The class of microarray games and the relevance index for genes

Nowadays, microarray technology is available to generate a huge amount of information on gene expression. This information must be statistically processed and analyzed, in particular, to identify those genes which are useful for the diagnosis and prognosis of specific diseases. We discuss the possibility of applying game-theoretical tools, like the Shapley value, to the analysis of gene expression data. Via a “truncation” technique, we build a coalitional game whose aim is to stress the relevance (“sufficiency”) of groups of genes for the specific disease we are interested in. The Shapley value of this game is used to select those genes which deserve further investigation. To justify the use of the Shapley value in this context, we axiomatically characterize it using properties with a genetic interpretation. The authors are grateful to two anonymous referees for their extremely helpful comments. An earlier version of this paper was presented at the VI Spanish Meeting on Game Theory and Practice, July 12–14, 2004, Elche, Spain. S. Moretti gratefully acknowledges the financial support of the EU project NewGeneris, European Union 6th FP (FOOD-CT-2005-016320).     

Transversality of the Shapley value

A few applications of the Shapley value are described. The main choice criterion is to look at quite diversified fields, to appreciate how wide is the terrain that has been explored and colonized using this and related tools. The title is inspired by a tutorial that one of the authors planned to deliver at the 7th meeting on Game Theory and Practice (Montreal, 2007), but was unable to do it for personal reasons. Thanks to Georges Zaccour whose invitation sparked the present survey.     

Computation of impurity Green’s functions in the tight-binding scheme

Summary A general method to calculate electronic Green’s functions in the tight-binding scheme is presented. The integrations are systematically reduced to the irreducible volume of the first Brillouin zone, so that a very short time is necessary for the computer’s work. The importance of symmetry planes, lines and points is stressed.

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Riassunto Si presenta un metodo generale per il calcolo delle funzioni di Green elettroniche nell’approssimazione degli elettroni fortemente legati. Le integrazioni sono sistematicamente ridotte al volume irriducibile della prima zona di Brillouin, in modo da ridurre notevolmente il tempo di calcolo. Si mette in risalto l’importanza di piani, linee e punti di simmetria.

     

Configurational correlations for chiral episulphides and episulphoxides by 1H NMR spectroscopy in optically active solvent

Optically active 2,2,2-trifluorophenylethanol, when used as NMR solvent, causes enantiomeric spectral dissimilarities for chiral episulphides and episulphoxides; the relative field positions of non-equivalent NMR resonances are analysed with respect to the absolute configuration of the solvated compounds.     

Cost allocation games with information costs

We propose a simple model which embeds cost allocation games into a richer structure to take into account that information on costs can be itself costly. The model is an outgrowth of experience on cost allocation for consortia of municipalities dealing with garbage collection.The authors thank an anonymous referee for having pointed out a mistake in the previous version of Lemma 1