Towards general super Casimir equations for 4D4D N=1{\mathcal N}=1 SCFTs

Applying the Casimir operator to four-point functions in CFTs allows us to find the conformal blocks for any external operators. In this work, we initiate the program to find the superconformal blocks, using the super Casimir operator, for $4D$ ${\mathcal N}=1$ SCFTs. We begin by finding the most general four-point function with zero $U(1)_R$-charge, including all the possible nilpotent structures allowed by the superconformal algebra. We then study particular cases where some of the operators satisfy shortening conditions. Finally, we obtain the super Casimir equations for four point-functions which contain a chiral and an anti-chiral field. We solve the super Casimir equations by writing the superconformal blocks as a sum of several conformal blocks.Comment: Added a missing term in eqs. (3.31) and (3.39). Section 4.3 corrected. Abstract fixe

Noncommutative Koszul Algebras from Combinatorial Topology

Associated to any uniform finite layered graph Gamma there is a noncommutative graded quadratic algebra A(Gamma) given by a construction due to Gelfand, Retakh, Serconek and Wilson. It is natural to ask when these algebras are Koszul. Unfortunately, a mistake in the literature states that all such algebras are Koszul. That is not the case and the theorem was recently retracted. We analyze the Koszul property of these algebras for two large classes of graphs associated to finite regular CW complexes, X. Our methods are primarily topological. We solve the Koszul problem by introducing new cohomology groups H_X(n,k), generalizing the usual cohomology groups H^n(X). Along with several other results, our methods give a new and primarily topological proof of a result of Serconek and Wilson and of Piontkovski.Comment: 22 pages, 1 figur

Interior of Distorted Black Holes

We study the interior of distorted static axisymmetric black holes. We obtain a general interior solution and study its asymptotics both near the horizon and singularity. As a special example, we apply the obtained results to the case of the so-called `caged' black holes.Comment: 12 pages, 16 figure

The irradiated ISM of ULIRGs

The nuclei of ULIRGs harbor massive young stars, an accreting central black hole, or both. Results are presented for molecular gas that is exposed to X-rays (1-100 keV, XDRs) and far-ultraviolet radiation (6-13.6 eV, PDRs). Attention is paid to species like HCO+, HCN, HNC, OH, H2O and CO. Line ratios of HCN/HCO+ and HNC/HCN discriminate between PDRs and XDRs. Very high J (>10) CO lines, observable with HIFI/Herschel, discriminate very well between XDRs and PDRs. In XDRs, it is easy to produce large abundances of warm (T>100 K) H2O and OH. In PDRs, only OH is produced similarly well.Comment: 5 pages, 6 figures, to appear in: IAU Symposium 242 Astrophysical Masers and their Environment

The Drosophila DIAP1 protein is required to prevent accumulation of a continuously generated, processed form of the apical caspase DRONC

Although loss of the inhibitor of apoptosis (LAP) protein DIAP1 has been shown to result in caspase activation and spontaneous cell death in Drosophila cells and embryos, the point at which DIAP1 normally functions to inhibit caspase activation is unknown. Depletion of the DIAP1 protein in Drosophila S2 cells or the Sf-IAP protein in Spodoptera frugiperda Sf21 cells by RNA interference (RNAi) or cycloheximide treatment resulted in rapid and widespread caspase-dependent apoptosis. Co-silencing of dronc or dark largely suppressed this apoptosis, indicating that DIAP1 is normally required to inhibit an activity dependent on these proteins. Silencing of dronc also inhibited DRICE processing following stimulation of apoptosis, demonstrating that DRONC functions as an apical caspase in S2 cells. Silencing of diap1 or treatment with UV light induced DRONC processing, which occurred in two steps. The first step appeared to occur continuously even in the absence of an apoptotic signal and to be dependent on DARK because full-length DRONC accumulated when dark was silenced in non-apoptotic cells. In addition, treatment with the proteasome inhibitor MG132 resulted in accumulation of this initially processed form of DRONC, but not full-length DRONC, in non-apoptotic cells. The second step in DRONC processing was observed only in apoptotic cells. These results indicate that the initial step in DRONC processing occurs continuously via a DARK-dependent mechanism in Drosophila cells and that DIAP1 is required to prevent excess accumulation of this first form of processed DRONC, presumably through its ability to act as a ubiquitin-protein ligase

