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arXiv 2020年

作者： Zhao, Ting Liu, Hongwei Liu, Zexian School of Mathematics and Statistics Xidian University Xi’an710126 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering computing AMSS Chinese Academy of Sciences Beijing100190 China

In this paper, two new subspace minimization conjugate gradient methods based on p−regularization models are proposed, where a special scaled norm in p−regularization model is analyzed. Different choices for special scaled norm lead to different solutions to the p−regularized subproblem. Based on the analyses of the solutions in a two-dimensional subspace, we derive new directions satisfying the sufficient descent condition. With a modified nonmonotone line search, we establish the global convergence of the proposed methods under mild assumptions. R−linear convergence of the proposed methods are also analyzed. Numerical results show that, for the CUTEr library, the proposed methods are superior to four conjugate gradient methods, which were proposed by Hager and Zhang (SIAM J Optim 16(1):170-192, 2005), Dai and Kou (SIAM J Optim 23(1):296-320, 2013), Liu and Liu (J Optim Theory Appl 180(3):879-906, 2019) and Li et al. (Comput Appl Math 38(1): 2019), respectively. Copyright © 2020, The Authors. All rights reserved.

关键词： Conjugate gradient method

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An improved gradient method with approximately optimal stepsize based on conic model for unconstrained optimization

arXiv

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arXiv 2019年

作者： Liu, Zexian Liu, Hongwei State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering computing AMSS Chinese Academy of Sciences Beijing1000190 China School of Mathematics and Statistics Xidian University Xi’an710126 China

A new type of stepsize, which was recently introduced by Liu and Liu (Optimization, 67(3), 427-440, 2018), is called approximately optimal stepsize and is quit efficient for gradient method. Interestingly, all gradient methods can be regarded as gradient methods with approximately optimal stepsizes. In this paper, based on the work (Numer. Algorithms 78(1), 21-39, 2018), we present an improved gradient method with approximately optimal stepsize based on conic model for unconstrained optimization. If the objective function f is not close to a quadratic on the line segment between the current and latest iterates, we construct a conic model to generate approximately optimal stepsize for gradient method if the conic model can be used;otherwise, we construct some quadratic models to generate approximately optimal stepsizes for gradient method. The convergence of the proposed method is analyzed under suitable conditions. Numerical comparisons with some well-known conjugate gradient software packages such as CG_DESCENT (SIAM J. Optim. 16(1), 170-192, 2005) and CGOPT (SIAM J. Optim. 23(1), 296-320, 2013) indicate the proposed method is very promising. Copyright © 2019, The Authors. All rights reserved.

关键词： Gradient methods

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A riemannian exponential augmented lagrangian method for computing the projection robust Wasserstein distance 23

A riemannian exponential augmented lagrangian method for com...

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Proceedings of the 37th International Conference on Neural Information Processing Systems

作者： Bo Jiang Ya-Feng Liu Ministry of Education Key Laboratory of NSLSCS School of Mathematical Sciences Nanjing Normal University Nanjing China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

Projection robust Wasserstein (PRW) distance is recently proposed to efficiently mitigate the curse of dimensionality in the classical Wasserstein distance. In this paper, by equivalently reformulating the computation of the PRW distance as an optimization problem over the Cartesian product of the Stiefel manifold and the Euclidean space with additional nonlinear inequality constraints, we propose a Riemannian exponential augmented Lagrangian method (REALM) for solving this problem. Compared with the existing Riemannian exponential penalty-based approaches, REALM can potentially avoid too small penalty parameters and exhibit more stable numerical performance. To solve the subproblems in REALM efficiently, we design an inexact Riemannian Barzilai-Borwein method with Sinkhorn iteration (iRBBS), which selects the stepsizes adaptively rather than tuning the step-sizes in efforts as done in the existing methods. We show that iRBBS can return an ε-stationary point of the original PRW distance problem within O(ε-3) iterations, which matches the best known iteration complexity result. Extensive numerical results demonstrate that our proposed methods outperform the state-of-the-art solvers for computing the PRW distance.

