The DP Color Function of Clique-Gluings of Graphs

DP-coloring (also called correspondence coloring) is a generalization of list coloring that has been widely studied in recent years after its introduction by Dvo\v{r}\'{a}k and Postle in 2015. As the analogue of the chromatic polynomial of a graph $G$, $P(G,m)$, the DP color function of $G$, denoted $P_{DP}(G,m)$, counts the minimum number of DP-colorings over all possible $m$-fold covers. Formulas for chromatic polynomials of clique-gluings of graphs are well-known, but the effect of such gluings on the DP color function is not well understood. In this paper we study the DP color function of $K_p$-gluings of graphs. Recently, Becker et. al. asked whether $P_{DP}(G,m) \leq (\prod_{i=1}^n P_{DP}(G_i,m))/\left( \prod_{i=0}^{p-1} (m-i) \right)^{n-1}$ whenever $m \geq p$, where the expression on the right is the DP-coloring analogue of the corresponding chromatic polynomial formula for a $K_p$-gluing of $G_1, \ldots, G_n$. Becker et. al. showed this inequality holds when $p=1$. In this paper we show this inequality holds for edge-gluings ($p=2$). On the other hand, we show it does not hold for triangle-gluings ($p=3$), which also answers a question of Dong and Yang (2021). Finally, we show a relaxed version, based on a class of $m$-fold covers that we conjecture would yield the fewest DP-colorings for a given graph, of the inequality holds when $p \geq 3$.Comment: 20 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:2104.1226

Physical conditions regulate the fungal to bacterial ratios of a tropical suspended soil

As a source of ‘suspended soils’, epiphytes contribute large amounts of organic matter to the canopy of tropical rain forests. Microbes associated with epiphytes are responsible for much of the nutrient cycling taking place in rain forest canopies. However, soils suspended far above the ground in living organisms differ from soil on the forest floor, and traditional predictors of soil microbial community composition and functioning (nutrient availability and the activity of soil organisms) are likely to be less important. We conducted an experiment in the rain forest biome at the Eden Project in Cornwall to explore how biotic and abiotic conditions determine microbial community composition and functioning in a suspended soil. To simulate their natural epiphytic lifestyle, 20 bird’s nest ferns (Asplenium nidus) were placed on a custom-built canopy platform suspended 8m above the ground. Ammonium nitrate and earthworm treatments were applied to ferns in a factorial design. Extracellular enzyme activity and Phospholipid Fatty Acid (PLFA) profiles were determined at zero, three and six months. We observed no significant differences in either enzyme activity or PLFA profiles between any of the treatments. Instead, we observed decreases in β-glucosidase and N-acetyl-glucosaminidase activity, and an increase in phenol oxidase activity across all treatments and controls. An increase in the relative abundance of fungi during the experiment meant that the microbial communities in the Eden Project ferns after six months were comparable with 20 ferns sampled from pristine tropical rain forest in Borneo

Soil methane sink capacity response to a long-term wildfire chronosequence in Northern Sweden

Boreal forests occupy nearly one fifth of the terrestrial land surface and are recognised as globally important regulators of carbon (C) cycling and greenhouse gas emissions. Carbon sequestration processes in these forests include assimilation of CO2 into biomass and subsequently into soil organic matter, and soil microbial oxidation of methane (CH4). In this study we explored how ecosystem retrogression, which drives vegetation change, regulates the important process of soil CH4 oxidation in boreal forests. We measured soil CH4 oxidation processes on a group of 30 forested islands in northern Sweden differing greatly in fire history, and collectively representing a retrogressive chronosequence, spanning 5000 years. Across these islands the build-up of soil organic matter was observed to increase with time since fire disturbance, with a significant correlation between greater humus depth and increased net soil CH4 oxidation rates. We suggest that this increase in net CH4 oxidation rates, in the absence of disturbance, results as deeper humus stores accumulate and provide niches for methanotrophs to thrive. By using this gradient we have discovered important regulatory controls on the stability of soil CH4 oxidation processes that could not have not been explored through shorter-term experiments. Our findings indicate that in the absence of human interventions such as fire suppression, and with increased wildfire frequency, the globally important boreal CH4 sink could be diminished

On renormalization group flows and the a-theorem in 6d

We study the extension of the approach to the a-theorem of Komargodski and Schwimmer to quantum field theories in d=6 spacetime dimensions. The dilaton effective action is obtained up to 6th order in derivatives. The anomaly flow a_UV - a_IR is the coefficient of the 6-derivative Euler anomaly term in this action. It then appears at order p^6 in the low energy limit of n-point scattering amplitudes of the dilaton for n > 3. The detailed structure with the correct anomaly coefficient is confirmed by direct calculation in two examples: (i) the case of explicitly broken conformal symmetry is illustrated by the free massive scalar field, and (ii) the case of spontaneously broken conformal symmetry is demonstrated by the (2,0) theory on the Coulomb branch. In the latter example, the dilaton is a dynamical field so 4-derivative terms in the action also affect n-point amplitudes at order p^6. The calculation in the (2,0) theory is done by analyzing an M5-brane probe in AdS_7 x S^4. Given the confirmation in two distinct models, we attempt to use dispersion relations to prove that the anomaly flow is positive in general. Unfortunately the 4-point matrix element of the Euler anomaly is proportional to stu and vanishes for forward scattering. Thus the optical theorem cannot be applied to show positivity. Instead the anomaly flow is given by a dispersion sum rule in which the integrand does not have definite sign. It may be possible to base a proof of the a-theorem on the analyticity and unitarity properties of the 6-point function, but our preliminary study reveals some difficulties.Comment: 41 pages, 5 figure

