Lexical Scope and Statistical Computing

Abstract

Programming environments such as S and Lisp-Stat have languages for performing computations, data storage mechanisms, and a graphical interface. These languages provide an interactive interface to data analysis that is invaluable. To take full advantage of these programming environments, statisticians must understand the differences between them. Ihaka and Gentleman introduced R, a version of S which uses a different scoping regimen. In some ways this makes R behave more like Lisp-Stat. This article discusses the concept of scoping rules and shows how lexical scope can enhance the functionality of a language.     

凸集的广义Reuleaux三角形

常宽凸集的面积最小者为Reulaux三角形，而非常宽凸集的面积最小者为何呢？它就是本文将给出的广义Reuleaux三角形△R。     

The hilbert function and the minimal free resolution of some gorenstein ideals of codimension 4

We give a construction for Gorenstein ideals of codimension 4 which we believe have maximal graded Betti numbers for their Hilbert function.     

A Localized Implementation of the Iterative Proportional Scaling Procedure for Gaussian Graphical Models

In this article, we propose localized implementations of the iterative proportional scaling (IPS) procedure by the strategy of partitioning cliques for computing maximum likelihood estimations in large Gaussian graphical models. We first divide the set of cliques into several nonoverlapping and nonempty blocks, and then adjust clique marginals in each block locally. Thus, high-order matrix operations can be avoided and the IPS procedure is accelerated. We modify the Swendsen–Wang Algorithm and apply the simulated annealing algorithm to find an approximation to the optimal partition which leads to the least complexity. This strategy of partitioning cliques can also speed up the existing IIPS and IHT procedures. Numerical experiments are presented to demonstrate the competitive performance of our new implementations and strategies.     

Generalizations of a Theorem of Datko and Pazy

This note gives necessary and sufficient conditions for exponential stability of semigroups of linear operators in Banach spaces. Generalizations of a well-known result due to Datko, Pazy and Neerven are obtained for the case of semigroups of operators that are not strongly continuous.     

区间直觉模糊数的新得分函数及其在多属性决策中的应用

通过对区间直觉模糊数的犹豫区间进行讨论,提出了区间直觉模糊数的新得分函数和精确函数,并讨论新的得分函数具有的性质,在此基础上给出了区间直觉模糊数的一种新的排序方法.进而,结合区间直觉模糊加权平均算子给出了属性值为区间直觉模糊数的多属性决策方法,并通过算例阐明该方法的可行性和有效性.     

An oriented coloring of planar graphs with girth at least five

An oriented k-coloring of an oriented graph G is a homomorphism from G to an oriented graph H of order k. We prove that every oriented graph with a maximum average degree less than and girth at least 5 has an oriented chromatic number at most 16. This implies that every oriented planar graph with girth at least 5 has an oriented chromatic number at most 16, that improves the previous known bound of 19 due to Borodin et al. [O.V. Borodin, A.V. Kostochka, J. Nešet?il, A. Raspaud, É. Sopena, On the maximum average degree and the oriented chromatic number of a graph, Discrete Math. 206 (1999) 77-89].     

Gradient type noises II - Systems of stochastic partial differential equations

The present paper is the second and main part of a study of partial differential equations under the influence of noisy perturbations. Existence and uniqueness of function solutions in the mild sense are obtained for a class of deterministic linear and semilinear parabolic boundary initial value problems. If the noise data are random, the results may be seen as a pathwise approach to SPDE's. For typical examples, such as spatially one-dimensional stochastic heat equations with additive or multiplicative perturbations of fractional Brownian type, we recover and extend known results. In addition, we propose to consider partial noises of low order.     

Lie symmetries of soliton equations with self-consistent sources via source generation procedure

In this paper, the ‘source generation’ procedure (SGP) proposed by Hu and Wang [X.B. Hu, H.Y. Wang, Construction of dKP and BKP equation with self-consistent sources, Inverse Problems 22 (2006) 1903-1920] is utilized to derive Lie symmetries of bilinear soliton equations with self-consistent sources (SESCS) such as KPESCS, BKPESCS, and differential-difference KPESCS. Furthermore, it is shown that these Lie symmetries constitute generators of the corresponding Lie symmetry algebras.     

Average size of -Selmer groups of elliptic curves, I

In this paper, we study a class of elliptic curves over with -torsion group , and prove that the average order of the -Selmer groups is bounded.