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Convergence rate for eigenvalues of the elastic Neumann–Poincaré operator on smooth and real analytic boundaries in two dimensions

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arXiv 2019年

作者： Ando, Kazunori Kang, Hyeonbae Miyanishi, Yoshihisa Department of Electrical and Electronic Engineering and Computer Science Ehime University Ehime790-8577 Japan Department of Mathematics Institute of Applied Mathematics Inha University Incheon22212 Korea Republic of Center for Mathematical Modeling and Data Science Osaka University Osaka560-8531 Japan

MSC Codes 47A75 (Primary) 31A10 (Secondary)The elastic Neumann–Poincaré operator is a boundary integral operator associated with the Lamé system of linear elasticity. It is known that if the boundary of a planar domain is smooth enough, it has eigenvalues converging to two different points determined by Lamé parameters. We show that eigenvalues converge at a polynomial rate on smooth boundaries and the convergence rate is determined by smoothness of the boundary. We also show that they converge at an exponential rate if the boundary of the domain is real analytic. Copyright © 2019, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

Spatiotemporal analysis of urban heatwaves using tukey g-and-h random field models

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arXiv 2020年

作者： Murakami, Daisuke Peters, Gareth W. Matsui, Tomoko Yamagata, Yoshiki Department of Data Science Institute of Statistical Mathematics 10-3 Midoricho Tokyo190-8562 Japan School of Mathematical and Computer Sciences Heriot-Watt University EdinburghEH14 4AS United Kingdom Department of Statistical Modeling Institute of Statistical Mathematics 10-3 Midoricho Tokyo190-8562 Japan Center for Global Environmental Research National Institute for Environmental Studies 16-2 Onogawa Ibaraki305-8506 Japan

The statistical quantification of temperature processes for the analysis of urban heat island (UHI) effects and local heat-waves is an increasingly important application domain in smart city dynamic modelling. This leads to the increased importance of real-time heatwave risk management on a fine grained spatial resolution. This study attempts to analyze and develop new methods for modelling the spatio-temporal behavior of ground temperatures. The developed models consider higher order stochastic spatial properties such as skewness and kurtosis, which are key components for understanding and describing local temperature uctuations and UHI's. The developed models are applied to the greater Tokyo metropolitan area for a detailed real world data case study. The analysis also demonstrates how to statistically incorporate a variety of real data sets. This includes remote sensed imagery and a variety of ground based monitoring site data to build models linking city and urban covariates to air temperature. The air temperature models are then used to capture high resolution spatial emulator outputs for ground surface temperature modelling. The main class of processes studied include the Tukey g-and-h processes for capturing spatial and temporal aspects of heat processes in urban environments. Copyright © 2020, The Authors. All rights reserved.

关键词： Atmospheric temperature

HYBRID ESTIMATION FOR ERGODIC DIFFUSION PROCESSES BASED ON NOISY DISCRETE OBSERVATIONS

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arXiv 2018年

作者： Kaino, Yusuke Nakakita, Shogo H. Uchida, Masayuki Graduate School of Engineering Science Osaka University Center for Mathematical Modeling and Data Science Osaka University JST CREST

We consider parametric estimation for ergodic diffusion processes with noisy sampled data based on the hybrid method, that is, the multi-step estimation with the initial Bayes type estimators. In order to select proper initial values for optimisation of the quasi likelihood function of ergodic diffusion processes with noisy observations, we construct the initial Bayes type estimator based on the local means of the noisy observations. The asymptotic properties of the initial Bayes type estimators and the hybrid multi-step estimators with the initial Bayes type estimators are shown, and a concrete example and the simulation results are given. Copyright © 2018, The Authors. All rights reserved.

关键词： Diffusion

A K-shell improved method for the importance of complex network nodes 7

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A K-shell improved method for the importance of complex netw...

7th IEEE data Driven Control and Learning Systems Conference, DDCLS 2018

作者： Jianmin, Xing Jianqiang, Chen Xiuwen, Sun Xinli, Zhang Ruikun, Zhang School of Mathematics and Physics Qingdao University of Science and Technology Qingdao266061 China Institute of Intelligence Science and Data Technology School of Mathematics and Physics Qingdao University of Science and Technology Qingdao266061 China Research Center for Mathematical Modeling School of Mathematics and Physics Qingdao University of Science and Technology Qingdao266061 China

ISBN: (纸本)9781538626184

In this paper, a weighted k-shell method is proposed to further improve the distinction of node importance by taking advantage of the number of iterations and edge weights when the node is deleted. The weighted k-shell decomposition method is applied to simple networks and complex networks respectively. The simulation results show that the improved method has low computational complexity, high result resolution and high accuracy. © 2018 IEEE.