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TRIANGULAR C^m INTERPOLATION BY RATIONAL FUNCTIONS

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Analysis in Theory and Applications 2000年第4期16卷 33-54页

作者： Xu Guoliang Chu Chuan Xue Weimin State Key Laboratory of Scientific and Engineering Computing ICMSEC Chinese Academy of SciencesBeijing 100080PRC Department of Mathematics Hong Kong Baptist UniversityKowloonHong Kong

Two general local Cm triangular interpolation schemes by rational functions from Cm data are proposed for any nonnegative integer m. The schemes can have either 2m+1 order algebraic precision if the required data are given on vertices and edges, or m+E[m/2]+1 or m+1 order algebraic precision if the data are given only at vertices. The orders of the interpolation error are estimated. Examples that show the correctness and effectiveness of the scheme are presented.

关键词： oscillatory integral operator multiplier singularity

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A RIEMANNIAN EXPONENTIAL AUGMENTED LAGRANGIAN METHOD FOR computing THE PROJECTION ROBUST WASSERSTEIN DISTANCE

arXiv

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arXiv 2022年

作者： Jiang, Bo Liu, Ya-Feng Key Laboratory for NSLSCS of Jiangsu Province School of Mathematical Sciences Nanjing Normal University Nanjing China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

Projecting the distance measures onto a low-dimensional space is an efficient way of mitigating the curse of dimensionality in the classical Wasserstein distance using optimal transport. The obtained maximized distance is referred to as projection robust Wasserstein (PRW) distance. In this paper, we equivalently reformulate the computation of the PRW distance as an optimization problem over the Cartesian product of the Stiefel manifold and the Euclidean space with additional nonlinear inequality constraints. We propose a Riemannian exponential augmented Lagrangian method (ReALM) with a global convergence guarantee to solve this problem. Compared with the existing approaches, ReALM can potentially avoid too small penalty parameters. Moreover, we propose a framework of inexact Riemannian gradient descent methods to solve the subproblems in ReALM efficiently. In particular, by using the special structure of the subproblem, we give a practical algorithm named as the inexact Riemannian Barzilai-Borwein method with Sinkhorn iteration (iRBBS). The remarkable features of iRBBS lie in that it performs a flexible number of Sinkhorn iterations to compute an inexact gradient with respect to the projection matrix of the problem and adopts the Barzilai-Borwein stepsize based on the inexact gradient information to improve the performance. We show that iRBBS can return an ǫ-stationary point of the original PRW distance problem within O(ǫ−3) iterations. Extensive numerical results on synthetic and real datasets demonstrate that our proposed ReALM as well as iRBBS outperform the state-of-the-art solvers for computing the PRW *** Codes 65K10, 90C26, 90C47 Copyright © 2022, The Authors. All rights reserved.

关键词： Constrained optimization

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On the convergence of stochastic gradient descent with bandwidth-based step size

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2023年第1期24卷 1990-2038页

作者： Xiaoyu Wang Ya-xiang Yuan Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China and University of Chinese Academy of Sciences Beijing China State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

We first propose a general step-size framework for the stochastic gradient descent(SGD) method: bandwidth-based step sizes that are allowed to vary within a banded region. The framework provides efficient and flexible step size selection in optimization, including cyclical and non-monotonic step sizes (e.g., triangular policy and cosine with restart), for which theoretical guarantees are rare. We provide state-of-the-art convergence guarantees for SGD under mild conditions and allow a large constant step size at the beginning of training. Moreover, we investigate the error bounds of SGD under the bandwidth step size where the boundary functions are in the same order and different orders, respectively. Finally, we propose a 1/t up-down policy and design novel non-monotonic step sizes. Numerical experiments demonstrate these bandwidth-based step sizes' efficiency and significant potential in training regularized logistic regression and several large-scale neural network tasks.

