Generalized Sobol sensitivity indices for dependent variables: numerical methods

The hierarchically orthogonal functional decomposition of any measurable function η of a random vector X=(X₁,?…?, X_p) consists in decomposing η(X) into a sum of increasing dimension functions depending only on a subvector of X. Even when X₁,?…?, X_p are assumed to be dependent, this decomposition is unique if the components are hierarchically orthogonal. That is, two of the components are orthogonal whenever all the variables involved in one of the summands are a subset of the variables involved in the other. Setting Y=η(X), this decomposition leads to the definition of generalized sensitivity indices able to quantify the uncertainty of Y due to each dependent input in X [Chastaing G, Gamboa F, Prieur C. Generalized Hoeffding–Sobol decomposition for dependent variables – application to sensitivity analysis. Electron J Statist. 2012;6:2420–2448]. In this paper, a numerical method is developed to identify the component functions of the decomposition using the hierarchical orthogonality property. Furthermore, the asymptotic properties of the components estimation is studied, as well as the numerical estimation of the generalized sensitivity indices of a toy model. Lastly, the method is applied to a model arising from a real-world problem.     

带状方程组并行列处理法贪心方法

利用列处理法贪心方法和分治策略,给出了一种求解任意相容性带状方程组的解或任意不相容性带状方程组最小二乘解的消息传递多指令流多数据流并行迭代解法,分析了解法的收敛性、计算复杂性和数值稳定性。该方法能使得各处理机上的负载基本平衡,得到了理想的加速比和并行效率。     

The asymptotic equivalence between the iterated improved 2sls estimator and the 3sls estimator

In this paper we show that the 3SLS estimator of a system of equations is asymptotically equivalent to an iterative 2SLS estimator applied to each equation, augmented with the residuals from the other equations. This result is a natural extension of Telser (1964).     

The asymptotic equivalence between the iterated improved 2sls estimator and the 3sls estimator

In this paper we show that the 3SLS estimator of a system of equations is asymptotically equivalent to an iterative 2SLS estimator applied to each equation, augmented with the residuals from the other equations. This result is a natural extension of Telser (1964).     

Idempotent and multivariate copulas with fractal support

Using special iterated function systems (IFS) Fredricks et al. (2005) constructed two-dimensional copulas with fractal supports and showed that for every s∈(1,2)$s\in (\mathrm{1,2})$ there exists a copula A whose support has Hausdorff dimension s. In the current paper we present a stronger version and prove that the same result holds for the subclass of idempotent copulas. Additionally we show that every doubly stochastic idempotent matrix N (having neither minimum nor maximum rank) induces a family of idempotent copulas such that, firstly, the corresponding Markov kernels transform according to N   and, secondly, the set of Hausdorff dimensions of the supports of elements of the family covers (1,2). Furthermore we generalize the IFS approach to arbitrary dimensions d≥2$d\ge 2$ and show that for every s∈(1,d)$s\in (1,d)$ we can find a d-dimensional copula whose support has Hausdorff dimension s.     

Importance of interpolation when constructing double-bootstrap confidence intervals

We show that, in the context of double-bootstrap confidence intervals, linear interpolation at the second level of the double bootstrap can reduce the simulation error component of coverage error by an order of magnitude. Intervals that are indistinguishable in terms of coverage error with theoretical, infinite simulation, double-bootstrap confidence intervals may be obtained at substantially less computational expense than by using the standard Monte Carlo approximation method. The intervals retain the simplicity of uniform bootstrap sampling and require no special analysis or computational techniques. Interpolation at the first level of the double bootstrap is shown to have a relatively minor effect on the simulation error.     

基于禁忌搜索的启发式求解背包问题算法

设计了一种基于禁忌搜索的遗传算法,利用遗传算法提供的并行搜索主框架,结合禁忌算法的个体串行搜索方式,能扩大搜索空间,快速实现全局优化。把基于禁忌搜索的遗传算法与启发式方法相结合用来求解背包问题,经过计算机仿真,其优化性能指标及搜索效率均有大幅度的提高。     

对“饕餮食人”为美说的质疑

中国的青铜器中有饕餮食人造型的酒器--卣.美学家认为"饕餮食人"表现了"由野蛮进入文明时代所必经的血与火的超人的历史力量",因而体现为一种狞厉的美.笔者认为,"饕餮食人"的造型并没有体现"超人的历史力量",也不表现美,而是周朝统治者为了告诫人们和子孙不要重蹈缙云氏不才之子(饕餮)和夏、商统治者因贪食而自取灭亡的覆辙而制造的.由于饕餮的面目是狰狞恐怖的,本性是贪婪的,所以它的形象是丑陋的.     

求解双基链的贪婪算法的研究与VB实现

标量乘法是影响椭圆曲线加密算法执行效率的一个重要因素,椭圆曲线的标量乘法方法很多,基于双基链的标量乘法是一种效率较好的算法,文中讨论求解整数的双基链表示的基本算法—贪婪算法的基本原理和在VB环境下的实现.     

混合遗传算法在矩形板材下料问题上的应用研究

根据基本遗传算法在解决板材下料优化中存在的问题,提出了将局部搜索算法和遗传算法相结合,取各自的优点来更好地解决矩形板材下料优化问题.