Rokhlin's Question and Quotients of Real Algebraic Surfaces by the Complex Conjugation

Complex algebraic surfaces defined over are considered. Local and global topological properties of their quotients by the complex conjugation are discussed. Bibliography: 9 titles.     

Direction trees

Given a finite set of noncollinear points in the real plane, it is shown that they can be connected to form a tree using lines, no two of which are parallel.     

Conjugate Direction Boosting

Boosting in the context of linear regression has become more attractive with the invention of least angle regression (LARS), where the connection between the lasso and forward stagewise fitting (boosting) has been established. Earlier it has been found that boosting is a functional gradient optimization. Instead of the gradient, we propose a conjugate direction method (CDBoost). As a result, we obtain a fast forward stepwise variable selection algorithm. The conjugate direction of CDBoost is analogous to the constrained gradient in boosting. Using this analogy, we generalize CDBoost to: (1) include small step sizes (shrinkage) which often improves prediction accuracy; and (2) the nonparametric setting with fitting methods such as trees or splines, where least angle regression and the lasso seem to be unfeasible. The step size in CDBoost has a tendency to govern the degree between L₀- and L₁-penalization. This makes CDBoost surprisingly flexible. We compare the different methods on simulated and real datasets. CDBoost achieves the best predictions mainly in complicated settings with correlated covariates, where it is difficult to determine the contribution of a given covariate to the response. The gain of CDBoost over boosting is especially high in sparse cases with high signal to noise ratio and few effective covariates.     

On comparing optimum Alternating Direction Preconditioning and Extrapolated Alternating Direction Implicit schemes

The purpose of this paper is to show the equivalence of Alternating Direction Preconditioning and Extrapolated Alternating Direction Implicit methods in the case of two-level one-parameter optimized schemes as far as convergence rates are concerned, and also to give optimum parameters for the numerical solution of the self-adjoint second-order elliptic partial differential equation and the biharmonic equation.     

ABS共轭方向算法

本文提出ＡＢＳ共轭方向算法，它可以产生一大类共轭方向．尤其，Ｄｅｎｎｉｓ和Ｔｕｒｎｅｒ（１９８７）提出的广义共轭方向方法也可以由该算法产生     

有穷正级亚纯函数的T方向和Borel方向

对任意正数λ,正整数q_1和q_2,记E_1={argz=θ_j|0∣θ_1＜θ_2<…＜θ_(q1)＜2π}及E_2={axgz=φ_j|0■1＜φ2＜…＜φq2＜2π},使得E_1∩E_2=■,则(1)存在复平面上的λ级亚纯函数f(z),恰以E_1∪E_2为其T方向且恰以E_2为其Borel方向,(2)存在复平面上的级与下级均为λ的亚纯函数g(z),恰以E_1∪E_2为其Borel方向且恰以E_2为其T方向．     

Turbulent Cascade Direction and Lagrangian Time-Asymmetry

Journal of Nonlinear Science - We establish Lagrangian formulae for energy conservation anomalies involving the discrepancy between short-time two-particle dispersion forward and backward in time....     

拟亚纯映射的Julia方向

研究了拟亚纯映射,得到了它的充满园和Julia方向。     

拟亚纯映射的奇异方向

研究了广泛的K-拟亚纯映射.导出了K-拟亚纯映射Borel方向的一个充分条件和一个充要条件,证明了关于平面上K-拟亚纯映射的Ju lia方向存在性的一个较精确定理.     

拟亚纯映射的S方向

本文定义了平面上拟亚纯映射的S方向,证明了当limr→∞S(r,f)lgr=∞时存在一条S方向,并且这一S方向还是Julia方向.     

亚纯函数的奇异方向

该文应用Ahlfors的覆盖曲面理论,讨论了复平面上超越亚纯函数的奇异 方向,证明了亚纯函数涉及一类有理函数的T方向的存在性,又一次证实了郑 建华的一个猜想.     

