Exploring the Superimposed Oscillations Parameter Space

The space of parameters characterizing an inflationary primordial power spectrum with small superimposed oscillations is explored using Monte Carlo methods. The most interesting region corresponding to high frequency oscillations is included in the analysis. The oscillations originate from some new physics taking place at the beginning of the inflationary phase and characterized by the new energy scale Mc. It is found that the standard slow-roll model remains the most probable one given the first year WMAP data. At the same time, the oscillatory models better fit the data on average, which is consistent with previous works on the subject. This is typical of a situation where volume effects in the parameter space play a significant role. Then, we find the amplitude of the oscillations to be less than 22% of the mean amplitude and the new scale Mc to be such that H/Mc < 6.6 x 10^(-4) at 1-sigma level, where H is the scale of inflation.Comment: 13 pages, 4 figures, uses iopart, matches published versio

General combination rules for qualitative and quantitative beliefs

Martin and Osswald \cite{Martin07} have recently proposed many generalizations of combination rules on quantitative beliefs in order to manage the conflict and to consider the specificity of the responses of the experts. Since the experts express themselves usually in natural language with linguistic labels, Smarandache and Dezert \cite{Li07} have introduced a mathematical framework for dealing directly also with qualitative beliefs. In this paper we recall some element of our previous works and propose the new combination rules, developed for the fusion of both qualitative or quantitative beliefs