Star formation, structure, and formation mechanism of cometary globules: NIR observations of CG 1 and CG 2

Cometary globule (CG) 1 and CG 2 are "classic" CGs in the Gum Nebula. They have compact heads and long dusty tails that point away from the centre of the Gum Nebula. We study the structure of CG 1 and CG 2 and the star formation in them to find clues to the CG formation mechanism. The two possible mechanisms, radiation-driven implosion (RDI) and a supernova (SN) blast wave, produce a characteristic mass distribution where the major part of the mass is situated in either the head (RDI) or the tail (SN). CG 1 and CG 2 were imaged in the near infrared (NIR) JsHKs bands. NIR photometry was used to locate NIR excess objects and to create extinction maps of the CGs. The A_V maps allow us to analyse the large-scale structure of CG 1 and CG 2. Archival images from the WISE and Spitzer satellites and HIRES-processed IRAS images were used to study the small-scale structure. In addition to the previously known CG 1 IRS 1 we discovered three new NIR-excess objects, two in CG 1 and one in CG 2. CG 2 IRS 1 is the first detection of star formation in CG 2. Spectral energy distribution (SED) fitting suggests the NIR-excess objects are young low-mass stars. CG 1 IRS 1 is probably a class I protostar in the head of CG 1. CG 1 IRS 1 drives a bipolar outflow, which is very weak in CO, but the cavity walls are seen in reflected light in our NIR and in the Spitzer 3.6 and 4.5 mum images. Strong emission from excited polycyclic aromatic hydrocarbon particles and very small grains were detected in the CG 1 tail. The total mass of CG 1 in the observed area is 41.9 Msun of which 16.8 Msun lies in the head. For CG 2 these values are 31.0 Msun total and 19.1 Msun in the head. The observed mass distribution does not offer a firm conclusion for the formation mechanism of these CGs: CG 1 is in too evolved a state, and in CG 2 part of the globule tail was outside the observed area. (abridged)Comment: Accepted for publication in A&A. 22 pages, 24 figures. JHKs photometry will be available electronicall

Intersection Graph of a Module

Let $V$ be a left $R$-module where $R$ is a (not necessarily commutative) ring with unit. The intersection graph \cG(V) of proper $R$-submodules of $V$ is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper $R$-submodules of $V,$ and there is an edge between two distinct vertices $U$ and $W$ if and only if $U\cap W\neq 0.$ We study these graphs to relate the combinatorial properties of \cG(V) to the algebraic properties of the $R$-module $V.$ We study connectedness, domination, finiteness, coloring, and planarity for \cG (V). For instance, we find the domination number of \cG (V). We also find the chromatic number of \cG(V) in some cases. Furthermore, we study cycles in \cG(V), and complete subgraphs in \cG (V) determining the structure of $V$ for which \cG(V) is planar

Non-CG methylation patterns shape the epigenetic landscape in Arabidopsis.

DNA methylation occurs in CG and non-CG sequence contexts. Non-CG methylation is abundant in plants and is mediated by CHROMOMETHYLASE (CMT) and DOMAINS REARRANGED METHYLTRANSFERASE (DRM) proteins; however, its roles remain poorly understood. Here we characterize the roles of non-CG methylation in Arabidopsis thaliana. We show that a poorly characterized methyltransferase, CMT2, is a functional methyltransferase in vitro and in vivo. CMT2 preferentially binds histone H3 Lys9 (H3K9) dimethylation and methylates non-CG cytosines that are regulated by H3K9 methylation. We revealed the contributions and redundancies between each non-CG methyltransferase in DNA methylation patterning and in regulating transcription. We also demonstrate extensive dependencies of small-RNA accumulation and H3K9 methylation patterning on non-CG methylation, suggesting self-reinforcing mechanisms between these epigenetic factors. The results suggest that non-CG methylation patterns are critical in shaping the landscapes of histone modification and small noncoding RNA

Antecedents of Voluntary Corporate Governance Disclosure: A Post-2007/08 Financial Crisis Evidence from the Influential UK Combined Code

Purpose: This study investigates the level of compliance with, and disclosure of, good corporate governance (CG) practices among UK publicly listed firms, and consequently ascertains whether board characteristics and ownership structure variables can explain observable differences in the extent of voluntary CG compliance and disclosure practices. Design/Methodology/Approach: The study uses one of the largest datasets to-date on compliance and disclosure of CG practices from 2008 to 2013 containing 120 CG provisions drawn from the 2010 UK Combined Code relating to 100 UK listed firms to conduct multiple regression analyses of the determinants of voluntary CG disclosures. A number of additional estimations, including two stage least squares, fixed-effects and lagged structures, are conducted in order to test the robustness of the findings. Findings: The results suggest that there is a substantial variation in the levels of compliance with, and disclosure of, good CG practices among the sampled UK firms. We also find that firms with larger board size, more independent outside directors and greater director diversity tend to disclose more CG information voluntarily, whereas the level of voluntary CG compliance and disclosure is insignificantly related to the existence of a separate CG committee and institutional ownership. Additionally, the results indicate that block ownership and managerial ownership impact negatively on voluntary CG compliance and disclosure practices. The findings are fairly robust across a number of econometric models that sufficiently address various endogeneity problems and alternative CG indices. Overall, the findings are generally consistent with the predictions of neo-institutional theory. Originality/Value: This paper extends, as well as contributes to the extant CG literature by offering new evidence on compliance with, and disclosure of, good CG recommendations contained in the 2010 UK Combined Code following the 2007/08 global financial crisis. This paper also advances the existing literature by offering new insights from a neo-institutional theoretical perspective of the impact of board and ownership mechanisms on voluntary CG compliance and disclosure practices. Keywords: Corporate governance; Board and ownership mechanisms; Comply or explain; Neo-institutional theory; UK Combined Cod

Error estimators and their analysis for CG, Bi-CG and GMRES

We present an analysis of the uncertainty in the convergence of iterative linear solvers when using relative residue as a stopping criterion, and the resulting over/under computation for a given tolerance in error. This shows that error estimation is indispensable for efficient and accurate solution of moderate to high conditioned linear systems ($\kappa>100$), where $\kappa$ is the condition number of the matrix. An $\mathcal{O}(1)$ error estimator for iterations of the CG (Conjugate Gradient) algorithm was proposed more than two decades ago. Recently, an $\mathcal{O}(k^2)$ error estimator was described for the GMRES (Generalized Minimal Residual) algorithm which allows for non-symmetric linear systems as well, where $k$ is the iteration number. We suggest a minor modification in this GMRES error estimation for increased stability. In this work, we also propose an $\mathcal{O}(n)$ error estimator for A-norm and $l_{2}$ norm of the error vector in Bi-CG (Bi-Conjugate Gradient) algorithm. The robust performance of these estimates as a stopping criterion results in increased savings and accuracy in computation, as condition number and size of problems increase

On the eigenvalues of Cayley graphs on the symmetric group generated by a complete multipartite set of transpositions

Given a finite simple graph \cG with $n$ vertices, we can construct the Cayley graph on the symmetric group $S_n$ generated by the edges of \cG, interpreted as transpositions. We show that, if \cG is complete multipartite, the eigenvalues of the Laplacian of \Cay(\cG) have a simple expression in terms of the irreducible characters of transpositions, and of the Littlewood-Richardson coefficients. As a consequence we can prove that the Laplacians of \cG and of \Cay(\cG) have the same first nontrivial eigenvalue. This is equivalent to saying that Aldous's conjecture, asserting that the random walk and the interchange process have the same spectral gap, holds for complete multipartite graphs.Comment: 29 pages. Includes modification which appear on the published version in J. Algebraic Combi