金融改革的方向和重点

金融变革的重点是什么？2012年4月28日的第五届中国CFO年会上,中国人民银行研究局局长张健华为我们拨开了重重迷雾。     

交替方向的扩散方程精细积分并行算法

给出了交替方向的二维扩散方程的精细积分算法，将一个时间步积分分为两个方向，使大规模矩阵的计算转化为一些小矩阵的计算，减小了每一步求解的计算量．对于方形区域的齐次方程，计算结果与全城精细积分完全相同，而计算量和存储量都要小得多．算例表明了算法具有较高的并行计算加速比和计算效率．     

Direction selection in stochastic directional distance functions

Researchers rely on the distance function to model multiple product production using multiple inputs. A stochastic directional distance function (SDDF) allows for noise in potentially all input and output variables. Yet, when estimated, the direction selected will affect the functional estimates because deviations from the estimated function are minimized in the specified direction. Specifically, the parameters of the parametric SDDF are point identified when the direction is specified; we show that the parameters of the parametric SDDF are set identified when multiple directions are considered. Further, the set of identified parameters can be narrowed via data-driven approaches to restrict the directions considered. We demonstrate a similar narrowing of the identified parameter set for a shape constrained nonparametric method, where the shape constraints impose standard features of a cost function such as monotonicity and convexity.Our Monte Carlo simulation studies reveal significant improvements, as measured by out of sample radial mean squared error, in functional estimates when we use a directional distance function with an appropriately selected direction and the errors are uncorrelated across variables. We show that these benefits increase as the correlation in error terms across variables increase. This correlation is a type of endogeneity that is common in production settings. From our Monte Carlo simulations we conclude that selecting a direction that is approximately orthogonal to the estimated function in the central region of the data gives significantly better estimates relative to the directions commonly used in the literature. For practitioners, our results imply that selecting a direction vector that has non-zero components for all variables that may have measurement error provides a significant improvement in the estimator’s performance. We illustrate these results using cost and production data from samples of approximately 500 US hospitals per year operating in 2007, 2008, and 2009, respectively, and find that the shape constrained nonparametric methods provide a significant increase in flexibility over second order local approximation parametric methods.     

解无约束最优化问题的块共轭方向法

在给出块共轭概念的基础上，提出了适合并行计算的向量组的块共轭化方法，进而得到解无约束最优化问题的并行块共轭方向法．有大量数值结果表明块共轭方向法具有工作量少．适用函数范围广等特点，是一种比较有效的无约束最优化方法．     

Feasible Direction Interior-Point Technique for Nonlinear Optimization

We propose a feasible direction approach for the minimization by interior-point algorithms of a smooth function under smooth equality and inequality constraints. It consists of the iterative solution in the primal and dual variables of the Karush–Kuhn–Tucker first-order optimality conditions. At each iteration, a descent direction is defined by solving a linear system. In a second stage, the linear system is perturbed so as to deflect the descent direction and obtain a feasible descent direction. A line search is then performed to get a new interior point and ensure global convergence. Based on this approach, first-order, Newton, and quasi-Newton algorithms can be obtained. To introduce the method, we consider first the inequality constrained problem and present a globally convergent basic algorithm. Particular first-order and quasi-Newton versions of this algorithm are also stated. Then, equality constraints are included. This method, which is simple to code, does not require the solution of quadratic programs and it is neither a penalty method nor a barrier method. Several practical applications and numerical results show that our method is strong and efficient.     

Parabolic Equations with Changing Direction of Time

Doklady Mathematics - A theorem about the behavior of Cauchy-type integrals at the endpoints of the integration contour and at discontinuity points of the density is stated, and its application to...     

An Extragradient-Based Alternating Direction Method for Convex Minimization

In this paper, we consider the problem of minimizing the sum of two convex functions subject to linear linking constraints. The classical alternating direction type methods usually assume that the two convex functions have relatively easy proximal mappings. However, many problems arising from statistics, image processing and other fields have the structure that while one of the two functions has an easy proximal mapping, the other function is smoothly convex but does not have an easy proximal mapping. Therefore, the classical alternating direction methods cannot be applied. To deal with the difficulty, we propose in this paper an alternating direction method based on extragradients. Under the assumption that the smooth function has a Lipschitz continuous gradient, we prove that the proposed method returns an \(\epsilon \)-optimal solution within \(O(1/\epsilon )\) iterations. We apply the proposed method to solve a new statistical model called fused logistic regression. Our numerical experiments show that the proposed method performs very well when solving the test problems. We also test the performance of the proposed method through solving the lasso problem arising from statistics and compare the result with several existing efficient solvers for this problem; the results are very encouraging.