关键词： stochastic gradient descent bandwidth-based step size non-asymptotic convergence non-monotonic step size machine learning

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Car-Parinello molecular dynamics simulations of thionitroxide and S-nitrosothiol in the gas phase, methanol, and water-A theoretical study of S-nitrosylation

Car-Parinello molecular dynamics simulations of thionitroxid...

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作者： Liang, Juan Cheng, Shang Li Hou, Jun Wei Xu, Zhen Hao Zhao, Yi-Lei State Key Laboratory of Microbial Metabolism School of Life Sciences and Biotechnology Shanghai Jiao Tong University Shanghai 200240 China Shanghai Center for Systems Biomedicine Shanghai Jiao Tong University Shanghai 200240 China MOE Laboratory of Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai 200240 China

A dilemma about whether thionitroxide radical (RSNHO) or S-nitrosothiol (RSNO) is observed in protein S-nitrosylation has arisen recently. To illustrate the effect of chemical environment on these structures, this paper presents quantum mechanical molecular dynamics of thionitroxide, and cis-and trans-S-nitrosothiols in the gas phase, methanol, and water. By using Car-Parrinello molecular dynamics (CPMD), we have observed that there is free rotation about the S-N bond at 300 K in thionitroxide, but no such rotation is observed for S-nitrosothiol. The C-S-N-O torsion angle distribution in thionitroxide is significantly dependent upon the surrounding environment, leading to either gauche-, cis-, or trans-conformation. In the case of S-nitrosothiol the C-S-N-O plane is twisted slightly by 5°-15° in the cis-isomer, while the periplanar structure is well-retained in the trans-isomer. The calculated results are in agreement with the X-ray crystallographic data of small molecular RSNO species. Interestingly, for both compounds, the CPMD simulations show that solvation can cause a decrease in the S-N bond length. Moreover, the oxygen atom of thionitroxide is found to be a good hydrogen-bond acceptor, forming an oxyanion-hole-like hydrogen bonding network. © Science China Press and Springer-Verlag Berlin Heidelberg 2012.

关键词： Molecular dynamics

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A biosensing system using a multiparameter nonlinear dynamic analysis of cardiomyocyte beating for drug-induced arrhythmia recognition

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Microsystems & Nanoengineering 2022年第3期8卷 277-290页

作者： Hao Wang Yue Wu Quchao Zou Wenjian Yang Zhongyuan Xu Hao Dong Zhjing Zhu Depeng Wang Tanxing Wang Ning Hu Diming Zhang State Key Laboratory of Optoelectronic Materials and Technologies Guangdong Province Key Laboratory of Display Material and TechnologySchool of Electronics and Information TechnologySun Yat-sen UniversityGuangzhou 510006China Research Center for Itelligent Sensing Systems Zhejiang LabHangzhou 311121China ZJU-Hangzhou Global Scientific and Technological Innovation Center Department of ChemistryThe Second Affiliated Hospital Zhejiang University School of MedicineDepartment of Clinical Medical EngineeringZhejiang UniversityHangzhou 310058China Key Laboratory of Novel Target and Drug Study for Neural Repair of Zhejang Province School of MedicineSchool of Computer&Computing ScienceZhejiang University City CollegeHangzhou 310015China School of Brain Science and Brain Medicine Zhejiang UniversityHangzhou 310058China College of Energy and Power Engineering Nanjing University of Aeronautics and AstronauticsNanjing 210016China E-LinkCare Meditech Co LtdHangzhou 310011China State Key Laboratory of Transducer Technology Chinese Academy of SciencesShanghai 200050China

