A new analytical framework for the understanding of Diophantus’s Arithmetica I–III

This study is the foundation of a new interpretation of the introduction and the three first books of Diophantus’s Arithmetica, one that opens the way to a historically correct contextualization of the work. Its purpose, as indicated in the title, is to renew the traditional discussion on the methods of problem-solving used by Diophantus, through the detailed exposition of a new analytical framework that aims to give an account of the coherence and progressive nature of the material included in the three first books of the Arithmetica. One outcome of this new ‘toolbox’ is a new conspectus of the problems and solutions contained in the latter, which is presented in appendix. The first part of the article clarifies, as a necessary preliminary, the key notions and terminology underlying our analysis. Among these new concepts is the notion of “method of invention,” which accounts in general for any way, by which “positions” (hypostaseis) are used in the Arithmetica. The next part proposes a complete inventory of the various methods of invention found in the three first books. Finally the last part presents the above mentioned conspectus and proposes a series of preliminary conclusions that can be drawn from it.     

First-principles investigation on initial stage of 2H-SiC(001) surface oxidation

We present comprehensive first-principles calculations on the initial stages of SiC oxidation by atomic oxygen on the 2H-SiC(001) surface. In order to study the kinetics of oxygen incorporation at the 2H-SiC(001) surface, we investigated adsorption and diffusion of oxygen atoms and SiO₂ nucleation. The adsorption sites, corresponding to the local minima of the potential energy surface (PES) for isolated adatoms, were identified through a comparative study of the adatom binding energy at different locations. We found that the Bridge (siloxane) site is preferred over other adsorption sites. There is no energy barrier at 0K for oxygen insertion into this site. The diffusion energy barriers that the adatom has to overcome when jumping between two adsorption sites were calculated. The premises of silica nucleation were investigated by calculating the modifications of the oxygen atom binding energy due to the interaction with neighboring adatoms. Supported by Snecma Propulsion Solide (Contract FPR No. 0539298A), Natural Science Foundation of China (Grant No 50802076) and Flying Star Program of Northwestern Polytechnical University of China     

The binary Kuiper-belt object 1998 WW31

The recent discovery of a binary asteroid during a spacecraft fly-by generated keen interest, because the orbital parameters of binaries can provide measures of the masses, and mutual eclipses could allow us to determine individual sizes and bulk densities. Several binary near-Earth, main-belt and Trojan asteroids have subsequently been discovered. The Kuiper belt-the region of space extending from Neptune (at 30 astronomical units) to well over 100 AU and believed to be the source of new short-period comets-has become a fascinating new window onto the formation of our Solar System since the first member object, not counting Pluto, was discovered in 1992 (ref. 13). Here we report that the Kuiper-belt object 1998 WW31 is binary with a highly eccentric orbit (eccentricity e approximately 0.8) and a long period (about 570 days), very different from the Pluto/Charon system, which was hitherto the only previously known binary in the Kuiper belt. Assuming a density in the range of 1 to 2 g cm-3, the albedo of the binary components is between 0.05 and 0.08, close to the value of 0.04 generally assumed for Kuiper-belt objects.     

Conformational change and protein-protein interactions of the fusion protein of Semliki Forest virus

Fusion of biological membranes is mediated by specific lipid-interacting proteins that induce the formation and expansion of an initial fusion pore. Here we report the crystal structure of the ectodomain of the Semliki Forest virus fusion glycoprotein E1 in its low-pH-induced trimeric form. E1 adopts a folded-back conformation that, in the final post-fusion form of the full-length protein, would bring the fusion peptide loop and the transmembrane anchor to the same end of a stable protein rod. The observed conformation of the fusion peptide loop is compatible with interactions only with the outer leaflet of the lipid bilayer. Crystal contacts between fusion peptide loops of adjacent E1 trimers, together with electron microscopy observations, suggest that in an early step of membrane fusion, an intermediate assembly of five trimers creates two opposing nipple-like deformations in the viral and target membranes, leading to formation of the fusion pore.     

