Maximal outerplanar graphs as chordal graphs, path-neighborhood graphs, and triangle graphs

Maximal outerplanar graphs are characterized using three different classes of graphs. A path-neighborhood graph is a connected graph in which every neighborhood induces a path. The triangle graph $T(G)$ has the triangles of the graph $G$ as its vertices, two of these being adjacent whenever as triangles in $G$ they share an edge. A graph is edge-triangular if every edge is in at least one triangle. The main results can be summarized as follows: the class of maximal outerplanar graphs is precisely the intersection of any of the two following classes: the chordal graphs, the path-neighborhood graphs, the edge-triangular graphs having a tree as triangle graph.maximal outerplanar graph;path-neighborhood graph;triangle graph;chordal graph;elimination ordering

A simple axiomatization of the median procedure on median graphs

A profile = (x1, ..., xk), of length k, in a finite connected graph G is a sequence of vertices of G, with repetitions allowed. A median x of is a vertex for which the sum of the distances from x to the vertices in the profile is minimum. The median function finds the set of all medians of a profile. Medians are important in location theory and consensus theory. A median graph is a graph for which every profile of length 3 has a unique median. Median graphs are well studied. They arise in many arenas, and have many applications. We establish a succinct axiomatic characterization of the median procedure on median graphs. This is a simplification of the characterization given by McMorris, Mulder and Roberts [17] in 1998. We show that the median procedure can be characterized on the class of all median graphs with only three simple and intuitively appealing axioms: anonymity, betweenness and consistency. We also extend a key result of the same paper, characterizing the median function for profiles of even length on median graphs

Chaotic Escape From an Open Vase-Shaped Cavity. II. Topological Theory

We present part II of a study of chaotic escape from an open two-dimensional vase-shaped cavity. A surface of section reveals that the chaotic dynamics is controlled by a homoclinic tangle, the union of stable and unstable manifolds attached to a hyperbolic fixed point. Furthermore, the surface of section rectifies escape-time graphs into sequences of escape segments; each sequence is called an epistrophe. Some of the escape segments (and therefore some of the epistrophes) are forced by the topology of the dynamics of the homoclinic tangle. These topologically forced structures can be predicted using the method called homotopic lobe dynamics (HLD). HLD takes a finite length of the unstable manifold and a judiciously altered topology and returns a set of symbolic dynamical equations that encode the folding and stretching of the unstable manifold. We present three applications of this method to three different lengths of the unstable manifold. Using each set of dynamical equations, we compute minimal sets of escape segments associated with the unstable manifold, and minimal sets associated with a burst of trajectories emanating from a point on the vase\u27s boundary. The topological theory predicts most of the early escape segments that are found in numerical computations

Maximal outerplanar graphs as chordal graphs, path-neighborhood graphs, and triangle graphs

Maximal outerplanar graphs are characterized using three different classes of graphs. A path-neighborhood graph is a connected graph in which every neighborhood induces a path. The triangle graph $T(G)$ has the triangles of the graph $G$ as its vertices, two of these being adjacent whenever as triangles in $G$ they share an edge. A graph is edge-triangular if every edge is in at least one triangle. The main results can be summarized as follows: the class of maximal outerplanar graphs is precisely the intersection of any of the two following classes: the chordal graphs, the path-neighborhood graphs, the edge-triangular graphs having a tree as triangle graph

Comparative study of different scattering geometries for the proposed Indian X-ray polarization measurement experiment using Geant4

Polarization measurements in X-rays can provide unique opportunity to study the behavior of matter and radiation under extreme magnetic fields and extreme gravitational fields. Unfortunately, over past two decades, when X-ray astronomy witnessed multiple order of magnitude improvement in temporal, spatial and spectral sensitivities, there is no (or very little) progress in the field of polarization measurements of astrophysical X-rays. Recently, a proposal has been submitted to ISRO for a dedicated small satellite based experiment to carry out X-ray polarization measurement, which aims to provide the first X-ray polarization measurements since 1976. This experiment will be based on the well known principle of polarization measurement by Thomson scattering and employs the baseline design of a central low Z scatterer surrounded by X-ray detectors to measure the angular intensity distribution of the scattered X-rays. The sensitivity of such experiment is determined by the collecting area, scattering and detection efficiency, X-ray detector background, and the modulation factor. Therefore, it is necessary to carefully select the scattering geometry which can provide the highest modulation factor and thus highest sensitivity within the specified experimental constraints. The effective way to determine optimum scattering geometry is by studying various possible scattering geometries by means of Monte Carlo simulations. Here we present results of our detailed comparative study based on Geant4 simulations of five different scattering geometries which can be considered within the weight and size constraints of the proposed small satellite based X-ray polarization measurement experiment.Comment: 14 pages, 6 figures, accepted for publication in "Nuclear Inst. and Methods in Physics Research, A

Chaotic Escape from an Open Vase-shaped Cavity. I. Numerical and Experimental Results

