Hierarchical Model-Based Clustering for Large Datasets

In recent years, hierarchical model-based clustering has provided promising results in a variety of applications. However, its use with large datasets has been hindered by a time and memory complexity that are at least quadratic in the number of observations. To overcome this difficulty, this article proposes to start the hierarchical agglomeration from an efficient classification of the data in many classes rather than from the usual set of singleton clusters. This initial partition is derived from a subgraph of the minimum spanning tree associated with the data. To this end, we develop graphical tools that assess the presence of clusters in the data and uncover observations difficult to classify. We use this approach to analyze two large, real datasets: a multiband MRI image of the human brain and data on global precipitation climatology. We use the real datasets to discuss ways of integrating the spatial information in the clustering analysis. We focus on two-stage methods, in which a second stage of processing using established methods is applied to the output from the algorithm presented in this article, viewed as a first stage.     

位移约束集成化处理的连续体结构拓扑优化

为解决多工况下多位移约束的连续体结构拓扑优化问题,引入了K-S函数对位移约束进行集成化处理.在建立优化模型时,基于莫尔定理按ICM方法导出约束点位移与设计变量之间的近似显函数关系,然后采用Lagrange乘子法进行求解.给出三个算例对该方法进行验证,并与ESO法、BESO法、MD法以及均匀化方法的结果进行比较.结果表明:该方法计算效率较高,并且能够计算出更合理的结构拓扑.     

Independent continuous mapping for topological optimization of frame structures

Based on the Independent Continuous Mapping method (ICM), a topological optimization model with continuous topological variables is built by introducing three filter functions for element weight, element allowable stress and element stiffness, which transform the 0-1 type discrete topological variables into continuous topological variables between 0 and 1. Two methods for the filter functions are adopted to avoid the structural singularity and recover falsely deleted elements: the weak material element method and the tiny section element method. Three criteria (no structural singularity, no violated constraints and no change of structural weight) are introduced to judge iteration convergence. These criteria allow finding an appropriate threshold by adjusting a discount factor in the iteration procedure. To improve the efficiency, the original optimization model is transformed into a dual problem according to the dual theory and solved in its dual space. By using MSC/Nastran as the structural solver and MSC/Patran as the developing platform, a topological optimization software of frame structures is accomplished. Numerical examples show that the ICM method is very efficient for the topological optimization of frame structures.The project supported by the National Natural Science Foundation of China (10472003) and Beijing Natural Science Foundation (3042002) The English text was polished by Yunming Chen.     

Natural and artificial light-harvesting systems utilizing the functions of carotenoids

Carotenoids are essential pigments in natural photosynthesis. They absorb in the blue–green region of the solar spectrum and transfer the absorbed energy to (bacterio-)chlorophylls, and so expand the wavelength range of light that is able to drive photosynthesis. This process is an example of singlet–singlet energy transfer and so carotenoids serve to enhance the overall efficiency of photosynthetic light reactions. Carotenoids also act to protect photosynthetic organisms from the harmful effects of excess exposure to light. In this case, triplet–triplet energy transfer from (bacterio-)chlorophyll to carotenoid plays a key role in this photoprotective reaction. In the light-harvesting pigment–protein complexes from purple photosynthetic bacteria and chlorophytes, carotenoids have an additional role, namely the structural stabilization of those complexes. In this article we review what is currently known about how carotenoids discharge these functions. The molecular architecture of photosynthetic systems will be outlined to provide a basis from which to describe the photochemistry of carotenoids, which underlies most of their important functions in photosynthesis. Then, the possibility to utilize the functions of carotenoids in artificial photosynthetic light-harvesting systems will be discussed. Some examples of the model systems are introduced.     

Extending the Iterative Convex Minorant Algorithm to the Cox Model for Interval-Censored Data

Abstract

The iterative convex minorant (ICM) algorithm proposed by Groeneboom and Wellner is fast in computing the NPMLE of the distribution function for interval censored data without covariates. We reformulate the ICM as a generalized gradient projection method (GGP), which leads to a natural extension to the Cox model. It is also easily extended to support Tibshirani's Lasso method. Some simulation results are also shown. For illustration we reanalyze two real datasets.     

