The Bertini irreducibility theorem for higher codimensional slices

In [3], Poonen and Slavov recently developed a novel approach to Bertini irreducibility theorems over an arbitrary field, based on random hyperplane slicing. In this paper, we extend their work by proving an analogous bound for the dimension of the exceptional locus in the setting of linear subspaces of higher codimensions.     

Comparison of Multivariate Matching Methods: Structures,Distances, and Algorithms

Abstract

A comparison and evaluation is made of recent proposals for multivariate matched sampling in observational studies, where the following three questions are answered: (1) Algorithms: In current statistical practice, matched samples are formed using “nearest available” matching, a greedy algorithm. Greedy matching does not minimize the total distance within matched pairs, though good algorithms exist for optimal matching that do minimize the total distance. How much better is optimal matching than greedy matching? We find that optimal matching is sometimes noticeably better than greedy matching in the sense of producing closely matched pairs, sometimes only marginally better, but it is no better than greedy matching in the sense of producing balanced matched samples. (2) Structures: In common practice, treated units are matched to one control, called pair matching or 1–1 matching, or treated units are matched to two controls, called 1–2 matching, and so on. It is known, however, that the optimal structure is a full matching in which a treated unit may have one or more controls or a control may have one or more treated units. Optimal 1 — k matching is compared to optimal full matching, finding that optimal full matching is often much better. (3) Distances: Matching involves defining a distance between covariate vectors, and several such distances exist. Three recent proposals are compared. Practical advice is summarized in a final section.     

Importance Sampling for p-value Computations in Multivariate Tests

Abstract

An importance sampling procedure is developed to approximate the distribution of an arbitrary function of the eigenvalues for a matrix beta random matrix or a Wishart random matrix. The procedure is easily implemented and provides confidence intervals for the p-values of many of the commonly used test statistics in multivariate analysis. An adaptive procedure allows for the control of either absolute error or relative error in this p-value estimation through the choice of importance sample size.     

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.     

Calibration of the complex matrix effects on the sampling of polycyclic aromatic hydrocarbons in milk samples using solid phase microextraction

Solid phase microextraction (SPME), a simple, fast and promising sampling technique, has been widely used for complex sample analysis. However, complex matrices could modify the absorption property of coatings as well as the uptake kinetics of analytes, eventually biasing the quantification results. In the current study, we demonstrated the feasibility of a developed calibration method for the analysis of polycyclic aromatic hydrocarbons (PAHs) in complex milk samples. Effects of the complex matrices on the SPME sampling process and the sampling conditions were investigated. Results showed that short exposure time (pre-equilibrium SPME, PE-SPME) could increase the lifetime of coatings, and the complex matrices in milk samples could significantly influence the sampling kinetics of SPME. In addition, the optimized sampling time, temperature and dilution factor for PAHs were 10 min, 85 °C and 20, respectively. The obtained LODs and LOQs of all the PAHs were 0.1–0.8 ng/mL and 1.4–4.7 ng/mL, respectively. Furthermore, the accuracy of the proposed PE-SPME method for milk sampling was validated by the recoveries of the studied compounds in two concentration levels, which ranged from 75% to 110% for all the compounds. Finally, the proposed method was applied to the screening of PAHs in milk samples.     

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.     

Physicochemical and Graph Theoretical Descriptors in Developmental Toxicity SAR: A Comparative Study

Abstract

Chemical insults to the developing fetus can lead to growth retardation, malformation, death, and functional deficits. The present study seeks to determine if physicochemical and/or graph theoretical parameters can be used to determine a structure-activity relationship (SAR) for developmental toxicity, and if consistency is observed among the selected features. The biological data utilized consists of a diverse series of compounds evaluated within the Chernoff-Kavlock in vivo mouse assay. Physicochemical parameters calculated correspond to electronic, steric, and transport properties. Graph theoretical parameters calculated include the simple, valence, and kappa indices. Both sets of parameters were independently applied to derive SARs in order to compare the quality of the respective models. Multiple random sampling, without replacement, was utilized to obtain ten training/test partitions. Models were built by linear discriminant analysis, decision trees, and neural networks respectively. Comparisons on identical sets of data were carried out to determine if any of the model building procedures had a significant advantage in terms of predictive performance. Furthermore, comparison of the features selected within and across the model building processes led to the determination of model consistency. Our results indicate that consistent features related to developmental toxicity are observed and that both physicochemical and graph theoretical parameters have equal utility.