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Some properties of solutions for two-dimensional choice problems reconsidered

100%

Lahiri S.

Control and Cybernetics

1999

tom Vol. 28, no 1

75-87

In this paper, we take up the problem of axiomatically characterizing what we have referred to in the paper as the additive choice function on the classical domain for choice problems. Apart from an impossibility result for the additive choice function, there is an axiomatic characterization, which as a by-product provides a counterexample to a conjecture for the egalitarian choice function. In an appendix, we provide a proof of an axiomatic characterization of the egalitarian choice function using a superadditivity axiom. In this paper, we also provide proofs of axiomatic characterizations of the family of non-symmetric Nash choice functions and the family of weighted hierarchies of choice functions. Our conclusion is that earlier axiomatizations are essentially preserved on the classical domain for choice problems. The proofs are significant in being non-trivial and very dissimilar to existing proofs for other domains.

Cancer classification based on gene expression data

100%

Fujarewicz K. , Rzeszowska-Wolny J.

Journal of Medical Informatics & Technologies

2000

tom Vol. 1

BI 23--27

Proper classification of cancer is a crucial aspect in diagnosis and choosing optimal medical therapy. It has been suggested, in recent years, that classification process of cancer can be done using gene expression monitoring. Usefulness of this approach has increased due to the new technique of gene expression monitoring – using so called "expression chips". Recently in [1, 3] a heuristic method of cancer classification, called weighted voting (WV) method, based on gene expression levels has been proposed and tested on a set of samples of acute myeloid leukemia (AML) and acute lymphoblastic leukemia (ALL). Here a more traditional approach to feature selection and classification is presented and tested on the same data set. Feature selection is performed using modified Sebestyen criterion and classification is done using linear classifying function trained by modified perception algorithm. Obtained results are better than results of the WV method. In cross-validation of initial set all 38 samples were classified correctly (WV – 1 incorrect) and only one sample from independent set was classified incorrectly (WV – 2 incorrect).