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

Speed of synchronization in complex networks of neural oscillators Analytic results based on Random Matrix Theory

We analyze the dynamics of networks of spiking neural oscillators. First, we present an exact linear stability theory of the synchronous state for networks of arbitrary connectivity. For general neuron rise functions, stability is determined by multiple operators, for which standard analysis is not suitable. We describe a general non-standard solution to the multi-operator problem. Subsequently, we derive a class of rise functions for which all stability operators become degenerate and standard eigenvalue analysis becomes a suitable tool. Interestingly, this class is found to consist of networks of leaky integrate and fire neurons. For random networks of inhibitory integrate-and-fire neurons, we then develop an analytical approach, based on the theory of random matrices, to precisely determine the eigenvalue distribution. This yields the asymptotic relaxation time for perturbations to the synchronous state which provides the characteristic time scale on which neurons can coordinate their activity in such networks. For networks with finite in-degree, i.e. finite number of presynaptic inputs per neuron, we find a speed limit to coordinating spiking activity: Even with arbitrarily strong interaction strengths neurons cannot synchronize faster than at a certain maximal speed determined by the typical in-degree.Comment: 17 pages, 12 figures, submitted to Chao

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

On polynomial digraphs

Let $\Phi(x,y)$ be a bivariate polynomial with complex coefficients. The zeroes of $\Phi(x,y)$ are given a combinatorial structure by considering them as arcs of a directed graph $G(\Phi)$. This paper studies some relationship between the polynomial $\Phi(x,y)$ and the structure of $G(\Phi)$.Comment: 13 pages, 6 figures, See also http://www-ma2.upc.edu/~montes

Operational Improvements From the Automatic Dependant Surveillance Broadcast In-Trail Procedure in the Pacific Organized Track System

The Federal Aviation Administration's Surveillance and Broadcast Services Program has supported implementation of the Automatic Dependant Surveillance Broadcast (ADS-B) In-Trail Procedure (ITP) on commercial revenue flights. ADS-B ITP is intended to be used in non-radar airspace that is employing procedural separation. Through the use of onboard tools, pilots are able to make a new type of altitude change request to an Air Traffic Service Provider (ATSP). The FAA, in partnership with United Airlines, is conducting flight trials of the ITP in revenue service in the Pacific. To support the expansion of flight trials to the rest of the US managed Pacific Airspace Region, a computerized batch study was conducted to investigate the operational impacts and potential benefits that can be gained through the use of the ITP in the Pacific Organized Track System (PACOTS). This study, which simulated the Oakland managed portion of the PACOTS, suggests that potential benefits in the PACOTS are significant with a considerable increase in time spent at optimum altitude and associated fuel savings

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

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

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

Environmental tolerances and drivers of deepwater seagrass change: implications and tools for coastal development management

While research has focused on shallow water coastal seagrasses over the last 20 years, little is known of the ecological role, tolerances and drivers of their deepwater (>10) counterparts. Within the Great Barrier Reef World Heritage Area, deepwater seagrasses are estimated to occupy more than 35,000 km2 of the reef lagoon. These deepwater meadows are often within the footprint of port and shipping activity where dredging, associated plumes and ship movements are major threats to their long term survival. We present initial findings from an ongoing research program to determine the drivers of seasonal and inter-annual change in deepwater tropical seagrasses. Seagrass abundance, seed bank status and recruitment, productivity, irradiance and temperature along with detailed spectral profiles have been measured in three geographically distinct deepwater seagrass meadows since early 2012. Manipulative lab experiments were initiated in mid-2013 to assess the adaptive photophysiological characteristics of the plants. This research will identify key environmental cues which will be used in developing local management strategies for mitigating coastal developmental impacts along the Great Barrier Reef