Vanishing Integral Relations and Expectation Values for Bloch Functions in Finite Domains

Integral identities for particular Bloch functions in finite periodic systems are derived. All following statements are proven for a finite domain consisting of an integer number of unit cells. It is shown that matrix elements of particular Bloch functions with respect to periodic differential operators vanish identically. The real valuedness, the time-independence and a summation property of the expectation values of periodic differential operators applied to superpositions of specific Bloch functions are derived.Comment: 10 page

Optical polarimetric monitoring of the type II-plateau SN 2005af

Aims. Core-collapse supernovae may show significant polarization that implies non-spherically symmetric explosions. We observed the type II-plateau SN 2005af using optical polarimetry in order to verify whether any asphericity is present in the supernova temporal evolution. Methods. We used the IAGPOL imaging polarimeter to obtain optical linear polarization measurements in R (five epochs) and V (one epoch) broadbands. Interstellar polarization was estimated from the field stars in the CCD frames. The optical polarimetric monitoring began around one month after the explosion and lasted ~30 days, between the plateau and the early nebular phase. Results. The weighted mean observed polarization in R band was [1.89 +/- 0.03]% at position angle (PA) 54 deg. After foreground subtraction, the level of the average intrinsic polarization for SN 2005af was ~0.5% with a slight enhancement during the plateau phase and a decline at early nebular phase. A rotation in PA on a time scale of days was also observed. The polarimetric evolution of SN 2005af in the observed epochs is consistent with an overall asphericity of ~20% and an inclination of ~30 deg. Evidence for a more complex, evolving asphericity, possibly involving clumps in the SN 2005af envelope, is found.Comment: 6 pages, 5 figures, to be published A&

Micrococcal Nuclease Does Not Substantially Bias Nucleosome Mapping

We have mapped sequence-directed nucleosome positioning on genomic DNA molecules using high-throughput sequencing. Chromatins, prepared by reconstitution with either chicken or frog histones, were separately digested to mononucleosomes using either micrococcal nuclease (MNase) or caspase-activated DNase (CAD). Both enzymes preferentially cleave internucleosomal (linker) DNA, although they do so by markedly different mechanisms. MNase has hitherto been very widely used to map nucleosomes, although concerns have been raised over its potential to introduce bias. Having identified the locations and quantified the strength of both the chicken or frog histone octamer binding sites on each DNA, the results obtained with the two enzymes were compared using a variety of criteria. Both enzymes displayed sequence specificity in their preferred cleavage sites, although the nature of this selectivity was distinct for the two enzymes. In addition, nucleosomes produced by CAD nuclease are 8–10 bp longer than those produced with MNase, with the CAD cleavage sites tending to be 4–5 bp further out from the nucleosomal dyad than the corresponding MNase cleavage sites. Despite these notable differences in cleavage behaviour, the two nucleases identified essentially equivalent patterns of nucleosome positioning sites on each of the DNAs tested, an observation that was independent of the histone type. These results indicate that biases in nucleosome positioning data collected using MNase are, under our conditions, not significant