Obstacle Numbers of Planar Graphs

Given finitely many connected polygonal obstacles $O_1,\dots,O_k$ in the plane and a set $P$ of points in general position and not in any obstacle, the {\em visibility graph} of $P$ with obstacles $O_1,\dots,O_k$ is the (geometric) graph with vertex set $P$, where two vertices are adjacent if the straight line segment joining them intersects no obstacle. The obstacle number of a graph $G$ is the smallest integer $k$ such that $G$ is the visibility graph of a set of points with $k$ obstacles. If $G$ is planar, we define the planar obstacle number of $G$ by further requiring that the visibility graph has no crossing edges (hence that it is a planar geometric drawing of $G$). In this paper, we prove that the maximum planar obstacle number of a planar graph of order $n$ is $n-3$, the maximum being attained (in particular) by maximal bipartite planar graphs. This displays a significant difference with the standard obstacle number, as we prove that the obstacle number of every bipartite planar graph (and more generally in the class PURE-2-DIR of intersection graphs of straight line segments in two directions) of order at least $3$ is $1$.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

On colouring point visibility graphs

In this paper we show that it can be decided in polynomial time whether or not the visibility graph of a given point set is 4-colourable, and such a 4-colouring, if it exists, can also be constructed in polynomial time. We show that the problem of deciding whether the visibility graph of a point set is 5-colourable, is NP-complete. We give an example of a point visibility graph that has chromatic number 6 while its clique number is only 4

Integrating spatial and temporal approaches for explaining bicycle crashes in high-risk areas in Antwerp (Belgium)

The majority of bicycle crash studies aim at determining risk factors and estimating crash risks by employing statistics. Accordingly, the goal of this paper is to evaluate bicycle-motor vehicle crashes by using spatial and temporal approaches to statistical data. The spatial approach (a weighted kernel density estimation approach) preliminarily estimates crash risks at the macro level, thereby avoiding the expensive work of collecting traffic counts; meanwhile, the temporal approach (negative binomial regression approach) focuses on crash data that occurred on urban arterials and includes traffic exposure at the micro level. The crash risk and risk factors of arterial roads associated with bicycle facilities and road environments were assessed using a database built from field surveys and five government agencies. This study analysed 4120 geocoded bicycle crashes in the city of Antwerp (CA, Belgium). The data sets covered five years (2014 to 2018), including all bicycle-motorized vehicle (BMV) crashes from police reports. Urban arterials were highlighted as high-risk areas through the spatial approach. This was as expected given that, due to heavy traffic and limited road space, bicycle facilities on arterial roads face many design problems. Through spatial and temporal approaches, the environmental characteristics of bicycle crashes on arterial roads were analysed at the micro level. Finally, this paper provides an insight that can be used by both the geography and transport fields to improve cycling safety on urban arterial roads

Quantification of miRNAs and Their Networks in the light of Integral Value Transformations

MicroRNAs (miRNAs) which are on average only 21-25 nucleotides long are key post-transcriptional regulators of gene expression in metazoans and plants. A proper quantitative understanding of miRNAs is required to comprehend their structures, functions, evolutions etc. In this paper, the nucleotide strings of miRNAs of three organisms namely Homo sapiens (hsa), Macaca mulatta (mml) and Pan troglodytes (ptr) have been quantified and classified based on some characterizing features. A network has been built up among the miRNAs for these three organisms through a class of discrete transformations namely Integral Value Transformations (IVTs), proposed by Sk. S. Hassan et al [1, 2]. Through this study we have been able to nullify or justify one given nucleotide string as a miRNA. This study will help us to recognize a given nucleotide string as a probable miRNA, without the requirement of any conventional biological experiment. This method can be amalgamated with the existing analysis pipelines, for small RNA sequencing data (designed for finding novel miRNA). This method would provide more confidence and would make the current analysis pipeline more efficient in predicting the probable candidates of miRNA for biological validation and filter out the improbable candidates

Computing the F-index of nanostar dendrimers

AbstractDendrimers are highly branched nanostructures and are considered a building block in nanotechnology with a variety of suitable applications. In this paper, a vertex degree-based topological index, namely, the F-index, which is defined as the sum of cubes of a graph's vertex degrees, is studied for certain dendrimers. In this study, we present exact expressions for the F-index and F-polynomial of six infinite classes of nanostar dendrimers

Exploring sex differences in diets and activity patterns through dental and skeletal studies in populations from ancient Corinth, Greece.

