Simplicity of C*-algebras associated to higher-rank graphs

We prove that if is a row-finite k-graph with no sources, thenthe associated C*-algebra is simple if and only if is cofinaland satisfies Kumjian and Pask's aperiodicity condition, knownas Condition (A). We prove that the aperiodicity condition isequivalent to a suitably modified version of Robertson and Steger'soriginal nonperiodicity condition (H3), which in particularinvolves only finite paths. We also characterise both cofinalityand aperiodicity of in terms of ideals in C*().     

Quantifying interactions between cell receptors and adhesion ligand-modified polymers in solution

Specific interactions between cells and cell-interactive polymers in solution were investigated by the fluorescence resonance energy transfer (FRET) technique and rheological measurements. The green fluorescence emission was dramatically reduced when rhodamine-stained cells were mixed with a fluorescein-labeled RGD-alginate solution, compared with those mixed with no RGD-containing alginate solution, which indicated an occurrence of FRET and existence of specific interactions between the cells and the polymers in solution. Rheological measurements also confirmed the formation of ordered structures of cell/polymer mixtures, caused by specific cell-polymer interactions. The FRET method was able to provide a useful means of investigating cell-polymer interactions, both in a qualitative and quantitative manner, and this approach to monitoring and controlling specific interactions between cells and polymers could be useful in the design and tailoring of polymeric carriers for cells, as well as for biological drugs, especially for tissue engineering applications.     

Photochemical generation of aziridinium imides: are Als bystanders or perpetrators in the ene reaction?

A non-equilibrating mixture of two aziridinium imides (AIs) resulting from the photoaddition of N-methyl-1,2,4-triazoline-3,5-dione and cycloheptene has been prepared. Warming the AIs produces only the product of the expected ene reaction with no back-reaction to starting materials. Even though one of the pair does not have the geometry necessary for hydrogen abstraction, both AIs disappear at essentially the same rate, showing that AIs cannot be the direct precursors of the ene product.     

Diffusion within ultrathin, dense nanoporous silica films

In this work the origin of permselectivity in dense silica films which possess a pore structure with pore sizes commensurate with the molecular size of the diffusing gas species is investigated. Much of the recently reported work in this field has involved the development of composite membrane films, and while it is generally assumed that the transport process of the gas species within the selective layer of these films is activated in nature, there are anomalies with this simplified picture. In this paper a new model is developed which, for the first time, explains the permselective behavior of the thin selective coatings ubiquitous to membrane separation processes. The model involves the existence of two primary transport domains within the solid film, one of which rapidly conducts the permeating gas (under non-Fickian conditions), while the second domain involves a slow diffusion mode characterized by normal Fickian transport. To validate the model, molecular dynamics simulations are conducted for diffusion of a number of simple gases (He, N(2), and CO(2)) within silica glasses over a range of solid densities. The silica media employed in these studies are based on a novel approach developed in this work for the construction of three-dimensionally periodic atomistic structures of silica of arbitrary density in which network bond connectivity is ensured. The results obtained from this work are in qualitative agreement with experimental observations and confirm the existence of dual mode transport which is central to the interpretation of the permselectivity in composite membranes systems.     

Alginate hydrogels as biomaterials

[Image: see text] Alginate hydrogels are proving to have a wide applicability as biomaterials. They have been used as scaffolds for tissue engineering, as delivery vehicles for drugs, and as model extracellular matrices for basic biological studies. These applications require tight control of a number of material properties including mechanical stiffness, swelling, degradation, cell attachment, and binding or release of bioactive molecules. Control over these properties can be achieved by chemical or physical modifications of the polysaccharide itself or the gels formed from alginate. The utility of these modified alginate gels as biomaterials has been demonstrated in a number of in vitro and in vivo studies.Micro-CT images of bone-like constructs that result from transplantation of osteoblasts on gels that degrade over a time frame of several months leading to improved bone formation.     

Cell-like equivalences and boundaries of CAT(0) groups

In 2000, Croke and Kleiner showed that a CAT(0) group G can admit more than one boundary. This contrasted with the situation for ??-hyperbolic groups, where it was well-known that each such group admitted a unique boundary??in a very stong sense. Prior to Croke and Kleiner??s discovery, it had been observed by Geoghegan and Bestvina that a weaker sort of uniquness does hold for boundaries of torsion free CAT(0) groups; in particular, any two such boundaries always have the same shape. Hence, the boundary really does carry significant information about the group itself. In an attempt to strengthen the correspondence between group and boundary, Bestvina asked whether boundaries of CAT(0) groups are unique up to cell-like equivalence. For the types of space that arise as boundaries of CAT(0) groups, this is a notion that is weaker than topological equivalence and stronger than shape equivalence. In this paper we explore the Bestvina Cell-like Equivalence Question. We describe a straightforward strategy with the potential for providing a fully general positive answer. We apply that strategy to a number of test cases and show that it succeeds??often in unexpectedly interesting ways.     

The geometry of spheres in free abelian groups

We study word metrics on ${\mathbb{Z}^d}$ by developing tools that are fine enough to measure dependence on the generating set. We obtain counting and distribution results for the words of length n. With this, we show that counting measure on spheres always converges to cone measure on a polyhedron (strongly, in an appropriate sense). Using the limit measure, we can reduce probabilistic questions about word metrics to problems in convex geometry of Euclidean space. We give several applications to the statistics of ??size-like?? functions.     

Generalizing the Croke-Kleiner construction

It is well known that every word hyperbolic group has a well-defined visual boundary. An example of C. Croke and B. Kleiner shows that the same cannot be said for CAT(0) groups. All boundaries of a CAT(0) group are, however, shape equivalent, as observed by M. Bestvina and R. Geoghegan. Bestvina has asked if they also satisfy the stronger condition of being cell-like equivalent. This article describes a construction which will produce CAT(0) groups with multiple boundaries. These groups have very complicated boundaries in high dimensions. It is our hope that their study may provide insight into Bestvina's question.