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We propose a latent-lognormal variance components model for counts that is analogous to the standard normal model for continuous measurements. We analyze gauge repeatability and reproducibility study data using Bayesian methods and illustrate the use of this latent-lognormal model with simulated and real data. [ABSTRACT FROM AUTHOR]

Abstract: Let ccl(G) denote the order of the largest complete minor in a graph G (also called the contraction clique number) and let denote a random graph on n vertices with edge probability p. Bollobás, Catlin and Erdős [Bollobás B., P.A. Catlin, and P. Erdős, Hadwiger''s conjecture is true for almost every graph, Europ. J. Combin. 1 (1980) 195–199] asymptotically determined when p is a constant. Łuczak, Pittel and Wierman [Łuczak T., B. Pittel, and J.C. Wierman, The structure of a random graph at the point of the phase transition, Trans. Amer. Math. Soc. 341 (1994) 721–748] gave bounds on when p is very close to 1/n, i.e. inside the phase transition. We show that for every there exists a constant C such that whenever then asymptotically almost surely , where . If for a constant , then asymptotically almost surely . This extends the results in [Bollobás B., P.A. Catlin, and P. Erdős, Hadwiger''s conjecture is true for almost every graph, Europ. J. Combin. 1 (1980) 195–199] and answers a question of Krivelevich and Sudakov [Krivelevich M., and B. Sudakov, Minors in expanding graphs, preprint 2006]. [Copyright &y& Elsevier]

The Oberwolfach problem, posed by Ringel in 1967, asks for a decomposition of K2n+1 into edge-disjoint copies of a given 2-factor. We show that this can be achieved for all large n. We actually prove a significantly more general result, which allows for decompositions into more general types of factors. In particular, this also resolves the Hamilton-Waterloo problem for large n. [ABSTRACT FROM AUTHOR]

The local resilience of a graph G with respect to a property P measures how much one has to change G locally in order to destroy P. We prove 'resilience' versions of several classical results about Hamiltonicity for the graph models Gn;p and Gn;d. In the setting of random regular graphs, we prove a resilience version of Dirac's theorem. More precisely, we show that, whenever d is suficiently large compared to " > 0, a.a.s. the following holds. Let G0 be any subgraph of the random n-vertex d-regular graph Gn;d with minimum degree at least (1=2 +)d. Then G0 is Hamiltonian. This proves a conjecture of Ben-Shimon, Krivelevich and Sudakov. For the binomial random graph Gn;p, we prove a resilience version of Pósa's Hamiltonicity condition, and show that a natural guess for a resilience version of Chvsatal's theorem fails to be true. [ABSTRACT FROM AUTHOR]