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Title: Splitting the unity, bisecting a graph: applications to stochastic Boolean systems
Authors: González, Luis 
UNESCO Clasification: 110202 Algebra de Boole
1208 Probabilidad
120199 Otras (especificar)
Issue Date: 2008
Project: Diagnostico y Prediccion de Recursos Eolicos y Solares. 
Simulacion Numerica de Campos de Viento Orientados A Procesos Atmofericos. 
Journal: Lecture Notes in Computer Science 
Conference: International Conference on Computational Science and Its Applications (ICCSA 2008) 
Abstract: This paper deals with the reliability and risk analysis of those complex systems depending on n stochastic Boolean variables. Each one of the 2(n) elementary states associated to such a system is given by its corresponding binary n-tuple of 0s and 1s. A symmetric fractal graph on 2(n) nodes (the so-called intrinsic order graph In) is used for displaying all the binary n-tuples in decreasing order of their occurrence probabilities. The successive bisections of this graph into smaller subgraphs one-to-one correspond to the successive splits of 1 as sum of the occurrence probabilities of those subgraphs. This iterative bisection process satisfies a nice property: if we replace each one of the subgraphs C (obtained after k successive bisections of the original intrinsic order graph I-n) by an unique node weighted by the sum of the probabilities of all vertices lying on C and we sort the new nodes in decreasing order of their weights, then the new condensed graph is exactly the intrinsic order graph I-k. Finally, based on these results, a new algorithm for estimating the unavailability of stochastic Boolean systems is presented.
ISBN: 978-3-540-69840-1
ISSN: 0302-9743
DOI: 10.1007/978-3-540-69848-7_77
Source: Computational Science And Its Applications - Iccsa 2008, Pt 2, Proceedings [ISSN 0302-9743] v. 5073, p. 970-986, (2008)
Appears in Collections:Actas de congresos
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