关键词： Complex networks

Fast Positioning of Rotating center Based on Correction of Finite Angle Deviation of CT System

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Fast Positioning of Rotating Center Based on Correction of F...

IEEE data Driven Control and Learning Systems Conference

作者： Deyu Duan Fahui Zhai Yuqin Cao Huaqiong Hou Shuguo Yang Research Center for Mathematical Modeling School of Mathematics and Physics Qingdao University of Science and Technology Institute of Intelligence Science & Data Technology School of Mathematics and Physics Qingdao University of Science and Technology

ISBN: (纸本)9781538626191

Note that it is very important to determine accurately the position of the center of Rotation (COR) to the image reconstruction in the CT scanning system, in this paper, we establish the model of fast determining COR by using the correction of finite angle deviation, moreover apply certain algorithms to achieve the center of rotation calibration. By simulating original signal or the original signal with noise, we obtain that the artifact of the reconstructed image is significantly less and the image quality is also raised, thus the center of rotation can be accurately determined. Compared with the known algorithms, the model in this paper has a small amount of calculation and strong resistance to random noise. Consequently, our model and algorithm are helpful for determining COR.

关键词： 2D-CT Finite Angle Deviation Improved Inverse Transformation of Radon Least Square Method White Gaussian Noise

Study on Stumbles of the Elderly from a Depth Perception Dependency Test

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Study on Stumbles of the Elderly from a Depth Perception Dep...

2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

作者： Emiko Uchiyama Toshihiro Mino Hiroki Obara Tomoki Tanaka Wataru Takano Yoshihiko Nakamura Katsuya Iijima graduate school of information science and technology university of Tokyo Hongo 7-3-1 Bunkyo-ku Tokyo Japan graduate school of medicine university of Tokyo Hongo 7-3-1 Bunkyo-ku Tokyo Japan center for mathematical modeling and data science Osaka University Japan institute of gerontology university of Tokyo Hongo 7-3-1 Bunkyo-ku Tokyo Japan

In this paper, we investigate the relationship between the depth perception and an approaching motion toward an object. We propose the depth perception dependency test, which is the combination of tests of a motion and depth perception based on the situation that an object is placed on the human's pathway. Firstly, as the motion test, we set the ball approach motion and asked elderly participants to approach and contact a ball by their foot, because this motion is easy to measure and requires localization skill and motion planning skill. The swing/support legs positions at the toeoff time of the swing leg just before contacting the ball was analyzed. Secondly, as the depth perception test, the pseudo3D image test was proposed. The coordinate transformation model for the calculation of the depth perception ability was also proposed. Through the proposed test and the proposed model, it was clarified that the participants who are regarded as perceiving the strong visual illusion perceive the objects closer than its real position, and their swing leg toe off positions in the ball approaching motion were significantly farther than other participants. Thus, it can be concluded that there was a relationship between the depth perception and the approaching motion that is thought to be a higher risk of stumbles.

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data-based Parameter Calibration Method of the Computed Tomography System

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Data-based Parameter Calibration Method of the Computed Tomo...

第37届中国控制会议

作者： Zhang Ruikun Shan Zhengduo Duan Deyu Xu Guangwei Zhang Xinli School of Mathematics and Physics Qingdao University of Science and Technology Big Data Research Center of School of Mathematics and Physics Qingdao University of Science and Technology Center for Mathematical Modeling Research Qingdao University of Science and Technology

This paper mainly studies data-based parameter calibration of the computed tomography（CT） system. By establishing a least squares algorithm model, CT system parameters were calibrated. First, the attenuation coefficient is calculated from the known data, and the relationship between the received information and the pitch of the X-ray transmission template is obtained by using the Lambert-beers principle. Then, by using the geometric relationship between the ray and the two-dimensional graph, the relationship model between the pitch and the variable to be sought is established. On this basis, we can get the multivariate linear equations which present the received information and the variables to be solved. Finally, the least square method is used to establish the target programming model which is based on the minimum square sum of the fitting value and the actual value of the received information. By using the genetic algorithm, the multiple linear equations are solved. Meanwhile, the deflection center and receiver unit spacing can be obtained.

