On the metric dimension of corona product graphs

Given a set of vertices $S=\{v_1,v_2,...,v_k\}$ of a connected graph $G$, the metric representation of a vertex $v$ of $G$ with respect to $S$ is the vector $r(v|S)=(d(v,v_1),d(v,v_2),...,d(v,v_k))$, where $d(v,v_i)$, $i\in \{1,...,k\}$ denotes the distance between $v$ and $v_i$. $S$ is a resolving set for $G$ if for every pair of vertices $u,v$ of $G$, $r(u|S)\ne r(v|S)$. The metric dimension of $G$, $dim(G)$, is the minimum cardinality of any resolving set for $G$. Let $G$ and $H$ be two graphs of order $n_1$ and $n_2$, respectively. The corona product $G\odot H$ is defined as the graph obtained from $G$ and $H$ by taking one copy of $G$ and $n_1$ copies of $H$ and joining by an edge each vertex from the $i^{th}$-copy of $H$ with the $i^{th}$-vertex of $G$. For any integer $k\ge 2$, we define the graph $G\odot^k H$ recursively from $G\odot H$ as $G\odot^k H=(G\odot^{k-1} H)\odot H$. We give several results on the metric dimension of $G\odot^k H$. For instance, we show that given two connected graphs $G$ and $H$ of order $n_1\ge 2$ and $n_2\ge 2$, respectively, if the diameter of $H$ is at most two, then $dim(G\odot^k H)=n_1(n_2+1)^{k-1}dim(H)$. Moreover, if $n_2\ge 7$ and the diameter of $H$ is greater than five or $H$ is a cycle graph, then $dim(G\odot^k H)=n_1(n_2+1)^{k-1}dim(K_1\odot H).

Identification of key structural elements for neuronal calcium sensor-1 function in the regulation of the temperature-dependency of locomotion in C. elegans

BACKGROUND: Intracellular Ca(2+) regulates many aspects of neuronal function through Ca(2+) binding to EF hand-containing Ca(2+) sensors that in turn bind target proteins to regulate their function. Amongst the sensors are the neuronal calcium sensor (NCS) family of proteins that are involved in multiple neuronal signalling pathways. Each NCS protein has specific and overlapping targets and physiological functions and specificity is likely to be determined by structural features within the proteins. Common to the NCS proteins is the exposure of a hydrophobic groove, allowing target binding in the Ca(2+)-loaded form. Structural analysis of NCS protein complexes with target peptides has indicated common and distinct aspects of target protein interaction. Two key differences between NCS proteins are the size of the hydrophobic groove that is exposed for interaction and the role of their non-conserved C-terminal tails. RESULTS: We characterised the role of NCS-1 in a temperature-dependent locomotion assay in C. elegans and identified a distinct phenotype in the ncs-1 null in which the worms do not show reduced locomotion at actually elevated temperature. Using rescue of this phenotype we showed that NCS-1 functions in AIY neurons. Structure/function analysis introducing single or double mutations within the hydrophobic groove based on information from characterised target complexes established that both N- and C-terminal pockets of the groove are functionally important and that deletion of the C-terminal tail of NCS-1 did not impair its ability to rescue. CONCLUSIONS: The current work has allowed physiological assessment of suggestions from structural studies on the key structural features that underlie the interaction of NCS-1 with its target proteins. The results are consistent with the notion that full length of the hydrophobic groove is required for the regulatory interactions underlying NCS-1 function whereas the C-terminal tail of NCS-1 is not essential. This has allowed discrimination between two potential modes of interaction of NCS-1 with its targets

Identification of key structural elements for neuronal calcium sensor-1 function in the regulation of the temperature-dependency of locomotion in C. elegans

