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ANNEALED IMPORTANCE SAMPLING FOR ISING MODELS WITH MIXED BOUNDARY CONDITIONS

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Journal of Computational Mathematics 2023年第3期41卷 542-550页

作者： lexing ying Department of Mathematics Stanford UniversityStanfordCA 94305USA

This note introduces a method for sampling Ising models with mixed boundary *** an application of annealed importance sampling and the Swendsen-Wang algorithm,the method adopts a sequence of intermediate distributions that keeps the temperature fixed but turns on the boundary condition *** numerical results show that the variance of the sample weights is relatively small.

关键词： Ising model Annealed importance sampling Swendsen-Wang algorithm

Solving Traveltime Tomography with Deep Learning

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Communications in Mathematics and Statistics 2023年第1期11卷 3-19页

作者： Yuwei Fan lexing ying Department of Mathematics Stanford UniversityStanfordCA 94305USA

This paper introduces a neural network approach for solving two-dimensional traveltime tomography(TT)problems based on the eikonal *** mathematical problem of TT is to recover the slowness field of a medium based on the boundary measurement of the traveltimes of waves going through the *** inverse map is high-dimensional and *** the circular tomography geometry,a perturbative analysis shows that the forward map can be approximated by a vectorized convolution operator in the angular *** by this and filtered backprojection,we propose an effective neural network architecture for the inverse map using the recently proposed BCR-Net,with weights learned from training *** results demonstrate the efficiency of the proposed neural networks.

关键词： Traveltime tomography Eikonal equation Inverse problem Neural networks Convolutional neural network

ACHIEVING ADVERSARIAL ROBUSTNESS REQUIRES AN ACTIVE TEACHER

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Journal of Computational Mathematics 2021年第6期39卷 880-896页

作者： Chao Ma lexing ying Department of Mathematics Stanford UniversityCaliforniaUSA

A new understanding of adversarial examples and adversarial robustness is proposedby decoupling the data generator and the label generator (which we call the teacher). Inour framework, adversarial robustness is a conditional concept—the student model is notabsolutely robust, but robust with respect to the teacher. Based on the new understanding, we claim that adversarial examples exist because the student cannot obtain sufficientinformation of the teacher from the training data. Various ways of achieving robustness iscompared. Theoretical and numerical evidence shows that to efficiently attain robustness,a teacher that actively provides its information to the student may be necessary.

关键词： Adversarial robustness Decoupled supervised learning Active teacher

A sweeping preconditioner for Yee＇s finite difference approximation of time-harmonic Maxwell＇s equations

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Frontiers of Mathematics in China 2012年第2期7卷 347-363页

作者： Paul TSUJI lexing ying ICES University of Texas at Austin Austin TX 78712 USA Department of Mathematics University of Texas at Austin Austin TX 78712 USA

This paper is concerned with the fast iterative solution of linear systems arising from finite difference discretizations in electromagnetics. The sweeping preconditioner with moving perfectly matched layers previously developed for the Helmholtz equation is adapted for the popular Yee grid scheme for wave propagation in inhomogeneous, anisotropic media. Preliminary numerical results are presented for typical examples.

关键词： Electromagnetic scattering Yee grid finite difference methods perfectly matched layers LDLT factorizations multifrontal method wave propagation in inhomogeneous and anisotropic media matrix preconditioners

Pole-Based Approximation of the Fermi-Dirac Function

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Chinese Annals of Mathematics,Series B 2009年第6期30卷 729-742页

作者： Lin LIN Jianfeng LU lexing ying Weinan E Dedicated to Professor Andrew Majda on the Occasion of his 60th Birthday

Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed:one uses the contour integral representation and conformal mapping,and the other is based on a version of the multipole representation of the Fermi-Dirac function that uses only simple *** representations have logarithmic computational *** are of great interest for electronic structure calculations.

关键词：狄拉克函数费米逼近极点结构计算复杂性极大电子

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Preface

Journal of Computational Mathematics 2021年第6期39卷 I0001-I0001页

作者： Shi Jin lexing ying Shanghai Jiao Tong University China Stanford University USA

Numerical Methods for Partial Differential Equations Numerical methods for partial differential equation have experienced steady developments in the past several *** of the remaining challenges fall into two categories,both of which are associated with the curse of the *** the first category,the function of the partial differential equation is high dimensional,with examples from many-body quantum nieclianics,molecular dynamics.

