Prodsimplicial-Neighborly Polytopes

Simultaneously generalizing both neighborly and neighborly cubical polytopes, we introduce PSN polytopes: their k-skeleton is combinatorially equivalent to that of a product of r simplices. We construct PSN polytopes by three different methods, the most versatile of which is an extension of Sanyal and Ziegler's "projecting deformed products" construction to products of arbitrary simple polytopes. For general r and k, the lowest dimension we achieve is 2k+r+1. Using topological obstructions similar to those introduced by Sanyal to bound the number of vertices of Minkowski sums, we show that this dimension is minimal if we additionally require that the PSN polytope is obtained as a projection of a polytope that is combinatorially equivalent to the product of r simplices, when the dimensions of these simplices are all large compared to k.Comment: 28 pages, 9 figures; minor correction

Polytopality and Cartesian products of graphs

We study the question of polytopality of graphs: when is a given graph the graph of a polytope? We first review the known necessary conditions for a graph to be polytopal, and we provide several families of graphs which satisfy all these conditions, but which nonetheless are not graphs of polytopes. Our main contribution concerns the polytopality of Cartesian products of non-polytopal graphs. On the one hand, we show that products of simple polytopes are the only simple polytopes whose graph is a product. On the other hand, we provide a general method to construct (non-simple) polytopal products whose factors are not polytopal.Comment: 21 pages, 10 figure

Confirmation of the Planetary Microlensing Signal and Star and Planet Mass Determinations for Event OGLE-2005-BLG-169

We present Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) observations of the source and lens stars for planetary microlensing event OGLE-2005-BLG-169, which confirm the relative proper motion prediction due to the planetary light curve signal observed for this event. This (and the companion Keck result) provide the first confirmation of a planetary microlensing signal, for which the deviation was only 2%. The follow-up observations determine the flux of the planetary host star in multiple passbands and remove light curve model ambiguity caused by sparse sampling of part of the light curve. This leads to a precise determination of the properties of the OGLE-2005-BLG-169Lb planetary system. Combining the constraints from the microlensing light curve with the photometry and astrometry of the HST/WFC3 data, we find star and planet masses of M_* = 0.69+- 0.02 M_solar and m_p = 14.1 +- 0.9 M_earth. The planetary microlens system is located toward the Galactic bulge at a distance of D_L = 4.1 +- 0.4 kpc, and the projected star-planet separation is a_perp = 3.5 +- 0.3 AU, corresponding to a semi-major axis of a = 4.0 (+2.2 -0.6) AU.Comment: 21 pages, including 5 figures, published in Ap

Initial Efforts to Manage IPE during the COVID-19 Pandemic: Reports from the Big Ten Academic Alliance

Purpose: The COVID-19 pandemic required higher education institutions to quickly transition to a virtual platform. This was challenging for those involved in interprofessional education (IPE), given the goal that students from two or more professions learn about, from, and with one another. The Big Ten IPE Alliance is a subgroup of the larger Big Ten Academic Alliance. The purpose of this paper is to share the collective experiences of multiple large, research intensive universities in addressing the challenge of implementing IPE programs under the conditions established by the COVID-19 pandemic. Methods: To better understand how the Big Ten schools dealt with the transition to virtual learning for didactic and clinical IPE given the COVID-19 pandemic, a subset of representatives from the Big Ten IPE Alliance met to discuss best practices for virtual learning in the IPE realm. Each participating university completed an electronic 14 question survey related to their IPE curriculum during the COVID-19 pandemic from March 2020 thru August 2020 and the responses were analyzed. Results: Four categories were identified as needing to be addressed to develop and implement successful interprofessional didactic and clinical experiences. The categories identified included content/assessment, virtual technologies, faculty and facilitators, and learners. Conclusions/Recommendations: Consider including authentic and innovative mechanisms to deliver IPE experiences that meet the learning needs and accreditation requirements. Interinstitutional collaborations such as within the Big Ten IPE Alliance can be beneficial in assessing current and future best practices in IPE

Brines from industrial water recycling: New ways to resource recovery

Stricter environmental regulation policies and freshwater as an increasingly valuable resource have led to global growth of zero liquid discharge (ZLD) processes in recent years. During this development, in addition to water, the recovery of recyclable materials, e.g. salts, from industrial wastewater and brines is considered more frequently. Within the framework of the HighCon research project, the subject of this study, a new ZLD process with the goal of pure single-salt recovery from industrial wastewater has been developed and investigated in a demonstrational setup at an industrial site. With regard to pure salts recovery, separating organic components is of great importance during the treatment of the concentrate arising from used water recycling. The removal of COD and of ions responsible for scaling worked very well using nanofiltration. The nanofiltration permeate containing the monovalent ions was pre-concentrated using electrodialysis and membrane distillation before selective crystallization for single-salt recovery was performed. An example economic case study for the newly developed ZLD process - based on demonstration results and considering optimization measures for a full-scale design - indicates that the costs are equal to those of a conventional ZLD process, which, however, does not provide inter alia the aforementioned benefit of single-salt recovery

BASS. XXXIV. A Catalog of the Nuclear Millimeter-wave Continuum Emission Properties of AGNs Constrained on Scales ≤ 100-200 pc

