General structure of Acalugaritei networks

Acalugaritei networks (ANs) are multidimensional evolutionary hierarchical networks. They are called hierarchical because the sets and subsets of components correspond to different ranks (levels), where: the set of “inferior” rank is the subset of rank zero (j = 0) of the set of immediately “superior” rank. The sets and subsets of components will be noted S_ij, where: i is the rank number of the set (i = 0,1,2,3); jis the rank number of the subset within the same set (j = 0,1,2, …, n). We will thus distinguish: \curr S_ij=(S_0j ⊂ S_1j⊂ S_2j⊂ S_3j). They are called evolutionary because the most comprehensive set of components is the set of evolutionary relations. They are called multidimensional because the components of the same rank can be classified according to n dimensions (n criteria: k_i where: i = 0, 1, 2,…, n). ANs are of different ranks (ANs_i, where: i = 0, 1, 2,…,n). In an AN of a certain rank, the set of fundamental components is the set of sequences of ANs of subordinated ranks.