关键词： Parameter Calibration data-based CT system Least Square Method Genetic Algorithm

DeePMD-kit v2: A software package for Deep Potential models

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arXiv 2023年

作者： Zeng, Jinzhe Zhang, Duo Lu, Denghui Mo, Pinghui Li, Zeyu Chen, Yixiao Rynik, Marián Huang, Li'ang Li, Ziyao Shi, Shaochen Wang, Yingze Ye, Haotian Tuo, Ping Yang, Jiabin Ding, Ye Li, Yifan Tisi, Davide Zeng, Qiyu Bao, Han Xia, Yu Huang, Jiameng Muraoka, Koki Wang, Yibo Chang, Junhan Yuan, Fengbo Bore, Sigbjørn Løland Cai, Chun Lin, Yinnian Wang, Bo Xu, Jiayan Zhu, Jia-Xin Luo, Chenxing Zhang, Yuzhi Goodall, Rhys E.A. Liang, Wenshuo Singh, Anurag Kumar Yao, Sikai Zhang, Jingchao Wentzcovitch, Renata Han, Jiequn Liu, Jie Jia, Weile York, Darrin M. Weinan, E. Car, Roberto Zhang, Linfeng Wang, Han Laboratory for Biomolecular Simulation Research Institute for Quantitative Biomedicine Department of Chemistry and Chemical Biology Rutgers University PiscatawayNJ08854 United States AI for Science Institute Beijing100080 China DP Technology Beijing100080 China Academy for Advanced Interdisciplinary Studies Peking University Beijing100871 China HEDPS CAPT College of Engineering Peking University Beijing100871 China College of Electrical and Information Engineering Hunan University Changsha China Yuanpei College Peking University Beijing100871 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States Department of Experimental Physics Comenius University Mlynská Dolina F2 Bratislava842 48 Slovakia Center for Quantum Information Institute for Interdisciplinary Information Sciences Tsinghua University Beijing100084 China Center for Data Science Peking University Beijing100871 China ByteDance Research Zhonghang Plaza No. 43 North 3rd Ring West Road Haidian District Beijing China College of Chemistry and Molecular Engineering Peking University Beijing100871 China Baidu Inc. Beijing China Key Laboratory of Structural Biology of Zhejiang Province School of Life Sciences Westlake University Zhejiang Hangzhou China Westlake AI Therapeutics Lab Westlake Laboratory of Life Sciences and Biomedicine Zhejiang Hangzhou China Department of Chemistry Princeton University PrincetonNJ08544 United States SISSA Scuola Internazionale Superiore di Studi Avanzati Trieste34136 Italy Laboratory of Computational Science and Modeling Institute of Materials École Polytechnique Fédérale de Lausanne Lausanne1015 Switzerland Department of Physics National University of Defense Technology Hunan Changsha410073 China State Key Lab of Processors Institute of Computing Technology Chinese Academy of Sciences Beijing China University of Chinese Academy of Sciences Beijing China School of Electronics Engineerin

DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials (MLP) known as Deep Potential (DP) models. This package, which was released in 2017, has been widely used in the fields of physics, chemistry, biology, and material science for studying atomistic systems. The current version of DeePMD-kit offers numerous advanced features such as DeepPot-SE, attention-based and hybrid descriptors, the ability to fit tensile properties, type embedding, model deviation, Deep Potential - Range Correction (DPRc), Deep Potential Long Range (DPLR), GPU support for customized operators, model compression, non-von Neumann molecular dynamics (NVNMD), and improved usability, including documentation, compiled binary packages, graphical user interfaces (GUI), and application programming interfaces (API). This article presents an overview of the current major version of the DeePMD-kit package, highlighting its features and technical details. Additionally, the article benchmarks the accuracy and efficiency of different models and discusses ongoing developments. © 2023, CC BY-NC-ND.

关键词： Molecular dynamics

Correction to: On the utility of RNA sample pooling to optimize cost and statistical power in RNA sequencing experiments

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BMC genomics 2020年第1期21卷 384页

作者： Alemu Takele Assefa Jo Vandesompele Olivier Thas Department of Data Analysis and Mathematical Modeling Ghent University 9000 Ghent Belgium. alemutakele.assefa@UGent.be. Department of Biomolecular Medicine Ghent University 9000 Ghent Belgium. Cancer Research Institute Ghent Ghent University Ghent Belgium. Center for Medical Genetics Ghent University Ghent Belgium. Department of Data Analysis and Mathematical Modeling Ghent University 9000 Ghent Belgium. National Institute for Applied Statistics Research Australia (NIASRA) University of Wollongong Wollongong Australia. Data Science Institute I-BioStat Hasselt University Hasselt Belgium.

An amendment to this paper has been published and can be accessed via the original article.

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