Prediction of inherited genomic susceptibility to 20 common cancer types by a supervised machine-learning method.

Prevention and early intervention are the most effective ways of avoiding or minimizing psychological, physical, and financial suffering from cancer. However, such proactive action requires the ability to predict the individual's susceptibility to cancer with a measure of probability. Of the triad of cancer-causing factors (inherited genomic susceptibility, environmental factors, and lifestyle factors), the inherited genomic component may be derivable from the recent public availability of a large body of whole-genome variation data. However, genome-wide association studies have so far showed limited success in predicting the inherited susceptibility to common cancers. We present here a multiple classification approach for predicting individuals' inherited genomic susceptibility to acquire the most likely phenotype among a panel of 20 major common cancer types plus 1 "healthy" type by application of a supervised machine-learning method under competing conditions among the cohorts of the 21 types. This approach suggests that, depending on the phenotypes of 5,919 individuals of "white" ethnic population in this study, (i) the portion of the cohort of a cancer type who acquired the observed type due to mostly inherited genomic susceptibility factors ranges from about 33 to 88% (or its corollary: the portion due to mostly environmental and lifestyle factors ranges from 12 to 67%), and (ii) on an individual level, the method also predicts individuals' inherited genomic susceptibility to acquire the other types ranked with associated probabilities. These probabilities may provide practical information for individuals, heath professionals, and health policymakers related to prevention and/or early intervention of cancer

A-coupled-expanding and distributional chaos

The concept of A-coupled-expanding map, which is one of the more natural and useful ideas generalized the horseshoe map, is well known as a criterion of chaos. It is well known that distributional chaos is one of the concepts which reflect strong chaotic behaviour. In this paper, we focus the relations between A-coupled-expanding and distributional chaos. We prove two theorems that give sufficient conditions for a strictly A-coupled-expanding map to be distributionally chaotic in the senses of two kinds, where A is an irreducible transition matrix.Comment: 10 page