Insect behaviour: arboreal ants build traps to capture prey

To meet their need for nitrogen in the restricted foraging environment provided by their host plants, some arboreal ants deploy group ambush tactics in order to capture flying and jumping prey that might otherwise escape. Here we show that the ant Allomerus decemarticulatus uses hair from the host plant's stem, which it cuts and binds together with a purpose-grown fungal mycelium, to build a spongy 'galleried' platform for trapping much larger insects. Ants beneath the platform reach through the holes and immobilize the prey, which is then stretched, transported and carved up by a swarm of nestmates. To our knowledge, the collective creation of a trap as a predatory strategy has not been described before in ants.     

Apolipoprotein L-I is the trypanosome lytic factor of human serum

Human sleeping sickness in east Africa is caused by the parasite Trypanosoma brucei rhodesiense. The basis of this pathology is the resistance of these parasites to lysis by normal human serum (NHS). Resistance to NHS is conferred by a gene that encodes a truncated form of the variant surface glycoprotein termed serum resistance associated protein (SRA). We show that SRA is a lysosomal protein, and that the amino-terminal alpha-helix of SRA is responsible for resistance to NHS. This domain interacts strongly with a carboxy-terminal alpha-helix of the human-specific serum protein apolipoprotein L-I (apoL-I). Depleting NHS of apoL-I, by incubation with SRA or anti-apoL-I, led to the complete loss of trypanolytic activity. Addition of native or recombinant apoL-I either to apoL-I-depleted NHS or to fetal calf serum induced lysis of NHS-sensitive, but not NHS-resistant, trypanosomes. Confocal microscopy demonstrated that apoL-I is taken up through the endocytic pathway into the lysosome. We propose that apoL-I is the trypanosome lytic factor of NHS, and that SRA confers resistance to lysis by interaction with apoL-I in the lysosome.     

Extra-embryonic function of Rb is essential for embryonic development and viability

The retinoblastoma (Rb) gene was the first tumour suppressor identified. Inactivation of Rb in mice results in unscheduled cell proliferation, apoptosis and widespread developmental defects, leading to embryonic death by day 14.5 (refs 2-4). However, the actual cause of the embryonic lethality has not been fully investigated. Here we show that loss of Rb leads to excessive proliferation of trophoblast cells and a severe disruption of the normal labyrinth architecture in the placenta. This is accompanied by a decrease in vascularization and a reduction in placental transport function. We used two complementary techniques-tetraploid aggregation and conditional knockout strategies-to demonstrate that Rb-deficient embryos supplied with a wild-type placenta can be carried to term, but die soon after birth. Most of the neurological and erythroid abnormalities thought to be responsible for the embryonic lethality of Rb-null animals were virtually absent in rescued Rb-null pups. These findings identify and define a key function of Rb in extra-embryonic cell lineages that is required for embryonic development and viability, and provide a mechanism for the cell autonomous versus non-cell autonomous roles of Rb in development.     

Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection

Modern computing technology is based on writing, storing and retrieving information encoded as magnetic bits. Although the giant magnetoresistance effect has improved the electrical read out of memory elements, magnetic writing remains the object of major research efforts. Despite several reports of methods to reverse the polarity of nanosized magnets by means of local electric fields and currents, the simple reversal of a high-coercivity, single-layer ferromagnet remains a challenge. Materials with large coercivity and perpendicular magnetic anisotropy represent the mainstay of data storage media, owing to their ability to retain a stable magnetization state over long periods of time and their amenability to miniaturization. However, the same anisotropy properties that make a material attractive for storage also make it hard to write to. Here we demonstrate switching of a perpendicularly magnetized cobalt dot driven by in-plane current injection at room temperature. Our device is composed of a thin cobalt layer with strong perpendicular anisotropy and Rashba interaction induced by asymmetric platinum and AlOx interface layers. The effective switching field is orthogonal to the direction of the magnetization and to the Rashba field. The symmetry of the switching field is consistent with the spin accumulation induced by the Rashba interaction and the spin-dependent mobility observed in non-magnetic semiconductors, as well as with the torque induced by the spin Hall effect in the platinum layer. Our measurements indicate that the switching efficiency increases with the magnetic anisotropy of the cobalt layer and the oxidation of the aluminium layer, which is uppermost, suggesting that the Rashba interaction has a key role in the reversal mechanism. To prove the potential of in-plane current switching for spintronic applications, we construct a reprogrammable magnetic switch that can be integrated into non-volatile memory and logic architectures. This device is simple, scalable and compatible with present-day magnetic recording technology.