The astronomical tables of Jacob ben David Bonjorn

Communicated by J. North     

Numerical solving of equations in the work of José Mariano Vallejo

The progress of Mathematics during the nineteenth century was characterised both by an enormous acquisition of new knowledge and by the attempts to introduce rigour in reasoning patterns and mathematical writing. Cauchy’s presentation of Mathematical Analysis was not immediately accepted, and many writers, though aware of that new style, did not use it in their own mathematical production. This paper is devoted to an episode of this sort that took place in Spain during the first half of the century: It deals with the presentation of a method for numerically solving algebraic equations by José Mariano Vallejo, a late Spanish follower of the Enlightenment ideas, politician, writer, and mathematician who published it in the fourth (1840) edition of his book Compendio de Matemáticas Puras y Mistas, claiming to have discovered it on his own. Vallejo’s main achievement was to write down the whole procedure in a very careful way taking into account the different types of roots, although he paid little attention to questions such as convergence checks and the fulfilment of the hypotheses of Rolle’s Theorem. For sure this lack of mathematical care prevented Vallejo to occupy a place among the forerunners of Computational Algebra.     

Interaction network containing conserved and essential protein complexes in Escherichia coli

Proteins often function as components of multi-subunit complexes. Despite its long history as a model organism, no large-scale analysis of protein complexes in Escherichia coli has yet been reported. To this end, we have targeted DNA cassettes into the E. coli chromosome to create carboxy-terminal, affinity-tagged alleles of 1,000 open reading frames (approximately 23% of the genome). A total of 857 proteins, including 198 of the most highly conserved, soluble non-ribosomal proteins essential in at least one bacterial species, were tagged successfully, whereas 648 could be purified to homogeneity and their interacting protein partners identified by mass spectrometry. An interaction network of protein complexes involved in diverse biological processes was uncovered and validated by sequential rounds of tagging and purification. This network includes many new interactions as well as interactions predicted based solely on genomic inference or limited phenotypic data. This study provides insight into the function of previously uncharacterized bacterial proteins and the overall topology of a microbial interaction network, the core components of which are broadly conserved across Prokaryota.     

Notch activity acts as a sensor for extracellular calcium during vertebrate left-right determination

During vertebrate embryo development, the breaking of the initial bilateral symmetry is translated into asymmetric gene expression around the node and/or in the lateral plate mesoderm. The earliest conserved feature of this asymmetric gene expression cascade is the left-sided expression of Nodal, which depends on the activity of the Notch signalling pathway. Here we present a mathematical model describing the dynamics of the Notch signalling pathway during chick embryo gastrulation, which reveals a complex and highly robust genetic network that locally activates Notch on the left side of Hensen's node. We identify the source of the asymmetric activation of Notch as a transient accumulation of extracellular calcium, which in turn depends on left-right differences in H+/K+-ATPase activity. Our results uncover a mechanism by which the Notch signalling pathway translates asymmetry in epigenetic factors into asymmetric gene expression around the node.     

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.     

Andalusian astronomy: al-Zîj al-Muqtabis of Ibn al-Kammâd

Communicated by J. North