Cardiovascular disease is the number one cause of death in ***,cardiotoxicity is one of the most important adverse effects assessed by arrhythmia recognition in drug ***,cell-based techniques developed for arhythmia recognition primarily employ linear methods such as time-domain analysis that detect and compare individual waveforms and thus fall short in some applications that require automated and efficient arrhythmia recognition from large *** carried out the frst report to develop a biosensing system that integrated impedance measurement and multiparameter nonlinear dynamic algorithm(MNDA)analysis for druginduced arrhythmia recognition and *** biosensing system cultured cardiomyocytes as physiologically relevant models,used interdigitated electrodes to detect the mechanical beating of the cardiomyocytes,and employed MNDA analysis to recognize drug-induced arrhythmia from the cardiomyocyte beating *** best performing MNDA parameter,approximate entropy,enabled the system to recognize the appearance of sertindoleand norepinephrine-induced arrhythmia in the *** MNDA reconstruction in phase space enabled the system to classify the different arrhythmias and quantify the severity of *** new biosensing system utilizing MNDA provides a promising and alternative method for drug-induced arrhythmia recognition and classification in cardiological and pharmaceutical applications.

关键词： arrhythmia cardio analysis

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Applied Mathematics and Computation: Preface

引用

Applied Mathematics and Computation (New York) 2006年第2 SPEC. ISS.期172卷 679-681页

作者： Bai, Zhong-Zhi Ching, Wai-Ki Ng, Michael K. State Key Laboratory of Scientific/Engineering Computing Institute of Comput. Math. and Scientific/Engrg. Computing Academy of Mathematics and Systems Science Beijing China Department of Mathematics University of Hong Kong Hong Kong Hong Kong

No abstract available

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Moiré cavity quantum electrodynamics

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Science Advances 2025年第21期11卷 eadv8115页

作者： Yu-Tong Wang Qi-Hang Ye Jun-Yong Yan Yufei Qiao Yu-Xin Liu Yong-Zheng Ye Chen Chen Xiao-Tian Cheng Chen-Hui Li Zi-Jian Zhang Cheng-Nian Huang Yun Meng Kai Zou Wen-Kang Zhan Chao Zhao Xiaolong Hu Clarence Augustine T. H. Tee Wei E. I. Sha Zhixiang Huang Huiyun Liu Chao-Yuan Jin Lei Ying Feng Liu State Key Laboratory of Extreme Photonics and Instrumentation College of Information Science and Electronic Engineering Zhejiang University Hangzhou 310027 China. School of Physics Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control Zhejiang University Hangzhou 310027 China. International Joint Innovation Center Zhejiang University Haining 314400 China. School of Precision Instrument and Optoelectronic Engineering Tianjin University Tianjin 300072 China. Key Laboratory of Optoelectronic Information Science and Technology Ministry of Education Tianjin 300072 China. Laboratory of Solid State Optoelectronics Information Technology Institute of Semiconductors Chinese Academy of Sciences Beijing 100083 China. College of Materials Science and Opto-Electronic Technology University of Chinese Academy of Science Beijing 101804 China. College of Physics and Electrical Information Engineering Zhejiang Normal University Hangzhou 310058 China. Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education Anhui University Hefei 230039 China. Department of Electronic and Electrical Engineering University College London London WC1E 7JE UK. ZJU-Hangzhou Global Scientific and Technological Innovation Center Zhejiang University Hangzhou Zhejiang 311200 China.

Quantum emitters are a key component in photonic quantum technologies. Enhancing single-photon emission by engineering their photonic environment is essential for improving overall efficiency in quantum information processing. However, this enhancement is often limited by the need for ultraprecise emitter placement within conventional photonic cavities. Inspired by the fascinating physics of moiré pattern, we propose a multilayer moiré photonic crystal with a robust isolated flatband. Theoretical analysis reveals that, with nearly infinite photonic density of states, the moiré cavity simultaneously has a high Purcell factor and large tolerance over the emitter’s position, breaking the constraints of conventional cavities. We then experimentally demonstrate various cavity quantum electrodynamic phenomena with a quantum dot in moiré cavity. A large tuning range (up to 40-fold) of quantum dot’s radiative lifetime is achieved through strong Purcell enhancement and inhibition effects. Our findings open the door for moiré flatband cavity–enhanced quantum light sources and quantum nodes for the quantum internet.

关键词： Quantum electronics

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