Number crunching vs. number theory: computers and FLT,from Kummer to SWAC (1850–1960), and beyond

The present article discusses the computational tools (both conceptual and material) used in various attempts to deal with individual cases of FLT, as well as the changing historical contexts in which these tools were developed and used, and affected research. It also explores the changing conceptions about the role of computations within the overall disciplinary picture of number theory, how they influenced research on the theorem, and the kinds of general insights thus achieved. After an overview of Kummer’s contributions and its immediate influence, I present work that favored intensive computations of particular cases of FLT as a legitimate, fruitful, and worth-pursuing number-theoretical endeavor, and that were part of a coherent and active, but essentially low-profile tradition within nineteenth century number theory. This work was related to table making activity that was encouraged by institutions and individuals whose motivations came mainly from applied mathematics, astronomy, and engineering, and seldom from number theory proper. A main section of the article is devoted to the fruitful collaboration between Harry S. Vandiver and Emma and Dick Lehmer. I show how their early work led to the hesitant introduction of electronic computers for research related with FLT. Their joint work became a milestone for computer-assisted activity in number theory at large.     

Mutations in the gene encoding the 3'-5' DNA exonuclease TREX1 cause Aicardi-Goutières syndrome at the AGS1 locus

Aicardi-Goutières syndrome (AGS) presents as a severe neurological brain disease and is a genetic mimic of the sequelae of transplacentally acquired viral infection. Evidence exists for a perturbation of innate immunity as a primary pathogenic event in the disease phenotype. Here, we show that TREX1, encoding the major mammalian 3' --> 5' DNA exonuclease, is the AGS1 gene, and AGS-causing mutations result in abrogation of TREX1 enzyme activity. Similar loss of function in the Trex1(-/-) mouse leads to an inflammatory phenotype. Our findings suggest an unanticipated role for TREX1 in processing or clearing anomalous DNA structures, failure of which results in the triggering of an abnormal innate immune response.     

近世代数与数学结构的起源：修订第二版

数学结构是20世纪数学中最具普遍性的一个概念。本书论述了这个概念的起源和产生过程的两个阶段，探讨了它在数学发展中的意义和作用。     

非均匀光照下人脸眼睛的定位方法

考虑非均匀光照下人脸眼睛的检测问题，提出了一种利用高频信息模板匹配方法从复杂图像中定位人脸眼睛的方法。选取80幅光线较好的人脸图像，对它们做光线规范化，提取Gabor高频特征，构造模板。利用统计模式识别的原理，在眼睛的大致区域进行模板匹配，突出眉毛与眼睛这一整体的大致位置，然后进行二值投影，最终确定人眼的准确位置。大量实验表明，该算法具有很高的精度和很强的鲁棒性。     

A centrosomal mechanism involving CDK5RAP2 and CENPJ controls brain size

Autosomal recessive primary microcephaly is a potential model in which to research genes involved in human brain growth. We show that two forms of the disorder result from homozygous mutations in the genes CDK5RAP2 and CENPJ. We found neuroepithelial expression of the genes during prenatal neurogenesis and protein localization to the spindle poles of mitotic cells, suggesting that a centrosomal mechanism controls neuron number in the developing mammalian brain.     

Mechanisms of valence selectivity in biological ion channels

Transmembrane ion channels play a crucial role in the existence of all living organisms. They partition the exterior from the interior of the cell, maintain the proper ionic gradient across the cell membrane and facilitate signaling between cells. To perform these functions, ion channels must be highly selective, allowing some types of ions to pass while blocking the passage of others. Here we review a number of studies that have helped to elucidate the mechanisms by which ion channels discriminate between ions of differing charge, focusing on four channel families as examples: gramicidin, ClC chloride, voltage-gated calcium and potassium channels. The recent availability of high-resolution structural data has meant that the specific inter-atomic interactions responsible for valence selectivity can be pinpointed. Not surprisingly, electrostatic considerations have been shown to play an important role in ion specificity, although many details of the origins of this discrimination remain to be determined. Received 4 September 2005; received after revision 17 October 2005; accepted 2 November 2005