Random Variable Generation Using Concavity Properties of Transformed Densities

Abstract

Algorithms are developed for constructing random variable generators for families of densities. The generators depend on the concavity structure of a transformation of the density. The resulting algorithms are rejection algorithms and the methods of this article are concerned with constructing good rejection algorithms for general densities.     

Predicting USCS soil classification from soil property variables using Random Forest

Soil classification systems are widely used for quickly and easily summarizing soil properties and provide a shorthand method of communication between scientists, engineers, and end-users. Two of the most widely used soil classification systems are the United States Department of Agriculture (USDA) textural soil classification system and the Unified Soil Classification System (USCS). Unfortunately, not all soil map units are classified according to the USDA or USCS systems, and previous attempts to provide a crosswalk table have been inconsistent. Random Forest machine learning model was used to create a USCS prediction model using USDA soil property variables. Important variables for predicting USCS code from available soil properties were USDA soil textures, percent organic material, and available water storage. Prediction error rates less than 2% were achieved compared to error rates of approximately 40% using crosswalk methods.     

A note on random walks with absorbing barriers and sequential Monte Carlo methods

In this article, we consider importance sampling (IS) and sequential Monte Carlo (SMC) methods in the context of one-dimensional random walks with absorbing barriers. In particular, we develop a very precise variance analysis for several IS and SMC procedures. We take advantage of some explicit spectral formulae available for these models to derive sharp and explicit estimates; this provides stability properties of the associated normalized Feynman–Kac semigroups. Our analysis allows one to compare the variance of SMC and IS techniques for these models. The work in this article is one of the few to consider an in-depth analysis of an SMC method for a particular model-type as well as variance comparison of SMC algorithms.     

Semiclassical matrix model for quantum chaotic transport with time-reversal symmetry

We show that the semiclassical approach to chaotic quantum transport in the presence of time-reversal symmetry can be described by a matrix model. In other words, we construct a matrix integral whose perturbative expansion satisfies the semiclassical diagrammatic rules for the calculation of transport statistics. One of the virtues of this approach is that it leads very naturally to the semiclassical derivation of universal predictions from random matrix theory.     

Random Copolymers of 1,5-Dioxepan-2-one

ABSTRACT

Copolymers of 1,5-dioxepan-2-one (DXO) and e-caprolactone (?-CL), δ-valerolactone (δ-VL) or L-lactide (LLA) have been synthesized and characterized. High molecular weight copolymers were obtained using stannous-2-ethyl hexanoate as catalyst in bulk. Reactivity ratios for the copolymerization of DXO and δ-VL were determined at 110°C as r_VL=0.5 and r_DXO=2.3. At high conversion, depolymerization of δ-VL occurred, resulting in lower molecular weight and variations in the copolymer composition.

Physical properties, such as crystallinity and melting temperature of the DXO-copolymers proved to be strongly dependent on the choice of comonomer and on the molar composition of the copolymers. DXO appears to be incorporated into the poly-?-caprolactone (PCL) crystals and to some extent into the poly-δ-valerolactone (PVL) crystals, resulting in a more gradual decrease in crystallinity with increasing amount of DXO.     

Search of truncation of (N−1) electron basis containing full connected triple excitations in computing main and satellite ionization potentials via Fock‐space coupled cluster approach

A valence‐universal multireference coupled cluster (VUMRCC) theory, realized via the eigenvalue independent partitioning (EIP) route, has been implemented with full inclusion of triples excitations for computing and analyzing the entire main and several satellite peaks in the ionization potential spectra of several molecules. The EIP‐VUMRCC method, unlike the traditional VUMRCC theory, allows divergence‐free homing‐in to satellite roots which would otherwise have been plagued by intruders, and is thus numerically more robust to obtain more efficient and dependable computational schemes allowing more extensive use of the approach. The computed ionization potentials (IPs) as a result of truncation of the (N−1) electron basis manifold involving virtual functions such as 2h‐p and 3h‐2p by different energy thresholds varying from 5 to 15 a.u. with 1 a.u. intervals as well as thresholds such as 20, 25, and 30 a.u. have been carefully looked into. Cutoff at around 25 a.u. turns out to be an optimal threshold. Molecules such as C₂H₄ and C₂H₂ (X = D,T), and N₂ and CO (X = D,T,Q) with Dunning's cc‐pVXZ bases have been investigated to determine all main and 2h‐p shake‐up and 3h‐2p double shake‐up satellite IPs. We believe that the present work will pave the way to a wider application of the method by providing main and satellite IPs for some problematic N‐electron closed shell systems. © 2013 Wiley Periodicals, Inc.     

R3中一类Kirchhoff型方程变号解的存在性及集中性

本文研究了一类Kirchhoff型方程。利用极大极小原理及惩罚函数方法,证明了上述方程变号解的存在性及集中性,我们的结果推广了文献[4]的结果。     

An analysis of cross-correlations in an emerging market

We apply random matrix theory to compare correlation matrix estimators C$C$ obtained from emerging market data. The correlation matrices are constructed from 10 years of daily data for stocks listed on the Johannesburg stock exchange (JSE) from January 1993 to December 2002. We test the spectral properties of C$C$ against random matrix predictions and find some agreement between the distributions of eigenvalues, nearest neighbour spacings, distributions of eigenvector components and the inverse participation ratios for eigenvectors. We show that interpolating both missing data and illiquid trading days with a zero-order hold increases agreement with RMT predictions. For the more realistic estimation of correlations in an emerging market, we suggest a pairwise measured-data correlation matrix. For the data set used, this approach suggests greater temporal stability for the leading eigenvectors. An interpretation of eigenvectors in terms of trading strategies is given, as opposed to classification by economic sectors.     

确定性矩阵可分离压缩成像

针对可分离压缩传感使用的可分离随机正交矩阵在处理大尺度图像等高维信号感知时难度太大或成本过高的问题,引入确定性测量矩阵,提出确定性矩阵可分离压缩传感,可将如托普利兹矩阵及循环矩阵等具有确定性结构的矩阵作为可分离压缩传感的左、右可分离矩阵.该方案可以降低独立元素的数目,从而显著降低前端物理实现的难度与成本.数值模拟实验分别评估了该方法在不同采样率及不同图像尺寸下的压缩重建性能,结果表明该方法在独立元素非常少的情形下得到与原随机正交矩阵相近的重建质量,证明了其可行性.