A Generalization of the Directed Graph Layering Problem

The Directed Layering Problem (DLP) solves a step of the widely used layer-based layout approach to automatically draw directed acyclic graphs. To cater for cyclic graphs, classically a preprocessing step is used that solves the Feedback Arc Set Problem (FASP)to make the graph acyclic before a layering is determined. Here, we present the Generalized Layering Problem (GLP) which solves the combination of DLP and FASP simultaneously, allowing general graphs as input. We show GLP to be NP- complete, present integer programming models to solve it, and perform thorough evaluations on different sets of graphs and with different implementations for the steps of the layer- based approach. We observe that GLP reduces the number of dummy nodes significantly, can produce more compact drawings and improves on graphs where DLP yields poor aspect ratios

Internal Transcribed Spacer 2 (nu ITS2 rRNA) Sequence-Structure Phylogenetics: Towards an Automated Reconstruction of the Green Algal Tree of Life

L). Some have advocated the use of the nuclear-encoded, internal transcribed spacer two (ITS2) as an alternative to the traditional chloroplast markers. However, the ITS2 is broadly perceived to be insufficiently conserved or to be confounded by introgression or biparental inheritance patterns, precluding its broad use in phylogenetic reconstruction or as a DNA barcode. A growing body of evidence has shown that simultaneous analysis of nucleotide data with secondary structure information can overcome at least some of the limitations of ITS2. The goal of this investigation was to assess the feasibility of an automated, sequence-structure approach for analysis of IT2 data from a large sampling of phylum Chlorophyta.Sequences and secondary structures from 591 chlorophycean, 741 trebouxiophycean and 938 ulvophycean algae, all obtained from the ITS2 Database, were aligned using a sequence structure-specific scoring matrix. Phylogenetic relationships were reconstructed by Profile Neighbor-Joining coupled with a sequence structure-specific, general time reversible substitution model. Results from analyses of the ITS2 data were robust at multiple nodes and showed considerable congruence with results from published phylogenetic analyses.Our observations on the power of automated, sequence-structure analyses of ITS2 to reconstruct phylum-level phylogenies of the green algae validate this approach to assessing diversity for large sets of chlorophytan taxa. Moreover, our results indicate that objections to the use of ITS2 for DNA barcoding should be weighed against the utility of an automated, data analysis approach with demonstrated power to reconstruct evolutionary patterns for highly divergent lineages

Error bounds for monomial convexification in polynomial optimization

Convex hulls of monomials have been widely studied in the literature, and monomial convexifications are implemented in global optimization software for relaxing polynomials. However, there has been no study of the error in the global optimum from such approaches. We give bounds on the worst-case error for convexifying a monomial over subsets of $[0,1]^n$. This implies additive error bounds for relaxing a polynomial optimization problem by convexifying each monomial separately. Our main error bounds depend primarily on the degree of the monomial, making them easy to compute. Since monomial convexification studies depend on the bounds on the associated variables, in the second part, we conduct an error analysis for a multilinear monomial over two different types of box constraints. As part of this analysis, we also derive the convex hull of a multilinear monomial over $[-1,1]^n$.Comment: 33 pages, 2 figures, to appear in journa

