Recursive partition and amalgamation with the exponential family: Theory and applications

The theory of tree-growing (RECPAM approach) is developed for outcome variables which are distributed as the canonical exponential family. The general RECPAM approach (consisting of three steps: recursive partition, pruning and amalgamation), is reviewed. This is seen as constructing a partition with maximal information content about a parameter to be predicted, followed by simplification by the elimination of ‘negligible’ information. The measure of information is defined for an exponential family outcome as a deviance difference, and appropriate modifications of pruning and amalgamation rules are discussed. It is further shown how the proposed approach makes it possible to develop tree-growing for situations usually treated by generalized linear models (GLIM). In particular, Poisson and logistic regression can be tree-structured. Moreover, censored survival data can be treated, as in GLIM, by observing a formal equivalence of the likelihood under random censoring and an appropriate Poisson model. Three examples are given of application to Poisson, binary and censored survival data.     

Sulfate Ions in Titania Polymorphs

Sol-gel titania was sulfated by using sulfuric acid as hydrolysis catalyst, or by impregnating with ammonium sulfate fresh samples prepared with nitric acid or ammonium hydroxide as hydrolysis catalyst. Samples were characterized with X-ray powder diffraction, infrared spectroscopy, thermogravimetry and atomic absorption spectroscopy. Sulfate ions were found anchored to brookite and anatase phases, because they have short O—O atomic bond lengths slightly larger than the largest O—O bond length of sulfate ion. Since the shortest O—O atomic bond in anatase is smaller than the one in brookite, the sulfate ions are then less deformed when they are anchored to anatase, and consequently more stable. Therefore when the sample temperature is raised, the brookite with sulfate ions was transformed mainly to anatase and not into rutile, which is the most probably transformation when these ions are not involved. Sulfate ions also hindered anatase and brookite crystallite growing and stabilized the crystalline structure of anatase. When the sulfate ions are lost the crystalline anatase phase is transformed into rutile, leaving a large number of vacancies that favored atom diffusion and consequently the growing of rutile crystallites. The crystalline evolution of the samples as a function of the annealing temperature is almost independent of the sulfating method.     

Reactions of fullerene C60 with methyl methacrylate radicals: A density functional theory study

We have investigated the stepwise addition of four growing methyl methacrylate (MMA) radicals to C₆₀ fullerene, taking into account all possible types of the formed adducts. This reaction set is a reliable approximation for understanding the MMA polymerization process in the presence of C₆₀ fullerene. We have analyzed the structures of the fullerene-MMA adducts and energy parameters of their formation (heat effects and activation enthalpies). We found that up to three MMA growing radicals are favorably attached to C₆₀ as the fullerene-MMA trisadduct is a stable radical of the allyl type. It is inactive for further radical addition, and the elimination of the hydrogen atom from the growing MMA radical becomes preferable. The effects of steric factors and structures of the products of multiple growing MMA radical additions to C₆₀ on the radical polymerization of MMA in the presence of C₆₀ fullerene are considered.     

On Generating Discrete Orthogonal Bivariate Polynomials

In this paper we present an algorithm for recursively generating orthogonal bivariate polynomials on a discrete set S ². For this purpose we employ commuting pairs of real symmetric matrices H, K ^n×n to obtain, in a certain sense, a two dimensional Hermitian Lanczos method. The resulting algorithm relies on a recurrence having a slowly growing length. Practical implementation issues an applications are considered. The method can be generalized to compute orthogonal polynomials depending on an arbitrary number of variables.     

