A review of statistical models for global optimization

A review of statistical models for global optimization is presented. Rationality of the search for a global minimum is formulated axiomatically and the features of the corresponding algorithm are derived from the axioms. Furthermore the results of some applications of the proposed algorithm are presented and the perspectives of the approach are discussed.     

Computation of efficient solutions of discretely distributed stochastic optimization problems

In engineering and economics often a certain vectorx of inputs or decisions must be chosen, subject to some constraints, such that the expected costs (or loss) arising from the deviation between the outputA() x of a stochastic linear systemxA()x and a desired stochastic target vectorb() are minimal. Hence, one has the following stochastic linear optimization problem minimizeF(x)=Eu(A()x b()) s.t.xD, (1) whereu is a convex loss function on ^m , (A(), b()) is a random (m,n + 1)-matrix, E denotes the expectation operator andD is a convex subset of ⁿ . Concrete problems of this type are e.g. stochastic linear programs with recourse, error minimization and optimal design problems, acid rain abatement methods, problems in scenario analysis and non-least square regression analysis.Solving (1), the loss functionu should be exactly known. However, in practice mostly there is some uncertainty in assigning appropriate penalty costs to the deviation between the outputA ()x and the targetb(). For finding in this situation solutions hedging against uncertainty a set of so-called efficient points of (1) is defined and a numerical procedure for determining these compromise solutions is derived. Several applications are discussed.     

Kinetic limits of the HPP cellular automaton

We study the Boltzmann-Grad limit in various versions of the two-dimensional HPP cellular automaton. In the completely deterministic case we prove convergence to an evolution that is not of kinetic type, a well-known phenomenon after Uchyiama's paper on the Broadwell gas, whereas the limiting equation becomes of kinetic type in the model with random collisions. The main part of the paper concerns the case where the collisions are deterministic and the randomness comes from inserting, between any two successive HPP updatings, ^- stirring updatings, <1 being any fixed positive number and a parameter which tends to 0. The initial measure is a product measure with average occupation numbers of the order of (low-density limit) and varying on distances of the order of ^–1. The limit as 0 of the system evolved for times of the order of ^-1- corresponds to the Boltzmann-Grad limit. We prove propagation of chaos and that the renormalized average occupation numbers (i.e., divided by) converge to the solution of the Broadwell equation. Convergence is proven at all times for which the solution of the Broadwell equation is bounded.     

Stochastic detection of motor protein-RNA complexes by single-channel current recording.

A label- and immobilization-free approach to detecting the reversible formation of complexes between nucleic acids and proteins at the single-molecule level is described. The voltage-driven translocation of individual oligoribonucleotides through a nanoscale protein pore is observed by single-channel current recordings. The oligoribonucleotide 5'-C25A(25)-3' gives rise to current blockades with an average duration of approximately 0.5 ms. In the presence of the RNA-binding ATPase P4, a viral packaging motor from bacteriophage phi8, longer events of tens to hundreds of milliseconds are observed. Upon addition of ATP the long events disappear, indicating the dissociation of the P4RNA complex. The frequency of events also depends on the concentration of P4 and the length of the oligoribonucleotide, thereby confirming the specificity of the P4RNA events. This study shows that single-channel current recordings can be used to monitor RNA-protein complex formation, thus opening up a new means to examine the motor activity of RNA- or DNA-processing enzymes.     

基于不完备频响函数的结构损伤统计识别研究

基于不完备频响函数数据,结合概率统计方法,提出了一种能同时考虑模型参数不确定性和测试噪声影响的结构损伤统计识别方法.首先,基于频响函数某一行向量在不同频率下的幅值数据,利用矩阵拉直运算建立了关于损伤系数的确定性识别方程.其次,假设模型参数误差和测试噪声为零均值的高斯随机变量,根据摄动理论,推导了损伤后结构刚度参数的前二...     

Computation of Entropy Production in Stratified Flames Based on Chemistry Tabulation and an Eulerian Transported Probability Density Function Approach

This contribution presents a straightforward strategy to investigate the entropy production in stratified premixed flames. The modeling approach is grounded on a chemistry tabulation strategy, large eddy simulation, and the Eulerian stochastic field method. This enables a combination of a detailed representation of the chemistry with an advanced model for the turbulence chemistry interaction, which is crucial to compute the various sources of exergy losses in combustion systems. First, using detailed reaction kinetic reference simulations in a simplified laminar stratified premixed flame, it is demonstrated that the tabulated chemistry is a suitable approach to compute the various sources of irreversibilities. Thereafter, the effects of the operating conditions on the entropy production are investigated. For this purpose, two operating conditions of the Darmstadt stratified burner with varying levels of shear have been considered. The investigations reveal that the contribution to the entropy production through mixing emerging from the chemical reaction is much larger than the one caused by the stratification. Moreover, it is shown that a stronger shear, realized through a larger Reynolds number, yields higher entropy production through heat, mixing and viscous dissipation and reduces the share by chemical reaction to the total entropy generated.     

A Bilinear Backlund Transformation and Lax Pair for a （1＋1）-Dimensional Differential-Difference sine-Gordon Equation

In this paper, we obtain a 1＋1 dimensional integrable differential-difference model for the sine-Gordon equation by Hirota＇s discretization method. A bilinear Backlund transformation and the associated Lax pair are also proposed/or this model.     

约束最小二乘估计的优良性

对于线性模型y=Xθ ε,ε服从椭球等高单峰分布,未知参数θ满足不等式约束a′θ≥0,证明了在参数估计优良性的集中概率准则下,θ的约束最小二乘估计θ~*优于最小二乘估计θ.     

基于三维参数随机L系统的虚拟植物生成算法

提出了一种基于三维参数随机L系统的虚拟植物生成算法.针对简单L系统生成植物形状单一的缺点,采用曲线论的Frenet标架作为三维基本框架,在对植物产生字符串进行递推迭代的同时,对其规则加入随机概率,使生成的字符串在具有随机性的同时又保留了自相似性.此外,对转角与步长均加入了随机扰动,使生成的植物形态在保持生物性状稳定性的同时又兼具了个体差异性,提高了生成植物的真实感.     

宽带随机混沌雷达高速目标速度估计与成像

随机混沌具有真随机性、对初值敏感、易于产生和控制等特点,频率步进信号易于工程实现和处理,结合两者的优势,提出了一种载频随机步进的随机混沌信号(RSCFSCS)模型,用于高速目标的速度估计和距离维高分辨成像。首先,通过非周期函数激励非线性系统,产生不可预测的随机混沌信号(SCS),经频率调制后用作基带子脉冲。同时,将SCS通过映射变换得到跳频编码(FHC),用来决定调频脉冲串的载频步进。RSCFSCS 速度估计包括粗搜索和精搜索,粗搜索采用固定步长,保证速度偏差小于速度分辨单元,而精搜索采用黄金分割搜索算法可得到精确的速度估计。最后,子脉冲经相干合成形成宽带信号,实现高分辨距离成像。数值仿真表明提出的信号模型和处理算法性能良好。