Representation of discrete sequences with high-dimensional iterated function systems

Iterated Function System (IFS) models have been used to represent discrete sequences where the attractor of the IFS is self-affine or piece-wise self-affine in R ² or R ³ (R is the set of real numbers). In this paper, the piece-wise hidden-variable fractal model is extended from R ³ to R ⁿ (n is an integer greater than 3), which is called the high-dimensional piece-wise hidden-variable fractal model. This new model uses a “mapping partial derivative” and a constrained inverse algorithm to identify the model parameters. The model values depend continuously on all the hidden variables. Therefore, the result is very general.     

非均匀调制随机激励下系统的非平稳响应分析

基于时域复模态分析，提出一种非均匀调制随机激励下系统非平稳响应特性的解析解法，用Ｎｉｉｇａｔａ地震激励模型作了说明．算例与仿真结果吻合良好．     

斜拉桥塔锚固区光弹性应力分析与等倾线图像处理

本文采用光弹性冻结应力法，对独塔斜拉桥塔锚固区进行了应力分析，给出了有关截面的边界应力分布及主应力迹线，从而为优化工程设计提供了重要的参考依据。本文还提出了一种新的提取等倾线的方法──图像对数增强相减法，实现了等倾线与等差线条纹的分离，同时使条纹得到了细化，提高了处理等倾线的速度与准确度。编制了自动绘制主应力迹线的程序，利用它绘制了桥塔截面的次主应力迹线。     

地铁车站地下拱型结构的光弹性应力分析

本文用三维光弹性法，对地铁车站地下拱型结构进行了实验应力分析并绘出主应力迹线。文中还提出对加压用乳胶气囊进行高温、高压预处理工艺，使乳胶气囊和模型曲面很好地吻合，从而提高了加载的准确度。     

含椭圆孔或裂纹的等参数正交异性板平面问题基本解

应用Ｃａｕｃｈｙ积分的方法，分别给出了含椭圆孔或裂纹的等参数正交异性板在任意面内集中载荷作用下的复应力函数基本解或应力强度因子基本解，这些基本解对于应用边界元法求解此类正交异性板或各向同性板的某些弹性力学和断裂力学问题具有重要的意义。     

HL-2A装置上边界间歇性事件与湍流粒子输运的统计学研究

通过对粒子概率分布函数的计算，发现在高等离子体密度下边界间歇性事件的爆发频率有所增加。通过条件平均的手段，正负间歇性事件得以区分，并发现了二者在空间上的不同特征。不同密度梯度下的湍流粒子输运计算表明，间歇性事件与湍流粒子输运之间存在密切联系，间歇性事件的存在能够大大增加湍流粒子输运的大小。在高等离子体密度时，间歇性事件的强度有所增加，而与之相应地，湍流粒子输运的大小也有所增强。     

Sparse Multicategory Generalized Distance Weighted Discrimination in Ultra-High Dimensions

Distance weighted discrimination (DWD) is an appealing classification method that is capable of overcoming data piling problems in high-dimensional settings. Especially when various sparsity structures are assumed in these settings, variable selection in multicategory classification poses great challenges. In this paper, we propose a multicategory generalized DWD (MgDWD) method that maintains intrinsic variable group structures during selection using a sparse group lasso penalty. Theoretically, we derive minimizer uniqueness for the penalized MgDWD loss function and consistency properties for the proposed classifier. We further develop an efficient algorithm based on the proximal operator to solve the optimization problem. The performance of MgDWD is evaluated using finite sample simulations and miRNA data from an HIV study.     

羟基对界面水分子的扰动与其对非离子型氢氟烃杂化表面活性剂聚集行为的改变

本文合成并比较了具有和不具有羟基的两种非离子型氢氟烃杂化表面活性剂，它们均表现出良好的热稳定性和优异的表面活性. 实验观察到羟基对改变其溶液的表面张力和所形成胶束的形态具有较大的影响. 该作用可归因于烷烃基团从空气/水表面上方到其下方的重排以及由羟基诱导的界面水结构的扰动. 本工作提供了一种通过修改界面处的取向结构来弱化碳氢链和碳氟链之间的不混溶性，从而利于设计具有不同界面性质表面活性剂的策略.     

VEGA: visual comparison of phylogenetic trees for evolutionary genome analysis (ChinaVis 2019)

In the field of evolutionary genome analysis, biologists seek to identify important genes or chromosome regions by comparing phylogenetic trees and analyzing the mutation at which locus might affect phenotypic traits. Unfortunately, the tree comparison and accompanying analysis are often performed manually. In this paper, we characterize the workflow of evolutionary genome analysis and present a task analysis for the fundamental questions asked by biologists during the analysis procedure. We propose two algorithms to enable quantitative tree comparison. One is to measure the differences between corresponding leaf nodes on two trees, and the other is to compute the classification inconsistency of each leaf node by comparing tree structure with a given biological classification. Configuring with the obtained difference and inconsistency, we present a visual analysis system, visual comparison of phylogenetic trees for evolutionary genome analysis, which not only enables biologists to intuitively explore trees but also identify locus which affects their traits by comparing SNP variants of selected leaf nodes. We conclude with case studies from two biologists who used our system to augment their previous manual analysis workflow and demonstrate that our system can reveal more insight.     

鬼成像中一些数学问题

鬼成像是一种与传统成像方式不同的通过光场涨落的高阶关联获得图像信息的新型成像方式。近年来,相比传统成像方式,鬼成像所拥有的一些优点如高灵敏度、超分辨能力、抗散射等,使其在遥感、多光谱成像、热X射线衍射成像等领域得到广泛研究。随着对鬼成像的广泛研究,数学理论和方法在其中发挥的作用愈显突出。例如,基于压缩感知理论,可以进行鬼成像系统采样方式优化、图像重构算法设计及图像重构质量分析等研究工作。本文旨在探索鬼成像中的一些有趣的数学问题,主要包括:系统预处理方法、光场优化及相位恢复问题。对这些问题的研究既可以丰富鬼成像理论,又能推动它在实际应用中的发展。