Shelters and Their Use by Fishes on Fringing Coral Reefs

Coral reef fish density and species richness are often higher at sites with more structural complexity. This association may be due to greater availability of shelters, but surprisingly little is known about the size and density of shelters and their use by coral reef fishes. We quantified shelter availability and use by fishes for the first time on a Caribbean coral reef by counting all holes and overhangs with a minimum entrance diameter ≥3 cm in 30 quadrats (25 m2) on two fringing reefs in Barbados. Shelter size was highly variable, ranging from 42 cm3 to over 4,000,000 cm3, with many more small than large shelters. On average, there were 3.8 shelters m−2, with a median volume of 1,200 cm3 and a total volume of 52,000 cm3m−2. The number of fish per occupied shelter ranged from 1 to 35 individual fishes belonging to 66 species, with a median of 1. The proportion of shelters occupied and the number of occupants increased strongly with shelter size. Shelter density and total volume increased with substrate complexity, and this relationship varied among reef zones. The density of shelter-using fish was much more strongly predicted by shelter density and median size than by substrate complexity and increased linearly with shelter density, indicating that shelter availability is a limiting resource for some coral reef fishes. The results demonstrate the importance of large shelters for fish density and support the hypothesis that structural complexity is associated with fish abundance, at least in part, due to its association with shelter availability. This information can help identify critical habitat for coral reef fishes, predict the effects of reductions in structural complexity of natural reefs and improve the design of artificial reefs

Biochar successfully replaces activated charcoal for in vitro culture of two white poplar clones reducing ethylene concentration

n/

Breaking the habit - the peculiar 2016 eruption of the unique recurrent nova M31N 2008-12a

Since its discovery in 2008, the Andromeda galaxy nova M31N 2008-12a has been observed in eruption every single year. This unprecedented frequency indicates an extreme object, with a massive white dwarf and a high accretion rate, which is the most promising candidate for the single-degenerate progenitor of a type-Ia supernova known to date. The previous three eruptions of M31N 2008-12a have displayed remarkably homogeneous multi-wavelength properties: (i) From a faint peak, the optical light curve declined rapidly by two magnitudes in less than two days; (ii) Early spectra showed initial high velocities that slowed down significantly within days and displayed clear He/N lines throughout; (iii) The supersoft X-ray source (SSS) phase of the nova began extremely early, six days after eruption, and only lasted for about two weeks. In contrast, the peculiar 2016 eruption was clearly different. Here we report (i) the considerable delay in the 2016 eruption date, (ii) the significantly shorter SSS phase, and (iii) the brighter optical peak magnitude (with a hitherto unobserved cusp shape). Early theoretical models suggest that these three different effects can be consistently understood as caused by a lower quiescence mass-accretion rate. The corresponding higher ignition mass caused a brighter peak in the free-free emission model. The less-massive accretion disk experienced greater disruption, consequently delaying re-establishment of effective accretion. Without the early refueling, the SSS phase was shortened. Observing the next few eruptions will determine whether the properties of the 2016 outburst make it a genuine outlier in the evolution of M31N 2008-12a

TIC 172900988: A transiting circumbinary planet detected in one sector of TESS data

We report the first discovery of a transiting circumbinary planet detected from a single sector of Transiting Exoplanet Survey Satellite (TESS) data. During Sector 21, the planet TIC 172900988b transited the primary star and then five days later it transited the secondary star. The binary is itself eclipsing, with a period P ≈ 19.7 days and an eccentricity e ≈ 0.45. Archival data from ASAS-SN, Evryscope, KELT, and SuperWASP reveal a prominent apsidal motion of the binary orbit, caused by the dynamical interactions between the binary and the planet. A comprehensive photodynamical analysis of the TESS, archival and follow-up data yields stellar masses and radii of M1 = 1.2384 ± 0.0007 Me and R1 = 1.3827 ± 0.0016 Re for the primary and M2 = 1.2019 ± 0.0007 Me and R2 = 1.3124 ± 0.0012 Re for the secondary. The radius of the planet is R3 = 11.25 ± 0.44 R (1.004 ± 0.039RJup). The planet's mass and orbital properties are not uniquely determined-there are six solutions with nearly equal likelihood. Specifically, we find that the planet's mass is in the range of 824 M3 981 M (2.65 M3 3.09MJup), its orbital period could be 188.8, 190.4, 194.0, 199.0, 200.4, or 204.1 days, and the eccentricity is between 0.02 and 0.09. At V = 10.141 mag, the system is accessible for high-resolution spectroscopic observations, e.g., the Rossiter-McLaughlin effect and transit spectroscopy