A Generalized Markov Sampler

A recent development of the Markov chain Monte Carlo (MCMC) technique is the emergence of MCMC samplers that allow transitions between different models. Such samplers make possible a range of computational tasks involving models, including model selection, model evaluation, model averaging and hypothesis testing. An example of this type of sampler is the reversible jump MCMC sampler, which is a generalization of the Metropolis–Hastings algorithm. Here, we present a new MCMC sampler of this type. The new sampler is a generalization of the Gibbs sampler, but somewhat surprisingly, it also turns out to encompass as particular cases all of the well-known MCMC samplers, including those of Metropolis, Barker, and Hastings. Moreover, the new sampler generalizes the reversible jump MCMC. It therefore appears to be a very general framework for MCMC sampling. This paper describes the new sampler and illustrates its use in three applications in Computational Biology, specifically determination of consensus sequences, phylogenetic inference and delineation of isochores via multiple change-point analysis.     

Asymptotic Analysis of a Hyperbolic Mixed Problem in One-Dimensional Viscoelasticity

We present an asymptotic analysis of the boundary-generated, small-amplitude, high-frequency waves in a one-dimensional, semi-infinite, viscoelastic solid characterized by a single-integral constitutive functional. The equations governing the wave motion constitute a 2×2 system of hyperbolic Volterra integrodifferential equations. The method of analysis is based on a single-wave expansion of nonlinear geometric optics.     

Decomposing the complete graph into cycles of many lengths

For all oddv 3 the complete graph onvK _v vertices can be decomposed intov – 2 edge disjoint cycles whose lengths are 3, 3, 4, 5,...,v – 1. Also, for all oddv 7,K _v can be decomposed intov – 3 edge disjoint cycles whose lengths are 3, 4,...,v – 4,v – 2,v – 1,v. Research supported by Australian Research Council grant A49130102     

Synthesis of the methanesulfonates of α-(4-chlorophenyl)-α-[1-(2-chlorophenyl)emenyl]-1H-1,2,4-triazole-1-ethanol and α-[1-(2-chlorophenyl)ethenyl]-α-(2,4-difluorophenyl)-1H-1,2,4-triazole-1-ethanol,alpha styryl carbinol antifungal agents

The methanesulfonates of (α-(4-chlorophenyl)-α-[1-(2-chlorophenyl)ethenyl]-1H-1,2,4-triazole-1-ethanol and α-[1-(2-chlorophenyl)ethenyl]-α-(2,4-difluorophenyl)-1H-1,2,4-triazole-1-ethanol ( 1a, b ) are orally effective α-styryl carbinol derivatives developed for the treatment and prevention of systemic fungal infections. Practical new processes amenable for the large-scale production of these compounds are described. Of note is the selection of dichlorostyrene as a convenient precursor of the styryl portion, modification of a sensitive Grignard addition into a realistic preparative reaction and the use of 1,2,4-triazole simultaneously as a base transfer agent and nucleophile.     

Bis(m-phenylene)-32-crown-10-based cryptands, powerful hosts for paraquat derivatives

Four new bis(m-phenylene)-32-crown-10-based cryptands with different third bridges were prepared. Their complexes with paraquat derivatives were studied by proton NMR spectroscopy, mass spectrometry, and X-ray analysis. It was found that these cryptands bind paraquat derivatives very strongly. Specifically, a diester cryptand with a pyridyl nitrogen atom located at a site occupied by either water or a PF(6) anion in analogous complexes exhibited the highest association constant K(a) = 5.0 x 10(6) M(-1) in acetone with paraquat, 9000 times greater than the crown ether system. X-ray structures of this and analogous complexes demonstrate that improved complexation with this host is a consequence of preorganization, adequate ring size for occupation by the guest, and the proper location of the pyridyl N-atom for binding to the beta-pyridinium hydrogens of the paraquat guests. This readily accessible cryptand is one of the most powerful hosts reported for paraquats.