Mediation and Judicial Review: An empirical research study

The aim of this research is to establish an independent evidence base for identifying the value and the limits of mediation as an alternative to, or used alongside, judicial review. It has been devised in response to claims made by government and mediation providers that mediation can lead to savings in costs as well as in court time, and provide remedies and solutions to disputes that cannot be offered by the court. These claims will be considered in the specifi c context of judicial review, which not only has an important constitutional function, but, compared to other forms of civil litigation, offers flexibility, low costs and speed

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

Better Synchronizability Predicted by Crossed Double Cycle

In this brief report, we propose a network model named crossed double cycles, which are completely symmetrical and can be considered as the extensions of nearest-neighboring lattices. The synchronizability, measured by eigenratio $R$, can be sharply enhanced by adjusting the only parameter, crossed length $m$. The eigenratio $R$ is shown very sensitive to the average distance $L$, and the smaller average distance will lead to better synchronizability. Furthermore, we find that, in a wide interval, the eigenratio $R$ approximately obeys a power-law form as $R\sim L^{1.5}$.Comment: 4 pages, 5 figure

Fundamental Cycles and Graph Embeddings

In this paper we present a new Good Characterization of maximum genus of a graph which makes a common generalization of the works of Xuong, Liu, and Fu et al. Based on this, we find a new polynomially bounded algorithm to find the maximum genus of a graph

Sitting time and health outcomes among Mexican origin adults: obesity as a mediator

Background: Sitting time and sedentary behaviors have been associated with adverse health outcomes including obesity, diabetes and cardiovascular disease (CVD) within non- Hispanic White populations. Similar associations have not been described within Hispanic populations despite their high CVD risk profile. This study aimed to assess the association between sitting time and obesity, self-reported diagnosed diabetes, hypertension and high cholesterol among a large cohort (N=11,268) of Mexican origin adults and to assess whether obesity mediated these associations. Methods: Using a cross-sectional design, data collected between 2004 and 2010 were analyzed in late 2010. Regression analyses evaluated associations between self-reported daily sitting hours and disease outcomes, controlling for demographics, employment status, family disease history, and light, moderate and strenuous physical activity. Results: Participants were mostly female (81.1%) Mexican origin adults. Sitting time was associated with increased odds of being obese, having diabetes and having hypertension, but not high cholesterol. Adjusted odds ratios of participants who reported sitting > 4 hours/day compared to those sitting 1-2 hours/day were for obesity OR=1.55 (95% CI 1.39, 1.73), p<.001, for diabetes OR=1.29 (95% CI, 1.09, 1.52), p=.003, for hypertension OR=1.17 (95% CI, 1.01, 1.37), p=.041. Associations controlled for physical activity and employment status. Effects on hypertension and diabetes were mediated by obesity. Conclusions: Sitting time was significantly associated with detrimental health outcomes, independent of physical activity. Obesity mediated these relationships for diabetes and hypertension. Future research should assess whether interventions addressing sitting time are feasible and effective among Mexican origin populations

Counting flags in triangle-free digraphs

Motivated by the Caccetta-Haggkvist Conjecture, we prove that every digraph on n vertices with minimum outdegree 0.3465n contains an oriented triangle. This improves the bound of 0.3532n of Hamburger, Haxell and Kostochka. The main new tool we use in our proof is the theory of flag algebras developed recently by Razborov.Comment: 19 pages, 7 figures; this is the final version to appear in Combinatoric

Finding 2-Edge and 2-Vertex Strongly Connected Components in Quadratic Time

We present faster algorithms for computing the 2-edge and 2-vertex strongly connected components of a directed graph, which are straightforward generalizations of strongly connected components. While in undirected graphs the 2-edge and 2-vertex connected components can be found in linear time, in directed graphs only rather simple $O(m n)$-time algorithms were known. We use a hierarchical sparsification technique to obtain algorithms that run in time $O(n^2)$. For 2-edge strongly connected components our algorithm gives the first running time improvement in 20 years. Additionally we present an $O(m^2 / \log{n})$-time algorithm for 2-edge strongly connected components, and thus improve over the $O(m n)$ running time also when $m = O(n)$. Our approach extends to k-edge and k-vertex strongly connected components for any constant k with a running time of $O(n^2 \log^2 n)$ for edges and $O(n^3)$ for vertices

Changes in precipitating snow chemistry with location and elevation in the California Sierra Nevada

Orographic snowfall in the Sierra Nevada Mountains is an important source of water for California and can vary significantly on an annual basis. The microphysical properties of orographic clouds and subsequent formation of precipitation are impacted, in part, by aerosols of varying size, number, and chemical composition, which are incorporated into clouds formed along the Sierra barrier. Herein, the physicochemical properties and sources of insoluble residues and soluble ions found in precipitation samples were explored for three sites of variable elevation in the Sierra Nevada during the 2012–2013 winter season. Residues were characterized using a suite of physicochemical techniques to determine the size‐resolved number concentrations and associated chemical composition. A transition in the aerosol sources that served as cloud seeds or were scavenged in‐cloud and below‐cloud was observed as a function of location and elevation. Anthropogenic influence from the Central Valley was dominant at the two lowest elevation sites (1900 and 2200 m above mean sea level (AMSL)), whereas long‐range transported mineral dust was a larger contributor at the highest elevation site where cleaner conditions were observed (2600 m AMSL). The residues and soluble ions observed provide insight into how multiple aerosol sources can impact cloud and precipitation formation processes, even over relatively small spatial scales. The transition with increasing elevation to aerosols that serve as ice nucleating particles may impact the properties and extent of snowfall in remote mountain regions where snowpack provides a vital supply of water.Key PointsPhysiochemical properties of particles found in precipitation were determinedBoth anthropogenic and natural sources contributed to the snow residue chemistrySnow residue sources varied depending on location and elevationPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/133563/1/jgrd53083-sup-0001-SI.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/133563/2/jgrd53083_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/133563/3/jgrd53083.pd

The generalized 3-edge-connectivity of lexicographic product graphs

The generalized $k$-edge-connectivity $\lambda_k(G)$ of a graph $G$ is a generalization of the concept of edge-connectivity. The lexicographic product of two graphs $G$ and $H$, denoted by $G\circ H$, is an important graph product. In this paper, we mainly study the generalized 3-edge-connectivity of $G \circ H$, and get upper and lower bounds of $\lambda_3(G \circ H)$. Moreover, all bounds are sharp.Comment: 14 page