Please use this identifier to cite or link to this item: http://hdl.handle.net/10553/44518
Title: Ranking intervals in complex stochastic Boolean systems using intrinsic ordering
Authors: González, Luis 
UNESCO Clasification: 110202 Algebra de Boole
12 Matemáticas
1208 Probabilidad
Issue Date: 2010
Project: Avances en Simulación de Campos de Viento y Radiación Solar. 
Journal: Lecture Notes in Electrical Engineering 
Conference: International Conference on Advances in Machine Learning and Systems Engineering 
Abstract: Many different phenomena, arising from scientific, technical or social areas, can be modeled by a system depending on a certain number n of random Boolean variables. The so-called complex stochastic Boolean systems (CSBSs) are characterized by the ordering between the occurrence probabilities Pr{u} of the 2 n associated binary strings of length n, i.e., u=(u 1,…,u n ) ∈ {0,1} n . The intrinsic order defined on {0,1} n provides us with a simple positional criterion for ordering the binary n-tuple probabilities without computing them, simply looking at the relative positions of their 0s and 1s. For every given binary n-tuple u, this paper presents two simple formulas – based on the positions of the 1-bits (0-bits, respectively) in u – for counting (and also for rapidly generating, if desired) all the binary n-tuples v whose occurrence probabilities Pr{v} are always less than or equal to (greater than or equal to, respectively) Pr{u}. Then, from these formulas, we determine the closed interval covering all possible values of the rank (position) of u in the list of all binary n-tuples arranged by decreasing order of their occurrence probabilities. Further, the length of this so-called ranking interval for u, also provides the number of binary n-tuples v incomparable by intrinsic order with u. Results are illustrated with the intrinsic order graph, i.e., the Hasse diagram of the partial intrinsic order.
URI: http://hdl.handle.net/10553/44518
ISBN: 978-90-481-9418-6
ISSN: 1876-1100
DOI: 10.1007/978-90-481-9419-3_31
Source: Ao SI., Rieger B., Amouzegar M. (eds) Machine Learning and Systems Engineering. Lecture Notes in Electrical Engineering, vol 68. Springer, Dordrecht
Appears in Collections:Actas de congresos
Show full item record

SCOPUSTM   
Citations

7
checked on Aug 9, 2020

Page view(s)

18
checked on Aug 8, 2020

Google ScholarTM

Check

Altmetric


Share



Export metadata



Items in accedaCRIS are protected by copyright, with all rights reserved, unless otherwise indicated.