On NP-Hardness of the Paired de Bruijn Sound Cycle Problem

The paired de Bruijn graph is an extension of de Bruijn graph incorporating mate pair information for genome assembly proposed by Mevdedev et al. However, unlike in an ordinary de Bruijn graph, not every path or cycle in a paired de Bruijn graph will spell a string, because there is an additional soundness constraint on the path. In this paper we show that the problem of checking if there is a sound cycle in a paired de Bruijn graph is NP-hard in general case. We also explore some of its special cases, as well as a modified version where the cycle must also pass through every edge.Comment: Peer-reviewed and presented as part of the 13th Workshop on Algorithms in Bioinformatics (WABI2013

Diffusion of Elements in the Interstellar Medium in Early-Type Galaxies

We consider the role of diffusion in the redistribution of elements in the hot interstellar medium (ISM) of early-type galaxies. It is well known that gravitational sedimentation can affect significantly the abundances of helium and heavy elements in the intracluster gas of massive galaxy clusters. The self-similarity of the temperature profiles and tight mass--temperature relation of relaxed cool-core clusters suggest that the maximum effect of sedimentation take place in the most massive virialized objects in the Universe. However, Chandra and XMM-Newton observations demonstrate more complex scaling relations between the masses of early-type galaxies and other parameters, such as the ISM temperature and gas mass fraction. An important fact is that early-type galaxies can show both decreasing and increasing radial temperature profiles. We have calculated the diffusion based on the observed gas density and temperature distributions for 13 early-type galaxies that belonging to the different environments and cover a wide range of X-ray luminosities. To estimate the maximum effect of sedimentation and thermal diffusion, we have solved the full set of Burgers' equations for a non-magnetized ISM plasma. The results obtained demonstrate a considerable increase of the He/H ratio within one effective radius for all galaxies of our sample. For galaxies with a flat or declining radial temperature profile the average increase of the helium abundance is 60\% in one billion years of diffusion. The revealed effect can introduce a significant bias in the metal abundance measurements based on X-ray spectroscopy and can affect the evolution of stars that could be formed from a gas with a high helium abundance.Comment: 15 pages, 9 figures, 3 tables, published in Astronomy Letters, 2017, Volume 43, Issue 5, pp.285-30

Impact of thermal diffusion and other abundance anomalies on cosmological uses of galaxy clusters

Depending on the topology of the magnetic field and characteristics of turbulent motions, diffusion can significantly affect the distribution of elements, in particular helium, in the intracluster medium (ICM). As has been noted previously, an incorrect assumption about the helium abundance will lead to an error in the iron abundance determined from X-ray spectroscopy. The corresponding effect on the temperature measurement is negligibly small. An incorrectly assumed helium abundance will also lead to a systematic error in angular distance measurements based on X-ray and Sunyaev-Zeldovich (SZ) observations of clusters of galaxies. Its magnitude is further amplified by the associated error in the metal abundance determination, the impact being larger at lower ICM temperatures. Overall, a factor of 2-5 error in the helium abundance will lead to an ~ 10-25 % error in the angular distance. We solve the full set of Burgers equations for a multi-component intracluster plasma to determine the maximal effect of diffusion on the interpretation of X-ray and microwave observations of clusters of galaxies. For an isothermal cluster, gravitational sedimentation can lead to up to a factor of ~ 5-10 enhancements of helium and metal abundances in the cluster center on a ~ 3-7 Gyr timescale. In cool-core clusters on the contrary, thermal diffusion can counteract gravitational sedimentation and effectively remove helium and metals from the cluster inner core. In either case, a significant, up to ~ 40 %, error in the metal abundances determined by means of X-ray spectroscopy is possible. The angular distance determined from X-ray and SZ data can be underestimated by up to ~ 10-25 %.Comment: 11 pages, 10 figure

NN-point amplitudes for d=2 c=1 Discrete States from String Field Theory

Starting from string field theory for 2d gravity coupled to c=1 matter we analyze N-point off-shell tree amplitudes of discrete states. The amplitudes exhibit the pole structure and we use the oscillator representation to extract the residues. The residues are generated by a simple effective action. We show that the effective action can be directly deduced from a string field action in a special transversal-like gauge.Comment: 12 pages, latex, 1 figur