Reliable and efficient reaction path and transition state finding for surface reactions with the growing string method

The computational challenge of fast and reliable transition state and reaction path optimization requires new methodological strategies to maintain low cost, high accuracy, and systematic searching capabilities. The growing string method using internal coordinates has proven to be highly effective for the study of molecular, gas phase reactions, but difficulties in choosing a suitable coordinate system for periodic systems has prevented its use for surface chemistry. New developments are therefore needed, and presented herein, to handle surface reactions which include atoms with large coordination numbers that cannot be treated using standard internal coordinates. The double‐ended and single‐ended growing string methods are implemented using a hybrid coordinate system, then benchmarked for a test set of 43 elementary reactions occurring on surfaces. These results show that the growing string method is at least 45% faster than the widely used climbing image‐nudged elastic band method, which also fails to converge in several of the test cases. Additionally, the surface growing string method has a unique single‐ended search method which can move outward from an initial structure to find the intermediates, transition states, and reaction paths simultaneously. This powerful explorative feature of single ended‐growing string method is demonstrated to uncover, for the first time, the mechanism for atomic layer deposition of TiN on Cu(111) surface. This reaction is found to proceed through multiple hydrogen‐transfer and ligand‐exchange events, while formation of H‐bonds stabilizes intermediates of the reaction. Purging gaseous products out of the reaction environment is the driving force for these reactions. © 2017 Wiley Periodicals, Inc.     

Higher order asymptotic solution of mode I crack growth in elastic-perfectly plastic media

A higher order asymptotic solution of near-tip field is studied for plane-atrain Mode-I quasi-static steady crack growth in the incompressible (v=1/2) elastic perfectly-plastic media. The results show that the near-tip stress and strain are fully continuous, and the strain possesses In (A/r) singularity at the crack tip. The expressions of the stress, strain and velocity in each region are also given. The project supported by National Natural Science Foundation of China     

A fast and efficient mesh segmentation method based on improved region growing

Mesh segmentation is one of the important issues in digital geometry processing. Region growing method has been proven to be a efficient method for 3D mesh segmentation. However, in mesh segmentation, feature line extraction algorithm is computationally costly, and the over-segmentation problem still exists during region merging processing. In order to tackle these problems, a fast and efficient mesh segmentation method based on improved region growing is proposed in this paper. Firstly, the dihedral angle of each non-boundary edge is defined and computed simply, then the sharp edges are detected and feature lines are extracted. After region growing process is finished, an improved region merging method will be performed in two steps by considering some geometric criteria. The experiment results show the feature line extraction algorithm can obtain the same geometric information fast with less computational costs and the improved region merging method can solve over-segmentation well.     

陕甘宁革命老区生态系统服务价值时空分异及影响因素研究

陕甘宁革命老区是黄土高原和黄河中上游的重点生态治理区,作为重要的生态屏障区,其生态治理意义重大。以陕甘宁革命老区为研究区域,基于改进的生态系统服务价值（ecosystem service value,ESV）当量因子法,利用地理探测器及地理加权回归（geographically weighted regression,GWR）模型,分析1995—2018年各县ESV时空变化特征、影响因素及各主导因素作用强度的空间分异特征。结果表明：（1）1995—2018年,陕甘宁革命老区ESV呈先下降后上升的特征,整体呈上升趋势,草地与林地对该区域ESV的贡献较大;（2）ESV空间等级转化呈现较显著的两极变化趋势,其中低级、高级ESV区域面积显著扩张,较高级ESV区域面积明显缩减;（3）地被覆盖度、人口密度、垦殖系数是ESV空间分异的主导因素,平均空间解释力超过0.378 0,自然、社会、经济因素间的交互协同增强了其对陕甘宁革命老区ESV的影响程度;（4）各主导因素对ESV的影响程度表现出空间异质性,其中地被覆盖度及垦殖系数的影响程度由东向西递减,人均GDP和人口密度的影响程度则由西向东递减。     

On the stability of two new two-step explicit methods for the numerical integration of second order initial value problem on a variable mesh

We present two novel two-step explicit methods for the numerical solution of the second order initial value problem on a variable mesh. In the case of a constant mesh the method is superstable in the sense of Chawla (1985). Numerical experimentation is provided to verify the stability analysis.     

区域稳定动力学研究(二)——基本原则

区域稳定动力学是一个多源、多层次、多子系统、多影响因素的复合动力学系统, 本文提出了研究这一复合动力学系统的六个基本原则, 即连续性原则、立体性原则、系统性原则、非线性原则、动态性原则及工程实用原则。