Optimally edge-colouring outerplanar graphs is in NC

We prove that every outerplanar graph can be optimally edge-coloured in polylogarithmic time using a polynomial number of processors on a parallel random access machine without write conflicts (P-RAM)

Parallel O(log(n)) time edge-colouring of trees and Halin graphs

We present parallel O(log(n))-time algorithms for optimal edge colouring of trees and Halin graphs with n processors on a a parallel random access machine without write conflicts (P-RAM). In the case of Halin graphs with a maximum degree of three, the colouring algorithm automatically finds every Hamiltonian cycle of the graph

Dense edge-disjoint embedding of binary trees in the mesh

We present an embedding of the complete binary tree with n leaves in the Vn x Vn mesh, for any n = 2exp(2m) where m is a positive integer. The embedding has the following properties: at most two tree nodes (one of which is a leaf) are mapped onto each mesh node, paths of the tree are mapped onto edge-disjoint paths in the mesh (each mesh edge considered as two anti-parallel directed edges) and the maximum distance from a leaf to the root of the tree is Vn + O (log n) mesh steps. This embedding facilitates efficient implementation of many P-RAM algorithms on the mesh, particularly those using the balanced binary tree technique. Such an embedding offers greater flexibility of use and improves the time complexity of these implementations by a constant factor compared with previously described embeddings

Disturbance regimes predictably alter diversity in an ecologically complex bacterial system

© The Author(s), 2016. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in mBio 7 (2016): e01372-16, doi:10.1128/mBio.01372-16.Diversity is often associated with the functional stability of ecological communities from microbes to macroorganisms. Understanding how diversity responds to environmental perturbations and the consequences of this relationship for ecosystem function are thus central challenges in microbial ecology. Unimodal diversity-disturbance relationships, in which maximum diversity occurs at intermediate levels of disturbance, have been predicted for ecosystems where life history tradeoffs separate organisms along a disturbance gradient. However, empirical support for such peaked relationships in macrosystems is mixed, and few studies have explored these relationships in microbial systems. Here we use complex microbial microcosm communities to systematically determine diversity-disturbance relationships over a range of disturbance regimes. We observed a reproducible switch between community states, which gave rise to transient diversity maxima when community states were forced to mix. Communities showed reduced compositional stability when diversity was highest. To further explore these dynamics, we formulated a simple model that reveals specific regimes under which diversity maxima are stable. Together, our results show how both unimodal and non-unimodal diversity-disturbance relationships can be observed as a system switches between two distinct microbial community states; this process likely occurs across a wide range of spatially and temporally heterogeneous microbial ecosystems

Overestimating Resource Value and Its Effects on Fighting Decisions

Much work in behavioral ecology has shown that animals fight over resources such as food, and that they make strategic decisions about when to engage in such fights. Here, we examine the evolution of one, heretofore unexamined, component of that strategic decision about whether to fight for a resource. We present the results of a computer simulation that examined the evolution of over- or underestimating the value of a resource (food) as a function of an individual's current hunger level. In our model, animals fought for food when they perceived their current food level to be below the mean for the environment. We considered seven strategies for estimating food value: 1) always underestimate food value, 2) always overestimate food value, 3) never over- or underestimate food value, 4) overestimate food value when hungry, 5) underestimate food value when hungry, 6) overestimate food value when relatively satiated, and 7) underestimate food value when relatively satiated. We first competed all seven strategies against each other when they began at approximately equal frequencies. In such a competition, two strategies–“always overestimate food value,” and “overestimate food value when hungry”–were very successful. We next competed each of these strategies against the default strategy of “never over- or underestimate,” when the default strategy was set at 99% of the population. Again, the strategies of “always overestimate food value” and “overestimate food value when hungry” fared well. Our results suggest that overestimating food value when deciding whether to fight should be favored by natural selection

The football fan and the pub: An enduring relationship

This paper draws on qualitative interviews with a sample of English football fans to explore their relationship with one enduring site for fandom practice, the pub. In doing so, the work discusses the significance of structuration processes as a means of explaining the transcendent nature of this relationship across time and space. The findings complement existing ethnographic observations to illustrate that a progressive and multifaceted relationship exists between the institution (the pub) and its customers (football fans), based on historical reference to fan culture, emotive connection to the pub as a football space, associated sociability and the perception of cultural stability

The Extragalactic Distance Scale Key Project XXVII. A Derivation of the Hubble Constant Using the Fundamental Plane and Dn-Sigma Relations in Leo I, Virgo, and Fornax

Using published photometry and spectroscopy, we construct the fundamental plane and D_n-Sigma relations in Leo I, Virgo and Fornax. The published Cepheid P-L relations to spirals in these clusters fixes the relation between angular size and metric distance for both the fundamental plane and D_n-Sigma relations. Using the locally calibrated fundamental plane, we infer distances to a sample of clusters with a mean redshift of cz \approx 6000 \kms, and derive a value of H_0=78+- 5+- 9 km/s/Mpc (random, systematic) for the local expansion rate. This value includes a correction for depth effects in the Cepheid distances to the nearby clusters, which decreased the deduced value of the expansion rate by 5% +- 5%. If one further adopts the metallicity correction to the Cepheid PL relation, as derived by the Key Project, the value of the Hubble constant would decrease by a further 6%+- 4%. These two sources of systematic error, when combined with a +- 6% error due to the uncertainty in the distance to the Large Magellanic Cloud, a +- 4% error due to uncertainties in the WFPC2 calibration, and several small sources of uncertainty in the fundamental plane analysis, combine to yield a total systematic uncertainty of +- 11%. We find that the values obtained using either the CMB, or a flow-field model, for the reference frame of the distant clusters, agree to within 1%. The Dn-Sigma relation also produces similar results, as expected from the correlated nature of the two scaling relations. A complete discussion of the sources of random and systematic error in this determination of the Hubble constant is also given, in order to facilitate comparison with the other secondary indicators being used by the Key Project.Comment: 21 pages, 3 figures, Accepted for publication in Ap

Dynamics of M-Theory Cosmology

A complete global analysis of spatially-flat, four-dimensional cosmologies derived from the type IIA string and M-theory effective actions is presented. A non--trivial Ramond-Ramond sector is included. The governing equations are written as a dynamical system. Asymptotically, the form fields are dynamically negligible, but play a crucial role in determining the possible intermediate behaviour of the solutions (i.e. the nature of the equilibrium points). The only past-attracting solution (source in the system) may be interpreted in the eleven-dimensional setting in terms of flat space. This source is unstable to the introduction of spatial curvature.Comment: 13 pages, 4 Postscript figures, uses graphics.sty, submitted to Phys. Rev.