We present a catalog of the millimeter-wave (mm-wave) continuum properties of 98 nearby (z < 0.05) active galactic nuclei (AGNs) selected from the 70 month Swift/BAT hard-X-ray catalog that have precisely determined X-ray spectral properties and subarcsecond-resolution Atacama Large Millimeter/submillimeter Array Band 6 (211-275 GHz) observations as of 2021 April. Due to the hard-X-ray (>10 keV) selection, the sample is nearly unbiased for obscured systems at least up to Compton-thick-level obscuration, and provides the largest number of AGNs with high-physical-resolution mm-wave data (less than or similar to 100-200 pc). Our catalog reports emission peak coordinates, spectral indices, and peak fluxes and luminosities at 1.3 mm (230 GHz). Additionally, high-resolution mm-wave images are provided. Using the images and creating radial surface brightness profiles of mm-wave emission, we identify emission extending from the central sources and isolated blob-like emission. Flags indicating the presence of these emission features are tabulated. Among 90 AGNs with significant detections of nuclear emission, 37 AGNs (approximate to 41%) appear to have both or one of extended or blob-like components. We, in particular, investigate AGNs that show well-resolved mm-wave components and find that these seem to have a variety of origins (i.e., a jet, radio lobes, a secondary AGN, stellar clusters, a narrow-line region, galaxy disk, active star formation regions, or AGN-driven outflows), and some components have currently unclear origins

BASS. XLII. The Relation between the Covering Factor of Dusty Gas and the Eddington Ratio in Nearby Active Galactic Nuclei

Accreting supermassive black holes (SMBHs) located at the centers of galaxies are typically surrounded by large quantities of gas and dust. The structure and evolution of this circumnuclear material can be studied at different wavelengths, from the submillimeter to the X-ray. Recent X-ray studies have shown that the covering factor of the obscuring material tends to decrease with increasing Eddington ratio, likely due to radiative feedback on dusty gas. Here we study a sample of 549 nearby (z less than or similar to 0.1) hard X-ray (14-195 keV) selected nonblazar active galactic nuclei (AGN) and use the ratio between the AGN infrared and bolometric luminosity as a proxy of the covering factor. We find that, in agreement with what has been found by X-ray studies of the same sample, the covering factor decreases with increasing Eddington ratio. We also confirm previous findings that showed that obscured AGN typically have larger covering factors than unobscured sources. Finally, we find that the median covering factors of AGN located in different regions of the column density-Eddington ratio diagram are in good agreement with what would be expected from a radiation-regulated growth of SMBHs

A hard X-ray view of luminous and ultra-luminous infrared galaxies in GOALS - I. AGN obscuration along the merger sequence

The merger of two or more galaxies can enhance the inflow of material from galactic scales into the close environments of active galactic nuclei (AGNs), obscuring and feeding the supermassive black hole (SMBH). Both recent simulations and observations of AGN in mergers have confirmed that mergers are related to strong nuclear obscuration. However, it is still unclear how AGN obscuration evolves in the last phases of the merger process. We study a sample of 60 luminous and ultra-luminous IR galaxies (U/LIRGs) from the GOALS sample observed by NuSTAR. We find that the fraction of AGNs that are Compton thick (CT;N-H >= 10(24)cm(-2) ) peaks at at a late merger stage, prior to coalescence, when the nuclei have projected separations (d(sep)) of 0.4-6 kpc. A similar peak is also observed in the median N-H [[(1.6 +/- 0.5) x 10(24) cm(-2)].]. The vast majority (85(-9)(+7) per cent)) of the AGNs in the final merger stages (d(sep) less than or similar to 10 kpc) are heavily obscured (N-H = 10(23) cm(-2)), and the median N-H of the accreting SMBHs in our sample is systematically higher than that of local hard X-ray-selected AGN, regardless of the merger stage. This implies that these objects have very obscured nuclear environments, with the gas almost completely covering the AGN in late mergers. CT AGNs tend to have systematically higher absorption-corrected X-ray luminosities than less obscured sources. This could either be due to an evolutionary effect, with more obscured sources accreting more rapidly because they have more gas available in their surroundings, or to a selection bias. The latter scenario would imply that we are still missing a large fraction of heavily obscured, lower luminosity (L2-10 less than or similar to 10(43) erg s(-1)) AGNs in U/LIRGs

BASS XLII: The relation between the covering factor of dusty gas and the Eddington ratio in nearby active galactic nuclei

Accreting supermassive black holes (SMBHs) located at the center of galaxies are typically surrounded by large quantities of gas and dust. The structure and evolution of this circumnuclear material can be studied at different wavelengths, from the submillimeter to the X-rays. Recent X-ray studies have shown that the covering factor of the obscuring material tends to decrease with increasing Eddington ratio, likely due to radiative feedback on dusty gas. Here we study a sample of 549 nearby (z<0.1) hard X-ray (14-195 keV) selected non-blazar active galactic nuclei (AGN), and use the ratio between the AGN infrared and bolometric luminosity as a proxy of the covering factor. We find that, in agreement with what has been found by X-ray studies of the same sample, the covering factor decreases with increasing Eddington ratio. We also confirm previous findings which showed that obscured AGN typically have larger covering factors than unobscured sources. Finally, we find that the median covering factors of AGN located in different regions of the column density-Eddington ratio diagram are in good agreement with what would be expected from a radiation-regulated growth of SMBHs.Comment: ApJ in pres