Learning multifractal structure in large networks

Generating random graphs to model networks has a rich history. In this paper, we analyze and improve upon the multifractal network generator (MFNG) introduced by Palla et al. We provide a new result on the probability of subgraphs existing in graphs generated with MFNG. From this result it follows that we can quickly compute moments of an important set of graph properties, such as the expected number of edges, stars, and cliques. Specifically, we show how to compute these moments in time complexity independent of the size of the graph and the number of recursive levels in the generative model. We leverage this theory to a new method of moments algorithm for fitting large networks to MFNG. Empirically, this new approach effectively simulates properties of several social and information networks. In terms of matching subgraph counts, our method outperforms similar algorithms used with the Stochastic Kronecker Graph model. Furthermore, we present a fast approximation algorithm to generate graph instances following the multi- fractal structure. The approximation scheme is an improvement over previous methods, which ran in time complexity quadratic in the number of vertices. Combined, our method of moments and fast sampling scheme provide the first scalable framework for effectively modeling large networks with MFNG

Opening the Treasure Chest in Carina

We have mapped the G287.84-0.82 cometary globule (with the Treasure Chest cluster embedded in it) in the South Pillars region of Carina (i) in [CII], 63micron [OI], and CO(11-10) using upGREAT on SOFIA and (ii) in J=2-1 transitions of CO, 13CO, C18O and J=3-2 transitions of H2CO using the APEX telescope in Chile. We probe the morphology, kinematics, and physical conditions of the molecular gas and the photon dominated regions (PDRs) in G287.84-0.82. The [CII] and [OI] emission suggest that the overall structure of the pillar (with red-shifted photo evaporating tails) is consistent with the effect of FUV radiation and winds from eta-Car and O stars in Trumpler 16. The gas in the head of the pillar is strongly influenced by the embedded cluster, whose brightest member is an O9.5V star, CPD-59 2661. The emission of the [CII] and [OI] lines peak at a position close to the embedded star, while all other tracers peak at another position lying to the north-east consistent with gas being compressed by the expanding PDR created by the embedded cluster. The molecular gas inside the globule is probed with the J=2-1 transitions of CO and isotopologues as well as H2CO, and analyzed using a non-LTE model (escape-probability approach), while we use PDR models to derive the physical conditions of the PDR. We identify at least two PDR gas components; the diffuse part (~10^4 cm^-3) is traced by [CII], while the dense (n~ 2-8x10^5 cm^-3) part is traced by [CII], [OI], CO(11-10). Using the F=2-1 transition of [13CII] detected at 50 positions in the region, we derive optical depths (0.9-5), excitation temperatures of [CII] (80-255 K), and N(C+) of 0.3-1x10^19 cm^-2. The total mass of the globule is ~1000 Msun, about half of which is traced by [CII]. The dense PDR gas has a thermal pressure of 10^7-10^8 K cm^-3, which is similar to the values observed in other regions.Comment: Accepted for publication in Astronomy and Astrophysics (abstract slightly abridged

High Spectral and Spatial Resolution Observations of the PDR Emission in the NGC2023 Reflection Nebula with SOFIA and APEX

We have mapped the NGC 2023 reflection nebula in [CII] and CO(11--10) with the heterodyne receiver GREAT on SOFIA and obtained slightly smaller maps in 13CO(3--2), CO(3--2), CO(4--3), CO(6--5), and CO(7--6) with APEX in Chile. We use these data to probe the morphology, kinematics, and physical conditions of the C II region, which is ionized by FUV radiation from the B2 star HD37903. The [CII] emission traces an ellipsoidal shell-like region at a position angle of ~ -50 deg, and is surrounded by a hot molecular shell. In the southeast, where the C II region expands into a dense, clumpy molecular cloud ridge, we see narrow and strong line emission from high-J CO lines, which comes from a thin, hot molecular shell surrounding the [CII] emission. The [CII] lines are broader and show photo evaporating gas flowing into the C II region. Based on the strength of the [13CII] F=2--1 line, the [CII] line appears to be somewhat optically thick over most of the nebula with an optical depth of a few. We model the physical conditions of the surrounding molecular cloud and the PDR emission using both RADEX and simple PDR models. The temperature of the CO emitting PDR shell is ~ 90 -- 120 K, with densities of 10^5 -- 10^6 cm^-3, as deduced from RADEX modeling. Our PDR modeling indicates that the PDR layer where [CII] emission dominates has somewhat lower densities, 10^4 to a few times 10^5 cm^-3Comment: Accepted by A&

Embryo rescue from seedless grapevines (Vitis vinifera L.) treated with growth retardants

The effects of two retardants (CCC and paclobutrazol) and the new compound XE 1019, applied before grapevine anthesis, were studied in order to increase the number of fertilised embryos and growing plantlets derived from in ovulo culture of seedless cultivars CG 102.011, Emperatriz and Malvinas. No significant differences were detected between treatments with CCC (400 and 800 mg . l-1, applied 2, 3 and 4 weeks before bloom), and the control in the cv. CG 102.011. The number of growing plantlets at 10 weeks after anthesis and at maturity was significantly higher than that from 8 weeks. In applications closer to bloom, CCC treatments increased the number of ovules per berry in the cultivars assayed. From all cultivars, only CG 102.011 showed a significant increase in plantlet production after CCC treatment when clusters were harvested the 10th week after bloom. It is believed that CCC would act through inhibition of endogenous gibberellin synthesis as the cause of ovule abortion. The idea is based on the fact that gibberellic acid can induce seedlessness in some seeded cultivars

Long-term denudation rates from the Central Andes (Chile) estimated from a digital elevation model using the black top hat function and inverse distance weighting : implications for the neogene climate of the Atacama Desert

