Catching the head, tail, and everything in between: a streaming algorithm for the degree distribution

The degree distribution is one of the most fundamental graph properties of interest for real-world graphs. It has been widely observed in numerous domains that graphs typically have a tailed or scale-free degree distribution. While the average degree is usually quite small, the variance is quite high and there are vertices with degrees at all scales. We focus on the problem of approximating the degree distribution of a large streaming graph, with small storage. We design an algorithm headtail, whose main novelty is a new estimator of infrequent degrees using truncated geometric random variables. We give a mathematical analysis of headtail and show that it has excellent behavior in practice. We can process streams will millions of edges with storage less than 1% and get extremely accurate approximations for all scales in the degree distribution. We also introduce a new notion of Relative Hausdorff distance between tailed histograms. Existing notions of distances between distributions are not suitable, since they ignore infrequent degrees in the tail. The Relative Hausdorff distance measures deviations at all scales, and is a more suitable distance for comparing degree distributions. By tracking this new measure, we are able to give strong empirical evidence of the convergence of headtail

Identification of a Histidine Metal Ligand in the \u3cem\u3eargE\u3c/em\u3e-Encoded \u3cem\u3eN\u3c/em\u3e-Acetyl-L-Ornithine Deacetylase from \u3cem\u3eEscherichia coli\u3c/em\u3e

The H355A, H355K, H80A, and H80K mutant enzymes of the argE-encoded N-acetyl-L-ornithine deacetylase (ArgE) from Escherichia coli were prepared, however, only the H355A enzyme was found to be soluble. Kinetic analysis of the Co(II)-loaded H355A exhibited activity levels that were 380-fold less than Co(II)-loaded WT ArgE. Electronic absorption spectra of Co(II)-loaded H355A-ArgE indicate that the bound Co(II) ion resides in a distorted, five-coordinate environment and Isothermal Titration Calorimetry (ITC) data for Zn(II) binding to the H355A enzyme provided a dissociation constant (Kd) of 39 μM. A three-dimensional homology model of ArgE was generated using the X-ray crystal structure of the dapE-encoded N-succinyl-L,L-diaminopimelic acid desuccinylase (DapE) from Haemophilus influenzae confirming the assignment of H355 as well as H80 as active site ligands

Structural Characterization of Zn(II)-, Co(II)-, and Mn(II)-loaded Forms of the argE-encoded \u3cem\u3eN\u3c/em\u3e-acetyl-L-ornithine Deacetylase from \u3cem\u3eEscherichia coli\u3c/em\u3e

The Zn, Co, and Mn K-edge extended X-ray absorption fine structure (EXAFS) spectra of the N-acetyl-l-ornithine deacetylase (ArgE) from Escherichia coli, loaded with one or two equivalents of divalent metal ions (i.e., [Zn(II)_(ArgE)], [Zn(II)Zn(II)(ArgE)], [Co(II)_(ArgE)], [Co(II)Co(II)(ArgE)], [Mn(II)_(ArgE)], and [Mn(II)Mn(II)(ArgE)]), were recorded. The Fourier transformed data (FT) for [Zn(II)_(ArgE)], [Zn(II)Zn(II)(ArgE)], [Co(II)_(ArgE)] and [Co(II)Co(II)(ArgE)] are dominated by a peak at 2.05 Å, that can be fit assuming five or six light atom (N,O) scatterers. Inclusion of multiple-scattering contributions from the outer-shell atoms of a histidine-imidazole ring resulted in reasonable Debye–Waller factors for these contributions and a slight reduction in the goodness-of-fit value (f′). Furthermore, the data best fit a model that included a M–M vector at 3.3 and 3.4 Å for Zn(II) and Co(II), respectively, suggesting the formation of a dinuclear site. Multiple scattering contributions from the outer-shell atoms of a histidine-imidazole rings are observed at ~ 3 and 4 Å for Zn(II)- and Co(II)-loaded ArgE suggesting at least one histidine ligand at each metal binding site. Likewise, EXAFS data for Mn(II)-loaded ArgE are dominated by a peak at 2.19 Å that was best fit assuming six light atom (N,O) scatterers. Due to poor signal to noise ratios for the Mn EXAFS spectra, no Mn–Mn vector could be modeled. Peak intensities for [M(II)_(ArgE)] vs. [M(II)M(II)(ArgE)] suggest the Zn(II), Co(II), and Mn(II) bind to ArgE in a cooperative manner. Since no structural data has been reported for any ArgE enzyme, the EXAFS data reported herein represent the first structural glimpse for ArgE enzymes. These data also provide a structural foundation for the future design of small molecules that function as inhibitors of ArgE and may potentially function as a new class of antibiotics

