Questions regarding the mathematics used in linked paper

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EverGreen1231
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Please forgive me if the question is too ambiguous. I've run into mathematics that I've never dealt with before (I only have encountered very basic probability and statistics). Correct me if I'm wrong, but think I see a bit of topology is used in the second and third sections (though this could simply be my ignorance showing), but it seems that most of it is based in probability theory. I found this while searching for papers that detail the use of Monte Carlo Methods for the analysis of Power distribution systems with the hope of determining a way to calculate the reliability of a single circuit breaker located on said system. I was hoping someone could give me direction toward some decrypting documents to lend a hand to my comprehension of this math.

Here's the paper:
http://www.researchgate.net/publication/249733974_SYSTEM_RELIABILITY_EVALUATION_USING_CONDITIONAL_MONTE_CARLO_METHODS

Any and all help would be much obliged.
 
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I looked at it briefly and don't think that sections 2 and 3 are topology as much as they are graph theory. It looks like graph theory is being used to partition the system into separate parts using disjoint paths and disjoint cuts. You can Google "reliability paths and cuts" to get references like http://www.sciencedirect.com/science/article/pii/S0166218X06002162 The expected reliability of the system is a function of the reliability of the parts of the resulting graph. I am not an expert in reliability, so that is as much as I can say.
 
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FactChecker said:
I looked at it briefly and don't think that sections 2 and 3 are topology as much as they are graph theory. It looks like graph theory is being used to partition the system into separate parts using disjoint paths and disjoint cuts. You can Google "reliability paths and cuts" to get references like http://www.sciencedirect.com/science/article/pii/S0166218X06002162 The expected reliability of the system is a function of the reliability of the parts of the resulting graph. I am not an expert in reliability, so that is as much as I can say.

Thank you for your reply. I'll check out your suggestions. :oldsmile: