Expansions for the Bollobas-Riordan polynomial of separable ribbon graphs

We define 2-decompositions of ribbon graphs, which generalise 2-sums and tensor products of graphs. We give formulae for the Bollobas-Riordan polynomial of such a 2-decomposition, and derive the classical Brylawski formula for the Tutte polynomial of a tensor product as a (very) special case. This study was initially motivated from knot theory, and we include an application of our formulae to mutation in knot diagrams.Comment: Version 2 has minor changes. To appear in Annals of Combinatoric

Kelp-associated microbes facilitate spatial subsidy in a detrital-based food web in a shoreline ecosystem

Microbes are ubiquitous but our knowledge of their effects on consumers is limited in benthic marine systems. Shorelines often form hotspots of microbial and detritivore activity due to the large amounts of detrital macrophytes that are exported from other coastal ecosystems, such as kelp forests, and accumulate in these systems. Shoreline ecosystems therefore provide a useful model system to examine microbial-detritivore interactions. We experimentally test whether bacteria in the biofilm of kelp provide a bottom-up influence on growth and reproductive output of detritivores in shorelines where detrital kelp accumulates, by manipulating the bacterial abundances on kelp (Ecklonia radiata). The growth rates for both male and female amphipods (Allorchestes compressa) were greater in treatments containing bacteria than those in which bacteria were reduced through antibiotic treatment, and this effect was greater for males offered aged kelp. The proportions of ovigerous females were greater when reared on kelp with intact bacteria, indicating a more rapid reproductive development in the presence of more bacteria. Bacterial abundance had little to no influence on nutrient content and palatability of kelp, based on tissue toughness, nitrogen and carbon content and C:N ratio. Thus, the most likely pathway for a microbial effect on detritivores was through feeding on kelp-associated bacteria. Regardless of the pathway, kelp-associated microbes have a strong influence on the fitness of a highly abundant detritivore that feeds preferentially on E. radiata in shoreline systems, and therefore form a hidden trophic step in this “brown” food web and a hotspot of secondary production

Bipartite partial duals and circuits in medial graphs

It is well known that a plane graph is Eulerian if and only if its geometric dual is bipartite. We extend this result to partial duals of plane graphs. We then characterize all bipartite partial duals of a plane graph in terms of oriented circuits in its medial graph.Comment: v2: minor changes. To appear in Combinatoric

Twistor theory on a finite graph

We show how the description of a shear-free ray congruence in Minkowski space as an evolving family of semi-conformal mappings can naturally be formulated on a finite graph. For this, we introduce the notion of holomorphic function on a graph. On a regular coloured graph of degree three, we recover the space-time picture. In the spirit of twistor theory, where a light ray is the more fundamental object from which space-time points should be derived, the line graph, whose points are the edges of the original graph, should be considered as the basic object. The Penrose twistor correspondence is discussed in this context

A report on the concentration, distribution and impact of certain trace metals from sewage treatment plants on the Chesapeake Bay

Population densities are ever increasing on the shores of the Chesapeake Bay and hence the flow of goods and services is being shifted to supply these people. This self perpetuating system demanismore and more of the surrounding envirorunent f or recreation, work and waste disposal. This is the case f or the Chesapeake and its sub- estuaries. According to Brush (1974), of the total fresh water input into the Chesapeake Bay, between 1 and 2 percent is treated sewage. Toxic components on these waters may be of paramount importance in the Bay ecosystem and ma;y have disastrous effects on the biota. It is essential then that the magnitude of the exist ing problem be determined and understood, and results and recommendations be made available to decision makers so that in the future we can control the inputs, properly select sewage outfall locations and preserve the Chesapeake Bey for future generations . This document is a first attempt at this

The Gibbs paradox, Black hole entropy and the thermodynamics of isolated horizons

This letter presents a new, solely thermodynamical argument for considering the states of the quantum isolated horizon of a black hole as distinguishable. We claim that only if the states are distinguishable, the thermodynamic entropy is an extensive quantity and can be well-defined. To show this, we make a comparison with a classical ideal gas system whose statistical description makes only sense if an additional 1/N!-factor is included in the state counting in order to cure the Gibbs paradox. The case of the statistical description of a quantum isolated horizon is elaborated, to make the claim evident.Comment: 8 pages, closest to the published version; taken from the author's diploma thesi

Cdc7 is a potent anti-cancer target in pancreatic cancer due to abrogation of the DNA origin activation checkpoint.