BACKGROUND: Intracellular Ca2+ regulates many aspects of neuronal function through Ca2+ binding to EF hand-containing Ca2+ sensors that in turn bind target proteins to regulate their function. Amongst the sensors are the neuronal calcium sensor (NCS) family of proteins that are involved in multiple neuronal signalling pathways. Each NCS protein has specific and overlapping targets and physiological functions and specificity is likely to be determined by structural features within the proteins. Common to the NCS proteins is the exposure of a hydrophobic groove, allowing target binding in the Ca2+-loaded form. Structural analysis of NCS protein complexes with target peptides has indicated common and distinct aspects of target protein interaction. Two key differences between NCS proteins are the size of the hydrophobic groove that is exposed for interaction and the role of their non-conserved C-terminal tails. RESULTS: We characterised the role of NCS-1 in a temperature-dependent locomotion assay in C. elegans and identified a distinct phenotype in the ncs-1 null in which the worms do not show reduced locomotion at actually elevated temperature. Using rescue of this phenotype we showed that NCS-1 functions in AIY neurons. Structure/function analysis introducing single or double mutations within the hydrophobic groove based on information from characterised target complexes established that both N- and C-terminal pockets of the groove are functionally important and that deletion of the C-terminal tail of NCS-1 did not impair its ability to rescue. CONCLUSIONS: The current work has allowed physiological assessment of suggestions from structural studies on the key structural features that underlie the interaction of NCS-1 with its target proteins. The results are consistent with the notion that full length of the hydrophobic groove is required for the regulatory interactions underlying NCS-1 function whereas the C-terminal tail of NCS-1 is not essential. This has allowed discrimination between two potential modes of interaction of NCS-1 with its targets

Trimodal cloudiness and tropical stable layers in simulations of radiative convective equilibrium

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95176/1/grl24304.pd

Observations of red-giant variable stars by Aboriginal Australians

Aboriginal Australians carefully observe the properties and positions of stars, including both overt and subtle changes in their brightness, for subsistence and social application. These observations are encoded in oral tradition. I examine two Aboriginal oral traditions from South Australia that describe the periodic changing brightness in three pulsating, red-giant variable stars: Betelgeuse (Alpha Orionis), Aldebaran (Alpha Tauri), and Antares (Alpha Scorpii). The Australian Aboriginal accounts stand as the only known descriptions of pulsating variable stars in any Indigenous oral tradition in the world. Researchers examining these oral traditions over the last century, including anthropologists and astronomers, missed the description of these stars as being variable in nature as the ethnographic record contained several misidentifications of stars and celestial objects. Arguably, ethnographers working on Indigenous Knowledge Systems should have academic training in both the natural and social sciences.Comment: The Australian Journal of Anthropology (2018

The Debrisoft ® monofilament debridement pad for use in acute or chronic wounds: A NICE medical technology guidance

As part of its Medical Technology Evaluation Programme, the National Institute for Health and Care Excellence (NICE) invited a manufacturer to provide clinical and economic evidence for the evaluation of the Debrisoft ® monofilament debridement pad for use in acute or chronic wounds. The University of Birmingham and Brunel University, acting as a consortium, was commissioned to act as an External Assessment Centre (EAC) for NICE, independently appraising the submission. This article is an overview of the original evidence submitted, the EAC’s findings and the final NICE guidance issued. The sponsor submitted a simple cost analysis to estimate the costs of using Debrisoft® to debride wounds compared with saline and gauze, hydrogel and larvae. Separate analyses were conducted for applications in home and applications in a clinic setting. The analysis took an UK National Health Service (NHS) perspective. It incorporated the costs of the technologies and supplementary technologies (such as dressings) and the costs of their application by a district nurse. The sponsor concluded that Debrisoft® was cost saving relative to the comparators. The EAC made amendments to the sponsor analysis to correct for errors and to reflect alternative assumptions. Debrisoft® remained cost saving in most analyses and savings ranged from £77 to £222 per patient compared with hydrogel, from £97 to £347 compared with saline and gauze, and from £180 to £484 compared with larvae depending on the assumptions included in the analysis and whether debridement took place in a home or clinic setting. All analyses were severely limited by the available data on effectiveness, in particular a lack of comparative studies and that the effectiveness data for the comparators came from studies reporting different clinical endpoints compared with Debrisoft®. The Medical Technologies Advisory Committee made a positive recommendation for adoption of Debrisoft® and this has been published as a NICE medical technology guidance (MTG17).The Birmingham and Brunel Consortium is funded by NICE to act as an External Assessment Centre for the Medical Technologies Evaluation Programme

The GALEX Arecibo SDSS Survey. I. Gas Fraction Scaling Relations of Massive Galaxies and First Data Release