We present part I in a two-part study of an open chaotic cavity shaped as a vase. The vase possesses an unstable periodic orbit in its neck. Trajectories passing through this orbit escape without return. For our analysis, we consider a family of trajectories launched from a point on the vase boundary. We imagine a vertical array of detectors past the unstable periodic orbit and, for each escaping trajectory, record the propagation time and the vertical detector position. We find that the escape time exhibits a complicated recursive structure. This recursive structure is explored in part I of our study. We present an approximation to the Helmholtz equation for waves escaping the vase. By choosing a set of detector points, we interpolate trajectories connecting the source to the different detector points. We use these interpolated classical trajectories to construct the solution to the wave equation at a detector point. Finally, we construct a plot of the detector position versus the escape time and compare this graph to the results of an experiment using classical ultrasound waves. We find that generally the classical trajectories organize the escaping ultrasound waves

Phage inducible islands in the gram-positive cocci

The SaPIs are a cohesive subfamily of extremely common phage-inducible chromosomal islands (PICIs) that reside quiescently at specific att sites in the staphylococcal chromosome and are induced by helper phages to excise and replicate. They are usually packaged in small capsids composed of phage virion proteins, giving rise to very high transfer frequencies, which they enhance by interfering with helper phage reproduction. As the SaPIs represent a highly successful biological strategy, with many natural Staphylococcus aureus strains containing two or more, we assumed that similar elements would be widespread in the Gram-positive cocci. On the basis of resemblance to the paradigmatic SaPI genome, we have readily identified large cohesive families of similar elements in the lactococci and pneumococci/streptococci plus a few such elements in Enterococcus faecalis. Based on extensive ortholog analyses, we found that the PICI elements in the four different genera all represent distinct but parallel lineages, suggesting that they represent convergent evolution towards a highly successful lifestyle. We have characterized in depth the enterococcal element, EfCIV583, and have shown that it very closely resembles the SaPIs in functionality as well as in genome organization, setting the stage for expansion of the study of elements of this type. In summary, our findings greatly broaden the PICI family to include elements from at least three genera of cocci

LR characterization of chirotopes of finite planar families of pairwise disjoint convex bodies

We extend the classical LR characterization of chirotopes of finite planar families of points to chirotopes of finite planar families of pairwise disjoint convex bodies: a map \c{hi} on the set of 3-subsets of a finite set I is a chirotope of finite planar families of pairwise disjoint convex bodies if and only if for every 3-, 4-, and 5-subset J of I the restriction of \c{hi} to the set of 3-subsets of J is a chirotope of finite planar families of pairwise disjoint convex bodies. Our main tool is the polarity map, i.e., the map that assigns to a convex body the set of lines missing its interior, from which we derive the key notion of arrangements of double pseudolines, introduced for the first time in this paper.Comment: 100 pages, 73 figures; accepted manuscript versio

Depicting the tree of life in museums: guiding principles from psychological research

The Tree of Life is revolutionizing our understanding of life on Earth, and, accordingly, evolutionary trees are increasingly important parts of exhibits on biodiversity and evolution. The authors argue that in using these trees to effectively communicate evolutionary principles, museums need to take into account research results from cognitive, developmental, and educational psychology while maintaining a focus on visitor engagement and enjoyment. Six guiding principles for depicting evolutionary trees in museum exhibits distilled from this research literature were used to evaluate five current or recent museum trees. One of the trees was then redesigned in light of the research while preserving the exhibit’s original learning goals. By attending both to traditional factors that influence museum exhibit design and to psychological research on how people understand diagrams in general and Tree of Life graphics in particular, museums can play a key role in fostering 21st century scientific literacy

A Model of Polarized X-ray Emission from Twinkling Synchrotron Supernova Shells

Synchrotron X-ray emission components were recently detected in many young supernova remnants (SNRs). There is even an emerging class - SN1006, RXJ1713.72-3946, Vela Jr, and others - that is dominated by non-thermal emission in X-rays, also probably of synchrotron origin. Such emission results from electrons/positrons accelerated well above TeV energies in the spectral cut-off regime. In the case of diffusive shock acceleration, which is the most promising acceleration mechanism in SNRs, very strong magnetic fluctuations with amplitudes well above the mean magnetic field must be present. Starting from such a fluctuating field, we have simulated images of polarized X-ray emission of SNR shells and show that these are highly clumpy with high polarizations up to 50%. Another distinct characteristic of this emission is the strong intermittency, resulting from the fluctuating field amplifications. The details of this "twinkling" polarized X-ray emission of SNRs depend strongly on the magnetic-field fluctuation spectra, providing a potentially sensitive diagnostic tool. We demonstrate that the predicted characteristics can be studied with instruments that are currently being considered. These can give unique information on magnetic-field characteristics and high-energy particle acceleration in SNRs.Comment: 7 pages, 8 figures, MNRAS (in press