In this paper, we present two vector-level software algorithms which essentially eliminate such bit-wise operations for Gaussian normal bases. Our analysis and timing results show that the software implementation of the proposed algorithm is faster than previously reported normal basis multiplication algorithms.
The Series ‘Topics in Molecular Organization and Engineering’ was initiated by
the Symposium ‘Molecules in Physics, Chemistry, and Biology’, which was held
in Paris in 1986. Appropriately dedicated to Professor Raymond Daudel, the
symposium was both broad in its scope and penetrating in its detail. The sections
of the symposium were: 1. The Concept of a Molecule; 2. Statics and Dynamics
of Isolated Molecules; 3. Molecular Interactions, Aggregates and Materials; 4.
Molecules in the Biological Sciences, and 5. Molecules in Neurobiology and So-
We analyse the mathematical structure of portfolio credit risk models with particular
regard to the modelling of dependence between default events in these models. We
explore the role of copulas in latent variable models (the approach that underlies KMV
and CreditMetrics) and use non-Gaussian copulas to present extensions to standard
industry models. We explore the role of the mixing distribution in Bernoulli mixture
models (the approach underlying CreditRisk+) and derive large portfolio approximations
for the loss distribution.
Lenses are an important part of most optical systems. Good results in optical measurements often rely on the best selection of lenses. In this chapter we develop the relations governing the passage of light rays through imaging elements on the basis of the paraxial approximation using matrix algebra. We also mention the aberrations occurring when rays deviate from this ideal Gaussian behaviour. Finally we go through some of the standard imaging systems.