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.     

Carbon emissions. The economic benefits of the Kyoto Protocol

The third Conference of the Parties in Kyoto set the target of reducing greenhouse-gas emissions by an average of 5.3% with respect to 1990 values by 2008-2012. One of the main objections to the protocol's ratification is that compliance would pose an unbearable economic burden on the countries involved. But we show here that this is not the case if costs apart from the direct costs of energy production are also considered. Costs are also incurred in rectifying damage to human health, material goods, agriculture and the environment related to greenhouse-gas emissions.     

Genome-wide association study identifies susceptibility loci for open angle glaucoma at TMCO1 and CDKN2B-AS1

We report a genome-wide association study for open-angle glaucoma (OAG) blindness using a discovery cohort of 590 individuals with severe visual field loss (cases) and 3,956 controls. We identified associated loci at TMCO1 (rs4656461[G] odds ratio (OR) = 1.68, P = 6.1 × 10(-10)) and CDKN2B-AS1 (rs4977756[A] OR = 1.50, P = 4.7 × 10(-9)). We replicated these associations in an independent cohort of cases with advanced OAG (rs4656461 P = 0.010; rs4977756 P = 0.042) and two additional cohorts of less severe OAG (rs4656461 combined discovery and replication P = 6.00 × 10(-14), OR = 1.51, 95% CI 1.35-1.68; rs4977756 combined P = 1.35 × 10(-14), OR = 1.39, 95% CI 1.28-1.51). We show retinal expression of genes at both loci in human ocular tissues. We also show that CDKN2A and CDKN2B are upregulated in the retina of a rat model of glaucoma.     

Orbital Kondo effect in carbon nanotubes

Progress in the fabrication of nanometre-scale electronic devices is opening new opportunities to uncover deeper aspects of the Kondo effect--a characteristic phenomenon in the physics of strongly correlated electrons. Artificial single-impurity Kondo systems have been realized in various nanostructures, including semiconductor quantum dots, carbon nanotubes and individual molecules. The Kondo effect is usually regarded as a spin-related phenomenon, namely the coherent exchange of the spin between a localized state and a Fermi sea of delocalized electrons. In principle, however, the role of the spin could be replaced by other degrees of freedom, such as an orbital quantum number. Here we show that the unique electronic structure of carbon nanotubes enables the observation of a purely orbital Kondo effect. We use a magnetic field to tune spin-polarized states into orbital degeneracy and conclude that the orbital quantum number is conserved during tunnelling. When orbital and spin degeneracies are present simultaneously, we observe a strongly enhanced Kondo effect, with a multiple splitting of the Kondo resonance at finite field and predicted to obey a so-called SU4 symmetry.     

确定含油气面积存在的问题及正确的方法

本文对传统的石油地质理论定义的含油气面积提出了异议,用倒转背斜油气藏、断层下盘油气藏和不整合面下油气藏的实例阐明在传统定义下确定含油气面积存在的问题,指出用这种方法确定的含油气面积小于实际面积。笔者将含油气面积定义为含油气体在水平面上的投影区域,并推荐了三种正确的确定方法、     

Dense genotyping identifies and localizes multiple common and rare variant association signals in celiac disease

Using variants from the 1000 Genomes Project pilot European CEU dataset and data from additional resequencing studies, we densely genotyped 183 non-HLA risk loci previously associated with immune-mediated diseases in 12,041 individuals with celiac disease (cases) and 12,228 controls. We identified 13 new celiac disease risk loci reaching genome-wide significance, bringing the number of known loci (including the HLA locus) to 40. We found multiple independent association signals at over one-third of these loci, a finding that is attributable to a combination of common, low-frequency and rare genetic variants. Compared to previously available data such as those from HapMap3, our dense genotyping in a large sample collection provided a higher resolution of the pattern of linkage disequilibrium and suggested localization of many signals to finer scale regions. In particular, 29 of the 54 fine-mapped signals seemed to be localized to single genes and, in some instances, to gene regulatory elements. Altogether, we define the complex genetic architecture of the risk regions of and refine the risk signals for celiac disease, providing the next step toward uncovering the causal mechanisms of the disease.     

The copper-transporting capacity of ATP7A mutants associated with Menkes disease is ameliorated by COMMD1 as a result of improved protein expression

Menkes disease (MD) is an X-linked recessive disorder characterized by copper deficiency resulting in a diminished function of copper-dependent enzymes. Most MD patients die in early childhood, although mild forms of MD have also been described. A diversity of mutations in the gene encoding of the Golgi-resident copper-transporting P_1B-type ATPase ATP7A underlies MD. To elucidate the molecular consequences of the ATP7A mutations, various mutations in ATP7A associated with distinct phenotypes of MD (L873R, C1000R, N1304S, and A1362D) were analyzed in detail. All mutants studied displayed changes in protein expression and intracellular localization parallel to a dramatic decline in their copper-transporting capacity compared to ATP7A the wild-type. We restored these observed defects in ATP7A mutant proteins by culturing the cells at 30°C, which improves the quality of protein folding, similar to that which as has recently has been demonstrated for misfolded ATP7B, a copper transporter homologous to ATP7A. Further, the effect of the canine copper toxicosis protein COMMD1 on ATP7A function was examined as COMMD1 has been shown to regulate the proteolysis of ATP7B proteins. Interestingly, in addition to adjusted growth temperature, binding of COMMD1 partially restored the expression, subcellular localization, and copper-exporting activities of the ATP7A mutants. However, no effect of pharmacological chaperones was observed. Together, the presented data might provide a new direction for developing therapies to improve the residual exporting activity of unstable ATP7A mutant proteins, and suggests a potential role for COMMD1 in this process.