Adjacency labeling schemes and induced-universal graphs

We describe a way of assigning labels to the vertices of any undirected graph on up to $n$ vertices, each composed of $n/2+O(1)$ bits, such that given the labels of two vertices, and no other information regarding the graph, it is possible to decide whether or not the vertices are adjacent in the graph. This is optimal, up to an additive constant, and constitutes the first improvement in almost 50 years of an $n/2+O(\log n)$ bound of Moon. As a consequence, we obtain an induced-universal graph for $n$-vertex graphs containing only $O(2^{n/2})$ vertices, which is optimal up to a multiplicative constant, solving an open problem of Vizing from 1968. We obtain similar tight results for directed graphs, tournaments and bipartite graphs

Ramified rectilinear polygons: coordinatization by dendrons

Simple rectilinear polygons (i.e. rectilinear polygons without holes or cutpoints) can be regarded as finite rectangular cell complexes coordinatized by two finite dendrons. The intrinsic $l_1$-metric is thus inherited from the product of the two finite dendrons via an isometric embedding. The rectangular cell complexes that share this same embedding property are called ramified rectilinear polygons. The links of vertices in these cell complexes may be arbitrary bipartite graphs, in contrast to simple rectilinear polygons where the links of points are either 4-cycles or paths of length at most 3. Ramified rectilinear polygons are particular instances of rectangular complexes obtained from cube-free median graphs, or equivalently simply connected rectangular complexes with triangle-free links. The underlying graphs of finite ramified rectilinear polygons can be recognized among graphs in linear time by a Lexicographic Breadth-First-Search. Whereas the symmetry of a simple rectilinear polygon is very restricted (with automorphism group being a subgroup of the dihedral group $D_4$), ramified rectilinear polygons are universal: every finite group is the automorphism group of some ramified rectilinear polygon.Comment: 27 pages, 6 figure

Kinetic Modelling of [Ga-68]Ga-DOTA-Siglec-9 in Porcine Osteomyelitis and Soft Tissue Infections

Background: [Ga-68]Ga-DOTA-Siglec-9 is a positron emission tomography (PET) radioligand for vascular adhesion protein 1 (VAP-1), a protein involved in leukocyte trafficking. The tracer facilitates the imaging of inflammation and infection. Here, we studied the pharmacokinetic modelling of [Ga-68]Ga-DOTA-Siglec-9 in osteomyelitis and soft tissue infections in pigs. Methods: Eight pigs with osteomyelitis and soft tissue infections in the right hind limb were dynamically PET scanned for 60 min along with arterial blood sampling. The fraction of radioactivity in the blood accounted for by the parent tracer was evaluated with radio-high-performance liquid chromatography. One- and two-tissue compartment models were used for pharmacokinetic evaluation. Post-mortem soft tissue samples from one pig were analysed with anti-VAP-1 immunofluorescence. In each analysis, the animal's non-infected left hind limb was used as a control. Results: Tracer uptake was elevated in soft tissue infections but remained low in osteomyelitis. The kinetics of [Ga-68]Ga-DOTA-Siglec-9 followed a reversible 2-tissue compartment model. The tracer metabolized quickly; however, taking this into account, produced more ambiguous results. Infected soft tissue samples showed endothelial cell surface expression of the Siglec-9 receptor VAP-1. Conclusion: The kinetics of [Ga-68]Ga-DOTA-Siglec-9 uptake in porcine soft tissue infections are best described by the 2-tissue compartment model.</div

Understanding the impact of more realistic low-dose, prolonged engineered nanomaterial exposure on genotoxicity using 3D models of the human liver

Abstract Background With the continued integration of engineered nanomaterials (ENMs) into everyday applications, it is important to understand their potential for inducing adverse human health effects. However, standard in vitro hazard characterisation approaches suffer limitations for evaluating ENM and so it is imperative to determine these potential hazards under more physiologically relevant and realistic exposure scenarios in target organ systems, to minimise the necessity for in vivo testing. The aim of this study was to determine if acute (24 h) and prolonged (120 h) exposures to five ENMs (TiO2, ZnO, Ag, BaSO4 and CeO2) would have a significantly different toxicological outcome (cytotoxicity, (pro-)inflammatory and genotoxic response) upon 3D human HepG2 liver spheroids. In addition, this study evaluated whether a more realistic, prolonged fractionated and repeated ENM dosing regime induces a significantly different toxicity outcome in liver spheroids as compared to a single, bolus prolonged exposure. Results Whilst it was found that the five ENMs did not impede liver functionality (e.g. albumin and urea production), induce cytotoxicity or an IL-8 (pro-)inflammatory response, all were found to cause significant genotoxicity following acute exposure. Most statistically significant genotoxic responses were not dose-dependent, with the exception of TiO2. Interestingly, the DNA damage effects observed following acute exposures, were not mirrored in the prolonged exposures, where only 0.2–5.0 µg/mL of ZnO ENMs were found to elicit significant (p ≤ 0.05) genotoxicity. When fractionated, repeated exposure regimes were performed with the test ENMs, no significant (p ≥ 0.05) difference was observed when compared to the single, bolus exposure regime. There was < 5.0% cytotoxicity observed across all exposures, and the mean difference in IL-8 cytokine release and genotoxicity between exposure regimes was 3.425 pg/mL and 0.181%, respectively. Conclusion In conclusion, whilst there was no difference between a single, bolus or fractionated, repeated ENM prolonged exposure regimes upon the toxicological output of 3D HepG2 liver spheroids, there was a difference between acute and prolonged exposures. This study highlights the importance of evaluating more realistic ENM exposures, thereby providing a future in vitro approach to better support ENM hazard assessment in a routine and easily accessible manner

Bioaccumulation and ecotoxicity of carbon nanotubes

Carbon nanotubes (CNT) have numerous industrial applications and may be released to the environment. In the aquatic environment, pristine or functionalized CNT have different dispersion behavior, potentially leading to different risks of exposure along the water column. Data included in this review indicate that CNT do not cross biological barriers readily. When internalized, only a minimal fraction of CNT translocate into organism body compartments. The reported CNT toxicity depends on exposure conditions, model organism, CNT-type, dispersion state and concentration. In the ecotoxicological tests, the aquatic organisms were generally found to be more sensitive than terrestrial organisms. Invertebrates were more sensitive than vertebrates. Single-walled CNT were found to be more toxic than double-/multi-walled CNT. Generally, the effect concentrations documented in literature were above current modeled average environmental concentrations. Measurement data are needed for estimation of environmental no-effect concentrations. Future studies with benchmark materials are needed to generate comparable results. Studies have to include better characterization of the starting materials, of the dispersions and of the biological fate, to obtain better knowledge of the exposure/effect relationships