Graphs with tiny vector chromatic numbers and huge chromatic numbers

Karger, Motwani, and Sudan [J. ACM, 45 (1998), pp. 246-265] introduced the notion of a vector coloring of a graph. In particular, they showed that every k-colorable graph is also vector k-colorable, and that for constant k, graphs that are vector k-colorable can be colored by roughly Δ^(1 - 2/k) colors. Here Δ is the maximum degree in the graph and is assumed to be of the order of n^5 for some 0 < δ < 1. Their results play a major role in the best approximation algorithms used for coloring and for maximum independent sets. We show that for every positive integer k there are graphs that are vector k-colorable but do not have independent sets significantly larger than n/Δ^(1- 2/k) (and hence cannot be colored with significantly fewer than Δ^(1-2/k) colors). For k = O(log n/log log n) we show vector k-colorable graphs that do not have independent sets of size (log n)^c, for some constant c. This shows that the vector chromatic number does not approximate the chromatic number within factors better than n/polylogn. As part of our proof, we analyze "property testing" algorithms that distinguish between graphs that have an independent set of size n/k, and graphs that are "far" from having such an independent set. Our bounds on the sample size improve previous bounds of Goldreich, Goldwasser, and Ron [J. ACM, 45 (1998), pp. 653-750] for this problem

Numerical studies on the link between radioisotopic signatures on Earth and the formation of the Local Bubble. I. 60Fe transport to the solar system by turbulent mixing of ejecta from nearby supernovae into a locally homogeneous ISM

The discovery of radionuclides like 60Fe with half-lives of million years in deep-sea crusts and sediments offers the unique possibility to date and locate nearby supernovae. We want to quantitatively establish that the 60Fe enhancement is the result of several supernovae which are also responsible for the formation of the Local Bubble, our Galactic habitat. We performed three-dimensional hydrodynamic adaptive mesh refinement simulations (with resolutions down to subparsec scale) of the Local Bubble and the neighbouring Loop I superbubble in different homogeneous, self-gravitating environments. For setting up the Local and Loop I superbubble, we took into account the time sequence and locations of the generating core-collapse supernova explosions, which were derived from the mass spectrum of the perished members of certain stellar moving groups. The release of 60Fe and its subsequent turbulent mixing process inside the superbubble cavities was followed via passive scalars, where the yields of the decaying radioisotope were adjusted according to recent stellar evolution calculations. The models are able to reproduce both the timing and the intensity of the 60Fe excess observed with rather high precision, provided that the external density does not exceed 0.3 cm-3 on average. Thus the two best-fit models presented here were obtained with background media mimicking the classical warm ionised and warm neutral medium. We also found that 60Fe (which is condensed onto dust grains) can be delivered to Earth via two physical mechanisms: either through individual fast-paced supernova blast waves, which cross the Earth's orbit sometimes even twice as a result of reflection from the Local Bubble's outer shell, or, alternatively, through the supershell of the Local Bubble itself, injecting the 60Fe content of all previous supernovae at once, but over a longer time range.Comment: 14 pages, 7 figures, accepted for publication in A&

Numerical studies on the link between radioisotopic signatures on Earth and the formation of the Local Bubble. II. Advanced modeling of interstellar 26Al, 53Mn, 60Fe, and 244Pu influxes as traces of past supernovae in the solar neighborhood

Measurements of long-lived radioisotopes provide a means, completely independent of other observational channels, to draw conclusions about near-Earth supernovae (SNe) and thus the origin of the Local Bubble (LB). First and foremost in this context is 60Fe, which has already been detected across the Earth and on the Moon. Using Gaia EDR3, we identified 14 SN explosions, with 13 occurring in UCL/LCC, and one in V1062 Sco, all being subgroups of the Sco-Cen OB association. The timing of these explosions was obtained by us through interpolation of rotating stellar evolution tracks via the initial masses of the already exploded massive stars. We further developed a new Monte Carlo-type approach for deriving the trajectories of the SN progenitors. We then performed 3D hydrodynamic simulations based on these initial conditions to explore the evolution of the LB in an inhomogeneous local interstellar medium and the transport of radioisotopes to Earth. The simulations include the stellar winds from the SN progenitors and additional radioisotopes (26Al, 53Mn, and 244Pu) besides 60Fe. We find that (i) our simulations are consistent with measurements of 60Fe, in particular, a peak 2-3 Myr before present, as well as 26Al, 53Mn, and 244Pu data, (ii) stellar winds contribute to the distribution of radioisotopes and also to the dynamics of the LB, (iii) the solar system (SS) entered the LB about 4.6 Myr ago, and (iv) the measured recent influx of 60Fe can be naturally explained by turbulent radioisotopic transport. Our simulations not only support the recent hypothesis that the LB triggered star formation in the solar vicinity through its expansion, but also suggest that the second, separate 60Fe peak measured at 6-9 Myr ago was generated by the passage of the SS through a neighboring superbubble (SB), possibly the Orion-Eridanus SB, prior to its current residence in the LB.Comment: 30 pages, 13 figures, accepted for publication in A&

