A Survey of the Representations of Rational Ruled Surfaces

The rational ruled surface is a typical modeling surface in computer aided geometric design. A rational ruled surface may have different representations with respective advantages and disadvantages. In this paper, the authors revisit the representations of ruled surfaces including the parametric form, algebraic form, homogenous form and Plücker form. Moreover, the transformations between these representations are proposed such as parametrization for an algebraic form, implicitization for a parametric form, proper reparametrization of an improper one and standardized reparametrization for a general parametrization. Based on these transformation algorithms, one can give a complete interchange graph for the different representations of a rational ruled surface. For rational surfaces given in algebraic form or parametric form not in the standard form of ruled surfaces, the characterization methods are recalled to identify the ruled surfaces from them.

     

Eight glacial cycles from an Antarctic ice core

The Antarctic Vostok ice core provided compelling evidence of the nature of climate, and of climate feedbacks, over the past 420,000 years. Marine records suggest that the amplitude of climate variability was smaller before that time, but such records are often poorly resolved. Moreover, it is not possible to infer the abundance of greenhouse gases in the atmosphere from marine records. Here we report the recovery of a deep ice core from Dome C, Antarctica, that provides a climate record for the past 740,000 years. For the four most recent glacial cycles, the data agree well with the record from Vostok. The earlier period, between 740,000 and 430,000 years ago, was characterized by less pronounced warmth in interglacial periods in Antarctica, but a higher proportion of each cycle was spent in the warm mode. The transition from glacial to interglacial conditions about 430,000 years ago (Termination V) resembles the transition into the present interglacial period in terms of the magnitude of change in temperatures and greenhouse gases, but there are significant differences in the patterns of change. The interglacial stage following Termination V was exceptionally long--28,000 years compared to, for example, the 12,000 years recorded so far in the present interglacial period. Given the similarities between this earlier warm period and today, our results may imply that without human intervention, a climate similar to the present one would extend well into the future.     

Developmental plasticity and human health

Many plants and animals are capable of developing in a variety of ways, forming characteristics that are well adapted to the environments in which they are likely to live. In adverse circumstances, for example, small size and slow metabolism can facilitate survival, whereas larger size and more rapid metabolism have advantages for reproductive success when resources are more abundant. Often these characteristics are induced in early life or are even set by cues to which their parents or grandparents were exposed. Individuals developmentally adapted to one environment may, however, be at risk when exposed to another when they are older. The biological evidence may be relevant to the understanding of human development and susceptibility to disease. As the nutritional state of many human mothers has improved around the world, the characteristics of their offspring--such as body size and metabolism--have also changed. Responsiveness to their mothers' condition before birth may generally prepare individuals so that they are best suited to the environment forecast by cues available in early life. Paradoxically, however, rapid improvements in nutrition and other environmental conditions may have damaging effects on the health of those people whose parents and grandparents lived in impoverished conditions. A fuller understanding of patterns of human plasticity in response to early nutrition and other environmental factors will have implications for the administration of public health.     

Whole-genome sequencing of rifampicin-resistant Mycobacterium tuberculosis strains identifies compensatory mutations in RNA polymerase genes

Epidemics of drug-resistant bacteria emerge worldwide, even as resistant strains frequently have reduced fitness compared to their drug-susceptible counterparts. Data from model systems suggest that the fitness cost of antimicrobial resistance can be reduced by compensatory mutations; however, there is limited evidence that compensatory evolution has any significant role in the success of drug-resistant bacteria in human populations. Here we describe a set of compensatory mutations in the RNA polymerase genes of rifampicin-resistant M. tuberculosis, the etiologic agent of human tuberculosis (TB). M. tuberculosis strains harboring these compensatory mutations showed a high competitive fitness in vitro. Moreover, these mutations were associated with high fitness in vivo, as determined by examining their relative clinical frequency across patient populations. Of note, in countries with the world's highest incidence of multidrug-resistant (MDR) TB, more than 30% of MDR clinical isolates had this form of mutation. Our findings support a role for compensatory evolution in the global epidemics of MDR TB.     

The (Na++K+)-ATPase activity in brain of quaking mice

Summary The (Na⁺+K⁺)- and Mg²⁺-dependent ATPase distribution in several brain areas has been investigated in Quaking mutant mice characterized by myelin deficiency. A marked decrease of (Na⁺+K⁺)-ATPase activity has been found in limbic structures, hypothalamus and cerebellum. The Mg²⁺-dependent activity did not change. A possible involvement of the impairment of the (Na⁺+K⁺)-ATPase activity in the seizure susceptibility of this mice is discussed.Chargée de Recherche au CNRS.