Sex and temporal differences are assessed in relation to dietary habits and activity patterns in three ancient populations from Corinth, Greece. The skeletal sample spans time from the Geometric to the Early Byzantine Period (9th c. BCE-5th c. CE). Dental caries and tooth wear have been proven to be reliable dietary indicators. Similarly, spinal osteoarthritis, spinal facet remodeling and Schmorl's nodes, have been used to infer activity patterns

Soft x-ray resonant magneto-optical Kerr effect as a depth-sensitive probe of magnetic heterogeneity: A simulation approach

We report a noticeable depth sensitivity of soft x-ray resonant magneto-optical Kerr effect able to resolve depth-varying magnetic heterostructures in ultrathin multilayer films. For various models of depth-varying magnetization orientations in an ultrathin Co layer of realistic complex layered structures, we have calculated the Kerr rotation, ellipticity, intensity spectra versus grazing incidence angle ??, and their hysteresis loops at different values of ?? for various photon energies ?? 's near the Co resonance regions. It is found from the simulation results that the Kerr effect has a much improved depth sensitivity and that its sensitivity varies remarkably with ?? and ?? in the vicinity of the resonance regions. These properties originate from a rich variety of wave interference effects superimposed with noticeable features of the refractive and absorptive optical effects near the resonance regions. Consequently, these allow us to resolve depth-varying magnetizations and their reversals varying with depth in a single magnetic layer and allow us to distinguish interface magnetism from the bulk properties in multilayer films. In this paper, the depth sensitivity of the Kerr effect with an atomic-scale resolution is demonstrated and discussed in details in several manners with the help of model simulations for various depth-varying spin configurations.open9

De-pollution efficacy of photocatalytic roofing granules

Photocatalytic building surfaces can harness sunlight to reduce urban air pollution. The NOx abatement capacity of TiO2-coated granules used in roofing products was evaluated for commercial product development. A laboratory test chamber and ancillary setup were built following conditions prescribed by ISO Standard 22197-1. It was validated by exposing reference P25-coated aluminum plates to a 3 L min−1 air flow enriched in 1 ppm NO under UVA irradiation (360 nm, 11.5 W m−2). We characterized prototype granule-surfaced asphalt shingles and loose granules prepared with different TiO2 loadings and post-treatment formulations. Tests performed at surface temperatures of 25 and 60 °C showed that NOx abatement was more effective at the higher temperature. Preliminary tests explored the use of 1 ppm NO2 and of 1 ppm and 0.3 ppm NO/NO2 mixtures. Specimens were aged in a laboratory accelerated weathering apparatus, and by exposure to the outdoor environment over periods that included dry and rainy seasons. Laboratory aging led to higher NO removal and NO2 formation rates, and the same catalyst activation was observed after field exposure with frequent precipitation. However, exposure during the dry season reduced the performance. This inactivation was mitigated by cleaning the surface of field-exposed specimens. Doubling the TiO2 loading led to a 50–150% increase in NO removal and NOx deposition rates. Application of different post-treatment coatings decreased NO removal rates (21–35%) and NOx deposition rates (26–74%) with respect to untreated granules. The mass balance of nitrogenated species was assessed by extracting granules after UV exposure in a 1 ppm NO-enriched atmosphere

Precision on leptonic mixing parameters at future neutrino oscillation experiments

We perform a comparison of the different future neutrino oscillation experiments based on the achievable precision in the determination of the fundamental parameters theta_{13} and the CP phase, delta, assuming that theta_{13} is in the range indicated by the recent Daya Bay measurement. We study the non-trivial dependence of the error on delta on its true value. When matter effects are small, the largest error is found at the points where CP violation is maximal, and the smallest at the CP conserving points. The situation is different when matter effects are sizable. As a result of this effect, the comparison of the physics reach of different experiments on the basis of the CP discovery potential, as usually done, can be misleading. We have compared various proposed super-beam, beta-beam and neutrino factory setups on the basis of the relative precision of theta_{13} and the error on delta. Neutrino factories, both high-energy or low-energy, outperform alternative beam technologies. An ultimate precision on theta_{13} below 3% and an error on delta of < 7^{\circ} at 1 sigma (1 d.o.f.) can be obtained at a neutrino factory.Comment: Minor changes, matches version accepted in JHEP. 30 pages, 9 figure

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