PubMed · 5098971
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G T Kneebone. 1971. Mathematical logic in relation to ordinary mathematics.. https://pubmed.ncbi.nlm.nih.gov/5098971/
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We study how the notions of importance of variables in Boolean functions as well as the sensitivities of the functions to changes in these variables impact the dynamical behavior of Boolean networks. The activity of a variable captures its influence on the output of the function and is a measure of that variable's importance. The average sensitivity of a Boolean function captures the smoothness of the function and is related to its internal homogeneity. In a random Boolean network, we show that the expected average sensitivity determines the well-known critical transition curve. We also discuss canalizing functions and the fact that the canalizing variables enjoy higher importance, as measured by their activities, than the noncanalizing variables. Finally, we demonstrate the important role of the average sensitivity in determining the dynamical behavior of a Boolean network.
Research in (medical) terminological knowledge representation is showing an increased interest in the family of Description Logics (DLs), as they allow for automatic reasoning. This interest is driven by an increase in demands on the quality of and reasoning ability with medical terminological knowledge. Recent advances in Computer Science have demonstrated the computational decidability and empirical tractability of quite expressive DLs. The question arises whether this expressivity is usable and useful. This paper motivates and describes an exploratory study to address this question by examining the surplus value of individual DL constructors based on an investigation of UMLS terms. Our study indicates that the disjunction and negation operators comprise very valuable extensions to current DLs. The impact of formalization depends on the involved semantic type; "Injury and Poisoning" is one of the semantic types in which a large portion of concepts will benefit from the extension.