We introduce the GALEX Arecibo SDSS Survey (GASS), an on-going large program that is gathering high quality HI-line spectra using the Arecibo radio telescope for an unbiased sample of ~1000 galaxies with stellar masses greater than 10^10 Msun and redshifts 0.025<z<0.05, selected from the SDSS spectroscopic and GALEX imaging surveys. The galaxies are observed until detected or until a low gas mass fraction limit (1.5-5%) is reached. This paper presents the first Data Release, consisting of ~20% of the final GASS sample. We use this data set to explore the main scaling relations of HI gas fraction with galaxy structure and NUV-r colour. A large fraction (~60%) of the galaxies in our sample are detected in HI. We find that the atomic gas fraction decreases strongly with stellar mass, stellar surface mass density and NUV-r colour, but is only weakly correlated with galaxy bulge-to-disk ratio (as measured by the concentration index of the r-band light). We also find that the fraction of galaxies with significant (more than a few percent) HI decreases sharply above a characteristic stellar surface mass density of 10^8.5 Msun kpc^-2. The fraction of gas-rich galaxies decreases much more smoothly with stellar mass. One of the key goals of GASS is to identify and quantify the incidence of galaxies that are transitioning between the blue, star-forming cloud and the red sequence of passively-evolving galaxies. Likely transition candidates can be identified as outliers from the mean scaling relations between gas fraction and other galaxy properties. [abridged]Comment: 25 pages, 12 figures. Accepted for publication in MNRAS. Version with high resolution figures available at http://www.mpa-garching.mpg.de/GASS/pubs.ph

The GALEX Arecibo SDSS Survey II: The Star Formation Efficiency of Massive Galaxies

We use measurements of the HI content, stellar mass and star formation rates in ~190 massive galaxies with stellar masses greater than 10^10 Msun, obtained from the Galex Arecibo SDSS Survey (GASS) described in Paper I (Catinella et al. 2010) to explore the global scaling relations associated with the bin-averaged ratio of the star formation rate over the HI mass, which we call the HI-based star formation efficiency (SFE). Unlike the mean specific star formation rate, which decreases with stellar mass and stellar mass surface density, the star formation efficiency remains relatively constant across the sample with a value close to SFE = 10^-9.5 yr^-1 (or an equivalent gas consumption timescale of ~3 Gyr). Specifically, we find little variation in SFE with stellar mass, stellar mass surface density, NUV-r color and concentration. We interpret these results as an indication that external processes or feedback mechanisms that control the gas supply are important for regulating star formation in massive galaxies. An investigation into the detailed distribution of SFEs reveals that approximately 5% of the sample shows high efficiencies with SFE > 10^-9 yr^-1, and we suggest that this is very likely due to a deficiency of cold gas rather than an excess star formation rate. Conversely, we also find a similar fraction of galaxies that appear to be gas-rich for their given specific star-formation rate, although these galaxies show both a higher than average gas fraction and lower than average specific star formation rate. Both of these populations are plausible candidates for "transition" galaxies, showing potential for a change (either decrease or increase) in their specific star formation rate in the near future. We also find that 36+/-5% of the total HI mass density and 47+/-5% of the total SFR density is found in galaxies with stellar mass greater than 10^10 Msun. [abridged]Comment: 18 pages, 11 figures. Accepted for publication in MNRAS. GASS publications and released data can be found at http://www.mpa-garching.mpg.de/GASS/index.ph

Establishing Lagrangian connections between observations within air masses crossing the Atlantic during the International Consortium for Atmospheric Research on Transport and Transformation experiment

The ITCT-Lagrangian-2K4 (Intercontinental Transport and Chemical Transformation) experiment was conceived with an aim to quantify the effects of photochemistry and mixing on the transformation of air masses in the free troposphere away from emissions. To this end, attempts were made to intercept and sample air masses several times during their journey across the North Atlantic using four aircraft based in New Hampshire (USA), Faial (Azores) and Creil (France). This article begins by describing forecasts from two Lagrangian models that were used to direct the aircraft into target air masses. A novel technique then identifies Lagrangian matches between flight segments. Two independent searches are conducted: for Lagrangian model matches and for pairs of whole air samples with matching hydrocarbon fingerprints. The information is filtered further by searching for matching hydrocarbon samples that are linked by matching trajectories. The quality of these "coincident matches'' is assessed using temperature, humidity and tracer observations. The technique pulls out five clear Lagrangian cases covering a variety of situations and these are examined in detail. The matching trajectories and hydrocarbon fingerprints are shown, and the downwind minus upwind differences in tracers are discussed