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

Discovery of an intermediate-luminosity red transient in M51 and its likely dust-obscured, infrared-variable progenitor

We present the discovery of an optical transient (OT) in Messier 51, designated M51 OT2019-1 (also ZTF19aadyppr, AT 2019abn, ATLAS19bzl), by the Zwicky Transient Facility (ZTF). The OT rose over 15 days to an observed luminosity of $M_r=-13$ (${\nu}L_{\nu}=9\times10^6~L_{\odot}$), in the luminosity gap between novae and typical supernovae (SNe). Spectra during the outburst show a red continuum, Balmer emission with a velocity width of $\approx400$ km s$^{-1}$, Ca II and [Ca II] emission, and absorption features characteristic of an F-type supergiant. The spectra and multiband light curves are similar to the so-called "SN impostors" and intermediate-luminosity red transients (ILRTs). We directly identify the likely progenitor in archival Spitzer Space Telescope imaging with a $4.5~\mu$m luminosity of $M_{[4.5]}\approx-12.2$ and a $[3.6]-[4.5]$ color redder than 0.74 mag, similar to those of the prototype ILRTs SN 2008S and NGC 300 OT2008-1. Intensive monitoring of M51 with Spitzer further reveals evidence for variability of the progenitor candidate at [4.5] in the years before the OT. The progenitor is not detected in pre-outburst Hubble Space Telescope optical and near-IR images. The optical colors during outburst combined with spectroscopic temperature constraints imply a higher reddening of $E(B-V)\approx0.7$ mag and higher intrinsic luminosity of $M_r\approx-14.9$ (${\nu}L_{\nu}=5.3\times10^7~L_{\odot}$) near peak than seen in previous ILRT candidates. Moreover, the extinction estimate is higher on the rise than on the plateau, suggestive of an extended phase of circumstellar dust destruction. These results, enabled by the early discovery of M51 OT2019-1 and extensive pre-outburst archival coverage, offer new clues about the debated origins of ILRTs and may challenge the hypothesis that they arise from the electron-capture induced collapse of extreme asymptotic giant branch stars.Comment: 21 pages, 5 figures, published in ApJ

Nonlinear Integer Programming

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations and those motivated by our desire to solve practical instances should and do inform one another. So it is with this viewpoint that we present the subject, and it is in this direction that we hope to spark further research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G. Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50 Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art Surveys, Springer-Verlag, 2009, ISBN 354068274

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

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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

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