Implementation of higher-order absorbing boundary conditions for the Einstein equations

We present an implementation of absorbing boundary conditions for the Einstein equations based on the recent work of Buchman and Sarbach. In this paper, we assume that spacetime may be linearized about Minkowski space close to the outer boundary, which is taken to be a coordinate sphere. We reformulate the boundary conditions as conditions on the gauge-invariant Regge-Wheeler-Zerilli scalars. Higher-order radial derivatives are eliminated by rewriting the boundary conditions as a system of ODEs for a set of auxiliary variables intrinsic to the boundary. From these we construct boundary data for a set of well-posed constraint-preserving boundary conditions for the Einstein equations in a first-order generalized harmonic formulation. This construction has direct applications to outer boundary conditions in simulations of isolated systems (e.g., binary black holes) as well as to the problem of Cauchy-perturbative matching. As a test problem for our numerical implementation, we consider linearized multipolar gravitational waves in TT gauge, with angular momentum numbers l=2 (Teukolsky waves), 3 and 4. We demonstrate that the perfectly absorbing boundary condition B_L of order L=l yields no spurious reflections to linear order in perturbation theory. This is in contrast to the lower-order absorbing boundary conditions B_L with L<l, which include the widely used freezing-Psi_0 boundary condition that imposes the vanishing of the Newman-Penrose scalar Psi_0.Comment: 25 pages, 9 figures. Minor clarifications. Final version to appear in Class. Quantum Grav

Isolation, establishment, and characterization of ex vivo equine melanoma cell cultures

Gray horses spontaneously develop metastatic melanomas that resemble human disease, and this is often accompanied with metastasis to other organs. Unlike in other species, the establishment of primary equine melanoma cultures that could be used to develop new therapeutic approaches has remained a major challenge. The purpose of the study was to develop a protocol for routine isolation and cultivation of primary equine melanocytes. Melanoma tissues were excised from 13 horses under local anesthesia, mainly from the perianal area. The melanoma cells were isolated from the melanoma tissue by serial enzymatic digestion using dispase and collagenase. Out of the 13 excised melanomas, cell cultures from eight melanomas were established, which corresponded to a success rate 62%. These cells showed different degrees of melanin pigmentation. Characterization of these cells using confocal microscopy, FACs analysis and western blotting showed that they expressed melanoma-associated antigens; Melan-A, MAGE-1, and MAGE-3, and PCNA expression was higher in fast-proliferating isolates. The protocol we developed and established proved successful for routine isolation and cultivation of primary equine melanoma cells. This method provided a large number of primary equine melanoma cells that could be used to study new therapeutic approaches for treatment of equine melanoma

Gemini GNIRS near-infrared spectroscopy of 50 quasars at z>~5.7

We report initial results from a large Gemini program to observe z>~5.7 quasars with GNIRS near-IR spectroscopy. Our sample includes 50 quasars with simultaneous ~0.85-2.5 micron spectra covering the rest-frame ultraviolet and major broad emission lines from Ly-alpha to MgII. We present spectral measurements for these quasars and compare to their lower-redshift counterparts at z=1.5-2.3. We find that when quasar luminosity is matched, there are no significant differences between the rest-UV spectra of z>~5.7 quasars and the low-z comparison sample. High-z quasars have similar continuum and emission line properties and occupy the same region in the black hole mass and luminosity space as the comparison sample, accreting at an average Eddington ratio of ~0.3. There is no evidence for super-Eddington accretion or hypermassive (>10^10 Msun) black holes within our sample. We find a mild excess of quasars with weak CIV lines relative to the control sample. Our results, corroborating earlier studies but with better statistics, demonstrate that these high-z quasars are already mature systems of accreting supermassive black holes operating with the same physical mechanisms as those at lower redshifts.Comment: replaced with the accepted version (ApJ); improved the fitting results and replaced all figures and tables (w/ minor changes); conclusions unchange

Probing the interstellar medium and star formation of the Most Luminous Quasar at z=6.3

We report new IRAM/PdBI, JCMT/SCUBA-2, and VLA observations of the ultraluminous quasar SDSSJ010013.02+280225.8 (hereafter, J0100+2802) at z=6.3, which hosts the most massive supermassive black hole (SMBH) of 1.24x10^10 Msun known at z>6. We detect the [C II] 158 $\mu$m fine structure line and molecular CO(6-5) line and continuum emission at 353 GHz, 260 GHz, and 3 GHz from this quasar. The CO(2-1) line and the underlying continuum at 32 GHz are also marginally detected. The [C II] and CO detections suggest active star formation and highly excited molecular gas in the quasar host galaxy. The redshift determined with the [C II] and CO lines shows a velocity offset of ~1000 km/s from that measured with the quasar Mg II line. The CO (2-1) line luminosity provides direct constraint on the molecular gas mass which is about (1.0+/-0.3)x10^10 Msun. We estimate the FIR luminosity to be (3.5+/-0.7)x10^12 Lsun, and the UV-to-FIR spectral energy distribution of J0100+2802 is consistent with the templates of the local optically luminous quasars. The derived [C II]-to-FIR luminosity ratio of J0100+2802 is 0.0010+/-0.0002, which is slightly higher than the values of the most FIR luminous quasars at z~6. We investigate the constraint on the host galaxy dynamical mass of J0100+2802 based on the [C II] line spectrum. It is likely that this ultraluminous quasar lies above the local SMBH-galaxy mass relationship, unless we are viewing the system at a small inclination angle.Comment: 19 pages, 4 figures, published by the Astrophysical Journal, minimal changes in acknowledgement to match the published versio

