Probabilistic-topological theory of systems with discrete interactions: II. Calculation of the hypergraph probabilistic representation; the difference a posteriori algorithm

Abstract

The scheme of calculations, which subsequently will be called the difference a posteriori algorithm (or just DAPOST), is formulated in a general and rigorous manner to make its application to different systems with discrete interactions (SDI) possible. The DAPOST enables one to calculate important probabilistic characteristics of SDI while having only general information about its composition and interactions between system elements. The DAPOST is easily adaptable to very different physicochemical and biophysical systems, especially to the problems of element aggregation and binding. When applied together with a hypergraph representation of the SDI under consideration the DAPOST allows construction of equivalent probabilistic representations of the hypergraph modelling the SDI, in this way often considerably simplifying calculations of the structure–property relationships of the SDI.