Synthesis,self‐assembly and adsorption of PEO–PLA block copolymers onto colloidal polystyrene

A series of amphiphilic block copolymers composed of poly(ethylene oxide) and poly(lactide) were synthesized and their solution properties studied using static and dynamic light scattering. These materials self‐assemble in aqueous media with the hydrodynamic radius increasing with increasing hydrophobic fraction in the copolymer. To ascertain the potential for use of these materials as degradable coatings in delivery applications, block copolymers of varying compositions were adsorbed onto a series of colloidal polystyrene particles with varying radii, and the thickness of the adsorbed layer was determined from changes in the hydrodynamic size. The adlayer thicknesses ranged from 3 to 14 nm with varying block copolymer compositions, and colloid radii. The trends fit well with theoretical models for adlayer thickness, with the exception of the smallest colloids. In these systems, we propose that the colloids may become encapsulated into the block copolymer assembly. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 244–252, 2008     

Crossed products of C*-algebras by endomorphisms

The concept of a twisted crossed product associated to a non-classical C^*-dynamical system is introduced and studied. The relationship between a covariant projective representation of the system and the corresponding induced representation of the twisted crossed product is investigated, particularly from the point of view of determining when the induced representation is faithful. Conditions are given on the C^*-dynamical system that ensure nuclearity, simplicity or primeness of the twisted crossed product.     

Lagrangian caps

We establish an h-principle for exact Lagrangian embeddings with concave Legendrian boundary. We prove, in particular, that in the complement of the unit ball B in the standard symplectic ${\mathbb{R}^{2n}, 2n \geq 6}$ R 2 n , 2 n ≥ 6 , there exists an embedded Lagrangian n-disc transversely attached to B along its Legendrian boundary, which is loose in the sense of Murphy (Loose Legendrian embeddings in high dimensional contact manifolds, arXiv:1201.2245, 2013).     

Exponential family mixed membership models for soft clustering of multivariate data

For several years, model-based clustering methods have successfully tackled many of the challenges presented by data-analysts. However, as the scope of data analysis has evolved, some problems may be beyond the standard mixture model framework. One such problem is when observations in a dataset come from overlapping clusters, whereby different clusters will possess similar parameters for multiple variables. In this setting, mixed membership models, a soft clustering approach whereby observations are not restricted to single cluster membership, have proved to be an effective tool. In this paper, a method for fitting mixed membership models to data generated by a member of an exponential family is outlined. The method is applied to count data obtained from an ultra running competition, and compared with a standard mixture model approach.     

Type I Toeplitz algebras

The class of Toeplitz algebras associated to ordered groups is important in the analysis of Toeplitz operators on the generalised Hardy spaces defined by such groups. The conditions under which these Toeplitz algebras are Type I C^*-algebras are investigated.     

Efficient Bayesian Inference for Multivariate Probit Models With Sparse Inverse Correlation Matrices

We propose a Bayesian approach for inference in the multivariate probit model, taking into account the association structure between binary observations. We model the association through the correlation matrix of the latent Gaussian variables. Conditional independence is imposed by setting some off-diagonal elements of the inverse correlation matrix to zero and this sparsity structure is modeled using a decomposable graphical model. We propose an efficient Markov chain Monte Carlo algorithm relying on a parameter expansion scheme to sample from the resulting posterior distribution. This algorithm updates the correlation matrix within a simple Gibbs sampling framework and allows us to infer the correlation structure from the data, generalizing methods used for inference in decomposable Gaussian graphical models to multivariate binary observations. We demonstrate the performance of this model and of the Markov chain Monte Carlo algorithm on simulated and real datasets. This article has online supplementary materials.     

O- radical ions on MgO: a tool for a structural description of the surface

The present contribution aims to show that detailed information on structure and location of surface defective sites (surface vacancies, low co-ordination sites) can be obtained by combining data on the chemical reactivity of polycrystalline surfaces and EPR data. The use of nitrous oxide for bleaching trapped electron centres at the surface of MgO produces a remarkable variety of O^- species, which differ in their values of the energy splitting (δE) term between the p_z and the other two p orbitals of the radical ion. This indicates the existence of a corresponding variety of surface traps having different structural features.