Affine arithmetic in matrix form for polynomial evaluation and algebraic curve drawing

This paper shows how tight bounds for the range of a bivariate polynomial can be found using a matrix method based on affine arithmetic. Then, this method is applied to drawing an algebraic curve with a hierarchical algorithm, which demonstrates that more accurate answers can be obtained more rapidly than using conventional interval arithmetic.     

Calmodulin interacts with MLO protein to regulate defence against mildew in barley

In plants, defence against specific isolates of a pathogen can be triggered by the presence of a corresponding race-specific resistance gene, whereas resistance of a more broad-spectrum nature can result from recessive, presumably loss-of-regulatory-function, mutations. An example of the latter are mlo mutations in barley, which have been successful in agriculture for the control of powdery mildew fungus (Blumeria graminis f. sp. hordei; Bgh). MLO protein resides in the plasma membrane, has seven transmembrane domains, and is the prototype of a sequence-diversified family unique to plants, reminiscent of the seven-transmembrane receptors in fungi and animals. In animals, these are known as G-protein-coupled receptors and exist in three main families, lacking sequence similarity, that are thought to be an example of molecular convergence. MLO seems to function independently of heterotrimeric G proteins. We have identified a domain in MLO that mediates a Ca2+-dependent interaction with calmodulin in vitro. Loss of calmodulin binding halves the ability of MLO to negatively regulate defence against powdery mildew in vivo. We propose a sensor role for MLO in the modulation of defence reactions.     

Deep convection in the Irminger Sea forced by the Greenland tip jet

Open-ocean deep convection, one of the processes by which deep waters of the world's oceans are formed, is restricted to a small number of locations (for example, the Mediterranean and Labrador seas). Recently, the southwest Irminger Sea has been suggested as an additional location for open-ocean deep convection. The deep water formed in the Irminger Sea has the characteristic temperature and salinity of the water mass that fills the mid-depth North Atlantic Ocean, which had been believed to be formed entirely in the Labrador basin. Here we show that the most likely cause of the convection in the Irminger Sea is a low-level atmospheric jet known as the Greenland tip jet, which forms periodically in the lee of Cape Farewell, Greenland, and is associated with elevated heat flux and strong wind stress curl. Using a history of tip-jet events derived from meteorological land station data and a regional oceanic numerical model, we demonstrate that deep convection can occur in this region when the North Atlantic Oscillation Index is high, which is consistent with observations. This mechanism of convection in the Irminger Sea differs significantly from those known to operate in the Labrador and Mediterranean seas.     

A very energetic supernova associated with the gamma-ray burst of 29 March 2003

Over the past five years evidence has mounted that long-duration (>2 s) gamma-ray bursts (GRBs)-the most luminous of all astronomical explosions-signal the collapse of massive stars in our Universe. This evidence was originally based on the probable association of one unusual GRB with a supernova, but now includes the association of GRBs with regions of massive star formation in distant galaxies, the appearance of supernova-like 'bumps' in the optical afterglow light curves of several bursts and lines of freshly synthesized elements in the spectra of a few X-ray afterglows. These observations support, but do not yet conclusively demonstrate, the idea that long-duration GRBs are associated with the deaths of massive stars, presumably arising from core collapse. Here we report evidence that a very energetic supernova (a hypernova) was temporally and spatially coincident with a GRB at redshift z = 0.1685. The timing of the supernova indicates that it exploded within a few days of the GRB, strongly suggesting that core-collapse events can give rise to GRBs, thereby favouring the 'collapsar' model.     

Evolution of the polarization of the optical afterglow of the gamma-ray burst GRB030329

The association of a supernova with GRB030329 strongly supports the 'collapsar' model of gamma-ray bursts, where a relativistic jet forms after the progenitor star collapses. Such jets cannot be spatially resolved because gamma-ray bursts lie at cosmological distances; their existence is instead inferred from 'breaks' in the light curves of the afterglows, and from the theoretical desire to reduce the estimated total energy of the burst by proposing that most of it comes out in narrow beams. Temporal evolution of the polarization of the afterglows may provide independent evidence for the jet structure of the relativistic outflow. Small-level polarization ( approximately 1-3 per cent) has been reported for a few bursts, but its temporal evolution has yet to be established. Here we report polarimetric observations of the afterglow of GRB030329. We establish the polarization light curve, detect sustained polarization at the per cent level, and find significant variability. The data imply that the afterglow magnetic field has a small coherence length and is mostly random, probably generated by turbulence, in contrast with the picture arising from the high polarization detected in the prompt gamma-rays from GRB021206 (ref. 18).     

Microwave oscillations of a nanomagnet driven by a spin-polarized current

The recent discovery that a spin-polarized electrical current can apply a large torque to a ferromagnet, through direct transfer of spin angular momentum, offers the possibility of manipulating magnetic-device elements without applying cumbersome magnetic fields. However, a central question remains unresolved: what type of magnetic motions can be generated by this torque? Theory predicts that spin transfer may be able to drive a nanomagnet into types of oscillatory magnetic modes not attainable with magnetic fields alone, but existing measurement techniques have provided only indirect evidence for dynamical states. The nature of the possible motions has not been determined. Here we demonstrate a technique that allows direct electrical measurements of microwave-frequency dynamics in individual nanomagnets, propelled by a d.c. spin-polarized current. We show that spin transfer can produce several different types of magnetic excitation. Although there is no mechanical motion, a simple magnetic-multilayer structure acts like a nanoscale motor; it converts energy from a d.c. electrical current into high-frequency magnetic rotations that might be applied in new devices including microwave sources and resonators.     

s-Consensus index method: An additional axiom

A consensus index method is an ordered pair consisting of a consensus method and a consensus index Day and McMorris (1985) have specified two minimal axioms, one which should be satisfied by the consensus method and the other by the consensus index The axiom for consensus indices is not satisfied by the s-consensus index In this paper, an additional axiom, which states that a consensus index equal to one implies profile unanimity, is proposed The s-consensus method together with a modification of the s-consensus index (i e, normalized by the number of distinct nontrivial clusters in the profile) is shown to satisfy the two axioms proposed by Day and McMorris and the new axiom