Characterization of the Catalytically Active Mn(II)-loaded \u3cem\u3eargE\u3c/em\u3e-encoded \u3cem\u3eN\u3c/em\u3e-acetyl-L-ornithine Deacetylase from \u3cem\u3eEscherichia coli\u3c/em\u3e

The catalytically competent Mn(II)-loaded form of the argE-encoded N-acetyl-l-ornithine deacetylase from Escherichia coli (ArgE) was characterized by kinetic, thermodynamic, and spectroscopic methods. Maximum N-acetyl-l-ornithine (NAO) hydrolytic activity was observed in the presence of one Mn(II) ion with k cat and K m values of 550 s−1 and 0.8 mM, respectively, providing a catalytic efficiency (k cat/K m) of 6.9 × 105 M−1 s−1. The ArgE dissociation constant (K d) for Mn(II) was determined to be 0.18 μM, correlating well with a value obtained by isothermal titration calorimetry of 0.30 μM for the first metal binding event and 5.3 μM for the second. An Arrhenius plot of the NAO hydrolysis for Mn(II)-loaded ArgE was linear from 15 to 55 °C, suggesting the rate-limiting step does not change as a function of temperature over this range. The activation energy, determined from the slope of this plot, was 50.3 kJ mol−1. Other thermodynamic parameters were ΔG ‡ = 58.1 kJ mol−1, ΔH ‡ = 47.7 kJ mol−1, and ΔS ‡ = –34.5 J mol−1 K−1. Similarly, plots of lnK m versus 1/T were linear, suggesting substrate binding is controlled by a single step. The natural product, [(2S,3R)-3-amino-2-hydroxy-4-phenylbutanoyl]leucine (bestatin), was found to be a competitive inhibitor of ArgE with a K i value of 67 μM. Electron paramagnetic resonance (EPR) data recorded for both [Mn(II)_(ArgE)] and [Mn(II)Mn(II)(ArgE)] indicate that the two Mn(II) ions form a dinuclear site. Moreover, the EPR spectrum of [Mn(II)Mn(II)(ArgE)] in the presence of bestatin indicates that bestatin binds to ArgE but does not form a µ-alkoxide bridge between the two metal ions

Turbulent mixing layers in supersonic protostellar outflows, with application to DG Tauri

Turbulent entrainment processes may play an important role in the outflows from young stellar objects at all stages of their evolution. In particular, lateral entrainment of ambient material by high-velocity, well-collimated protostellar jets may be the cause of the multiple emission-line velocity components observed in the microjet-scale outflows driven by classical T Tauri stars. Intermediate-velocity outflow components may be emitted by a turbulent, shock- excited mixing layer along the boundaries of the jet. We present a formalism for describing such a mixing layer based on Reynolds decomposition of quantities measuring fundamental properties of the gas. In this model, the molecular wind from large disc radii provides a continual supply of material for entrainment. We calculate the total stress profile in the mixing layer, which allows us to estimate the dissipation of turbulent energy, and hence the luminosity of the layer. We utilize MAPPINGS IV shock models to determine the fraction of total emission that occurs in [Fe II] 1.644 {\mu}m line emission in order to facilitate comparison to previous observations of the young stellar object DG Tauri. Our model accurately estimates the luminosity and changes in mass outflow rate of the intermediate-velocity component of the DG Tau approaching outflow. Therefore, we propose that this component represents a turbulent mixing layer surrounding the well-collimated jet in this object. Finally, we compare and contrast our model to previous work in the field.Comment: 18 pages, 13 figures, accepted for publication in MNRA

The radial evolution of solar wind speeds

The WSA-ENLIL model predicts significant evolution of the solar wind speed. Along a flux tube the solar wind speed at 1.0 AU and beyond is found to be significantly altered from the solar wind speed in the outer corona at 0.1 AU, with most of the change occurring within a few tenths of an AU from the Sun. The evolution of the solar wind speed is most pronounced during solar minimum for solar wind with observed speeds at 1.0 AU between 400 and 500 km/s, while the fastest and slowest solar wind experiences little acceleration or deceleration. Solar wind ionic charge state observations made near 1.0 AU during solar minimum are found to be consistent with a large fraction of the intermediate-speed solar wind having been accelerated or decelerated from slower or faster speeds. This paper sets the groundwork for understanding the evolution of wind speed with distance, which is critical for interpreting the solar wind composition observations near Earth and throughout the inner heliosphere. We show from composition observations that the intermediate-speed solar wind (400-500 km/s) represents a mix of what was originally fast and slow solar wind, which implies a more bimodal solar wind in the corona than observed at 1.0 AU

