Geometric variational problems of statistical mechanics and of combinatorics

We present the geometric solutions of the various extremal problems of statistical mechanics and combinatorics. Together with the Wulff construction, which predicts the shape of the crystals, we discuss the construction which exhibits the shape of a typical Young diagram and of a typical skyscraper.Comment: 10 page

Self-Focusing Dynamics of Coupled Optical Beams

We theoretically and experimentally investigate the mutual collapse dynamics of two spatially separated optical beams in a Kerr medium. Depending on the initial power, beam separation, and the relative phase, we observe repulsion or attraction, which in the latter case reveals a sharp transition to a single collapsing beam. This transition to fusion of the beams is accompanied by an increase in the collapse distance, indicating the effect of the nonlinear coupling on the individual collapse dynamics. Our results shed light on the basic nonlinear interaction between self-focused beams and provide a mechanism to control the collapse dynamics of such beams.Comment: 5 pages, 4 figure

The origin of the Narrow Line Region of Mrk 3: an overpressured jet cocoon

We have obtained HST FOC long-slit optical spectroscopy of the Narrow Line Region of the Seyfert 2 galaxy Mrk 3. In the region cospatial with the radio-jet the velocity field is highly perturbed and shows two velocity systems separated by as much as 1700 km/s. We interpret this to be the consequence of the rapid expansion of a cocoon of hot gas, shocked and heated by the radio-emitting outflow, which compresses and accelerates the ambient gas. The NLR itself is essentially a cylindrical shell expanding supersonically. From the size and velocity of the expanding region, we derive an upper limit to the radio-source age, ~ 2 E42 erg/s required to inflate the cocoon and estimate that the jet minimum advance speed is 3 E-3 pc per year. The total kinetic energy of the high velocity NLR gas can be estimated as ~6 E54 erg, comparable to the total energy carried by the jet over its lifetime and this quantitatively supports the idea that the NLR gas is accelerated by the jet. If the advance speed of Mrk 3 is representative of the Seyfert population then these sources must also be short lived and probably recurrent. The jet kinetic luminosity of Mrk 3 is between 2 and 3 orders of magnitude smaller than that derived for radio-loud AGNs with similar emission-line luminosity. On the other hand, the fraction of jet power dissipated in radio-emission is similar. We speculate that the main distinction between radio-quiet and radio-loud AGN is ascribed to a difference in jet power rather than to a different efficiency in synchrotron emission production.Comment: 13 pages, 8 figures, Astrophysical Journal in pres

What's in your next-generation sequence data? An exploration of unmapped DNA and RNA sequence reads from the bovine reference individual.

BackgroundNext-generation sequencing projects commonly commence by aligning reads to a reference genome assembly. While improvements in alignment algorithms and computational hardware have greatly enhanced the efficiency and accuracy of alignments, a significant percentage of reads often remain unmapped.ResultsWe generated de novo assemblies of unmapped reads from the DNA and RNA sequencing of the Bos taurus reference individual and identified the closest matching sequence to each contig by alignment to the NCBI non-redundant nucleotide database using BLAST. As expected, many of these contigs represent vertebrate sequence that is absent, incomplete, or misassembled in the UMD3.1 reference assembly. However, numerous additional contigs represent invertebrate species. Most prominent were several species of Spirurid nematodes and a blood-borne parasite, Babesia bigemina. These species are either not present in the US or are not known to infect taurine cattle and the reference animal appears to have been host to unsequenced sister species.ConclusionsWe demonstrate the importance of exploring unmapped reads to ascertain sequences that are either absent or misassembled in the reference assembly and for detecting sequences indicative of parasitic or commensal organisms