考虑破损-安全的连续体结构拓扑优化ICM方法

本文瞄准连续体在破损-安全考虑下的结构拓扑优化问题,旨在克服传统模型求解所得最终构型存在的弊病,避免结构因缺乏合理的冗余结构而敏感于局部破坏,实现破损-安全的目标. 首先,梳理了以往虽然用到却并不明晰的4个概念:结构局部破损模式、结构局部破损区域、结构破损状况、结构破损状况的预估分布. 之后,基于独立连续映射(ICM)方法,对该问题建立了力学性能约束下结构体积极小化的模型. 建立目标函数时,利用Minimax的概念将可能出现的结构破损状况对应的所有结构体积目标转化为原结构的唯一结构体积目标,克服了多目标问题的困难. 建立近似约束函数时,将可能出现的所有结构破损状况对应的力学性能的约束皆考虑进去,既能处理载荷单工况也能处理载荷多工况. 最后,以位移约束为例,建立了优化模型并求解. 单工况及多工况位移约束拓扑优化算例验证了算法的有效性. 结果表明:本方法相比于不考虑破损-安全的拓扑优化设计,得到的最优拓扑更复杂,体积比更大即所用材料更多,亦即最优结构具有更多的冗余,此正是考虑破损-安全设计原则的结果. 本文的研究对于航空、航天、其他水、陆等领域运载工具以及其他工程结构在意外破坏、战争创伤或恐怖袭击下的结构设计,乃是非常重要的进展.      

频率约束的三维连续体结构动力拓扑优化设计

针对频率约束和结构重量最小的动力拓扑优化问题, 基于(independent continuous mapping, ICM)独立、连续、映射方法,建立了频率约束下的三维连续体拓扑优化模型. 利用瑞利商和一阶泰勒展式对频率约束进行了显式化处理,并采用幂函数与复合指数函数作为过滤函数,将优化模型进行了标准化转换, 利用对偶理论及数学规划法进行了求解. 另外,利用质量矩阵和刚度矩阵过滤函数比值与动态约束处理了局部模态和模态交换等数值问题. 最后,通过应用两类不同过滤函数的数值算例表明了文中模型及方法在处理动力拓扑优化问题上的合理性与有效性.      

基于ICM方法的多工况位移约束下板壳结构拓扑优化设计

基于ICM方法,建立了多种载荷工况下受位移约束极小化结构重量的拓扑优化近似显式模型,采用精确对偶映射下的序列二次规划算法进行求解,得到了结构的最优拓扑.数值算例表明:ICM方法也可以很好地应用于多工况下板壳结构拓扑优化设计,且收敛快,稳定性好;边界条件和位移约束值都会影响结构的最优拓扑;多工况最优传力路径不是各个单工况最优传力路径的简单叠加.     

频率约束板结构拓扑优化

本文利用ICM（独立、连续、映射）方法建立了频率约束下平板结构重量最轻的拓扑优化模型。采用指数函数作为单元重量、单元质量及单元刚度的过滤函数。通过瑞利商对刚度过滤函数倒变量的泰勒一阶展式,将频率约束近似显式化。利用对偶理论将含有大量设计变量的约束优化模型转化为易于求解的少设计变量拟无约束优化模型,通过序列二次规划将转化模型进行求解,提高了求解的效率。本文选择MSC.Patran&Nastran软件及PCL二次开发语言构架了平板结构频率约束拓扑优化问题的软件。数值算例表明：本文的方法具有迭代稳定性和收敛高效性。     

Plate/shell topological optimization subjected to linear buckling constraints by adopting composite exponential filtering function

In this paper, a model of topology optimization with linear buckling constraints is established based on an independent and continuous mapping method to minimize the plate/shell structure weight. A composite exponential function (CEF) is selected as filtering functions for element weight, the element stiffness matrix and the element geomet-ric stiffness matrix, which recognize the design variables, and to implement the changing process of design variables from“discrete”to“continuous”and back to“discrete”. The buck-ling constraints are approximated as explicit formulations based on the Taylor expansion and the filtering function. The optimization model is transformed to dual programming and solved by the dual sequence quadratic programming algo-rithm. Finally, three numerical examples with power function and CEF as filter function are analyzed and discussed to demonstrate the feasibility and efficiency of the proposed method.