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

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

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

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

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

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

Addition of long-acting beta2-agonists to inhaled corticosteroids for chronic asthma in children

Background Long-acting beta2-agonists (LABA) in combination with inhaled corticosteroids (ICS) are increasingly prescribed for children with asthma. Objectives To assess the safety and efficacy of adding a LABA to an ICS in children and adolescents with asthma. To determine whether the benefit of LABA was influenced by baseline severity of airway obstruction, the dose of ICS to which it was added or with which it was compared, the type of LABA used, the number of devices used to deliver combination therapy and trial duration. Search methods We searched the Cochrane Airways Group Asthma Trials Register until January 2015. Selection criteria We included randomised controlled trials testing the combination of LABA and ICS versus the same, or an increased, dose of ICS for at least four weeks in children and adolescents with asthma. The main outcome was the rate of exacerbations requiring rescue oral steroids. Secondary outcomes included markers of exacerbation, pulmonary function, symptoms, quality of life, adverse events and withdrawals. Data collection and analysis Two review authors assessed studies independently for methodological quality and extracted data. We obtained confirmation from trialists when possible. Main results We included in this review a total of 33 trials representing 39 control-intervention comparisons and randomly assigning 6381 children. Most participants were inadequately controlled on their current ICS dose. We assessed the addition of LABA to ICS (1) versus the same dose of ICS, and (2) versus an increased dose of ICS. LABA added to ICS was compared with the same dose of ICS in 28 studies. Mean age of participants was 11 years, and males accounted for 59% of the study population. Mean forced expiratory volume in one second (FEV1) at baseline was ≥ 80% of predicted in 18 studies, 61% to 79% of predicted in six studies and unreported in the remaining studies. Participants were inadequately controlled before randomisation in all but four studies. There was no significant group difference in exacerbations requiring oral steroids (risk ratio (RR) 0.95, 95% confidence interval (CI) 0.70 to 1.28, 12 studies, 1669 children; moderate-quality evidence) with addition of LABA to ICS compared with ICS alone. There was no statistically significant group difference in hospital admissions (RR 1.74, 95% CI 0.90 to 3.36, seven studies, 1292 children; moderate-quality evidence)nor in serious adverse events (RR 1.17, 95% CI 0.75 to 1.85, 17 studies, N = 4021; moderate-quality evidence). Withdrawals occurred significantly less frequently with the addition of LABA (23 studies, 471 children, RR 0.80, 95% CI 0.67 to 0.94; low-quality evidence). Compared with ICS alone, addition of LABA led to significantly greater improvement in FEV1 (nine studies, 1942 children, inverse variance (IV) 0.08 L, 95% CI 0.06 to 0.10; mean difference (MD) 2.99%, 95% CI 0.86 to 5.11, seven studies, 534 children; low-quality evidence), morning peak expiratory flow (PEF) (16 studies, 3934 children, IV 10.20 L/min, 95% CI 8.14 to 12.26), reduction in use of daytime rescue inhalations (MD -0.07 puffs/d, 95% CI -0.11 to -0.02, seven studies; 1798 children) and reduction in use of nighttime rescue inhalations (MD -0.08 puffs/d, 95% CI -0.13 to -0.03, three studies, 672 children). No significant group difference was noted in exercise-induced % fall in FEV1, symptom-free days, asthma symptom score, quality of life, use of reliever medication and adverse events. A total of 11 studies assessed the addition of LABA to ICS therapy versus an increased dose of ICS with random assignment of 1628 children. Mean age of participants was 10 years, and 64% were male. Baseline mean FEV1 was ≥ 80% of predicted. All trials enrolled participants who were inadequately controlled on a baseline inhaled steroid dose equivalent to 400 µg/d of beclomethasone equivalent or less. There was no significant group differences in risk of exacerbation requiring oral steroids with the combination of LABA and ICS versus a double dose of ICS (RR 1.69, 95% CI 0.85 to 3.32, three studies, 581 children; moderate-quality evidence) nor in risk of hospital admission (RR 1.90, 95% CI 0.65 to 5.54, four studies, 1008 children; moderate-quality evidence). No statistical significant group difference was noted in serious adverse events (RR 1.54, 95% CI 0.81 to 2.94, seven studies, N = 1343; moderate-quality evidence) and no statistically significant differences in overall risk of all-cause withdrawals (RR 0.96, 95% CI 0.67 to 1.37, eight studies, 1491 children; moderate-quality evidence). Compared with double the dose of ICS, use of LABA was associated with significantly greater improvement in morning PEF (MD 8.73 L/min, 95% CI 5.15 to 12.31, five studies, 1283 children; moderate-quality evidence), but data were insufficient to aggregate on other markers of asthma symptoms, rescue medication use and nighttime awakening. There was no group difference in risk of overall adverse effects, A significant group difference was observed in linear growth over 12 months, clearly indicating lower growth velocity in the higher ICS dose group (two studies: MD 1.21 cm/y, 95% CI 0.72 to 1.70). Authors' conclusions In children with persistent asthma, the addition of LABA to ICS was not associated with a significant reduction in the rate of exacerbations requiring systemic steroids, but it was superior for improving lung function compared with the same or higher doses of ICS. No differences in adverse effects were apparent, with the exception of greater growth with the use of ICS and LABA compared with a higher ICS dose. The trend towards increased risk of hospital admission with LABA, irrespective of the dose of ICS, is a matter of concern and requires further monitoring

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