Attenuation of Replication-Competent Adenovirus Serotype 26 Vaccines by Vectorization

Replication-competent adenovirus (rcAd)-based vaccine vectors may theoretically provide immunological advantages over replication-incompetent Ad vectors, but they also raise additional potential clinical and regulatory issues. We produced replication-competent Ad serotype 26 (rcAd26) vectors by adding the E1 region back into a replication-incompetent Ad26 vector backbone with the E3 or E3/E4 regions deleted. We assessed the effect of vectorization on the replicative capacity of the rcAd26 vaccines. Attenuation occurred in a stepwise fashion, with E3 deletion, E4 deletion, and human immunodeficiency virus type 1 (HIV-1) envelope (Env) gene insertion all contributing to reduced replicative capacity compared to that with the wild-type Ad26 vector. The rcAd26 vector with E3 and E4 deleted and containing the Env transgene exhibited 2.7- to 4.4-log-lower replicative capacity than that of the wild-type Ad26 in vitro. This rcAd26 vector is currently being evaluated in a phase 1 clinical trial. Attenuation as a result of vectorization and transgene insertion has implications for the clinical development of replication-competent vaccine vectors

AP-1 and KIF13A coordinate endosomal sorting and positioning during melanosome biogenesis

The clathrin adaptor protein AP-1 and the motor KIF13A work together to deliver cargo into maturing melanosomes

A Candidate Dual AGN at z=1.175

The X-ray source CXOXBJ142607.6+353351 (CXOJ1426+35), which was identified in a 172 ks Chandra image in the Bootes field, shows double-peaked rest-frame optical/UV emission lines, separated by 0.69" (5.5 kpc) in the spatial dimension and by 690 km s^-1 in the velocity dimension. The high excitation lines and emission line ratios indicate both systems are ionized by an AGN continuum, and the double-peaked profile resembles that of candidate dual AGN. At a redshift of z=1.175, this source is the highest redshift candidate dual AGN yet identified. However, many sources have similar emission line profiles for which other interpretations are favored. We have analyzed the substantial archival data available in this field, as well as acquired near-infrared (NIR) adaptive optics (AO) imaging and NIR slit spectroscopy. The X-ray spectrum is hard, implying a column density of several 10^23 cm^-2. Though heavily obscured, the source is also one of the brightest in the field, with an absorption-corrected 2-10 keV luminosity of ~10^45 erg s^-1. Outflows driven by an accretion disk may produce the double-peaked lines if the central engine accretes near the Eddington limit. However, we may be seeing the narrow line regions of two AGN following a galactic merger. While the AO image reveals only a single source, a second AGN would easily be obscured by the significant extinction inferred from the X-ray data. Understanding the physical processes producing the complex emission line profiles seen in CXOJ1426+35 and related sources is important for interpreting the growing population of dual AGN candidates.Comment: 18 pages and 9 figures. Accepted for publication in The Astrophysical Journa

Felony Murder and Capital Punishment: an Examination of the Deterrence Question

A proper test of the deterrent effect of the death penalty must consider capital homicides. However, the criterion variable in most investigations has been total homicides—most of which bear no legal or theoretical relationship to capital punishment. To address this fundamental data problem, this investigation used Federal Bureau of Investigation data for 1976–1987 to examine the relationship between capital punishment and felony murder, the most common type of capital homicide. We conducted time series analyses of monthly felony murder rates, the frequency of executions, and the amount and type of television coverage of executions over the period. The analyses revealed occasional departures (for vehicle theft and narcotics killings) from the null hypotheses. However, on balance, and in line with the vast majority of capital punishment studies, this investigation found no consistent evidence that executions and the television coverage they receive are associated significantly with rates for total, index, or different types of felony murder

Imaging Single Retrovirus Entry through Alternative Receptor Isoforms and Intermediates of Virus-Endosome Fusion

A large group of viruses rely on low pH to activate their fusion proteins that merge the viral envelope with an endosomal membrane, releasing the viral nucleocapsid. A critical barrier to understanding these events has been the lack of approaches to study virus-cell membrane fusion within acidic endosomes, the natural sites of virus nucleocapsid capsid entry into the cytosol. Here we have investigated these events using the highly tractable subgroup A avian sarcoma and leukosis virus envelope glycoprotein (EnvA)-TVA receptor system. Through labeling EnvA pseudotyped viruses with a pH-sensitive fluorescent marker, we imaged their entry into mildly acidic compartments. We found that cells expressing the transmembrane receptor (TVA950) internalized the virus much faster than those expressing the GPI-anchored receptor isoform (TVA800). Surprisingly, TVA800 did not accelerate virus uptake compared to cells lacking the receptor. Subsequent steps of virus entry were visualized by incorporating a small viral content marker that was released into the cytosol as a result of fusion. EnvA-dependent fusion with TVA800-expressing cells occurred shortly after endocytosis and delivery into acidic endosomes, whereas fusion of viruses internalized through TVA950 was delayed. In the latter case, a relatively stable hemifusion-like intermediate preceded the fusion pore opening. The apparent size and stability of nascent fusion pores depended on the TVA isoforms and their expression levels, with TVA950 supporting more robust pores and a higher efficiency of infection compared to TVA800. These results demonstrate that surface receptor density and the intracellular trafficking pathway used are important determinants of efficient EnvA-mediated membrane fusion, and suggest that early fusion intermediates play a critical role in establishing low pH-dependent virus entry from within acidic endosomes