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.     

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.     

Genome sequence and analysis of the tuber crop potato

Potato (Solanum tuberosum L.) is the world's most important non-grain food crop and is central to global food security. It is clonally propagated, highly heterozygous, autotetraploid, and suffers acute inbreeding depression. Here we use a homozygous doubled-monoploid potato clone to sequence and assemble 86% of the 844-megabase genome. We predict 39,031 protein-coding genes and present evidence for at least two genome duplication events indicative of a palaeopolyploid origin. As the first genome sequence of an asterid, the potato genome reveals 2,642 genes specific to this large angiosperm clade. We also sequenced a heterozygous diploid clone and show that gene presence/absence variants and other potentially deleterious mutations occur frequently and are a likely cause of inbreeding depression. Gene family expansion, tissue-specific expression and recruitment of genes to new pathways contributed to the evolution of tuber development. The potato genome sequence provides a platform for genetic improvement of this vital crop.     

Intermediates in the transformation of phosphonates to phosphate by bacteria

Phosphorus is an essential element for all known forms of life. In living systems, phosphorus is an integral component of nucleic acids, carbohydrates and phospholipids, where it is incorporated as a derivative of phosphate. However, most Gram-negative bacteria have the capability to use phosphonates as a nutritional source of phosphorus under conditions of phosphate starvation. In these organisms, methylphosphonate is converted to phosphate and methane. In a formal sense, this transformation is a hydrolytic cleavage of a carbon-phosphorus (C-P) bond, but a general enzymatic mechanism for the activation and conversion of alkylphosphonates to phosphate and an alkane has not been elucidated despite much effort for more than two decades. The actual mechanism for C-P bond cleavage is likely to be a radical-based transformation. In Escherichia coli, the catalytic machinery for the C-P lyase reaction has been localized to the phn gene cluster. This operon consists of the 14 genes phnC, phnD, …, phnP. Genetic and biochemical experiments have demonstrated that the genes phnG, phnH, …, phnM encode proteins that are essential for the conversion of phosphonates to phosphate and that the proteins encoded by the other genes in the operon have auxiliary functions. There are no functional annotations for any of the seven proteins considered essential for C-P bond cleavage. Here we show that methylphosphonate reacts with MgATP to form α-D-ribose-1-methylphosphonate-5-triphosphate (RPnTP) and adenine. The triphosphate moiety of RPnTP is hydrolysed to pyrophosphate and α-D-ribose-1-methylphosphonate-5-phosphate (PRPn). The C-P bond of PRPn is subsequently cleaved in a radical-based reaction producing α-D-ribose-1,2-cyclic-phosphate-5-phosphate and methane in the presence of S-adenosyl-L-methionine. Substantial quantities of phosphonates are produced worldwide for industrial processes, detergents, herbicides and pharmaceuticals. Our elucidation of the chemical steps for the biodegradation of alkylphosphonates shows how these compounds can be metabolized and recycled to phosphate.