ABSTRACT
In this contribution, we specify the conditions for assuring the validity of the synergy of the distribution of probabilities of occurrence. We also study the subsequent restriction on the maximal extension of the strict concavity region on the parameter space of Sharma-Mittal entropy measures, which has been derived in a previous paper in this journal. The present paper is then a necessary complement to that publication. Some applications of the techniques introduced here are applied to protein domain families (Pfam databases, versions 27.0 and 35.0). The results will show evidence of their usefulness for testing the classification work performed with methods of alignment that are used by expert biologists.
ABSTRACT
The Khinchin-Shannon generalized inequalities for entropy measures in Information Theory, are a paradigm which can be used to test the Synergy of the distributions of probabilities of occurrence in physical systems. The rich algebraic structure associated with the introduction of escort probabilities seems to be essential for deriving these inequalities for the two-parameter Sharma-Mittal set of entropy measures. We also emphasize the derivation of these inequalities for the special cases of one-parameter Havrda-Charvat's, Rényi's and Landsberg-Vedral's entropy measures.
ABSTRACT
A study of the fundamental requirements which are used in the mathematical modelling of biomolecular structure is presented in this work. The visualisation of smooth spatial curves through an ordered set of points corresponding to atom sites is then considered. It is emphasised that the restrictions introduced by the choice of Euclidean Geometry as a natural paradigm lead usually to helices as the natural solution. However, some arguments are also presented for the consideration of curves which satisfy only one of the requirements or none.
