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.     

Experimental validation of inter-subspecific genetic diversity in rice represented by the differences between the DNA sequences of ‘Nipponbare’ and ‘93-11’

The pedigrees of three sequenced rice cultivars were analyzed to show that a majority of the genetic composition of 'Nipponbare' originates from japonica cultivars while the minority originates from indica cultivars. In contrast, '93-11' is derived mainly from indica cultivars with a smaller contribution from japonica cultivars. All ancestors of 'Guang lu ai 4' appeared to be indica lines. A set of molecular markers (46 InDels and 53 SSRs) polymorphic between 'Nipponbare' and '93-11' were examined in 46 typical indica and 47 typical japonica cultivars selected from 443 accessions according to Cheng's index. All cultivars were divided into indica and japonica groups without overlapping when clustered by Cheng's index, InDels and SSRs. Much higher InDel and SSR diversity between groups than within groups implies that the marker polymorphisms between 'Nipponbare' and '93-11' represent a large proportion of inter-subspecific diversity. About 85% of indica cultivars and more than 90% of japonica cultivars were confirmed to have the same PCR banding patterns as '93-11' and 'Nipponbare', respectively. Some polymorphic loci between 'Nipponbare' and '93-11' cannot be validated in other indica and japonica cultivars, either as subspecies-specific but not predominant alleles, or alleles not specific between the two groups. It was concluded that molecular markers developed from sequence polymorphism between 'Nipponbare' and '93-11' often represent inter-subspecific diversity, although some exceptions were sensitive to either particular marker loci or particular cultivars.     

An endoribonuclease-prepared siRNA screen in human cells identifies genes essential for cell division

RNA interference (RNAi) is an evolutionarily conserved defence mechanism whereby genes are specifically silenced through degradation of messenger RNAs; this process is mediated by homologous double-stranded (ds)RNA molecules. In invertebrates, long dsRNAs have been used for genome-wide screens and have provided insights into gene functions. Because long dsRNA triggers a nonspecific interferon response in many vertebrates, short interfering (si)RNA or short hairpin (sh)RNAs must be used for these organisms to ensure specific gene silencing. Here we report the generation of a genome-scale library of endoribonuclease-prepared short interfering (esi)RNAs from a sequence-verified complementary DNA collection representing 15,497 human genes. We used 5,305 esiRNAs from this library to screen for genes required for cell division in HeLa cells. Using a primary high-throughput cell viability screen followed by a secondary high content videomicroscopy assay, we identified 37 genes required for cell division. These include several splicing factors for which knockdown generates mitotic spindle defects. In addition, a putative nuclear-export terminator was found to speed up cell proliferation and mitotic progression after knockdown. Thus, our study uncovers new aspects of cell division and establishes esiRNA as a versatile approach for genomic RNAi screens in mammalian cells.     

Enhancements of energetic particles near the heliospheric termination shock

The spacecraft Voyager 1 is at a distance greater than 85 au from the Sun, in the vicinity of the termination shock that marks the abrupt slowing of the supersonic solar wind and the beginning of the extended and unexplored distant heliosphere. This shock is expected to accelerate 'anomalous cosmic rays', as well as to re-accelerate Galactic cosmic rays and low-energy particles from the inner Solar System. Here we report a significant increase in the numbers of energetic ions and electrons that persisted for seven months beginning in mid-2002. This increase differs from any previously observed in that there was a simultaneous increase in Galactic cosmic ray ions and electrons, anomalous cosmic rays and low-energy ions. The low-intensity level and spectral energy distribution of the anomalous cosmic rays, however, indicates that Voyager 1 still has not reached the termination shock. Rather, the observed increase is an expected precursor event. We argue that the radial anisotropy of the cosmic rays is expected to be small in the foreshock region, as is observed.     

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.     

Senescence surveillance of pre-malignant hepatocytes limits liver cancer development

Upon the aberrant activation of oncogenes, normal cells can enter the cellular senescence program, a state of stable cell-cycle arrest, which represents an important barrier against tumour development in vivo. Senescent cells communicate with their environment by secreting various cytokines and growth factors, and it was reported that this 'secretory phenotype' can have pro- as well as anti-tumorigenic effects. Here we show that oncogene-induced senescence occurs in otherwise normal murine hepatocytes in vivo. Pre-malignant senescent hepatocytes secrete chemo- and cytokines and are subject to immune-mediated clearance (designated as 'senescence surveillance'), which depends on an intact CD4(+) T-cell-mediated adaptive immune response. Impaired immune surveillance of pre-malignant senescent hepatocytes results in the development of murine hepatocellular carcinomas (HCCs), thus showing that senescence surveillance is important for tumour suppression in vivo. In accordance with these observations, ras-specific Th1 lymphocytes could be detected in mice, in which oncogene-induced senescence had been triggered by hepatic expression of Nras(G12V). We also found that CD4(+) T cells require monocytes/macrophages to execute the clearance of senescent hepatocytes. Our study indicates that senescence surveillance represents an important extrinsic component of the senescence anti-tumour barrier, and illustrates how the cellular senescence program is involved in tumour immune surveillance by mounting specific immune responses against antigens expressed in pre-malignant senescent cells.