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

Gully Formation at the Haughton Impact Structure (Arctic Canada) Through the Melting of Snow and Ground Ice, with Implications for Gully Formation on Mars

The formation of gullies on Mars has been the topic of active debate and scientific study since their first discovery by Malin and Edgett in 2000. Several mechanisms have been proposed to account for gully formation on Mars, from dry mass movement processes, release of water or brine from subsurface aquifers, and the melting of near-surface ground ice or snowpacks. In their global documentation of martian gullies, report that gullies are confined to ~2783S and ~2872N latitudes and span all longitudes. Gullies on Mars have been documented on impact crater walls and central uplifts, isolated massifs, and on canyon walls, with crater walls being the most common situation. In order to better understand gully formation on Mars, we have been conducting field studies in the Canadian High Arctic over the past several summers, most recently in summer 2018 and 2019 under the auspices of the Canadian Space Agency-funded Icy Mars Analogue Program. It is notable that the majority of previous studies in the Arctic and Antarctica, including our recent work on Devon Island, have focused on gullies formed on slopes generated by regular endogenic geological processes and in regular bedrock. How-ever, as noted above, meteorite impact craters are the most dominant setting for gullies on Mars. Impact craters provide an environment with diverse lithologies including impact-generated and impact-modified rocks and slope angle, and thus greatly variable hill slope processes could occur within a localized area. Here, we investigate the formation of gullies within the Haughton impact structure and compare them to gullies formed in unimpacted target rock in the nearby Thomas Lee Inle

Self-organization of collaboration networks

We study collaboration networks in terms of evolving, self-organizing bipartite graph models. We propose a model of a growing network, which combines preferential edge attachment with the bipartite structure, generic for collaboration networks. The model depends exclusively on basic properties of the network, such as the total number of collaborators and acts of collaboration, the mean size of collaborations, etc. The simplest model defined within this framework already allows us to describe many of the main topological characteristics (degree distribution, clustering coefficient, etc.) of one-mode projections of several real collaboration networks, without parameter fitting. We explain the observed dependence of the local clustering on degree and the degree--degree correlations in terms of the ``aging'' of collaborators and their physical impossibility to participate in an unlimited number of collaborations.Comment: 10 pages, 8 figure

Spectral Measures of Bipartivity in Complex Networks

We introduce a quantitative measure of network bipartivity as a proportion of even to total number of closed walks in the network. Spectral graph theory is used to quantify how close to bipartite a network is and the extent to which individual nodes and edges contribute to the global network bipartivity. It is shown that the bipartivity characterizes the network structure and can be related to the efficiency of semantic or communication networks, trophic interactions in food webs, construction principles in metabolic networks, or communities in social networks.Comment: 16 pages, 1 figure, 1 tabl

Light thresholds for seagrasses of the GBRWHA: a synthesis and guiding document. Including knowledge gaps and future priorities

[Extract] This synthesis contains light thresholds for seagrass species in the Great Barrier Reef World Heritage Area (GBRWHA). The thresholds can be applied to ensure protection of seagrasses from activities that impact water quality and the light environment over the short-term, such as coastal and port developments. Thresholds for long-term maintenance of seagrasses are also proposed

Bend it like Beckham: embodying the motor skills of famous athletes.

Observing an action activates the same representations as does the actual performance of the action. Here we show for the first time that the action system can also be activated in the complete absence of action perception. When the participants had to identify the faces of famous athletes, the responses were influenced by their similarity to the motor skills of the athletes. Thus, the motor skills of the viewed athletes were retrieved automatically during person identification and had a direct influence on the action system of the observer. However, our results also indicated that motor behaviours that are implicit characteristics of other people are represented differently from when actions are directly observed. That is, unlike the facilitatory effects reported when actions were seen, the embodiment of the motor behaviour that is not concurrently perceived gave rise to contrast effects where responses similar to the behaviour of the athletes were inhibited

A Comparison between the Zero Forcing Number and the Strong Metric Dimension of Graphs

The \emph{zero forcing number}, $Z(G)$, of a graph $G$ is the minimum cardinality of a set $S$ of black vertices (whereas vertices in $V(G)-S$ are colored white) such that $V(G)$ is turned black after finitely many applications of "the color-change rule": a white vertex is converted black if it is the only white neighbor of a black vertex. The \emph{strong metric dimension}, $sdim(G)$, of a graph $G$ is the minimum among cardinalities of all strong resolving sets: $W \subseteq V(G)$ is a \emph{strong resolving set} of $G$ if for any $u, v \in V(G)$, there exists an $x \in W$ such that either $u$ lies on an $x-v$ geodesic or $v$ lies on an $x-u$ geodesic. In this paper, we prove that $Z(G) \le sdim(G)+3r(G)$ for a connected graph $G$, where $r(G)$ is the cycle rank of $G$. Further, we prove the sharp bound $Z(G) \leq sdim(G)$ when $G$ is a tree or a unicyclic graph, and we characterize trees $T$ attaining $Z(T)=sdim(T)$. It is easy to see that $sdim(T+e)-sdim(T)$ can be arbitrarily large for a tree $T$; we prove that $sdim(T+e) \ge sdim(T)-2$ and show that the bound is sharp.Comment: 8 pages, 5 figure

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

SURF IA Conflict Detection and Resolution Algorithm Evaluation

The Enhanced Traffic Situational Awareness on the Airport Surface with Indications and Alerts (SURF IA) algorithm was evaluated in a fast-time batch simulation study at the National Aeronautics and Space Administration (NASA) Langley Research Center. SURF IA is designed to increase flight crew situation awareness of the runway environment and facilitate an appropriate and timely response to potential conflict situations. The purpose of the study was to evaluate the performance of the SURF IA algorithm under various runway scenarios, multiple levels of conflict detection and resolution (CD&R) system equipage, and various levels of horizontal position accuracy. This paper gives an overview of the SURF IA concept, simulation study, and results. Runway incursions are a serious aviation safety hazard. As such, the FAA is committed to reducing the severity, number, and rate of runway incursions by implementing a combination of guidance, education, outreach, training, technology, infrastructure, and risk identification and mitigation initiatives [1]. Progress has been made in reducing the number of serious incursions - from a high of 67 in Fiscal Year (FY) 2000 to 6 in FY2010. However, the rate of all incursions has risen steadily over recent years - from a rate of 12.3 incursions per million operations in FY2005 to a rate of 18.9 incursions per million operations in FY2010 [1, 2]. The National Transportation Safety Board (NTSB) also considers runway incursions to be a serious aviation safety hazard, listing runway incursion prevention as one of their most wanted transportation safety improvements [3]. The NTSB recommends that immediate warning of probable collisions/incursions be given directly to flight crews in the cockpit [4]