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.

Relative energetics and structural properties of zirconia using a self-consistent tight-binding model

We describe an empirical, self-consistent, orthogonal tight-binding model for zirconia, which allows for the polarizability of the anions at dipole and quadrupole levels and for crystal field splitting of the cation d orbitals, This is achieved by mixing the orbitals of different symmetry on a site with coupling coefficients driven by the Coulomb potentials up to octapole level. The additional forces on atoms due to the self-consistency and polarizabilities are exactly obtained by straightforward electrostatics, by analogy with the Hellmann-Feynman theorem as applied in first-principles calculations. The model correctly orders the zero temperature energies of all zirconia polymorphs. The Zr-O matrix elements of the Hamiltonian, which measure covalency, make a greater contribution than the polarizability to the energy differences between phases. Results for elastic constants of the cubic and tetragonal phases and phonon frequencies of the cubic phase are also presented and compared with some experimental data and first-principles calculations. We suggest that the model will be useful for studying finite temperature effects by means of molecular dynamics.