Labeling the nodes in the intrinsic order graph with their weights

[EN] This paper deals with the study of some new properties of the intrinsic order graph. The intrinsic order graph is the natural graphical representation of a complex stochastic Boolean system (CSBS). A CSBS is a system depending on an arbitrarily large number n of mutually independent random Boolean variables. The intrinsic order graph displays its 2n vertices (associated to the CSBS) from top to bottom, in decreasing order of their occurrence probabilities. New relations between the intrinsic ordering and the Hamming weight (i.e., the number of 1-bits in a binary n-tuple) are derived. Further, the distribution of the weights of the 2n nodes in the intrinsic order graph is analyzed…

Intrinsic Order and Hamming Weight

[EN]The intrinsic order is a partial order relation defined on the set {0, 1} n of all binary n-tuples. This ordering enables one to automatically compare binary n-tuple probabilities without computing them, just looking at the relative positions of their 0s & 1s. In this paper, new relations between the intrinsic ordering and the Hamming weight (i.e., the number of 1-bits in a binary n-tuple) are derived. All theoretical results are rigorously proved and illustrated through the intrinsic order graph…