3 resultados para Natural Numbers

em Université de Lausanne, Switzerland


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Fraud is as old as Mankind. There are an enormous number of historical documents which show the interaction between truth and untruth; therefore it is not really surprising that the prevalence of publication discrepancies is increasing. More surprising is that new cases especially in the medical field generate such a huge astonishment. In financial mathematics a statistical tool for detection of fraud is known which uses the knowledge of Newcomb and Benford regarding the distribution of natural numbers. This distribution is not equal and lower numbers are more likely to be detected compared to higher ones. In this investigation all numbers contained in the blinded abstracts of the 2009 annual meeting of the Swiss Society of Anesthesia and Resuscitation (SGAR) were recorded and analyzed regarding the distribution. A manipulated abstract was also included in the investigation. The χ(2)-test was used to determine statistical differences between expected and observed counts of numbers. There was also a faked abstract integrated in the investigation. A p<0.05 was considered significant. The distribution of the 1,800 numbers in the 77 submitted abstracts followed Benford's law. The manipulated abstract was detected by statistical means (difference in expected versus observed p<0.05). Statistics cannot prove whether the content is true or not but can give some serious hints to look into the details in such conspicuous material. These are the first results of a test for the distribution of numbers presented in medical research.

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An unusual subset of mature T cells expresses natural killer (NK) cell-related surface markers such as interleukin-2 receptor beta (IL-2R beta; CD122) and the polymorphic antigen NK1.1. These "NK-like" T cells are distinguished by their highly skewed V alpha and V beta repertoire and by their ability to rapidly produce large amounts of IL-4 upon T cell receptor (TCR) engagement. The inbred mouse strain SJL (which expresses NK1.1 on its NK cells) has recently been reported to lack NK1.1+ T cells and consequently to be deficient in IL-4 production upon TCR stimulation. We show here, however, that SJL mice have normal numbers of IL-2R beta+ T cells with a skewed V beta repertoire characteristic of "NK-like" T cells. Furthermore lack of NK1.1 expression on IL-2R beta+ T cells in SJL mice was found by backcross analysis to be controlled by a single recessive gene closely linked to the NKR-P1 complex on chromosome 6 (which encodes the NK1.1 antigen). Analysis of a panel of inbred mouse strains further demonstrated that lack of NK1.1 expression on IL-2R beta+ T cells segregated with NKR-P1 genotype (as assessed by restriction fragment length polymorphism) and thus was not restricted to the SJL strain. In contrast, defective TCR induced IL-4 production (which appeared to be a unique property of SJL mice) seems to be controlled by two recessive genes unlinked to NKR-P1. Collectively, our data indicate that "NK-like" T cells develop normally in SJL mice despite genetically distinct defects in NK1.1 expression and inducible IL-4 production.

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The principal objective of the knot theory is to provide a simple way of classifying and ordering all the knot types. Here, we propose a natural classification of knots based on their intrinsic position in the knot space that is defined by the set of knots to which a given knot can be converted by individual intersegmental passages. In addition, we characterize various knots using a set of simple quantum numbers that can be determined upon inspection of minimal crossing diagram of a knot. These numbers include: crossing number; average three-dimensional writhe; number of topological domains; and the average relaxation value