The natures of numbers in and around Bombelli’s L’algebra

The purpose of this article is to analyse the mathematical practices leading to Rafael Bombelli’s L’algebra (1572). The context for the analysis is the Italian algebra practiced by abbacus masters and Renaissance mathematicians of the fourteenth to sixteenth centuries. We will focus here on the semiotic aspects of algebraic practices and on the organisation of knowledge. Our purpose is to show how symbols that stand for underdetermined meanings combine with shifting principles of organisation to change the character of algebra.     

Robustness-epistasis link shapes the fitness landscape of a randomly drifting protein

The distribution of fitness effects of protein mutations is still unknown. Of particular interest is whether accumulating deleterious mutations interact, and how the resulting epistatic effects shape the protein's fitness landscape. Here we apply a model system in which bacterial fitness correlates with the enzymatic activity of TEM-1 beta-lactamase (antibiotic degradation). Subjecting TEM-1 to random mutational drift and purifying selection (to purge deleterious mutations) produced changes in its fitness landscape indicative of negative epistasis; that is, the combined deleterious effects of mutations were, on average, larger than expected from the multiplication of their individual effects. As observed in computational systems, negative epistasis was tightly associated with higher tolerance to mutations (robustness). Thus, under a low selection pressure, a large fraction of mutations was initially tolerated (high robustness), but as mutations accumulated, their fitness toll increased, resulting in the observed negative epistasis. These findings, supported by FoldX stability computations of the mutational effects, prompt a new model in which the mutational robustness (or neutrality) observed in proteins, and other biological systems, is due primarily to a stability margin, or threshold, that buffers the deleterious physico-chemical effects of mutations on fitness. Threshold robustness is inherently epistatic-once the stability threshold is exhausted, the deleterious effects of mutations become fully pronounced, thereby making proteins far less robust than generally assumed.     

A giant Ordovician anomalocaridid

Anomalocaridids, giant lightly sclerotized invertebrate predators, occur in a number of exceptionally preserved early and middle Cambrian (542-501?million years ago) biotas and have come to symbolize the unfamiliar morphologies displayed by stem organisms in faunas of the Burgess Shale type. They are characterized by a pair of anterior, segmented appendages, a circlet of plates around the mouth, and an elongate segmented trunk lacking true tergites with a pair of flexible lateral lobes per segment. Disarticulated body parts, such as the anterior appendages and oral circlet, had been assigned to a range of taxonomic groups--but the discovery of complete specimens from the middle Cambrian Burgess Shale showed that these disparate elements all belong to a single kind of animal. Phylogenetic analyses support a position of anomalocaridids in the arthropod stem, as a sister group to the euarthropods. The anomalocaridids were the largest animals in Cambrian communities. The youngest unequivocal examples occur in the middle Cambrian Marjum Formation of Utah but an arthropod retaining some anomalocaridid characteristics is present in the Devonian of Germany. Here we report the post-Cambrian occurrence of anomalocaridids, from the Early Ordovician (488-472?million years ago) Fezouata Biota in southeastern Morocco, including specimens larger than any in Cambrian biotas. These giant animals were an important element of some marine communities for about 30?million years longer than previously realized. The Moroccan specimens confirm the presence of a dorsal array of flexible blades attached to a transverse rachis on the trunk segments; these blades probably functioned as gills.     

利用雅可比椭圆函数计算强非线性杜芬振子的周期响应

应用雅可比椭圆函数及均值方法计算求解受到简谐外激扰的强非线性杜芬振荡系统＋ａυ＋γυ３＝ε（－βυ＋ＦｃｏｓΩＴ）的稳态周期响应。首先利用雅可比椭圆函数给出无扰动系统的周期解。然后，采用对无扰动系统周期解进行扰动的方法，求扰动系统的周期解。在这个过程中，采用均值方法对问题进行了简化。并通过对所得解的讨论与分析，最终得到原问题的稳态周期响应。实例验证的结果表明，我们所介绍的方法是成功的。并可应用于求解其它强非线性系统的周期响应。     

The kinetics of sulphatase A

Résumé Les cinétiques de l'hydrolyse du sulfate de nitrocatéchol par la sulfatase A sont très anormaux parce qu'il n'y a aucune relation linéaire entre la vitesse de la réaction et la concentration de l'enzyme. La réaction tient trois phases: dans la première, la vitesse décroît rapidement, dans la deuxième, elle diminue de plus en plus tandis qu'elle s'accroît dans la troisième. La réaction est très sensible à la composition du mélange réactionel, et l'addition des produits de la réaction, particulièrement le sulfate inorganique, augmente la vitesse de l'hydrolyse. En utilisant comme substrat lep-nitrophénylsulfate, ces irrégularités ne sont pas constatées.Une interprétation de ces résultats est présentée!     

Measuring intense rotation and dissipation in turbulent flows

Turbulent flows are highly intermittent--for example, they exhibit intense bursts of vorticity and strain. Kolmogorov theory describes such behaviour in the form of energy cascades from large to small spatial and temporal scales, where energy is dissipated as heat. But the causes of high intermittency in turbulence, which show non-gaussian statistics, are not well understood. Such intermittency can be important, for example, for enhancing the mixing of chemicals, by producing sharp drops in local pressure that can induce cavitation (damaging mechanical components and biological organisms), and by causing intense vortices in atmospheric flows. Here we present observations of the three components of velocity and all nine velocity gradients within a small volume, which allow us to determine simultaneously the dissipation (a measure of strain) and enstrophy (a measure of rotational energy) of a turbulent flow. Combining the statistics of all measurements and the evolution of individual bursts, we find that a typical sequence for intense events begins with rapid strain growth, followed by rising vorticity and a final sudden decline in stretching. We suggest two mechanisms which can produce these characteristics, depending whether they are due to the advection of coherent structures through our observed volume or caused locally.     

The dynamics of actin-based motility depend on surface parameters

In cells, actin polymerization at the plasma membrane is induced by the recruitment of proteins such as the Arp2/3 complex, and the zyxin/VASP complex. The physical mechanism of force generation by actin polymerization has been described theoretically using various approaches, but lacks support from experimental data. By the use of reconstituted motility medium, we find that the Wiskott Aldrich syndrome protein (WASP) subdomain, known as VCA, is sufficient to induce actin polymerization and movement when grafted on microspheres. Changes in the surface density of VCA protein or in the microsphere diameter markedly affect the velocity regime, shifting from a continuous to a jerky movement resembling that of the mutated 'hopping' Listeria. These results highlight how simple physical parameters such as surface geometry and protein density directly affect spatially controlled actin polymerization, and play a fundamental role in actin-dependent movement.