The Final SDSS High-Redshift Quasar Sample of 52 Quasars at z>5.7

We present the discovery of nine quasars at $z\sim6$ identified in the Sloan Digital Sky Survey (SDSS) imaging data. This completes our survey of $z\sim6$ quasars in the SDSS footprint. Our final sample consists of 52 quasars at $5.7<z\le6.4$, including 29 quasars with $z_{\rm AB}\le20$ mag selected from 11,240 deg$^2$ of the SDSS single-epoch imaging survey (the main survey), 10 quasars with $20\le z_{\rm AB}\le20.5$ selected from 4223 deg$^2$ of the SDSS overlap regions (regions with two or more imaging scans), and 13 quasars down to $z_{\rm AB}\approx22$ mag from the 277 deg$^2$ in Stripe 82. They span a wide luminosity range of $-29.0\le M_{1450}\le-24.5$. This well-defined sample is used to derive the quasar luminosity function (QLF) at $z\sim6$. After combining our SDSS sample with two faint ($M_{1450}\ge-23$ mag) quasars from the literature, we obtain the parameters for a double power-law fit to the QLF. The bright-end slope $\beta$ of the QLF is well constrained to be $\beta=-2.8\pm0.2$. Due to the small number of low-luminosity quasars, the faint-end slope $\alpha$ and the characteristic magnitude $M_{1450}^{\ast}$ are less well constrained, with $\alpha=-1.90_{-0.44}^{+0.58}$ and $M^{\ast}=-25.2_{-3.8}^{+1.2}$ mag. The spatial density of luminous quasars, parametrized as $\rho(M_{1450}<-26,z)=\rho(z=6)\,10^{k(z-6)}$, drops rapidly from $z\sim5$ to 6, with $k=-0.72\pm0.11$. Based on our fitted QLF and assuming an IGM clumping factor of $C=3$, we find that the observed quasar population cannot provide enough photons to ionize the $z\sim6$ IGM at $\sim90$\% confidence. Quasars may still provide a significant fraction of the required photons, although much larger samples of faint quasars are needed for more stringent constraints on the quasar contribution to reionization.Comment: 20 pages, 12 figures, Accepted for publication in The Astrophysical Journa

Model Factory for Additive Manufacturing of Mechatronic Products: Interconnecting World-class Technology Partnerships with Leading AM Players

AbstractThe additive manufacturing (AM) model factory's aim is to establish a leading-edge learning academy for the digital and generative production of innovative mechatronic products, where the complete value chain is integrated on a single site. Short courses and deep dives enable easier access to the state of the art technologies and increase the awareness for their potentials. Anchored in key industries such as automotive, aerospace, and medical by major OEMs and regional SMEs, the AM model factory cooperates with world-class partners and leading market players. This paper displays the model factory's setup, selected technologies, exemplary courses, and benefits

Analysis of Neptune's 2017 Bright Equatorial Storm

We report the discovery of a large ($\sim$8500 km diameter) infrared-bright storm at Neptune's equator in June 2017. We tracked the storm over a period of 7 months with high-cadence infrared snapshot imaging, carried out on 14 nights at the 10 meter Keck II telescope and 17 nights at the Shane 120 inch reflector at Lick Observatory. The cloud feature was larger and more persistent than any equatorial clouds seen before on Neptune, remaining intermittently active from at least 10 June to 31 December 2017. Our Keck and Lick observations were augmented by very high-cadence images from the amateur community, which permitted the determination of accurate drift rates for the cloud feature. Its zonal drift speed was variable from 10 June to at least 25 July, but remained a constant $237.4 \pm 0.2$ m s$^{-1}$ from 30 September until at least 15 November. The pressure of the cloud top was determined from radiative transfer calculations to be 0.3-0.6 bar; this value remained constant over the course of the observations. Multiple cloud break-up events, in which a bright cloud band wrapped around Neptune's equator, were observed over the course of our observations. No "dark spot" vortices were seen near the equator in HST imaging on 6 and 7 October. The size and pressure of the storm are consistent with moist convection or a planetary-scale wave as the energy source of convective upwelling, but more modeling is required to determine the driver of this equatorial disturbance as well as the triggers for and dynamics of the observed cloud break-up events.Comment: 42 pages, 14 figures, 6 tables; Accepted to Icaru