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

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

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

Depleted pyrochlore antiferromagnets

I consider the class of "depleted pyrochlore" lattices of corner-sharing triangles, made by removing spins from a pyrochlore lattice such that every tetrahedron loses exactly one. Previously known examples are the "hyperkagome" and "kagome staircase". I give criteria in terms of loops for whether a given depleted lattice can order analogous to the kagome \sqrt{3} \times \sqrt{three} state, and also show how the pseudo-dipolar correlations (due to local constraints) generalize to even the random depleted case.Comment: 6pp IOP latex, 1 figure; Proc. "Highly Frustrated Magnetism 2008", Sept 2008, Braunschwei

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

Resolving domination in graphs

summary:For an ordered set $W =\lbrace w_1, w_2, \cdots , w_k\rbrace$ of vertices and a vertex $v$ in a connected graph $G$, the (metric) representation of $v$ with respect to $W$ is the $k$-vector $r(v|W) = (d(v, w_1),d(v, w_2) ,\cdots , d(v, w_k))$, where $d(x,y)$ represents the distance between the vertices $x$ and $y$. The set $W$ is a resolving set for $G$ if distinct vertices of $G$ have distinct representations with respect to $W$. A resolving set of minimum cardinality is called a minimum resolving set or a basis and the cardinality of a basis for $G$ is its dimension $\dim G$. A set $S$ of vertices in $G$ is a dominating set for $G$ if every vertex of $G$ that is not in $S$ is adjacent to some vertex of $S$. The minimum cardinality of a dominating set is the domination number $\gamma (G)$. A set of vertices of a graph $G$ that is both resolving and dominating is a resolving dominating set. The minimum cardinality of a resolving dominating set is called the resolving domination number $\gamma _r(G)$. In this paper, we investigate the relationship among these three parameters

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

Observations of the high vibrational levels of the B′′B̄ 1Σ+u state of H2

Double-resonance laser spectroscopy via the E F 1Σ+g, v\u27 = 6, J\u27 = 0–2 state was used to probe the high vibrational levels of the B′′B̄ 1Σ+u state of molecular hydrogen. Resonantly enhanced multiphotonionization spectra were recorded by detecting ion production as a function of energy using a time of flight mass spectrometer. New measurements of energies for the v = 51–66 levels for the B00B ̄ state of H2 are reported, which, taken with previous results, span the v = 46–69 vibrational levels. Results for energy levels are compared to theoretical close-coupled calculations [L. Wolniewicz, T. Orlikowski, and G. Staszewska, J. Mol. Spectrosc. 238, 118–126 (2006)]. The average difference between the 84 measured energies and calculated energies is 3.8 cm–1 with a standard deviation of 5.3 cm–1. This level of agreement showcases the success of the theoretical calculations in accounting for the strong rovibronic mixing of the 1Σu+ and 1Πu+ states. Due to the ion-pair character of the outer well, the observed energies of the vibrational levels below the third dissociation limit smoothly connect with previously observed energies of ion-pair states above this limit. The results provide an opportunity for testing a heavy Rydberg multi-channel quantum defect analysis of the high vibrational states below the third dissociation limit

Observations of High Vibrational Levels of the 4fσ 41Σ+ u State of H2

Resonantly enhanced multiphoton ionization via the EF 1Σg+, v′ = 6 double-well state has been used to probe the energy region below the third dissociation limit of H2 where several high vibrational levels of the 41Σu+ state are expected. Theoretical ab initio potential energy curves for this state predict a deep inner well and shallow outer well where vibrational levels above v = 8 are expected to exhibit the double-well character of the state. Since the 41Σu+ state has f-state character, transitions to it from the ground state are nominally forbidden. However, the d character of the outer well of the EF 1Σg+ state allows access to this state. We report observations of transitions to the v = 9–12 levels of the 41Σu+ state and compare their energies to predicted energies calculated from an ab initio potential energy curve with adiabatic corrections. Assignments are based on measured energies and linewidths, rotational constants, and expected transition strengths. The amount of agreement between the predicted values and the observations is mixed, with the largest discrepancies arising for the v = 9 level, owing to strong nonadiabatic electronic mixing in this energy region