Spatial Mixing of Coloring Random Graphs

We study the strong spatial mixing (decay of correlation) property of proper $q$-colorings of random graph $G(n, d/n)$ with a fixed $d$. The strong spatial mixing of coloring and related models have been extensively studied on graphs with bounded maximum degree. However, for typical classes of graphs with bounded average degree, such as $G(n, d/n)$, an easy counterexample shows that colorings do not exhibit strong spatial mixing with high probability. Nevertheless, we show that for $q\ge\alpha d+\beta$ with $\alpha>2$ and sufficiently large $\beta=O(1)$, with high probability proper $q$-colorings of random graph $G(n, d/n)$ exhibit strong spatial mixing with respect to an arbitrarily fixed vertex. This is the first strong spatial mixing result for colorings of graphs with unbounded maximum degree. Our analysis of strong spatial mixing establishes a block-wise correlation decay instead of the standard point-wise decay, which may be of interest by itself, especially for graphs with unbounded degree

Water Quality Monitoring in the Buck Creek Watershed and Facilitation of Buck Creek Watershed Partnership

The “Water Quality Monitoring in the Buck Creek Watershed and Facilitation of Buck Creek Watershed Partnership” project was developed to continue water quality monitoring on Buck Creek and to continue to engage watershed stakeholders during the Buck Creek WPP review process. This project continued monthly monitoring of Buck Creek when flowing water was present and kept the watershed partnership engaged through public meetings and semi-annual newsletters. Water quality monitoring began in May 2011 during the early stages of the most intense one-year drought on record in Texas and ran through April 2013. While much of the state returned to a semi-normal state of moisture conditions, the Texas Panhandle did not fare so well. The drought coupled with increased groundwater pumping to keep crops viable yielded sufficient water to sample in the creek during four sampling dates in this two-year period

Association patterns and foraging behaviour in natural and artificial guppy shoals

Animal groups are often nonrandom assemblages of individuals that tend to be assorted by factors such as sex, body size, relatedness and familiarity. Laboratory studies using fish have shown that familiarity among shoal members confers a number of benefits to individuals, such as increased foraging success. However, it is unclear whether fish in natural shoals obtain these benefits through association with familiars. We investigated whether naturally occurring shoals of guppies, Poecilia reticulata, are more adept at learning a novel foraging task than artificial (in which we selected shoal members randomly) shoals. We used social network analysis to compare the structures of natural and artificial shoals and examined whether shoal organization predicts patterns of foraging behaviour. Fish in natural shoals benefited from increased success in the novel foraging task compared with fish in artificial shoals. Individuals in natural shoals showed a reduced latency to approach the novel feeder, followed more and formed smaller subgroups compared to artificial shoals. Our findings show that fish in natural shoals do gain foraging benefits and that this may be facilitated by a reduced perception of risk among familiarized individuals and/or enhanced social learning mediated by following other individuals and small group sizes. Although the structure of shoals was stable over time, we found no direct relationship between shoal social structure and patterns of foraging behaviour

Sampling Hypergraphs with Given Degrees

There is a well-known connection between hypergraphs and bipartite graphs, obtained by treating the incidence matrix of the hypergraph as the biadjacency matrix of a bipartite graph. We use this connection to describe and analyse a rejection sampling algorithm for sampling simple uniform hypergraphs with a given degree sequence. Our algorithm uses, as a black box, an algorithm $\mathcal{A}$ for sampling bipartite graphs with given degrees, uniformly or nearly uniformly, in (expected) polynomial time. The expected runtime of the hypergraph sampling algorithm depends on the (expected) runtime of the bipartite graph sampling algorithm $\mathcal{A}$, and the probability that a uniformly random bipartite graph with given degrees corresponds to a simple hypergraph. We give some conditions on the hypergraph degree sequence which guarantee that this probability is bounded below by a constant

The Contribution of the Cosmological Constant to the Relativistic Bending of Light Revisited

We study the effect of the cosmological constant $\Lambda$ on the bending of light by a concentrated spherically symmetric mass. Contrarily to previous claims, we show that when the Schwarzschild-de Sitter geometry is taken into account, $\Lambda$ does indeed contribute to the bending.Comment: 5 pages, 2 figure

Generalized Swiss-cheese cosmologies: Mass scales

We generalize the Swiss-cheese cosmologies so as to include nonzero linear momenta of the associated boundary surfaces. The evolution of mass scales in these generalized cosmologies is studied for a variety of models for the background without having to specify any details within the local inhomogeneities. We find that the final effective gravitational mass and size of the evolving inhomogeneities depends on their linear momenta but these properties are essentially unaffected by the details of the background model.Comment: 10 pages, 14 figures, 1 table, revtex4, Published form (with minor corrections

Examining the relationship between work-related factors and work-family-related factors on work-family conflict

The current work-family conflict literature is characterized by limitations in focus and methodology, particularly with a failure to link work-family conflict with work-family policies. This study compares the influence of work-related factors and work-family related factors on work-family conflict in two directions. A local government organization in New Zealand was the setting. Findings show that work factors account for a significant component of both work-to-family and family-to-work conflict, although this is far greater on work-family conflict. Work-family practice use had little influence on work-family practices was found to positively associate with family-work conflict. Overall, the finds suggest managers in search of reducing employee conflict should focus directly upon work factors such as workload, rather than see to use work-family practices as the primary way to reduce conflict