PURPOSE: Cdc7 is a serine/threonine kinase which is responsible for the 'firing' of replication origins leading to initiation of DNA replication. Inhibition or depletion of Cdc7 in normal cells triggers a DNA origin activation checkpoint causing a reversible G1 arrest. Here we investigate Cdc7 as a novel therapeutic target in pancreatic cancer. EXPERIMENTAL DESIGN: Cdc7 target validation was performed by immunoexpression profiling in a cohort of 73 patients with pancreatic adenocarcinoma including 24 controls. Secondly Cdc7 kinase was targeted in Capan-1 and PANC-1 pancreatic cancer cell line models using either an siRNA against Cdc7 or alternatively a small molecule inhibitor (SMI) of Cdc7 (PHA-767491). RESULTS: Cdc7 was significantly overexpressed in pancreatic adenocarcinoma compared to benign pancreatic tissue (median LI 34.3% vs. 1.3%; P<0.0001). Cdc7 knockdown using siRNA in Capan-1 and PANC-1 cells resulted in marked apoptotic cell death when compared with control cells. A prominent sub-G1 peak was seen on flow cytometry (sub-G1 51% vs. 3% and 45% vs. 0.7% in Capan-1 and PANC-1 cells, respectively). Annexin V labelling confirmed apoptosis in 64% vs. 11% and 75% vs. 8%, respectively. Western blotting showed cleavage of PARP-1 and caspase-3 and presence of γH2A.X. TUNEL assay showed strong staining in treated cells. These results were mirrored following Cdc7 kinase inhibition with PHA-767491. CONCLUSIONS: Our findings show that Cdc7 is a potent anti-cancer target in pancreatic adenocarcinoma and that Cdc7 immunoexpression levels might be used as a companion diagnostic to predict response to therapeutic siRNAs or SMIs directed against this kinase

Assessing the accuracy of quantitative molecular microbial profiling

This is the final version of the article. Available from MDPI via the DOI in this record.The application of high-throughput sequencing in profiling microbial communities is providing an unprecedented ability to investigate microbiomes. Such studies typically apply one of two methods: amplicon sequencing using PCR to target a conserved orthologous sequence (typically the 16S ribosomal RNA gene) or whole (meta)genome sequencing (WGS). Both methods have been used to catalog the microbial taxa present in a sample and quantify their respective abundances. However, a comparison of the inherent precision or bias of the different sequencing approaches has not been performed. We previously developed a metagenomic control material (MCM) to investigate error when performing different sequencing strategies. Amplicon sequencing using four different primer strategies and two 16S rRNA regions was examined (Roche 454 Junior) and compared to WGS (Illumina HiSeq). All sequencing methods generally performed comparably and in good agreement with organism specific digital PCR (dPCR); WGS notably demonstrated very high precision. Where discrepancies between relative abundances occurred they tended to differ by less than twofold. Our findings suggest that when alternative sequencing approaches are used for microbial molecular profiling they can perform with good reproducibility, but care should be taken when comparing small differences between distinct methods. This work provides a foundation for future work comparing relative differences between samples and the impact of extraction methods. We also highlight the value of control materials when conducting microbial profiling studies to benchmark methods and set appropriate thresholds.The authors acknowledge funding from the European Metrology Research Programme joint research project “INFECT MET” (http://infectmet.lgcgroup.com) (an EMRP project, jointly funded by the EMRP participating countries within EURAMET and the European Union) and the UK National Measurement System for funding of this work and for the support of Thomas Laver by the BBSRC Industrial Case Studentship award BB/H016120/1