On the Foundations of Constructive Mathematics – Especially in Relation to the Theory of Continuous Functions

We discuss the foundations of constructive mathematics, including recursive mathematics and intuitionism, in relation to classical mathematics. There are connections with the foundations of physics, due to the way in which the different branches of mathematics reflect reality. Many different axioms and their interrelationship are discussed. We show that there is a fundamental problem in BISH (Bishop’s school of constructive mathematics) with regard to its current definition of ‘continuous function’. This problem is closely related to the definition in BISH of ‘locally compact’. Possible approaches to this problem are discussed. Topology seems to be a key to understanding many issues. We offer several new simplifying axioms, which can form bridges between the various branches of constructive mathematics and classical mathematics (‘reuniting the antipodes’). We give a simplification of basic intuitionistic theory, especially with regard to so-called ‘bar induction’. We then plead for a limited number of axiomatic systems, which differentiate between the various branches of mathematics. Finally, in the appendix we offer BISH an elegant topological definition of ‘locally compact’, which unlike the current definition is equivalent to the usual classical and/or intuitionistic definition in classical and intuitionistic mathematics, respectively.     

Error rates in quadratic discrimination with constraints on the covariance matrices

In multivariate discrimination of several normal populations, the optimal classification procedure is based on quadratic discriminant functions. We compare expected error rates of the quadratic classification procedure if the covariance matrices are estimated under the following four models: (i) arbitrary covariance matrices, (ii) common principal components, (iii) proportional covariance matrices, and (iv) identical covariance matrices. Using Monte Carlo simulation to estimate expected error rates, we study the performance of the four discrimination procedures for five different parameter setups corresponding to standard situations that have been used in the literature. The procedures are examined for sample sizes ranging from 10 to 60, and for two to four groups. Our results quantify the extent to which a parsimonious method reduces error rates, and demonstrate that choosing a simple method of discrimination is often beneficial even if the underlying model assumptions are wrong.The authors wish to thank the editor and three referees for their helpful comments on the first draft of this article. M. J. Schmid supported by grants no. 2.724-0.85 and 2.038-0.86 of the Swiss National Science Foundation.     

近红外光谱技术鉴别海面溢油

近红外光谱技术分析速度快、效率高、成本低、重现性好,典型的无损分析;主要用于样品类别鉴定和纯度检验.近红外光谱技术结合模式识别方法,在纯品油种类的鉴别中已得到成功应用[1,2],本实验室也初步建立了纯品油近红外谱图数据库[3],但该法在实际海面溢油样品的鉴别中应用仍甚少.     

Antioxidant survey to assess antagonism to redox stress using a prokaryotic and an eukaryotic system

Using a prokaryote (Escherichia coli) and a metazoa-resembling eukaryote (Ochromonas danica), we surveyed antioxidants which might overcome redox stress imposed by menadione sodium bisulphite (MD) and buthionine sulphoximine (BSO). BSO oxidant stress was evident only inO. danica; MD oxidant stress was evident in both organisms. Glutathione, its precursors, e.g. cysteine, homocysteine, and 2-oxo-4-thiazolidine carboxylic acid, and red blood cells, emerged as prime antioxidants for relieving BSO and MD oxidant stress. BSO and MD oxidant activity and antioxidant-annulling effect inO. danica were judged comparable to those found in animal cells whereas the resultsE. coli were not entirely equivalent. TheO. danica system emerged as a practical, rapid, and useful system for pinpointing oxidant stressors and antioxidants, and shows promise for studies with mammalian systems.     

Cell-free expression and in meso crystallisation of an integral membrane kinase for structure determination

Membrane proteins are key elements in cell physiology and drug targeting, but getting a high-resolution structure by crystallographic means is still enormously challenging. Novel strategies are in big demand to facilitate the structure determination process that will ultimately hasten the day when sequence information alone can provide a three-dimensional model. Cell-free or in vitro expression enables rapid access to large quantities of high-quality membrane proteins suitable for an array of applications. Despite its impressive efficiency, to date only two membrane proteins produced by the in vitro approach have yielded crystal structures. Here, we have analysed synergies of cell-free expression and crystallisation in lipid mesophases for generating an X-ray structure of the integral membrane enzyme diacylglycerol kinase to 2.28-Å resolution. The quality of cellular and cell-free-expressed kinase samples has been evaluated systematically by comparing (1) spectroscopic properties, (2) purity and oligomer formation, (3) lipid content and (4) functionality. DgkA is the first membrane enzyme crystallised based on cell-free expression. The study provides a basic standard for the crystallisation of cell-free-expressed membrane proteins and the methods detailed here should prove generally useful and contribute to accelerating the pace at which membrane protein structures are solved.     

Signal Diffusion Mapping: Optimal Forecasting with Time‐Varying Lags

We introduce a new methodology for forecasting, which we call signal diffusion mapping. Our approach accommodates features of real‐world financial data which have been ignored historically in existing forecasting methodologies. Our method builds upon well‐established and accepted methods from other areas of statistical analysis. We develop and adapt those models for use in forecasting. We also present tests of our model on data in which we demonstrate the efficacy of our approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Infection of young Douglas-firs by dwarf mistletoe in the Southwest

Studies in several areas in Arizona and New Mexico show that dwarf mistletoe ( Arceuthobium douglasii ) is rare in young Douglas-firs growing under infected overstories. Less than 5% of the Douglas-firs under 26 years old and less than 6% of those under 1.4m tall were infected in 77 mistletoe-infested stands. Both percent infection and mean dwarf mistletoe rating of young Douglas-firs increased as tree age, height, and stand dwarf mistletoe ratings increased.