A methodology for determining long-term denudation rates from morphologic markers in a Digital Elevation Model (DEM) is checked by a comparative study of two drainage basins in the Precordillera of the Central Andes. In both cases the initial configuration of an incised pediment surface has been restored by using two different methods: the Black Top Hat (BTH) function and the Inverse Distance Weighting (IDW) interpolation. Where vertical incision and hillslope erosion are recorded, the 1DW appears to be the most adequate to reconstitute the pediment surfaces. Conversely, where only vertical incision is observed, the BTH describes more precisely the former pediment surfaces and it is easier to solve. By subtracting the DEM from the reconstructed marker we calculated an eroded volume, and estimated its uncertainty by considering Root Mean Square Error (RMSE) and DEM grid error. For the last similar to 10 Myr we obtained long-term denudation rates of 7.33 +/- 1.6 m/Myr in the San Andres drainage basin and 13.59 +/- 1.9 m/Myr in the El Salado drainage basin. These estimations are largely in agreement with other reported estimates of long-term denudation rates in the Atacama Desert. Comparison with long-term denudation rates reported in a wide range of climatic regimes suggests that our estimates cannot be explained by the current rainfall in the Precordillera. However they could be explained by a rainfall similar to that reported 40 km to the east in the Puna. This suggests that during the time span concerned the geomorphologic evolution of the study area, this evolution is dominated by an orographically controlled rainfall pattern. The preserved pediment surface and the small long term denudation rates determined in this study also indicate that the Precordillera was never reached by humid tropical air masses and precipitation as currently observed in the Altiplano during the summer months

Abundant Z-cyanomethanimine in the interstellar medium: paving the way to the synthesis of adenine

We report the first detection in the interstellar medium of the Z-isomer of cyanomethanimine (HNCHCN), an HCN dimer proposed as precursor of adenine. We identified six transitions of Z-cyanomethanimine, along with five transitions of E-cyanomethanimine, using IRAM 30m observations towards the Galactic Center quiescent molecular cloud G+0.693. The Z-isomer has a column density of (2.0$\pm$0.6)$\times$10$^{14}$ cm$^{-2}$ and an abundance of 1.5$\times$10$^{-9}$. The relative abundance ratio between the isomers is [Z/E]$\sim$6. This value cannot be explained by the two chemical formation routes previously proposed (gas-phase and grain surface), which predicts abundances ratios between 0.9 and 1.5. The observed [Z/E] ratio is in good agreement with thermodynamic equilibrium at the gas kinetic temperature (130$-$210 K). Since isomerization is not possible in the ISM, the two species may be formed at high temperature. New chemical models, including surface chemistry on dust grains and gas-phase reactions, should be explored to explain our findings. Whatever the formation mechanism, the high abundance of Z-HNCHCN shows that precursors of adenine are efficiently formed in the ISM.Comment: Accepted in Monthly Notices of the Royal Astronomical Society Letter

Complex organic molecules in the Galactic Centre: the N-bearing family

We present an unbiased spectral line survey toward the Galactic Centre (GC) quiescent giant molecular cloud (QGMC), G+0.693 using the GBT and IRAM 30$\,$ telescopes. Our study highlights an extremely rich organic inventory of abundant amounts of nitrogen (N)-bearing species in a source without signatures of star formation. We report the detection of 17 N-bearing species in this source, of which 8 are complex organic molecules (COMs). A comparison of the derived abundances relative to H$_2$ is made across various galactic and extragalactic environments. We conclude that the unique chemistry in this source is likely to be dominated by low-velocity shocks with X-rays/cosmic rays also playing an important role in the chemistry. Like previous findings obtained for O-bearing molecules, our results for N-bearing species suggest a more efficient hydrogenation of these species on dust grains in G+0.693 than in hot cores in the Galactic disk, as a consequence of the low dust temperatures coupled with energetic processing by X-ray/cosmic ray radiation in the GC.Comment: 24 pages, 23 figures, 7 tables, accepted for publication in MNRA

Chemical Features in the Circumnuclear Disk of the Galactic Center

The circumnuclear disk (CND) of the Galactic Center is exposed to many energetic phenomena coming from the supermassive black hole Sgr A* and stellar activities. These energetic activities can affect the chemical composition in the CND by the interaction with UV-photons, cosmic-rays, X-rays, and shock waves. We aim to constrain the physical conditions present in the CND by chemical modeling of observed molecular species detected towards it. We analyzed a selected set of molecular line data taken toward a position in the southwest lobe of the CND with the IRAM 30m and APEX 12-meter telescopes and derived the column density of each molecule using a large velocity gradient (LVG) analysis. The determined chemical composition is compared with a time-dependent gas-grain chemical model based on the UCL\_CHEM code that includes the effects of shock waves with varying physical parameters. Molecules such as CO, HCN, HCO$^+$, HNC, CS, SO, SiO, NO, CN, H$_2$CO, HC$_3$N, N$_2$H$^+$ and H$_3$O$^+$ are detected and their column densities are obtained. Total hydrogen densities obtained from LVG analysis range between $2 \times 10^4$ and $1 \times 10^6\,$cm$^{-3}$ and most species indicate values around several $\times 10^5\,$cm$^{-3}$, which are lower than values corresponding to the Roche limit, which shows that the CND is tidally unstable. The chemical models show good agreement with the observations in cases where the density is $\sim10^4\,$cm$^{-3}$, the cosmic-ray ionization rate is high, $>10^{-15} \,$s$^{-1}$, or shocks with velocities $> 40\,$km s$^{-1}$ have occurred. Comparison of models and observations favors a scenario where the cosmic-ray ionization rate in the CND is high, but precise effects of other factors such as shocks, density structures, UV-photons and X-rays from the Sgr A* must be examined with higher spatial resolution data.Comment: 17 Pages, 13 figures, accepted for publication in A&