A minimal axiom group for rough set based on quasi-ordering

Rough set axiomatization is one aspect of rough set study to characterize rough set theory using dependable and minimal axiom groups. Thus, rough set theory can be studied by logic and axiom system methods. The classic rough set theory is based on equivalent relation, but rough set theory based on reflexive and transitive relation (called quasi-ordering) has wide applications in the real world. To characterize topological rough set theory, an axiom group named RT, consisting of 4 axioms, is proposed. It is proved that the axiom group reliability in characterizing rough set theory based on similar relation is reasonable. Simultaneously, the minimization of the axiom group, which requires that each axiom is an equation and each is independent, is proved. The axiom group is helpful for researching rough set theory by logic and axiom system methods.     

Tristable nematic liquid-crystal device using micropatterned surface alignment

It has long been appreciated that liquid-crystal (LC) devices in which the LC molecules adopt multiple stable orientations could drastically reduce the power consumption required for high-information-content displays. But for the commonly used nematic LCs, which are intrinsically uniaxial in symmetry, no industrially feasible multi-stable LC device has been realized. Recently we demonstrated how bistability can be robustly engineered into a nematic LC device, by patterning a substrate with an orientational chequerboard pattern that enforces orthogonal LC alignment in neighbouring square domains. As a result of the four-fold symmetry of the pattern, the two diagonal axes of the chequerboard become equally stable macroscopic orientations. Here we extend this symmetry approach to obtain a tristable surface-aligned nematic LC. A microscopic pattern exhibiting six-fold symmetry is inscribed on a polyimide surface using the stylus of an atomic force microscope. The hexagonal symmetry of the microscopic orientational domains in turn gives rise to three stable macroscopic LC orientations, which are mutually switchable by an in-plane electric field. The resulting switching mode is surface driven, and hence should be compatible with demanding flexible display applications.     

Density-dependent mortality and the latitudinal gradient in species diversity

Ecologists have long postulated that density-dependent mortality maintains high tree diversity in the tropics. If species experience greater mortality when abundant, then more rare species can persist. Agents of density-dependent mortality (such as host-specific predators, and pathogens) may be more prevalent or have stronger effects in tropical forests, because they are not limited by climatic factors. If so, decreasing density-dependent mortality with increasing latitude could partially explain the observed latitudinal gradient in tree diversity. This hypothesis has never been tested with latitudinal data. Here we show that several temperate tree species experience density-dependent mortality between seed dispersal and seedling establishment. The proportion of species affected is equivalent to that in tropical forests, failing to support the hypothesis that this mechanism is more prevalent at tropical latitudes. We further show that density-dependent mortality is misinterpreted in previous studies. Our results and evidence from other studies suggest that density-dependent mortality is important in many forests. Thus, unless the strength of density-dependent mortality varies with latitude, this mechanism is not likely to explain the high diversity of tropical forests.     

Biochemical networking contributes more to genetic buffering in human and mouse metabolic pathways than does gene duplication

During evolution different genes evolve at unequal rates, reflecting the varying functional constraints on phenotype. An important contributor to this variation is genetic buffering, which reduces the potential detrimental effects of mutations. We studied whether gene duplication and redundant metabolic networks affect genetic buffering by comparing the evolutionary rate of 242 human and mouse orthologous genes involved in metabolic pathways. A gene with a redundant network is defined as one for which the structural layout of metabolic pathways provides an alternative metabolic route that can, in principle, compensate for the loss of a protein function encoded by the gene. We found that genes with redundant networks evolve at similar rates as did genes without redundant networks, [corrected] but no significant difference was detected between single-copy genes and gene families. This implies that redundancy in metabolic networks provides significantly more genetic buffering than do gene families. We also found that genes encoding proteins involved in glycolysis and gluconeogenesis showed as a group a distinct pattern of variation, in contrast to genes involved in other pathways. These results suggest that redundant networks provide genetic buffering and contribute to the functional diversification of metabolic pathways.     

Ultraviolet emissions from the magnetic footprints of Io, Ganymede and Europa on Jupiter

Io leaves a magnetic footprint on Jupiter's upper atmosphere that appears as a spot of ultraviolet emission that remains fixed underneath Io as Jupiter rotates. The specific physical mechanisms responsible for generating those emissions are not well understood, but in general the spot seems to arise because of an electromagnetic interaction between Jupiter's magnetic field and the plasma surrounding Io, driving currents of around 1 million amperes down through Jupiter's ionosphere. The other galilean satellites may also leave footprints, and the presence or absence of such footprints should illuminate the underlying physical mechanism by revealing the strengths of the currents linking the satellites to Jupiter. Here we report persistent, faint, far-ultraviolet emission from the jovian footprints of Ganymede and Europa. We also show that Io's magnetic footprint extends well beyond the immediate vicinity of Io's flux-tube interaction with Jupiter, and much farther than predicted theoretically; the emission persists for several hours downstream. We infer from these data that Ganymede and Europa have persistent interactions with Jupiter's magnetic field despite their thin atmospheres.     

Gate-induced superconductivity in a solution-processed organic polymer film

The electrical and optical properties of conjugated polymers have received considerable attention in the context of potentially low-cost replacements for conventional metals and inorganic semiconductors. Charge transport in these organic materials has been characterized in both the doped-metallic and the semiconducting state, but superconductivity has not hitherto been observed in these polymers. Here we report a distinct metal-insulator transition and metallic levels of conductivity in a polymer field-effect transistor. The active material is solution-cast regioregular poly(3-hexylthiophene), which forms relatively well ordered films owing to self-organization, and which yields a high charge carrier mobility (0.05-0.1 cm2 V(-1) s(-1)) at room temperature. At temperatures below approximately 2.35 K with sheet carrier densities exceeding 2.5 x 10(14) cm(-2), the polythiophene film becomes superconducting. The appearance of superconductivity seems to be closely related to the self-assembly properties of the polymer, as the introduction of additional disorder is found to suppress superconductivity. Our findings therefore demonstrate the feasibility of tuning the electrical properties of conjugated polymers over the largest range possible-from insulating to superconducting.