum Nanoelectronics Laboratory Department of Physics University of California Berkeley California 94720 USA Research Laboratory of Electronics Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA Computational Research Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA Canadian Institute for Advanced Research Toronto Canada

Detecting traveling photons is an essential primitive for many quantum-information processing tasks. We introduce a single-photon detector design operating in the microwave domain, based on a weakly nonlinear metamaterial where the nonlinearity is provided by a large number of Josephson junctions. The combination of weak nonlinearity and large spatial extent circumvents well-known obstacles limiting approaches based on a localized Kerr medium. Using numerical many-body simulations we show that the single-photon detection fidelity increases with the length of the metamaterial to approach one at experimentally realistic lengths. A remarkable feature of the detector is that the metamaterial approach allows for a large detection bandwidth. The detector is nondestructive and the photon population wavepacket is minimally disturbed by the detection. This detector design offers promising possibilities for quantum information processing, quantum optics and metrology in the microwave frequency domain.

关键词： Josephson effect Quantum information architectures & platforms Quantum information with solid state qubits Quantum sensing Metamaterials Optical sources & detectors Superconducting devices Microwave techniques

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Electron charge qubits with 0.1 millisecond coherence time

arXiv

引用

arXiv 2022年

作者： Zhou, Xianjing Li, Xinhao Chen, Qianfan Koolstra, Gerwin Yang, Ge Dizdar, Brennan Huang, Yizhong Wang, Christopher S. Han, Xu Zhang, Xufeng Schuster, David I. Jin, Dafei Center for Nanoscale Materials Argonne National Laboratory LemontIL60439 United States Pritzker School of Molecular Engineering University of Chicago ChicagoIL60637 United States Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States The NSF AI Institute for Artificial Intelligence and Fundamental Interactions United States Computer Science and Artificial Intelligence Laboratory Massachusetts Institute of Technology CambridgeMA02139 United States James Franck Institute Department of Physics University of Chicago ChicagoIL60637 United States Department of Electrical and Computer Engineering Northeastern University BostonMA02115 United States Department of Applied Physics Stanford University StanfordCA94305 United States Department of Physics and Astronomy University of Notre Dame Notre DameIN46556 United States

Electron charge qubits are compelling candidates for solid-state quantum computing because of their inherent simplicity in qubit design, fabrication, control, and readout. However, all existing electron charge qubits, built upon conventional semiconductors and superconductors, suffer from severe charge noise that limits the coherence time to the order of 1 microsecond. Here, we report our experimental realization of ultralongcoherence electron charge qubits, based upon isolated single electrons trapped on an ultraclean solid neon surface in vacuum. Quantum information is encoded in the motional states of an electron that is strongly coupled with microwave photons in an on-chip superconducting resonator. The measured relaxation time T1 and coherence time T2 are both on the order of 0.1 milliseconds. The single-shot readout fidelity without using a quantum-limited amplifier is 98.1%. The average single-qubit gate fidelity using Clifford-based randomized benchmarking is 99.97%. Simultaneous strong coupling of two qubits with the same resonator is demonstrated, as a first step toward two-qubit entangling gates for universal quantum computing. These results manifest that the electron-on-solid-neon (eNe) charge qubits outperform all existing charge qubits to date and rival state-of-the-art superconducting transmon qubits, offering an appealing platform for quantum computing. Copyright © 2022, The Authors. All rights reserved.

关键词： Superconducting resonators

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From hexagonal to rocksalt structure: A computational study of gallium selenide under hydrostatic pressure

引用

Physical Review B 2023年第20期108卷 205150-205150页

作者： Vo Khuong Dien Nguyen Thanh Tien Nguyen Duy Khanh Nguyen Thi Ngoc Han Ming-Fa Lin Department of Electrophysics National Yang Ming Chiao Tung University Hsinchu 300 Taiwan College of Natural Sciences Can Tho University 3-2 Road Can Tho City 94000 Vietnam Laboratory for Computational Physics Institute for Computational Science and Artificial Intelligence Van Lang University Ho Chi Minh City 700000 Vietnam Faculty of Mechanical - Electrical and Computer Engineering School of Technology Van Lang University Ho Chi Minh City 700000 Vietnam Fschool Can Tho FPT University 600 Nguyen Van Cu Street Can Tho City 900000 Vietnam Department of Physics National Cheng Kung University 701 Tainan Taiwan Hierarchical Green-Energy Material (Hi-GEM) Research Center National Cheng Kung University 701 Tainan Taiwan

The understanding of pressure-dependent fundamental properties of materials is very essential, not only for basic scientific knowledge but also for advanced technological applications. Experimental observations have fully revealed the hexagonal-to-rocksalt phase transition in the GaSe system under high pressure. In this article we systematically investigate the pressure-induced structural phase transition and related phonon, electronic, and optical properties of hexagonal ɛ−GaSe through a complete first-principles theoretical framework developed by the density-functional-theory calculations. The study focuses on geometric optimization, electronic band structures, electron localization functions, phonon spectra, dielectric properties, and optical spectra of the GaSe system under hydrostatic pressure. This work also includes an analysis of the phase transformation mechanism using the solid-state nudged elastic band method. Our research sheds light on the physics of structural phase transitions in layered materials and offers potential for the development of pressure-manipulated electronics and optoelectronics.

关键词： Charge Chemical bonding Critical phenomena Dielectric properties Electrical properties Excitons First-principles calculations Lattice dynamics Mechanical deformation Photonics Plasmonics Pressure effects Specific phase transitions Superconductors

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E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials

arXiv

引用

arXiv 2021年

作者： Batzner, Simon Musaelian, Albert Sun, Lixin Geiger, Mario Mailoa, Jonathan P. Kornbluth, Mordechai Molinari, Nicola Smidt, Tess E. Kozinsky, Boris John A. Paulson School of Engineering and Applied Sciences Harvard University CambridgeMA02138 United States École Polytechnique Fédérale de Lausanne Lausanne1015 Switzerland Robert Bosch Research and Technology Center CambridgeMA02139 United States Computational Research Division Center for Advanced Mathematics for Energy Research Applications Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science CambridgeMA02142 United States

This work presents Neural Equivariant Interatomic Potentials (NequIP), an E(3)-equivariant neural network approach for learning interatomic potentials from ab-initio calculations for molecular dynamics simulations. While most contemporary symmetry-aware models use invariant convolutions and only act on scalars, NequIP employs E(3)-equivariant convolutions for interactions of geometric tensors, resulting in a more information-rich and faithful representation of atomic environments. The method achieves state-of-the-art accuracy on a challenging and diverse set of molecules and materials while exhibiting remarkable data efficiency. NequIP outperforms existing models with up to three orders of magnitude fewer training data, challenging the widely held belief that deep neural networks require massive training sets. The high data efficiency of the method allows for the construction of accurate potentials using high-order quantum chemical level of theory as reference and enables high-fidelity molecular dynamics simulations over long time scales. Copyright © 2021, The Authors. All rights reserved.

关键词： Convolution

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