Graded Relative Evidence

Relative Evidential Supports (RES) was developed and justified several years ago as a non-numeric apparatus that allows us to compare evidential supports for alternative conclusions when making a decision. An extension called Graded Relative Evidence (GRE) of the RES concept of pairwise balancing and trading-off of evidence is reported here which keeps its basic features of simplicity and perspicacity but enriches its modelling fidelity by permitting very modest and intuitive variations in degrees of outweighing (which the essentially binary RES does not). The formal justification is very simply based on linkages to RES and to the Dempster - Shafer theory of evidence. The use of the simple extension is illustrated and to a small degree further justified empirically by application to a topical scientific debate about what is called the Congo Crossover Conjecture here. This decision-making instance is chosen because of the wealth of evidence that has been accumulated on both sides of the debate and the range of evidence strengths manifested in it. The conjecture is that the advent of Aids was in the late 1950s in the Congo when a vaccine for polio was allegedly cultivated in the kidneys of chimpanzees which allowed the Aids infection to cross over to humans from primates. © 2005 Springer.

Development of composite tissue scaffolds containing naturally sourced mircoporous hydroxyapatite

The aims of this work were to investigate the conversion of a marine alga into hydroxyapatite (HA), and furthermore to design a composite bone tissue engineering scaffold comprising the synthesised HA within a porous bioresorbable polymer. The marine alga Phymatolithon calcareum, which exhibits a calcium carbonate honeycomb structure, with a natural architecture of interconnecting permeable pores (microporosity 4-11 mu m), provided the initial raw material for this study. The objective was to convert the alga into hydroxyapatite while maintaining its porous morphology using a sequential pyrolysis and chemical synthesis processes. Semi-quantitative XRD analysis of the post-hydrothermal material (pyrolised at 700-750 degrees C), indicated that the calcium phosphate (CaP) ceramic most likely consisted of a calcium carbonate macroporous lattice, with hydroxyapatite crystals on the surface of the macropores. Cell visibility (cytotoxicity) investigations of osteogenic cells were conducted on the CaP ceramic (i.e., the material post-hydrothermal analysis) which was found to be non-cytotoxic and displayed good biocompatibility when seeded with MG63 cells. Furthermore, a hot press scaffold fabrication technique was developed to produce a composite scaffold of CaP (derived from the marine alga) in a polycaprolactone (PCL) matrix. A salt leaching technique was further explored to introduce macroporosity to the structure (50-200 mu m). Analysis indicated that the scaffold contained both micro/macroporosity and mechanical strength, considered necessary for bone tissue engineering applications. (C) 2008 Published by Elsevier B.V.

Enantiomeric programming in tripodal transition metal scaffolds

A new route to the isolation of the enantiopure tris- chelate complex (Delta/Lambda)- fac-[Ru( L-1)(3)] 21 (where L-1 is 2,2'-bipyridine-5-carboxylic acid) is demonstrated, where the transition metal centre retains the memory of the chirality present in a simple tripodal tether used to control the metal centred geometry.

High-solid-content hydroxyapatite slurry for the production of bone substitute scaffolds

Key to various bone substitute scaffold production techniques is the development of free-flowing ceramic slurry with optimum theological properties. The aim is to achieve a colloidal suspension with as high a solid content as possible while maintaining a low viscosity which easily penetrates the pores of relevant sacrificial templates. The following investigation describes the optimization of a hydroxyapatite slip and demonstrates its potential application in scaffold production. Using predominantly spherical particles of hydroxyapatite of between 0.82 mu m and 16.2 mu m, coupled with a 2 wt % addition of the anionic polyelectrolyte, ammonium polyacrylate, an 80 wt % (55.9 vol %) hydroxyapatite solid loaded slip with a viscosity of approximately 126 mPa s has been developed. Its ability to infiltrate and replicate porous preforms has been shown using polyurethane foam. The enhanced particle packing achieved has allowed for the production of scaffolds with highly dense and uniform grain structures. The results represent a significant improvement in current slurry production techniques and can be utilized to develop high-density ceramic bone substitute scaffolds.

SK1 of graded division algebras

The reduced Whitehead group $\SK$ of a graded division algebra graded by a torsion-free abelian group is studied. It is observed that the computations here are much more straightforward than in the non-graded setting. Bridges to the ungraded case are then established by the following two theorems: It is proved that $\SK$ of a tame valued division algebra over a henselian field coincides with $\SK$ of its associated graded division algebra. Furthermore, it is shown that $\SK$ of a graded division algebra is isomorphic to $\SK$ of its quotient division algebra. The first theorem gives the established formulas for the reduced Whitehead group of certain valued division algebras in a unified manner, whereas the latter theorem covers the stability of reduced Whitehead groups, and also describes $\SK$ for generic abelian crossed products.

Unitary SK1 of unitary and graded division algebras

The reduced unitary Whitehead group $\SK$ of a graded division algebra equipped with a unitary involution (i.e., an involution of the second kind) and graded by a torsion-free abelian group is studied. It is shown that calculations in the graded setting are much simpler than their nongraded counterparts. The bridge to the non-graded case is established by proving that the unitary $\SK$ of a tame valued division algebra wih a unitary involution over a henselian field coincides with the unitary $\SK$ of its associated graded division algebra. As a consequence, the graded approach allows us not only to recover results available in the literature with substantially easier proofs, but also to calculate the unitary $\SK$ for much wider classes of division algebras over henselian fields.