\u3cem\u3eargE\u3c/em\u3e-Encoded \u3cem\u3eN\u3c/em\u3e-Acetyl-l-Ornithine Deacetylase from \u3cem\u3eEscherichia coli\u3c/em\u3e Contains a Dinuclear Metalloactive Site

The catalytic and structural properties of the argE-encoded N-acetyl-l-ornithine deacetylase (ArgE) from Escherichia coli were investigated. On the basis of kinetic and ITC (isothermal titration calorimetry) data, Zn(II) binds to ArgE with Kd values that differ by ∼20 times. Moreover, ArgE exhibits ∼90% of its full catalytic activity upon addition of one metal ion. Therefore, ArgE behaves similarly to the aminopeptidase from Aeromonas proteolytica (AAP) in that one metal ion is the catalytic metal ion while the second likely plays a structural role. The N-acetyl-l-ornithine (NAO) deacetylase activity of ArgE showed a linear temperature dependence from 20 to 45 °C, indicating that the rate-limiting step does not change over this temperature range. The activation energy for NAO hydrolysis by ArgE was 25.6 kJ/mol when loaded with Zn(II) and 34.3 kJ/mol when loaded with Co(II). Electronic absorption and EPR (electron paramagnetic resonance) spectra of [Co·(ArgE)] and [CoCo(ArgE)] indicate that both divalent metal binding sites are five coordinate. In addition, EPR data show clear evidence of spin−spin coupling between the Co(II) ions in the active site but only after addition of a second equivalent of Co(II). Combination of these data provides the first physical evidence that the ArgE from E. coli contains a dinuclear Zn(II) active site, similar to AAP and the carboxypeptidase G2 from Pseudomonas sp. strain RS-16 (CPG2)

Multi-epoch Sub-arcsecond [Fe II] Spectroimaging of the DG Tau Outflows with NIFS. II. On the Nature of the Bipolar Outflow Asymmetry

The origin of bipolar outflow asymmetry in young stellar objects (YSOs) remains poorly understood. It may be due to an intrinsically asymmetric outflow launch mechanism, or it may be caused by the effects of the ambient medium surrounding the YSO. Answering this question is an important step in understanding outflow launching. We have investigated the bipolar outflows driven by the T Tauri star DG Tauri on scales of hundreds of AU, using the Near-infrared Integral Field Spectrograph (NIFS) on Gemini North. The approaching outflow consists of a well-collimated jet, nested within a lower-velocity disc wind. The receding outflow is composed of a single-component bubble-like structure. We analyse the kinemat- ics of the receding outflow using kinetic models, and determine that it is a quasi-stationary bubble with an expanding internal velocity field. We propose that this bubble forms because the receding counterjet from DG Tau is obstructed by a clumpy ambient medium above the circumstellar disc surface, based on similarities between this structure and those found in the modeling of active galactic nuclei outflows. We find evidence of interaction between the obscured counterjet and clumpy ambient material, which we attribute to the large molecular envelope around the DG Tau system. An analytical model of a momentum-driven bubble is shown to be consistent with our interpretation. We conclude that the bipolar outflow from DG Tau is intrinsically symmetric, and the observed asymmetries are due to environmental effects. This mechanism can potentially be used to explain the observed bipolar asymmetries in other YSO outflows.Comment: 16 pages, 10 figures, accepted for publication in MNRA

Temperature-dependent Hall scattering factor and drift mobility in remotely doped Si:B/SiGe/Si heterostructures

Hall-and-Strip measurements on modulation-doped SiGe heterostructures and combined Hall and capacitance–voltage measurements on metal-oxide-semiconductor (MOS)-gated enhancement mode structures have been used to deduce Hall scattering factors, rH, in the Si1 – xGex two-dimensional hole gas. At 300 K, rH was found to be equal to 0.4 for x = 0.2 and x = 0.3. Knowing rH, it is possible to calculate the 300 K drift mobilities in the modulation-doped structures which are found to be 400 cm2 V – 1 s – 1 at a carrier density of 3.3 × 1011 cm – 2 for x = 0.2 and 300 cm2 V – 1 s – 1 at 6.3 × 1011 cm – 2 for x = 0.3, factors of between 1.5 and 2.0 greater than a Si pMOS control