On matrices for which norm bounds are attained

Let $\|A\|_{p,q}$ be the norm induced on the matrix $A$ with $n$ rows and $m$ columns by the H\"older $\ell_p$ and $\ell_q$ norms on $R^n$ and $R^m$ (or $C^n$ and $C^m$), respectively. It is easy to find an upper bound for the ratio $\|A\|_{r,s}/\|A\|_{p,q}$. In this paper we study the classes of matrices for which the upper bound is attained. We shall show that for fixed $A$, attainment of the bound depends only on the signs of $r-p$ and $s-q$. Various criteria depending on these signs are obtained. For the special case $p=q=2$, the set of all matrices for which the bound is attained is generated by means of singular value decompositions

Simulated Heatwaves Lead to Upregulated Chemical Defense of a Marine Foundation Macrophyte Against Microbial Colonizers

Climate change is characterized not only by an increase in mean temperature, but also an increase in the variability around the means causing extreme events like marine heatwaves. These events are expected to have strong influence on the ecology of marine foundation species such as the eelgrass Zostera marina. Bacterial and macroscopicfoulersareubiquitousinthemarineenvironment;theycanhavedetrimental impacts on macrophytes and warming is known to enhance bacterial fouling. Thus, to investigate the consequence of heatwaves on the chemical defense of eelgrass against microbial colonizers, we incubated Z. marina plants in the Kiel Outdoor Benthocosm system under ambient control conditions and two different heatwave treatments: a treatment experiencing two spring heatwaves followed by a summer heatwave, and a treatment only experiencing just the summer heatwave. The capacity to deter microbial colonizers was found to be significantly up-regulated in Z. marina from both heatwave treatments in comparison to Z. marina under control conditions, suggesting defense regulation of Z. marina in response to marine heatwaves. We conclude climate extremes such as heatwaves can trigger a regulation in the defense capacity, which could be necessary for resilience against climate change scenarios. Such dynamics in rapid regulation of defense capacity as found in this study could also apply to other host plant – microbe interactions under scenarios of ongoing climate change or extreme climate events like heatwaves

Spin-polarized surface states close to adatoms on Cu(111)

We present a theoretical study of surface states close to 3d transition metal adatoms (Cr, Mn, Fe, Co, Ni and Cu) on a Cu(111) surface in terms of an embedding technique using the fully relativistic Korringa-Kohn-Rostoker method. For each of the adatoms we found resonances in the s-like states to be attributed to a localization of the surface states in the presence of an impurity. We studied the change of the s-like densities of states in the vicinity of the surface state band-edge due to scattering effects mediated via the adatom's d-orbitals. The obtained results show that a magnetic impurity causes spin-polarization of the surface states. In particular, the long-range oscillations of the spin-polarized s-like density of states around an Fe adatom are demonstrated.Comment: 5 pages, 5 figures, submitted to PR

Microbial “gardening” by a seaweed holobiont: Surface metabolites attract protective and deter pathogenic epibacterial settlement

Epimicrobial communities on seaweed surfaces usually contain not only potentially pathogenic but also potentially beneficial micro‐organisms. Capacity of terrestrial plants for chemically mediated recruitment, that is, “gardening” of bacterial communities in the rhizosphere was recently demonstrated. Empirical evidence directly linking such chemical “gardening” with the beneficial role of gardened microbes in terrestrial plants is rare and largely missing for aquatic macrophytes. Here, we demonstrate that our model invasive seaweed holobiont Agarophyton vermiculophyllum possesses beneficial microbiota on its surface that provide protection from bacterial pathogens. Metabolites from the algal holobiont’s surface reduced settlement of opportunistic pathogens but attracted protective epibacterial settlement. We tested 58 different bacterial species (isolated from the surface of A. vermiculophyllum ) individually in tip bleaching assays. Kordia algicida was identified as a “significant pathogen” inducing a bleaching disease. In addition, nine other species significantly reduced the risk of algal bleaching and were thus “significantly protective”. Additionally, two “potential pathogens” and 10 “potential protectors” were identified. When 19 significant and potential protectors and 3 significant and potential pathogens were tested together, the protective strains fully prevented bleaching, suggesting that a component of A. vermiculophyllum’s epimicrobiome provides an associational defence against pathogens. Chemically mediated selective recruitment of microbes was demonstrated in bioassays, where A. vermiculophyllum surface metabolites attracted the settlement of protective strains, but reduced settlement of pathogens. Synthesis . The capacity of an aquatic macrophyte to chemically “garden” protective micro‐organisms to the benefit of strengthened disease resistance is demonstrated for the first time. Such a role of surface chemistry in “gardening” of microbes as found in the current study could also be applicable to other host plant—microbe interactions. Our results may open new avenues towards manipulation of the surface microbiome of seaweeds via chemical “gardening,” enhancing sustainable production of healthy seaweeds

A New Ultra-dense Group of Obscured Emission-Line Galaxies

We present the discovery of an isolated compact group of galaxies that is extremely dense (median projected galaxy separation: 6.9 kpc), has a very low velocity dispersion ($\sigma_{\rm 2D}$ = 67 km s$^{-1}$), and where all observed members show emission lines and are morphologically disturbed. These properties, together with the lack of spirals and the presence of a prominent tidal tail make this group one of the most evolved compact groups.Comment: 15 pages,LaTeX, 2figures. A Postscript figure with spectra is available at ftp://astro.uibk.ac.at/pub/weinberger/ . Accepted for publication in ApJ Letter

Candidate Tidal Dwarf Galaxies in the Compact Group CG J1720-67.8

This is the second part of a detailed study of the ultracompact group CG J1720-67.8: in the first part we have focused the attention on the three main galaxies of the group and we have identified a number of candidate tidal dwarf galaxies (TDGs). Here we concentrate on these candidate TDGs. Absolute photometry of these objects in BVRJHKs bands confirms their relatively blue colors, as we already expected from the inspection of optical and near-infrared color maps and from the presence of emission-lines in the optical spectra. The physical conditions in such candidate TDGs are investigated through the application of photoionization models, while the optical colors are compared with grids of spectrophotometric evolutionary synthesis models from the literature. Although from our data self-gravitation cannot be proved for these objects, their general properties are consistent with those of other TDG candidates. Additionally we present the photometry of a few ``knots'' detected in the immediate surroundings of CG J1720-67.8 and consider the possibility that these objects might belong to a dwarf population associated with the compact group.Comment: Accepted for publication in the Astrophysical Journa