Conspiracy in bacterial genomes

The rank ordered distribution of the codon usage frequencies for 123 bacteriae is best fitted by a three parameters function that is the sum of a constant, an exponential and a linear term in the rank n. The parameters depend (two parabolically) from the total GC content. The rank ordered distribution of the amino acids is fitted by a straight line. The Shannon entropy computed over all the codons is well fitted by a parabola in the GC content, while the partial entropies computed over subsets of the codons show peculiar different behavior, exhibiting therefore a first conspiracy effect. Moreover the sum of the codon usage frequencies over particular sets, e.g. with C and A (respectively G and U) as i-th nucleotide, shows a clear linear dependence from the GC content, exhibiting another conspiracy effect.Comment: revised version: introduction and conclusion enhanced, references added, figures added, some tables remove

Coexistence and competition of local- and long-range polar orders in a ferroelectric relaxor

We have performed a series of neutron diffuse scattering measurements on a single crystal of the solid solution Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_3$ (PZN) doped with 8% PbTiO$_3$ (PT), a relaxor compound with a Curie temperature T$_C \sim 450$ K, in an effort to study the change in local polar orders from the polar nanoregions (PNR) when the material enters the ferroelectric phase. The diffuse scattering intensity increases monotonically upon cooling in zero field, while the rate of increase varies dramatically around different Bragg peaks. These results can be explained by assuming that corresponding changes occur in the ratio of the optic and acoustic components of the atomic displacements within the PNR. Cooling in the presence of a modest electric field $\vec{E}$ oriented along the [111] direction alters the shape of diffuse scattering in reciprocal space, but does not eliminate the scattering as would be expected in the case of a classic ferroelectric material. This suggests that a field-induced redistribution of the PNR has taken place

The Complexity of Datalog on Linear Orders

We study the program complexity of datalog on both finite and infinite linear orders. Our main result states that on all linear orders with at least two elements, the nonemptiness problem for datalog is EXPTIME-complete. While containment of the nonemptiness problem in EXPTIME is known for finite linear orders and actually for arbitrary finite structures, it is not obvious for infinite linear orders. It sharply contrasts the situation on other infinite structures; for example, the datalog nonemptiness problem on an infinite successor structure is undecidable. We extend our upper bound results to infinite linear orders with constants. As an application, we show that the datalog nonemptiness problem on Allen's interval algebra is EXPTIME-complete.Comment: 21 page