Convex Independence in Permutation Graphs

A set C of vertices of a graph is P_3-convex if every vertex outside C has at most one neighbor in C. The convex hull \sigma(A) of a set A is the smallest P_3-convex set that contains A. A set M is convexly independent if for every vertex x \in M, x \notin \sigma(M-x). We show that the maximal number of vertices that a convexly independent set in a permutation graph can have, can be computed in polynomial time

The Partial Visibility Representation Extension Problem

For a graph $G$, a function $\psi$ is called a \emph{bar visibility representation} of $G$ when for each vertex $v \in V(G)$, $\psi(v)$ is a horizontal line segment (\emph{bar}) and $uv \in E(G)$ iff there is an unobstructed, vertical, $\varepsilon$-wide line of sight between $\psi(u)$ and $\psi(v)$. Graphs admitting such representations are well understood (via simple characterizations) and recognizable in linear time. For a directed graph $G$, a bar visibility representation $\psi$ of $G$, additionally, puts the bar $\psi(u)$ strictly below the bar $\psi(v)$ for each directed edge $(u,v)$ of $G$. We study a generalization of the recognition problem where a function $\psi'$ defined on a subset $V'$ of $V(G)$ is given and the question is whether there is a bar visibility representation $\psi$ of $G$ with $\psi(v) = \psi'(v)$ for every $v \in V'$. We show that for undirected graphs this problem together with closely related problems are \NP-complete, but for certain cases involving directed graphs it is solvable in polynomial time.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Sub-wavelength surface IR imaging of soft-condensed matter

Outlined here is a technique for sub-wavelength infrared surface imaging performed using a phase matched optical parametric oscillator laser and an atomic force microscope as the detection mechanism. The technique uses a novel surface excitation illumination approach to perform simultaneously chemical mapping and AFM topography imaging with an image resolution of 200 nm. This method was demonstrated by imaging polystyrene micro-structures

Visibility Representations of Boxes in 2.5 Dimensions

We initiate the study of 2.5D box visibility representations (2.5D-BR) where vertices are mapped to 3D boxes having the bottom face in the plane $z=0$ and edges are unobstructed lines of sight parallel to the $x$- or $y$-axis. We prove that: $(i)$ Every complete bipartite graph admits a 2.5D-BR; $(ii)$ The complete graph $K_n$ admits a 2.5D-BR if and only if $n \leq 19$; $(iii)$ Every graph with pathwidth at most $7$ admits a 2.5D-BR, which can be computed in linear time. We then turn our attention to 2.5D grid box representations (2.5D-GBR) which are 2.5D-BRs such that the bottom face of every box is a unit square at integer coordinates. We show that an $n$-vertex graph that admits a 2.5D-GBR has at most $4n - 6 \sqrt{n}$ edges and this bound is tight. Finally, we prove that deciding whether a given graph $G$ admits a 2.5D-GBR with a given footprint is NP-complete. The footprint of a 2.5D-BR $\Gamma$ is the set of bottom faces of the boxes in $\Gamma$.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Preparation and characterization of polypyrrole/graphene nanocomposite films and their electrochemical performance

A one-step electrochemical process had been employed to synthesize nanocomposite films of polypyrrole/graphene (PPy/GR) by electrochemical polymerisation on indium tin oxide (ITO) from an aqueous solution containing pyrrole monomer, graphene oxide (GO) nanosheets and sodium p-toluenesulfonate (NapTS). The X-ray diffraction (XRD) patterns showed that the typical peak of GO at 9.9o was missing from the nanocomposite’s diffraction pattern, suggesting that the GO had been stripped off of its oxygenous groups after the reaction. We postulated that a nanocomposite film was produced through a layer-by-layer deposition based on field emission scanning electron microscope (FESEM) images. The Raman spectroscopy profiles exhibited that the D/G intensity ratio (ID/IG) of PPy was not altered by the inclusion of GO due to the low concentration of the material used. However, the concentration was sufficient to increase the specific capacitance of the nanocomposite by 20 times compared to that of pure PPy, reflecting a synergistic effect between PPy and GR, as analysed by a three-electrode electrochemical cell. The electrochemical performance of the nanocomposites was affected by varying the deposition parameters such as concentrations of pyrrole and GO, scan rate, deposition time and deposition potential

Orally Administered P22 Phage Tailspike Protein Reduces Salmonella Colonization in Chickens: Prospects of a Novel Therapy against Bacterial Infections

One of the major causes of morbidity and mortality in man and economically important animals is bacterial infections of the gastrointestinal (GI) tract. The emergence of difficult-to-treat infections, primarily caused by antibiotic resistant bacteria, demands for alternatives to antibiotic therapy. Currently, one of the emerging therapeutic alternatives is the use of lytic bacteriophages. In an effort to exploit the target specificity and therapeutic potential of bacteriophages, we examined the utility of bacteriophage tailspike proteins (Tsps). Among the best-characterized Tsps is that from the Podoviridae P22 bacteriophage, which recognizes the lipopolysaccharides of Salmonella enterica serovar Typhimurium. In this study, we utilized a truncated, functionally equivalent version of the P22 tailspike protein, P22sTsp, as a prototype to demonstrate the therapeutic potential of Tsps in the GI tract of chickens. Bacterial agglutination assays showed that P22sTsp was capable of agglutinating S. Typhimurium at levels similar to antibodies and incubating the Tsp with chicken GI fluids showed no proteolytic activity against the Tsp. Testing P22sTsp against the three major GI proteases showed that P22sTsp was resistant to trypsin and partially to chymotrypsin, but sensitive to pepsin. However, in formulated form for oral administration, P22sTsp was resistant to all three proteases. When administered orally to chickens, P22sTsp significantly reduced Salmonella colonization in the gut and its further penetration into internal organs. In in vitro assays, P22sTsp effectively retarded Salmonella motility, a factor implicated in bacterial colonization and invasion, suggesting that the in vivo decolonization ability of P22sTsp may, at least in part, be due to its ability to interfere with motility… Our findings show promise in terms of opening novel Tsp-based oral therapeutic approaches against bacterial infections in production animals and potentially in humans