On Metric Dimension of Functigraphs

The \emph{metric dimension} of a graph $G$, denoted by $\dim(G)$, is the minimum number of vertices such that each vertex is uniquely determined by its distances to the chosen vertices. Let $G_1$ and $G_2$ be disjoint copies of a graph $G$ and let $f: V(G_1) \rightarrow V(G_2)$ be a function. Then a \emph{functigraph} $C(G, f)=(V, E)$ has the vertex set $V=V(G_1) \cup V(G_2)$ and the edge set $E=E(G_1) \cup E(G_2) \cup \{uv \mid v=f(u)\}$. We study how metric dimension behaves in passing from $G$ to $C(G,f)$ by first showing that $2 \le \dim(C(G, f)) \le 2n-3$, if $G$ is a connected graph of order $n \ge 3$ and $f$ is any function. We further investigate the metric dimension of functigraphs on complete graphs and on cycles.Comment: 10 pages, 7 figure

Colourings of cubic graphs inducing isomorphic monochromatic subgraphs

A $k$-bisection of a bridgeless cubic graph $G$ is a $2$-colouring of its vertex set such that the colour classes have the same cardinality and all connected components in the two subgraphs induced by the colour classes (monochromatic components in what follows) have order at most $k$. Ban and Linial conjectured that every bridgeless cubic graph admits a $2$-bisection except for the Petersen graph. A similar problem for the edge set of cubic graphs has been studied: Wormald conjectured that every cubic graph $G$ with $|E(G)| \equiv 0 \pmod 2$ has a $2$-edge colouring such that the two monochromatic subgraphs are isomorphic linear forests (i.e. a forest whose components are paths). Finally, Ando conjectured that every cubic graph admits a bisection such that the two induced monochromatic subgraphs are isomorphic. In this paper, we give a detailed insight into the conjectures of Ban-Linial and Wormald and provide evidence of a strong relation of both of them with Ando's conjecture. Furthermore, we also give computational and theoretical evidence in their support. As a result, we pose some open problems stronger than the above mentioned conjectures. Moreover, we prove Ban-Linial's conjecture for cubic cycle permutation graphs. As a by-product of studying $2$-edge colourings of cubic graphs having linear forests as monochromatic components, we also give a negative answer to a problem posed by Jackson and Wormald about certain decompositions of cubic graphs into linear forests.Comment: 33 pages; submitted for publicatio

Operational Improvements From Using the In-Trail Procedure in the North Atlantic Organized Track System

This paper explains the computerized batch processing experiment examining the operational impacts of the introduction of Automatic Dependent Surveillance-Broadcast (ADS-B) equipment and the In-Trail Procedure (ITP) to the North Atlantic Organized Track System. This experiment was conducted using the Traffic Manager (TMX), a desktop simulation capable of simulating airspace environments and aircraft operations. ADS-B equipment can enable the use of new ground and airborne procedures, such as the ITP. ITP is among the first of these new procedures, which will make use of improved situation awareness in the local surrounding airspace of ADS-B equipped aircraft to enable more efficient oceanic flight level changes. The collected data were analyzed with respect to multiple operationally relevant parameters including fuel burn, request approval rates, and the distribution of fuel savings. This experiment showed that through the use of ADS-B or ADS-B and the ITP that operational improvements and benefits could be achieved

On Graph-Theoretic Identifications of Adinkras, Supersymmetry Representations and Superfields

In this paper we discuss off-shell representations of N-extended supersymmetry in one dimension, ie, N-extended supersymmetric quantum mechanics, and following earlier work on the subject codify them in terms of certain graphs, called Adinkras. This framework provides a method of generating all Adinkras with the same topology, and so also all the corresponding irreducible supersymmetric multiplets. We develop some graph theoretic techniques to understand these diagrams in terms of a relatively small amount of information, namely, at what heights various vertices of the graph should be "hung". We then show how Adinkras that are the graphs of N-dimensional cubes can be obtained as the Adinkra for superfields satisfying constraints that involve superderivatives. This dramatically widens the range of supermultiplets that can be described using the superspace formalism and organizes them. Other topologies for Adinkras are possible, and we show that it is reasonable that these are also the result of constraining superfields using superderivatives. The family of Adinkras with an N-cubical topology, and so also the sequence of corresponding irreducible supersymmetric multiplets, are arranged in a cyclical sequence called the main sequence. We produce the N=1 and N=2 main sequences in detail, and indicate some aspects of the situation for higher N.Comment: LaTeX, 58 pages, 52 illustrations in color; minor typos correcte

Continuity of heavy Rydberg behaviour in the ungerade ion-pair states of H 2

Heavy Rydberg behaviour and absolute quantum defects are reported for resonances in the ungerade manifold of H2 above the (1s, 3l) dissociation limit. The continuity of the vibrational progression of the B\u27\u27B-bar state through the crossing with the 3p asymptote is demonstrated and a predominantly diabatic picture of the vibrational motion emerges, indicating that the ion-pair resonances possess little 61Σu+ state character

Divergence in Dialogue

Copyright: 2014 Healey et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.This work was supported by the Economic and Social Research Council (ESRC; http://www.esrc.ac.uk/) through the DynDial project (Dynamics of Conversational Dialogue, RES-062-23-0962) and the Engineering and Physical Sciences Research Council (EPSRC; http://www.epsrc.ac.uk/) through the RISER project (Robust Incremental Semantic Resources for Dialogue, EP/J010383/1). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Confirmatory factor analysis of the Test of Performance Strategies (TOPS) among adolescent athletes

The aim of the present study was to examine the factorial validity of the Test of Performance Strategies (TOPS; Thomas et al., 1999) among adolescent athletes using confirmatory factor analysis. The TOPS was designed to assess eight psychological strategies used in competition (i.e. activation, automaticity, emotional control, goal-setting, imagery, negative thinking, relaxation and self-talk,) and eight used in practice (the same strategies except negative thinking is replaced by attentional control). National-level athletes (n = 584) completed the 64-item TOPS during training camps. Fit indices provided partial support for the overall measurement model for the competition items (robust comparative fit index = 0.92, Tucker-Lewis index = 0.88, root mean square error of approximation = 0.05) but minimal support for the training items (robust comparative fit index = 0.86, Tucker-Lewis index = 0.81, root mean square error of approximation = 0.06). For the competition items, the automaticity, goal-setting, relaxation and self-talk scales showed good fit, whereas the activation, emotional control, imagery and negative thinking scales did not. For the practice items, the attentional control, emotional control, goal-setting, imagery and self-talk scales showed good fit, whereas the activation, automaticity and relaxation scales did not. Overall, it appears that the factorial validity of the TOPS for use with adolescents is questionable at present and further development is required

Operational Improvements From the In-Trail Procedure in the North Atlantic Organized Track System

This paper explains the computerized batch processing experiment examining the operational impacts of the introduction of Automatic Dependent Surveillance-Broadcast (ADS-B) equipment and the In-Trail Procedure (ITP) to the North Atlantic Organized Track System (NATOTS). This experiment was conducted using the Traffic Manager (TMX), a desktop simulation capable of simulating airspace environments and aircraft operations. ADS-B equipment can enable the use of new ground and airborne procedures, such as the ITP. The ITP is among the first of these new procedures, which will make use of improved situation awareness in the local surrounding airspace of ADS-B equipped aircraft to enable more efficient oceanic flight level changes. The data collected were analyzed with respect to multiple operationally relevant parameters including fuel burn, request approval rates, and the distribution of fuel savings. This experiment showed that through the use of ADS-B or ADS-B and the ITP that operational improvements and benefits could be achieved