关键词： dynamics equation dimensionality

Isobaric Vapor–Liquid Equilibrium for tert-Butyl Alcohol + Water + Propane-1,3-Diol + 1-Ethyl-3-Methylimidazolium Chloride at 101.3 kPa

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Transactions of Tianjin University 2018年第5期24卷 424-433页

作者： Xianbao Cui Qinglong Cheng Haofei Liu lexing Xue Jinbo Zhou ying Zhang Tianyang Feng Kai Zhang State Key Laboratory of Chemical Engineering School of Chemical Engineering and TechnologyTianjin University Lanzhou Petrochemical Research Center of Petrochemical Research Institute PetroChina Co.Ltd

In this study, we used a mixture of organic liquid propane-1,3-diol and ionic liquid 1-ethyl-3-methylimidazolium chloride([emim]Cl) as the entrainer to separate tert-butyl alcohol(TBA) + water. We measured the isobaric vapor–liquid equilibrium(VLE) for the quaternary system TBA + water + propane-1,3-diol + [emim]Cl at 101.3 kPa, and found the VLE data to be well correlated with the nonrandom two-liquid model. These results show that the mixed solvent of propane-1,3-diol + [emim]Cl can increase the relative volatility of TBA to water and break the azeotropic point. We found no notable synergetic effect between them, and observed that the liquid mixed solvent of propane-1,3-diol and [emim]Cl had lower viscosity than [emim]Cl, which makes it a promising entrainer for separating the TBA + water azeotrope in industrial applications.

关键词： tert-Butyl alcohol·Water·Propane-1-3-diol·1-Ethyl-3-methylimidazolium chloride·Vapor–liquid equilibrium

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不同围岩条件下隧道爆破开挖技术

铁道建筑技术 2016年第S1期 504-506,540页

作者：蒋跃飞应俊宋志伟余乐兴浙江省高能爆破工程有限公司浙江杭州 310030

隧道开挖爆破作业复杂多样，需根据不同的作业条件和围岩类型采用不同的爆破方法。在舟山西堠隧道开挖过程中遇到非常多变的地质坏境条件，诸如地下溶洞、断层、围岩类型变化大等问题。针对这些特点我们运用了不同的爆破开挖方法，特别... 详细信息

隧道开挖爆破作业复杂多样，需根据不同的作业条件和围岩类型采用不同的爆破方法。在舟山西堠隧道开挖过程中遇到非常多变的地质坏境条件，诸如地下溶洞、断层、围岩类型变化大等问题。针对这些特点我们运用了不同的爆破开挖方法，特别是在Ⅱ、Ⅲ、Ⅳ、Ⅴ类不同地质围岩段，有针对性地采取了差别化的爆破开挖方法，取到了较好的爆破效果和经济效益。本文对西堠隧道爆破开挖施工经验进行了总结，可供同类工程借鉴及参考。

关键词：隧道开挖地质环境围岩类别爆破施工

CT值对甲状腺良性单纯粗钙化结节诊断的价值

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中华内分泌外科杂志 2018年第1期12卷 43-46页

作者：魏培英张乐星韩志江吴英丁金旺浙江省杭州市第一人民医院放射科杭州市310000 浙江省杭州市第一人民医院肿瘤外科杭州市310000

目的探讨CT值对甲状腺良性单纯粗钙化结节（benign solitary coarse calcification nodules，BCCN）诊断的价值。方法回顾分析经手术病理证实的55例56枚良性BCCN的平均CT值和最大CT值，并与32例33枚PTC进行对照，观察平均CT值和最大CT值... 详细信息

目的探讨CT值对甲状腺良性单纯粗钙化结节（benign solitary coarse calcification nodules，BCCN）诊断的价值。方法回顾分析经手术病理证实的55例56枚良性BCCN的平均CT值和最大CT值，并与32例33枚PTC进行对照，观察平均CT值和最大CT值在BCCN和PTC中的分布差异，通过受试者工作特异度曲线（ROC）获得平均CT值和最大CT值在BCCN和PTC中的最佳阈值。结果平均CT值在BCCN和PTC中具有统计学差异（Z=-4.035，P=0.000），ROC曲线下面积为0.757（95%置信空间0.657~0.857），临界值为743.4 Hu时约登指数最大，敏感性和特异性分别为48.2%和93.9%，临界值为891.1Hu时，敏感性为21.4%，特异度为100%；最大CT值在BCCN和PTC中差异具有统计学意义（Z=-4.319，P=0.000），ROC曲线下面积为0.775（95%置信空间0.681~0.869），临界值为1 201.5 Hu时约登指数最大，敏感性和特异性分别为57.1%和91.0%，临界值为1 373.5 Hu时，敏感性为42.9%，特异度为100%。结论CT值对BCCN的诊断具有重要的价值，具有高度的特异性，与平均CT值比较，最大CT值具有相对更高的敏感性，为减少不必要的手术创伤提供重要依据。

关键词：甲状腺结节甲状腺肿瘤钙化体层摄影术 X线计算机