Sequential Monte Carlo with transformations

This paper examines methodology for performing Bayesian inference sequentially on a sequence of posteriors on spaces of different dimensions. For this, we use sequential Monte Carlo samplers, introducing the innovation of using deterministic transformations to move particles effectively between target distributions with different dimensions. This approach, combined with adaptive methods, yields an extremely flexible and general algorithm for Bayesian model comparison that is suitable for use in applications where the acceptance rate in reversible jump Markov chain Monte Carlo is low. We use this approach on model comparison for mixture models, and for inferring coalescent trees sequentially, as data arrives

Trees and Matchings

In this article, Temperley's bijection between spanning trees of the square grid on the one hand, and perfect matchings (also known as dimer coverings) of the square grid on the other, is extended to the setting of general planar directed (and undirected) graphs, where edges carry nonnegative weights that induce a weighting on the set of spanning trees. We show that the weighted, directed spanning trees (often called arborescences) of any planar graph G can be put into a one-to-one weight-preserving correspondence with the perfect matchings of a related planar graph H. One special case of this result is a bijection between perfect matchings of the hexagonal honeycomb lattice and directed spanning trees of a triangular lattice. Another special case gives a correspondence between perfect matchings of the ``square-octagon'' lattice and directed weighted spanning trees on a directed weighted version of the cartesian lattice. In conjunction with results of Kenyon, our main theorem allows us to compute the measures of all cylinder events for random spanning trees on any (directed, weighted) planar graph. Conversely, in cases where the perfect matching model arises from a tree model, Wilson's algorithm allows us to quickly generate random samples of perfect matchings.Comment: 32 pages, 19 figures (minor revisions from version 1

Topological properties defined by nets

AbstractNets are used to generalize a result of Murtinová and to define and study a class of properties related to sequential compactness

Spaces in which compact subsets are closed and the lattice of T1T_1-topologies on a set

summary:We obtain some new properties of the class of KC-spaces, that is, those topological spaces in which compact sets are closed. The results are used to generalize theorems of Anderson [1] and Steiner and Steiner [12] concerning complementation in the lattice of $T_1$-topologies on a set $X$

Which topologies can have immediate successors in the lattice of T1-topologies?

[EN] We give a new characterization of those topologies which have an immediate successor or cover in the lattice of T1-topologies on a set and show that certain classes of compact and countably compact topologies do not have covers.Research supported by Consejo Nacional de Ciencia y Tecnología (México), grant 38164-E and Fundacão de Amparo a Pesquisa do Estado de São Paulo (Brasil)Alas, OT.; Wilson, RG. (2004). Which topologies can have immediate successors in the lattice of T1-topologies?. Applied General Topology. 5(2):231-242. doi:10.4995/agt.2004.1972.SWORD2312425

An audit of antenatal education facilitated by physiotherapists in Western Australian public hospitals

This paper reports on the delivery of antenatal education by physiotherapists in Western Australia in 2012, including the location of antenatal education providers, number of mothers attending, qualifications of physiotherapists involved, allocation of physiotherapy hours, the content of the education, and strategies used to enhance learning in the classes. A survey was emailed to the physiotherapists in 31 hospitals with maternity services that were funded by the Department of Health Western Australia. Antenatal education facilitated by a physiotherapist was provided at 25/30 (83.3%) hospitals. Four physiotherapists had postgraduate women’s health qualifications and all the antenatal education classes provided information about pelvic floor muscle exercises. There was a wide variation in pelvic floor muscle exercise prescription. Fewer than 50% of first-time mothers who give birth in the public sector have attended physiotherapy facilitated antenatal education classes

Energies and wave functions for a soft-core Coulomb potential

For the family of model soft Coulomb potentials represented by V(r) = -\frac{Z}{(r^q+\beta^q)^{\frac{1}{q}}}, with the parameters Z>0, \beta>0, q \ge 1, it is shown analytically that the potentials and eigenvalues, E_{\nu\ell}, are monotonic in each parameter. The potential envelope method is applied to obtain approximate analytic estimates in terms of the known exact spectra for pure power potentials. For the case q =1, the Asymptotic Iteration Method is used to find exact analytic results for the eigenvalues E_{\nu\ell} and corresponding wave functions, expressed in terms of Z and \beta. A proof is presented establishing the general concavity of the scaled electron density near the nucleus resulting from the truncated potentials for all q. Based on an analysis of extensive numerical calculations, it is conjectured that the crossing between the pair of states [(\nu,\ell),(\nu',\ell')], is given by the condition \nu'\geq (\nu+1) and \ell' \geq (\ell+3). The significance of these results for the interaction of an intense laser field with an atom is pointed out. Differences in the observed level-crossing effects between the soft potentials and the hydrogen atom confined inside an impenetrable sphere are discussed.Comment: 13 pages, 5 figures, title change, minor revision