Computer theorem proving in math

We give an overview of issues surrounding computer-verified theorem proving in the standard pure-mathematical context. This is based on my talk at the PQR conference (Brussels, June 2003)

Evaluation of the quantitative prediction of a trend reversal on the Japanese stock market in 1999

In January 1999, the authors published a quantitative prediction that the Nikkei index should recover from its 14 year low in January 1999 and reach $\approx 20500$ a year later. The purpose of the present paper is to evaluate the performance of this specific prediction as well as the underlying model: the forecast, performed at a time when the Nikkei was at its lowest (as we can now judge in hindsight), has correctly captured the change of trend as well as the quantitative evolution of the Nikkei index since its inception. As the change of trend from sluggish to recovery was estimated quite unlikely by many observers at that time, a Bayesian analysis shows that a skeptical (resp. neutral) Bayesian sees her prior belief in our model amplified into a posterior belief 19 times larger (resp. reach the 95% level).Comment: 6 pages including 2 figure

On-line list colouring of random graphs

In this paper, the on-line list colouring of binomial random graphs G(n,p) is studied. We show that the on-line choice number of G(n,p) is asymptotically almost surely asymptotic to the chromatic number of G(n,p), provided that the average degree d=p(n-1) tends to infinity faster than (log log n)^1/3(log n)^2n^(2/3). For sparser graphs, we are slightly less successful; we show that if d>(log n)^(2+epsilon) for some epsilon>0, then the on-line choice number is larger than the chromatic number by at most a multiplicative factor of C, where C in [2,4], depending on the range of d. Also, for d=O(1), the on-line choice number is by at most a multiplicative constant factor larger than the chromatic number

Identification et caracterisation fonctionnelle et structurale des recepteurs a l'insuline au niveau des hepatocytes. Tentative d'identification du systeme de transport des acides amines au niveau de la membrane plasmique des hepatocytes

SIGLECNRS-CDST / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc