Hamiltonicity of 3-arc graphs

An arc of a graph is an oriented edge and a 3-arc is a 4-tuple $(v,u,x,y)$ of vertices such that both $(v,u,x)$ and $(u,x,y)$ are paths of length two. The 3-arc graph of a graph $G$ is defined to have vertices the arcs of $G$ such that two arcs $uv, xy$ are adjacent if and only if $(v,u,x,y)$ is a 3-arc of $G$. In this paper we prove that any connected 3-arc graph is Hamiltonian, and all iterative 3-arc graphs of any connected graph of minimum degree at least three are Hamiltonian. As a consequence we obtain that if a vertex-transitive graph is isomorphic to the 3-arc graph of a connected arc-transitive graph of degree at least three, then it is Hamiltonian. This confirms the well known conjecture, that all vertex-transitive graphs with finitely many exceptions are Hamiltonian, for a large family of vertex-transitive graphs. We also prove that if a graph with at least four vertices is Hamilton-connected, then so are its iterative 3-arc graphs.Comment: in press Graphs and Combinatorics, 201

Contact Representations of Graphs in 3D

We study contact representations of graphs in which vertices are represented by axis-aligned polyhedra in 3D and edges are realized by non-zero area common boundaries between corresponding polyhedra. We show that for every 3-connected planar graph, there exists a simultaneous representation of the graph and its dual with 3D boxes. We give a linear-time algorithm for constructing such a representation. This result extends the existing primal-dual contact representations of planar graphs in 2D using circles and triangles. While contact graphs in 2D directly correspond to planar graphs, we next study representations of non-planar graphs in 3D. In particular we consider representations of optimal 1-planar graphs. A graph is 1-planar if there exists a drawing in the plane where each edge is crossed at most once, and an optimal n-vertex 1-planar graph has the maximum (4n - 8) number of edges. We describe a linear-time algorithm for representing optimal 1-planar graphs without separating 4-cycles with 3D boxes. However, not every optimal 1-planar graph admits a representation with boxes. Hence, we consider contact representations with the next simplest axis-aligned 3D object, L-shaped polyhedra. We provide a quadratic-time algorithm for representing optimal 1-planar graph with L-shaped polyhedra

Police legitimacy among immigrants in Europe: institutional frames and group position

Research on the antecedents of police legitimacy has begun to stress the relevance of a wide range of factors – beyond performance – in shaping public judgements of police (e.g. Jackson et al 2012; Antrobus et al 2015; Mehozay and Factor 2016; Weitzer and Tuch 2006). The ways in which people experience not just policing and but also their wider social, cultural and economic environment – and the location of both police and policed within structures of power, authority and affect – have important effects on lay judgements of police which, in turn, constitute the empirical legitimacy of this foundational state institution

Crystallographic structure of ultrathin Fe films on Cu(100)

We report bcc-like crystal structures in 2-4 ML Fe films grown on fcc Cu(100) using scanning tunneling microscopy. The local bcc structure provides a straightforward explanation for their frequently reported outstanding magnetic properties, i.e., ferromagnetic ordering in all layers with a Curie temperature above 300 K. The non-pseudomorphic structure, which becomes pseudomorphic above 4 ML film thickness is unexpected in terms of conventional rules of thin film growth and stresses the importance of finite thickness effects in ferromagnetic ultrathin films.Comment: 4 pages, 3 figures, RevTeX/LaTeX2.0