Comments on geometric and universal open string tachyons near fivebranes

In a recent paper (hep-th/0703157), Sen studied unstable D-branes in NS5-branes backgrounds and argued that in the strong curvature regime the universal open string tachyon (on D-branes of the wrong dimensionality) and the geometric tachyon (on D-branes that are BPS in flat space but not in this background) may become equivalent. We study in this note an example of a non-BPS suspended D-brane vs. a BPS D-brane at equal distance between two fivebranes. We use boundary worldsheet CFT methods to show that these two unstable branes are identical.Comment: 8 pages, 1 figure; ver. 2 to appear in JHEP: one comment, refs and appendices adde

On Scaling Solutions with a Dissipative Fluid

We study the asymptotic behaviour of scaling solutions with a dissipative fluid and we show that, contrary to recent claims, the existence of stable accelerating attractor solution which solves the `energy' coincidence problem depends crucially on the chosen equations of state for the thermodynamical variables. We discuss two types of equations of state, one which contradicts this claim, and one which supports it.Comment: 8 pages and 5 figures; to appear in Class. Quantum Gra

Generalised Bose-Einstein phase transition in large-mm component spin glasses

It is proposed to understand finite dimensional spin glasses using a $1/m$ expansion, where $m$ is the number of spin components. It is shown that this approach predicts a replica symmetric state in finite dimensions. The point about which the expansion is made, the infinite-$m$ limit, has been studied in the mean-field limit in detail and has a very unusual phase transition, rather similar to a Bose-Einstein phase transition but with $N^{2/5}$ macroscopically occupied low-lying states.Comment: 4 pages (plus a few lines), 3 figures. v2: minor error corrected. v3: numerics supplemented by analytical arguments, references added, figure of density of states adde

Establishment of prophylactic enoxaparin dosing recommendations to achieve targeted anti-factor Xa concentrations in children with CHD

Background Enoxaparin may be used to prevent central venous catheter-related thrombosis in patients with CHD. We aimed to determine whether current enoxaparin dosing regimens effectively achieve anti-factor Xa concentrations within prophylactic goal ranges in this patient population. Methods We implemented a formal protocol aimed at reducing central venous catheter-related thrombosis in children with CHD in January, 2016. Standard empiric prophylactic enoxaparin dosing regimens were used – for example, 0.75 mg/kg/dose every 12 hours for patients <2 months of age and 0.5 mg/kg/dose every 12 hours for patients ⩾2 months of age – with anti-factor Xa goal range of 0.25–0.49 IU/ml. Patients <2 years of age who received enoxaparin and had at least one valid steady-state anti-factor Xa measurement between 25 January, 2016 and 31 August, 2016 were retrospectively reviewed. Results During the study period, 47 patients had 186 anti-factor Xa concentrations measured, of which 20 (11%) were above and 112 (60%) were below the prophylactic goal range. Anti-factor Xa concentrations within the goal range were ultimately achieved in 31 patients. Median dose required to achieve anti-factor Xa concentrations within the prophylactic range was 0.89 mg/kg/dose (25, 75%: 0.75, 1.11) for patients <2 months (n=23 patients) and 0.79 mg/kg/dose (25, 75%: 0.62, 1.11) for patients ⩾2 months (n=8 patients). Conclusions Enoxaparin doses required to achieve prophylactic anti-factor Xa concentrations in young children with CHD were consistently higher than the currently recommended prophylactic dosing regimens. Further study is needed to determine whether dose titration to achieve prophylactic anti-factor Xa concentrations is effective in preventing central venous catheter-related thrombosis