On the probabilistic approach to heterogeneous structure interactions in agent-based computational models

A New Formula for Partitions in a Set of Entities into Empty and Nonempty Subsets, and Its Application to Stochastic and Agent-Based Computational Models

“…The recent discussions about the gap sed computational models and stochastic analytical models have stimulated the research on this topic [3,10]. In such context, the article supports a unified probabilistic approach to simulation of multi-agent interactions in heterogeneous complex systems.…”

“…Equivalently, they count the number of different equivalence relations with precisely k equivalence classes that can be defined on an n element set, and they can be calculated using the explicit formula gives the nth Bell number, that is the total number of partitions of a cluster with n entities or agents [2]. The question arises when the empty subsets or clusters are needed to be used in the models, for example, with heterogeneous structure interactions and, subsequently, the partition by Stirling numbers of the second kind becomes inappropriate to count partitions in such complex systems [3].…”