A prothrombinase-based assay for detection of resistance to activated protein C

In this paper we present a new method for the detection of resistance to activated protein C (APC) that is based on direct measurement of the effect of APC an the cofactor activity of plasma factor Va. The factor V present in a diluted plasma sample was activated with thrombin and its sensitivity towards APC was subsequently determined by incubation with phospholipids and APC; The loss of factor Va cofactor activity was quantified in a prothrombinase system containing purified prothrombin. factor Xa and phospholipid vesicles and using a chromogenic assay for quantitation of thrombin formation. The reaction conditions were optimized in order to distinguish normal, heterozygous and homozygous APC-resistant plasmas. Maximal differences in the response of these plasmas towards ATC were observed when factor Va was inactivated by APC in the absence of protein S and when the: cofactor activity of factor Va was determined at a low factor Xa concentration (0.3 nM).Addition of 0.2 nM APC and 20 mu M phospholipid vesicles to a 1000-fold diluted sample of thrombin-activated normal plasma resulted in loss of mon than 85% of the cofactor activity factor Va within 6 min. Under the same conditions, APC inactivated similar to 60% and similar to 20% of the factor Va present in plasma samples from APC-resistant individuals that were heterozygous or homozygous for the mutation Arg(506)-->Gln in factor V, respectively. Discrimination between the plasma samples from normal and heterozygous and homozygous APC-resistant individuals was facilitated by introduction of the so-called APC-sensitivity ratio (APC-sr). The APC-sr was defined as the ratio of the factor Va cofactor activities determined in thrombin-activated plasma samples after 6 min incubation with or without 0.2 nM APC and was multiplied by as 100 to obtain integers (APC-sr = {factor Va(+APC)/factor Va(-APC)} x 100). Clear differences were observed between the APC-sr of plasmas from normal healthy volunteers (APC-sr: 8-20, n = 33) and from individuals that were heterozygous (APC-sr: 35-50, n = 17) or homozygous APC resistant (APC-sr: 82-88, n = 7). There was no mutual overlap between the APC-sr of normal plasmas and plasmas from heterozygous or homozygous APC resistant individuals (p < 0.0001), In all cases our test gave the same result as the DNA-based assay. Since the test is performed on a highly diluted plasma sample there is no interference by conditions that affect APC resistance tests that are based on clotting time determinations (e.g. coagulation factor deficiencies, oral anticoagulation, heparin treatment. the presence of lupus anticoagulants, pregnancy or the use of oral contraceptives). Furthermore, we show that part of the factor Va assay can be performed on an autoanalyzer which increases the number of plasma samples that can be handled simultaneously

Triangle-Free Penny Graphs: Degeneracy, Choosability, and Edge Count

We show that triangle-free penny graphs have degeneracy at most two, list coloring number (choosability) at most three, diameter $D=\Omega(\sqrt n)$, and at most $\min\bigl(2n-\Omega(\sqrt n),2n-D-2\bigr)$ edges.Comment: 10 pages, 2 figures. To appear at the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Pixel and Voxel Representations of Graphs

We study contact representations for graphs, which we call pixel representations in 2D and voxel representations in 3D. Our representations are based on the unit square grid whose cells we call pixels in 2D and voxels in 3D. Two pixels are adjacent if they share an edge, two voxels if they share a face. We call a connected set of pixels or voxels a blob. Given a graph, we represent its vertices by disjoint blobs such that two blobs contain adjacent pixels or voxels if and only if the corresponding vertices are adjacent. We are interested in the size of a representation, which is the number of pixels or voxels it consists of. We first show that finding minimum-size representations is NP-complete. Then, we bound representation sizes needed for certain graph classes. In 2D, we show that, for $k$-outerplanar graphs with $n$ vertices, $\Theta(kn)$ pixels are always sufficient and sometimes necessary. In particular, outerplanar graphs can be represented with a linear number of pixels, whereas general planar graphs sometimes need a quadratic number. In 3D, $\Theta(n^2)$ voxels are always sufficient and sometimes necessary for any $n$-vertex graph. We improve this bound to $\Theta(n\cdot \tau)$ for graphs of treewidth $\tau$ and to $O((g+1)^2n\log^2n)$ for graphs of genus $g$. In particular, planar graphs admit representations with $O(n\log^2n)$ voxels

Models and metaphors: complexity theory and through-life management in the built environment

Complexity thinking may have both modelling and metaphorical applications in the through-life management of the built environment. These two distinct approaches are examined and compared. In the first instance, some of the sources of complexity in the design, construction and maintenance of the built environment are identified. The metaphorical use of complexity in management thinking and its application in the built environment are briefly examined. This is followed by an exploration of modelling techniques relevant to built environment concerns. Non-linear and complex mathematical techniques such as fuzzy logic, cellular automata and attractors, may be applicable to their analysis. Existing software tools are identified and examples of successful built environment applications of complexity modelling are given. Some issues that arise include the definition of phenomena in a mathematically usable way, the functionality of available software and the possibility of going beyond representational modelling. Further questions arising from the application of complexity thinking are discussed, including the possibilities for confusion that arise from the use of metaphor. The metaphor of a 'commentary machine' is suggested as a possible way forward and it is suggested that an appropriate linguistic analysis can in certain situations reduce perceived complexity